Classifications

• • 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
  • A61B3/103—Objective types, i.e. instruments for examining the eyes independent of the patients' perceptions or reactions for determining refraction, e.g. refractometers, skiascopes
• • 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
• • 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

• Various objective techniques can be used to measure the spherical and cylindrical refractive errors of the human eye. They are fast and constitute an attractive alternative to performing a subjective refraction. Objective refraction is not only useful but often essential, for example, when examining young children and patients with mental or language difficulties. However, one major concern is the ability to properly determine objectively the refraction of the observer. Since all those objective methods are based on the light reflected -from the retina and emerging from the eye, the ocular aberrations reduce the accuracy of the measurement. The eye suffers from many higher-order aberrations beyond defocus and astigmatism, which introduce defects on the pattern of light detected.
• photorefractive methods are based on paraxial optical analysis, and it has been shown that there can be a significant degree of measurement uncertainty when the spherical aberration of the normal human eye is considered. Aberrations also influence the retinoscopic measure.
• autorefractors provide reliable measurements of the refractive state of the eye, their limitations in accuracy and repeatability are well known. For example, there are discrepancies between autorefractive and subjective measurements, especially with astigmatism, or when the degree of ametropia is large. Such discrepancies are described in M.
• Elliott et al "Repeatability and accuracy of automated refraction: A comparison of the Nikon NRK-8000, the Nidek AR-1000, and subjective refraction," Optom. Vis.
• Figure 1 A The simplest case of vision correction is shown in Figure 1 A, in which the only error is of focus. That is, the rays R passing through the edge of the pupil 103 of the eye
• paraxial plane 110 which is spatially separated from the plane 112 of the retina. Accordingly, the only correction required is to shift the plane of focus from the paraxial plane 110 to the retinal plane 112.
• the images before, at and after the paraxial plane 110 are shown as 124, 126 and 128, respectively.
• FIG. IB shows an example of the image formation by a myopic eye 102' with negative spherical aberration. Without spherical aberration, all the rays R' would focus on the paraxial plane 110, and then the refraction of the eye would be calculated from the spherical negative lens required to displace the focus plane to the plane 112 lying on the retina. However, due to spherical aberration, the rays R passing through the edge of the pupil 103 converge at a plane 104 closer to the eye (marginal plane). That simple example shows how the distribution of rays in different planes produces images 114-122 with different quality. The refraction of that eye should be the one required for displacing a plane of "best image" to the retina.
• FIG. lC Such a situation is shown in Figure lC.
• the rays R" and R'" from different locations in the pupil 103 of the eye 102" have focal points which are not coincident or even coaxial.
• the images taken at various locations are shown as 130, 132 and 134. hi cases in which not all aberrations can be corrected, or in which all aberrations can be only partially corrected, it is necessary to determine which of the images 130, 132 and 134 is the best image.
• the best image is not, or at least not necessarily, achieved by correcting the defocus and astigmatism corresponding to the paraxial approximation, which does not consider the effect of higher order aberrations.
• the question then is what is such a "best image.”
• the best image would correspond to a plane where the size of the spot is minimum. That plane, shown in Figure IB as 106, is called the plane of least confusion (LC) and, for example, for a system aberrated with spherical aberration lies at 3/4 of the distance between the paraxial and marginal planes.
• LC plane of least confusion
• the plane 108 where the root-mean-square (RMS) radius of the spot is minimum h the example of Figure IB, that plane lies midway between the marginal and paraxial planes.
• RMS root-mean-square
• the spots determined geometrically do not accurately reflect the point spread function (PSF), which is the computed retinal image based on the results of the wavefront sensor and which should be calculated based on the diffraction of the light at the exit pupil.
• PSF point spread function
• the distribution of light in a real image is usually very different from the image predicted geometrically with ray tracing. Any consideration about image quality should be done using diffraction theory.
• Second-order polynomials, Z°' ⁇ 2 represent
• the RMS of the wave aberration has been used as a measure of how aberrated an eye is and as a metric of image quality: the lower the RMS, the better the image quality.
