WO2010005457A1 - Techniques de traitement de données ophtalmiques - Google Patents

Techniques de traitement de données ophtalmiques Download PDF

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WO2010005457A1
WO2010005457A1 PCT/US2009/002687 US2009002687W WO2010005457A1 WO 2010005457 A1 WO2010005457 A1 WO 2010005457A1 US 2009002687 W US2009002687 W US 2009002687W WO 2010005457 A1 WO2010005457 A1 WO 2010005457A1
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wavefront
vergence
coefficients
information
exemplary method
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PCT/US2009/002687
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Larry N. Thibos
Jayoung Nam
Daoud Robert Iskander
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Indiana University Research & Technology Corporation
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    • 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
    • A61B3/0016—Operational features thereof
    • A61B3/0025—Operational features thereof characterised by electronic signal processing, e.g. eye models

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  • the technical field relates generally to ophthalmic data processing techniques, and more particularly but not exclusively to methods of processing measured wavefront data to determine ophthalmic prescriptions.
  • Ophthalmic data processing of ocular wavefront aberrations is important for a number of ophthalmic instruments including Hartmann Shack wavefront sensors, Hartmann-Moire wavefront sensor, diffraction wavefront sensors, curvature sensors, various interferometers, scanning laser ophthalmoscopes, scanning fundus cameras, nerve fiber analyzers, optical coherence tomography systems, retina imaging instruments such as laser ray tracing instruments and point spread function cameras or other ophthalmic sensor systems that employ adaptive optics, for example, to improve performance by measuring and then correcting the eye's aberrations.
  • Present approaches to processing ophthalmic data suffer from a number of limitations and disadvantages including those relating to introduction of processing or systemic error, computational complexity and intensity, esoteric data output and others. There is a need for the unique and inventive ophthalmic data processing techniques disclosed herein. BRIEF DESCRIPTION OF THE FIGURES
  • Fig. 1 illustrates a simplified schematic diagram of an exemplary ophthalmic wavefront sensor.
  • Fig. 2 illustrates an exemplary coordinate system.
  • Fig. 3 illustrates an exemplary coordinate system.
  • Fig. 4 illustrates an exemplary process for determining an ophthalmic prescription.
  • Fig. 5 illustrates an exemplary process for reconstructing a wavefront
  • Fig. 6 illustrates an exemplary second order quadratic surface which is identical to an exemplary original wavefront when determined based upon any of a first exemplary method, second exemplary method, or a third exemplary method.
  • Figs. 7a, 7b, 7c and 7d illustrate a comparison of a wavefront and equivalent quadratic surfaces.
  • Fig. 7a illustrates an exemplary original wavefront.
  • Fig. 7b illustrates an exemplary equivalent quadric determined based upon a first exemplary method.
  • Fig. 7c illustrates an exemplary equivalent quadric determined based upon a second exemplary method.
  • Fig. 7d illustrates an exemplary equivalent quadric determined based upon a third exemplary method.
  • Figs. 8a, 8b, 8c and 8d illustrate a comparison of a wavefront and equivalent quadratic surfaces.
  • Fig. 8a illustrates an exemplary original wavefront.
  • Fig. 8b illustrates an exemplary equivalent quadric determined based upon a first exemplary method.
  • Fig. 8c illustrates an exemplary equivalent quadric determined based upon a second exemplary method.
  • Fig. 8d illustrates an exemplary equivalent quadric determined based upon a third exemplary method.
  • Figs. 9a, 9b, 9c and 9d illustrate a comparison of a exemplary wavefront and exemplary equivalent quadratic surfaces.
  • Fig. 9a illustrates an original wavefront with a Seidel aberration.
  • tig. yo illustrates an exemplary equivalent quadric determined based upon a first exemplary method.
  • Fig. 9c illustrates an exemplary equivalent quadric determined based upon a second exemplary method.
  • Fig. 9d illustrates an exemplary equivalent quadric determined based upon a third exemplary method.
  • Fig. 10a illustrates an exemplary wavefront vergence map.
  • Fig. 10b illustrates an exemplary wavefront vergence map.
  • Fig. 10c illustrates an exemplary wavefront vergence map.
  • Fig. 11a illustrates an exemplary wavefront vergence map.
  • Fig. l ib illustrates an exemplary wavefront vergence map.
  • Fig. 12 illustrates an exemplary vergence map.
  • Figs. 13a illustrates an exemplary original wavefront.
  • Fig. 13b illustrates an exemplary an exemplary wavefront for an equivalent quadratic determined according to a first exemplary method.
  • Fig. 13c illustrates an exemplary wavefront for an equivalent quadratic determined according to a second exemplary method.
  • Fig. 13d illustrates the resulting wavefront for the equivalent quadratic determined according to a third exemplary method.
