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Title:
SPHERICAL ABERRATION REDUCTION SYSTEMS AND METHODS
Document Type and Number:
WIPO Patent Application WO/2018/102624
Kind Code:
A1
Abstract:
A system for determining a vision treatment for an eye of a patient is provided which comprises a memory configured to store programmed instructions and data. The system also comprises a processor in communication with the memory. The processor is configured to receive an original target profile for the eye of the patient. The processor is also configured to obtain a cut-off spatial domain kernel filter and convolve the original target profile with the cut-off spatial domain kernel filter to provide a convolved target profile. The processor is further configured to determine the vision treatment based on the convolved target profile.

Inventors:
DAI GUANG-MING (US)
CHERNYAK DIMITRI (US)
Application Number:
PCT/US2017/064098
Publication Date:
June 07, 2018
Filing Date:
November 30, 2017
Export Citation:
Click for automatic bibliography generation   Help
Assignee:
AMO DEV LLC (US)
International Classes:
A61F9/008
Foreign References:
US20150066466A12015-03-05
US20140095137A12014-04-03
US20140095137A12014-04-03
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US5683379A1997-11-04
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US5807379A1998-09-15
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US4770172A1988-09-13
US4773414A1988-09-27
US5207668A1993-05-04
US5108388A1992-04-28
US5219343A1993-06-15
US5163934A1992-11-17
US6004313A1999-12-21
US6095651A2000-08-01
US6271915B12001-08-07
US9498117B22016-11-22
US6099125A2000-08-08
US6000800A1999-12-14
US5258791A1993-11-02
Other References:
DAVID HUANG ET AL: "Mathematical model of corneal surface smoothing after laser refractive surgery", AMERICAN JOURNAL OF OPHTHALMOLOGY, vol. 135, no. 3, 1 March 2003 (2003-03-01), pages 267 - 278, XP055092244, ISSN: 0002-9394, DOI: 10.1016/S0002-9394(02)01942-6
FABRIKANT ET AL.: "Optimization Of Linear Filtering Model To Predict Post-LASIK Corneal Smoothing Based On Training Data Sets", APPLIED MATHEMATICS, vol. 4, 2013, pages 1694 - 1701
DAI ET AL.: "Outcomes For Clinical Studies To Reduce Post-Operative Induction Of Spherical Aberration For Myopic LASIK Surgeries", ARVO, 2016
Attorney, Agent or Firm:
PANG, Andrew Y. (US)
Download PDF:
Claims:
CLAIMS

What is claimed is:

1. A computer implemented method of determining a vision treatment for an eye of a patient, the method comprising: receiving an original target profile for the eye of the patient; obtaining a cut-off spatial domain kernel filter; convolving the original target profile with the cut-off spatial domain kernel filter to provide a convolved target profile; and determining the vision treatment based on the convolved target profile.

2. The method of claim 1, wherein the cut-off spatial domain kernel filter is based on one of an inverse Fourier transform and a Fourier domain noise filter.

3. The method of claim 2, wherein the Fourier domain noise filter is based on at least one of a conjugate of a Fourier domain complex matrix and a modulus of a Fourier domain complex matrix.

4. The method of claim 3, wherein the Fourier domain noise filter is characterized by a fraction having a numerator comprising a conjugate of a Fourier domain complex matrix and a denominator comprising a modulus of the Fourier domain complex matrix.

5. The method of claim 1, wherein the original target profile comprises an original refractive spherical equivalent value within a 4 mm diameter area, and the convolved target profile comprises a target refractive spherical equivalent value within a 4 mm diameter area.

6. The method of claim 5, further comprising scaling the original refractive spherical equivalent using the target refractive spherical equivalent value.

7. The method of claim 1, further comprising elevating the convolved target profile so that a lowest point on the convolved target profile is zero or greater.

8. The method of claim 1, wherein the convolved target profile comprises a transition zone having a transition zone radius, the method further comprising applying a damping multiplier at the transition zone radius or at a location equal to or less than a distance, determined by zero curvature within the transition zone, of the transition zone radius.

9. The method of claim 1, further comprising generating a target shape comprising an optical zone having a periphery, and convolving the original target profile causes a change in the target shape equal to or less than a distance, determined by zero curvature within a transition zone, from the periphery of the optical zone.

10. A system for determining a vision treatment for an eye of a patient, the system comprising: a memory configured to store programmed instructions and data; and a processor in communication with the memory and configured to: receive an original target profile for the eye of the patient; obtain a cut-off spatial domain kernel filter; convolve the original target with the cut-off spatial domain kernel filter to provide a convolved target profile; and determine the vision treatment based on the convolved target profile.

11. The system of claim 10, wherein the cut-off spatial domain kernel filter is based on one of an inverse Fourier transform and a Fourier domain noise filter.

12. The system of claim 11, wherein the Fourier domain noise filter is based on at least one of a conjugate of a Fourier domain complex matrix and a modulus of a Fourier domain complex matrix.

13. The system of claim 12, wherein the Fourier domain noise filter is characterized by a fraction having a numerator comprising a conjugate of a Fourier domain complex matrix and a denominator comprising a modulus of the Fourier domain complex matrix.

14. The system of claim 10, wherein the original target profile comprises an original refractive spherical equivalent value within a 4 mm diameter area, and the convolved target profile comprises a target refractive spherical equivalent value within a 4 mm diameter area.

15. The system of claim 14, wherein the processor is further configured to scale the original refractive spherical equivalent using the target refractive spherical equivalent value.

16. The system of claim 10, wherein the processor is further configured to elevate the convolved target profile so that a lowest point on the convolved target profile is zero or greater.

17. The system of claim 10, wherein the convolved target profile comprises a transition zone having a transition zone radius, and the processor is further configured to apply a damping multiplier at the transition zone radius or at a location equal to or less than a predetermined distance, determined by zero curvature within the transition zone, of the transition zone radius.

18. The system of claim 10, wherein the processor is further configured to generate a target shape comprising an optical zone having a periphery, and convolving the original target profile causes a change in the target shape equal to or less than a distance, determined by zero curvature within a transition zone, from the periphery of the optical zone.

19. A non-transitory computer readable medium including instructions which when executed cause a computer to execute a method of determining a vision treatment for an eye of a patient, the method comprising: receiving an original target profile for the eye of the patient;

obtaining a cut-off spatial domain kernel filter; convolving the original target profile with the cut-off spatial domain kernel filter to provide a convolved target profile; and determining the vision treatment based on the convolved target profile.

20. The non-transitory computer readable medium of claim 19, wherein the method further comprise scaling an original refractive spherical equivalent using a target refractive spherical equivalent value.

Description:
SPHERICAL ABERRATION REDUCTION SYSTEMS AND METHODS

CROSS-REFERENCES TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Patent Application No. 62/428,981, filed December 1, 2016, which is incorporated by reference as if fully set forth.

[0002] The application is related to U.S. Patent Publication 2014/0095137, the content of which is incorporated herein by reference.

SUMMARY

[0003] Embodiments described herein related to the field of vision treatment, and in particular, to systems and methods for generating or modifying optical treatment shapes.

[0004] Embodiments disclosed herein provide systems and methods for obtaining a modified ablation target that reduces, minimizes or eliminates, a systematic trend in post-operatively induced spherical aberration. In some embodiments, the modification of the target shape introduces a small increase in the ablation depth to facilitate safe and effective treatments. In some emodiments, the modification of the target shape changes the peripheral cornea profile, which can affect the SA without changing the central refractive power.

[0005] Embodiments disclosed herein provide a computer implemented method of determining a vision treatment for an eye of a patient. The method includes receiving an original target profile for the eye of the patient. The method also includes obtaining a cut-off spatial domain kernel filter and convolving the original target profile using the cut-off spatial domain kernel filter to provide a convolved target profile. The method further includes determining the vision treatment based on the convolved target profile. [0006] Embodiments disclosed herein provide a system for determining a vision treatment for an eye of a patient. The system includes a memory configured to store programmed instructions and data and a processor in communication with the memory. The processor is configured to receive an original target profile for the eye of the patient and obtain a cut-off spatial domain kernel filter. The processor is also configured to convolve the original target with the cut-off spatial domain kernel filter to provide a convolved target profile. The processor is further configured to determine the vision treatment based on the convolved target profile.

[0007] Embodiments disclosed herein provide a non-transitory computer readable medium including instructions which when executed cause a computer to execute a method of determining a vision treatment for an eye of a patient. The method includes receiving an original target profile for the eye of the patient. The method also includes obtaining a cut-off spatial domain kernel filter. The method further includes convolving the original target profile with the cut-off spatial domain kernel filter to provide a convolved target profile and determining the vision treatment based on the convolved target profile.

[0008] Embodiments also include administering the determined vision treatment to the patient.

[0009] In some embodiments, the spatial domain kernel filter is based on an inverse Fourier transform of a Fourier domain noise filter. In some aspects, the Fourier domain noise filter is based on a conjugate of a Fourier domain complex matrix. In other aspects, the Fourier domain noise filter is based on a modulus of a Fourier domain complex matrix. In other aspects, the Fourier domain noise filter is based on a conjugate of a Fourier domain complex matrix and a modulus of the Fourier domain complex matrix. According to some embodiments, the Fourier domain noise filter is characterized by a fraction having a numerator comprising a conjugate of a Fourier domain complex matrix and a denominator comprising a modulus of the Fourier domain complex matrix. In some cases, the Fourier domain complex matrix is characterized by the formula:

where o represents a diffusion coefficient, k x and k y represent frequency domain variables, and dL represents a mesh size. In some cases, o has a value of 0.35 mm and dL has a value of 0.1 mm. Optionally, o may have a value within a range from about 0.2 mm to about 0.5 mm. In some cases, o may have a value within a range from about 0.33 mm to about 0.4 mm. Optionally, the denominator can be characterized by the expression | K(k x , k y ) | n , where n is an integer having a value of 2 or more. In some instances, the denominator can be characterized by the expression [ | K(k x , k y ) | n + SNR 2 ] where n is an integer having a value of 2 or more and SNR represents a signal to noise ratio value. In some instances, the convolved profile includes a transition zone radius, and a method may further include zeroing the convolved profile at locations outside of the transition zone radius.

[0010] In some embodiments, the original target profile may include an original refractive spherical equivalent value within a 4 mm diameter area, and the convolved target profile may include a target refractive spherical equivalent value within a 4 mm diameter area. Optionally, the method may further include scaling the original refractive spherical equivalent with the target refractive spherical equivalent value. Some methods may also include elevating the convolved profile so that a lowest point on the convolved profile is zero or greater. In some instances, a convolved profile includes a transition zone radius, and methods may include applying a damping multiplier at or near the transition zone radius. In some instances, the target shape includes an optical zone having a periphery, and the convolution effects a change in the target shape near the periphery of the optical zone.

[0011] Exemplary systems may include an input that receives an original target profile for the eye of the patient, and a convolution module (e.g., programmed instructions) which convolves the original target profile with a spatial domain kernel filter. The spatial domain kernel filter can be based on an inverse Fourier transform of a Fourier domain noise filter. Systems may also include a treatment generation or determination module that determines the vision treatment based on the convolved profile. In some instances, the Fourier domain noise filter is based on a conjugate of a Fourier domain complex matrix. In some instances, the Fourier domain noise filter is based on a modulus of a Fourier domain complex matrix.

[0012] Embodiments disclosed herein provide systems and methods for determining a vision treatment for an eye of a patient. Exemplary methods include receiving, (e.g. at a processing device), an original target profile for the eye of the patient, and obtaining a cut-off spatial domain kernel filter, where the cut-off spatial domain kernel filter is based on an inverse Fourier transform of a Fourier domain noise filter. Methods may further include convolving the original target profile with the cut-off spatial domain kernel filter, and determining the vision treatment based on the convolved profile. Exemplary systems may include a processing device, including a processor, that receives an original target profile for the eye of the patient, and a convolution module that convolves the original target profile with a cut-off spatial domain kernel filter, where the cut-off spatial domain kernel filter is based on an inverse Fourier transform of a Fourier domain noise filter. The processing device may be configured to execute programmed instructs (e.g., a treatment module) that determines the vision treatment based on the convolved profile.

