Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
  • G01B11/00—Measuring arrangements characterised by the use of optical techniques
  • G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
  • G01B11/255—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures for measuring radius of curvature
• • A—HUMAN NECESSITIES
  • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
  • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
  • A61B3/00—Apparatus for testing the eyes; Instruments for examining the eyes
  • A61B3/10—Objective types, i.e. instruments for examining the eyes independent of the patients' perceptions or reactions
  • A61B3/107—Objective types, i.e. instruments for examining the eyes independent of the patients' perceptions or reactions for determining the shape or measuring the curvature of the cornea

Definitions

• This invention relates to instruments for measuring surface topography, and more particularly, to such instruments known as keratoscopes.
• Gersten et al US patent 4,863,260 discloses a computer-controlled corneal mapping systems for providing quantita ⁇ tive topographic information about a corneal surface illuminated with a structured light pattern, such as a series of concentric light bands. Because the edges of the light pattern bands must be ascertained, a considerable amount of image processing is required, including various curve-fitting algorithms in order to re-construct the corneal topography.
• the topography of a three-dimensional specular surface such as a cornea
• a three-dimensional specular surface such as a cornea
• the inverse transform is taken and then the inverse tangent of the quotient of the imaginary and real portions of the inverse transform are computed to obtain the local spatial phase.
• the local spatial phase may be "unwrapped" and the unwrapped phase differentiated to obtain the instantaneous local spatial frequencies at discrete pixels. These local spatial frequencies may then be mapped to the known diopters of the spheres by a process of curve f itting .
• the local spatial phase is "unwrapped" to obtain continuous values of local spatial phase with distance from the optical axis of the image.
• the distances from the optical axis at which predetermined values of the local spatial phase occur correspond to the positions of the illuminated rings of the pattern.
• the distances obtained from processing images of surfaces whose dioptric powers are known are compared and tabulated with corresponding distances in the original illuminated object to determine the local magnification produced by each surface. Images of surfaces having unknown dioptric powers may then be mapped to diopters by consulting the tabulation. Accuracy beyond that determined by the granularity of pixel position is obtained.
• the accuracy of topographic analysis is enhanced by allowing the locating light beams to remain on while the image is being acquired and by eliminating the effect of the glare during image processing.
• Mislocation of the apex of the surface in the x, y, or z direction is detected by determining the location of the light beams in the image and any such mislocation, such as may arise from inadvertent movement of the subject is compensated for.
• Fig. 1 is a sectional view showing a quasi-spherical specular surface properly positioned in the conical Placido disc apparatus of prior art patent 4,863,260, while Figs. lA and IB show the surface too closely and too remotely positioned, respectively;
• Fig. 2A shows one of the rings reflected in the image of the quasi-spherical surface, while Fig. 2B shows exaggerated glare spots in the image;
• Fig. 3A is a plot of the intensity of surface illumination versus radial distance for a quasi-periodic pattern reflected from the specular surface;
• Figs. 3B and 3C show the corresponding wrapped and unwrapped local spatial phase of the processed image;
• Figs, 3D and 3E show the unfiltered and filtered Fourier spectra of a processed image;
• Fig. 4 is a flow chart for processing the scanned image to relate local spatial frequency at regularly-spaced pixel positions to diopters of refraction
• Figs. 5A and 5B are flow charts for procedures involved in processing the image of a specular surface to remove the effects of glare and improper positioning of the surface;
• Figs. 6A and 6B are flow charts for processing the scanned image to relate distances obtained from the unwrapped local spatial phase to diopters of refraction.
• Figs. 7 and 8 are photographs of a human cornea shown before and after processing to remove the effects of glare.
• Fig. 1 there is shown a section through the prior art illuminated Placido disc cone device 10 described in U.S. patent 4,863,260 and in US patent 5,416,539.
• Cone 10 causes a quasi-periodic mire pattern to be reflected from a quasi-spherical specular surface 6, such as a human cornea or polished steel ball, positioned at its left-hand side.
• Cone 10 has a hollow, substantially cylindrical bore 11.
• a light source (not shown) is positioned at the right-hand side base of cone 10.