• a fact that has supported that use is that the RMS correlates, for small aberrations, with another popular metric also used as a criterion of image quality, the Strehl ratio, defined as the peak of irradiance of the PSF. A large value of Strehl ratio indicates a good image quality.
• Strehl ratio and RMS of the wave aberration are inversely proportional: when the Strehl ratio is maximum, the RMS is minimum.
• An advantage of that is that the RMS of the wave
• any correction of the refractive errors of the eye, or of a set of higher-order aberrations, could be determined by setting to zero the corresponding Zernike
• the RMS minimization technique uses the coefficients and a ' from the
• the paraxial technique extracts the total defocus and astigmatism in the wave aberration.
• Both of the above techniques which are based on the pupil plane and use the data of the wave aberration itself, fail when higher-order aberrations increase.
• the difference between the subjective and objective determinations of the aberration increases with the RMS of the wavefront aberration, as shown in Fig. ID, in which curve (1) indicates the RMS minimization technique and curve (2) indicates the paraxial technique.
• the higher-order aberration in the population has been found to average 0.3 ⁇ , as shown in Fig. IE.
• the above-noted techniques do not work for approximately half of the population and can introduce errors of up to one diopter.
• the above and other objects are achieved through a computational system and method which determine the refractive error of the eye from measurements of its wave aberration.
• the procedure calculates the combination of sphere and cylinder that optimizes one or more metrics based on the distribution of light in the retinal image, which is affected by the higher-order aberrations.
• the retinal image which is the distribution of light on the retinal or image plane, is calculated from the results of a Shack-Hartmann or other detector.
• a metric based directly on the retinal image can be computed, or a metric which is a proxy for the retinal image can be used. Any metric on the image plane can be used, and one or more metrics can be used.
• the method yields an optimum image that is correlated with the subj ective best retinal image. Since the method is computational, a computer is the only hardware required, and it can be combined with a wavefront sensor in a compact instrument.
• the present invention takes into account the fact that while pupil-plane metrics do not accurately predict the subjective refraction, image-plane metrics do. While the techniques of the prior art were adequate for only about 25% of subjects with a precision of ⁇ 0.25 D or 50% of subjects with a precision of ⁇ 0.5 D, the present invention will provide suitable correction for most subjects with errors ⁇ 0.25 D.
• both the peak and the tails of the metric value can be used; that is, information from the curve of the metric other than the location of the maximum can be used.
• the width of the curve can be used for "tolerancing," since a narrower curve indicates a lower tolerance and thus a more critical need for accurate correction.
• An example is better fitting of a contact lens which corrects sphere and not astigmatism for subjects with a large tolerance to astigmatism.
• autorefraction which is limited to a single pupil size
• the present invention is not so limited.
• the present invention allows the subj ective refraction to be calculated for any pupil size equal to or smaller than the pupil size over which the wave aberration was measured.
• the present invention is further directed to a second application flowing from the above-noted computational system and method.
• spectacles and contact lenses have been successfully used to correct defocus and astigmatism (second-order aberrations), they leave the higher-order aberrations uncorrected.
• a conventional correction offers a sufficient improvement.
• the higher- order aberrations have a significant impact on the retinal image quality in normal eyes for large pupils and also for small pupils in old subj ects or in abnormal subj ects such as post refractive surgery or keratoconus patients.
• the use of an adaptive optical system has successfully corrected higher-order aberrations and provided normal eyes with supernormal optical quality.
• Recent developments make viable the idea of implementing supercorrecting procedures.
• lathe technology allows the manufacture of contact lenses with nearly any aberration profile, and there is an ongoing effort to refine laser refractive surgery to the point that it can correct other defects besides conventional refractive errors.
• the aberrations to be corrected are selected, or all of the aberrations are corrected partially. For example, if n aberrations can be measured, m ⁇ n aberrations can be corrected.