BRIEF DESCRIPTION OF THE DRAWINGS

[0013] A more detailed understanding can be had from the following description, given by way of example in conjunction with the accompanying drawings wherein:

[0014] FIG. 1 illustrates a laser ablation system according to an embodiment described herein; [0015] FIG. 2 illustrates a simplified computer system according to an embodiment described herein;

[0016] FIG. 3 illustrates a wavefront measurement system according to an embodiment described herein;

[0017] FIG. 3 A illustrates another wavefront measurement system according to another embodiment described herein;

[0018] FIG. 4 depicts aspects of a method for determining a vision treatment for an eye, according to embodiments described herein;

[0019] FIG. 5 depicts aspects of a method for modifying a target shape according to embodiments described herein;

[0020] FIG. 6A shows post-operative values and FIG. 6B shows aspects of optical and transition zones according to embodiments described herein;

[0021] FIG. 7 shows aspects of simulated epithelium thickness profiles according to embodiments described herein;

[0022] FIGS. 8A and 8B show aspects of flap SA and sigma relationships according to embodiments described herein;

[0023] FIGS. 9A to 9C depict aspects of post-operative SA and pre-operative MRSE or SE relationships according to embodiments described herein;

[0024] FIGS. 10A and 10B illustrate aspects of spherical aberration errors for deconvolution according to embodiments described herein;

[0025] FIGS. 11A and 11B show aspects of rescaling coefficients and refraction errors, respectively, according to embodiments described herein;

[0026] FIGS. 12A and 12B depict aspects of effects of deconvolution on cylinder refraction according to embodiments described herein;

[0027] FIGS. 12C and 12D illustrate aspects of ablation profile modifications according to embodiments described herein;

[0028] FIGS. 13A to 13C depict aspects of pre-operative MRSE (Manifest Refraction Spherical Equivalent) according to embodiments described herein; [0029] FIGS. 14A and 14B illustrate aspects of ablation profile modifications according to embodiments described herein;

[0030] FIGS. 15A and 15B show aspects of pre-operative MRSE according to embodiments described herein;

[0031] FIGS. 16A and 16B show aspects of differences between modified targets and original targets according to embodiments described herein;

[0032] FIG. 17 depicts aspects of shows post-operating secondary spherical aberration according to embodiments described herein;

[0033] FIG. 18 depicts aspects of methods for generating a target shape, according to embodiments described herein;

[0034] FIG. 19 depicts aspects of relationships between RMS error and size of s (pixels), according to embodiments described herein;

[0035] FIG. 20 illustrates aspects of deconvolution methods according to embodiments described herein;

[0036] FIGS. 21A and 2 IB show aspects of ablation profile changes or modifications according to embodiments described herein;

[0037] FIG. 22 illustrates aspects of induced SA according to embodiments described herein;

[0038] FIG. 23 illustrates aspects of deconvolution effects according to embodiments described herein;

[0039] FIG. 24 illustrates aspects of radial compensation function according to embodiments described herein;

[0040] FIG. 25 illustrates aspects of target shape modification according to embodiments described herein;

[0041] FIG. 26 shows aspects of induced SA according to embodiments described herein;

[0042] FIG. 27 illustrates aspects of low pass filter according to embodiments described herein; [0043] FIGS. 28A and 28B illustrate aspects of kernel and inverse kernel according to embodiments described herein;

[0044] FIG. 29 illustrates aspects of treatment target deconvolution according to embodiments described herein;

[0045] FIG. 30 depicts aspects of target verification according to embodiments described herein;

[0046] FIGS. 31A to 31C illustrate aspects of residual error with deconvolution according to embodiments described herein;

[0047] FIGS. 32A and 32B depict aspects of expected and inversed convolved targets according to embodiments described herein;

[0048] FIG. 33 illustrates aspects of low pass filter according to embodiments described herein;

[0049] FIG. 34 illustrates aspects of post-operative SA according to embodiments described herein;

[0050] FIGS. 35A and 35B show aspects of vision condition cases according to embodiments described herein;

[0051] FIG. 36 depicts aspects of a method for obtaining free parameter values for a kernel, according to embodiments described herein;

[0052] FIGS. 37A-37D depict aspects of regression plots, according to embodiments described herein;

[0053] FIGS. 38A and 38B depict aspects of kernels, according to embodiments described herein;

[0054] FIG. 39 depicts aspects of smoothing kernel formulas, according to embodiments described herein;

[0055] FIG. 40 depicts aspects of an signal-to-noise ratio determination, according to embodiments described herein;

[0056] FIGS. 41A-41D depict results obtained using an improved kernel, according to embodiments described herein; [0057] FIG. 42 depicts a comparison of inverse kernel profiles for a previously known kernel and a new kernel according to embodiments described herein;

[0058] FIG. 43 depicts a comparison of power spectrums for a previously known kernel and a new kernel according to embodiments described herein;

[0059] FIG. 44 depicts a comparison of power spectrums of inverse kernels for a previously known kernel and a new kernel according to embodiments described herein;

[0060] FIG. 45 depicts a comparison of ablation profiles for myopia, according to embodiments described herein;

[0061] FIG. 46 depicts a comparison of ablation depth changes for myopia, according to embodiments described herein;

[0062] FIG. 47 depicts a comparison of ablation profiles for hyperopia, according to embodiments described herein; and

[0063] FIG. 48 depicts a comparison of ablation depth changes for hyperopia, according to embodiments described herein.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0064] The post-operative induction of high-order aberrations (HO As), and in particular spherical aberration (SA), remains an important issue for laser vision correction technology. It has been found that post-operative cornea remodeling is a significant root cause of SA induction. One effect of the cornea remodeling involves the smoothing of epithelium at the anterior surface of the eye, where the epithelium tends to grow thicker and fill in the dips of the cornea surface as created by refractive surgery. Epithelial smoothing can result in regression following refractive surgery and lead to induced high-order aberrations that are particularly strong for high myopia and hyperopia cases.

[0065] Certain techniques have been proposed for minimizing induced postoperative SA, including linear adjustment of the basis data and nomogram adjustments. Although such techniques can provide benefits to patients in need thereof, further improvements would be desirable. Embodiments described herein address such outstanding needs.

[0066] Embodiments disclosed herein utilize deconvolution techniques, based on a cornea smoothing model, to obtain an ablation target or treatment shape that induces little or no post-operative SA. In some instances, these ablation targets or treatment shapes can provide a post-operative SA that is equal to or below a naturally occurring amount of SA.

[0067] The techniques disclosed herein can be readily adapted for use with existing laser systems. By providing a more accurate (and hence, for example, less variable) methodology for treating optical errors of an eye, embodiments described herein facilitate sculpting of the cornea or other opthalmological tissues so that treated eyes may consistently and reliably receive the desired optical correction resulting in improved vision.

[0068] Embodiments described herein can be readily adapted for use with existing laser systems and other optical treatment devices. Although system, software, and method embodiments are described primarily in the context of a laser eye surgery system, it should be understood that embodiments may be adapted for use in or in combination with alternative eye treatment procedures, systems, or modalities, such as spectacle lenses, intraocular lenses, accommodating IOLs, contact lenses, corneal ring implants, collagenous corneal tissue thermal remodeling, corneal inlays, corneal onlays, other corneal implants or grafts, and the like. Relatedly, systems, software, and methods according to embodiments are well suited for customizing any of these treatment modalities to a specific patient. Thus, for example, embodiments encompass custom preformed lenses, intraocular lenses, custom contact lenses, custom corneal implants, and the like, which can be configured to treat or ameliorate any of a variety of vision conditions in a particular patient based on their unique ocular characteristics or anatomy. Additionally, the modified ablation target or target shape may be implemented via other non-ablative laser therapies, such as laser-incised custom lenticule shapes and subsequent extraction and laser-based corneal incision patterns.

[0069] Some embodiments disclosed herein can be carried out in conjunction with treatments provided by any of a variety of laser devices, including without limitation the WaveScan® System and the STAE S4® Excimer Laser System both by Abbott Medical Optics Inc., the WaveLight® Allegretto Wave® Eye-Q laser, the Schwind Amaris™ lasers, the 217P excimer workstation by Technolas PerfectVision GmbH, the Mel 80™ laser by Carl Zeiss Meditec, Inc., and the like.

[0070] Turning now to the drawings, FIG. 1 illustrates a laser eye surgery system 10, including a laser 12 that produces a laser beam 14. Laser 12 is optically coupled to laser delivery optics 16, which directs laser beam 14 to an eye E of patient P. A delivery optics support structure (not shown here for clarity) extends from a frame 18 supporting laser 12. A microscope 20 is mounted on the delivery optics support structure, the microscope often being used to image a cornea of eye E.

[0071] [0001] Laser 12 generally comprises an excimer laser, ideally comprising an argon-fluorine laser producing pulses of laser light having a wavelength of approximately 193 nm. Laser 12 will preferably be designed to provide a feedback stabilized fluence at the patient's eye, dehvered via dehvery optics 16. Embodiments described herein may also be useful with alternative sources of ultraviolet or infrared radiation, particularly those adapted to controllably ablate the corneal tissue without causing significant damage to adjacent and/or underlying tissues of the eye. Such sources include, but are not limited to, solid state lasers and other devices which can generate energy in the ultraviolet wavelength between about 185 and 205 nm and/or those which utilize frequency-multiplying techniques. Hence, although an excimer laser is the illustrative source of an ablating beam, other lasers may be used.

[0072] The exemplary [0002] laser system 10 includes a computer processing device 22. Processing device 22 may include one or more processors, user interface devices such as a keyboard, a display monitor, and the like. Processing device 22 may also include memory (e.g., volatile or non-volatile memory) and a storage device, such as a floppy disk, an optical disk, a data tape, a magnetic or optical disk drive. Processing device 22 may also include a network interface (e.g., network interface controller) configured to communicate with a wired or wireless network. Tangible storage media 29 may take the form of a floppy disk, an optical disk, a data tape, a volatile or non-volatile memory, RAM, or the like. One or more processors of the processing device 22 can be used to process (e.g., fetch, read, write, store and execute) programmed instructions (e.g., modules) stored on the tangible storage media 29 to perform any of the methods described herein. Tangible storage media 29 may optionally embody wavefront sensor data, wavefront gradients, a wavefront elevation map, a treatment map, a corneal elevation map, and/or an ablation table. Processing device 22 may be configured to receive programmed instructions from tangible storage media 29 via a physical input device (e.g., port) of processing device 22, as well as remotely from tangible storage media 29 via one or more wired networks (e.g., Ethernet) or wireless networks (e.g., via wireless protocols such as as infrared, Bluetooth, Wi-Fi or the like).

[0073] Laser 12 and delivery optics 16 will generally direct laser beam 14 to the eye of patient P under the direction of a computer 22. Computer 22 will often selectively adjust laser beam 14 to expose portions of the cornea to the pulses of laser energy so as to effect a predetermined sculpting of the cornea and alter the refractive characteristics of the eye. In many embodiments, both laser beam 14 and the laser delivery optical system 16 will be under computer control of processing device 22 to effect the desired laser sculpting process, with the processor effecting (and optionally modifying) the pattern of laser pulses. The pattern of pulses may by summarized in machine readable data of tangible storage media 29 in the form of a treatment table, and the treatment table may be adjusted according to feedback input into processing device 22 from an automated image analysis system in response to feedback data provided from an ablation monitoring system feedback system. Optionally, the feedback may be manually entered into the processor by a system operator. Such feedback might be provided by integrating the wavefront measurement system described below with the laser treatment system 10, and processing device 22 may continue and/or terminate a sculpting treatment in response to the feedback, and may optionally also modify the planned sculpting based at least in part on the feedback. Measurement systems are further described in U.S. Patent No. 6,315,413, the full disclosure of which is incorporated herein by reference.

[0074] Laser beam 14 may be adjusted to produce the desired sculpting using a variety of alternative mechanisms. The laser beam 14 may be selectively limited using one or more variable apertures. An exemplary variable aperture system having a variable iris and a variable width slit is described in U.S. Patent No. 5,713,892, the full disclosure of which is incorporated herein by reference. The laser beam may also be tailored by varying the size and offset of the laser spot from an axis of the eye, as described in U.S. Patent Nos. 5,683,379, 6,203,539, and 6,331, 177, the full disclosures of which are incorporated herein by reference.

[0075] Still further alternatives are possible, including scanning of the laser beam over the surface of the eye and controlling the number of pulses and/or dwell time at each location, as described, for example, by U.S. Patent No. 4,665,913, the full disclosure of which is incorporated herein by reference; using masks in the optical path of laser beam 14 which ablate to vary the profile of the beam incident on the cornea, as described in U.S. Patent No. 5,807,379, the full disclosure of which is incorporated herein by reference; hybrid profile-scanning systems in which a variable size beam (typically controlled by a variable width slit and/or variable diameter iris diaphragm) is scanned across the cornea; or the like. The computer programs and control methodology for these laser pattern tailoring techniques are well described in the patent literature. [0076] Additional components and subsystems may be included with laser system 10, as should be understood by those of skill in the art. For example, spatial and/or temporal integrators may be included to control the distribution of energy within the laser beam, as described in U.S. Patent No. 5,646,791, the full disclosure of which is incorporated herein by reference. Ablation effluent evacuators/filters, aspirators, and other ancillary components of the laser surgery system are known in the art. Further details of suitable systems for performing a laser ablation procedure can be found in commonly assigned U.S. Pat. Nos. 4,665,913, 4,669,466, 4,732, 148, 4,770, 172, 4,773,414, 5,207,668, 5, 108,388, 5,219,343, 5,646,791 and 5, 163,934, the complete disclosures of which are incorporated herein by reference. Suitable systems also include commercially available refractive laser systems such as those manufactured and/or sold by Alcon, Bausch & Lomb, Nidek, WaveLight, LaserSight, Schwind, Zeiss-Meditec, and the like. Basis data can be further characterized for particular lasers or operating conditions, by taking into account localized environmental variables such as temperature, humidity, airflow, and aspiration.

[0077] FIG. 2 is a simplified block diagram of an exemplary computer system 22 that may be used by the laser surgical system 10. Computer system 22 typically includes at least one processor 52 which may communicate with a number of peripheral devices via a bus subsystem 54. These peripheral devices may include a storage subsystem 56, comprising a memory subsystem 58 and a file storage subsystem 60, user interface input devices 62, user interface output devices 64, and a network interface subsystem 66. Network interface subsystem 66 provides an interface to outside networks 68 and/or other devices, such as the wavefront measurement system 30.

[0078] User interface input devices 62 may include a keyboard, pointing devices such as a mouse, trackball, touch pad, or graphics tablet, a scanner, foot pedals, a joystick, a touchscreen incorporated into the display, audio input devices such as voice recognition systems, microphones, and other types of input devices. User input devices 62 will often be used to download a computer executable code from a tangible storage media 29 embodying any of the methods. In general, use of the term "input device" is intended to include a variety of conventional and proprietary devices and ways to input information into computer system 22.

[0079] User interface output devices 64 may include a display subsystem, a printer, a fax machine, or non-visual displays such as audio output devices. The display subsystem may be a cathode ray tube (CRT), a flat-panel device such as a liquid crystal display (LCD), a projection device, or the like. The display subsystem may also provide a non-visual display such as via audio output devices. In general, use of the term "output device" is intended to include a variety of conventional and proprietary devices and ways to output information from computer system 22 to a user.

