Patent Application: US-13960208-A

Abstract:
an imaging apparatus for simultaneously determining optical parameters of the eye comprising : a light source for illuminating at least a portion of the eye pupil ; an illumination optical system for directing light rays emitted from the light source into the eye ; a light receiving optical system for guiding the light rays reflected from the eye to a detector unit , wherein the detector unit detects an image intensity distribution from the light rays reflected from the eye ; and an arithmetic unit for determining optical characteristics of the eye by parameter estimation is provided .

Description:
the following nonlimiting description is intended to provide examples of some embodiments of this invention and further information about the operation of the invention . applicant does not intend to be bound by the theory presented . the term “ electromagnetic radiation ” and “ light ” are used synonymously in the present description and refer to waves of electric and magnetic fields . “ optical communication ” refers to a configuration of two or more elements wherein one or more beams of electromagnetic radiation are capable of propagating from one element to the other element . elements in optical communication may be in direct optical communication or indirect optical communication . “ direct optical communication ” refers to a configuration of two or more elements wherein one or more beams of electromagnetic radiation propagate directly from a first device element to another without use of optical components for steering and / or combining the beams . “ indirect optical communication ” on the other hand refers to a configuration of two or more elements wherein one or more beams of electromagnetic radiation propagate between two elements via one or more device components including , but not limited to , wave guides , fiber optic elements , reflectors , filters , prisms , lenses , gratings and any combination of these device components . although the description is provided here with specific components , it is understood that other components such as fiber optics and waveguides may be used in the invention . the operation and use of other components is well understood by one of ordinary skill in the art . also , the description is provided here with minimal optics components in the system . it is understood that other optics , such as filters , lens and other optics may be used with the system to provide the necessary or desired beam shaping and direction , for example . the operation and selection of such optics is well understood by one of ordinary skill in the art . in one embodiment , the methods and devices described herein are used in the visible portion of the spectrum . in one embodiment , the methods and devices described herein are used in the infrared portion of the spectrum . a general description of the parameter estimation is described next , followed by more specific examples of the invention . the examples and description provided are not intended to limit the invention . an accurate probability model for the eye is built by use of an optical design program . an optical model for the eye with unknown geometrical parameters ( e . g ., navarro schematic eye model , although other eye models may be used ) is used to start , since these parameters vary among patients . the data are chosen as the raw detector outputs from one or more shack - hartmann wavefront sensors , or other imaging systems that may be used . in contrast to conventional wavefront sensing , centroid estimation , wavefront reconstruction , and wavefront correction are not performed , since the process of centroid estimation results in severe information loss . noise is added to the probability model , such as poisson noise or gaussian electronic noise , and a set of data is generated for a particular set of ocular parameters to describe an individual patient . once the data set is generated , estimating methods such as ml estimation are used to determine patient - specific parameters . in the case of uncorrelated gaussian noise , ml estimation reduces to least - squares fitting between the data and the output of our optical design program . this final step is the inverse problem , involving an optimization algorithm that performs a search through parameter space ( by proposing changes to the set of parameters ) to find the set of parameters that maximizes the likelihood ( the probability of occurrence of the data that are observed ) or minimizes some other cost function . simulated annealing is a feasible global optimization algorithm for dealing with large parameter spaces that have complicated surfaces , although other general algorithms are available as well , as known in the art . each iteration in the inverse problem requires a solution to the forward problem , which in turn utilizes the optical design program to compute the output data for a particular set of parameters . the data are compared to the output of the program at each proposed point in parameter space , and the cost function of interest ( e . g the likelihood ) is determined . finally , the optimization routine returns the values for the set of parameters that optimizes the cost function , and these values are presented as results . the data consist of the raw detector outputs from a shack - hartmann wfs usually used for measurement of aberrations in human eyes , as illustrated in fig1 a - b , rather than the wavefront estimate derived from the raw data . for the use described here , relay optics in the shack - hartmann wfs can be excluded . the center of the lenslet array is placed at a suitable distance from the corneal apex . in one embodiment , this distance is 10 mm from the corneal apex . this distance can vary . the number of lenslets can be varied . in one embodiment , an 18 × 18 lenslet array of 400 μm square lenslets was used . in another embodiment , an array of 600 μm square lenslets was used . in one embodiment , larger or smaller lenslets can be used . the light source , power , bandwidth , and wavelength can be varied , as known in the art . in one embodiment , a visible or infrared light is used . the power of the light source is sufficient to generate the desired data , but not so great as to cause damage to the eye . the angle between the laser beam and the optical axis of the eye is denoted α . the angle between the laser beam and the optical axis of the eye can vary between + 15 and − 15 degrees , for example . the various effects of viewing the angle at an oblique angle , such as the elliptical appearance of the pupil of the eye due to perspective elongation , can be taken into account , as known in the art . in the clinical system developed by straub et al ., a narrow collimated beam from a laser diode centered at 780 nm with a 30 - nm bandwidth produces a point source on the retina , which acts as a laser beacon and fills the dilated pupil upon reflection . in our example , a single wavelength of 780 nm was used for simplicity and to reduce computation time . the eye was illuminated with a gaussian beam ( 2 mm at fwhm ) at multiple angles of 0 , 6 , and 12 degrees in the vertical direction to assess both on - axis and off - axis aberrations such as coma and astigmatism . the center of the beam was coincident with the intersection of the optic axis and anterior corneal surface . the aberrated retinal spot was treated as a perfect diffuse scatterer , but did not account for scattering within the ocular media or internal reflections . furthermore , relay optics as used in the clinical configuration to conjugate the exit pupil of the eye to the wfs were excluded , and the lenslet array 10 mm away from the corneal apex . relay optics can be used in this invention , as known in the art . global wavefront tip and tilt were discarded by rotating the wfs for off - axis angles . a beamsplitter was not incorporated into this example , but a beamsplitter such as a pellicle beamsplitter to reduce unwanted back - reflections can be included . the lenslet array sampled the aberrated wavefront and produced a grid of focused spots on a detector placed in the focal plane . generally , the amount of displacement of each spot from its ideal , on - axis location is proportional to the local average slope of the wavefront at the respective lenslet , while finer details of the aberrated wavefront manifest in the spot profiles . therefore , both the spot positions and profiles provide useful information about aberrations in the eye . this method does not involve centroid estimation as in conventional wavefront sensing , and the data consist of all pixel intensity values in the focal plane of the wfs , which are referred to as the raw detector outputs . for this example , a commercially available micro - wfs , consisting of an array of 600 × 600 μm 2 lenslets with a focal length of 24 mm was used . the detector pixels had a pitch of 10 μm , and the peak snr was 10 3 . an optical design program was designed in matlab , which performs non - paraxial ray - tracing through quadric surfaces , and simulated a trial set of data for ocular parameters comparable to those in the navarro wide - angle schematic eye model , as provided in table 1 . other eye models may be used , as known in the art . the chromatic dispersion model developed by atchison and smith was used to calculate refractive indices at 780 nm . therefore , an effective refractive index for the crystalline lens is used in this example . a grin distribution can also be incorporated , if desired . in addition , the lens was decentered by 0 . 20 mm in the horizontal direction and − 0 . 