INTRA-ORAL THREE-DIMENSIONAL IMAGING SYSTEM

RELATED APPLICATIONS

This application claims the benefit of the earlier filing date of U.S. Provisional Patent Application Serial No. 60/984,452, filed November 1, 2007, titled "High Accuracy Three- Dimensional Imaging of Polished and Translucent Material" and U.S. Provisional Patent Application Serial No. 60/984,467, filed November 1, 2007, titled "Fiber-Based Accordion Fringe Interferometry," the entireties of which are incorporated herein by reference.

FIELD OF THE INVENTION

The invention relates generally to the measurement of surface contours and more particularly to a non-contact apparatus using accordion fringe interferometry (AFI) for the three-dimensional measurement of intra-oral objects.

BACKGROUND OF THE INVENTION

The process for determining the shape of teeth according to traditional dentistry generally includes the use of impression materials, molds or castings. This process is typically slow and prone to material handling errors. After obtaining the impression of the patient's teeth, the mold or impression material is removed from the mouth of the patient and a solid model of the patient's teeth is made from the impression. The impression material or the solid model is sent to a dental laboratory. The solid model is used in the fabrication of one or more corrective or replacement dental components such as artificial teeth, crowns or orthodontic appliances. Inaccuracies and errors introduced at any time during the process can result in an improper fit of the dental component and may limit the ability to secure and retain the dental component in the correct location.

U.S. Patent No. 4,964,770 describes a process for making artificial teeth. The process includes projecting contour lines onto the patient's teeth and detecting the contour lines using a camera. The location of the projected contour lines is shifted multiple times by a precision motion of the projector and detected by the camera at each position. Camera data are processed to determine contour data for the teeth. The contour data may be provided to a numerically controlled fabrication machine for the generation of the artificial teeth or for

orthodontic appliances or for use with dental implantology. The process is subject to inaccuracies as displacement of the contour lines is based on changing the location of the projector. Moreover, the length of time required to obtain the camera data for all sets of contour lines is a significant inconvenience to the dental patient and makes the measurement more sensitive to motion of the projection source, teeth and camera.

Material characteristics of teeth can further limit the ability to obtain accurate three- dimensional data. Teeth are typically translucent therefore a portion of the light incident on the surface of a tooth is scattered from the surface while some of the light penetrates the surface and is internally scattered over a depth below the surface. Furthermore, backscatter can occur at the interface of tooth enamel and dentin if there is sufficient penetration of the incident light. Translucency can prevent an accurate determination of the surface contour of teeth using optical techniques. For example, projected contour lines may appear shifted from their actual location and may have poor contrast. In some instances, translucency causes measurements based on optical techniques to indicate an apparent surface that is beneath the true surface. To overcome difficulties due to translucency, dentists often apply powders such as titanium dioxide to teeth. The application of powder is a further inconvenience that adds more time to the measurement process, introduces measurement uncertainty and can interfere with adhesives or other bonding agents used to fasten the replacement tooth.

SUMMARY OF THE INVENTION In one aspect, the invention features a method for determining three-dimensional position information of a surface of a translucent object having a wavelength-dependent transmittance characteristic and a wavelength-dependent reflectance characteristic. The surface of the translucent object is illuminated with optical radiation having a predetermined wavelength emitted from a pair of optical sources. The optical radiation emitted from each optical source is coherent with respect to the optical radiation emitted from the other optical source. Optical radiation scattered by the surface and scattered from below the surface of the translucent object is detected. The predetermined wavelength is selected so that the optical radiation scattered from below the surface and detected provides a substantially constant background intensity relative to optical radiation that is scattered from the surface and detected. A phase of the optical radiation emitted from one of the optical sources is changed

relative to a phase of the optical radiation emitted from the other optical source as determined at a point on the surface of the translucent object. Optical radiation scattered by the surface and scattered from below the surface of the translucent object after the change of the phase is detected. Three-dimensional position information of the surface of the translucent object is calculated in response to the radiation detected before and after the change of the phase.