[0080] Storage subsystem 56 can store the basic programming and data constructs that provide the functionality of the various embodiments. For example, a database and modules implementing the functionality of the methods, as described herein, may be stored in storage subsystem 56. These software modules are generally executed by processor 52. In a distributed environment, the software modules may be stored on a plurality of computer systems and executed by processors of the plurality of computer systems. Storage subsystem 56 typically comprises memory subsystem 58 and file storage subsystem 60.

[0081] Memory subsystem 58 typically includes a number of memories including a main random access memory (RAM) 70 for storage of instructions and data during program execution and a read only memory (ROM) 72 in which fixed instructions are stored. File storage subsystem 60 provides persistent (nonvolatile) storage for program and data files, and may include tangible storage media 29 (FIG. 1) which may optionally embody wavefront sensor data, wavefront gradients, a wavefront elevation map, a treatment map, and/or an ablation table. File storage subsystem 60 may include a hard disk drive, a floppy disk drive along with associated removable media, a Compact Digital Read Only Memory (CD- ROM) drive, an optical drive, DVD, CD-R, CD-RW, solid-state removable memory, and/or other removable media cartridges or disks. One or more of the drives may be located at remote locations on other connected computers at other sites coupled to computer system 22. The modules implementing the functionality may be stored by file storage subsystem 60.

[0082] Bus subsystem 54 provides a mechanism for letting the various components and subsystems of computer system 22 communicate with each other as intended. The various subsystems and components of computer system 22 need not be at the same physical location but may be distributed at various locations within a distributed network. Although bus subsystem 54 is shown schematically as a single bus, alternate embodiments of the bus subsystem may utilize multiple busses.

[0083] Computer system 22 itself can be of varying types including a personal computer, a portable computer, a workstation, a computer terminal, a network computer, a control system in a wavefront measurement system or laser surgical system, a mainframe, or any other data processing system. Due to the ever- changing nature of computers and networks, the description of computer system 22 depicted in FIG. 2 is intended only as a specific example for purposes of illustrating one embodiment. Many other configurations of computer system 22 are possible having more or less components than the computer system depicted in Fig. 2.

[0084] Referring now to FIG. 3, one embodiment of a wavefront measurement system 30 is schematically illustrated in simplified form. In very general terms, wavefront measurement system 30 is configured to sense local slopes of a gradient map exiting the patient's eye. Devices based on the Hartmann-Shack principle generally include a lenslet array to sample the gradient map uniformly over an aperture, which is typically the exit pupil of the eye. Thereafter, the local slopes of the gradient map are analyzed so as to reconstruct the wavefront surface or map.

[0085] More specifically, one wavefront measurement system 30 includes an image source 32, such as a laser, which projects a source image through optical tissues 34 of eye E so as to form an image 44 upon a surface of retina R. The image from retina R is transmitted by the optical system of the eye (e.g., optical tissues 34) and imaged onto a wavefront sensor 36 by system optics 37. The wavefront sensor 36 communicates signals to a computer system 22' for measurement of the optical errors in the optical tissues 34 and/or determination of an optical tissue ablation treatment program. Computer 22' may include the same or similar hardware as the computer system 22 illustrated in FIGS. 1 and 2. Computer system 22' may be in communication with computer system 22 that directs the laser surgery system 10, or some or all of the components of computer system 22, 22' of the wavefront measurement system 30 and laser surgery system 10 may be combined or separate. If desired, data from wavefront sensor 36 may be transmitted to a laser computer system 22 via tangible media 29, via an I/O port, via an networking connection 66 such as an intranet or the Internet, or the like.

[0086] Wavefront sensor 36 generally comprises a lenslet array 38 and an image sensor 40. As the image from retina R is transmitted through optical tissues 34 and imaged onto a surface of image sensor 40 and an image of the eye pupil P is similarly imaged onto a surface of lenslet array 38, the lenslet array separates the transmitted image into an array of beamlets 42, and (in combination with other optical components of the system) images the separated beamlets on the surface of sensor 40. Sensor 40 typically comprises a charged couple device or "CCD," and senses the characteristics of these individual beamlets, which can be used to determine the characteristics of an associated region of optical tissues 34. In particular, where image 44 comprises a point or small spot of light, a location of the transmitted spot as imaged by a beamlet can directly indicate a local gradient of the associated region of optical tissue.

[0087] Eye E generally defines an anterior orientation ANT and a posterior orientation POS. Image source 32 generally projects an image in a posterior orientation through optical tissues 34 onto retina R as indicated in FIG. 3. Optical tissues 34 again transmit image 44 from the retina anteriorly toward wavefront sensor 36. Image 44 actually formed on retina R may be distorted by any imperfections in the eye's optical system when the image source is originally transmitted by optical tissues 34. Optionally, image source projection optics 46 may be configured or adapted to decrease any distortion of image 44.

[0088] In some embodiments, image source optics 46 may decrease lower order optical errors by compensating for spherical and/or cylindrical errors of optical tissues 34. Higher order optical errors of the optical tissues may also be compensated through the use of an adaptive optic element, such as a deformable mirror (described below). Use of an image source 32 selected to define a point or small spot at image 44 upon retina R may facilitate the analysis of the data provided by wavefront sensor 36. Distortion of image 44 may be limited by transmitting a source image through a central region 48 of optical tissues 34 which is smaller than a pupil 50, as the central portion of the pupil may be less prone to optical errors than the peripheral portion. Regardless of the particular image source structure, it will be generally be beneficial to have a well-defined and accurately formed image 44 on retina R.

[0089] In one embodiment, the wavefront data may be stored in a computer readable medium 29 or a memory of the wavefront sensor system 30 in two separate arrays containing the x and y wavefront gradient values obtained from image spot analysis of the Hartmann-Shack sensor images, plus the x and y pupil center offsets from the nominal center of the Hartmann-Shack lenslet array, as measured by the pupil camera 51 (FIG. 3) image. Such information contains all the available information on the wavefront error of the eye and is sufficient to reconstruct the wavefront or any portion of it. In such embodiments, there is no need to reprocess the Hartmann-Shack image more than once, and the data space required to store the gradient array is not large. For example, to accommodate an image of a pupil with an 8 mm diameter, an array of a 20 x 20 size (i.e., 400 elements) is often sufficient. As can be appreciated, in other embodiments, the wavefront data may be stored in a memory of the wavefront sensor system in a single array or multiple arrays.

[0090] While the methods will generally be described with reference to sensing of an image 44, it should be understood that a series of wavefront sensor data readings may be taken. For example, a time series of wavefront data readings may help to provide a more accurate overall determination of the ocular tissue aberrations. As the ocular tissues can vary in shape over a brief period of time, a plurality of temporally separated wavefront sensor measurements can avoid relying on a single snapshot of the optical characteristics as the basis for a refractive correcting procedure. Still further alternatives are also available, including taking wavefront sensor data of the eye with the eye in differing configurations, positions, and/or orientations. For example, a patient will often help maintain alignment of the eye with wavefront measurement system 30 by focusing on a fixation target, as described in U.S. Patent No. 6,004,313, the full disclosure of which is incorporated herein by reference. By varying a position of the fixation target as described in that reference, optical characteristics of the eye may be determined while the eye accommodates or adapts to image a field of view at a varying distance and/or angles.

[0091] The location of the optical axis of the eye may be verified by reference to the data provided from a pupil camera 52. In the exemplary embodiment, a pupil camera 52 images pupil 50 so as to determine a position of the pupil for registration of the wavefront sensor data relative to the optical tissues.

[0092] An alternative embodiment of a wavefront measurement system is illustrated in FIG. 3A. The major components of the system of FIG. 3A are similar to those of FIG. 3. Additionally, FIG. 3A includes an adaptive optical element 53 in the form of a deformable mirror. The source image is reflected from deformable mirror 98 during transmission to retina R, and the deformable mirror is also along the optical path used to form the transmitted image between retina R and imaging sensor 40. Deformable mirror 98 can be controllably deformed by computer system 22 to limit distortion of the image formed on the retina or of subsequent images formed of the images formed on the retina, and may enhance the accuracy of the resultant wavefront data. The structure and use of the system of FIG. 3A are more fully described in U.S. Patent No. 6,095,651, the full disclosure of which is incorporated herein by reference.

[0093] The components of an embodiment of a wavefront measurement system for measuring the eye and ablations may comprise elements of a WaveScan® System. One embodiment includes a WaveScan® System with a deformable mirror as described above. An alternate embodiment of a wavefront measuring system is described in U.S. Patent No. 6,271,915, the full disclosure of which is incorporated herein by reference. It is appreciated that any wavefront aberrometer could be employed for use with embodiments disclosed herein.

[0094] Post-Operative Aberrations

[0095] Refractive procedures may, in some cases, induce certain aberrations in an eye of a patient. For example, it is believed that laser-assisted in situ keratomileusis (LASIK) surgeries can induce high order aberrations, and in particular spherical aberration (SA). Spherical aberration is a special type of high order aberration that can affect night vision, and involves off-axis rays entering the eye with different heights of focus at different locations.

[0096] Embodiments encompass systems and methods for reducing, eliminating, or otherwise compensating for such post-operative inductions. For example, whereas an original target shape applied to the eye may lead to induced aberrations, it is possible to deconvolve the original target shape so as to obtain a modified target shape, such that when the modified target shape is applied to the eye, there are fewer or less pronounced induced aberrations.

[0097] FIG. 4 depicts aspects of a method 400 for determining a vision treatment for an eye of a patient As shown here, the method includes receiving (e.g. at an input) an original target profile for the eye of the patient as indicated by block 410. Method 400 also includes obtaining a spatial domain kernel filter as indicated by block 420. The spatial domain kernel filter can be based on an inverse Fourier transform of a Fourier domain noise filter. Further, the method may include convolving the original target profile with the spatial domain kernel filter as indicated by block 430. As illustrated here, method 400 also may include determining the vision treatment based on the convolved profile as indicated by block 440. According to some embodiments, methods may include administering the vision treatment to the patient as indicated by block 450.

[0098] FIG. 5 depicts aspects of a method for modifying a target shape according to embodiments. As shown here, a modification method 500 includes obtaining a target shape as indicated by block 510. Often, the target shape or profile will have an optical zone and a transition zone. In some cases, a target shape may refer to an intended optical surface designed to achieve a given refractive correction. A method 500 for modifying or deconvolving a target shape may also include offsetting an inner boundary of the transition zone (e.g. by about 0.1 mm in diameter), as indicated by block 520. Further, the method may include inputting, receiving, or reading in an inverse smoothing kernel as described elsewhere herein. As illustrated by block 530, methods may include applying a deconvolution to a target profile, for example as a low pass filter multiplied with the target profile as discussed below with reference to Equation 14. Methods may also include zeroing out an ablation profile at distances greater than the transition zone radius, as indicated by block 540. In some cases, methods may include rescaling a deconvolved target, for example as indicated by block 550, so that its Zernike defocus term within the 4 mm diameter is the same as for the original target. In some instances, the rescaling factor can be 1.0. Optionally, methods may include elevating the entire ablation profile, as depicted by block 560, so that the lowest point on the ablation profile is zero. This elevation technique can help to ensure that the ablation profile does not have negative heights. In some instances, methods may include applying a damping multiplier (e.g. Equation 17) to the periphery of the transition zone, as indicated by block 570. Optionally, a modification or deconvolution method can be implemented before application of a cosine compensation step.

[0099] Post-Operative Epithelial Smoothing And Spherical Aberration

[00100] As noted above, cornea remodeling following treatment with a refractive target shape can induce SA, for example due to smoothing of epithelium at the anterior surface of the eye. To develop techniques that compensate for such remodeling, it is helpful to simulate the post-operative epithelium smoothing process with a model. An exemplary model may define the shape of the postoperative cornea surface as a convolution of an ablation target profile with a low- pass filter (LPF), as follows:

/ 'j l post-op = / n j pre-op - K " ® ^ T A

Equation 1

where T i s the ablation target profile. K = K(x,y) is the LPF kernel, which has the following Fourier transform:

K(k x , k ) = —

Equation 2

K(x,y), the LPF kernel, can be considered as a spatial domain representation. The Fourier transform of K(x,y) (i.e. K(kx, ky) or F[K]), can be considered as a frequency or Fourier domain representation.

According to some embodiments, the Fourier transform F[K], or K(kx, ky), may be a squared Butterworth low-pass filter of the first order, which can be applied to the treatment target T in order to obtain the wavefront change due to corneal smoothing. In some instances, the Fourier transform of the LPF kernel can be defined by or based on a single diffusion coefficient σ , which has a unit of length.

[00101] In some instances, the post-operative induced spherical aberration can be computed with a Zernike decomposition of the simulated post-operative cornea surface after the smoothing, as follows:

SA post _ op = SA pre _ op - SA(K ® T) Equation 3

[00102] The spherical aberration computed by Zernike decomposition of a given target can be represented by the function SA(T), where SA(T) refers to SA from the target T.

[00103] According to an exemplary experimental embodiment, a target for each eye in a US IDE clinical study was computed as follows:

T = scale T controller

Equation 4

[00104] According to some embodiments, T controller may refer to a target created by production code. Such a target can be created according to various options. For example, the target shape can be generated based on input such as measured preoperative Zernike coefficients with added flap-induced spherical aberration (e.g. flapSA). The target shape can also be generated with or without applying a cosine correction (e.g. warping adjustment). In some cases, the target can be generated based on scaling and/or physician adjustments. Target shapes may also be generated based on keratometry parameters. For example, if available, keratometry parameters kl, k2, k2a may be used. Optionally, for example if keratometry parameters are not available, default values of kl = 43.5, k2 = 43.5, k2a = 0 may be used.