• the present invention permits a determination of the values of the compensation aberrations in the correcting method required to optimize the subject's vision. For example, in some countries it is common to correct for sphere but not astigmatism. The present invention provides an improved way to do so. As another example, since the eye is not stable, residual aberrations cannot be avoided. The present invention minimizes problems caused by such residual aberrations.
• the second part of the present invention provides a computational procedure to design an optimum pattern of a customized correction of a few aberrations of the eye besides astigmatism and defocus.
• the procedure considers the effect of the remaining aberrations that have been left uncorrected to calculate the adequate values of the aberrations to be corrected in order to achieve the best image quality.
• the computational procedure calculates the prescription of the refractive error of a subject based on the optimum values of those metrics.
• the present invention is based on the surprising discovery that when correction is carried out in accordance with a metric measured on the image plane, it is not necessary to take into account the brain's preference in image quality.
• the use of a metric which takes the brain into account produces no significant difference.
• corrections would have to take into account the brain's preference in image quality. For that reason, techniques from astronomy, in which such effects do not arise, would not have been considered. Thus, computation is significantly simplified over what the inventors originally thought was required.
• wavefront sensors can improve objective refraction by using image-plane metrics (or quantities which function as proxies for image-plane metrics) to incorporate the effect of higher-order aberrations.
• the present invention allows the prediction of subjective refraction from any reliable wavefront device and performs substantially better than current autorefractors.
• Some limitations of autorefractors are: the pupil size; the level of radiation (often low) returning from the retina and analyzed by the detector; the fact that the target, such as a grating, is blurred twice in its double pass through the eye's optics; and the fact that current autorefractors estimate three and only three parameters (sphere, cylinder and axis).
• the present invention can optimize the correction for any number of aberrations, from defocus alone to as many aberrations as have been measured.
• the present invention is applicable to any technique for correction, including contact lenses, intraocular lenses, spectacles, laser refractive surgery, and adaptive optics.
• the present invention allows prescribing a correction based on the patient's tolerance to departures from the optimum correction.
• the patient's tolerance to a contact lens that corrects only sphere and not astigmatism can be objectively estimated.
• proxy metric it has been found empirically that in many subj ects, the best image can be predicted from the aberration coefficients. If the aberration coefficients can be used to calculate two results whose errors have opposite signs, the proxy metric can be a simple average or a weighted average.
• Figs. 1A-1C show examples of image formation by eyes having various degrees of aberration
• Figs. ID and IE show the results of prior-art techniques for vision correction
• Fig. 2 shows a flow chart of operations performed in determining a refractive correction needed, assuming monochromatic light
• Fig. 3 shows a modification of the flow chart of Fig. 2 to take chromatic defocus into account
• Fig. 3A shows a search for an optimum metric in one dimension of three- dimensional space
• Fig. 4 shows examples of the parameter search of Fig. 2 for an eye with small aberrations and an eye with large aberrations
• Fig. 5 shows an example of the calculation of an optimal aberration for a subject using the technique of Fig. 3;
• Figs. 6 A and 6B show the values of different metrics at different image planes
• Fig. 7 shows an apparatus for implementing the operations of Fig. 2 or Fig. 3
• Figs. 8A-8F show a comparison of subjective and objective refraction as determined through various image metrics
• Fig. 9 shows the root mean square error (RMSE) of residual refraction after correction through the use of various image metrics
• Fig. 10 shows the dependence of the discrepancy between subjective and objective refraction on the RMS of the wave aberration
• Fig. 11 shows the dependence of tolerance to refractive errors on higher-order aberrations
• Figs. 12A and 12B show a comparison between metric tolerance and subjective acuity tolerance
• Figs. 13 A and 13B show binocular refraction correction
• Figs. 14A-14C show simulated images of a scene viewed by a subject after various types of correction
• Figs. 15 A- 15 C show the correlation between the subj ective spherical equivalent and the objective spherical equivalent according to experimental results taken with a preferred embodiment of the present invention and with two other techniques;
• Figs. 16A-16C show the error between subjective and objective spherical equivalent as a function of the spherical aberration for the same experimental results;
• Figs. 17A-17C show the correlation between the subjective and objective cylinder for the same experimental results
• Figs. 18A-18C show the error between subjective and objective cylinder as a function of the amount of higher order aberrations for the same experimental results.