10 mm in the vertical direction , which agrees with the experimental range of crystalline lens misalignments . wfs data was generated by tracing a 256 × 256 grid of rays , although about 60 % of the rays survived the double - pass after the random retinal reflection and vignetting at the pupil . next , it was assumed that the system is not photon - starved and gaussian statistics were used to represent electronic noise . for detector elements that are i . i . d . ( independent and identically distributed ) and noise that is independent of the illumination level , the probability density function ( pdf ) from which the data are drawn is given by pr ⁡ ( g ❘ 0 ) = ∏ m = 1 m ⁢ 1 2 ⁢ πσ 2 ⁢ exp [ - [ g m - g _ m ⁡ ( 0 ) ] 2 2 ⁢ σ 2 ] , ( 1 ) where g is the m × 1 vector set of random data , θ is the set of estimable parameters , and σ 2 is the variance in each detector element . furthermore , overbars are used to denote means , such that g m ( θ ) represents the average value of the m th detector element evaluated at θ . since the noise is zero - mean gaussian , g m ( θ ) is simply the output of the optical design program . the variance was calculated to obtain a peak snr of 10 3 and noise was applied in the data using a gaussian random number generator . after generating the data , knowledge of the values of selected parameters was disregarded and the selected parameters were estimated by maximizing the likelihood . essentially , ml estimation returns the θ argument which maximizes the probability of occurrence of the observed data , defined as θ ^ m ⁢ ⁢ l ≡ argmax θ ⁢ ⁢ pr ( g ❘ θ ) , ( 2 ) where { circumflex over ( θ )} represents an estimate of the vector set of parameters . since the logarithm increases monotonically with its argument , eq . ( 2 ) can be rewritten as for a purely gaussian noise model with i . i . d . detector elements , it can be shown that ml estimation according to eq . ( 3 ) reduces to nonlinear least - squares fitting between the data and the output of the optical design program : immediate advantages are that ml estimation is efficient ( i . e ., unbiased and yields the best possible variance ) if an efficient estimator exists , and that it is asymptotically unbiased as more photons are acquired . however , one challenge is that an accurate probability model must be used that includes all sources of randomness ( e . g ., photon noise and electronic noise ) as well as fluctuations of ocular aberrations associated with live imaging of the eye , including the tear film effect . the performance of the ml estimator can be analyzed with the fisher information matrix ( fim ), denoted f , because it describes the ability to estimate a vector set of parameters and is related to the sensitivity of the data to changes in those parameters . for a vector parameter of p real components , the fim is a p × p symmetric matrix with components given by f jk = 〈 [ ∂ ∂ θ j ⁢ ln ⁢ ⁢ pr ⁡ ( g ❘ 0 ) ] ⁡ [ ∂ ∂ θ k ⁢ ln ⁢ ⁢ pr ⁡ ( g ❘ 0 ) ] 〉 g ❘ 0 , ( 5 ) where the angle brackets denote the average . mathematically , it is the covariance matrix of the gradient of the logarithm of the likelihood . therefore , off - diagonal entries in the fim indicate coupling between different pairs of parameters ; stronger coupling leads to greater noise in the parameter estimates . for gaussian i . i . d . data , the fim components reduce to f jk = 1 σ 2 ⁢ ∑ m = 1 m ⁢ ∂ g _ m ⁡ ( 0 ) ∂ θ j ⁢ ∂ g _ m ⁡ ( 0 ) ∂ θ k , ( 6 ) which depend on the average data vector evaluated at the set of parameters and are inversely proportional to the variance in the detector elements [ 33 ]. inversion of the fim provides the cramer - rao lower bound ( crb ) on the variance ( i . e . the theoretical minimum possible variance ) of the parameter estimates . it is well known that the variance of any unbiased estimate obeys the cramér - rao inequality : [ k θ ] nn = var {{ circumflex over ( θ )} n }≧[ f − 1 ] nn . ( 7 ) for an efficient estimator , the inverse of the fim is the covariance matrix of the parameter estimates ; thus , its off - diagonal elements represent coupling between these estimates . the fim , its inverse , and the crbs were calculated for the chosen subset of parameters using the optical design program . in general , the fim can be computed for any system configuration and therefore used to design and optimize the system that acquires the wfs data to be used as input to the inverse optical design , prior to clinical application . that system is referred to as the inverse design system . adjustable system parameters to increase fisher information include the beam size , beam angle , lenslet array geometry , detector element spacing , and variance in the detector elements . additionally , data from multiple beam angles can serve to decouple pairs of ocular parameters in the fim , which could improve parameter estimability . the embodiment of using multiple beam angles is included here , and can be carried out without undue experimentation by one of ordinary skill in the art . the geometrical eye model corresponding to the ocular parameters provided in table 1 and crystalline lens decentrations stated earlier is illustrated in fig2 , which was generated using the optical design program . this program performs non - paraxial ray - tracing through second - order surfaces ( e . g ., conic or biconic surfaces ) using the vector form of snell &# 39 ; s law . sample rays for the multiple beam angles ( i . e . 