RELATED APPLICATION

This application claims the benefit of priority from U.S. Patent Application No. 61/410,006, filed November 4, 2010, the contents of which are hereby incorporated by reference as if fully set forth herein.

FIELD AND BACKGROUND OF THE INVENTION

The present invention, in some embodiments thereof, relates to optics and, more particularly, but not exclusively, to a method and device for characterizing an optical system.

Lenses in an optical system, e.g., a projector or a camera, may have diverse properties such as image resolution, flare and chromatic aberration on account of variation in production process thereof. Since the diversity of the properties of the lenses exert influence on the performances of the system, it is oftentimes desired to evaluate the properties of image resolution, flare and chromatic aberration before the optical system is assembled.

A known technique for testing a lens employs a flat template which is placed at the plane of focus and photographed, viewed on a video screen, or otherwise used in conjunction with any optical viewing system. The light received from the test template constitutes an image which is then processed by a computer to evaluate the resolution of the lens. A Modulation Transfer Function (MTF) value is typically generally used as a resolution evaluation value for evaluating the resolution of the lens. The MTF describes the way that the lens transfers contrast as a function of the spatial frequency, and is typically defined as the ratio between the modulation of the image and the modulation of the object at the respective frequency.

Known templates for testing resolution commonly comprise sharply printed characters, lines or patterns in white printed on black or vice versa. One such pattern is the U.S. Air Force (USAF) 1951 pattern which is a collection of small patches, each being a set of equally spaced bars and spaces of Ronchi Rulings (an agreement of equally spaced bars and spaces) of increasing density. The patches come in groups of two, at orthogonal orientations to each other, for simultaneous testing the radial and sagittal response of imaging systems in terms of spatial frequency response and the corresponding contrast. Calculation of MTF using such bar targets can be found in D. N. Grimes, "Imaging of Tri-Bar Targets and the Theoretical Resolution Limit in Partially Coherent Illumination", JOSA 61, No. 7, 870-876 (1971); Jaiswal et al. "Resolution for a general two-bar target", App. Opt. 15 , No. 8, 1911-1912 (1976); Sitter et al., "Method for the measurement of the modulation transfer function of sampled imaging systems from bar-target patterns, App. Opt. 34, No. 4, 746-751 (1995); and Boreman et al., "Modulation Transfer Function Measurement Using Three- and Four-bar Targets", App. Opt. 34 , No. 11, 8050-8052 (1995).

Also known is a template which includes a random black and white pattern of a flat power spectrum [Backman et al., "Random target method for fast MTF inspection", Opt. Exp. 12, No. 12, 2610-2615 (2004)]. The measuring process includes acquisition of two images, one without and one with the random target. The images are processed and the MTF is calculated.

SUMMARY OF THE INVENTION

According to some embodiments of the invention the present invention there is provided a method of characterizing an optical system. The method comprises: using the optical system to acquire an image from a template having at least one alternating brightness pattern along a pair of orthogonal directions over at least a portion of the template, wherein for' each direction of the pair a period characterizing the alternating brightness pattern along the direction is positive and being either constant or monotonic in a non-random manner; and analyzing the image thereby characterizing the optical system.

According to some embodiments of the invention the alternating pattern(s) comprises a plurality of alternating patterns being distinguishable from one another.

According to some embodiments of the invention for each of the two orthogonal directions a period characterizing the alternating brightness pattern is constant over a respective pattern.

According to some embodiments of the invention the analysis comprises calculating a modulation transfer function. According to some embodiments of the invention the analysis comprises calculating a phase transfer function.

According to some embodiments of the invention the analysis comprises calculating an optical transfer function.

According to an aspect of some embodiments of the present invention there is provided a device for characterizing an optical system. The device comprises a device body having a surface being patterned with at least one alternating brightness pattern along a pair of orthogonal directions over at least a portion of the template, wherein for each direction of the pair a period characterizing the alternating brightness pattern along the direction is positive and being either constant or monotonic in a non-random manner.

According to an aspect of some embodiments of the present invention there is provided a computer-readable medium having stored thereon a computer program for characterizing an optical system. The computer program, when executed by a data processing system, causes the data processing system to receive an image of a template having at least one alternating brightness pattern along a pair of orthogonal directions over at least a portion of the template, wherein for each direction of the pair a period characterizing the alternating brightness pattern along the direction is positive and being either constant or monotonic in a non-random manner.

