Abstract:
A system and method of calibrating and measuring optical properties of an imaging optical device is disclosed in which a structure of uniformly periodic linear elements is imaged using the optical device being calibrated. This image is obtained with the optical axis of the device at an angle α with respect to a normal to the uniformly periodic structure. This is done by situating the linear elements on the hypotenuse of a wedge, i.e., a right-angled triangular prism. The image is then taken with the optical axis of the optical device oriented vertically. An advantage of the arrangement is that the structure of uniformly periodic linear elements does not need to be carefully focused making the system quick and easy to implement.

Description:
CLAIM OF PRIORITY 
       [0001]    This application claims priority to U.S. Application Ser. No. 62/129,459 filed on Mar. 6, 2015, the contents of which are herein fully incorporated by reference in its entirety. 
     
    
     FIELD OF THE INVENTION 
       [0002]    This invention relates to the calibration of an imaging system and to the measurement of fundamental and operational properties of an optical system including magnification, focal length, field curvature, distortion, and depth of focus. 
       BACKGROUND OF THE INVENTION 
       [0003]    Magnifying systems such as microscopic imaging systems are commonly used for conducting research, quantitative characterization and screening in various applications, such as semiconductors fabrication, pharmaceutical research, biomedical and biotechnology laboratories, aerospace and automotive parts manufacturing. 
         [0004]    In order to accurately and precisely compute the spatial properties of the elements being imaged, a microscopic imaging system must be calibrated beforehand. Calibration parameters are typically obtained by measuring attributes of a reference image taken of an object having known physical dimension and shape. The calibration parameters can be complex, as their purpose is to compensate for many types of deformations and in-homogeneities introduced by the imaging system. Existing calibration procedures, therefore, tend to be complex, time consuming and usually require skilled technicians to perform them. 
         [0005]    Simpler, less time consuming yet accurate calibration tools and methods are therefore desirable. 
       Description of Related Art 
       [0006]    US Patent Application 20140169637 to Reto Zuest et al. published on Jun. 19, 2014 entitled “Method for Self-Calibration of a Microscope Apparatus”” that describes a method for calibrating a microscope apparatus having a variable optical magnification system and a detector device is disclosed. First, a calibrating mode is performed, wherein an image of an object is captured at a known reference magnification value, two characteristic reference points are determined in the image, a reference distance between the two reference points is determined, and a correlation is determined between the reference distance and the reference magnification value. Later, a measuring mode is implemented, in which a current image of the object is captured at a second magnification value, the two characteristic reference points are identified therein, a current distance between the current reference points is determined, and the second magnification value is determined from the current distance based on the correlation between the reference distance and the reference magnification value. 
         [0007]    U.S. Pat. No. 8,401,269 to Laroche et al. issued on Mar. 19, 2013 entitled “System and method for automatic measurements and calibration of computerized magnifying instruments”” that describes a system and method for automatic measurements and calibration of computerized magnifying instruments. More particularly, the method includes an automatic calibration aspect, which includes obtaining an optimized digital image of a reference object including at least one standardized landmark feature, and establishing calibration parameters based on one or more measured attributes of the landmark feature. The method further describes a calibration aspect, which includes providing calibration parameters, obtaining a digital image including at least one known attribute, measuring at least one known attribute and comparing the measured value with the known value. The method further includes an aspect of automatic measurement of an attribute of one or more object, which includes retrieving calibration parameters, acquiring a digital image and measuring the attribute. The system includes an object support, a reference object including one or more standardized landmark features, and an automatically readable identification means. 
         [0008]    U.S. Pat. No. 4,055,376 to Daberko issued on Oct. 25, 1977 entitled “Calibration reticle for measuring microscopes”” that describes a calibration reticle for measuring microscopes is disclosed in which a calibrated distance is established by calibration reference lines whose locations are defined by selected features of the calibration pattern. Preferably, the calibration reference lines are not physically manifest on the calibration reticle, except by the selected features which specify the locations of the calibration reference lines. 
