Method and system for determining an eyeglass prescription

Abstract

The invention is directed to a method for determining an eyeglass prescription for an eye, in particular through the use of a non-transitory computer readable medium. The method includes the steps of providing a measurement indicative of the refractive properties of the eye; establishing an optimization space corresponding to a plurality of possible eyeglass prescriptions for the eye; determining a merit function, wherein a value of the merit function corresponds to a visual function of the eye when corrected using one of the plurality of possible eyeglass prescriptions within the optimization space, wherein the merit function includes a term depending on a magnitude of a corrective astigmatism of the one of the plurality of possible eyeglass prescriptions and causing a less optimal value of the merit function the higher the magnitude of the corrective astigmatism and/or the higher the magnitude of a difference between the corrective astigmatism and a subjective corrective astigmatism; and determining the eyeglass prescription by optimizing the value of the merit function. The invention is further directed to a system for determining an eyeglass prescription and a corresponding computer program product.

Claims

1. A method for determining an eyeglass prescription for an eye, the method comprising the steps of: providing a measurement indicative of the refractive properties of the eye; establishing an optimization space corresponding to a plurality of possible eyeglass prescriptions for the eye; determining a merit function, wherein a value of the merit function corresponds to a visual function of the eye when corrected using one of the plurality of possible eyeglass prescriptions within the optimization space, wherein the merit function comprises a term depending on a magnitude of a corrective astigmatism of the one of the plurality of possible eyeglass prescriptions and causing a less optimal value of the merit function the higher the magnitude of the corrective astigmatism and/or the higher the magnitude of a difference between the corrective astigmatism and a subjective corrective astigmatism; and, determining the eyeglass prescription by optimizing the value of the merit function.

2. The method of claim 1, wherein establishing the optimization space comprises defining ranges for one or more parameters characterizing the eyeglass prescription.

3. The method of claim 1, wherein optimizing the value of the merit function comprises iteratively determining a corrected wavefront indicative of the refractive properties of the eye and the corresponding possible eyeglass prescription.

4. The method of claim 1, wherein the eyeglass prescription is determined either by optimizing the value of the merit function to a maximum, and wherein the term has a smaller value the higher the magnitude of the corrective astigmatism of one of the plurality of the possible eyeglass prescriptions, or by optimizing the value of the merit function to a minimum, and wherein the term has a larger value the higher the magnitude of the corrective astigmatism of one of the plurality of the possible eyeglass prescriptions.

5. The method of claim 1, wherein the visual function is an acuity value of the eye when corrected or a blur value of the eye when corrected.

6. The method according to claim 1, wherein the term is proportional to the magnitude of the corrective astigmatism.

7. The method of claim 1, wherein the term has the form of $\pm \underset{i=1}{\overset{n}{.Math.}}{C}_i.Math.{\mathrm{MOA}}^i$ wherein MOA is the magnitude of the corrective astigmatism of one of the plurality of possible eyeglass prescriptions, n is an order constant and C.sub.i are the coefficients for the respective orders.

8. The method of claim 1, wherein the term has the form of
±C.Math.e.sup.MOA wherein MOA is the magnitude of the corrective astigmatism of one of the plurality of possible eyeglass prescriptions, e is the mathematical constant e and C is a proportionality coefficient.

9. The method of claim 1, the method further comprising the step of outputting the eyeglass prescription.

10. The method of claim 1, wherein the step of providing a measurement is conducted at a first site, and wherein the steps of establishing an optimization space, determining a merit function and determining the eyeglass prescription by optimizing the value of the merit function are conducted at a second site remote from the first site, and wherein the provided measurement is transmitted from the first site to the second site via a data network.

11. The method according to claim 1, wherein the method is for determining an eyeglass prescription for an eye through the use of a non-transitory computer readable medium.