• Figs. 19A- 19C show the correlation between the subj ective and obj ective axes of astigmatism for the same experimental results.
• Wave aberration is the difference in optical path between marginal rays and rays passing through the center of the exit pupil. It can be expressed as a linear combination
• n the order of the aberration is indicated by n.
• Second-order coefficients represent:
• Pupil function is defined as:
• A(r, ⁇ ) is the amplitude transmitted through the pupil (which in the preferred embodiment will be assumed to be equal to 1 within the pupil, and 0 outside the pupil), and W(r,0) is the wave aberration.
• Point spread function is the distribution of irradiance on the image plane that the eye forms of a point source. It can be calculated from the pupil function by means of a Fourier transform (FT):
• Modulation transfer function is the modulus of the so-called optical transfer function (OTF), which is the Fourier transform of the PSF.
• NSF Neural contrast sensitivity function
• Contrast sensitivity function is the standard measurement of how sensitive observers are to gratings with different spatial frequencies. Since both optical factors and neural factors are implicated, the CSF is ultimately a description of the visual performance of the subject. For example, the maximum spatial frequency that can be detected (i.e., when the CSF falls to zero) gives a measure of the observer's visual acuity.
• the CSF can be determined subjectively by finding the lowest contrast
• the CSF can be obtained as the product of the optical modulation transfer function and the neural contrast sensitivity:
• Strehl ratio is the peak value of the PSF or, equivalently, the volume or energy of the MTF.
• Variance of the PSF measures the difference between the lowest values of the PSF and the highest values. The larger the variance, the sharper the PSF. It is calculated mathematically as:
• Entropy of the PSF The entropy of an image is a measure of how spread the irradiance is from the center; i.e., it is a measure of the effective area of the image.
• the entropy of the PSF is calculated as:
• the aberration-free PSF (Airy image) possesses the minimum entropy. Any aberration leads to increased entropy.
• Encircled energy (within Airy disk) of the PSF The encircled energy that falls within a small area around the peak of the image can solve the potential problem with the Strehl ratio, since it would measure the intensity integrated in an region rather than the single peak of intensity.
• a convenient metric is the encircled energy calculated as the fraction of light in the PSF that falls within an area corresponding to the Airy disk.
• the Airy disk encircles 84% of the total energy in the PSF.
• the encircled energy could be implemented with a disk encircling more or less of the total energy, as various circumstances warrant.
• ⁇ a indicates the axis of the astigmatism.
• ro is the radius of the pupil that the wave aberration describes.
• the wave aberration of the lens is expressed in Zernike polynomials, the wave aberration is: W + a '2 ⁇ Z ⁇ 2 . (11)
• Strehl ratio entropy of the PSF
• variance of the PSF entropy of the PSF
• MTFa defined as the integral of the MTF within the range of discriminable frequencies, from 0 to 60 c/deg
• CSFa defined as the integral of the CSF, which is obtained as the product of the MTF and the neural CSF.
• the wave aberration (W) of the eye expressed in Zernike polynomials in step 202 is the input data. Let ⁇ o be the wavelength for which that wave aberration has been measured. From W we extract the second-order Zernike coefficients, a°' ⁇ 2 , in step 204, yielding a "higher-order wave aberration":
• W h -o is composed of higher-order aberrations, some of which are balanced with defocus and astigmatism in the sense of minimum RMS. If the minimum RMS corresponded to the best image, the refractive correction of the eye would be obtained directly from the
• That pupil function characterizes the higher-order aberrations of the subject and does not need to be calculated anymore.
• the pupil functions are then:
• Those pupil functions are independent of the subject. They can thus be calculated once and stored to be used anytime, thereby enhancing computational efficiency.
• the sampling of the space of search can be determined from the minimum step difference in focus that a subject can detect.