[00105] It is possible to simulate the cornea thickness after smoothing using an LPF model. For example, FIG. 7 shows simulated epithelium thickness profiles after smoothing (High Myopia study, case ID=21011 OD, -7.4D/-1.5D x 179). For this illustration, pre-operative epithelium was assumed uniform and 50 um thick. Corneal smoothing after a myopic ablation may lead to epithelium diffusion, from high curvature areas on the peripheral transition zone, toward the center where the curvature is smaller. As a result, the epithelium may become thicker in the center and thinner on the periphery of the ablation target. This effect may help explain partial regression after myopia refractive surgery. [00106] Using available clinical data, a smoothed target was compared with the observed 6M corneal change within 6 mm and 5.5 mm diameter optical zone. A diffusion coefficient σ was estimated based on the comparison. In some cases, the comparison can be performed with a linear least-square fit of the model to the observed SA change, as described elsewhere herein. According to some embodiments, the fitting procedure yielded an estimation of σ and its confidence interval for each value of flap SA.

[00107] Various independent estimations of σ were used, including (a) RMS match for low and high Myopia (6M), (b) and Hyperopia (6M - 9M), and (c) slope- based estimation for low Myopia (6M). For example, FIGS. 8A and 8B depict optimized sigma vs. flap induced SA (simulations for clinical studies) for WFD = 6 mm and WFD = 5.5 mm, respectively. The dashed lines represent confidence intervals. WFD refers to a wavefront diameter.

[00108] As flap-induced aberrations typically do not depend on the type of the subsequent treatment, it is possible to assume that the optimal values for flap SA and σ can be chosen within the crossing of confidence intervals for these three estimates (e.g. circled data points in FIGS. 8A and 8B). These points can define optimal values approximately σ = 0.3 mm, flapSA = 0.09 um for 6 mm wavefront and σ = 0.45 mm, flapSA = 0.09 um for 5.5 mm wavefront. Some clinical observations for a flap incision without a subsequent ablation show close values for the flap induced SA (e.g. A a P SA ≡ °- 01 um ).

[00109] It is possible to compare simulated and observed post-operative SA (e.g. with WFD=6 mm). For example, as depicted in FIGS. 9A, B, and C, an estimated diffusion coefficient ^ ^ ^mm for 6 mm wavefront diameter may be validated by comparison of simulated post-operative SA with the actual observed values. A fl a P$ A = 0 09 um was assume( j f or a n data sets. In some embodiments, this value might be different for mechanical microkeratome and IntraLase® femtosecond laser treatments. As illustrated here, trend lines for simulated and observed data can be almost identical for myopia and high myopia data and rather close for other data sets.

[00110] Hence, it is understood that epithelial smoothing subsequent to refractive surgery can induce SA, and that simulation of smoothing can be helpful in developing approaches that compensate for the smoothing. In some cases, it is possible to define the shape of the post-operative cornea surface as a convolution of an ablation target profile with a low-pass filter (LPF).

[00111] In some cases, the post-operative epithelium smoothing process can be simulated by defining the shape of the post-operative cornea surface as a convolution of the ablation target profile with a low-pass filter (LPF) as follows (spatial domain):

h„ = h - op - K(x, y) ® T(x, y)

Equation 5

[00112] where h stands for the elevation maps, ® denotes a convolution, T(x, y) is the ablation target profile and K(x, y) is a low pass filter (LPF) kernel, which has the following Fourier transform

Equation 6

[00113] Equation 6, which is in the Fourier domain, represents a squared Butterworth low-pass filter of the first order, which can be applied to the treatment target in order to obtain the wavefront change due to the corneal smoothing. It can be defined by a single diffusion coefficient o, which has a unit of length. For some discrete case embodiments, the 101 x 101 mesh size can be dL = 0.1 mm. Based on optimizations using data from certain clinical trials, a sigma of 0.35 mm was determined to best explain that observed data.

[00114] According to some embodiments, K(x, y) is in the spatial domain, and is a Fourier transform of K(kx, ky). Here, kx and ky are Fourier domain or frequency domain variables. According to some embodiments, K(x, y) is an LPF kernel that can be exemplified by a 101 x 101 matrix or by a 3-D surface expressed in matrix form where x and y are spatial domain variables.

[00115] Matching Simulation Results Vs. Observed Data

[00116] According to some embodiments, it is possible to match or compare simulated post-operative SA with observed 6M post-operative SA using linear least-square fit of the model to the observed SA change by minimizing the following function:

Equation 7

[00117] Here SA pre -op SA pos t-op and are spherical aberration values for preoperational and 6M post-operative wavefront measurements, flapSA is the immediate flap-induced SA value before the smoothing, and N is the number of eyes. It is possible to compute this function (F) for different flapSA and diffusion coefficients σ, and for each flapSA to find the value Omin where fitting residual is minimal. SA (K ® T) refers to the SA of the target T after LPF

[00118] The confidence interval for the optimized can be roughly estimated as:

Equation 8

[00119] Here std is a standard deviation, computed for the ensemble of eyes with the optimized value σ = Omin

[00120] Both optimized σ and its confidence interval can depend on the value of flapSA. This dependence can be computed separately for myopic (6M) and hyperopic (6M-9M) eyes, for example as depicted in FIGS. 8 A and 8B. Hence, it is possible to have two independent estimations for optimized flapSA and σ . [00121] An alternative estimation of these values can be obtained from matching the simulated vs. observed trend slopes, as follows:

eyes

Equation 9

[00122] Here, ASA = SA ( - K ® T "> ~ ( SA po«-o P ~ SA P re- op _ The op timize d σ can provide a simulated slope that is the same as the observed slope. A confidence interval for this estimate can be defined as 95% confidence interval for the slope of linear regression, as follows:

Equation 10

- 1 %

s x = stdev(SE D ) [00123] Here, T o.o2s - L - } J " x · Χ"·— pre-op ' s y stdev(SA post _ op ) ^ r pj ie slope-based estimation was calculated for a Myopia study.

[00124] Offset Transition Zone

[00125] In some instances, a target shape or ablation target profile will include an optical zone and a transition zone. The aggregate of the optical zone and transition zone may be referred to as an ablation zone, corresponding to the entire corneal region covered by a laser ablation. The optical zone may refer to a corneal region which received a full intended refractive treatment. A transition zone may refer to a corneal region outside of the optical zone but inside of the ablation zone. Often, a transition zone receives a treatment that is not strictly optically correct. With returning reference to FIG. 5, exemplary methods may also include offsetting an inner boundary of the transition zone, as indicated by step 520. According to some embodiments, an original target shape may include a transition zone starting at about 0.25 mm inside the boundary of the optical zone. It is possible that such a target may induce some post-operative SA, independent of any effect cornea smoothing may have on post-operative SA. Hence, a total induced SA may include a target-induced SA combined with a subsequent smoothing-induced SA.

[00126] For example, FIG. 6A depicts post-operative values, in microns, simulated with σ = °· 3 mm for study data (n = 340), for SA as indicated in Table 1.

[00127] As shown here, a target-induced SA (□) may be reduced or even completely eliminated with a small offset of the transition zone (0). In some cases, the offset of the transition zone may cause sharper gradients in the peripheral target. A 0.05 mm radial shift of the inner boundary of the transition zone away from the center of the optical zone, for example as shown in FIG. 6B, (corresponding to a diameter change of 0.1 mm), can make the trend slope for target-induced SA vs. pre-operative SE about twice as small and bring the magnitude of target-induced SA (0) below 0.1 um level, which may be considered negligible. In some instances, by offsetting the inner boundary of the transition zone (e.g. by about 0.1 mm in diameter), the target induced SA can be reduced by about 50% (e.g. 0.1 mm change in diameter). As depicted here, correcting the target induced SA can be effective to remove post-operative SA.

[00128] Deconvolution

[00129] With returning reference to FIG. 5, a method of modifying a target shape can also include applying a deconvolution to the target profile or shape, as indicated by step 530. For example, methods may include applying a low pass filter (LPF) deconvolution (e.g. with o = 0.35 mm) to the target profile. Sigma (o) can refer to a diffusion coefficient related to the strength of an LPF process.

[00130] According to some embodiments, the application of a deconvolution transformation to an original target can operate to compensate for the area of high curvature, which can be a significant cause of post-operatively induced SA.

[00131] In some instances, an LPF kernel for a deconvolution may be the same as the one optimized to fit an observed induced post-operative SA, for example such as those described above in connection with the post-operative epithelial smoothing and spherical aberration. Corneal smoothing, simulated as convolution with an identical or similar LPF kernel, can bring the cornea back to the desired shape.

[00132] In some instances, high-frequency variations may be suppressed by diffusion or LPF convolution. Restoration of such suppressed variations by deconvolution may introduce inaccuracies, which may also be influenced by a signal-to-noise level.

[00133] Embodiments encompass the use of deconvolution techniques which can reduce the degree to which suppressed variations may introduce such inaccuracies. For example, deconvolution techniques may involve the use of a deconvolution filter, combining an LPF kernel, K, and a signal-to-noise ratio, SNR. The Fourier transform of such a filter can be expressed as follows:

K (k ) + SNR 2

Equation 11

[00134] Here K(k) represents a Fourier transform of a LPF kernel, the asterisks refers to a complex conjugate, and SNR is the signal-to-noise ratio. According to some embodiments, the SNR is assumed to be constant. The value of SNR can define which scales will be restored by the deconvolution, reversing diffusion effect on them. In some instances, SNR can be 0.1. If the SNR is excessively small, many small features may be amplified. If the SNR is excessively large, only relatively large features will be amplified. In exemplary embodiments, SNR has a value within a range from 0 to 0.1.

[00135] If there are no noises and SNR = 0, deconvolution should bring back exactly the original target, which existed before the LPF was applied. Where finite noises are present, small features may be irreversibly lost after low-pass filtering and, therefore, deconvolution may restore the original target only with a finite accuracy. The error of restoration can be estimated with applying a LPF to a target and then using deconvolution to restore it and compare it with the original target.

[00136] FIG. 10A shows spherical aberration RMS errors for deconvolution for different SNR values, estimated for study targets (n = 340) with σ = 0.3 mm, where WFD = 6 mm. As depicted here, with SNR = 0.1, all SA RMS errors are below 0.07 um level. FIG. 10B shows SA errors for a similar deconvolution, estimated for study targets (n=515) with o = 0.28 mm.

[00137] Any small and narrow dips in the measured pre-operative wavefront may be amplified by the deconvolution. This may result in small-size features that are too narrow to resolve with laser pulses, which are often restricted to a width of about 1 mm.

[00138] In some cases, it is not necessary or desirable to ablate these very narrow features, as they may be flattened by the smoothing process. What is more, these features may also have little influence on the vision quality. In some cases, it is possible to effect the deconvolution so as to neglect or minimize these features and amplify only relatively large-scale features of the ablation target. For example, this can be done by optimizing the SNR value in a deconvolution process. It has been found that by using SNR > 0.1, for example, any features smaller than 0.5 mm are not amplified by deconvolution. Hence, SNR = 0.1 may be used a default parameter.

[00139] A deconvolved target typically has an oscillating profile at the periphery. These oscillations may be mainly caused by boundaries between the optical zone, transition zone, and an edge of the finite-size target, where either the target profile or its derivatives have sharp changes.

[00140] Embodiments encompass the use of deconvolution and related techniques to compensate for the post-operative induction of high order aberrations (HOAs), and in particular spherical aberration (SA). Accordingly, the visual quality of patients receiving treatments according to these techniques provides desirable results, particularly in the management of night vision symptoms. Often, deconvolution procedures will result in treatment target shape changes equal to or less than a distance determined by zero curvature within the transition zone from the periphery of the optical zone. For example, within a central 4 mm area, the refraction of a modified target shape may be similar or identical to that of an original target shape.

[00141] According to some embodiments, to obtain a new or modified target shape, a deconvolution process can be employed as follows:

Equation 12

[00142] where F( ) stands for a Fourier transform, * denotes a complex conjugate, Tcurrent is an original treatment target, Tnew is the new target that is intended to remove the post-operative SA, and KINV is the inverse kernel of K. The SNR can be used to prevent or inhibit noise amplification and oscillation at the edge. In some instances, a SNR value of 0.1 may be suitable for practical purposes. To prevent or as a substitute for real-time calculation of the Fourier transforms, the inverse kernel KINV can be pre-calculated and applied in real-time as a lookup table or a resource file. A suitable SNR value can prevent the denominator from being zero or excessively small, which may otherwise results in the matrix quotient being unreasonably large.

[00143] According to some embodiments, an inverse kernel can be exemplified as a convolution kernel that operates like a deconvolution procedure. In this sense, a deconvolution operation may be considered to be an inverse procedure of a convolution operation.

[00144] Embodiments encompass techniques for calculating an inverse smoothing kernel KINV. Whereas a low pass filter (e.g. Butterworth kernel) such as K(x, y) is in the Fourier domain, the inverse kernel is in the spatial domain. Instead of implementing a Fourier transform, it is possible to perform a spatial convolution implemented as multiplication.

[00145] In some cases, embodiments encompass rapid convolution calculations (e.g. in the order of several milliseconds) for UI (user interface) manipulation, in a practical implementation. A normal implementation for a spatial 2-D convolution may involve four netted loops each with 101 elements. Such embodiments may be related to the 101 x 101 mesh size cases discussed above in the paragraph following Equation 6. A 2-D spatial convolution can be written as follows:

T new ( i) = T CURRML ® K INV = ∑ ∑T cumnl (i - k, j - l)K, NV (k, l)

Equation 13

[00146] where KINV is the 2-D inverse smoothing kernel. In some cases, K(kx, ky) may be a Butterworth of the first kind, and its inverse may have an actual size that is only a few pixels wide. Therefore, Equation 13 may be rewritten as follows:

T new (i, j) = T currml ® K INV = ± T currml (i - k - l)K INV (51 + k,51 +

Equation 14

[00147] where the inverse kernel size is treated as (2s + 1) x (2s + 1) in size. When s = 17, or the inverse kernel frame size of 35 x 35, RMS error using Equation B is about 0.01 microns. With s = 37, use of Equation 14 may be about 7 times faster than Equation 13, but the error is within 0.001 microns. FIG. 19 shows the relationship between the RMS error and the size of s (pixels), with a simulation of 515 eyes. This figure depicts the RMS error as a function of s when Equation 14 is used (e.g. in contrast to Equation 17 as discussed below).