12. A method for manufacturing a visual aid, the method comprising the steps of: determining an eyeglass prescription according to the following steps: providing a measurement indicative of the refractive properties of the eye; establishing an optimization space corresponding to a plurality of possible eyeglass prescriptions for the eye; determining a merit function, wherein a value of the merit function corresponds to a visual function of the eye when corrected using one of the plurality of possible eyeglass prescriptions within the optimization space, wherein the merit function comprises a term depending on a magnitude of a corrective astigmatism of the one of the plurality of possible eyeglass prescriptions and causing a less optimal value of the merit function the higher the magnitude of the corrective astigmatism and/or the higher the magnitude of a difference between the corrective astigmatism and a subjective corrective astigmatism; and, determining the eyeglass prescription by optimizing the value of the merit function; and, the method further comprising: manufacturing the visual aid according to the eyeglass prescription.

13. A system for determining an eyeglass prescription for an eye, comprising a processing unit configured to receive information about a measurement indicative of the refractive properties of the eye, to establish an optimization space corresponding to a plurality of eyeglass prescriptions for the eye, to determine a merit function, wherein a value of the merit function corresponds to a visual function of the eye when corrected using one of the plurality of possible eyeglass prescriptions within the optimization space, wherein the merit function comprises a term depending on a magnitude of a corrective astigmatism of the possible eyeglass prescription and causing a less optimal value of the merit function the higher the magnitude of the corrective astigmatism and/or the higher the magnitude of a difference between the corrective astigmatism and a subjective corrective astigmatism, and to determine the eyeglass prescription by optimizing the value of the merit function.

14. The system of claim 13, wherein the system further comprises an output device configured to output the determined eyeglass prescription.

15. The system of claim 13 further comprising a wavefront aberrometer located at a first site, wherein the processing unit is located at a second site, and wherein the first site and the second site are connected via a data network.

16. The system of claim 15, wherein the system further comprises an output device configured to output the determined eyeglass prescription.

17. A non-transitory computer program product comprising program code means for carrying out the steps of a method for determining an eyeglass prescription for an eye, the method comprising the steps of: providing a measurement indicative of the refractive properties of the eye; establishing an optimization space corresponding to a plurality of possible eyeglass prescriptions for the eye; determining a merit function, wherein a value of the merit function corresponds to a visual function of the eye when corrected using one of the plurality of possible eyeglass prescriptions within the optimization space, wherein the merit function comprises a term depending on a magnitude of a corrective astigmatism of the one of the plurality of possible eyeglass prescriptions and causing a less optimal value of the merit function the higher the magnitude of the corrective astigmatism and/or the higher the magnitude of a difference between the corrective astigmatism and a subjective corrective astigmatism; and, determining the eyeglass prescription by optimizing the value of the merit function.

18. The non-transitory computer program product of claim 17, wherein the program code means are for carrying out the steps of the method when the computer program product is run on a computer or processing unit.

19. The method of claim 1, wherein said term depending on a magnitude of a corrective astigmatism is a punishing term.

20. The system of claim 13, wherein said term depending on a magnitude of a corrective astigmatism is a punishing term.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The invention will now be described with reference to the drawings wherein:

(2) FIG. 1 shows an embodiment of a method for determining an eyeglass prescription for an eye;

(3) FIG. 2 shows an embodiment of a method for manufacturing a visual aid;

(4) FIG. 3 shows a diagram explaining the advantages of the current invention;

(5) FIG. 4 shows a further diagram explaining the advantages of the current invention;

(6) FIG. 5 shows an embodiment of a system;

(7) FIG. 6 shows a further embodiment of a system; and,

(8) FIG. 7 shows a further embodiment of a system.

DETAILED DESCRIPTION OF THE INVENTION

(9) Referring to FIG. 1, an embodiment of a method 100 generally includes a number of steps, as illustrated by the flow chart. In a first step, 110, the optical phase error of a patient's eye is measured using an objective method. Typically, this involves measuring a wavefront reflected from the eye using an appropriate sensor. Examples of sensors include various wavefront aberrometers, such as Hartmann-Shack wavefront sensors, Tscherning aberrometers, Talbot aberrometers, and double-pass aberrometers. The functional principal of a wavefront aberrometer is described in U.S. Pat. No. 6,382,795, which also includes a synopsis of a number of different variants.