• a spacing of 0.1 microns between values of the Zernike coefficients c°' ⁇ 2 is adequate. For example, for a 4 mm pupil, that step
• total pupil functions in step 210 as the product of the higher- order pupil function, p ⁇ ,. 0 , and every second-order pupil function that cover the space of search, p s . 0 :
• the space of search is typically a three-dimensional space, i.e., defocus, astigmatism and axis of astigmatism.
• Fig. 3 A shows the metric value plotted against one dimension, namely, defocus.
• a small error between the maximum of the metric and the subjectively determined optimum correction would indicate that the metric is a good predictor of subjective refraction.
• the optimum wave aberration of the eye after correcting defocus and astigmatism, as determined in step 218, should be:
• the refraction of the subject as determined in step 220 will be:
• Figure 4 shows an example of the search for parameters c 2 ' ⁇ 2 for two eyes with
• the gray level indicates the value of one of the metrics of image quality. For the less aberrated eye, the maximum value of the metric is obtained
• Pci ⁇ ro A - ex ⁇ ⁇ c Z° , (21) ⁇ i
• c Chm is the Zernike coefficient that represents the defocus for every wavelength
• ⁇ is the wavelength taking values within the visible spectrum.
• the reference wavelength for free chromatic aberration is 555 nm, coincident with the maximum of photopic sensitivity.
• the polychromatic PSF is calculated by integrating the monochromatic PSF across the spectral distribution weighted with the standard spectral sensitivity, V( ⁇ ), of the eye.
• Figure 5 shows an example in a subject. From the original wave aberration of the eye we calculated the optimum wave aberration after a compensation of defocus and astigmatism. The sphere and cylinder of the correcting lens prescribed for that eye are obtained. An extension of the procedure outlined consists of doing a search of the best parameters to implement a customized correction of a few higher-order aberrations besides astigmatism and defocus. As an example, if one can make an aspherical contact lens to correct the spherical aberration of the eye, our procedure can yield the optimum value of aberration that the lens should correct in order to achieve the best image quality in the presence of the uncorrected aberrations.
• Figures 6A and 6B show the value of the different metrics at different image planes.
• the plane of 0 diopters is the paraxial plane.
• the vertical dashed line indicates the plane of the RMS minimum.
• Two examples are shown, one with only spherical aberration (the value for the average eye) in Figure 6A, and other with all the higher- order aberrations of a typical eye in Fig. 6B.
• the case shown in Fig. 6B the astigmatism has been optimized, and only the dependence on defocus is shown. The following can be observed:
• the minimum RMS does not correspond to the maximum of the other metrics. -For the eye with only spherical aberration, one can see that the Strehl ratio exhibits two global maxima symmetrically around the plane of minimum RMS.
• Figure 7 shows an experimental system to measure the subjective refraction and the wave aberration of the subject.
• the apparatus is based on a Shack-Hartmann sensor, which is well known in the art.
• the subject sees through the system a Snellen chart presented on a CRT.
• the subj ective refraction and the wave aberration measurements are performed under the same conditions.
• the subject is shown a Snellen chart 702 on a CRT, an LCD screen, or a similar device.
• the Snellen chart can be printed, or another chart can be used.
• the Snellen chart 702 is imaged through a beamsplitter 704, a conjugate lens system 706, another beamsplitter 708, and optionally a removable sphere-cylindrical correction system 710 onto the retina of the subj ect' s eye E.
• Light from a laser diode 712 is directed through the beamsplitter 708 onto the retina of the subject's eye E.
• the light from the laser diode 712 reflected from the retina passes through the beamsplitter 708, the conjugate lens system 706 and the beamsplitter 704 into a Shack-Hartmann sensor 714, which includes a lenticular array 716 and a CCD or other photodetector array 718.
• the Shack-Hartmann sensor 714 produces an output which is directed to a computer 720 programmed to perform the technique of Fig. 2 or Fig. 3.
• a widely-available Pentium El-class computer suffices.
• the computer 720 outputs the optimal wave aberration of Fig.2 or 3, step 218, and the required refractive correction of Fig. 2 or 3, step 220.
