The present invention relates to a method and apparatus for determining the visual acuity of an eye by analysing the wave front information of the eye, in particular by analysing a corresponding point spread function (PSF).
WO 02/30273 A1 relates to the determination of ocular refraction from wavefront aberration data and an optimum customized correction is designed. The eye's wave aberration is measured by using a detector such as a Shack-Hartmann detector. From the aberration, an image metric is calculated, and the second-order aberrations which optimize that metric are determined. From that optimization, the refractive correction required for the eye is determined. The image metric is one of several metrics indicating the quality of the image on the retinal plane or a proxy for such a metric. The required refractive correction can be used to form a lens or to control eye surgery. It further relates to five different metrics of image quality, i.e. Strehl ratio, entropy of the point spread function (PSF), variance of the PSF, MTFa, defined as the integral of the modulation transfer function (MTF) within the range of discriminable frequencies, from 0 to 60 c/deg, and CSFa, defined as the integral of the contrast sensitivity function (CSF), which is obtained as the product of the MTF and the neural CSF. Further reference is made to the encircled energy of the PSF that falls within a small area around the peak of the image. As a metric the encircled energy calculated as the fraction of light in the PSF within an area corresponding to the Airy disk is mentioned. This document is silent on how to provide a value for the visual acuity.
WO 03/092485 A1 relates to a vision metric, called the sharpness metric, which indicates the subjective sharpness of a patient's vision by taking into account both the wavefront aberration and the retinal response to the image. A retinal image quality function such as the point spread function is convolved by a neural quality function, and the maximum of the convolution over the retinal plane provides the sharpness metric. The sharpness metric can be used to control eye surgery or the fabrication of a lens.
U.S. Pat. No. 5,777,719 describes a method and apparatus for improving vision and the resolution of retinal images. It specifically relates to a Hartmann-Shack wavefront sensor for acquiring the wavefront information of an eye. More specifically, a point source produced on the retina of a living eye by a laser beam is reflected from the retina and received at a lenslet array of a Hartmann-Shack wavefront sensor such that each of the lenslets in the lenslet array forms an aerial image of the retinal point source on a CCD camera located adjacent the lenslet array. The output signal from the CCD camera is acquired by a computer which processes the signal and produces a correction signal which may be used to control a compensating optical or wavefront compensation device such as a deformable mirror. It may also be used to fabricate a contact lens or intraocular lens, or to guide a surgical procedure to correct the aberrations of the eye. For showing the result of the correction of aberrations of the eye, reference is made to the point spread function (PSF) computed from the wave aberration. It is shown that after compensation, the PSF or a particular subject has a full-width at half height (FWHH) of 2.0 microns, which shall be close to the value of 1.9 microns expected from diffraction alone.
In US 2004/0119942 A1 and U.S. Pat. No. 6,659,613 B2, methods and systems for measuring local scattering and aberration properties of optical media are described. A Hartmann-Shack calibration image of a measurement system is acquired to define a first plurality of point spread functions. A Hartmann-Shack test image of the medium is acquired to define a second plurality of point spread functions. A shift is determined between the test image and the calibration image. A point spread of each of the second plurality of point spread functions is measured, each of the second plurality of point spread functions including a component due to optical aberration of the medium and a component due to scatter. The component due to optical aberration is determined using the shift. The component due to optical aberration is deconvolved to determine the component due to scatter.
U.S. Pat. No. 6,499,843 B1 relates to a customized vision correction method which comprises obtaining a wavefront aberration measurement of a patient's eye and providing a display of the wave front aberration measurement in the form of either a picture, a computer simulation, a graphic display, and a mathematical representation of the wavefront. Specific reference is made to analyzing a point spread function for determining a Strehl ratio.
The object of the present invention is to provide a method and an apparatus for determining the visual acuity of an eye by analysing the wavefront information of the eye.
This object is solved with the features of the claims.
The present invention specifically allows to determine the visual acuity dependent on pupil diameter and object distance or state of accommodation.
The present invention is based on analysing the acquired wavefront information of an eye, in particular by analysing the point spread function of the eye. The point spread function is the image that the eye forms of a point source.
The point spread function for a typical eye shows a specific intensity distribution for a corresponding pupil size. When seen in three dimensions, the intensity over the area may be compared to a mountainous area comprising hills and valleys. The peaks of the hills represent the high intensity, whereas the valleys represent areas of lower intensity.