(10) The measurement data is used as an input for a processing unit, typically including an electronic processor (e.g., a computer). The processing unit establishes a multi-dimensional optimization space (step 120), for which the processing unit calculates a merit function corresponding to, for example, the visual acuity of the eye. The dimensions of the optimization space typically correspond to the sphero-cylindrical corrections characterizing an eyeglass prescription (e.g., sphere, cylinder, and axis). The ranges for each of the dimensions of the optimization space can be set by the eye care professional, or preset by the processing unit. For example, the algorithm for establishing the optimization space can default to a certain range for each dimension, or the default can be over-ridden by the eye care professional based on the professional's experience with the patient. The values for the sphero-cylindrical corrections within each range can be established as desired. For example, each dimension can include a preset number of values (e.g., 10 or more, 100 or more), so that the incremental change between the values is determined by the range. Alternatively, or additionally, the incremental change between the values can be preset, in which case the number of values for each dimension is determined by setting the range. In some embodiments, the values can correspond to stock lens values within the range in each dimension.

(11) As an example, an optimization space can be established based on the patient's pre-existing prescription, where the ranges for sphere and cylinder are set from −5 diopters to +5 diopters about the sphere and cylinder values of the pre-existing prescription. The values can be incremented, for example, by 0.25 diopters within each range.

(12) Typically, the result is an optimization space that is composed of a finite number of (sphere, cylinder, axis) or (mean power (‘M’), J.sub.0, J.sub.45) co-ordinates for which a merit function can be evaluated.

(13) In some embodiments, the optimization space is composed of a single space. For example, each point in the optimization space can be a three component vector, e.g., having components corresponding to sphere, cylinder and axis or alternatively the Jackson cylinder components (M, J.sub.0, J.sub.45). In certain embodiments, the optimization space is divided into multiple optimization subspaces, such as two optimization subspaces. For example, each point in the first subspace can be a value for the sphere correction or defocus, and the components of a point in the second subspace can be values for cylinder and axis or the Jackson cylinder components (J.sub.0, J.sub.45). In a third step, in either case, a surface representing the wavefront of the optical correction for each co-ordinate in the optimization space or subspace is created and subtracted from the original wavefront, which yields a series of corrected wavefronts (step 130).

(14) Then in a fourth step, for each of those wavefronts a merit function is calculated (step 140), which correlates with either visual acuity, contrast sensitivity or with another measure of visual performance, or correlates with a combination of those measures of visual performance.

(15) In general, when the optimization space is divided into more than one subspace, the correction for the first subspace (e.g., sphere) should be determined first, and then subtracted from the measured wavefront before determining the correction for the second subspace (e.g., cylinder and axis).

(16) In order to calculate the data, for each point in the optimization space, a corresponding corrected wavefront is calculated. The corrected wavefront is the measured wavefront corrected by the corresponding spherical correction value. Specifically, in certain embodiments, the corrected wavefront is the original wavefront on which, depending on the point in the optimization space, a spherical surface (here referred to as spherical correction value) is added. The shape of this spherical surface at any radial location, r in millimeters, is given by the following equation:

(17) $\mathrm{SphericalShape}=C_2^0\sqrt{3}\left(2{\left(\frac{r}{r_0}\right)}^2-1\right)$
where r.sub.0 is the pupil radius in millimeters and

(18) $C_2^0=-\frac{{\mathrm{Dr}}_0^2}{4\sqrt{3}}$
where D is the point in the sphere power optimization subspace, in diopters.

(19) Then, a merit function value for each of the resulting corrected wavefronts is calculated. In general, merit function values can be calculated in a variety of ways. In certain example embodiments, the merit function may be calculated according to the methods disclosed in U.S. patent application Ser. No. 11/840,688, entitled “APPARATUS AND METHOD FOR DETERMINING AN EYEGLASS PRESCRIPTION FOR A VISION DEFECT OF AN EYE,” filed on Aug. 17, 2007 (now published as US 2009/0015787), the entire contents of which are incorporated herein by reference and for which features protection may be sought.