In another aspect, the invention features an intra-oral imaging device for determining three-dimensional position information of a surface of a translucent object. The device includes a pair of optical sources, a phase shifter, a detector array and a processor. Each optical source emits optical radiation at a predetermined wavelength and is coherent with respect to the optical radiation emitted by the other optical source. The phase shifter is coupled to one of the optical sources to change a phase of the optical radiation emitted from the optical source relative to a phase of the optical radiation emitted from the other optical source. The detector array receives optical radiation scattered from the surface and from below the surface of the translucent object. The predetermined wavelength of the optical sources is selected so that the optical radiation scattered from below the surface and received at the detector array yields a substantially constant background intensity relative to the optical radiation scattered from the surface and received at the detector array. The processor is in communication with the detector array and receives signals generated by the detector array. The processor calculates three-dimensional position information for the surface of the translucent object in response to the received optical radiation scattered from the surface before and after the change in the phase of the optical radiation emitted from one of the optical sources relative to the phase of optical radiation emitted from the other optical source.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and further advantages of this invention may be better understood by referring to the following description in conjunction with the accompanying drawings, in which like numerals indicate like structural elements and features in the various figures. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention.

FIG. 1 illustrates an embodiment of an imaging device for determining three- dimensional position information of a surface of an object according to the invention

FIG. 2 is a flowchart representation of an embodiment of a method for determining three-dimensional position information of a surface of an object according to the invention.

FIG. 3 is a vector illustration of radiation from the two single mode optical fibers of FIG. 1 as incident on the surface of a translucent object. FIG. 4A illustrates the illumination of a flat surface by a pair of optical fibers.

FIG. 4B illustrates the fringe pattern at the flat surface of FIG. 4A.

FIG. 4C illustrates the vertical intensity profile of a portion of the fringe pattern depicted in FIG. 4B.

FIG. 5A shows the displacement of an optical fiber to change the relative phase of the radiation emitted from the two optical fibers of FIG. 4A.

FIG. 5B illustrates a lateral shift of the fringe pattern of FIG. 4B due to a change in the relative phase of the radiation emitted from the two optical fibers according to FIG. 5 A.

FIG. 5C illustrates the vertical intensity profile for a portion of the fringe pattern depicted in FIG. 5B. FIG. 5D illustrates a fiber stretching technique for changing the relative phase of the radiation emitted from the two optical fibers of FIG. 4A.

FIG. 6 A shows a change in the separation of the fiber ends of the two optical fibers of FIG. 4 A used to modify the spatial frequency of a fringe pattern.

FIG. 6B illustrates the fringe pattern resulting from the configuration of optical fibers shown in FIG. 6A.

FIG. 6C illustrates vertical intensity profiles for a portion of the fringe patterns depicted in FIG. 4B and FIG. 6B.

FIG. 7 illustrates a structure for use in an embodiment of an intra-oral device according to the invention. FIG. 8 illustrates a configuration of two structures for use in an embodiment of an intra-oral device according to the invention.

DETAILED DESCRIPTION

In brief overview, the present invention relates to a device based on accordion fringe interferometry (AFI) principles that are useful for real-time three-dimensional imaging of objects. The device can be used in a wide variety of applications including, for example, intra-oral imaging for restorative dentistry and orthodontics, handheld three-dimensional scanners and probes for industrial applications such as measurement and inspection, and compact three-dimensional machine vision sensors. Compact and substantially insensitive to motion between the device and the objects to be measured, the device is advantageously adapted for scanning translucent objects and intra-oral surfaces such as the surfaces of teeth, gum tissue and various dental structures and materials.

The device can be fabricated from inexpensive components used in the high volume consumer electronics and telecommunications industries. In one embodiment, portions of the device are packaged as a small wand that is easily held and maneuvered by a dental professional. A remote electrical power supply and optical source enable a more compact wand. Although the device utilizes AFI measurement techniques as described in U.S. Patent No. 5,870,191 to Shirley et al, the device does not use a grating and lens to generate coherent point sources of radiation as in other AFI configurations. Instead, radiation is emitted from a pair of optical fibers and is used to illuminate objects to be measured with interferometric fringes. Consequently, movement of a macroscopic grating which requires several milliseconds or more to effect a phase shift is unnecessary. A fiber-based phase shifter is used to change the relative phase (i.e., the difference in phase) of the radiation emitted from the exit ends of the two optical fibers in a few microseconds or less. Optical radiation scattered from surfaces and subsurface regions of illuminated objects is received by a detector array. Electrical signals are generated by the detector array in response to the received radiation. A processor receives the electrical signals and calculates three- dimensional position information of object surfaces based on changes in the relative phase of the emitted optical radiation and the received optical radiation scattered by the surfaces. The device preferably utilizes a source of optical radiation having a wavelength between about 350 nm and 500 nm to reduce measurement error associated with penetration of the incident radiation into the subsurface regions of translucent objects.