0 , 6 , and 12 degrees ) used in this study are also plotted . the trial set of wfs data used as input to the inverse optical design problem are provided in fig3 ( a - c ) . the respective focal spots on the retina are shown in fig4 ( a - c ) with the coordinate system centered on the optical axis , such that the position on the retina can be read from the axes . in this study , the optical model used a reduced set of ocular parameters including the posterior radius , thickness , and refractive index of the cornea , the thickness and index of the anterior chamber , and the anterior and posterior radius , thickness , and equivalent index of the crystalline lens . the fim of the system including data from all beam angles is displayed on a logarithmic scale shown in fig5 a , with values ranging from 10 . 145 to 17 . 375 . this matrix is order - specific , and the indices of the estimated parameters are listed in table 1 . note that the jk th entry has units of [ units of j th parameter ] − 1 [ units of k th parameter ] − 1 . the large values in the fim indicate that the data are very sensitive to changes in the parameters , but that the magnitudes of off - diagonal entries reveal a high degree of undesired coupling between pairs of parameters . this is intuitive since first - order geometrical parameters combine to form various optical quantities , such as refractive index and thickness in optical path length , and curvatures and indices in optical power . an adverse effect of parameter coupling is that an error in one parameter estimate will cause errors in the estimates of all other parameters , while it introduces many local minima in the likelihood surface . the fim was inverted as shown in fig5 a , also on a logarithmic scale , and the diagonal entries were read off to determine the crb for each parameter estimate . the corresponding standard deviations ( i . e ., square - roots ) are given in table 2 . these diminutive values permit the estimation of parameters to high precisions even under pessimistic noise levels since a peak snr of only 10 3 was implemented , and the theoretical lower bound on the variances can immediately be improved by decreasing the variance in the detector pixels . however , the performance of the ml estimator relies greatly on an accurate forward model of the system , particularly when real data are used . complexity can be added to the basic likelihood model by incorporating other noise sources , coherence properties of the source as well as the retinal reflection , a grin distribution in the crystalline lens , the stiles - crawford effect , scattering within the ocular media , fresnel reflections between the ocular surfaces , topography of the corneal surface , and the optical effect of the tear film . these effects are known in the art . stray light , misalignments , or other effects that may contribute to estimation errors can be taken into account by methods known in the art . algorithms that implement a likelihood approach to estimating parameters perform a search through parameter space to find a point that maximizes the probability of generating the observed data . virtually all search algorithms locate an extremum via iterative methods that execute in a variable number of steps , depending on the starting location , the complexity of the probability surface , and values selected for convergence factors . one challenge in this method of parameter estimation is that the estimation step is very time consuming , especially since a complicated surface with many local features and strong coupling between parameters is used . a proficient global search algorithm tailored to the probability surface can be used and will provide advantages in the computation resources needed . the algorithm used may involve prior information obtained from statistical studies or by other reliable modalities such as corneal topography , which can be used to select a starting point or put limits on the parameter values to narrow the search space . an approximate method based on optimization with reverse ray - tracing can be used to provide a starting point for the likelihood approach . this study used a custom simplex algorithm for the optimization and a nearby starting point to avoid stagnation in local basins of the surface . the estimated parameters from the analysis described here are listed in table 2 , including the true values used to generate data , the starting point in the ml search , the final estimates , and the fractional error in each estimate . the parameters were estimated to two or three decimal places of accuracy for radii and thicknesses and four to five decimal places for refractive indices . all errors were within a fraction of a percent , indicating very good agreement between the true and estimated values . the reconstructed eye model shows precise overlap , as illustrated in fig6 . although the corneal anterior radius was not estimated assuming that its value is known from direct measurements , it was plotted in the reconstruction to indicate the estimated corneal thickness . when normalized by the detector variance and total number of elements , the sum - of - squares described in eqn . 4 is 401 . 779 at the starting point , 1 . 65236 at the termination point in the optimization , and 0 . 