(20) For example, in some embodiments, at least two submetrics can be determined for one of the parameter sets in different stages of the propagation of light through the optical system represented by the eye and an optic corresponding to the eyeglass prescription. In other words, the light passes through the optical system represented by the eye and the optic. One now considers the deviation of the light ray compared to the ideal case, as expressed through a quality metric (submetric), when the light ray has traversed (propagated through) the system represented by the eye and the correction by different travel distances. A propagation in the reverse direction, e.g., directed from the system represented by the eye and the optic towards the object, is likewise conceivable. The propagation being considered here is not tied to a fixed direction through the system represented by the eye and the correction, but can be carried out for any desired number of directions (e.g., in general directions of the line of sight).

(21) These submetrics can include, for example, ray quality metrics such as for example metrics that measure the Strehl ratio or the energy of the point-image washout function enclosed within the Airy disc.

(22) An overall metric which reflects in particular the quality of the caustic (“caustic metric”) can be determined from a weighted sum of the previously determined submetrics. In some embodiments, all submetrics are given equal weight in the determination of the overall metric (caustic metric). In certain embodiments, a submetric of a preferred propagation stage is weighted more heavily than the submetrics in the propagation stages before and/or behind this preferred propagation stage. If one uses for example submetrics that take the image quality in different planes into account, then the submetric for the image on the retina (which corresponds to the submetric in the preferred propagation stage) would preferably be given more weight than the submetric for an image before or behind the retina of the eye. The weight ratio could be for example 60/40. Detailed explanation of such an example of possible metrics is given in document US 2010/0039614 A1, the disclosure of which is herein incorporated by reference and for which features protection may be sought.

(23) According to the current invention, the merit function comprises a term that takes into account the magnitude of the corrective astigmatism found in the optimized solution for the eyeglass prescription. Hence, this so-called “punishing term” leads to a less optimal result of the visual function the higher the magnitude of the possible prescription is and/or the higher the magnitude of a difference between the corrective astigmatism and a subjective corrective astigmatism provided by subjective refraction is. The subjective corrective prescription including the subjective corrective astigmatism may be provided as a fixed number or may be been measured via subjective refraction techniques earlier. By this, solutions with lower magnitudes of astigmatism or lower magnitudes of deviations from the subjective corrective astigmatism will be preferred. For example, the visual function may be effective blur and this visual function may become minimized during optimization. Then, the term may be set as being proportional to the magnitude of the corrective astigmatism. Hence, as will be laid out in further details below, the term may be +0.15 times the astigmatism magnitude of the possible eyeglass prescription. All units are diopters and a lower astigmatism solution will, hence, be preferred.

(24) As an example, it may be assumed the merit function is the squared dioptric difference between the measured wavefront's paraxial curvature and the objective prescription. Considering only Zernike aberrations through fourth order such a merit function may be given by

(25) $\mathrm{metric}={\left(m+\frac{c_2^{0}4\sqrt{3}-c_4^{0}12\sqrt{5}}{r^2}\right)}^2+{\left(j_0+\frac{c_2^{2}2\sqrt{6}-c_4^{2}6\sqrt{10}}{r^2}\right)}^2+{\left(j_{45}+\frac{c_2^{2}2\sqrt{6}-c_4^{2}6\sqrt{10}}{r^2}\right)}^2,$
where the c.sub.n.sup.m are the Zernike coefficients, r is the pupil radius, and m, j.sub.0, and j.sub.45 are the components of the trial prescription. In this case the optimal prescription components M, J.sub.0, and J.sub.45, are the those which minimize the merit function, and are given by

(26) $M=\frac{-c_2^{0}4\sqrt{3}+c_4^{0}12\sqrt{5}}{r^2}$$J_0=\frac{-c_2^{2}2\sqrt{6}+c_4^{2}6\sqrt{10}}{r^2}$$J_{45}=\frac{-c_2^{-2}2\sqrt{6}+c_4^{-2}6\sqrt{10}}{r^2}.$

(27) An example of a modified merit function, metric′, which punishes the magnitude of astigmatism, in particular the departure of the objective cyl from that obtained by a subjective refraction, would be
metric′=metric+k((j.sub.0−J.sub.0).sup.2+(j.sub.45−J.sub.45).sup.2).