FIG. 1 illustrates an embodiment of an imaging device for determining three- dimensional position information of a surface of an object 10 according to the invention. FIG. 2 is a flowchart representation of an embodiment of a method 100 for determining three- dimensional position information of a surface of an object (e.g., object 10) according to the invention. In the illustrated embodiment, the object 10 is a translucent object such as an intra-oral object (i.e., an object located in the mouth of a patent). For example, the object 10 may be a natural or artificial tooth. Optical radiation is launched into a pair of single mode optical fibers 14A and 14B from a master optical source (not shown). In one embodiment, the optical fibers 14 are coupled by a fiber splitter so that optical radiation is launched into an input end of a single optical fiber. The object 10 is illuminated (step 110) with the diverging radiation emitted from the exit ends of the fibers 14. In one embodiment, the radiation emitted from the two fibers 14 is polarized in a common orientation.

Some of the radiation incident on the translucent object 140 is scattered from the surface while some of the radiation penetrates into a subsurface region (i.e., a volume below the surface) where it is scattered. An image of the surface of the object 10 is formed by an imaging element or lens 18 on an array of photodetectors 22 such as a two-dimensional charge coupled device (CCD) imaging array. The detector array 22 provides an output signal to a processor 26. The output signal includes information on the intensity of the radiation received (steps 120 and 140) at each photodetector in the array 22. An optional polarizer 30 is oriented to coincide with the main polarization component of the scattered radiation. A control module 34 controls the operation of the radiation emitted from the optical fibers 14. The control module 34 includes a phase shifter 36 that adjusts (step 130) the relative phase of the radiation emitted by the two fibers 14 as determined at the surface of the object 10. The control module 34 also includes a spatial frequency controller 38 that adjust the pitch of interference fringes 32 in the illumination pattern at the object surface. The fringes 32 are the result of interference of the coherent radiation emitted from the optical fibers 14. The spatial frequency of the fringe pattern, i.e., the inverse of the separation of the fringes 32, is determined by the separation D of the ends of the optical fibers 14, the distance from the ends of the fibers to the object, and the wavelength of the radiation. The processor 26 and control module 34 communicate to coordinate the processing of signals from the photodetector array 22 with respect to changes to the spatial frequency and the relative phase, and the processor

26 determines (step 150) the three-dimensional information for the surface according to the detected radiation. In a preferred embodiment, the processor 26 includes multiple central processing units ("CPUs") for parallel processing to increase the data processing rate and to output the final measurement data in less time. FIG. 3 is a vector illustration of the radiation 40 from the two single mode optical fibers as incident on the surface 42 of the translucent object 10. A portion of the incident radiation 40 is scattered from the surface 42 while a portion of the incident radiation 40 penetrates and is scattered from within the object 10 below the surface 42. The wavelength of the incident radiation, and the wavelength-dependent reflectance characteristic and wavelength-dependent transmittance characteristic of the object material, determine the relative contributions to the radiation scattered from the object surface 42 and the radiation scattered within the subsurface region.

Referring also to FIG. 1, the photodetector array 22 receives an image of the fringe pattern projected onto the surface 42 of the object 10; however, the radiation scattered in the subsurface region degrades the image of the fringe pattern. If the scattered radiation contribution from the subsurface region is significant relative to the scattered radiation contribution from the surface 42, the apparent location (i.e., apparent phase) of the fringe pattern on the surface 42 can be different than the actual location. The method of the invention exploits a counter-intuitive approach to reducing measurement errors due to translucent internal scatter by utilizing an illumination wavelength which increases internal scatter near the surface. The illumination wavelength exhibiting a high coefficient of internal scattering is combined with a high spatial frequency fringe pattern such that a nearly uniform photon flux is created just below the surface. The subsurface scatter contributes a substantially constant background to the image of the surface 42 at the photodetector array 22. The background contribution is ignored by the phase analysis, and the magnitude of the residual error induced by any remaining spatially- varying intensity contribution is further reduced in significance if the contribution is close to the surface 42. Measurements performed according to the method of the invention provide greater accuracy when using radiation having a wavelength predetermined from the wavelength-dependent reflectance

characteristic and wavelength-dependent transmittance characteristic of the object material to improve the surface scattering contribution relative to the subsurface scattering contribution.