• a series of opaque bands 9 divides the otherwise transparent bore 11 into a series of illuminated rings 13, of which only rings 13-1 and 13-2, spaced the distance S apart, are individually labelled in Fig.l. In the illustrated embodiment, each of rings 13 is of the same diameter h.
• the specular surface 6 reflects a virtual image of the illuminated rings 13.
• each ring would be reflected, as shown in Fig. 2A, as a circle 13'.
• Fig. 2B greatly enlarged sectors of three illustrative virtual image rings, 13-1', 13-2' and 13- 3', are shown.
• Fig. 1 shows an edge view of only one of these virtual image rings, 13'. Ring 13' appears to lie at some distance beneath the specular surface 6.
• a ray incident upon a spherical mirror aimed at the focus, f will be reflected parallel to the optical axis and will produce a virtual image which appears to lie beneath the surface of the sphere while a ray directed perpendicular to the surface toward the surface's center of curvature will be directed back upon itself.
• the reflected ray should be projected parallel to the optical axis until it intersects the ray directed to the center of the sphere. This is illustrated in Fig. 1 with respect to two rays 13f and 13c from illuminated object ring 13-1 of cone 10.
• Ray 13c is directed to the center of curvature, C, of spherical surface 6 while ray 13f is directed to the focus, (which lies a distance f beneath the surface) .
• the plane of the virtual image 13' of object ring 13-1 is located by projecting reflected ray 13f parallel to the optical axis until it strikes the projection of ray 13c.
• the virtual image ring 13' is defined by the intersection of light ray 13c, which is directed perpendicular to the specular surface 6, i.e., toward its center of curvature, C, and the backward extension of ray 13f, which passes through the focus of specular surface 6, parallel to optical axis A-C.
• specular surface 6 As explained in the aforementioned '260 patent, the proper positioning of specular surface 6 is indicated when intersecting light beams LI and L2 (advantageously laser beams) converge at single point A at the apex of the specular surface 6.
• point A When surface 6 is properly positioned so that point A is on the optical (Z) axis which runs through the center of bore 11 of cone 10, point A will lie in the center of the field of camera 41 and the distance _ between point A and the camera 41 is accurately known.
• the reflection 17' of fixation light 17 from pellicle 16 will also appear at point A. If, however, surface 6 is positioned too far into bore 11 (Fig. 1A) , or too far out of bore 11 (Fig.
• the image of surface 6 is acquired by electronic camera 41, through lens 40.
• Processor 42 scans the image acquired by camera 41 in a direction orthogonal to the illuminated pattern that is reflected from surface 6, e.g., an illuminated ring pattern is scanned radially.
• bore 11 of cone 10 were provided with illuminated longitudinal stripes (not shown) parallel to the axis of the cylindrical bore 11, such longitudinal stripes would cause a pattern of radial lines to be reflected from quasi-spherical surface 6 and orthogonal scanning of such radial lines would be in a circular direction.
• Fig. 3A shows the waveform of video intensity versus orthogonal scanning distance in the image acquired by processor 42.
• the average frequency of the waveform is determined by the average spacing (see, for example, illustrative spacing "S", Fig. 1) of the illuminated rings of the Placido disc source of the light pattern.
• S illustrative spacing
• Fig. 1 the average spacing of the illuminated rings of the Placido disc source of the light pattern.
• the instantaneous spatial frequency of the pattern will vary as surface imperfections distort the local light pattern.
• the frequency spectrum of the video image scanned orthogonally to the quasi-periodic pattern may be ascertained by taking a discrete Fourier transform of the scanned image, using an analytic filter to suppress all side lobes and negative spatial frequencies in the Fourier spectrum except for the narrow band of frequencies adjoining the fundamental spatial frequency, taking the inverse transform and finding the inverse tangent of the quotient of the imaginary and real portions of the inverse transform to obtain the instantaneous spatial phase.
• the Fourier spectrum of the two-dimensional image is shown in Fig. 3D.
• the Fourier spectrum of the image after processing to suppress all side lobes and negative frequencies is shown in Fig. 3E.