         [0009]    U.S. Pat. No. 6,026,172 to Lewis, Jr. et al. issued on Feb. 15, 2000 entitled “System and method for zoom lens calibration and method using same”” that describes using marks of known dimensions and size, and spacing, a zoom lens may be calibrated in either or both the X and Y spatial directions. A system comprising an image capture device, positioning means, position encoder means, operator interface, and processing unit permits this method to be advantageously applied to a wide variety of web inspection/control functions, including but not limited to initial web registration, multiple color ink registration, lateral web positioning, repeat length calculations, image capture synchronization, thermal/mechanical differential compensation, and accurate registration of objects within an image to other objects within an image or to a mechanical reference on a machine. Since the Zoom Calibration method permits a system to be constructed with both wide/variable field of view and accurate distance measurement positioning and calibration, all of the web inspection/control functions traditionally used in the web printing industry may be implemented with a single inspection/control system using a multitasking approach with the same inspection/control hardware. This permits rapid implementation of old and new web inspection/control functions at a greatly reduced cost as compared to traditional fixed lens systems, as well as permitting a degree of automation, remote access, diagnostic control, quality assurance, and product quality control heretofore not possible with conventional web inspection/control systems. 
       BRIEF SUMMARY OF THE INVENTION 
       [0010]    An inventive system and method of calibrating and measuring optical properties of an imaging optical device is disclosed. 
         [0011]    In a preferred embodiment, a structure of uniformly periodic linear elements is imaged using the optical device being calibrated or measured. This calibration image is preferably obtained when the optical device is oriented with its optical axis at an acute angle α with respect to a normal to the uniformly periodic structure. This angle α is preferably in a range of 5 to 85 degrees. However, in some embodiments, the angle may range from 0 to 5 degrees. This arrangement may be facilitated by, for instance, having a device in which the linear elements are situated on the hypotenuse of a wedge, with the wedge being shaped as a right-angled triangular prism. The optical axis then only has to be vertical, which may be easily and accurately achieved using a plumb-bob. One way to create such a device may be to have a precision Ronchi ruling plate fixed to the hypotenuse of an accurately machined wedge having an angle α between its base and the plane of its hypotenuse. 
         [0012]    An advantage of the arrangement is that the structure of uniformly periodic linear elements does not necessarily need to be carefully focused in order to do the calibration. This latitude in performing the calibration in the manner of the present invention, may make the system quick and easy to use. 
         [0013]    A first example of how this device may be used to obtain an optical property of an optical imaging device may be illustrated by the steps involved in determining its magnification. 
         [0014]    First, a position of sharpest focus on the calibration image may be determined. This may be done by using image sharpness or contrast ratio, or a combination thereof to determine a quasi-periodic function representing the imaged periodic line elements. By determining the fundamental Fourier frequency of that function, and its quadrature function, a zero-phase angle between them may indicate the position of sharpest focus to sub-pixel accuracy. Having found the position of sharpest focus, the periodicity D in this region may be measured and compared to the periodicity d of structure of uniformly periodic linear elements. As the linear elements spaced with periodicity d are on a slope of angle α, the magnification may be calculated using the formula: 
         [0000]        m=D /( d  cos(α))   (1)
 
         [0015]    where m is the magnification. 
         [0016]    In a preferred embodiment, the calibration image may be a digital image, and it may be relayed to a computer. The computer may be programmed to automatically locate the position of sharpest focus, calculate the periodicity D at that region and, knowing the values of d and angle α, automatically calculate the magnification m using an algorithm that may incorporate equation 1. 
         [0017]    As will be shown in the detailed description below, analogous measurements and calculations may also provide optical properties such as, but not limited to, focal length, field curvature, distortion, and depth of focus. 
         [0018]    Enhancements and alterations may be made to the wedge discussed above. For instance a second structure of uniformly periodic linear elements may be attached to the side of the wedge. This second structure may be oriented on a plane parallel to the base of the wedge with the second linear elements also oriented parallel to the first. Such an arrangement may, for instance, be used in a situation where the optical axis of the optical imaging device may not be precisely normal to the base of the wedge. This second structure of uniformly periodic linear elements may then be used to calculate the actual angle between the normal to the hypotenuse plane of the wedge and the optical axis of the optical imaging device, as will be described in detail later. 
         [0019]    One further embodiment of the device may be a device that may be folded flat for more economical storage, but then transformed into a wedge for use. This too is described in detail later. 
         [0020]    Therefore, the present invention succeeds in conferring the following, and others not mentioned, desirable and useful benefits and objectives. 
         [0021]    It is an object of the present invention to provide a quick and simple apparatus for, and method of, determining optical properties of an optical imaging system. 