  • Fig. 14 illustrates an exemplary vergence map.
  • Fig. 15a illustrates a contour map for an exemplary original wavefront.
  • Fig. 15b illustrates a contour map for an exemplary equivalent quadratic determined in accordance with a first exemplary method.
  • Fig. 15c illustrates a contour map for an exemplary equivalent quadratic determined in accordance with a second exemplary method.
  • Fig. 15d illustrates a contour map for an exemplary equivalent quadratic determined in accordance with a third exemplary method.
  • Fig. 16a illustrates exemplary comparison curves for an exemplary coefficient M.
  • Fig. 16b illustrates exemplary comparison curves for an exemplary coefficient J 0 .
  • Fig. 16c illustrates exemplary comparison curves for an exemplary coefficient J 45 .
  • Fig. 17 illustrates exemplary pairwise comparison curves.
  • Fig. 1 illustrates a simplified schematic diagram of an exemplary ophthalmic wavefront sensor system 100.
  • System 100 includes laser 110 which is operable to emit laser beam 120.
  • Laser beam 120 is directed to optics system 130 which directs laser beam 120 though pupil 142 to spot 150 on the retina of eye 140.
  • Wavefront 160 is reflected from spot 150, exits through pupil 142 of eye 140, and travels through optics system 130 to sensor system 170.
  • Sensor system 170 includes a sensor which is operable to measure information of wavefront 160.
  • Sensor system 170 provides measured information of wavefront 160, such as wavefront slope information, to processing system 180 which includes computer executable instruction operable to perform processing operations on the measured information including the operations described herein.
  • system 100 is one simplified example of an ophthalmic wavefront sensor system and that a number of embodiments include additional or alternate ophthalmic sensor systems including, for example, Hartmann Shack wavefront sensors, Hartmann-Moire wavefront sensor, diffraction wavefront sensors, curvature sensors, various interferometers, scanning laser ophthalmoscopes, scanning fundus cameras, nerve fiber analyzers, optical coherence tomography systems, retina imaging instruments such as laser ray tracing instruments and point spread function cameras or other ophthalmic sensor systems that employ adaptive optics, for example, to improve performance by measuring and then correcting the eye's aberrations.
  • ophthalmic sensor systems including, for example, Hartmann Shack wavefront sensors, Hartmann-Moire wavefront sensor, diffraction wavefront sensors, curvature sensors, various interferometers, scanning laser ophthalmoscopes, scanning fundus cameras, nerve fiber analyzers, optical coherence tomography systems, retina imaging instruments such as laser ray tracing instruments and point spread function cameras or other
  • Sensor system 170 is operable to provide measured information of wavefront 160 to processing system 180.
  • processing system 180 includes one or more microprocessors, ASICs and/or other processing means operable to execute instructions, and computer readable medium or media configured to store computer executable instructions, for example one or more memory modules configured with software, firmware or combinations thereof.
  • processing system is operable to determine ophthalmic prescriptions directly from the slope measurements without requiring wavefront reconstruction.
  • Processing system 180 can perform such operations by fitting the measurement data with a set of orthonormal basis functions which are referred to herein as Zemike Radial Slope Polynomial(s) ("ZRSP(s)").
  • ZRSPs provide a complete, linearly independent orthonormal set of basis functions for describing the radial component of wavefront slope over circular pupils.
  • a linear transformation from the wavefront domain to the refractive error domain is not necessary for determining ophthalmic prescriptions when using ZRSPs, because an equivalent quadratic wavefront (for example the best sphero- cylindrical approximation to a vergence map) can be obtained directly from coefficients of ZRSPs fit to wavefront slope measurements obtained by ophthalmic wavefront sensors, hi some embodiments an ophthalmic prescription is provided in terms of M (spherical lens diopter power), J 0 (cross-cylindrical diopter power), and J 45 (cross-cylinder diopter power). In some embodiments an ophthalmic prescription is provided in terms of S (spherical diopters), C (cylinder diopters), and A (cylinder axis degrees) " derived from M, Jo and J45.
  • processing system 180 is operable to determine wavefront maps and wavefront error or aberration maps, hi some embodiments coefficients for wavefront error or aberration are recovered from coefficients of ZRSPs and a linear transformation is used to perform wavefront reconstruction. Some embodiments determine second order aberrations. Some embodiments determine second, fourth, sixth, eighth, tenth, twelfth and/or higher order aberrations. Some embodiments determine odd-order aberrations including, first, third, fifth, seventh, eleventh or higher order aberrations. Some methods recover both even and odd order aberrations.
  • Fig. 2 illustrates a coordinate system 200 including x axis 210, y axis 220, z axis 230, power vector 240 and point 250.
  • Point 250 is described by three numbers (M, J 0 ,J 45 ) , which correspond to the concatenation of three lenses: a spherical lens of power M , a cross-cylinder with principal powers +J 0 on the horizontal meridian and -J 0 on the vertical meridian, and a second cross-cylinder with principal powers +J 45 on the 45° oblique meridian and -J 45 on the 135° oblique meridian.
  • M spherical lens of power M
  • a cross-cylinder with principal powers +J 0 on the horizontal meridian and -J 0 on the vertical meridian and a second cross-cylinder with principal powers +J 45 on the 45° oblique meridian and -J 45 on the 135° oblique
  • (M, J 0 , J 45 ) can be represented as coordinates of a point in 3-dimensional space with each of the (x,y,z) axes of the coordinate reterence trame having units of diopters.
  • a power vector drawn from the origin to this point in dioptric space is a concise geometric representation of refractive prescriptions that is amenable to quantitative analysis.
  • the coordinates of power vectors such as power vector 240 are proportional to second-order ZRSP coefficients that describe the wavefront error produced by sphero-cylindrical lenses.
  • wavefront refraction can be described based on an equivalent quadratic, which is defined as the sphero-cylindrical wavefront that represents the eye's wavefront aberration map.
  • An ophthalmic prescription represents the lens that optimally corrects the equivalent quadratic wavefront, and provides a corrective prescription.
  • Certain exemplary embodiments describe optical aberrations such as refractive error of a patient's eye with a vergence map.
  • Vergence is a measure of the convergence or divergence of a pair of light rays, defined as the reciprocal of the distance between a point of reference and the point at which the rays intersect. More rigorously vergence V(r, ⁇ ) is defined as a meridional property of an optical system defined over the limiting circular aperture of the system. There is a connection between measured vergence errors associated with a wavefront of light, measured wavefront slopes, and reconstructed wavefront phase.
  • the radial component of wavefront slope can be used to compute vergence errors by dividing by the radial distance of the pupil entry point to the pupil center.
  • the resulting two- dimensional map of vergence errors can be used to uniquely determine wavefront aberrations.
  • the prescription for a sphero-cylindrical correcting lens can be derived from vergence maps directly, without requiring wavefront reconstruction.
  • Fig. 3 illustrates a coordinate system 300 for wavefront vergence V ⁇ r, ⁇ ) .
  • the (x, y, z) coordinates are constructed such that the z-axis is the chief ray and the x, y plane is perpendicular to the z-axis at the center of the exit pupil 442.
  • the plane of the diagram intersects the (x, y) plane in a line which becomes a radial r-axis inclined at angle ⁇ to the horizontal.
  • the z-axis is orthogonal to the wavefront but not necessarily orthogonal to the exit pupil.
  • the chief ray is used as a reference z-axis which is perpendicular to the wavefront at the pupil center.
  • the pupil center is used as the origin of a Cartesian coordinate reference frame used to specify the system's known wavefront error W(r, ⁇ ) in polar coordinates.
  • Fig. 3 illustrates the general case of central or peripheral vision.
  • the path of the chief ray from object point to the foveal center is also the primary line- of-sight.
  • the path of the chief ray from object point to the retinal location of interest is a secondary line-of-sight.
  • the axial component of vergence is sufficient to reconstruct wavefront phase even when skew rays are present.
  • the one dimensional function V ⁇ ) can be referred to a power profile.
  • the power vector coordinates (M, J 0 , J 45 ) are the coefficients of a Fourier series expansion of the power profile.
  • the minus sign in this and similar equations herein reflects the fact that prescriptions for correcting lenses have the opposite sign of ocular wavefront errors.
  • Some embodiments use a second exemplary method which includes a technique of vergence analysis including least-squares fitting of a vergence map with orthogonal basis functions.
  • Some embodiments fit a full, 2-dimensional vergence map with a weighted sum of three basis functions ⁇ 1, cos 29, sin 29 ⁇ , which are orthogonal on the circular domain.
  • the coefficients M , J 0 and J 45 can be obtained by determining the inner product of the vergence map with each basis function.
  • the coefficient M can be obtained in accordance with Equation 3: the coefficient J 0 can be obtained in accordance with Equation 4: d the coefficient J 45 can be obtained in accordance with Equation 5: ⁇ . max
  • the parameter T n ⁇ x is the radius of the circular domain of the pupil.
  • Some embodiments use a third exemplary method which includes a technique of vergence analysis including pooling vergence over a radius by radial averaging. Pooling vergences spanning the full diameter of the pupil for any given meridian reduces a 2- dimensional vergence map to a 1 -dimensional power profile, from which power vectors can be derived by Fourier analysis. Some embodiments take the arithmetic average as one way to perform this pooling. Some embodiments use another approach in which the coefficient M can be obtained in accordance with Equation 6: L
  • Equation 7 The coefficient J 0 can be obtained in accordance with Equation 7:
  • Equation 8 Some embodiments utilize another approach in which the coefficient M can be obtained in accordance with Equation 9: J the coefficient J 0 can be obtained in accordance with Equation 10: the coefficient J 45 can be obtained in accordance with Equation 11 :
  • Other embodiments use additional or alternate weighting functions.
  • the wavefront W is the sum of the second order Zernike functions as described by Equation 12: the radial slope of the wavefront is described by Equation 13: and the vergence map is described by Equation 14:
  • the first exemplary method gives the power vector components:
  • the second exemplary method and third exemplary method give the same answer for this case of second order sphero-cylindrical refractive errors.
  • An illustrative comparison of the first exemplary method, the second exemplary method and the third exemplary method in the case of higher order aberrations is as follows. W is the sum of defocus and spherical aberration as described by Equation 15:
  • Equation 16 The radial slope of the wavefront W is obtained by differentiation as described by Equation 16:
  • the second exemplary method a least-squares fit over the whole pupil, gives the power vector components:
  • the third exemplary method averaging vergence over the pupil diameter for each meridian, gives the power vector components: O.
  • the power vectors determined according to the first exemplary method are:
  • the power vectors determined according to the second exemplary method are:
  • the power vectors determined according to the second exemplary method are:
  • the first, second and third exemplary methods produce the same results for operations that contain only second-order aberrations of defocus and astigmatism. For higher order aberrations, the first, second and third exemplary methods produce different results.
  • the method of choice for a given application may be selected based upon a number of factors, including the appropriateness of the underlying assumptions of each method for each specific application.
  • Equation 3 Expanding the set of orthogonal basis functions used in Equations 3, 4 and 5 allows vergence to be represented efficiently by a vector of coefficients that include, and extend, the original power vector coordinates and their associated equivalent quadratic.
  • the wavefront PT is a weighted sum of Zernike functions and the goal is to expand the corresponding vergence map with an appropriate set of basis functions
  • the definition of vergence, V dW I dr ⁇ I r , rearranged as rV - dW I dr can be used to expand the radial component of wavefront slope and then use that result to expand vergence using basis functions.
  • An exemplary candidate for basis functions for wavefront slope is the radial derivatives of Zernike functions described by Equation 18: dZ ⁇ m ⁇ p, ⁇ ) dp
  • Equation 18 the radial derivatives of Zernike functions is used to define a new set of orthogonal basis functions described by Equation 19: where n ⁇ 0,
  • TM are orthogonal because of the trigonometric functions. For a fixed frequency m , and are orthogonal because of the construction of the ZRSPs. The first few examples of are shown in Table 1 below:
  • Table 1 A list of the new basis function Y n m (p, ⁇ ) , n ⁇ 4.
  • ZRSPs of any order can be determined as follows.
  • the angular functions are determined from the sine and cosine functions.
  • the radial functions /?TM(p) are determined in accordance with the following equation:
  • the norm alization function N is:
  • pV the complete expansion of vergence V over the entire pupil can be found by dividing the expansion in Equation 20 by p to give Equation 22: . tig. 4 illustrates an exemplary process 400 for determining an ophthalmic prescription.
  • Process 400 can be implemented in software, hardware, firmware or a combination thereof and a number of systems, for example, processing system 180 described above.
  • Process 400 includes operations 410, 420, 430, 440, 450 and 460. Some embodiments include additional, alternate or fewer operations.
  • Operation 410 determines a measured wavefront information map, such as a wavefront aberration map, from an optical system including a patient's eye, for example by receiving wavefront information, such as wavefront slope information from a wavefront sensor system such as sensor system 170 described above of from another system and storing it in a computer readable medium or media.
  • a measured wavefront information map such as a wavefront aberration map
  • Operation 420 converts the measured wavefront information from an x, y coordinate system to a radial coordinate system.
  • Ophthalmic instruments such as ocular wavefront aberrometers often measure the x- slopes and y- slopes of the wavefront as a pair of values (dW/dx , dW/dy) at each sample point on the pupil.
  • the radial slope of the wavefront in the meridional plane can be determined by forming an inner product of the slope vector with the directional vector (cos ⁇ , sin ⁇ ) .
  • the radial slopes are dimensionless quantities which can be described as:
  • Operation 430 fits the wavefront slope measurements with ZRSPs using one or more of the techniques described herein.
  • Operation 440 determines a vergence map from the ZRSPs.
  • Operation 450 determines power vector coordinates (M, J 0 , J 45 ) based upon the two- dimensional wavefront vergence map. Exemplary techniques for determining power vectors from ZRSPs where the slope BW I dr of the wavefront is known on the circular domain of radius r max (mm) are also provided. The slope of the wavefront on the scaled pupil domain is described by Equation 23:
  • Equation 25 To derive power vectors from the vergence map, the first, second and third exemplary method described above can be used.
  • the vergence map V in can be reorganized by the order of r as follows: ⁇ r max y J ' -
  • Equation 26 the Jo component of the power vector is described by Equation 27: the J 4 5 component of the power vector is described by Equation 28:
  • the weighting coefficients for J 0 and J 45 in Equations 27 and 28 are ⁇ /2 times the weighting coefficients for M in equation 26.
  • the denominators for the power vectors are r ma , while the usual formulas for the power vectors for the wavefront itself contains r ⁇ .
  • Equation 29 the M component of the power vector is described by Equation 29:
  • the Jo component of the power vector is described by Equation 30:
  • Equation 31 the J 45 component of the power vector is described by Equation 31 :
  • Equation 32 the Jo component of the power vector is described by Equation 33: the J 45 component of the power vector is described by Equation 34:
  • Operation 460 determines an ophthalmic prescription based upon the power vector values (M, J 0 , J 45 ) .
  • the power vector values (M 5 J 05 J 45 ) are provided as the prescription.
  • the power vector values (M , J 0 , J 45 ) are converted and presented in terms of S (spherical diopters), C (cylinder diopters), and A (cylinder axis degrees).
  • some embodiments utilize a form of the first exemplary method described herein, some embodiments utilize a form of the second exemplary method described herein, and some embodiments utilize a form of the third exemplary method described herein.
  • Additional embodiments utilize additional least squares fitting techniques, additional paraxial curvature matching techniques, equivalent quadratic fitting techniques, standard deviation of wavefront fitting techniques, peak-valley fitting techniques, RMS fitting techniques, pupil fraction for wavefront (critical pupil) fitting techniques, pupil fraction for wavefront (tessellation) fitting techniques, pupil fraction for slope (tessellation) fitting techniques, pupil fraction for slope (critical pupil) fitting techniques, average blur strength fitting techniques, pupil fraction for curvature (tessellation) fitting techniques, pupil fraction for curvature fitting techniques, pupil fraction for curvature fitting techniques, 50% width (min) fitting techniques, equivalent width (min) fitting techniques, 2nd moment square root (min) fitting techniques, half width at half height (arcmin) fitting techniques, correlation width (min) fitting techniques, Strehl ratio in space domain fitting techniques, light in the bucket (norm)
  • AU members of this family are maximally tangent at the pupil center, where their power profiles are identical, but they differ in their higher-order aberration content.
  • the series approximating W are as follows
  • Equation 24 For each W n , the radial slope of W n can be determined and represent it in terms of basis functions Y n using Equation 24. Power vectors can then be computed using Equations
  • the second and third exemplary methods yield power vectors that depend on the conic constant P of the quadratic surface.
  • the second and third exemplary methods take account of the actual, non-parabolic shape of the meridional cross-section when attempting to represent the wavefront with an equivalent quadratic.
  • the fourth order approximation to W the M component of the power vector is described by Equation 38: the Jo component of the power vector is described by Equation 39: nd the J 45 component of the power vector is described by Equation 40:
  • Equation 41 the Jo component of the power vector is described by Equation 42:
  • Equation 43 the J 4 5 component of the power vector is described by Equation 43 :
  • Equation 44 the M component of the power vector is described by Equation 44: the Jo component of the power vector is described by Equation 45:
  • Equation 46 Equation 46
  • Equation 47 the M component of the power vector is described by Equation 47: the Jo component of the power vector is described by Equation 48: the J 4S component of the power vector is described by Equation 49:
  • the power vector are determined in accordance with Equations 26-28 using Zernike radial slope coefficients BTM .
  • the resulting first few power vectors are:
  • the power vector are determined in accordance with Equations 29-31 and the resulting first few power vectors are:
  • the power vector are determined in accordance with Equations 32-34 and the resulting first few power vectors are:
  • the power vectors for Zernike aberrations of any desired order can be obtained utilizing the additive property of power vectors. For example, to obtain the 6th order Zernike approximations to the wavefront W , then the resulting spherical equivalent M is the sum of the three M values given above. Similarly, the astigmatism values J 0 and J 45 are summed across orders.
  • the power vectors according to the first exemplary method are as follows:
  • the power vectors according to the second exemplary method are as follows:
  • the power vectors according to the third exemplary method are as follows: Note that Zernike polynomials balance higher-order terms with lower order terms to achieve mutual orthogonality. These lower-order r 1 terms are responsible for the presence of higher- order Zernike coefficients in the paraxial power vector solution. A similar misinterpretation must be avoided for the results of the second and third exemplary methods.
  • the smaller weight given to higher-order Zernike coefficients in the power vector for the second exemplary method compared to the first exemplary method means that the wavefront polynomial terms in r 4 and r 6 are contributing more in the second exemplary method than the first exemplary method.
  • the third exemplary method (radial pooling) provides an intermediate weight to the higher-order polynomial terms. Note that Zernike spherical aberration makes no contribution to M in the second exemplary method due to the nature of spatial integration it implements across the pupil.
  • Fig. 5 illustrates an exemplary process 500 for method for recovery of wavefront Zernike coefficients from the vergence coefficients for ZRSPs.
  • Process 500 can be implemented in software, hardware, firmware or a combination thereof and a number of systems, tor example, processing system 180 described above.
  • Process 500 includes operations 510, 520, 530, and 540.
  • Operation 510 determines a wavefront information map such as a wavefront aberration map of an optical system including a patient's eye, for example, by receiving wavefront aberration information, such as wavefront slope information for a wavefront sensor system such as sensor system 170 described above.
  • Operation 520 determines a two- dimensional wavefront vergence map based upon the wavefront slope map to express the radial derivatives of Zernike polynomials as a weighted sum of ZRSPs.
  • the vector of Zernike coefficients C k for single index notation can be described as a vector representation for the wavefront surface W in an abstract space spanned by the orthonormal Zernike basis functions ⁇ Z k ⁇ .
  • the radial derivative dW I dr oi W shares the same Zernike coefficients C k as their representation, but the underlying space is spanned by dZ k I dp , the radial derivatives of the Zernike functions.
  • These basis functions are not mutually orthogonal and its representation vector becomes non-unique; however, each basis function dZ k I dp can be re- expanded as a linear sum of the ZRSPs Y 1 , following a single indexing schemes, where the order / is lower than k as described by Equation 50:
  • Equation 51 Operation 530 determines Zernike coefficients from the weighting coefficients of the
  • Operation 540 determines a wavefront map.
  • the summations are all well defined for interchanging the indices.
  • the Zernike radial slope coefficient B 1 can now be found as l/ ⁇ max ⁇ - ⁇ tt Q for each / .
  • An equivalent expression is
  • This operator T is the inverse of S , it implicitly has the scaling factor T 11111x .
  • T is the inverse of S , it implicitly has the scaling factor T 11111x .
  • S 2 is found as a non-singular diagonal matrix as follows:
  • the scaling factor r max has not been recited, but it shall be understood that the resulting matrices can be scaled by a scaling factor such as T m11x .
  • T m11x For higher orders, the operators are no longer diagonal, but are still non-singular sparse matrices.
  • S 3 and S ⁇ as a reference.
  • T n S ⁇ * for any order n as follows:
  • the pupil radius is 3 mm.
  • the radial slopes dW I dr of the wavefront aberration map W are numerically determined.
  • the Zernike radial slope coefficients B ⁇ for dW I dr can be determined using the least squares fitting as described above.
  • the power vectors can.be calculated from these coefficients BTM using the formulas described in Equations 26-34 above. AU the power vectors from the three methods are essentially identical and the differences between the methods are negligible of order 0(10 ⁇ 13 ) as set forth in Table 2 below:
  • Table 2 Power vectors (D) obtained from the Zernike radial slope coefficients 5TM .
  • the three exemplary different methods for calculating power vectors provide three equivalent quadratic surfaces that approximate the original wavefront map. These equivalent quadratic surfaces are not expected to be identical, except when the wavefront map comprises second order aberrations only.
  • the three methods compute the same power vectors as shown in Table 2.
  • the equivalent quadratics constructed from the power vectors using the three methods are identical to each other, and also to the original wavefront up to additive constants.
  • An exemplary second order quadratic surface determined by the first, second or third exemplary method is illustrated in Fig. 6 .
  • the expected power vectors are shown in Table 3 below.
  • Table 3 Power vectors (D) obtained from the Zernike radial slope coefficients B ⁇ .
  • the wavefront W 2Z 4 0 -0.5Z 4 2 .
  • W Z 2 "2 + 3Z 2 0 + 2Z 2 2 + 2Z 4 0 - 0.5Z 4 2 .
  • the total power vectors are obtained as the sum of Table 2 and Table 3 as shown in Table 4 below.
  • Table 4 Power vectors (D) obtained from the Zernike radial slope coefficients BTM .
  • the wavefront W Z ⁇ 2 + 3Z° + 2Z 2 + 2Z 4 - 0.5Z 4 .
  • the power vectors calculated from the first, second and third exemplary method methods diverge.
  • the first exemplary method finds positive values
  • the second exemplary method does not affect M from the newly added spherical aberration.
  • the third exemplary method significantly increases the M values to -0.3218 (D).
  • Z 4 has different impacts on J 0 .
  • the J 0 value almost doubled.
  • the J 0 value is about 67% of that from the second order aberration map.
  • the J 0 value stays about the same.
  • the equivalent quadratic surfaces calculated from the power vectors by the first, second and third exemplary methods are shown in Figs. 7b, 7c and 7d, respectively.
  • the equivalent quadratic from the first exemplary method changes the sign of the mean curvature of the wavefront surface.
  • the equivalent quadratic from the second exemplary method shows changes only in J 0 .
  • the equivalent quadratic becomes a hyperbolic surface.
  • Contour maps of the original wavefront and the equivalent quadratics determined by the first, second and third exemplary methods are shown in Fig. 8a, 8b, 8c and 8d, respectively, and provide additional details about the principal directions of the surfaces, hi general, the denser the contour curves the steeper the equivalent quadratics. The brighter the contour curves the higher the levels.
  • the orientation of the paraxial iso-level contours matches the original wavefront.
  • the shape and orientation of contour curves are influenced by the higher terms.
  • the astigmatism value J 0 became dominant and the two principal directions have opposite signs.
  • the additional wavefront W 1 affects M only and the astigmatism components stay the same.
  • the level of effectiveness on M from W 1 varies on the method being applied.
  • Fig. 9a illustrates the original Seidel aerated wavefront.
  • the equivalent quadratic surfaces calculated from the power vectors by the first, second and third exemplary methods are shown in Figs. 9b, 9c and 9d, respectively.
  • process 500 provides a number of methods of reconstructing the wavefront from the Zernike radial slope coefficients 5TM through a linear transform T .
  • the reconstructed wavefronts are almost identical with the original wavefronts of error of usually 0(10 ⁇ 13 ) up to additive constants.
  • the reconstruction algorithm for higher order aberrations has as the same accuracy as for lower order aberrations when the wavefronts are in the form of polynomials.
  • FIGs. 10a, 10b, and 10c show wavefront vergence maps derived from Z 2 2 , Z 2 , and Z 2 for J 45 , M, and Jo, respectively.
  • the wavefronts have only second order aberrations and the power vectors computed from the first, second and third exemplary methods are identical.
  • the power vectors of any wavefront that is represented as a linear combination of these individual aberrations will be equal to the linear combination of their individual power vectors.
  • W 1 Z 2 2 + Z 2 2
  • the wavefront vergence maps for W ⁇ and PT 2 are shown in Figs. 11a and lib, respectively.
  • the axis of the minus cylinder is identified as the axis of the more negative values referenced in the legend, which is denoted by the dashed lines.
  • the amount of cylinder can be estimated by subtracting the magnitude of the vergence map along the A + 90° axis (more positive value) from that of the vergence map along the a axis (more negative value).
  • Equation 60 Equation 60
  • W 1 Z 2 "2 + 3Z 2 0 + 2Z 2 2 .
  • This particular value of C 4 was chosen so that W 2 would have paraxial curvature equal but opposite to wavefront W x and therefore W 2 would neutralize paraxial defocus when added to W 1 . Since wavefront W 2 lacks astigmatism, the only non-zero component of the power vector is the spherical equivalent M. The exact value of M depend on the method being used as described below in Table 5.
  • the paraxial first exemplary method reports M > 0 because wavefront W 2 is diverging near the pupil center, thus requires a positive correcting lens.
  • the third exemplary method reports an intermediate value because of the way it weights the pupil.
  • W 3 Z 2 "2 + 3Z 2 0 + 2Z 2 2 + 0.7746Z 4 0 .
  • the vergence map for Equation 61 is more complicated than a sphero-cylindrical map due to the inclusion of spherical aberration.
  • the power vector prescription for the correcting lens can still be estimated from this vergence map.
  • Table 6 Power Vectors for Equation 61.
  • Fig. 13a The original wavefront for equation 61 is shown in Fig. 13a.
  • Fig. 13b illustrates the resulting wavefront for the equivalent quadratic according to the first exemplary method.
  • the other two methods provide a different result.
  • Fig. 13c illustrates the resulting wavefront for the equivalent quadratic according to the second exemplary method.
  • Fig. 13d illustrates the resulting wavefront for the equivalent quadratic according to the third exemplary method.
  • the result using the power vectors above are shown in Figs. 13b, 13c and 13d for the first, second and third exemplary methods respectively.
  • the equivalent quadratic W e from the first exemplary method has principal curvatures of the opposite signs.
  • the equivalent quadratics from the second exemplary method and 3 still hold positive mean curvatures.
  • the shape of the surface is flatter in the third exemplary method than in Second exemplary method, which implies the magnitude of the mean curvature of the surface is smaller in third exemplary method.
  • wavefront W 4 1.1228Z 4 2 + 1.0328Z 4 consisting of pure secondary astigmatism with axis at 25 degrees.
  • This example demonstrates a case of overcompensation of paraxial astigmatism when W 4 is added to W x ⁇
  • the equivalent quadratic for wavefront W 4 is specified by the power vectors in Table 7.
  • Table 8 the corresponding vergence map for wavefront W 5 is given in Fig. 14.
  • J 0 and J 45 are positive.
  • J 0 and J 45 are positive.
  • J 0 decreases, and an intermediate result is given by third exemplary method.
  • a contour map for the original wavefront is shown in Fig. 15a.
  • Contour maps for equivalent quadratics W e for the first, second, and third exemplary methods are shown in
  • the equivalent quadratic W e from the first exemplary method keeps the orientation of the paraxial part of the original wavefront.
  • the shape of the equivalent quadratic from second exemplary method changes its orientation along the position of the higher order aberrations included.
  • the equivalent quadratic from third exemplary method shows an intermediate shape between the first exemplary method and the second exemplary method.
  • the examples considered above show that the power vector prescription for the equivalent quadratic wavefront depends on the method used to establish that equivalence. To gain some insight into the clinical significance of the differences between the three different methods described above, power vector prescriptions for a population of 89 normal eyes have been compared to determine the magnitude of the difference between the three methods. The preferred method depends on many factors, including precision and accuracy with respect to an accepted standard for a given population or desired correction.
  • the subjective, mean spherical refractive errors (M) for the study population varied from -10.25 D to 1.125D with an average of -2.07D and a standard deviation of 2.46D.
  • the measurement wavelength was 840 nm.
  • the pupil diameters varied from 2.92 mm to 7.72 mm with an average of 6.32 mm and a standard deviation of 0.86 mm.
  • Curves 1601 are the first exemplary method minus the second exemplary method.
  • Curves 1602 are the first exemplary method minus the third exemplary method.
  • Curves 1602 are the second exemplary method minus the third exemplary method.
  • Fig. 16a shows these three comparison curves for M.
  • the mean and standard deviation for the three comparison curves are shown below in Table 9.
  • Fig. 16b shows these three comparison curves for J 0 .
  • the mean and standard deviation for the three comparison curves are shown below in Table 10.
  • Fig. 16c shows these three comparison curves for J 45 .
  • the mean and standard deviation for the three comparison curves are shown below in Table 11.
  • the length of a power vector is a good predictor of the visual impact of sphero-cylindrical blur. For each eye and each pairwise comparison of methods, blur strength was determined as the square root ot the sum of squared differences of the power vector components,
  • the three histograms have different widths, which reflect their different standard deviations.
  • the narrowest histogram is for the second and third exemplary methods, which indicates that their prescriptions agree more closely with each other than they do with the prescription from the first exemplary method.
  • the mean difference between the second and third exemplary methods is less than 0.25D, but for some eyes can reach clinical significance.
  • the population mean differences are clinically significant (> 0.25D) and can be as much as 1 diopter or more for some eyes.

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Abstract

L'invention porte sur des techniques de traitement de données ophtalmiques. L'un des modes de réalisation est un procédé qui comprend l'orientation vers un œil d'une lumière efficace pour refléter un front d'ondes à partir de l'œil, la mesure d'informations sur le front d'ondes, l'ajustement des informations mesurées à l'aide de fonctions de base qui sont mutuellement orthogonales, la détermination d'informations de vergence sur la base des informations mesurées ajustées et la détermination d'une prescription ophtalmique pour l'œil sur la base des coefficients des fonctions de base. D'autres modes de réalisation comprennent des procédés de modélisation et de détermination d'une carte d'aberration de front d'ondes pour les yeux d'un patient.
PCT/US2009/002687 2008-07-10 2009-05-01 Techniques de traitement de données ophtalmiques WO2010005457A1 (fr)

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Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20070115432A1 (en) * 2003-12-12 2007-05-24 Thibos Larry N System and method for Optimizing clinical optic prescriptions

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20070115432A1 (en) * 2003-12-12 2007-05-24 Thibos Larry N System and method for Optimizing clinical optic prescriptions

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
ACOSTA ET AL.: "Paraxial Optics of Astigmatic Systems: Relations Between the Wavefront and the Ray Picture Approaches", OPTOM VIS SCI 2007;84:E72-E78, 1 January 2007 (2007-01-01), Retrieved from the Internet <URL:http://journals.lww.com/optvissci/pages/articleviewer.aspx?year=2007&issue=01000&article=00014&type=abstract> [retrieved on 20090722] *
THIBOS ET AL.: "Standards for reporting the optical aberrations of eyes", VISION SCIENCE AND ITS APPLICATIONS TOPS, vol. 35, 2002, Retrieved from the Internet <URL:http://research.opt.indiana.edu/Library/VSIA/VSIA-2000_taskforce/Standards_TOPS4.pdf> [retrieved on 20090722] *

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