• the real component, R(x), of the inverse transform has the form:
• the instantaneous phase is a saw-tooth or ramp-like function, shown in Fig. 3B, having discontinuities every 2 ⁇ r radians.
• the derivative of the instantaneous phase waveform is the instantaneous frequency (which also has discontinuities every 2ir radians) :
• phase unwrapping which employs threshholding and numerical interpolation, as described, for example, in the article by Mitsuo Takeda, Hideki Ina and Soiji Kobayashi entitled “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry", published in J. Opt Soc. Am, vol. 72, no. 1, January 1982 at pp. 156 - 160, see also, the article by Jose M. Tribolet, entitled “A New Phase Unwrapping Algorithm”, published in the IEEE Transactions on Acoustics, Speech, and Signal Processing, VOl ASSP-25, No. 2, April 1977, pp.170-177.
• the unwrapped phase may be differentiated to obtain the instantaneous local spatial frequencies which may then be mapped to diopters by a process of curve fitting.
• the images of a plurality of known specular surfaces having known dioptric powers of refraction must be processed to obtain the local spatial frequencies exhibited by the illuminated rings in each image.
• the local spatial frequencies exhibited by the illuminated pattern reflected from each of the known surfaces are then mapped to their known dioptric powers by using a curve fitting technique such as least mean squares curve fitting, in which the coefficients of a polynomial to relate these frequencies to diopters is determined, e.g.:
• the local spatial frequencies obtained from processing the image of an unknown corneal surface may be employed with the determined polynomial to ascertain the corresponding diopters of that surface.
• Fig. 3C shows the video intensity I (x) encountered in the x direction of scanning (i.e., orthogonally to the quasi-periodic pattern).
• I (x) encountered in the x direction of scanning (i.e., orthogonally to the quasi-periodic pattern).
• the first and second 2 ⁇ points in the processed image occur at the distances, x r1 and x r2 from the center of scanning, e.g., from the optical axis.
• the radial scanning distance at each 2v point is the radius of a ring in the image and twice this radius is the diameter h' of the ring.
• diameter of the illustrative illuminated ring 13-1 on the bore 11 of Placido disc cone 10 is h.
• the ratio h/h' of the size of the original object to the size of its reflected image is the magnification M produced by the specular surface 6.
• FIG. 3C shows that the unwrapped local spatial phase gives a continuous series of values intermediate each set of 2 ⁇ points.
• the dimension h is constant.
• Each 2 ⁇ point corresponds to a ring in the image but the dimension h' of each such image ring is determined by the local magnification of surface 6 at the point.
• the intermediate scanning distances corresponding to the "imaginary" intermediate rings in the image.
• magnification corresponding to each of these intermediate spatial phase points may be ascertained simply by dividing the corresponding intermediate scanning distance n x r M by the constant dimension h, without need of any curve fitting.
• Step 501 entitled "load matched filter” loads an image of a paradigm laser spot GS f , which is used as a matched filter.
• the paradigm laser spot is obtained by averaging the values obtained by the appearance of the laser spot on a plurality of different size and color eyes.
• Step 502. labeled "compute RMS filter”, computes the RMS value of the paradigm laser spot GS f by taking the square root of the sum of the squared values of the video intensity found over the area of GS f .
• Step 503. labelled “find laser spot” compares the video intensity I ( ⁇ ) of the illuminated surface on a pixel by pixel basis with the RMS value of spot GS that was obtained in step 502. A laser spot is identified when the video intensity I ( ⁇ ) of a scanned spot exceeds the RMS value of the spot GS, calculated as follows:
• L is the pixel-length of the filter data and OFFSET is the offset to the video data.
• the video data is convolved with the filter data for various values of OFFSET .
• X c is the maximum number of pixels ("pels") in the scanned line.
• Step 504. labelled "clear laser spot 5" calls the procedure detailed in steps 510 through 520 which clears the actual laser spot GS that is found in the scanned image.
• Step 505. labelled “compute axial misalignment” computes the axial misalignment of point A, after laser spot GS has been cleared from the image being processed.
• laser beam LI travels through a tunnel in cone 10 which is at a fixed angle, illustratively, 38 degrees, to the optical axis, Z.