998794 at the true global minimum . ( as the number of pixels increases , the true minimum should approach unity using the normalization stated above .) other ml search algorithms can be used in finding the true minimum and achieving the cramér - rao bounds . as mentioned previously , this is a very complicated and high - dimensional probability surface with many local minima and strong coupling between various ocular parameters . in the example shown herein , a basic simplex search algorithm was used to estimate a reduced set of ocular parameters from simulated wavefront sensor data using maximum - likelihood ( ml ) estimation . simplex algorithms essentially perform straightforward minimization , in which the search only accepts downhill moves along the surface to be minimized . this process leads to the quickest nearby solution , even if it corresponds to a local , but not optimal , solution . to circumvent this problem , a nearby starting point was used in the parameter - space to avoid stagnation in local basins of the surface , simply to demonstrate the ability of ml estimation in solving the inverse problem at hand . however , in clinical practice , the values of the parameters are truly unknown and such a good starting point can not be assumed . one solution is to use a global optimization algorithm that can deal with a complicated surface containing many local optima . one technique that can be used for global optimization is simulated annealing . this technique was originally developed by metropolis et al . ( 1953 ) in the context of statistical mechanics , an application of probability theory which includes a mathematical framework for dealing with large populations of atoms or molecules . a simple algorithm was created to simulate the thermodynamic equation of state for a complex system of atoms by monte carlo sampling . however , the general applicability to optimization problems was later recognized by kirkpatrick et al . ( 1983 , 1984 ) by using the metropolis algorithm and making clever analogies to statistical mechanics while simulating the physical process of annealing as in materials science . a detailed discussion of this technique is provided in the references included herein . simulated annealing is a stochastic algorithm that provides a good approximation to the global optimum of a given function in a high - dimensional search space with many local extrema , since transitions out of a local optimum are always possible during the search based on a probability criterion . it is able to process objective functions with high degrees of nonlinearities , discontinuities , and randomness due to noise sources . it can also distinguish between large - scale features and finer “ wrinkles ” in the function , both of which became evident in the problem here . furthermore , the parameter - space of interest can contain arbitrary boundary conditions and constraints , allowing prior information about the human eye to be incorporated , including known statistical variations across a population . most important , simulated annealing guarantees the true solution under very stringent conditions , but satisfying these requirements would lead to the global optimum much too slowly for practical use . instead , the conditions are relaxed to trade - off computational time and optimality of the solution . even with this compromise if simulated annealing does not find the true solution , it will find a near - optimal one . although simulated annealing is very promising in many aspects , its major criticism is high computational demand compared to straightforward optimization methods . an adaptive form of simulated annealing developed by corana et al . ( 1987 ), which considers unique physical constraints ( e . g ., finite ranges ) for each parameter , as well as different sensitivities of the cost function along different parameter axes was used . this particular algorithm also optimizes computational time by attempting to maintain a one - to - one ratio between the number of accepted and rejected moves , thereby searching the parameter - space efficiently . the same set of ocular parameters was estimated as before , although the true values were slightly modified . furthermore , the same system configuration as described above was used , except a single beam angle of 0 degrees was used and traced a 128 × 128 grid of rays to decrease computational time . since there is a twelve - fold reduction in information compared to the initial study , the cramér - rao lower bound ( crb ) was noticeably larger , as shown in the table below . in the search space , the value of the normalized objective function was 226 . 74 at the upper limit , 313 . 09 at the lower limit , and 35 . 709 at the starting point . at the termination point of the optimization , the function value was 1 . 0012 , yielding a fractional error of 2 . 2 × 10 − 3 compared to that of the true minimum , 0 . 99898 . therefore , using simulated annealing allows a significantly larger search space to be explored that is comparable to known statistical variations and use of a reasonable starting point , yet still obtain accurate estimates of ocular parameters by means of inverse optical design . 