         [0022]    It is another object of the present invention to provide a robust, inexpensive yet highly accurate method of, determining optical properties of an optical imaging system. 
         [0023]    Yet another object of the present invention is to provide a system that can automatically determine the magnification, focal length, field curvature, distortion, and depth of focus of an optical imaging system with a high degree of accuracy. 
     
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
         [0024]      FIG. 1  shows an isometric schematic layout of an optical measuring device of the present invention. 
           [0025]      FIG. 2  shows a further isometric schematic layout of an optical measuring device of the present invention. 
           [0026]      FIG. 3  shows a schematic flow diagram of some steps of the method of the present invention. 
           [0027]      FIG. 4A  shows a schematic cross-section of an exemplary uniformly periodic structure. 
           [0028]      FIG. 4B  shows a schematic cross-section of an exemplary imaged periodic structure. 
           [0029]      FIG. 4C  shows a depiction of a calibration image including a schematic, exaggerated view of a region of interest used to determine magnification of an optical device. 
           [0030]      FIG. 5  shows an exaggerated, schematic view of a region of interest of a calibration image used to determine an effective focal length of an optical device. 
           [0031]      FIG. 6  shows an exaggerated schematic view of a region of interest of a calibration image used to determine a depth of field of an optical device. 
           [0032]      FIG. 7  shows a depiction of a calibration image and three regions of interest used to determine a field curvature of an optical device. 
           [0033]      FIG. 8  shows an exaggerated schematic view of three regions of interest of a calibration image used to determine a field curvature of an optical device. 
           [0034]      FIG. 9  shows a depiction of a calibration image and a region of interest used to determine a distortion of an optical device. 
           [0035]      FIG. 10  shows an exaggerated schematic view of a region of interest of a calibration image used to determine a distortion of an optical device. 
           [0036]      FIG. 11  shows a schematic, isometric view of one preferred embodiment of a wedge of the present invention. 
           [0037]      FIG. 12  shows a schematic, isometric view of a further preferred embodiment of a wedge device of the present invention. 
           [0038]      FIG. 13A  shows a schematic, isometric view of yet a further preferred embodiment of a wedge device of the present invention arranged for storage. 
           [0039]      FIG. 13B  shows a schematic, isometric view of yet a further preferred embodiment of a wedge device of the present invention arranged for use. 
           [0040]      FIG. 14  shows a schematic, front view of an object image having fiducial markers added using the method of this invention. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0041]    The preferred embodiments of the present invention will now be described with reference to the drawings. Identical elements in the various figures are identified with the same reference numerals. 
         [0042]    Various embodiments of the present invention are described in detail. Such embodiments are provided by way of explanation of the present invention, which is not intended to be limited thereto. In fact, those of ordinary skill in the art may appreciate upon reading the present specification and viewing the present drawings that various modifications and variations can be made thereto. 
         [0043]      FIG. 1  shows an isometric schematic layout of an optical measuring device of the present invention. An imaging optical device  105  is shown imaging a structure of uniformly periodic linear elements  111  to create a calibration image  120 . The structure of uniformly periodic linear elements  111  is preferably located on a first planar surface  115 . The optical axis  125  of the optical device  105  is shown oriented at an angle acute angle α  130  with respect to the normal  135  of the first planar surface. 
         [0044]    Both the normal  135  of the first planar surface and the optical axis  125  of the optical device are shown as being in a plane  140  normal to the first planar surface and perpendicular to the linear elements  114  of the structure of uniformly periodic linear elements  111 , i.e., along the direction of periodicity  116 . 
         [0045]    The arrangement of  FIG. 1  may be used to calibrate an imaging optical device  105  by determining one or more optical properties of the imaging optical device  105  such as, but not limited to, a focal length, a magnification, a depth of field, a measure of field curvature or distortion, or some combination thereof. 
         [0046]    This may, for instance, be done by determining a periodicity D of the imaged periodic structure in a position of sharpest focus. The required optical property or properties of the optical device may then be calculated using mathematical formulas involving the periodicity d, the acute angle α and the imaged periodicity D, as will be described in more detail below. 