• laser beam LI instead of striking surface 6 at point A, will strike the surface at some distance above point A, such as at distance "!*'.
• laser beam LI will strike the surface at some distance "D” below point A.
• the depth error, ⁇ Z measured along the optical axis, in the positioning of point A is calculated by the following:
• R is the average radius of the specular surface, e.g. , 7.85 mm for the average human cornea.
• ⁇ Z is obtained from equation (10) above.
• the constants A and B are computed by processing a series of images of known diopter specular surface steel balls that have each deliberately been moved a known increment ⁇ Z away from point A and employing > the least squares method to relate the measured diopters to the known diopters of each such surface.
• Step 505 advantageously may also correct for any lateral misalignment, that is, a displacement of the apex of the cornea of the patient's eye from the assumed position, point "A" (Fig. 1) , in the X or Y
• the origin for the radius of curvature, R is at point 0,0,0 and the coordinates of point A are x, y, z.
• Equation (14) can be simplified by resorting to a Taylor series expansion and neglecting all terms after the first two. Accordingly, :
• Equation (16) can similarly be simplified to yield:
• PowerPtr is an array containing the observed dioptric powers of the map from the Fourier processing of the two-dimensional image, indexed by current ring number, iring, and current angle, jphi (both integer numbers) .
• the angl of the sinusoidal function, sin( (iring/ring_total_for_cone) is the fraction of the current ring number, iring, divided by the maximum number of rings, ring_total_for_cone.
• the quantity dx is the displacement ⁇ x in the X direction of the point "A", as measured from the departure of the position of the fixation ligh 17', Fig. 1 from the center of the frame buffer of processor 42 storing the digitized information acquired by camera 41.
• KMetric Index / r_c is th dioptric power at the radius r e. —.
• Step 506 labelled "find iris laser spot 2" examines the video intensity values in the region of point A (see Fig. 1) of the scanned image. When video intensity values exceeding the predetermined value expected for the image 17' of the fixation light 17 (see Fig. 1) , Step 507. labelled “clear laser spot 8" i executed. This procedure is detailed in steps 530 through 539. Clear Laser Spot 5 (Steps 510-5191 : This procedure clears the laser spot GS from the image bein processed.
• Step 511 initializes the scanning angle ⁇ for the acquisition of video data, I ( ⁇ ) along the scan line.
• Step 512 loads the video data, I ( ⁇ ) obtained along the scan line.
• Step 513 performs a fast Fourier transform (FFT) of the video data along the scan line.
• FFT fast Fourier transform
• Step 514 finds the peak value of the Fourier transform.
• Step 515 filters the signal around the peak value.
• Step 516 scales the FFT data to ensure that the image being placed on the screen is neither too light nor too dark.
• Step 517 performs an inverse FFT.
• Step 518 stores the results of processing the scan line data.
• Step 519 increments the scan angle until the maximum value is reached. Steps 511 through 519 are then performed again until, illustratively, 256 radial scans are performed.
• Step 531 initializes the scan radius to STATRAD the starting radius of the iris so that the laser spot can be found in this area.
• STATRAD the starting radius of the iris
• Steps 532 through 535. 536 and 538 These steps are similar to steps 512 through 515, 517 and 518, except that the data being operated upon is data pertaining to the iris portion of the eye.
• Step 537 labelled "DC restoration of image” restores the DC of the video signal in the area of laser spot GS, which is much brighter than the DC levels elsewhere in the image, to the DC level existing in the adjacent sectors A-l and Bl, (see Fig. 2B) .
• Figs. 6A and 6B are flow charts for processing the two- dimensional image of a three-dimensional surface to ascertain th diopters of refraction present over the surface.
• steps 601 through 609 and 620 and 630 are illustrated. Of these steps, steps 601 through 609 are roughly comparable to steps 401 through 409 of Fig. 4.
• Fig. 6B shows the details of step 620 of Fig. 6A in which the distance perpendicular to the optical axis corresponding to each incremental value of local spatial phase i obtained so that diopters can be found as a function of incremental values of perpendicular distance rather than as a function of increments fixed by pixel position.