(28) Where J.sub.0 and J.sub.45 are the cyl components of the subjective refraction, and k is a constant that controls the magnitude of the penalty. The cyl components that maximize this new metric, J′.sub.0 and J′.sub.45 are simply given by

(29) $J_0^{\prime }=\frac{J_0+{\mathrm{kJ}}_0}{1+k}$$J_{45}^{\prime }=\frac{J_{45}+{\mathrm{kj}}_{45}}{1+k}.$

(30) It shall be noted that for this simple metric the final cyl components are just weighted averages of the components found using the metric and the components from the subjective refraction.

(31) As a numerical example, it may be assumed a patient with a 4 mm pupil diameter having the measured values of a prescription of +1 diopter of sphere with −2 diopters of cyl (minus cyl convention) at 0 degrees, or equivalently M=1.00, J.sub.0−1.00, and J.sub.45=0. Further, c.sub.2.sup.0=0.5774, C.sub.2.sup.2=0.8165, C.sub.4.sup.2=0.0527, and all other Zernike coefficients equal zero. Entering these numbers into the expressions for M, J.sub.0, and J.sub.45 using the metric yields M=1.00, J.sub.0=1.25, and J.sub.45=0. Using the result of the modified metric with k=0.5 gives M′=1.00, J′.sub.0=1.17, and J′.sub.45=0.

(32) In this simple example the modified metric pushes the objectively derived cyl closer to the subjectively prescribed cyl as expected. For more complex merit functions and eye aberrations the extra cyl penalty can also systematically scale down local optima that are far from the prescribed cyl, allowing the algorithm to locate the locally optimal values which are closest to the subjective result.

(33) Last, in step 160, the eyeglass prescription is determined as the result of the optimization process.

(34) FIG. 2 shows an embodiment of a manufacturing method 200. Such manufacturing method may start in a starting step 205. Then, the method 100 to determine the corresponding eyeglass prescription may be conducted. Then, in a step 170, the visual aid, for example a spectacle lens, may be manufactured. The method then ends in step 210.

(35) Alternatively, after the determination of the eyeglass prescription in step 100, the eyeglass prescription may be outputted in a step 180. The output may be on an electronic display, via a printer or may be an output storing device that stores the eyeglass prescription. The method then ends in a step 215.

(36) In FIG. 3, the chart 220 shows the distributions of the differences between the calculated astigmatism and the astigmatism prescribed by the subjective refractions for just over 9000 eyes. The “without term” curve represents the differences using known metrics, and the “with term” curve shows the distribution after adding a so-called “rubber band” penalty proportionally based on the magnitude of the astigmatism. In this data set, all eyes whose prescribed astigmatism was exactly zero (about 10% of the original set) were removed, since they would bias the results.

(37) The penalty term was set to 0.15 times the magnitude of the astigmatism. In other words, rather than minimizing the effective blur, it was minimized the blur estimate plus 0.15 times the estimated astigmatism, all in diopters. Hence lower astigmatism solutions were favored.

(38) The median difference to the conventional metric for this data set was 0.11 diopters, the conventional metric having higher astigmatism magnitudes than subjective refraction. With the modified metric the median difference was eliminated; reduced to 0.00. At the same time the width of the distribution was not significantly affected by the shift. The 25 to 75 percentile differences were −0.059 to 0.301 diopters for the conventional metric, for a width of 0.360, while the range was a more symmetric −0.168 to 0.178, for a width of 0.348 diopters for the modified metric.

(39) In FIG. 4, the before and after curves for the magnitude of the astigmatism differences (as apposed to the differences in the cyl magnitudes) are shown. Here the distribution for the modified metric is slightly narrower. For eyes whose cyl moved by more than 0.01 diopters, eyes moving closer to the subjective prescription outnumbered those moving farther away by a ratio of about 2 to 1.