         [0047]    This optical property may then be used to adjust or alter an image taken by the calibrated optical device. For instance if the optical property is the magnification of the optical device, the alteration may, for instance, be adding one or more fiducial scale or distance markers to the image. If the optical property is distortion, the image may, for instance, automatically remove the distortion from the image to produce an undistorted image. In a further preferred embodiment of the invention, fiducial markers may be applied to the image and the distortion may be mathematically applied to produce more accurate measurements between those fiducial markers. 
         [0048]      FIG. 2  shows a further isometric schematic layout of an optical measuring device of the present invention. In this embodiment, the structure of uniformly periodic linear elements  111  may be placed on a flat slanted surface that may, for instance, be the hypotenuse surface  161  of a right triangular prism or wedge  155 . 
         [0049]    Orienting the optical axis  125  of the optical device normal to a flat, base surface  165  of the wedge  155  may result in it being at an acute angle α  130  with respect to the normal  135  of the wedge&#39;s  155  hypotenuse surface  161 . 
         [0050]    Arranging for the optical axis to be vertical may easily and accurately be done using, for instance, a plumb-bob. Arranging for the base surface may easily and accurately be done using, for instance, a spirit level. 
         [0051]    The angle between the hypotenuse surface  161  and the flat, base surface  165  may also be equal to the acute angle α  130 . In a preferred embodiment, the acute angle α  130  may be in a range of 5 to 85 degrees, and more preferably in a range of 30 to 60 degrees and most preferably in a range of 45 degrees+/−5 degrees. Having the angle α  130  close to 45 degrees may, for instance, simplify some of the calculations necessary to arrive at the optical properties, and may, therefore, speed up the process. However, in some embodiments, the angle may range from 0 to 5 degrees. 
         [0052]    The calibration image may be recorded by a digital image capture device  175  such as, but not limited to, a digital camera. The recorded digital image may then be transferred to a digital computer  145 . The digital computer  145  may, for instance, contain a digital processor  146  and digital memory  147 . A suitable set of instructions  148  may be stored in the digital memory  147  that may allow the digital processor  146  the necessary function to perform the calculations necessary to make the calculations described in more detail below. The digital computer  145 , in part or in its entirety, may be located distant from the imaging device being tested, or “in the cloud” in current parlance. It may also, in part or entirely, actually be a part of the imaging device. 
         [0053]    A digital display screen  170  may also be functionally connected to the digital computer  145  and may be used to display the digital image  150 . 
         [0054]      FIG. 3  shows a schematic flow diagram of some steps of the method of the present invention. 
         [0055]    In step  301 : Provide Uniformly Periodic Structure, a structure having uniformly periodic linear elements  111  on it, may be provided. One such structure may be the well-known Ronchi ruling or grating. A Ronchi ruling or grating may be a constant-interval bar and space square wave optical target that may have a high edge definition and contrast ratio. Ronchi rulings may be manufactured through photolithographic deposition of chrome on glass or optical substrates. Such a structure may be applied directly to the hypotenuse face of a precision wedge to form a Ronchi wedge. 
         [0056]    The same, or similar, technology may also be used to produce a structure having the linear elements shaped and placed to form a sinusoidal grating placed directly on, or manufactured onto it. Such a sinusoidal grating may have sinusoidally varying height, opacity of reflectivity, or some combination thereof. 
         [0057]    In step  302 : Image Structure with Optical Device Having Optical Axis at Angle a to the Normal of the Periodic Structure, an image may be taken of the structure of uniformly periodic linear elements using the optical imaging device being calibrated. 
         [0058]    In a preferred embodiment, the angle between the imaging devices optical axis and the grating surface may be achieved by having the linear elements on the hypotenuse surface of a wedge, and imaging perpendicularly down. 
         [0059]    In a preferred embodiment, the image may be a digital image. 
         [0060]    In step  303 , this digital image of the periodic structure may be examined by, for example, transferring it as a matrix of pixels to the memory on a digital computer. This matrix may then be digitally processed using a programmed digital microprocessor. 
         [0061]    For instance, a first step may be to determine orientation of the imaged grid (fringe) pattern with respect to the frame of the image. 
         [0062]    The nominal orientation the fringes may be vertical, i.e. the assumption is that the lines of the fringes should be parallel to the edge of the image in one dimension and normal to them at the orthogonal edge. 
         [0063]    Calculating the fringe angle the nominal vertical can be done simply, to a pixel accuracy, or using a more complex formula. 