• the latter can be supplied to a lens fabrication, surgical correction, adaptive optics, or image simulation system 722, which can prepare a spectacle lens, a contact lens, or an intraocular lens to correct the eye's wave aberration, control a surgical technique upon the eye E to correct the aberration, provide adaptive optics such as a deformable mirror to provide a counter-aberration, or simulate an image showing how the subject would view a scene after correction of aberrations.
• a lens fabrication, surgical correction, adaptive optics, or image simulation system 722 which can prepare a spectacle lens, a contact lens, or an intraocular lens to correct the eye's wave aberration, control a surgical technique upon the eye E to correct the aberration, provide adaptive optics such as a deformable mirror to provide a counter-aberration, or simulate an image showing how the subject would view a scene after correction of aberrations.
• FIGS. 8A-8F show the comparison of the subjective refraction with the estimated objective refraction for the 6 eyes.
• Fig. 8 A shows the refraction calculated by the RMS and paraxial approximations.
• Figs. 8B-8F show the refraction calculated by using the following metrics: Strehl ratio, entropy of the PSF, variance of the PSF, area of the MTF between 0 and 60 c/deg, and area of the CSF.
• the refraction is expressed in diopters.
• Figure 10 shows the dependence of the discrepancy between the subjective and the objective refraction shown in Figures 8A-8F, on the RMS of the wave aberration.
• the higher-order aberrations (not defocus and astigmatism) are included.
• the error in the refraction estimated with the other metrics shows no dependence with the amount of higher-order aberrations.
• Figure 11 shows that higher-order aberrations also influence the eye's tolerance to refractive errors. That figure shows curves of a metric value against refractive error in diopters for two eyes. The curve for eye 1 shows a much greater slope from its peak, and thus a lower tolerance to refractive errors, than the curve for eye 2.
• Figures 12A and 12B show metric tolerance curves plotted along with subjective acuity tolerance for two eyes. As shown, the two types of tolerances follow each other closely.
• 13A and 13B which show curves of a metric value plotted against diopters for the right and left eyes, respectively.
• the arrow marked M indicates the best monocular correction for the right eye, while the arrow marked B indicates the best binocular correction based on a balance with the worse of the two eyes. Binocular balancing takes into account the different needs of different subjects.
• binocular balancing determines how successful correction will be over a range of distances (depth of field) other than infinity.
• any metric which is a proxy for an image-plane metric i.e., which reflects the quality of the image on the image plane
• any metric which is a proxy for an image-plane metric i.e., which reflects the quality of the image on the image plane
• the average can be a simple average (50%-50%) or a weighted average.
• the average is a proxy for the quality of the image on the image plane, which neither the RMS technique nor the paraxial technique could provide on its own.
• the objective procedure described yields an accurate value for the subjective refraction of the subject. It seems that the different image quality metrics proposed produce similar results. However, some of them, as for example the CSF, could perform a more robust role, since they present single peaks and narrower windows of tolerance.
• the curves of tolerance described above indicate that the present invention can be implemented to be an intelligent method to prescribe a customized ocular refraction considering several factors such as accepted tolerance, the subject's working conditions, pupil diameter, etc.
• Figs. 14A-14C Another practical application will be disclosed with reference to Figs. 14A-14C.
• the optimization of an image metric allows not only an estimation of the subjective refraction, but also a simulation of scenes that the subject would see after a best correction. Simulated images are often used to see how the subject sees the real image with aberrations. Usually these simulated images are calculated by using pupil plane methods, so that they do not truly correspond to the actual images that the observer sees.
• An example is set forth in Figs. 14A-14C.
• the aberrations of a typical eye were used to calculate the image of a scene through the eye's optics when the eye is best corrected for defocus and astigmatism.
• Fig. 14B shows a simulated image assuming optimization of image-plane metrics, while Figs.
• FIG. 14A and 14C show simulated images assuming optimization of pupil-plane metrics by the paraxial approximation and minimum RMS, respectively.
• a comparison of Fig. 14B withFigs. 14A and 14C shows that the optimization of image-plane metrics produces the least blurred image.
• Images can be simulated after a best correction, whether the correction is for defocus and astigmatism, for defocus only, or for any set of aberrations.
• the simulation of images would be an important complementary feature in an instrument. Depending on the particular aberrations of each subject, the retinal images maybe very different, and it is very important to have an estimation of those images when one is going to apply a correction. Just an example: if the simulated images correcting and not correcting the astigmatism of an eye are similar in appearance, that would indicate that the correction will not provide much benefit. It will be readily apparent from the above that the present invention provides an advantage over the prior art in terms of reliable measurement.
• _ WF rms prediction a method based on the pupil plane that uses the aberration coefficients analytically to minimize the rms of the wave aberration
• _ AUTO which corresponds to measurements with a commercially available autorefractor
• Figs. 15A-15C show the correlation between subjective spherical equivalent and the objective spherical equivalent from WF, AUTO, and optimization (OPT), respectively, in diopters. All show a correlation coefficient close to one. However, the methods differ substantially in the accuracy with which the subj ective spherical equivalent can be predicted.
• Figs. 16A- 16C show the error between the subjective and objective spherical equivalent as a function of the spherical aberration in microns for WF, AUTO and OPT, respectively.
• the average error (RMSE), in spherical equivalent, across the 146 eyes was as follows: WF: 0.6 ⁇ 0.7 D
• OPT 2 % The following can be concluded about the spherical equivalent prediction. First, WF is clearly worse than AUTO and OPT, and their failure increases with the aberrations. Second, AUTO and OPT are similar, although OPT is better (see RMSE and the standard deviation).
• Figs. 17A-17C show the correlation between subjective and objective cylinder in diopters for WF, AUTO, and OPT, respectively. As can be seen, OPT offers the best correlation and the slope closest to one.
• Figs. 18A-18C show the error between subjective and objective cylinder as a function of the amount of higher order aberrations in microns for WF, AUTO and OPT, respectively. WF and AUTO are aberration-dependent, but OPT is not.
• Figs. 19A-19C show the correlation between subjective and objective axis of astigmatism in degrees for WF, AUTO, and optimization (OPT), respectively.
• the average error (RMSE) in cylinder is as follows:
• OPT ⁇ 1 %
• WF metric optimization method
• AUTOrefractometer predicts the sphere reasonably well, but the error in cylinder depends on the aberrations. OPT is better that AUTO.
• OPTimization is used, the error in sphere and the error in astigmatism do not depend on aberrations.
• OPT metric optimization
• the pupil plane method shows errors. That means that there is a variability due to factors others than aberrations.
• the OPT method reduces the error due to aberrations, but not below the limit of experimental variability. It is anticipated that OPT would have performed even better had pupil size been accurately measured and taken into account in computing OPT. Indeed, one of the advantages of refracting the eye from wave front sensing instead of an autorefractor is that the refraction can be computed for any desired pupil size.
• the variability is caused partly by the precision of subj ective refraction, and partly by the fact that the measurements in the subject population were done without paralyzing the accommodation, which can easily introduce errors of 0.25-0.5 D.
• the WA is relatively robust to small changes in accommodation except coefficient c 4 . That could explain why the cylinder can be predicted by metric optimization with precision higher that 0.25 D, but the sphere can be predicted with less precision.
• the WA of one person's eye measured in one city was similar to that of the same eye taken in another city, but with changes in defocus. If experimental errors in c 4 of the WA are present, that variability cannot be reduced with any method. The better the accuracy in the WA data, the better the coefficients can be used to predict the refraction.

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• 2001
  • 2001-10-04 US US09/969,600 patent/US6511180B2/en not_active Expired - Lifetime
  • 2001-10-04 WO PCT/US2001/031025 patent/WO2002030273A1/en active IP Right Grant
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  • 2001-10-04 CN CNB018188117A patent/CN100333685C/zh not_active Expired - Fee Related
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