[00148] Zero Out [00149] With returning reference to FIG. 5, a method of modifying a target shape can also include zeroing out an ablation profile at distances greater than the transition zone radius, as indicated by step 540.

[00150] Typically, no ablation is performed beyond the end of transition zone. Hence, it is possible to zero-out the ablation profile at distances greater than the transition zone outer radius, ^z , as discussed elsewhere herein, for example with regard to FIGS. 12C and 12D.

[00151] A zeroing-out procedure can be included, so as to prevent artifacts and the like that might occur as a result of performing convolution or decon volution. For example convolution or deconvolution may inadvertently or unintentionally introduce nonzero or negative values at positions outside of the transition zone. A zeroing-out operation can be instituted as a safeguard, so as to ensure that such non-zero or negative values are removed, which could otherwise cause complications for a tissue ablation protocol.

[00152] Rescaling Deconvolved Target

[00153] As shown in FIG. 5, a method of modifying a target shape can also include rescaling a deconvolved target, as indicated by step 550. For example, a deconvolved target can be rescaled so that its Zernike defocus term within a 4 mm diameter is the same as that for an original target. In this way, the spherical equivalent refraction of a modified or deconvolved target can be the same as that for an original target. In some instances, a rescaling procedure can be performed to ensure that the refractive power for a deconvolved target is the same as that for an original target. In some cases, the refractive power for a deconvolved target is the same as that for an original target and no rescaling step is performed.

[00154] According to some embodiments, an original target shape may perform adequately for correcting or treating refraction errors, and hence a modified target shape based on the original target shape may be generated so that the refraction of the modified target is the same as for the original target. This can be achieved, for example, by rescaling of the deconvolved target so that its defocus Zernike term within the 4 mm area (which defines wavefront -based SE) is the same as for the current target. A rescaling coefficient, which is the ratio of the defocus terms for the current and de-convolved targets, may be expressed as follows:

SE

rescale = c -≡≡^

SE de—conv

Equation 15

[00155] The rescaling coefficient may be close to 1, and distributed as shown in FIGS. 11A and 11B. For example, a rescaling coefficient may have a mean value of 1.003, such as that which was found for US IDE studies. In such instances, rescaling may not be needed, in practical terms. In no rescaling is performed, then resulting refraction errors may be below 0.1 D, for example as shown in FIG. 11A. Hence, it may be possible to neglect or ignore such small values. FIG. 11B shows a distribution of SE re-scaling coefficients and refraction errors without rescaling for the studies (n = 340).

[00156] According to some embodiments, deconvolution may also affect the cylinder refraction. A magnitude of this effect is illustrated in FIGS. 12A and 12B. Here, it is possible to see a comparison of X, Y components of astigmatism for an original target and a deconvolved target (simulated for the studies, n = 340). The deconvolved targets show slightly higher astigmatism, as compared with the original targets, although the difference is less than 1%.

[00157] According to some embodiments, a current or original target Tcurrent yields good matching to low order aberrations, and a scaling can be performed such that the refractive spherical equivalent over 4 mm of the new or modified target is the same as that of the current or original target. Exemplary studies have shown that such a scaling factor is about unity. Therefore, a scaling factor of 1.0 can be assumed in some cases.

[00158] Elevating Ablation Profile [00159] As shown in FIG. 5, a method of modifying a target shape can also include elevating an ablation profile, as indicated by step 560. For example, in order to make all ablation values be non-negative, it is possible to elevate the entire ablation profile so that the lowest point on the ablation profile is zero or otherwise non-negative. In this way, the ablation profile can be generated so that it does not have negative heights.

[00160] Damping Periphery Of Transition Zone

[00161] As shown in FIG. 5, a method of modifying a target shape can also include damping a periphery of a transition zone, as indicated by step 570. For example, a damping multiplier or multiplication factor may be applied which suppresses the fluctuations of the periphery of the target shape. In some embodiments, after certain adjustments are made (e.g. such as the adjustment discussed above), a peripheral part of the ablation profile may have a small bump, which may be the result of a cut-off at the end of the transition zone. Ablating such a bump may require a sequence of many small laser pulses around the transition zone periphery. In some cases, this may cause a substantial reduction of speed in the entire ablation process. In some cases, the bump may not be needed because it lies away from the optical zone and its influence on the wavefront within the optical zone after smoothing may be very limited. Embodiments encompass the application of a damping multiplier to the periphery of the transition zone, starting from the distance R b = R TZ ~ 0.5mm foUows:

Equation 16

[00162] Such a damping multiplier or factor can be used to eliminate or diminish the bump.

[00163] FIG. 12C shows an X cross-section of modifications of an ablation profile, and FIG. 12D shows a Y cross-section of modifications of an ablation profile. In some embodiments, modifications of an ablation profile (e.g. high myopia study, case ID = 21011 OD) may include target deconvolution with σ = 0-35 mm, as well as an elevation modification, or a cut-off beyond the transition zone.

[00164] In some cases, a different wavefront diameter may use or benefit from a different diffusion coefficient (e.g. for an LPF model) to match post-operative measurements. In some cases, it is possible to use an approximated value of = 0.35 mm> which is between optimized values for 6 mm and 5.5 mm wavefront diameters, as discussed elsewhere herein. Using a diffusion coefficient such as this for the target deconvolution, it is possible to predict or calculate a substantial reduction of induced SA for both WFD = 6 mm and WFD = 5 mm and also additional ablation depth requirement. For example, FIG. 13A depicts a simulated post-operative SA for a 6 mm wavefront, FIG. 13B depicts a simulated postoperative SA for a 5.5 mm wavefront, and FIG. 13C depicts an extra ablation that may benefit a deconvolved target. As such, these figures demonstrate the effect of deconvolution on post-smoothing SA and on additional maximum ablation depth.

[00165] Because deconvolution may amplify noises, the tail or outer periphery of the ablation profile may have some bumps. To remove such bumps, a damping multiplier can be applied as

Equation 17

[00166] where T is the new target after damping, T is the target after Equation 14 and R is a variable in radius. RTZ is the transition zone radius, and the cutoff radius Rb = RTZ - 0.5 mm. This damping multiplier can effectively and substantially eliminate the bumps.

[00167] Results And Data Analysis

[00168] Based on certain codes for treatment target creation, the following two phases of simulation studies were conducted. A first phase involved optimizing a one-parameter diffusion coefficient such that it best explains the clinically observed 6M post-operative spherical aberrations with the same surgical parameters as these eyes were treated. A second phase involved verifying that with the use of an optimized diffusion coefficient, the expected post-operative spherical aberration is significantly reduced when a deconvolution algorithm is used.

[00169] Optimization of a diffusion coefficient was based on data from various clinical studies and trials, as well as data from commercial sites. Only eyes with pre-operative and 6M (3M for iDesign™ system) post-operative wavefront measurements with at least 6 mm diameter were used. As such, 340 eyes were from the study, 169 eyes from the commercial sites, and 39 eyes from iDesign™ system based study. Of the 340 eyes from US IDE, 158 were in the low to moderate myopia cohort, 75 in the high myopia cohort, 26 from hyperopia cohort, 47 from the monovision cohort (dominant eyes only), and 34 from the mixed astigmatism cohort.

[00170] As explained elsewhere herein, a comparison between a simulated and an observed post-operative spherical aberration can be performed for a given diffusion coefficient. An optimization process was chosen such that the simulated post-operative spherical aberration has a substantially identical slope as compared with a pre-operative spherical equivalent to that of the observed post-operative spherical aberration.

[00171] Because of variations of the sample size in different cohorts, the 95% confidence bands are different for different cohort. A small overlap area can be identified for these 95% confidence bands. The optimized diffusion coefficient of 0.35 mm was obtained from the overlap area.

[00172] According to some embodiments, deconvolution, which can be used to reduce post-operative spherical aberrations, is a physical-model-backed approach. It is based on the smoothing effect observed from the clinical data. Therefore, not only can it account for the increase of the post-operative spherical aberration, but it can also account for the induction of other high order aberrations, such as coma, secondary astigmatism, and secondary spherical aberration. Furthermore, as discussed elsewhere herein, it provides a smaller ablation depth as compared with other techniques (e.g. larger optical zone, larger keratometric values) used to target the same level of spherical aberration reduction.

[00173] Many of the target shape modification discussed herein can operate to change a peripheral area of the target so as to reduce the induction of SA. It is possible to compare such methods, for example when their parameters are selected to generate a small slope of SA vs. SE trend, as indicated in Table 2. The parameters in this table were selected for the simulation to achieve a slope of SA vs. SE trend that is about the same as the slope from the observed clinical data.

Table 2

[00174] Table 2 provides a comparison of three methods of target modifications, simulated for data from the studies. Parameters for each modification method were chosen to bring the magnitude of simulated slope of postoperative SA vs SE trend line down to 0.01. The simulated average post-op SA (<SA>), the worst case SA (max I SA | ), the average extra ablation depth (<extraH>), and the worst case (max extraH) are also shown. Sigma (o) is a diffusion coefficient related to the strength of an LPF process, described elsewhere herein. As shown in Table 2, a deconvolution method (sigma) can virtually eliminate both the mean SA and the SA vs. SE trend slope. Similarly, a widened optical zone method (dOZ) and a cosine correction adjustment method (dK) can also virtually eliminate both the mean SA and the SA vs. SE trend slope. Compared with widened optical zone and cosine adjustment methods, deconvolution techniques often require lower amounts of ablation, and hence can provide useful solutions where saving or maintaining more tissue is desired. [00175] FIG. 14A shows an X cross-section of modifications of an ablation profile, and FIG. 14B shows a Y cross-section of modifications of an ablation profile. These modifications of an ablation target are simulated for a high myopia study (study ID = 21011 OD, -7.4D/-1.5D x 179°). Simulation was performed for a wider optical zone approach (dOZ = 0.4mm), an adjusted cornea curvature for cosine correction approach (dK = 25D), and a deconvolution approach ( σ = 0-35 mm ) When evaluating the expected post-operative SA, it may be helpful to consider that simulations may only show the changing SA vs SE trend line after the target modification. In reality the post-operative SA may deviate from the trend line due to some other factors which are not accounted for. These deviations can be estimated for the current target as follows:

XCA — C/t ( 6M ) _ C/t (post-op)

GO/1— l observed >~>^ simulated

Equation 18

[00176] Assuming that the same deviations from the trend line can apply to a modified target, it is possible to add <¾>A to the simulated post-operative SA values of every modified target, which can provide a realistic estimate of post-operative distribution of SA. For example, FIGS. 15A and 15B, depict post-operative SA for observed study data (n = 340) and expected post-operative SA for de-convolved targets, simulated with cr = 0-35 mm f or the same eyes, for a 6 mm wavefront and 5.5 mm wavefront, respectively.

[00177] In addition to piston differences which may be present between the original and modified targets, there may be other shape differences as well. According to some embodiments, the following metrics can be used to compare shape differences:

Δ = (H - max( ff )) - {H cumnt - max( H cunent ) )

Equation 19

[00178] where H refers to ablation depth or target height.

[00179] As illustrated in FIGS. 16A and 16B, target shapes subsequent to smoothing for two modification methods, namely widening optical zone (dOZ) and deconvolution (sigma) are almost identical within the 6 mm optical zone. These figures show the differences (i.e. X and Y cross-sections, respectively) between a modified target and an original target, subsequent to smoothing, simulated for a high myopia case (ID = 21011 OD, -7.4D/-1.5D x 179°). Simulations were performed for a wider optical zone (dOZ = 0.4 mm), an adjusted corneal curvature for cosine correction (dK = 25 D), and a deconvolution ( σ = 0-35 mm )

[00180] A cosine adjustment can make a different shape with a substantially higher secondary spherical aberration, as depicted in FIG. 17. In some cases, software or systems may allow both a user-defined optical zone and a user-defined adjustment of corneal curvature (e.g. defining the cosine correction), and these two adjustments can be used for validation for a deconvolution technique. In some cases, a wider optical zone, may provide a closer approximation than a curvature adjustment. FIG. 17 shows a post-operating secondary spherical aberration (WFD =6 mm), simulated for study data (n=340). Simulation was performed for original targets and for modified targets with a wider optical zone (dOZ = 0.4 mm), an adjusted corneal curvature for cosine correction (dK = 25 D), and a deconvolution ( a = 0.35 mm ).

[00181] In sum, the three methods for modification of an ablation target (widening optical zone, adjusting cosine correction, and deconvolution) are capable of eliminating a systematic trend in post-operatively induced spherical aberration. As shown here, the ablation profiles for these modifications can present different depths, and deconvolution can provide a technique which results in a maximum of tissue retention. That is, the amount of ablation associated with deconvolution is smaller than that of the other methods. In some instances, widened optical zone and deconvolution techniques may yield almost identical corneal shapes after smoothing. In some cases, a widened optical zone technique (e.g. based on a user- defined optical zone) may be used as a validation for a deconvolution technique.

[00182] Treatment Target Creation [00183] As noted elsewhere herein, a treatment target shape may represent or correspond to an intended optical surface that is designed to achieve a particular refractive correction. FIG. 18 depicts a method 1800 for generating a target shape, according to embodiments. Method 1800 may include obtaining a wavefront corresponding to a pupil plane, as indicated by module 1805. For example, for target creation, the input can be a Fourier-based wavefront, which represents the ocular aberrations on the pupil plane. Typically, a laser ablation is performed on the corneal surface, and hence to obtain the target shape the ocular aberrations are propagated from the pupil plane to the corneal surface. Accordingly, methods may include propagating the wavefront, as indicated by step 1810, and obtaining a wavefront corresponding to a corneal plane, as indicated by step 1815. Any physician adjustments or nomogram adjustments can also be represented on the corneal surface first before they are combined with the ocular aberrations. Hence, the process of obtaining a wavefront at the corneal plane may also be based on an internal sphere adjustment, as indicated by step 1820, or on a physician adjustment (e.g. Sph + Cyl), as indicated by step 1825, or both.