According to some embodiments of the invention the at least one alternating pattern is a chessboard pattern.

According to some embodiments of the invention the alternating pattern(s) comprises a plurality of alternating patterns being distinguishable from one another.

According to some embodiments of the invention the alternating patterns are arranged parallel to a Cartesian system of coordinates.

According to some embodiments of the invention for each of the two orthogonal directions a period characterizing the alternating brightness pattern is constant over a respective pattern.

According to some embodiments of the invention the two orthogonal directions are parallel to a radial direction and an azimuthal direction of a polar system of coordinates.

According to some embodiments of the invention a period characterizing the alternating brightness pattern gradually vary along the radial direction. According to some embodiments of the invention a period characterizing the alternating brightness pattern is constant along the azimuthal direction.

Unless otherwise defined, all technical and/or scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the invention pertains. Although methods and materials similar or equivalent to those described herein can be used in the practice or testing of embodiments of the invention, exemplary methods and/or materials are described below. In case of conflict, the patent specification, including definitions, will control. In addition, the materials, methods, and examples are illustrative only and are not intended to be necessarily limiting.

Implementation of the method and/or system of embodiments of the invention can involve performing or completing selected tasks manually, automatically, Or a combination thereof. Moreover, according to actual instrumentation and equipment of embodiments of the method and/or system of the invention, several selected tasks could be implemented by hardware, by software or by firmware or by a combination thereof using an operating system.

For example, hardware for performing selected tasks according to embodiments of the invention could be implemented as a chip or a circuit. As software, selected tasks according to embodiments of the invention could be implemented as a plurality of software instructions being executed by a computer using any suitable operating system. In an exemplary embodiment of the invention, one or more tasks according to exemplary embodiments of method and/or system as described herein are performed by a data processor, such as a computing platform for executing a plurality of instructions. Optionally, the data processor includes a volatile memory for storing instructions and/or data and/or a non-volatile storage, for example, a magnetic hard-disk and/or removable media, for storing instructions and/or data. Optionally, a network connection is provided as well. A display and/or a user input device such as a keyboard or mouse are optionally provided as well.

BRIEF DESCRIPTION OF THE DRAWINGS

Some embodiments of the invention are herein described, by way of example only, with reference to the accompanying drawings. With specific reference now to the drawings in detail, it is stressed that the particulars shown are by way of example and for purposes of illustrative discussion of embodiments of the invention. In this regard, the description taken with the drawings makes apparent to those skilled in the art how embodiments of the invention may be practiced.

In the drawings:

FIGs. 1 A-B are schematic illustrations of an imaging system with a narrow slit pupil (FIG. 1A), and a corresponding MTF (FIG. IB);

FIGs. 2A-B are schematic illustrations of an imaging system with a circular slit pupil (FIG. 2A), and a corresponding MTF (FIG. 2B);

FIGs. 3A and 3B are schematic illustrations of a spoke target for characterizing an imaging system, where the image of a spoke target is shown in an in-focus (FIG. 3A) an out-of-focus (FIG. 3B) conditions;

FIGs. 4A and 4B depict a one-dimensional MTF of the spoke target corresponding to a slit pupil (FIG. 4A) and circular pupil (FIG. 4B), for an out-of-focus condition.

FIG. 5 is a schematic illustration a two-dimension barcode;

FIG. 6 are schematic illustrations of a template suitable for characterizing an optical system in embodiments of the present invention in which the characteristic pattern of the template is described by means of a Cartesian coordinate system;

FIG. 7 are schematic illustrations of a template suitable for characterizing an optical system in embodiments of the present invention in which the characteristic pattern of the template is described by means of a polar coordinate system;

FIGs. 8A-F are schematic illustration of relations between the period of the template and the coordinate describing the template, according to some embodiments of the present invention;

FIG. 9 is a schematic illustration of a monotonic period along a radial direction, according to some embodiments of the present invention;

FIG. 10 is a flowchart diagram of a method suitable for characterizing an optical system according to various exemplary embodiments of the present invention;

FIG. 11 is a schematic illustration of a side view of a setup suitable for executing a method for characterizing an optical system, according to some embodiments of the present invention; FIGs. 12A and 12B show a US AF 1951 template (FIG. 12A) and template according to some embodiments of the present invention (FIG. 12B);

FIGs. 13A-B show a spoke target with 50 spokes (FIG. 13A), and corresponding computer simulation results (FIG. 13A);

FIGs. 14A-B show polar chessboard template in accordance with some embodiments of the present invention (FIG. 14A), and corresponding computer simulation results (FIG. 14A);

FIGs. 15A-F show various templates used in computer simulations performed according to some embodiments of the present invention;

FIGs. 16A-F show computer simulations results for a spoke target (FIGs. 16A,

16C and 16E), and a polar chessboard template according to some embodiments of the present invention (FIGs. 16B, 16D and 16F);

FIGs. 17A-B show a spoke target (FIG. 17A) and a template according to some embodiments of the present invention (FIG. 17B) which were used in experiments performed by the present inventors;

FIGs. 18A-C show signal traces in an in-focus condition along 3 circles drawn in FIGs. 17A and 17B;

FIG. 19 shows MTF of an optical system in an in-focus condition;

FIGs. 20A and 20B are similar to FIGs. 17A and 17B, but for out-of-focus condition;

FIGs. 21A-C show signal traces in an in-focus condition along 3 circles drawn in FIGs. 20A and 20B; and

FIG. 22 shows an optical transfer function of an optical system in an out-of-focus condition.

DESCRIPTION OF SPECIFIC EMBODIMENTS OF THE INVENTION

The present invention, in some embodiments thereof, relates to optics and, more particularly, but not exclusively, to a method and device for characterizing an optical system.

For purposes of better understanding some embodiments of the present invention, as illustrated in FIGs. 6-12 and 14-22 of the drawings, reference is first made to the principles of one-dimensional lens testing, as illustrated in FIGs. 1-5. FIG. 1A shows an imaging system 20 under test. System 20 receives light of and typically converts it into an electrical signal.

As used herein, light means radiant energy having wavelengths within the electromagnetic spectrum. Thus, light includes, but is not limited to, infrared radiation, visible light, ultraviolet radiation and X-rays.

The MTF of system 20 is measured by obtaining the response of system 20 in one dimension, removing shading and offset from the signal, and calculating the magnitude (modulus) of the Fourier Transform from the filtered signal. The response of system 20 is obtained by simulating an optical impulse function input signal, which, in the case of FIG. 1A, is a slit pupil or aperture 12, to the sensor of system 20 and sampling the generated signal.

Slit pupil 12 is formed in a slit mask 18 and is illuminated by light from a light source 10. In FIG. 1A, source 10 provides back illumination. Such slit pupils are known to those skilled in the art of optical systems.

Slit 12 is focused onto system 20 by collimating lens 14. The collimation is achieved by placing target mask 18 at the focal plane of lens 14. Collimating lenses are also well known to those skilled in the art.

A typical calculated MTF as a function of a normalized spatial frequency is illustrated in FIG. IB. As shown, the MTF is generally linear as a function of the spatial frequency, with a negative slope.

FIG. 2A is similar to FIG. 1A except that system 20 is tested using a circular pupil 16 rather than a narrow slit pupil. The corresponding MTF is depicted in FIG. 2B. As shown, the MTF for a circular pupil has a deviation from linearity, particularly for higher spatial frequencies. For normalized frequencies below 0.5-0.6, the absolute value of the slope is higher than the respective value as calculated for the slit pupil, whereas for normalized frequencies above 0.7, the absolute value of the slope is lower than the respective value as calculated for the slit pupil.

It is noted that even though the MTF in FIG. 2B has been evaluated for a circular pupil, it is still, essentially, a one-dimensional MTF, albeit with circular symmetry. As such, it should be coined "ID MTF". Such MTF is referred to herein as "one- dimensional circular MTF". FIGs. 3A and 3B are illustration of a spoke target for characterizing an imaging system, where the image of a spoke target is shown in an in-focus (FIG. 3A) an out-of- focus (FIG. 3B) conditions. As shown the out-of-focus image exhibits contrast reversal or lacks some spatial frequencies.

The out-of-focus condition is typically cauterized by a phase parameter ψ which measures the quadratic phase added to the pupil function when the imaging system is not in-focus. The phase parameter ψ can be calculated according to the equation:

where D is the dimension of the pupil (length of the slit in case of a slit pupil, and diameter in case of a circular pupil), λ is the wavelength of the light, / is the focal length of the system, and <i _obj and d _img are the distances to the object and image, respectively. Thus, for ψ = 0 the system is in perfect focus. For small values of ψ (typically less than 1), a system is considered "diffraction limited". The phase parameter characterizing the out-of-focus condition shown in FIG. 3B is ψ=5.

FIGs. 4A and 4B depict the one-dimensional MTF of the spoke target corresponding to a slit pupil (FIG. 4A) and circular pupil (FIG. 4B), for an out-of-focus condition of for ψ = 5. As shown, the MTF is non-monotonic with two clear dips aside for the minimum at a normalized frequency of 1. For the slit pupil, the first dip occurs at lower spatial frequency compared to the circular function, and therefore at low spatial frequencies the MTF decreases more rapidly for the slit pupil than for the circular pupil. At normalized frequencies above the first dip, the MTF is flatter than for the circular pupil than for the slit pupil.

The physical explanation for contrast reduction and inversion is that at an out-of- focus condition the point spread function is wide and thus captures information from the addressed area as well as from its adjacent features. As such, when the center of the point spread function hits a dark region, it acquires light also from adjacent regions that may be bright, thus providing a somehow brighter output. Likewise, when it hits a bright region, the total acquired intensity is dimmer, since the expanded point spread function covers adjacent regions, from which no energy is reflected, if they are dark. Contrast reversal occurs when the energy collected from a bright region is lower than that acquired from a dark one in view of the above.

In the case of barcode reading, for example, this effect prevents proper decoding and identification. When decoding two-dimension barcodes, such as, for example, the two-dimension barcode shown in FIG. 5, the severity of this effect is enhanced. FIG. 5 shows that bright regions may be surrounded by dark regions, and likewise dark regions may be surrounded by bright regions not only along the horizontal direction, as one encounters with one-dimensional barcodes, but also in the vertical direction.

It was found by the present inventors that for two-dimensional barcode imagers, the received signal has lower contrast compared to the signal that is obtainable from detecting one-dimensional barcodes of same density.

Before explaining at least one embodiment of the invention in detail, it is to be understood that the invention is not necessarily limited in its application to the details of construction and the arrangement of the components and/or methods set forth in the following description and/or illustrated in the drawings and/or the Examples. The invention is capable of other embodiments or of being practiced or carried out in various ways.

The present inventors have devised a technique which allows better characterization of optical systems. The technique of the present embodiments is based on a template, referred to herein as template 60.

Two representative and non-limiting examples of template 60 are illustrated in FIGs. 6 and 7. Template 60 has one or more brightness patterns 62. In the illustrations of FIGs. 6 and 7, template 60 has one alternating brightness pattern, but this need not necessarily be the case, since, for some applications, it may be desired for template 60 to have several patterns, as further detailed hereinbelow.

Brightness pattern 62 is an alternating brightness pattern along a pair of orthogonal directions 64, 66 over at least a portion of the template. Typically, but not obligatorily, pattern 62 exhibits a chessboard pattern, although the elementary unit of the chessboard is not necessarily a square and may be of any shape. For example, the elementary units of pattern 62 can be hexagons (the so called honeycomb pattern) or any other polygon. Several types of elementary units can also be used. For example, pattern 62 can include two or more types of polygons arranged to ^" tile template 60 or part thereof. Also contemplated are round elementary units (e.g., circles, ellipses), and other elementary units with one or more curved sides.

FIG. 6 shows an exemplified embodiment in which the directions 64 and 66 are drawn parallel to the axes of a Cartesian coordinate system, and FIG. 7 shows an exemplified embodiment in which the directions 64 and 66 are drawn are drawn parallel to the axes of a Polar coordinate system. Other pairs of directions are not excluded from the scope of the present invention.

The exemplary pattern shown in FIG. 6 is a modification of a one-dimensional bar pattern into a two-dimensional chessboard pattern. A one-dimensional bar pattern is found, for example, in a single patch of the so called USAF 1951 target, wherein each patch consists of 3 bars and 2 spaces. USAF 1951 targets are shown in the Examples section that follows.

The exemplary pattern shown in FIG. 7 is a modification of the spoke pattern (see FIG. 3A) into a two-dimensional chessboard pattern. Unlike the spoke pattern which is, essentially, a one-dimensional pattern since it exhibits alternating pattern only along the azimuthal direction but not along the radial direction, pattern 62 of FIG. 7 is a two-dimensional pattern since it exhibits an alternating pattern along the azimuthal as well as the radial directions.

For each of directions 64 and 66, the period characterizing pattern 62 is positive and is either constant or monotonic in a non-random manner along the respective direction. Generally, the two orthogonal directions 64 and 66 span a system of coordinates referred to herein as coordinate ξ and coordinate η. Thus, in accordance with the present embodiments, the period of pattern 62 is either a monotonic function or a constant function of each coordinate. Some exemplary embodiments are illustrated in FIGs. 8A-F.

FIGs. 8A-B illustrate an exemplary embodiment in which the period along a direction parallel to the ξ coordinate is constant as a function of ξ and the period ά _Ά along a direction parallel to the η coordinate is constant as a function of η. Note that although both ά _ξ and are constants as a function of their respective coordinate, they are not necessarily the same. In FIGs. 8A-B, for example, ά _ξ > ά .

FIGs. 8C-D illustrate an exemplary embodiment in which the period d^- along a direction parallel to the ξ coordinate is a monotonic function of ξ and the period ά _Ά along a direction parallel to the η coordinate is a monotonic function of η. In FIGs. 8C- D, ά _ξ increases with ξ and ά _Ά decreases with η, but other combinations are not excluded from the scope of the present invention.

FIGs. 8E-F illustrate an exemplary embodiment in which the period along a direction parallel to the ξ coordinate is a monotonic function of ξ and the period ά _Ά along a direction parallel to the η coordinate is constant as a function of η.

Referring again to FIG. 6, the ξ and η coordinates are realized as the horizontal and vertical coordinates of a Cartesian coordinate system. In the in the representative example shown in FIG. 6, pattern 62 has a non-zero constant period d _y along the vertical direction y and a non-zero constant period d _x along the horizontal direction x. Thus, in FIG. 6, pattern 62 exhibits symmetry under translations along the horizontal and vertical axes, albeit not necessarily with the same period. When d _x = d _y pattern 62 exhibits also symmetry under 90° rotations.

In FIG. 7, the ξ and η coordinates are realized as the radial and azimuthal coordinates of a polar coordinate system. In the representative example shown in FIG. 7, pattern 62 has a non-zero constant period ά along the azimuthal direction φ and a gradually varying period d _r (r) along the horizontal direction r. Thus, in FIG. 7, pattern 62 exhibits symmetry under rotations at integer multiplication of the period άφ with respect to the center of pattern 62. For clarity of presentation, d _r (r) is not drawn in FIG. 7, but the skilled person would know how to extract the period from FIG. 7, based on the following description. In FIG. 7, the period d _r (r) is gradually decreasing inwardly toward the origin of the polar coordinate system. The monotonic dependence of d,(r) on r is illustrated, together with a schematic polar coordinate system in FIG. 9. Although the dependence of d _r on r is shown as linear, this need not necessarily be the case, since, for some applications, a non-linear dependence of d _r on r may be employed.

In various exemplary embodiments of the invention template 60 comprises a plurality of patterns which are distinguishable from one another. The patterns are optionally and preferably distinguishable both spatially and in terms of the periodicity. Spatial distinction can be realized by spaces, e.g., white spaces, separating two adjacent patterns. Preferable, the separating space is larger than half the period of each of the patterns adjacent the space. In terms of periodicity, two adjacent patterns on the template have different periods or period variations. In some embodiments of the present invention any two patterns on template 60 have different periods or period variations. A representative example of a template having a plurality of distinguishable patterns is provided in the Examples section that follows (see, e.g., FIG. 12B).

In any of the above embodiments, template 60 can be formed on a physical surface, preferably a planar physical surface using any technique suitable for patterning a surface. For example, template 60 can be printed, engraved, lithographed, burned or projected onto the surface. It is expected that during the life of a patent maturing from this application many relevant patterning technologies will be developed and the scope of the term "formed" is intended to include all such new technologies a priori.

FIG. 10 is a flowchart diagram of a method suitable for characterizing an optical system according to various exemplary embodiments of the present invention. Selected operations of the method can be embodied on a tangible medium such as a computer for performing the method operations. Selected operations of the method can be embodied on a computer readable medium, comprising computer readable instructions for carrying out the method operations. Selected, operations of the method can also be embodied in electronic device having digital computer capabilities arranged to run the computer program on the tangible medium or execute the instruction on a computer readable medium.

Computer programs implementing the method of this invention can commonly be distributed to users on a distribution medium such as, but not limited to, a CD-ROM or a flash drive. From the distribution medium, the computer programs can be copied to a hard disk or a similar intermediate storage medium. The computer programs can be run by loading the computer instructions either from their distribution medium or their intermediate storage medium into the execution memory of the computer, configuring the computer to act in accordance with the method of this invention. All these operations are well-known to those skilled in the art of computer systems.

The method begins at 90 and continues to 91 at which the optical system is used for acquiring an image from a two-dimensional template, such as template 60 described above. The method continues to 92 at which the image is analyzed, for example, using a data processor such as a general purpose computer or a dedicated circuitry, for characterizing the optical system. The analysis optionally and preferably includes calculation of MTF. Optionally, the analysis includes calculation of a phase transfer function (PTF). The analysis can also include calculation of an optical transfer function (OTF), which is typically the multiplication of MTF by PTF. These quantities are known in the art and appear in many textbooks. Calculation procedure suitable for the present embodiments is found, for example, in J.W Goodman, Introduction to Fourier Optics, McGraw-Hill, Second Edition, New York 1996, 126-151.

The method ends at 93.

FIG. 11 is a schematic illustration of a side view of a setup suitable for executing the method of the present embodiments. The setup includes a device 100 for characterizing an optical system 102. Device 100 comprises a body 104 having a surface 106, which is patterned, for example, according to template 60 (not shown, see, e.g., FIGs, 6 and 7) described above. In various exemplary embodiments of the invention surface 106 is pattern 60. Device 100 is positioned such that surface 106 is facing system 102. The setup also comprises a data processor 108. System 102 acquires an image of the pattern on surface 106 (e.g., pattern 62) and transmits image data to processor 108 which receives the data and analyzes the image, for example, by calculating MTF, PTF and/or OTF.

The word "exemplary" is used herein to mean "serving as an example, instance or illustration." Any embodiment described as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments and/or to exclude the incorporation of features from other embodiments.

The word "optionally" is used herein to mean "is provided in some embodiments and not provided in other embodiments." Any particular embodiment of the invention may include a plurality of "optional" features unless such features conflict.

The terms "comprises", "comprising", "includes", "including", "having" and their conjugates mean "including but not limited to".

The term "consisting of means "including and limited to".

The term "consisting essentially of" means that the composition, method or structure may include additional ingredients, steps and/or parts, but only if the additional ingredients, steps and/or parts do not materially alter the basic and novel characteristics of the claimed composition, method or structure. As used herein, the singular form "a", "an" and "the" include plural references unless the context clearly dictates otherwise. For example, the term "a compound" or "at least one compound" may include a plurality of compounds, including mixtures thereof.

It is appreciated that certain features of the invention, which are, for clarity, described in the context of separate embodiments, may also be provided in combination in a single embodiment. Conversely, various features of the invention, which are, for brevity, described in the context of a single embodiment, may also be provided separately or in any suitable subcombination or as suitable in any other described embodiment of the invention. Certain features described in the context of various embodiments are not to be considered essential features of those embodiments, unless the embodiment is inoperative without those elements.

Various embodiments and aspects of the present invention as delineated hereinabove and as claimed in the claims section below find experimental support in the following examples.

EXAMPLES

Reference is now made to the following examples, which together with the above descriptions illustrate some embodiments of the invention in a non limiting fashion.

FIGs. 12A and 12B show a USAF 1951 template (FIG. 12A) and template 60 according to some embodiments of the present invention (FIG. 12B). Template 60 comprises a plurality of patterns 62. Template 60 can comprise, for example, 5x5 squares, starting with large structures and then progressively smaller structures. This is — advantage since it allows the user who is familiar the one-dimensional USAF 1951 template (3 bars and 2 spaces) to adapt the analysis to the case of the template of the present embodiments. In FIGs. 12A and 12B only two 6-element groups are shown.

A template which comprises a plurality of polar patters similar to the pattern shown in FIG. 7 can also be employed. The polar patterns can be arranged on a rectangular or polar grid, as desired. Preferably, on such template each polar pattern has a different starting spatial frequency. Example 1

Computer Simulations

The contrast obtainable with an imaging system exhibiting a circular pupil spread function was carried by computer simulations.

Computer simulations where employed for a conventional spoke target with 50 spokes (see FIG. 13A), and a polar chessboard template in accordance with some embodiments of the present invention (see FIG. 14A). The polar chessboard template included 11 steps, with a starting frequency of 2 line pairs ^" per millimeter and a step size of about 12 %. The simulations included calculation of contrast along a circular path at approximately half the distance between the center and the periphery of the polar pattern. The path is shown as a circular line in FIGs. 13A and 14A. The contrast was calculated according to the equation:

Contrast - max " mm

/ +/ · (EQ. 2) max ' min

where / _max is the maximum value and / _min is the minimum value of the sampled signal encountered along the path. The simulations were performed under an out-of-focus condition characterized by a phase parameter ψ of about 1.

The simulation results for the conventional spoke target and the template of the present embodiments are shown in FIGs. 13B and 14B, respectively. For the conventional spoke target, the obtained contrast was found to be about 90 % (FIG. 13B) while for the template of the present embodiments the obtained contrast was found to be about 55 % (FIG. 14B). Thus, the contrast level provided by the two-dimensional template of the present embodiments is lower than that obtained with a conventional circular spoke target. The present inventors found that the contrast obtained using a conventional spoke target is an overestimation of the correct contrast, and therefore consider the contrast obtained using the two-dimensional template of the present embodiments more accurate.

Computer simulations where also performed for a Cartesian chessboard template in accordance with some embodiments of the present invention and compared to simulations performed for a conventional USAF 1951 template. The templates used for the simulations are shown in FIGs. 15A-F, where the USAF 1951 target is shown in 11 000319

16

FIGs. 15A, 15C and 15E and the template of the present embodiments is shown in FIGs. 15B, 15D and 15F. FIGs. 15A-B correspond to an in-focus condition (phase parameter ψ=0), FIGs. 15C-D correspond to an out-of-focus conditions characterized by a phase parameter ψ of about 2 and FIGs. 15E-F correspond to an out-of-focus conditions characterized by a phase parameter ψ of about 5. Contrast reversals as well as loss of certain frequencies was observed, particularly for ψ=5.

FIGs. 16A-F present computer simulations performed for a conventional spoke target, and a polar chessboard template in accordance with some embodiments of the present invention. The conventional spoke target is shown in FIGs. 16A, 16C and 16E and the template of the present embodiments is shown in FIGs. 16B, 16D and 16F. FIGs. 16A-B correspond to an in-focus condition (phase parameter ψ=0), FIGs. 16C-D correspond to an out-of-focus conditions characterized by a phase parameter ψ of about 2 and FIGs. 16E-F correspond to an out-of-focus conditions characterized by a phase parameter ψ of about 5. Contrast reversals as well as loss of certain frequencies was observed, particularly for ψ=5.

For the pattern of the present embodiments (FIGs. 16B, 16E and 16F) at every distance, the radial step size, measured at the middle of the zone, is approximately equal to the azimuthal step size. The radial step was set in accordance with the following equation:

where 5 is the number of spokes (16 in the present example) and N is the ordinary number of the step, starting from N=l at the peripheral edge of the pattern.

As shown in FIGs. 16A-F the blur is more pronounced at high frequencies (towards the center) and the response becomes "nil" (gray region with no visible structure) for some range of spatial frequencies. Notice that the blur circle occurs at lower spatial frequencies (larger radii in the present example) for the template of the present embodiments, in comparison to the conventional spoke target. Contrast reversals was observed for ψ=5. Example 2

Optical Imaging

A commercial RGB camera [uEYE® 1225], equipped with a CMOS detector with a resolution of 752x480 pixels and a pixel dimension of 6 microns was utilized. The camera was equipped with a lens having an effective focal length of 16mm [Computar® M1614W], aperture size of 1mm and a field of view (FOV) of 45 degrees along the sensor diagonal.

The target was incoherently illuminated by ambient room light. The nominal distance has been set at 23cm, the contrast level at 3 different spatial frequencies was evaluated for the nominal focal distance as well as for an out-of-focus condition of ψ=5 (about 26cm). Evaluations were made using Matlab® tools.

Each experiment was performed using a conventional spoke target (FIG. 17A) and using the template of the present embodiments (FIG. 17B) as a target. FIGs. 17A and 17B correspond to in-focus condition. The red, green and blue circles mark the paths the 3 different spatial frequencies.

FIGs. 18A-C show signal traces in an in-focus condition along the 3 circles drawn in FIGs. 17A and 17B. The RGB traces correspond to the conventional target and the black traces correspond to the template of the present embodiments. As shown, the signals obtained from the conventional target are almost identical to those obtained from the template of the present embodiments.

FIG. 19 shows the MTF of the optical system in an in-focus condition. The theoretical MTF is shown in a thick solid line (magenta), and the experimental values as measured for the conventional spoke target are shown in a dashed line. The RGB dots represent the contrast at the selected test frequencies. Since for the in-focus condition the contrast is practically the same for the conventional target and the template of the present embodiments, each RGB dot can be considered as representing both experiments.

FIGs. 20A and 20B are similar to FIGs. 17A and 17B, but for out-of-focus condition characterized by a phase parameter ψ of about 5. It so happens that for such a defocus condition, the green curve in FIG. 20B hits a region where the contrast level is close to 0. The blue curve corresponds to a region that provides contrast reversal for the template of the present embodiments (FIG. 20B), but no contrast reversal for the conventional target (FIG. 20A).

FIGs. 21A-C show signal traces in an out-of-focus condition characterized by ψ=5 along the 3 circles drawn in FIGs. 20A and 20B. The RGB traces correspond to the conventional target and the black traces correspond to the template of the present embodiments.

As shown in FIG. 21B (corresponding to the green circle in FIGs. 20A-B) there was significant reduction of contrast for the signal obtained from the template of the present embodiments, whereas only minor reduction was observed for the conventional target. As shown in FIG. 21C (corresponding to the blue circle in FIGs. 20A-B) there is a contrast reversal for the signal obtained from the template of the present embodiments, but not for the conventional target. The present inventors found that the contrast obtained using the conventional spoke target is an overestimation of the correct contrast, and therefore consider the contrast obtained using the two-dimensional template of the present embodiments more accurate.

FIG. 22 shows the OTF of the optical system in an out-of-focus condition characterized by ψ=5. The theoretical OTF is shown in a thick solid line (magenta), and the experimental values as measured for the conventional spoke target are shown in a dashed line. The RGB full dots represent the contrast, as measured at the selected test frequencies, for the conventional spoke target, and RGB open dots represent the contrast, as measured at the selected test frequencies, for the template of the present embodiments. As shown, the OTF values obtained using the template of the present embodiments are significantly lower than those obtained using conventional spoke target, thus confirming the inventors' hypothesis that the conventional spoke target provides an overestimation of the contrast.

Herein, the term "about" when used in conjunction with a value X, means any value between 0.9X and 1.1X, inclusive.

Throughout this application, various embodiments of this invention may be presented in a range format. It should be understood that the description in range format is merely for convenience and brevity and should not be construed as an inflexible limitation on the scope of the invention. Accordingly, the description of a range should !9

be considered to have specifically disclosed all the possible subranges as well as individual numerical values within that range. For example, description of a range such as from 1 to 6 should be considered to have specifically disclosed subranges such as from 1 to 3, from 1 to 4, from 1 to 5, from 2 to 4, from 2 to 6, from 3 to 6 etc., as well as individual numbers within that range, for example, 1, 2, 3, 4, 5, and 6. This applies regardless of the breadth of the range.

Whenever a numerical range is indicated herein, it is meant to include any cited numeral (fractional or integral) within the indicated range. The phrases "ranging/ranges between" a first indicate number and a second indicate number and "ranging/ranges from" a first indicate number "to" a second indicate number are used herein interchangeably and are meant to include the first and second indicated numbers and all the fractional and integral numerals therebetween.

Although the invention has been described in conjunction with specific embodiments thereof, it is evident that many alternatives, modifications and variations will be apparent to those skilled in the art. Accordingly, it is intended to embrace all such alternatives, modifications and variations that fall within the spirit and broad scope of the appended claims.

All publications, patents and patent applications mentioned in this specification are herein incorporated in their entirety by reference into the specification, to the same extent as if each individual publication, patent or patent application was specifically and individually indicated to be incorporated herein by reference. In addition, citation or identification of any reference in this application shall not be construed as an admission that such reference is available as prior art to the present invention. To the extent that section headings are used, they should not be construed as necessarily limiting.