(40) FIG. 5 shows an embodiment of a system 10 according to the current invention. A system 10 for determining an eyeglass prescription for an eye comprises a processing unit 14 configured to receive information about a measurement indicative of the refractive properties of the eye, to establish an optimization space corresponding to a plurality of eyeglass prescriptions for the eye, to determine a merit function, wherein a value of the merit function corresponds to a visual function of the eye when corrected using one of the plurality of possible eyeglass prescriptions within the optimization space, wherein the merit function comprises a term depending on a magnitude of a corrective astigmatism of the possible eyeglass prescription and causing a less optimal value of the merit function the higher the magnitude of the corrective astigmatism, and to determine the eyeglass prescription by optimizing the value of the merit function.

(41) FIG. 6 shows a further embodiment of the system 10 according to the current invention. The optical wavefront aberration of a patient's eye of the wavefront aberration can be determined via an aberrometer 12. Further, a subjective refraction may also be determinable. The calculation of the eyeglass prescription is then conducted on the processing unit 14. The processing unit 14 may comprise a computer program product 15 that stores executable program code to execute the methods explained above. Then, the system 10 may further comprise an output device 16 that may be a display, a printer or a storing device to output the determined eyeglass prescription to the output device 16. The aberrometer 12 is connected to the processing unit 14 via a line 18. The processing unit 14 is connected to the output device 16 via a line 20. Both lines 18 and 20 may each be a wired connection or a wireless connection for data transfer between the processing unit 14 from and to the aberrometer 12 and the output device 16.

(42) By this, the system 10 is able to automatically determine an eyeglass prescription based on data provided via an aberrometer. However, instead of an aberrometer 12, the data underlying the optimization process may be also be acquired via the line 18 from a storing device that stores a multitude of patients' data acquired previously.

(43) In FIG. 7, a further embodiment of the system 10′ is shown. The aberrometer 12 may be located at a first site 26. The processing unit 14 is located at a second site 28. The output device 16 may be located at a third site 30 or may be also located at the first site 26. Further, a manufacturing unit 32 from a manufacturing visual aid may be present at either the third site 30 or the first site 26.

(44) The first site 26, the second site 28 and the third site 30 are remote from each other. The first site 26 is connected with the second site 28 via a data network 22. The second site 28 and the third site 30 are connected via a data network 24. By this, it may be possible that refraction data provided via the aberrometer 12 can be sent to the processing unit 14. Further, a subjective refraction, in particular a subjective corrective astigmatism, may also be sent to the processing unit 14, for example from the first site 26 or any other site. Further, for example, the determined eyeglass prescription may then be sent back to the first site, for example a spectacle shop, to be recognized by an ophthalmologist and provided to, for example, the possible wearer. Further, the eyeglass prescription determined can also be forwarded to a remote manufacturing unit to manufacture the respective visual aid. The manufacturing unit can be located at the first site 26. In this case, the data of the aberrometer is transmitted via connection 22 to the processing unit 14 at the second site 28 and then, the calculated eyeglass prescription is transferred back to the first site 26 and its possible manufacturing unit 32. Alternatively, from the second site 28, the determined eyeglass prescription can be transferred to a third site 30 with a possible manufacturing unit 32 to manufacture the visual aid. Last, it is possible that from this third site 30, the manufactured visual aid is then shipped to the first site 26 as indicated by the arrow 34.

(45) While the foregoing discussion refers to implementations for correcting up to second order aberrations, in general, the invention is not limited to second order aberrations. For example, in some embodiments, the methods can be expanded to allow refraction using higher order aberrations. In such cases, the optimization space is expanded by one or more additional dimensions, e.g., for higher order aberrations, such as spherical aberration and/or coma. Such a higher order refraction can then be used by the eyecare professional to specify an ophthalmic correction that includes higher order correction by altering the phase of the incident wavefront in the plane of the pupil according to the prescribed higher order aberration correction.

(46) Furthermore, while the embodiments discussed above are in reference to eye glass visual aids, in general, the techniques can be applied to determining a prescription for contact lenses or refractive surgery as well, which are to be considered as “visual aids”. A number of embodiments have been described.

(47) It is understood that the foregoing description is that of the preferred embodiments of the invention and that various changes and modifications may be made thereto without departing from the spirit and scope of the invention as defined in the appended claims.