         [0064]    In the simple method, the algorithm simply compares two horizontal lines of pixels that are separated vertically from each other by N pixels. By cross-correlating those rows, a distance D that one has to be displaced horizontally to produce a maximum value or correlation peak can be found. The pixel accurate fringe angle ø is then given by the equation: 
         [0000]      Ø=Tan( D/N )   (2)
 
         [0065]    The complex method makes use of finding the phase of a fundamental sine wave, or first harmonic of a row of pixels, i.e., the largest amplitude sine wave that is part of a set of Fourier terms that describe the row of fringes. This can be found by first normalizing the image of the grid to remove any intensity non-uniformity that might have been introduced by the imaging process. This can be accomplished using a low pass filter. 
         [0066]    The 1 st  harmonic, l 1 (x)=A cos(2πx+φ) can be found by applying a Fourier transform to the row of pixels, high pass filtering them to remove the less relevant elements of the Fourier transform, then applying an inverse Fourier transform. 
         [0067]    The quadrature signal for this same row of pixels can be obtained by applying a Hilbert transform to the 1 st  harmonic to obtain l 2 (x)=A sin(2πx+φ). 
         [0068]    A phase φ between the two signals may be calculated as: 
         [0000]      φ=arctan( l   1   /l   2 )   (3)
 
         [0069]    A zero degree phase angle can then be interpolated as a subpixel accurate location. 
         [0070]    By calculating a separation Dp of the subpixel accurate zero degree phase angle on two different horizontal rows, N pixels apart, a more accurate fringe angle 
         [0000]      Ø=Tan( Dp/N )   (4)
 
         [0071]    In Step  304 : Calculate Angle of Orientation of Optical Axis and Normal. This is described in detail below in connection with  FIG. 4 . 
         [0072]    In Step  305 : Calculate Optical Property of Optical Device by Analyzing and Comparing Imaged Periodic Structure to the Uniformly Periodic Structure. 
         [0073]    Such optical properties may include characteristics such as, but not limited to, best focus, optical focal length, depth of field, magnification, and distortion, or some combination thereof, as is discussed in detail below. 
         [0074]    In Step  306 : Obtain an Image of an Object Using the Optical Device, the optical device may be used to obtain an image that is preferably a digital object image. 
         [0075]    In Step  307 : Modify the Object Image using the Optical Property. This may take the form of using a digital processor to adjust the digital optical image taken in Step  306  using one of the optical properties calculated in Step  305 . The image may, for instance, be altered in some way such as, but not limited to, having distortion removed using a knowledge of field curvature or distortion, or having fiducial makers placed on its base on a knowledge of the magnification, or some combination thereof. 
         [0076]      FIG. 4A  shows a schematic cross-section of an exemplary uniformly periodic structure. As shown the structure of uniformly periodic linear elements  111  has a period d and therefore a frequency  1 /d. The structure of uniformly periodic linear elements  111  may, as shown in  FIG. 4A , closely resemble a sine wave. 
         [0077]      FIG. 4B  shows a schematic cross-section of an exemplary imaged periodic structure. As shown in an exaggerated way in  FIG. 4B , both the amplitude and the periodicity D may vary. This is due to the image being taken at an angle, resulting in a changing magnification across the field of view, and because the image only has one position of sharpest focus  181 , with the image gradually going out of focus in both directions away from the position of sharpest focus  181 . For only pixel accurate calculations, the periodicity D may however be taken as the periodicity at the position of sharpest focus  181 . 
         [0078]      FIG. 4C  shows a plan view depiction of a calibration image including a schematic, exaggerated view of a region of interest used to determine magnification of an optical device. 
         [0079]    A region of interest  190  may be selected from a calibration image  120 . That region of interest  190  is shown as the magnified and exaggerated region of interest  195 . 
         [0080]    This region of interest  190  may be used to locate the position of sharpest focus  181  using a number of options such as, but not limited to, edge detection, high spectral frequency detection, or modulation strength, or a combination thereof. 
         [0081]    Edge detection typically measures edge strength. 
         [0082]    On the right side of the region of interest  190  there are lines  210  that are more magnified than the lines at sharpest focus  181  and have a greater blurring  215  than the lines at position of sharpest focus  181 . 