1 . j . tabernero , a . benito , v . nourrit , and p . artal , “ instrument for measuring the misalignments of ocular surfaces ,” opt . express 14 , 10945 ( 2006 ). http :// www . opticsexpress . org / abstract . cfm ? id = 116620 2 . p . rosales and s . marcos , “ phakometry and lens tilt and decentration using a custom - 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280 ( 1987 ). all references throughout this application , for example patent documents including issued or granted patents or equivalents ; patent application publications ; and non - patent literature documents or other source material ; are hereby incorporated by reference herein in their entireties , as though individually incorporated by reference , to the extent each reference is at least partially not inconsistent with the disclosure in this application ( for example , a reference that is partially inconsistent is incorporated by reference except for the partially inconsistent portion of the reference ). all patents and publications mentioned in the specification are indicative of the levels of skill of those skilled in the art to which the invention pertains . references cited herein are incorporated by reference herein in their entirety to indicate the state of the art , in some cases as of their filing date , and it is intended that this information can be employed herein , if needed , to exclude ( for example , to disclaim ) specific embodiments that are in the prior art . for example , when a structure is claimed , it should be understood that structures known in the prior art , including certain structures disclosed in the references disclosed herein ( particularly in referenced patent documents ), are not intended to be included in the claim . when a group of substituents is disclosed herein , it is understood that all individual members of those groups and all subgroups of the group members , and classes of group members that can be formed using the substituents are disclosed separately . when a markush group or other grouping is used herein , all individual members of the group and all combinations and subcombinations possible of the group are intended to be individually included in the disclosure . every formulation or combination of components described or exemplified can be used to practice the invention , unless otherwise stated . specific names of optics and other materials are intended to be exemplary , as it is known that one of ordinary skill in the art can name the same optics and materials differently . one of ordinary skill in the art will appreciate that methods , device elements , starting materials , imaging methods , and analysis methods other than those specifically exemplified can be employed in the practice of the invention without resort to undue experimentation . all art - known functional equivalents , of any such methods , device elements , starting materials , imaging methods , and analysis methods are intended to be included in this invention . whenever a range is given in the specification , for example , a distance range , all intermediate ranges and subranges , as well as all individual values included in the ranges given are intended to be included in the disclosure . as used herein , “ comprising ” is synonymous with “ including ,” “ containing ,” or “ characterized by ,” and is inclusive or open - ended and does not exclude additional , unrecited elements or method steps . as used herein , “ consisting of ” excludes any element , step , or ingredient not specified in the claim element . as used herein , “ consisting essentially of ” does not exclude materials or steps that do not materially affect the basic and novel characteristics of the claim . any recitation herein of the term “ comprising ”, particularly in a description of components of a structure or in a description of elements of a device , is understood to encompass those structures and methods consisting essentially of and consisting of the recited components or elements . the invention illustratively described herein suitably may be practiced in the absence of any element or elements , limitation or limitations which is not specifically disclosed herein . the terms and expressions which have been employed are used as terms of description and not of limitation , and there is no intention in the use of such terms and expressions of excluding any equivalents of the features shown and described or portions thereof , but it is recognized that various modifications are possible within the scope of the invention claimed . thus , it should be understood that although the present invention has been specifically disclosed by preferred embodiments and optional features , modification and variation of the concepts herein disclosed may be resorted to by those skilled in the art , and that such modifications and variations are considered to be within the scope of this invention as defined by the appended claims . in general the terms and phrases used herein have their art - recognized meaning , which can be found by reference to standard texts , journal references and contexts known to those skilled in the art . the definitions are provided to clarify their specific use in the context of the invention .