According to the method of the present invention, a point spread function of the eye is analysed by comparing the intensities of the point spread function with a selectable intensity level. The parts of the point spread function having an intensity being larger than the selectable intensity level are determined as relevant part of the PSF. The relevant part represents a cross section through the hills of the point spread function at the selected intensity level. When seen from the top, the cross sections through respective hills in the point spread function form one or more areas. As a further step, an ellipse is drawn which circumscribes the one or more areas formed by the cross sections through the hills. According to the present invention, the result ellipse represents an image quality metric.
According to a preferred embodiment of the present invention, the length of the long axis of the ellipse is taken as an image quality metric. According to a further preferred embodiment of the invention, the relation between the long axis and the short axis of the ellipse is taken as an image quality metric.
Preferably the enclosed area of the ellipse has to be similar to the area of inside the convex hull around the relevant regions.
One way to visualize a convex hull is to put an elastic band around all the points, and let it wrap as tight as it can. The resultant polygon is a convex hull. A more formal mathematical definition is as follows: A convex hull is the smallest convex polygon that contains all points. A polygon is convex if and only if, for any two points inside the polygon, the line segment between these points is inside the polygon.
According to a preferred embodiment of the present invention, the long axis can be substituted by the longest distance in the relevant part of the PSF and the short axis can be substituted by the maximum distance in the perpendicular direction to this axis.
According to a preferred embodiment of the present invention, the enclosed area in between the boundary points of the relevant part of the PSF is taken as an image quality metric.
Best Mode of Fitting the Long Axis and the Short Axis:
A monochromatic PSF for light of the wavelength 550 nm is used. Find the centre of the above described relevant data. The coordinates of the centre are the mean value of the minimum and maximum in each Cartesian direction. As a further step, a circle is drawn around this centre which circumscribes the one or more areas formed by the cross sections through the hills. According to the present invention, the diameter of this circle represents the long axis. As a further step, the area inside the convex hull around the relevant data is determined. The short axis is approximated by following equation:short_axis=long_axis*(area_inside_convex_hull/area_inside_circle)  (1)
According to a preferred embodiment of the present invention, the long and the short axis are transformed into the visual acuity of the eye. Two nearby small objects can be separated by the eye if the centres of their pictures on the retina are separated at least by the length of the long axis of the ellipse. The reciprocal angle between these nearby objects is proportional to the visual acuity. The relation between the long axis and the short axis of the ellipse is taken to derive a correction factor for the visual acuity. The visual acuity is predicted using following equations:VA_predicted=d_VA1/(long_axis*Corr)  (2)Corr=0.5*(1+short_axis/long_axis)  (3)d_VA1 is the theoretical distance of the centres of retinal pictures of two nearby objects seen under an angle of 1 minute (Definition for a visual acuity of 1 or 20/20). The value of d_VA1 is approximated with a constant value of 5 μm. VA_predicted is the predicted visual acuity in a decimal scale.
The correction factor is equal to 1 if the long axis is equal to the short axis (circle shape of the relevant area) and it converges to 0.5 for a negligible small short axis. This is in line with observation that an undercorrection in sphere of about −1 dpt causes about twice the decrease in visual acuity compared to an undercorrection in cylinder of −1 dpt.
According to a preferred embodiment of the invention, the method steps are repeated at least one time for the same point spread function using a different selectable intensity level which is preferably smaller or greater than the first selected intensity level. Again, an ellipse is determined which by its form and size represents an image quality metric, wherein preferably the long axis and/or the relation between the long and the short axis of the ellipse is taken as an image quality metric. The selectable intensity level is preferably between 40% to 80% of the maximum of intensity of the point spread function. More preferably, the selectable intensity value is taken from a range of 50% to 70% of the maximum intensity. Most preferably, the selectable intensity value is 60% of the maximum intensity.
According to a further preferred embodiment of the present invention, the method is performed at least one further time for the point spread function of the same eye, but for a different pupil size. Again, the method is preferably performed more than one time by using a selected intensity level.
According to a further preferred embodiment of the present invention, the method is performed for point spread functions of the same eye, but for at least two different states of accommodation the wavefront is modified with different spherical additions. This simulates the cycles of accommodation and relaxation which the eye usually does to find the status for the optimum visual acuity. Also smaller object distances are simulated by modifying the focus. Again, the method is preferably performed more than one time by using a selected intensity level.
For a range of pupil diameters that can be expected under usual daylight conditions and a range of accommodation states of the eye the visual acuity is calculated for the same eye. The highest value of these results is the predicted visual acuity that can be compared with the visual acuity determined using test charts. The pupil size for daylight conditions and the possible accommodation has to be adjusted individually for each eye.