[00184] In some instances, parameters such as optical zone size and the ablation zone size, which may be user-defined, can be used to determine the ablation or target shape within such zones. Thus, the process of obtaining a raw or original target shape, as indicated by step 1830, may be based on a selection or definition of an optical zone, an ablation zone, or both, as indicated by step 1835.

[00185] A deconvolution technique can be used to deconvolved the raw or original shape, so as to obtain a deconvolved shape, as indicated by step 1840. Such a deconvolution can operate to reduce post-operative spherical aberration. Once the deconvolved shape is obtained, a scaling factor can be applied, as indicated by step 1845, and a cosine effect modification that compensates for the loss of energy due to the curved cornea can be applied, as indicated by step 1850. Hence, the final target shape can be determined based on the deconvolved shape, as indicated by step 1855, optionally considering a scaling factor, a cosine effect, or both.

[00186] In some instances a nomogram adjustment can be applied, as indicated by step 1860, when obtaining the final target shape. Following creation of the final or modified target shape, as indicated by step 1855, the target shape can be transmitted to a treatment table generation engine.

[00187] Exemplary Techniques for Target Shape Deconvolution

[00188] As explained elsewhere herein, treatment target shapes can lead to induced aberrations, and deconvolution can be applied to such treatment target shapes so as to reduce or inhibit the induced aberrations.

[00189] FIG. 20 depicts aspects of a deconvolution method 2000 for a target shape, according to embodiments. As illustrated here, method 2000 of deconvolving a target shape may include obtaining a mesh size as indicated by step 2005 and obtaining a diffusion coefficient as indicated by step 2010. Method 2000 may also include obtaining a complex matrix, in Fourier domain, based on a mesh size and diffusion coefficient as indicated by step 2015.

[00190] Complex Matrix

[00191] According to some embodiments, a complex matrix K(kx, ky) can be applied to a treatment target to obtain a wavefront change due to corneal smoothing The complex matrix can be considered to represent a three dimensional matrix in a Fourier or frequency domain. In some cases, the complex matrix may be a squared Butterworth low-pass filter of the first order. Other types of low-pass filters may be suitable for use with embodiments. In some cases, a low-pass filter may refer to a function or operation that makes details smoother by suppressing high spatial frequency information.

[00192] In some instances, the Fourier domain complex matrix can be expressed as follows: Equation 20

[00193] where o represents a diffusion coefficient, kx and ky represent frequency domain variables, and dL represents a mesh size. Optionally, the diffusion coefficient o can have a value of 0.35 mm and the mesh size dL can have a value of 0.1 mm. In some instances, the diffusion coefficient can have a value with a range from about 0.2 to about 0.5 (see, e.g. FIG. 8A). In some instances, the diffusion coefficient can have a value with a range from about 0.33 to about 0.4 (see, e.g. FIG. 33).

[00194] In some instances, the term Fourier transform as used herein may refer to a transform operation. In some instances, the term Fourier transform as used herein may refer to a complex valued function produced by a transform process.

[00195] Mesh Size

[00196] In an exemplary discrete case, a complex matrix K (kx, ky) can be based on a 101 x 101 mesh size of dL = 0.1 mm. Often, such matrix formats (e.g. 101 x 101) are used when characterizing treatment planning. In some cases, a mesh size or dL may refer to the spacing or spatial distance between two neighboring pixels. In some cases, dL may refer to the pixel resolution in the kernel, which can be 101 x 101 in pixel frame size or 10 mm x 10 mm in space. When a discrete Fourier transform is involved, it is possible to represent the frame in 101 x 101, although it may no longer be 0.1 mm because it is in frequency domain (more like cycles per degree). Hence, dL may involve a 0.1 mm spacing in the spatial domain.

[00197] In some instances, selection of a kernel or matrix format may represent a balance between accuracy and speed concerns. For example, a larger kernel or matrix format such as 101 x 101 may provide greater relative accuracy and lower relative speed, whereas a smaller kernel or matrix format such as 25 x 25 may provide lower relative accuracy and greater relative speed.

[00198] Diffusion Coefficient [00199] As noted above, a complex matrix can also be based on a diffusion coefficient o. Typically, a diffusion coefficient o has a unit of length. This parameter can describe the strength of corneal smoothing during and after a refractive surgical procedure, and as such can be considered as a biologically related parameter. The parameter can be used to characterize a single individual, or a group of individuals. Based on the analysis of results from several clinical trials, it has been discovered that a diffusion coefficient o of 0.35 mm is consistent with such observed data. In some instances, a diffusion coefficient can have a value within a range from about 0.2 mm to about 0.5 mm. In some instances, a diffusion coefficient can have a value of about 0.3 mm.

[00200] Because a Fourier domain complex matrix can be based on the mesh size, the diffusion coefficient, or both, it follows that a corresponding spatial domain kernel filter, as discussed elsewhere herein can also be based on the mesh size, the diffusion coefficient, or both.

[00201] According to some embodiments, an LPF can be used to emulate the diffusion of corneal tissue cells. Exemplary techniques may involve estimating or receiving a diffusion coefficient value, and using that value to effect a compensation for a high order aberration before administering a treatment such as a laser vision corrective procedure. By pre-compensating for high order aberrations, it is possible to obtain an outcome with a reduced amount of high order aberrations.

[00202] Diffusion coefficients may be evaluated based on simulations. For example, a diffusion coefficient o value can be selected for application to clinical data in a deconvolution procedure as described herein, and the expected outcome (e.g. deconvolved target shape) can be compared to the actual outcome (e.g. clinical data). The diffusion coefficient can be adjusted or optimized so as to reduce or minimize variance or a standard deviation in the comparison results. Exemplary adjustment or optimization techniques are described elsewhere herein, for example in connection with FIGS. 25 to 28 A. [00203] Relatedly, embodiments encompass systems and methods for adjusting refractive surgery parameters, which may include a diffusion coefficient, for use in a vision treatement. An exemplary method may include inputting or receiving a refractive case, determining a model optical surface shape based on the refractive case and a set of refractive surgery system parameters, comparing the refractive case and the model optical surface shape to determine an aberration induced by the set of refractive surgery system parameters, adjusting the set of refractive surgery system parameters so as to inhibit the induced aberration, and administering the refractive treatment to a patient. The refractive treatment can be based on the adjusted set of refractive surgery system parameters.

[00204] Matrix Quotient

[00205] As depicted by step 2020, methods may include calculating a matrix quotient, where the dividend includes a conjugate of a Fourier domain complex matrix (e.g. K*(kx, ky), and the divisor includes the sum of a squared modulus of the Fourier domain complex matrix and a signal to noise ratio value. In some cases, the signal to noise ratio value may be a squared value. An exemplary matrix quotient can be expressed as follows:

Equation 21

[00206] In some cases, the denominator or divisor of the matrix quotient can be characterized at least in part by the expression | K(kx, ky) | n, where n is an integer having a value of 2 or more. In some cases, the denominator or divisor of the matrix quotient can be characterized at least in part by the expression [ | K(kx, ky) I n + SNR2] where n is an integer having a value of 2 or more and SNR represents a signal to noise ratio value. Equation 21 may refer to a filtering process that is in the frequency domain. A complex conjugate may be part of the filtering process.

[00207] Spatial Domain Kernel Filter [00208] As depicted by step 2025, methods may also include obtaining a kernel filter, in the spatial domain, based on an inverse Fourier transform of the matrix quotient. An exemplary kernel filter can be expressed as follows: Equation 22

[00209] In some cases, the kernel filter of Equation 22 can be provided as a pre-calculated or pre-defined matrix, and can be used or saved as a lookup table. As discussed elsewhere herein, this kernel filter can also be referred to as an inverse kernel KINV. Optionally, this kernel filter can be referred to as K (x, y). This spatial domain filter or inverse kernel can also be provided as a low pass filter, such as a Butterworth or Gaussian filter. Optionally, the spatial domain kernel filter can present a grid or matrix that reflects how the filtered value of a pixel depends on neighboring pixel values, and is independent of the target shape.

[00210] Convolving Raw Target

[00211] As depicted by step 2035, methods may include convolving a raw or original target shape with the spatial domain kernel filter. Optionally, methods may include receiving, at an input, an original target profile or shape for the eye of the patient, as indicated by step 2030. As shown here, the spatial domain kernel filter can be based on an inverse Fourier transform of a Fourier domain noise filter, for example, which may be based on a conjugate of a Fourier domain complex matrix, on a modulus of a Fourier domain complex matrix, or on a combination thereof. In some instances, a Fourier domain noise filter can be characterized by fraction having a numerator comprising a conjugate of a Fourier domain complex matrix and a denominator comprising a modulus of the Fourier domain complex matrix. Method 2000 indicates that an original target shape Tcurrent (x, y) can be convolved with a spatial domain kernel filter so as to obtain a deconvolved shape Tnew (x, y), as indicated by step 2040. In some instances, the deconvolved shape 2040 emphasizes curvature changes, or corners, sharp edges, sharp transitions, and the like. In some cases, methods may involve the application of a low pass filter deconvolution to a target profile having a slightly extended optical zone. In some instances, parameters of a low pass filter can be optimized by comparing an LPF model prediction against observed clinical data.

[00212] Other Refinements

[00213] As depicted by step 2045, methods may include additional refinements of a shape prior to transmitting the shape to a treatment table engine. For example, a convolved profile may include a transition zone radius, and exemplary techniques may include zeroing the convolved profile at locations outside of the transition zone radius. In some cases, an original target profile may have an original refractive spherical equivalent value within a 4 mm diameter area, and the convolved target profile may have a target refractive spherical equivalent value within a 4 mm diameter area, and method 2000 may include scaling the original refractive spherical equivalent with the target refractive spherical equivalent value. In some cases, methods may include elevating the convolved profile so that a lowest point on the convolved profile is zero or greater. In some cases, a convolved profile may include a transition zone radius, and methods may involve applying a damping multiplier at the transition zone radius RTZ or equal to or less than a distance determined by zero curvature within the transition zone from the transition zone radius RTZ. In some instances, refinement can be performed prior to, or subsequent to, deconvolution, with an equivalent effect.

[00214] As discussed elsewhere herein, a deconvolved target may have an oscillating profile at the periphery. Such oscillations may be caused by boundaries between the optical zone, transition zone, and edge of the finite-size target, where either the target profile or its derivatives have sharp changes. In some instances, it may be helpful to elevate the entire ablation profile so that the lowest point on the ablation profile is zero, or so that all ablation values are non-negative. What is more, it may be helpful to zero-out the ablation profile at distances greater than the transition zone radius, τ ζ , where no ablation is desired beyond the end of the transition zone. Such refinements are illustrated in the X and Y target cross- sections of FIG. 21 A, which depicts modifications of an ablation profile (high myopia study, case ID=21011 OD) including deconvolution ( cr = 0.28mm ) ; elevation, and cut-off beyond the transition zone. In some cases, after such refinements or adjustments are made, only the peripheral curvature will be changed, for example as depicted in FIG. 2 IB, which shows a change of ablation profile after target deconvolution (High Myopia study, case ID=21011, OD, -7.4D/- 1.5D x 179 deg).

[00215] In some instances, an original target shape may operate to effectively address refraction errors, and hence it may be desirable to maintain the refraction of the modified target at the same value as the refraction of the original target. This can be done with rescaling of the deconvolved target so that its defocusing term within the 4 mm area is the same as for the original target.

[00216] In addition to, or following some or all of the above mentioned adjustments, the peripheral part of the ablation profile may have a small bump, which results mainly from the cut-off at the end of the transition zone, for example as depicted in FIG. 21A. Ablating such a bump may involve application of a sequence of many small laser pulses around the transition zone periphery. In some instances, this may lead to a substantial slow-down of the entire ablation process. Yet this bump may be unnecessary, because it lies away from the optical zone and its influence on the wavefront within the optical zone shall be rather small after healing. With this consideration, it is possible to apply a damping multiplier to the periphery of the transition zone, as described elsewhere herein.

[00217] Spherical Aberration and Related Topics

[00218] As discussed elsewhere herein, spherical aberration (SA) may be induced by a target shape, a healing effect, or a combination thereof. In some cases, it is possible to reduce or even completely eliminate target-induced SA by implementing a small offset of the transition zone. In some original target shapes, the inner boundary of the transition zone is located within the optical zone, e.g. at about 0.25 mm from the edge of the optical zone. In addressing target-induced SA, it may be helpful to shift the transition zone boundary, by moving it farther from the center of the optical zone. In this way, the target-induced SA can be decreased, although squeeze the transition zone and cause sharper gradients in the peripheral target. In some instances, this may mean there will be a narrower transition zone band. In some instances, shifting the the inner boundary of the transition zone away from the center of the optical zone by a distance of about 0.1 mm can operate to reduce the target-induced SA to a level below 0.1 um, which may be considered negligible.

[00219] FIG. 22 shows a simulated induced SA immediately after ablation (target-induced) and after healing (total) for a target with an inner boundary of the transition zone shifted outward by 0.1 mm, using a healing model where σ = 0.28mm As shown here, after healing, the total SA reached a level of about 0.3 um.

[00220] In order to compensate for the spread of the high curvature, which is a main cause of post-healing induced SA, it is helpful to apply a deconvolution transformation to the original target. In some cases, the LPF core for deconvolution is the same as the one optimized to fit observed induced postoperative SA. Then healing, simulated as convolution with the same LPF core, can bring the healed cornea back to the desired shape.

[00221] FIG. 23 shows the effect of deconvolution on post-healing SA (left panel) and additional maximum ablation depth (right panel) simulated with <7 = 0.28mm f or studies (n=515). Relatedly, Table 3 shows simulated changes in post-healing SA and extra ablation, caused by deconvolution and additional adjustments of an original target. Statistics for studies: Myopia and High Myopia (n=327), Hyperopia (n=43), and all studies together (n=515). old SA(SE) new SA(SE) max <extra max

Slope Slope <SA> jSA| Afo{> extAb

Myopia & H -0.04 -0.01 0.01 0.08 4.3 8.9

Hyperopia •0.03 -0.02 •0.05 0.11 5 7.6

ASS US :D£ -0.04 •0.01 0.00 0.1 4.2 9.S

Table 3

[00222] FIG. 24 depicts a radial compensation function (RCF) for a deconvolved target in a high myopia case, according to embodiments. Specifically, a radial compensation function was calculated for a deconvolved target corresponding to a High Myopia study (case ID=21011 OD, -7.4D/-1.5D x 179 deg.). As shown here, the RCF is almost flat in the central part and decreases in the periphery.

[00223] FIG. 25 schematically illustrates techniques for obtaining and implementing a modified target shape, according to embodiments. As shown here, study data can be used to derive parameters of a kernel for simulating a low-pass filtering process, for corneal healing and the like. Embodiments may also include optimizing the parameters by using a clinical data set. These techniques may also involve evaluating the extent to which observed spherical aberration is attributed to error, due to an imperfect optical treatment shape. In some instances, methods may also include addressing target shape induced SA by providing transition zone adjustments, optical zone extension adjustments, or both. In some cases, a deconvolution (e.g. inverse of low pass filter) may boost the total treatment depth. Techniques may also involve running a revised target controller (e.g. without a cosine effect) with a low-pass filter, to evaluate the extent to which SA for a clinical data set correlates with observed SA, or to evaluate the extent to which postoperative refractions correlate with what is expected based on the clinical data. The Optimized Kernel Parameter can be related to LPF, and sigma can represent the diffusion coefficient. Hence, as shown in FIG. 25, with a clinical data set 2510, a kernel optimization process 2512 can be employed such that simulation can be performed to obtain the optimized kernel parameter (sigma) 2514. According to some embodiment, the value of sigma = 0.35 was found to correspond to an optimized kernel parameter. For a practical implementation, the clinical data 2510 can be sent to a research version of Target Controller 2518 (in matlab), which is identical to the production Target Controller 2526 (in C++). It can be derived from the Target Controller 2518 that induction of spherical aberration (SA) 2520 occurs in the target so a removal of a target-induced SA can be implemented in a revised Target Controller 2522. The revised Target Controller 2522 can implement a new optical zone (OZ) extension algorithm 2528, and a new Transition Zone algorithm 2530. With all the revisions, the Revised Target Controller 2522 can be tested with data set 2524, which can be the same as (or different from) data set 2510. The Revised Target Controller 2522 can then be verified with SA and MRSE (manifest refraction in spherical equivalent) in 2537.

[00224] Shape Induced SA

[00225] FIG. 26 shows a total induced SA (left panel, 0.188+0.139 for myopia and -0.110+0.179 for hyperopia) and a shape-induced SA (right panel, 0.064+0.049 for myopia and -0.071+0.038 for hyperopia) after taking into account a low-pass filtering effect, according to embodiments. When considering the mean, it is possible to observe that shape-induced SA consists of 1/3 of the total SA for myopia and more than ½ for hyperopia. When considering the trend line slope, it is possible to observe that shape-induced SA consists of more than ½ for myopia and less than ¼ for hyperopia. Therefore, a shape-induced SA can be a significant component for an observed post-surgery spherical aberration. For the data presented in FIG. 26, the healing effect for the shape-induced SA was included in the simulation.

[00226] Low Pass Filter

[00227] Assuming that a particular theoretical target shape provides a best fit for low order correction it is possible to perform an optimization as follows. First, an ablation target for an eye (e.g. an eye from a study) can be calculated according to a respective scaling factor and sphere adjustment. Second, a low pass filter (e.g. Butterworth or Gaussian) can be applied to obtain a healed shape. Third, a residual shape can be obtained by subtracting the healed shape from a preoperative CV (Custom Vue®) treatment shape. Fourth, a residual error in SA (e.g. predicted SA) can be calculated. Fifth, a merit function can be calculated. For example, the merit function may be the square root of the average sum of the square difference between the observed SA and the predicted SA. FIG. 27 shows aspects of optimization of a low pass filter, according to embodiments. FIGS. 28A and 28B show aspects of a kernel and an inverse kernel, according to embodiments.

[00228] Shape Deconvolution and Verification

[00229] According to some embodiments, it is possible to process a target shape as follows. First, a theoretical target is created, optionally using a zone-extended target algorithm. The target shape is then convolved with an inverse kernel. The convolved shape is them lifted to avoid negative ablation. A scaling factor can then be applied to preserved SE over a 4 mm zone. Subsequently, a cosine effect can be applied. FIG. 29 depicts aspects of a treatment target deconvolution according to embodiments.

[00230] According to some embodiments, it is possible to verify such target shape procedures as follows. First, obtain a theoretical target shape for an eye (e.g. each eye from a study set). Second, obtain a deconvolved target by convolving the target shape with an inverse kernel. Third, convolve the target with a determined kernel (e.g. healed target). Fourth, calculate the difference between the theoretical target and the simulated healed target (e.g. healed target subtracted from theoretical target). FIG. 30 depicts aspects of a target verification procedure according to embodiments. FIGS. 31A, 3 IB, and 31C depict residual error with deconvolution, according to embodiments.

[00231] FIGS. 32A and 32B depict expected targets (left column), inversed convolved targets (middle column), and the difference between expected and inversed convolved targets (right column), according to embodiments.

[00232] Optimization of Kernel [00233] FIG. 33 depicts CV data from a study (515 eyes, including myopia, hyperopia, high myopia, and mixed cases, as well as VSS-R™ treatment data from a Canadian study (77 eyes, including myopia [mostly], and a few hyperopia and mixed cases). FIG. 33 indicates that the optimized sigma for various data sets suggests a range between about 0.33 mm and about 0.40 mm.

[00234] Post-Operative SA (Expected vs. Actual)

[00235] FIG. 34 depicts actual vs. expected post-operative spherical aberrations.

[00236] Other Features

[00237] FIGS. 35A and 35B depict cylinder like cases (top row of FIG. 35A), mixed cases (bottom row of FIG. 35A), and hyperopia cases (FIG. 35B), according to embodiments.

[00238] Reducing Post-Operative Induction of Spherical Aberration

[00239] Conventional techniques for using an optimized linear filter (OLF) model to reduce post-operative induction of spherical aberration for myopic LASIK surgeries are discussed in Fabrikant et al., "Optimization Of Linear Filtering Model To Predict Post-LASIK Corneal Smoothing Based On Training Data Sets" Applied Mathematics 4, 1694-1701 (2013), the contents of which are incorporated herein by reference.

[00240] Embodiments described herein improve the predicted clinical outcome by utilizing an optimized linear filter for reducing the post-operative induction of spherical aberration (e.g. for LASIK surgeries). For example, embodiments include improving the predicted clinical outcome without a kernel having a wing which causes instability. Predictability of intended versus achieved refractions is increased by including both myopic and hyperopic data. In addition, various weighting factors are used for fine-tuning (e.g. weighting factors for myopia and/or hyperopia). Embodiments described herein include determining an effective SNR (signal to noise ratio) value in the decon volution. As described herein, the power spectrums for the improved OLF as well as the inverse kernel against those of previously known kernels are compared to demonstrate similarity in the spatial frequency domain.

[00241] Using a previously known kernel, the outcomes of a clinical study in Dai et al., "Outcomes For Clinical Studies To Reduce Post-Operative Induction Of Spherical Aberration For Myopic LASIK Surgeries," ARVO Abstract, 2016, the content of which is incorporated herein by reference, is analyzed. The previously known kernel resulted in sub-optimal reduction of spherical aberration in the clinical study. As described in the study, by using a new kernel (e.g. a bound kernel, with no wings), results include biological support which provide stable optimization, correspond to a natural limit on the kernel size, and provide a reduction in the amount of fluctuation in the power spectrum. Certain unbound kernels (without wings) do not provide such advantages. Embodiments include analytical solutions for the cut-off of bound kernels at a zero first-derivative for 2- parameter, 3-parameter and 4-parameter kernels. Embodiments attain an optimized kernel both in speed and precision and include a new kernel resulting in similar ablation depth to a currently known wavefront guided treatment (e.g. Custom Vue) for myopia and about 25% deeper for hyperopia.

[00242] FIG. 36 is a diagram illustrating aspects of an exemplary method 3600 for obtaining free parameter values (e.g. si, S2, S3, and s 4 ) for a kernel 3602, according to embodiments. According to some embodiments, the initial values for the parameters can be automatically generated, for example via an optimization algorithm rule. In some cases, an algorithm such as an iterative algorithm can be used to develop free parameter values of the kernel. The iterative optimization may be selected from the group consisting of Downhill Simplex method, Direction set method, and Simulated Annealing method, or the like. The kernel 3602 can be implemented or otherwise processed according to any of the kernel techniques discussed elsewhere herein.

[00243] An optimizer value o can be determined by the following Equation 23:

[00244] In this equation, g m corresponds to a weight for myopia (e.g. 3604 in FIG. 36) and gh corresponds to a weight for hyperopia (e.g. block 3606 in FIG. 36). Such weighting for myopia and/or hyperopia can help contribute to or improve the overall accuracy of optimizer. The weights wi, W2, W3, and w 4 (e.g. blocks 3612, 3614, 3616, and 3618 in FIG. 36) correspond to four regression plots, illustrated in FIGS. 37A, 37B, 37C, and 37D, respectively. The four regression plots in FIG. 36 are illustrated in FIG. 6 as Post SA vs Pre SE (block 3622), Post SA vs Pre SA (block 3624), Achieved SE vs Intended SE (block 3626), and Post 2SA vs Pre SE (block 3628), respectively.

[00245] As depicted in block 3630 of FIG. 36, exemplary techniques can involve determining the optimizer value (e.g. o) and/or assessing the value of the optimizer value. For example, block 3630 can involve determining whether the optimizer value is sufficiently small, or whether it exceeds a certain threshold. According to some embodiments, the threshold can correspond to the speed of optimization. Generally speaking, a smaller value for the threshold relates to a longer optimization time. Generally, a sufficiently small value for the optimizer value represents a desirable result. Hence, if the optimizer value is sufficiently small, then the process can terminate, for example as depicted by block 3650. At that stage, the kernel parameters can be used for further implementation, as discussed elsewhere herein. If, however, the optimizer value is not sufficiently small, then the process can involve adjusting the parameters, for example as depicted by block 3660. Adjustment of the parameter can involve, for example, adjusting the kernel parameters (si, S2, S3, and s 4 ) for kernel 3602. According to some embodiments, the parameters can be automatically adjusted, for example via an optimization algorithm rule. In some cases, an algorithm such as an iterative algorithm can be used to adjust free parameter values of the kernel. The iterative optimization may be selected from the group consisting of Downhill Simplex method, Direction set method, and Simulated Annealing method, or the like.

[00246] According to embodiments, the optimizer value (e.g. o) can be determined by a numerical process, and not an analytical process. This can be achieved by the use of numerical methods with actual data.

[00247] It is noted that the optimizer value o in block 3630 of FIG. 36 is not the same as the diffusion coefficient o in block 2010 of FIG. 20.

[00248] According to some embodiments, Intended vs. Achieved SE in general correlates with PostSE vs PreSE, although the values may be different. According to some embodiments, Intended vs Achieved means PreSE = Intended SE, and PreSE - PostSE = Achieved SE.

[00249] With returning reference to Equation 23, s corresponds to the standard deviation of a certain set of data (e.g. regression chart). Specifically, si stands for the standard deviation of postSA (first chart, post SA vs preSE), s2 stands for the standard deviation of postSA (second chart, postSA vs preSA; hence s2 can be equivalent to si), s3 stands for the standard deviation of postSE (third chart), and s4 stands for the standard deviation of post 2SA (fourth chart, post-op secondary spherical aberration). The equation also includes gd (e.g. 3642 in FIG. 36), which corresponds to the weight of a depth factor (e.g. 3640 in FIG. 36), wm (e.g. 3645 in FIG. 36) corresponds to a weight for myopia depth (e.g. 3644 in FIG. 36), and wh (e.g. 3647 in FIG. 36) corresponds to a weight for hyperopia depth (e.g. 3646 in FIG. 36). Average ablation depths for simulated and observed are represented as d and d 0 , respectively. Specifically, d m represents average simulated ablation depth for myopia, d m0 represents average observed ablation depth for myopia, d h represents average simulated ablation depth for hyperopia, and d h0 represents average observed ablation depth for hyperopia.

[00250] Table 4 provides exemplary values for certain variables of Equation 23. By implementing such fine-tuned values, it is possible to obtain a desirable optimized linear filter. Table 4

Symbol Function Value

Weighting for Post SA vs Pre SE slope 1 w 2 Weighting for Post SA vs Pre SA slope 0 w 3 Weighting for Achieved SE vs Intended SE slope 400 w 4 Weighting for Post 2SA vs Pre SE slope 0 gm Relative weighting for myopia for SA/2SA vs SE 0.5

slope

gh Relative weighting for hyperopia for SA/2SA vs SE 0.5

slope

gd Weighting for ablation depth factor 5 w m Relative weighting for myopia for depth factor 0.3 w h Relative weighting for hyperopia for depth factor 0.7

[00251] Applicant has discovered that certain weight values (e.g. wi, W2, W3, w 4 , Wm, Wh, and the like) f or Equation 23 can provide an optimal OLF. In this way, the regression plots represent a fitting of the model (e.g. optimized linear filter model) to the clinical data (e.g. element 3601 in FIG. 36). Hence, this relates to minimization of the difference between a model and the data.

[00252] Data for certain variables (e.g. a and a of Equation 23) can be fitted with regression as depicted in Equations 24 and 25, provided below:

Simulated y(x) = ax + β

Observed y( x ) = a + β [00253] The regression plots in FIGS. 37A, 37B, 37C, and 37D are based on Equations 24 and 25.

[00254] FIGS. 38A and 38B are an example of an optimized linear filter obtained using techniques as disclosed herein. The X axis is the spatial distance in mm, and the Y axis is the normalized intensity (no unit). FIG. 38A depicts aspects of certain requirements for a monotonic decreasing edge. As shown here, (a) represents a previously optimized kernel, (b) represents a bound kernel, and (c) represents an unbound kernel, where the unbound kernel has a wing. As discussed elsewhere herein, an unbounded kernel (e.g. line (c)) has no biological support, has an unstable optimization, has no natural limit on the kernel size, and presents a wing issue. In contrast, implementation of a bound kernel (e.g. line (b)) having no wings (for example due to a cut-off (d) as depicted in FIG. 38B) makes it possible to achieve results that have biological support, that provide stable optimization, that correspond to a natural limit on the kernel size, and that provide a reduction in the amount of fluctuation in the power spectrum. Power spectrum data is shown in FIGS. 43 and 44, for example. If a power spectrum fluctuates, it is not smooth, and has values that go up and down slightly.

[00255] With returning reference to FIG. 36, once a sufficiently small optimizer value is obtained (e.g. block 3650), it is then possible to use those specific parameter values (e.g. si, s2, s3, and s4 for kernel 3602) in Equation 26, provided below.

1

K(r; s lt s 2 , s 3 , s 4 ) — -g -g

1 + - i ί _

' 2 4 ' 6 8

Sl S 2 S 3 S 4

[00256] By calculating the first derivative of the kernel (c) and setting that value to zero, it is possible to determine the position of the cut-off value (d) depicted in FIG. 38B. Hence, the peripheral tails (e) can be removed and replaced or padded with zero values. As shown here, r represents the distance from the center. Hence, when r > d, it is possible to set K = 0. [00257] As noted elsewhere herein, Applicant has developed analytical solutions for the cut-off of bound kernels at zero first-derivative for 2-, 3-, and 4- parameter kernels. According to some embodiments, any of the parameter variations of the instant case (e.g. 2, 3, or 4 parameters) can be used with any of the multi-scale embodiments (e.g. dual scale, triple scale) described in US 9,498, 117, the contents of which are incorporated herein by reference.

[00258] Once an assumption or determination for the parameter values (e.g. si, s2, s3, and s4 for kernel 3602) have been obtained for a kernel (e.g. Equation 26), it is possible to use that kernel to convolve a treatment target (e.g. provided in numerical numbers) as described elsewhere herein. Further, it is possible to process clinical eye data (e.g. clinical data for a set of eyes) where each eye has a target. Thereafter, it is possible to calculate post-operative refractions, where preoperative refractions are known. After the spherical aberrations and refractions are obtained, it is possible to perform a regression, and based on the regression, obtain a fit as described in Equations 24 and 25.

[00259] Hence, for each of the following four cases provided below a regression graph can be obtained, as depicted in Table 5.

[00260] For example, for each case, it is possible to derive a regression graph equation such as Equation 24, reproduced below.

Simulated y(x) = αχ + β [00261] Also, it is possible to derive a regression graph equation such as Equation 25, reproduced below.

Observed y( x ) = a + β

[00262] Hence, it is possible to have one equation (e.g. Eq. 25) that is calculated and which is always the same for real data, and another equation (e.g. Eq. 24) that is for simulated data. According to some embodiments, the kernel is continuously changing. According to some embodiments, for each iteration, the kernel parameters are changed according to an optimization algorithm. At any given moment, for a kernel that is being used (e.g. Equation 26 with specific values for parameters si, s2, s3, and s4) for a number of eyes (e.g. 200 eyes), it is possible to generate a simulated regression plot having certain a and 6 values (e.g. Equation 24) and to compare those simulated a and 6 values to observed a and 6 values, where the comparision of a valuescan be represented as Δα, as shown in Equation 23.

[00263] According to some embodiments, Δα for the first case of Table 5 (post- op SA vs. pre-op MRSE) can be calculated as Δαΐ = al - a. A similar approach can be followed to obtain Δα2, Δα3, and Δα4.

[00264] FIG. 39 depicts various formulas for smoothing kernels that can be implemented in the techniques disclosed herein, according to embodiments.

[00265] Error may be introduced by a variety of sources, including for example, SE slopes, SA slopes, and/or depth factors. In some cases, error from various sources can be balanced. In some cases, errors for the fitting are being addressed, and the ablation depth is also being addressed, and it may be desirable to balance these concerns.

[00266] Various approaches can be used when determining a kernel, according to embodiments described herein. For example, in some instances it is possible to use separate SE slopes between myopia and hyperopia. In some instances it is possible to use combined myopia and hyperopia data for the SE slope optimization. In some cases, it is possible to use an increased weight (e.g. having a value within a range from 1 to 400) to account for SE slope optimization. In some cases, it is possible to use added ablation depth in the optimization.

[00267] If a kernel is not strong enough, then it may not be possible to achieve the expected or desired reduction of induced spherical aberration. According to some embodiments, the kernel can have a scaling factor of about 0.6541. In some cases, a bound kernel can have a scaling factor of about 0.6391.

[00268] As an example, and according to Equation 27 provided below, it is possible to provide a target, that when convolved with a smoothing kernel, yields a stabilized cornea with induced SA, but good SE.

T(x,y) ® K(r) = S(x,y)

[00269] According to Equations 28 and 29 below, it is possible to obtain an inverse kernel, and then a new target can be obtained such that when convolved with the kernel, it will yield a stabilized cornea with no SA and the same SE.

T'(x, y) = T(x,y) ® V(r)

T'(x,y) <g> K(r) = S'(x,y)

[00270] In some embodiments, the inverse of an optimized linear filter can be carried out by means of Wiener Filtering (in Frequency Domain) according to Equation 30 below.

K * (k)

V(k) ~ |K(k) | 2 + SNR 2

[00271] The inverse kernel in Spatial Domain can be obtained by a Fourier transform of V(k). The signal-to-noise ratio (SNR or S/N) can be determined based on the amount of noise provided by the kernel.

[00272] Certain known techniques use a value of 0.1 for SNR. Applicant has discovered that using a value of 0.01 for SNR can provide improved performance, based on a simulation using 287 eyes with convolution of K(r) and V(r).

[00273] FIG. 40 depicts aspects of an SNR determination, according to embodiments, using Equation 31 provided below.

W(x,y) <g) V(r) <g) K(r) = W'(x, y) [00274] In some embodiments, it may be desirable for W'(x,y) to have 4-mm refraction that is identical to that of W(x,y). As shown in FIG. 40, the correlation for the SE between the two can be plotted and the slope (a) and intercept (b) examined. With SNR = 0.01, the slope is 0.996 and intercept only 0.02 D.

[00275] FIGS. 41A, 41B, 41C, and 41D depict results obtained using an improved kernel, according to embodiments described herein. Specifically, FIG. 41A illustrates results for post-op SA vs. pre-op MRSE for observed, modeled with kernel, and simulated after deconvolution embodiments. FIG. 4 IB illustrates results for post-op SA vs. pre-op SA for observed, modeled with kernel, and simulated after deconvolution embodiments. FIG. 41C illustrates results for achieved vs. intended SE for observed, modeled with kernel, and simulated after deconvolution embodiments. FIG. 41D illustrates results for post-op 2SA secondary vs. pre-op MRSE for observed, modeled with kernel, and simulated after deconvolution embodiments.

[00276] Table 6 illustrates a comparison between a known 2 parameter kernel, a new 4 parameter kernel that was developed according to embodiments, and a previously known wavefront guided treatment (e.g. Custom Vue). Based on this comparison, it can be seen that the new 4 parameter kernel provides improved performance.

(4 mm Rx) Hyperopia -0.438 D -0.335 D -0.375 D

Total -0.129 D -0.424 D -0.437 D

Expected Myopia 8.9% 0.5% N/A

% Depth

Hyperopia 30.7% 25.5% N/A

Increase

Total 11.2% 3.2% N/A

[00278] FIG. 42 depicts a comparison of inverse kernel profiles for (a) a previously known kernel (b) and a new kernel according to embodiments.

[00279] FIG. 43 depicts a comparison of power spectrums for (a) a previously known kernel (b) and a new kernel according to embodiments.

[00280] FIG. 44 depicts a comparison of power spectrums of inverse kernels for

(a) a previously known kernel (b) and a new kernel according to embodiments.

[00281] FIG. 45 depicts a comparison of ablation profiles for -4 DS (myopia), including (a) a previously known wavefront guided treatment (e.g. Custom Vue), (b) a previously known kernel, and (c) a new kernel according to embodiments. As shown here, the depth results for the new kernel (c) are an improvement over the depth results of the previously known kernel (b).

[00282] FIG. 46 depicts a comparison of ablation depth changes for -4 DS (myopia) for (a) a previously known kernel (b) and a new kernel according to embodiments. As shown here, the ablation depth change results for the new kernel

(b) are an improvement over the ablation depth change results of the previously known kernel (a).

[00283] FIG. 47 depicts a comparison of ablation profiles for +3 DS (hyperopia), including (a) a previously known wavefront guided treatment (e.g. Custom Vue), (b) a previously known kernel, and (c) a new kernel according to embodiments. As shown here, the ablation depth results for the new kernel (c) are about the same as the ablation depth results of the previously known kernel (b). [00284] FIG. 48 depicts a comparison of ablation depth changes for +3 DS (hyperopia) for (a) a previously known kernel (b) and a new kernel according to embodiments. As shown here, the ablation depth change results for the new kernel (b) are about the same as the ablation depth change results of the previously known kernel (a).

[00285] Table 7 illustrates a comparison between a known kernel, and a new kernel that was developed according to embodiments.

[00286] Applicant has discovered that the known kernel may not be sufficiently strong, thus resulting in sub-optimal reduction of spherical aberration. Applicant has also discovered that, compared with unbound kernels, bound kernels are advantageous because they can have biological support, they can provide stable optimization, they can provide a natural limit on the kernel size, and they can provide a reduction in power spectrum fluctuation. Applicant has obtained solutions for limiting the cut-off for bound kernels in 2-, 3-, and 4-parameters. What is more, Applicant has developed a multi-level optimization approach. Further, Applicant has developed an approach that involves introducing a plurality of weighting functions and optimizing a 4-parameter bound kernel. Applicant has discovered that a newly developed kernel is about the same depth as a currently known wavefront guided treatment (e.g. Custom Vue) for myopia and about 25% deeper for hyperopia.

[00287] Any of the systems or methods disclosed herein can incorporate one or more of the features described in Appendix A of U.S. Provisional Patent Application No. 62/428,981, filed December 1, 2016, which is incorporated by reference as if fully set forth.

[00288] All patent filings, scientific journals, books, treatises, and other publications and materials discussed in this application are hereby incorporated by reference for all purposes. A variety of modifications are possible within the scope. A variety of parameters, variables, factors, and the like can be incorporated into the exemplary method steps or system modules. While the specific embodiments have been described in some detail, by way of example and for clarity of understanding, a variety of adaptations, changes, and modifications will be obvious to those of skill in the art. Although embodiments disclosed herein are described with specific reference to a wavefront system using lenslets, other suitable wavefront systems that measure angles of light passing through the eye may be employed. For example, systems using the principles of ray tracing aberrometry, tscherning aberrometry, and dynamic skiascopy may be used with embodiments disclosed herein. The above systems are available from TRACEY Technologies of Bellaire, Texas, Wavelight of Erlangen, Germany, and Nidek, Inc. of Fremont, California, respectively. Embodiments may also be practiced with a spatially resolved refractometer as described in U.S. Patent Nos. 6,099, 125; 6,000,800; and 5,258,791, the full disclosures of which are incorporated herein by reference. Treatments that may benefit from the embodiments include intraocular lenses, contact lenses, spectacles and other surgical methods in addition to refractive laser corneal surgery.

[00289] All features of the described systems and/or devices are applicable to the described methods mutatis mutandis, and vice versa. Each of the calculations discussed herein may be performed using a computer or other processor having hardware, software, and/or firmware. The methods or flow charts provided herein may be implemented in a computer program, software, or firmware incorporated in a non-transitory computer-readable storage medium for execution by a general purpose computer or a processor. Examples of non-transitory computer-readable storage mediums include a read only memory (ROM), a random access memory (RAM), a register, cache memory, semiconductor memory devices, magnetic media such as internal hard disks and removable disks, magneto-optical media, and optical media such as CD-ROM disks, and digital versatile disks (DVDs).

[00290] The methods and apparatuses may be provided in one or more kits for such use. The kits may comprise a system for profiling an optical surface, such as an optical surface of an eye, and instructions for use. Optionally, such kits may further include any of the other system components described in relation to the embodiments described herein and any other materials or items relevant to the embodiments. The instructions for use can set forth any of the methods as described above.

[00291] While the above provides a full and complete disclosure of exemplary embodiments, various modifications, alternate constructions and equivalents may be employed as desired. Consequently, although the embodiments have been described in some detail, by way of example and for clarity of understanding, a variety of modifications, changes, and adaptations will be obvious to those of skill in the art. Accordingly, the above description and illustrations should not be construed as limiting the embodiments, which can be defined by the claims.