For three-dimensional imaging of living, natural teeth, wavelengths in the lower visible and near ultraviolet (UV) range (e.g., 350 to 500 nm) provide a higher coefficient of subsurface scattering than longer wavelengths due to the wavelength-dependent characteristics of enamel and dentin. In one embodiment of an intra-oral imaging device, the radiation source is a commercially-available blue laser diode having an operating wavelength of 405 nm (e.g., model no. BCL-050-405 available from Crystal Laser of Reno, Nevada).

In another embodiment of an intra-oral imaging device, the spatial frequency of the fringe pattern at the surface 42 is predetermined so that subsurface scattering of radiation that penetrates the object 10 from one fringe overlaps the subsurface scatter from the two neighboring fringes, and thus diffuses the fringes 32 that propagate below the surface. As a result, the scattered subsurface radiation provides a substantially constant background to the detected fringe pattern. In a preferred embodiment, the spatial frequency of the fringe pattern is at least 1 fringe/mm.

FIG. 4A illustrates how radiation emitted from a pair of single mode optical fibers 14 illuminates a flat surface 46 resulting in the fringe pattern shown in FIG. 4B where a dark horizontal line indicates the greatest intensity for each fringe. The fringes have a sinusoidal intensity profile as shown in FIG. 4C for a vertical slice through the boxed region 50 of FIG. 4B. To rapidly change the relative phase of the radiation emitted from the two fibers 14, the phase shifter 36 includes a translation module to move the end of one of the fibers 14B along the fiber axis (i.e., z-axis) to displace the end of the fiber 14B from its original position by a distance δ as shown in FIG. 5 A. Thus if the fiber end is moved through a distance that is one-third of the wavelength λ (i.e., δ =— ) of the radiation, the relative phase shift is 120°.

FIGS. 5B and 5C illustrate the shift in the fringe pattern that results from a 120° phase shift. In one embodiment, the mechanism used to translate the fiber end is a translation stage that can accurately position the end of the fiber 14B along the z-axis in either direction.

FIG. 5D illustrates a different technique for obtaining a relative phase shift. In this technique, the phase shifter 36 includes a fiber stretch mechanism to stretch one of the optical

fibers 14B along a length L while its end remains fixed in location. The stretching alters the physical properties of the fiber 14B such as its length, index of refraction, and birefringence. As a result, the effective optical path length of the fiber 14B is changed and the phase of the radiation emitted from the fiber 14B is changed relative to the phase of the radiation emitted from the other fiber 14 A. This change in the relative phase results in a lateral shift of the fringe pattern as shown, for example, in FIG. 5B and FIG. 5C. In an alternative embodiment, the phase shifter 36 includes a fiber compression mechanism to compress or "pinch" one of the optical fibers 14 along a radial fiber axis (i.e., an axis in the x-y plane).

For a constant wavelength, the spatial frequency of the fringe pattern is adjusted by controlling the separation D of the fiber ends. FIG. 6A shows how the separation D of the fiber ends is decreased relative to the fibers 14 of FIG. 4A. As a result, the fringe pattern and the fringes within the fringe pattern are broadened as shown in FIG. 6B and FIG. 6C. In one embodiment, the spatial frequency controller 38 (FIG. 1) includes a translation module to translate the end of at least one of the optical fibers 14 along a transverse axis defined between the fiber ends (i.e., the illustrated x-axis) in either direction. The separation distance D is decreased to reduce the spatial frequency or increased to increase the spatial frequency. Preferably, both fiber ends are translated equal distances in opposite directions so that the position of the midpoint between the fiber ends is unchanged and the fringe pattern is not laterally shifted. FIG. 7 illustrates a structure 62 having axial and lateral flexures for use in an embodiment of an intra-oral device according to the invention. Two single mode optical fibers 14 are fixed by clamps 66 to a substrate 70. The substrate 70 can be fabricated from aluminum or another material depending on the tolerance to temperature variations and fabrication capabilities. Two piezoelectric actuators 74A and 74B are secured to the substrate 70. The actuators 74 provide a means to change the separation distance between the exit ends of the optical fibers 14 and to change the axial position of the exit end of one fiber 14B. Initially, a control signal is applied to each actuator 74 to adjust its position approximately to a midrange position within an operating range (e.g., + 1 μm range). Optical fiber 14A is then clamped to the lateral flexure portion of the substrate 70. Next, optical fiber 14B is positioned and adjusted along its fiber axis to maximize the contrast of the fringe pattern, and

then clamped to the axial flexure portion of the substrate 70. During measurements, the axial piezoelectric actuator 74A adjusts the axial position of the end of the optical fiber 14B over a portion of the actuator range to cause a shift in the relative phase by the desired amount (e.g., +120° and -120°). The lateral piezoelectric actuator 74B adjusts the separation of the ends of the two fibers 14 within a range of + 1 μm to cause a change in the spatial frequency of the fringe pattern by a desired value.