         [0083]    Similarly, on the left side of the region of interest  190  there are lines  205  that are less magnified than the lines at sharpest focus  181 , but also have a greater blurring  215  than the lines at position of sharpest focus  181 . 
         [0084]    Edge detection can use these lines to measure the edge strength of each line. This edge strength may then be plotted as a focus function, with edge strength on a vertical axis and line position on the horizontal axis. This focus function may then be thresholded to eliminate “dead space” where edge data is missing. A suitable curve such as, but not limited to, a Gaussian or a parabola may then be fitted to the focus function. The peak of such a curve may then indicate a subpixel accurate position of sharpest focus  181 . 
         [0085]    Modulation strength may be used in a similar fashion. Modulation strength is a measure of the line intensity above the local background  220  intensity, i.e., the ratio of the peak to the valley. This modulation strength may be plotted as a focus function, with modulation strength on a vertical axis and line position, perpendicular to the direction of the fringe pattern, on the horizontal axis. This focus function may then be thresholded to eliminate “dead space” where edge data is missing. A suitable curve such as, but not limited to, a Gaussian or a parabola may then be fitted to the focus function. The peak of such a curve may then indicate a subpixel accurate position of sharpest focus  181 . 
         [0086]    A further approach is to use high spectral frequency detection. 
         [0087]    This may be used because perfect image of a Ronchi ruling may consist of alternating regions of dark and bright lines. A single row of pixels may, therefore, exhibit a square wave pattern, i.e., a dark region followed by a bright region. Each region of a well-focused image may have uniform intensity. Mathematically, this square wave may be represented as the sum of sine waves starting with the fundamental frequency (f) of the ruling pattern and adding decreasing amounts of each higher harmonic frequency (2f, 3f, 4f, . . . ). 
         [0088]    A defocused image of this ruling may, however, have the harmonic frequencies of the suppressed, and the suppression effect may be stronger for the higher order harmonics, and may also be stronger for more defocus, so that a defocused image of the Ronchi ruling may resemble a sine wave. This effect may be used to estimate how well the focus is by filtering out the fundamental frequency, leaving only the higher order harmonics. The regions that become progressively more out-of-focus may contain fewer higher-order harmonics. The part of the image with the most higher-order harmonics may, therefore, be the part that is best focused. 
         [0089]    By repeating this for each row of pixels, the position of sharpest focus  181  for each row may be calculated. 
         [0090]    Having found the position of sharpest focus, the periodicity D in this region may be measured and compared to the periodicity d of structure of uniformly periodic linear elements. As the linear elements spaced with periodicity d are on a slope of angle α, the magnification m may be calculated using the formula: 
         [0000]        m=D /( d  cos(α))   (5)
 
         [0091]      FIG. 5  shows an exaggerated, schematic view of a region of interest of a calibration image used to determine an effective focal length of an optical device. 
         [0092]    The effective focal length ef of an optical device may be automatically obtained using an algorithm that obtains at least the magnifications m 1  and m 2  at two locations x 1  and x 2  in said calibration image, the two locations being separated by a distance Dx measured parallel to the direction of periodicity of the grating. 
         [0093]    The magnifications m 1  and m 2  may be calculated by determining the periodicity d 1  at location x 1    225 , the periodicity d 2  at location x 2    230 . The magnifications m 1  and m 2  may then be given by: 
         [0000]        m   1   =d   1   /d    (6)
 
         [0000]        m   2   =d   2   /d    (7)
 
         [0094]    Where d is the periodicity of the original grid. 
         [0095]    The vertical distance Hx (not shown) between the points on the original grid imaged to x 1  and x 2  may be calculated using the method described below in connection with determining the depth of focus, described in connection with  FIG. 6 . 
         [0096]    The effective focal length ef may then be described by the equation: 
         [0000]        ef=f ( m   1   , m   2   , Hx )   (8)
 
         [0097]    In a preferred embodiment, a greater number of magnifications may be calculated, each at additional point. These added measurements may then be combined to produce a more accurate result. Alternately, a function may be fitted to the multiple measurements using an equation containing the focal length and resulting magnification at a distance, to produce an estimate of the focal length using all of the measurements made. 
         [0098]      FIG. 6  shows an exaggerated schematic view of a region of interest of a calibration image used to determine a depth of field of an optical device. 
         [0099]    In order to determine the acceptable field of view, an acceptable degradation of focus, fd needs to be determined. This may for instance be done using edge detection, which typically measures edge strength; or using modulation strength, which is a measure of the line intensity above the local background  220  intensity, i.e., the ratio of the peak to the valley. 
         [0100]    By defining an acceptable threshold fd of either edge strength, or modulation strength, a digital processor may be programmed to automatically locate a first position  226  where the threshold is met on a magnified region of interest  195  of a digital calibration image stored in a computer memory. Similarly, a second position  231  may be located where the threshold is reached going in the other direction from the position of optimum focus. 
         [0101]    By measuring the length L between the first and the second positions, and knowing the angle α that the optical axis of the device is oriented with respect to a normal to the planar surface on which the uniformly periodic structure is situated, the vertical distance on the original grating along the axis of the lens between the first and second positions can be calculated. This vertical distance may be the depth of focus df of the imaging device and may be calculated by the formula: 
         [0000]        df=L  cos(α)   (9)
 
         [0102]      FIG. 7  shows a depiction of a calibration image and three regions of interest used to determine a field curvature of an optical device. 
         [0103]    Three horizontally oriented regions of interest  245  separated from each other by a distance measured parallel to the parallel lines are obtained from a calibration image  120 . 
         [0104]      FIG. 8  shows an exaggerated schematic view of three regions of interest of a calibration image used to determine a field curvature of an optical device. 
         [0105]    This may be done by first determining a focal position f xy    240  at least of each of an upper strip  250 , a middle strip  251  and a lower strip  252  of the calibration image. 
         [0106]    The focal position f xy ,  240  may, for instance, be done using the method for finding a position of sharpest focus detailed above. 
         [0107]    In this method, edge detection may measure the edge strength of each line. This edge strength may then be plotted as a focus function, with edge strength on a vertical axis and line position on the horizontal axis. This focus function may then be thresholded to eliminate “dead space” where edge data is missing. A suitable curve such as, but not limited to, a Gaussian or a parabola may then be fitted to the focus function. The peak of such a curve may then indicate a subpixel accurate position of sharpest focus that may be translated into a focal position f xy ,  240  by measuring the y position of the line of pixels analyzed. 
         [0108]    An analogous process can be done using modulation strength. This may be a measure of the line intensity above the local background intensity, i.e., the ratio of the peak to the valley. 
         [0109]    Having found a focal position f xy ,  240  for each region, a curve  255  may be fitted to the focal points. That curve  255  may be the field curvature c of the lens, or may be an indicator of the field curvature. 
         [0110]      FIG. 9  shows a depiction of a calibration image and a region of interest used to determine a distortion of an optical device. In this instance one of the parallel lines  270  of the calibration image  120  may be selected using a vertical region of interest. 
         [0111]      FIG. 10  shows an exaggerated schematic view of a region of interest of a calibration image used to determine a distortion of an optical device. 
         [0112]    The exaggerated view  275  of a selected parallel line is depicted in two shadings to indicate blurring at an edge. 
         [0113]    The curvature  265  of one or more of the parallel lines may be obtained using the same or similar algorithms as discussed above with regard to  FIG. 8  in connection with determining a field of curvature. 
         [0114]    Once the curvature  265  of a line has been determined, the distortion dx  260  may be defined as the distance between a tangent to the curve and drawn parallel to the nominal vertical direction of the lines in the grid, measured horizontally at a selected point at which the distortion is required to be measured. 
         [0115]      FIG. 11  shows a schematic, isometric view of one preferred embodiment of a wedge of the present invention. 
         [0116]    The wedge  155  has a flat, base surface  165  and a first planar surface  115 . The first planar surface  115  contains a structure of uniformly periodic linear elements  111  and is separated from the flat, base surface  165  by an acute angle α  130 . 
         [0117]    The wedge  155  may be machined, additively manufactured or extruded from any suitable material such as, but not limited to, plastic, glass, aluminum, stainless steel or titanium, or some combination thereof. 
         [0118]    The wedge  155  may also be composed of at least two elements such as, but not limited to, the triangular prism itself and a separate structure attached to the hypotenuse of the triangular prism that may be the structure of uniformly periodic linear elements  111 . The structure of uniformly periodic linear elements  111  may, for instance, be a well-known Ronchi ruling. 
         [0119]      FIG. 12  shows a schematic, isometric view of a further preferred embodiment of a wedge device of the present invention. 
         [0120]    The wedge device shown in  FIG. 12  has the planar surface  115  with uniformly periodic linear elements  111  having a first periodicity, separated from a flat, base surface  165  by the acute angle α  130 . In addition there is a second flat plane  285  having a second structure of uniformly periodic linear elements  280 . The periodicity of the first and second uniformly periodic elements may, or may not, have the same periodicity. Having the same periodicity may, for instance, reduce manufacturing costs, while having different periodicities may, for instance, simplify the analysis of calibration images. 
         [0121]    As the second flat plane may be located adjacent to the first flat plane, with the linear elements each being oriented parallel to each other device, imaging of the second uniformly periodic structure may be used to obtain a measure of an angle between said optical axis of the optical device and a normal to the flat base surface. This measurement may either be used to orient the optical axis of the imaging device to be normal to the flat, base surface  165 , or it may be used with the known acute angle α  130  to more accurately measure the actual angle between the optical axis of the imaging device and the normal to the first planar surface  115 . 
         [0122]    For instance, using the methods described above in connection with  FIG. 6  in determining the depth of focus. 
         [0123]    For instance, the tilt of the flat, base surface  165  may be determined by methods such as, but not limited to, using edge detection or modulation detection to determine magnifications at two positions separated along a distance perpendicular to the direction of the linear elements. Knowing the distance between the two measured magnifications, the tilt, i.e., the angle to which the optical axis of the imaging device is not perpendicular to the flat, base surface  165  may then be determined by rearranging the equations above to solve for the angle. 
         [0124]      FIG. 13A  shows a schematic, isometric view of yet a further preferred embodiment of a wedge device of the present invention arranged for storage while  FIG. 13B  shows the wedge device arranged for use. 
         [0125]    The first planar surface  115  having the first uniformly periodic linear elements  111  may be attached to the second flat plane  285  having the second uniformly periodic linear elements  280  by a first pivot  290 . 
         [0126]    There may also a pivoting support piece  305  attached to the second flat plane  285  by a second pivot  295 . 
         [0127]    When arranged for storage, as shown in  FIG. 13A , the first planar surface  115  may be pivoted down so that it is parallel with the second flat plane  285 , while the pivoting support piece  305  is also arranged to be parallel to the second flat plane  285 . This arrangement makes the device convenient for storage and for transportation. 
         [0128]    When arranged for use, as shown in  FIG. 13B , both the first planar surface  115  and the pivoting support piece  305  have been pivoted up so that the first planar surface  115  may now be supported by the pivoting support piece  305  at a required acute angle α  130 . This arrangement may be held in place by a suitable latching element temporary fixing the first planar surface  115  to the pivoting support piece  305 . This latching may, for instance, be done mechanically or using suitable magnets. 
         [0129]      FIG. 14  shows a schematic, front view of an object image having fiducial markers added using the method of this invention. 
         [0130]    The object image  152  may have an image of an object  151  taken using the imaging device. The object image  152  may then have one or more fiducial markers  191  added to or associated with the image. These fiducial marker  191  may rely on optical properties of the imaging device determined during calibration using one or more of the methods described above such as, but not limited to, magnification. The fiducial marker  191  may take the form of additions such as, but not limited to, scale readings, show limits or desired sizing, a circular or arc radius or diameter, linear distance or angle between image features, or some combination thereof. 
         [0131]    Although this application has been described with regard to the situation in which the structure of uniformly periodic linear elements has the linear elements perpendicular to the sides of the wedge, one of skill in the optical and mathematical arts may apply similar methodologies as those described in the application, to a wedge device in which the linear elements are parallel to the sides of the wedge. 
         [0132]    For instance, a point of best focus with such a wedge may be calculated by taken a number of regions of the calibration images normal to the imaged linear elements. A degree of focus may then be found in each of these regions, and by then fitting a curve to those measurements, a sub-pixel determination of the point of best focus may be made. 
         [0133]    Similar methods may be used to obtain other optical properties of the imaging device using such a wedge in which the lines are parallel to the edges of the wedge. 
         [0134]    Although this invention has been described with a certain degree of particularity, it is to be understood that the present disclosure has been made only by way of illustration and that numerous changes in the details of construction and arrangement of parts may be resorted to without departing from the spirit and the scope of the invention.