• Steps 601 and 602 These steps acquire the two-dimensional video image of the three-dimensional surface whose topography is to be measured and are comparable to steps 401, 402 and 403 of flow chart Fig. 4.
• Steps 605 and 606 These steps perform the Fourier transform on the acquired two-dimensional video data and employ a Hubert transform and band-pass filter to suppress negative frequencies and all sidebands in the Fourier spectrum allowing only the majo sideband of the first harmonic to pass to the next step. These steps are alternative, preferred processing steps to steps 404 through 406 of Fig. 4.
• Step 607 performs the inverse Fourier transform to obtain the complex analytical signal having real and imaginary portions and is comparable to step 407 of Fig. 4.
• Step 608 obtains the arc tangent of the quotient of the real an imaginary portions of the complex signal to obtain the wrapped spatial phase and is comparable to step 408 of Fig. 4.
• Step 609 This step performs the step of phase-unwrapping and is comparable to step 409 of Fig. 4 which differentiates the . discontinuous local spatial phase obtained in step 408 to obtain continuous values of local spatial frequency. However, unlike step 409, step 609 advantageously re-integrates the continuous values of local spatial frequency to obtain continuous values of local spatial phase.
• Step 620 This procedure is detailed in Fig. 6B. Briefly, the continuous values of local spatial phase are inspected to ascertain the radial distance from the optical axis at which the local spatial phase exhibits values that are multiples of 2 ⁇ r. These local spatial phase values occur at the positions where the surface being measured reflects each of the rings in the illuminated pattern.
• Step 630 This step samples the continuous values of local spatial phase and, during the calibration phase when the images of a plurality of known surfaces are processed, relates the local spatial phase values using a least-means-squares procedure to the known dioptric powers of the surfaces.
• a calibration matrix of dioptric power vs. spatial phase values is assembled. Thereafter, the calibration matrix is employed to ascertain the dioptric powers exhibited by an unknown surface from the processing of its image to yield continuous values of local spatial phase.
• Step 621 sets the count for ring# to 1 at the start of the procedure for finding the distances obtaining at values of local spatial that are multiples of 2 ⁇ .
• Step 622 sets the variable ringposphase to the count provided by step 621 multiplied by 2 ⁇ .
• Step 623 increments the count of the counter for the array "ipix" which is an array (signified by the use of square brackets) of local spatial phase values exhibited at the pixel positions of the processed image.
• Step 624 determines whether the phase value exhibited in the current pixel position of the array is less than the variable ringposphase and whether the end of the array has been reached.
• Step 625 determines for each increment of local spatial phase the corresponding distance in the image.
• Step 626 increments the count for ring #.
• Step 627 determines whether the maximum number of ring positions, illustratively 25, has been reached. If not, processing continues with a repetition of steps 622 through 627
• Fig. 4 is a flow chart of the basic steps for analyzing a two-dimensional image of a three-dimensional surface and employing discrete Fourier transform processing to relate local spatial frequencies in the processed image to the three- dimensional radius or diopters of refraction of the surface.
• steps 401 entitled “locate 1st ring circumference” and 402 entitled “locate center of 1st ring subpixel offsets x & y” locate the point from which the pattern in the image will be scanned in step 403.
• line 9 et seq. of the aforementioned Gersten, et al, patent 4,863,269 the center point is determined from the first ring pattern appearing in the image.
• the Hamming window filter in step 404 so that the side lobes of the Fourier spectrum obtained in the FFT step 405 will be suppressed.
• the Fourier spectra is subjected to a Hahn filter in step 406 so that only major side bands of the first harmonic are passed.
• the inverse Fourier transform is obtained in step 407, the arctangent of the quotient of the imaginary divided by the real components of the inverse transform yields the local spatial phase in step 408.
• the local spatial phase is differentiated in step 409 to obtain the local spatial frequency and, in step 410, a polynomial is found using the leas squares curve fitting technique to map the local spatial frequencies to diopters from the processed images of a number of known surfaces.
• the dioptric powers obtained from the processing are plotted in their correct positions.
• sample_meridian debug, ringl, itheta, -xmean

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