FIG. 8 illustrates a device configuration employing two structures 78 and 82 for use in an embodiment of an intra-oral device according to the invention. The two single mode optical fibers 14 are fixed by clamps 66 to structures 78 and 82. One piezoelectric actuator 74B is integrated into one structure 82 to enable a controlled change in the separation distance between the ends of the optical fibers 14. The other piezoelectric actuator 74 A is used to stretch an optical fiber 14A (as described for FIG. 4D) and thereby change the relative phase between the radiation emitted from the ends of the two fibers 14. During initial configuration setup, control signals position the actuators 74 near the midpoints of their respective ranges of motion. Optical fiber 14B is then clamped to the structure 78 near the center of the lateral flexure portion and near the exit end. Optical fiber 14A is then clamped to the structure 78 near the center of the lateral flexure and near the entrance end. The axial piezoelectric actuator 74A is used to stretch one optical fiber 14A on expansion and to stretch the other optical fiber 14B on contraction. Stretching of the optical fibers 14 in this manner causes a shift in the relative phase of the radiation emitted from the ends of the fibers 14 by the desired amount (e.g., +120° and -120°). As the fiber clamps 66 are in contact with the sheathing of each fiber 14, the linear motion of the actuator 74A generally is substantially greater than the actual increase in length of the stretched optical fiber 14. Furthermore, the optical path length of the optical radiation is dependent on the length and the index of refraction of each optical fiber 14. Consequently, the desired relative phase shift is preferably determined by calibrating an initial position for each phase, and then by dynamically tracking fringe motion and applying a compensation offset.

In an alternative embodiment, a second separation of the optical fibers 14 is effectively accomplished by selectively enabling a third optical fiber (not shown) spaced the proper distance from the first fiber 14B. Thus the translation mechanism can be eliminated.

After completing attachment to the first structure 78, the optical fibers 14 are attached to the second structure 82 that includes a lateral piezoelectric actuator 74B for achieving a desired separation of the fiber ends. In one embodiment, the first and second structures 78 and 82 are separated by at least 50 mm to provide sufficient slack in the two optical fibers 14 so that motion of one actuator 74 does not affect the control of the fibers 14 by the other actuator 74.

Environmental instability can limit the ability to perform accurate measurements using AFI principles. In particular, measurement accuracy is degraded according to the error between the commanded phase shift and the actual phase shift applied to the fringe pattern. The phase shifting techniques described above impart a small optical path length difference of a few hundred nanometers or less between the two radiation beams. Consequently, temperature drift and mechanical creep can be sources of error in the relative phase. Capacitance gauges can be used to monitor axial shifts in optical fiber position and stretching or compression actuation for the phase shifting techniques described above; however, in some embodiments such electro-mechanical monitoring may not accurately correspond to changes imparted to the relative phase.

In a preferred embodiment, a control system based on fringe monitoring is used to establish the desired relative phase and to maintain fringe stability. Referring again to FIG. 1, a portion of the fringe pattern is "sampled" by an optical element 54 and received by a fringe position sensor 58 that determines the location of a fringe within a small region of the fringe pattern. In one embodiment, the fringe position sensor 58 is a detector array. In other embodiments the fringe position sensor includes a configuration of one or more detectors that can sense a change in the position of a fringe. In another embodiment, the fringe pattern detector may be a section of the detector array 22. The fringe position detector array 58 can have a low pixel count as only one fringe in the fringe pattern is monitored. The optical element 54 can be a mirror having a dimension that is approximately equal to the width of a fringe at the mirror. The reflected radiation is directed to the detector array 58 which provides image data to the processor 26. The image data are processed to monitor the location of the sampled fringe in the field of view of the detector array 58. If the processor 26 determines that the fringe is "drifting" and therefore that there is a displacement error in

the fringe pattern, the phase shifter 36 adjusts the relative phase to counteract the drift. Thus the displacement error is substantially cancelled and the fringe pattern remains stable.

While the invention has been shown and described with reference to specific embodiments, it should be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention.

What is claimed is: