Classifications

• • G—PHYSICS
  • G02—OPTICS
  • G02C—SPECTACLES; SUNGLASSES OR GOGGLES INSOFAR AS THEY HAVE THE SAME FEATURES AS SPECTACLES; CONTACT LENSES
  • G02C7/00—Optical parts
  • G02C7/02—Lenses; Lens systems ; Methods of designing lenses
  • G02C7/024—Methods of designing ophthalmic lenses
  • G02C7/027—Methods of designing ophthalmic lenses considering wearer's parameters
• • 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
  • A61B3/1015—Objective types, i.e. instruments for examining the eyes independent of the patients' perceptions or reactions for wavefront analysis
• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B33—ADDITIVE MANUFACTURING TECHNOLOGY
  • B33Y—ADDITIVE MANUFACTURING, i.e. MANUFACTURING OF THREE-DIMENSIONAL [3-D] OBJECTS BY ADDITIVE DEPOSITION, ADDITIVE AGGLOMERATION OR ADDITIVE LAYERING, e.g. BY 3-D PRINTING, STEREOLITHOGRAPHY OR SELECTIVE LASER SINTERING
  • B33Y80/00—Products made by additive manufacturing
• • G—PHYSICS
  • G02—OPTICS
  • G02C—SPECTACLES; SUNGLASSES OR GOGGLES INSOFAR AS THEY HAVE THE SAME FEATURES AS SPECTACLES; CONTACT LENSES
  • G02C2202/00—Generic optical aspects applicable to one or more of the subgroups of G02C7/00
  • G02C2202/22—Correction of higher order and chromatic aberrations, wave front measurement and calculation

Definitions

• Ocular lenses are worn by many people to correct vision problems. Vision problems are caused by aberrations of the light rays entering the eyes. These include low order aberrations, such as myopia, hyperopia, and astigmatism, and higher order aberrations, such as spherical, coma, trefoil, and chromatic aberrations. Because the distortion introduced by aberrations into an optical system significantly degrades the quality of the images on the image plane of such system, there are advantages to the reduction of those aberrations.
• Ocular lenses are typically made by writing prescriptions to lens blanks. This is accomplished by altering the topography of the surface of a lens blank.
• the subject invention provides methods for determining a wavefront for a lens from a patient's measured wavefront.
• the wavefront can be used for producing a spectacle lens with optimal correction across the entire lens taking into account the patient's complete measured wavefront.
• Specific embodiments can also take into account one or more additional factors such as vertex distance, SEG height, pantoscopic tilt, and use conditions.
• the lens wavefront can be achieved by optimizing a corrected wavefront, where the corrected wavefront is the combined effect of the patient's measured wavefront and the lens wavefront.
• the optimization of the corrected wavefront involves representing the measured wavefront and the lens wavefront on a grid.
• the grid can lie in a plane.
• a subset of the grid can be used for the representation of the measured wavefront at a point on the grid so as to take into account the portions of the measured wavefront that contribute to the corrected wavefront at that point on the grid.
• Figure 1 shows the steps for a method for producing a spectacle lens in accordance with an embodiment of the subject invention.
• Figure 2 shows a flow chart in accordance with an embodiment of the subject invention.
• Figure 3 shows a top view of spectacle and pupil samples as images at particular shift (gaze).
• Figure 4 shows a side view of spectacle and eye, on the left with corresponding dotted lines, with gaze rotation shown by the curved arrow and the rotated eye and corresponding dotted lines the curved arrow is pointing to and gaze shift shown by the straight arrow and the shifted eye and corresponding dotted lines the straight arrow is pointing to on the right.
• Figure 5 shows a schematic representation of an approximation of representing the z-th direction as the z-th shift.
• Figure 7 shows a schematic representation of a transverse correction for a contact lens application.
• Figure 8 shows a schematic representation of a lens blank with a monofocal higher-order region and a transition zone.
• Figure 9 shows a lens image
• Figures 10A-10D show an example of trefoil.
• Figures 11A-11D show an example of coma.
• Figures 12A-12D show an example of spherical aberration.
• the subject invention provides methods for determining a wavefront for a lens from a patient's measured wavefront.
• the wavefront can be used for producing a spectacle lens with optimal correction across the entire lens taking into account the patient's complete measured wavefront.
• Specific embodiments can also take into account one or more additional factors such as vertex distance, fitting height, pantoscopic tilt, and use conditions.
• the lens wavefront can be achieved by optimizing a corrected wavefront, where the corrected wavefront is the combined effect of the patient's measured wavefront and the lens wavefront.
• the optimization of the corrected wavefront can involve representing the measured wavefront and the lens wavefront on a grid.
• the grid can lie in a plane.
• a subset of the grid can be used for the representation of the measured wavefront at a point on the grid so as to take into account the portions of the measured wavefront that contribute to the corrected wavefront at that point on the grid.
• One embodiment of the invention utilizes the hill climbing optimization technique used in the Gaussian Least Squares Fit and point spread optimization software to fit an optimal wavefront across a specified surface larger than that of the measured wavefront.
• the desired wavefront is projected from a number of points emanating in multiple directions from a nominal axis of rotation
• the wavefront pattern used can be solely based upon the low order, or can also include some or all the high order as well.
• Each position of the wavefront as projected from the center of the eye can be convolved with a weighting function across the lens to enhance or emphasize the wavefront in certain areas while allowing other areas to be de-emphasized.
• the wavefront is best fit along a surface representing a paraxial lens representing the neutral axis of a lens.
• This paraxial lens is fixed in space at a specified central vertex distance and follows the basic lens design curvature of the chosen blank lens.
• the basic lens design curvature may be simply derived from the central lower-order prescription or may be used in conjunction with the high order and other factors such as vertex distance.
• the final wavefront can be fitted with one or more of the following inputs:
• FIG. 1 shows the steps for one embodiment of a method for producing a spectacle lens in accordance with the subject invention and Figure 2 shows a flowchart indicating the flow of information in accordance with an embodiment of a wavefront optimization method.
• vertex distance and its effect on the lens power and astigmatism can be compensated for in the wavefront fitting process.
• the output of the wavefront fitting software process (steps 1 & 2 in Figure 1) is a set of instructions that facilitates production of a custom lens.
• the instructions may include a surface map for front and/or back surfaces of a lens, or a points file that can be fed into a freeform lens generator, to cut custom front and back surfaces.
• Other approaches may utilize a changeable refractive index layer within the lens blank that can be customized with the information from the fitting software.
• Yet another approach can use an inkjet deposition of different refractive indices across a lens surface to generate a corrected wavefront based on the fitting software output.
• stereo lithography may be used in conjunction with casting, or combination of any of the above techniques can be combined to achieve the custom lens manufacturing.
• Step 3 in Figure 1 represents a freeform grinding approach to lens manufacturing.
• Casting, inkjet, and sandwiched changeable refractive index approaches as known in the art, can also be utilized.
• the final step in the wavefront fitting software can generate shape of the front and back surface of the lens to achieve the given wavefront. Development of the shape of the front and back surface can also take into account the distortions from lens thickness variations to minimize distortions.
• the output of the fitted wavefront software can, in an embodiment, be a points file, which can subsequently be transferred into a freeform lens generator for manufacturing the lens.
• the resulting lens can be essentially optimized across the entire lens and customized for each patient based on all the input parameters.
• This freeform grinding technique can be utilized in conjunction with the refractive index changing material to further tune or enhance the refractive properties after lens grinding and polishing.
• a grid of shifts (rather than rotations) for measured and target pupil wavefronts is used, represented mathematically by images.
• the target wavefront can be used as the lens wavefront. From the measured wavefront, the target wavefront can be determined via one or more embodiments of the invention. A variety of configurations can be used to implement the target wavefront via an eyeglass for the patient.
• a single lens with two surfaces can be used to create an eyeglass for a patient, where one or both of the lens surfaces can be controlled to modify the wavefront for the lens.
• two lens blanks each having two surfaces can be used with a variable index polymeric material between the two lens blanks, where one or more of the four lens blank surfaces and/or the polymeric material can be controlled to effect the wavefront for the lens.
• the lens surface(s) and/or variable cured index of the polymeric material of the polymeric material are described in a two-dimensional plane corresponding to the height of the surface(s) or the projection of the index layer(s) onto a plane. Aberrations are measured as components in an orthogonal expansion of the pupil sampled on the same grid spacing.
• the grid spacing is about 0.5 mm and in another embodiment the grid spacing is about 0.1 mm.
• the components can be made orthogonal for the chosen pupil size due to discrete sampling.
• the components can be made orthogonal through a process such as Gram- Schmidt orthogonalization.
• Orthogonal components of aberrations for pupils centered at a specific point on the spectacle may then be computed by sample-by-sample multiplication (inner product) of the aberration component image with the lens (height or projection) image centered at the point of interest, as in Figure 3.
• Figure 3 shows a top view of spectacle and pupil samples as images at particular shift (gaze), which can be used for computation of aberrations for pupils having a diameter of 3 samples, centered at a chosen coordinate on a spectacle grid having a diameter of 8 samples.
• Zernike polynomials are orthogonal and when samples are taken, approximations of Zernike polynomials can be created. In one embodiment, the approximations of Zernike polynomials can then be modified to make orthogonal polynomials, so as to create new polynomials.
• Non-squared pupil shapes may be formed by zeroing select points within the square of pupil diameter.
• the process of computing the inner product centered at all possible locations on the grid is a cross correlation
• An image can be produced for each Zernike via the cross-correlation.
• the image for each Zernike can be used to create a target and an error.
• the error can be used to produce an error discrimination, or a weighted sum of all pixels in the image square.
• a grid size and spacing is chosen to represent the lens and pupil in a plane. An example of such a grid is shown in Figure 3.
• the aberrations of interest are orthogonalized on the grid at the chosen pupil size. Then a given aberration centered at every point may be estimated by cross-correlation of the orthogonalized Zernike image and the spectacle image, resulting in an image for each Zernike component.
• An error image for each point on the lens may be estimated as a difference between the computed and desired Zernike aberration centered at each point in the image.
• the desired correction is, to a first approximation, assumed to be constant in this plane with a shift corresponding to a given gaze angle.
• the rotation is otherwise neglected as shown in Figure 2.
• the effect of rotation can be compensated by providing a spatially-varying correction target.
• the spatially-varying target can be approximated by rotating the paraxial target.
• Simple convolution may be replaced with a more exact geometric calculation of the ray-surface intersection corresponding to a ray-tracing-style algorithm over a fixed grid.
• Other grid geometries may be used (e.g., hexagonal instead of rectangular). The result is essentially a spatially varying sample spacing and convolution, increasing computation time.
• Other metrics of surface error may be computed from the Zernike component error images, as done with single pupil representations. Images of sphere/cylinder/values (or errors from desired) may be computed by applying the usual conversion on a pixel-by-pixel basis for example.
• Total root-mean-square may be represented by either the sum of all component terms squared for a particular pupil location, or the sum of all pixels squared (and properly normalized) within the pupil. This may be achieved by cross-correlations of a pupil-sized aperture of ones with an image of the lens values squared.
• Total high order may be computed by subtracting the low order
• High order error may be computed by also subtracting the target high order images, squared pixel-by-pixel. For certain error choices optimizing error this may be mathematically equivalent to known regularization algorithms.
• a total error discriminant may be generated by summing desired error images over the entire lens.
• a pixel-by-pixel weighting may be incorporated to selectively weight the error at various regions in the lens, and this may be done independently for each Zernike component. Standard optimization procedures (e.g., convex programming) may be used to produce a lens image that minimizes the error discriminant. If the lens image is sufficiently small, the cross-correlation may be represented as a matrix multiplication further simplifying the application of optimization algorithms known in the art.
• Constraints on the error may also be used in the optimization that would be represented by constraint images of max and/or min Zernike components or functions thereof.
• An example of a constraint that can be utilized is that the error for a certain Zernike cannot be above a certain threshold for a certain area.
• Free-floating points such as boundaries, may be handled by setting weights to zero or very small for those points. This allows the optimized region to be smaller than the actual grid, the optimized region to have an arbitrary shape, and/or the optimized region to only be optimized for points that will ultimately be used.
• the patient-selected frame outline may be input as the region of optimization.
• an attempt can be made to optimize a certain shape inside of the lenses, such as the spectacle shape.
• An example of a certain shape that can be optimized is to optimize within the shape of the frame that the lens will be used by, for example, using a zero weight outside of the frame.
• Fixed points which are given prior to optimization and remain unchanged, may be provided by using the points to compute correction but not applying it to them in the optimization algorithm. This can be used for boundaries, so as to only optimize for certain portions of lenses.
• Grid(s) of constraints may be converted into a weighting and/or target (for unconstrained optimization) via a separate optimization procedure.
• Multiple surfaces may be optimized simultaneously.
• two grids can be optimized simultaneously or each grid point can have two numbers associated with it to be optimized.
• the patient's prescription (including high order) may be used as target, including deterministic variations with gaze if available.
• N Total number of pixels on side of (square) spectacle OPD matrix.
• p Pupil aberration OPD, n pupil aberration in the (i,j) th position if it changes with gaze.
• An assumption can be made that an optimization of image quality for a lens over a range of gaze angles can be well approximated by an optimization of image quality over a range of translations.
• the rotation of the eye relative to the lens is, therefore, ignored in this example.
• the desired OPD calculated through optimization can be converted to, for example, a surface or pair of surfaces via a ray-tracing application.
• the corrected wavefront aberration in the (i,jf position, including both the pupil aberration p and the corresponding apertured portion of the spectacle s is described as
• a, p, and s are matrices.
• the total error to be optimized will be a function of all the a, .
• the matrices can have zeroes as entries for input data or output data that is, for example, circular, rectangular, or has a non-square pattern.
• the simplest function is the total squared error over all shifts with weightings over both the shifts and the pupil, which can be represented as shown in Equation (2).
• One approach to optimize the corrected wavefront is to preferentially select certain Zernike terms to be corrected or excluded.
• An example of preferential selection of certain Zernike terms is to only correct astigmatism for a Progressive- Addition Lens (PAL) design.
• PAL Progressive- Addition Lens
• To select the component of the chosen Zernike term(s) from the full wavefront aberration we make use of the orthonomality of Zernikes and simply take the inner product of each Zernike with the wavefront in Equation (1).
• Particular Zernike components of the aberration can be selectively weighted by weighting the component in (3)
• the appropriate w k may be set to zero to ignore certain components.
• Figures 1 OA- 1 OD Some simulated examples for certain zernike terms are provided in Figures 1 OA- 1 OD, Figures 11 A- 11 D, and Figures 12A- 12D, where Figures 1 OA- 1 OD show an example of trefoil, Figures 1 IA-I ID show an example of coma, and Figures
• FIGS. 12A-12D show an example of spherical aberration. Note that the amplitudes are normalized for a 1 um rms aberration, and the y-axis is normalized to the zernike diameter. One-dimensional cross-sections of the lens, error are provided. Again, Figures 10A- 1OD show the results for trefoil; Figures 1 IA-I ID show the results for coma; and Figures 12A-12D show the results for spherical aberration.
• Example 1 several different methods can be reflected in different choices of g, the matrix describing weighting or error over pupil, with q /y being effective pupil aberration for the i,j position and h being a matrix describing weighting of wavefront over pupil. Examples of several methods are provided in Table 1.
• Another approach can require an "unknown prescribed Zernike”. .
• This can be used, for example, to yield a tilt that is constant (as possible) over the lens but not necessarily zero. For certain aberrations this can result in an improved vision quality by allowing some magnification, which in this treatment can be referred to as linear distortion.
• This can be achieved by iteratively varying the values for c i des i red ⁇ d C 2 desmd with some allowable range and choosing the pair that results in the lowest error minimum.
• An approach at optimizing a metric based on the point-spread function can be performed via consideration of the spatial "bandwidth" as a metric of the PSF at a specific gaze angle. If a wavefront can be described as a two- dimensional single-component FM signal, then its local spatial frequency content at a given point can be estimated forom the spatial derivatives of the phase. By estimating the average mean squared value of the spatial derivative of the wavefront, an estimate of the bandwidth of the PSF can be produced.
• D is a matrix that computes the averaged local derivative via finite differences. There is a variety of possible choices for D to approximate a derivative.
• D can be selected to approximate a second derivative, in order to approximate power matching.
• optimization can be performed using a standard iterative approach such as Gradient Descent with some chosen boundary conditions. These boundary conditions can describe the required outcome at the edges of the lens as well as in zones in its interior. A variety of different applications can be addressed by selecting these regions.
• Transition zone based lens designs have the requirement of perfection for the axial ray and for the correction at some outer radius to be a constant (or low- order). Therefore, the single zone's correction can be predetermined as some high- order correction, then the optimization can vary only a narrow region outside this zone to find the optimum lens. The remaining region outside this transition zone can be required to be some flat or low-order correction.
• PAL' s Progressive- Addition Lenses
• the lens can be optimized to similarly reduce distortion.
• the lens can be optimized to reduced distortion via, for example, power matching, matching second order wavefronts only, or full-wavefront matching with a varying tilt.
• This Example uses a method for optimizing the correction "programmed" onto a higher-order contact lens.
• Contact lenses can be designed to be in a certain orientation, but can still rotate with respect to this orientation and can slide as well so as to become decentralized. The unpredictable rotation and decentration of the lens during normal wearing can be addressed. Given a range of rotations and decentrations, the contact lens design is optimized to improve vision throughout the entire range by minimizing the total wavefront error summed over the ranges.
• the optimum over decentrations may be computed as in Equation (7) provided in Example 1.
• the optimum over rotations is computed as follows.
• the error discriminant is:
• the desired final programmed size can be determined and the information describing the eye aberration can be projected into a larger "transition" radius.
• Figure 9 shows an example of the pupil region and the transition region.
• the extrapolation is continuous while decaying toward zero. Alternatively, these can be achieved after the optimization.
• Optimizing with respect to rotation and decentration can be performed independently. They may be done in either order depending on the expectation of the physical behavior, yielding results that may not be exactly the same depending on the rotational symmetry of the decentration range.
• the transition region may be deemphasized by applying a decaying apodization. Further, the entire image may be refit with Zernike polynomials.

Landscapes

• Health & Medical Sciences (AREA)
• Life Sciences & Earth Sciences (AREA)
• Ophthalmology & Optometry (AREA)
• Physics & Mathematics (AREA)
• General Health & Medical Sciences (AREA)
• Engineering & Computer Science (AREA)
• Optics & Photonics (AREA)
• Biophysics (AREA)
• General Physics & Mathematics (AREA)
• Biomedical Technology (AREA)
• Heart & Thoracic Surgery (AREA)
• Medical Informatics (AREA)
• Molecular Biology (AREA)
• Surgery (AREA)
• Animal Behavior & Ethology (AREA)
• Public Health (AREA)
• Veterinary Medicine (AREA)
• Eyeglasses (AREA)

Priority Applications (2)

Applications Claiming Priority (2)

Publications (1)

Family

ID=40788195

Family Applications (1)

Country Status (4)

Families Citing this family (12)

Citations (2)

Family Cites Families (20)

• 2007
  • 2007-12-21 US US11/963,609 patent/US7832863B2/en active Active
• 2008
  • 2008-12-16 WO PCT/US2008/087035 patent/WO2009085774A1/en not_active Ceased
  • 2008-12-16 EP EP08867870A patent/EP2238551A4/en not_active Withdrawn
  • 2008-12-16 JP JP2010539712A patent/JP5976275B2/ja not_active Expired - Fee Related
• 2010
  • 2010-04-06 US US12/755,345 patent/US20100195047A1/en not_active Abandoned

Patent Citations (2)

Non-Patent Citations (1)

Also Published As

Similar Documents

Legal Events