E-mail: thibos
indiana.edu
Introduction | Methods | Results | Discussion | References
indiana.edu
Introduction | Methods | Results | Discussion | References
We evaluated the potential of using a liquid crystal spatial light modulator with 127 elements in an hexagonal array to correct focussing errors of the human eye. Refractive errors were induced by placing ophthalmic lenses of known power in front of the eye. A HEX-127 (Meadowlark, Inc.) spatial light modulator (SLM) was imaged in the entrance pupil of the eye and programmed to generate refractive power of the same magnitude as the ophthalmic lens but of the opposite sign. When the induced error was no greater than 1.5 diopters, the SLM satisfactorily corrected the induced error and the measured visual acuity was comparable to that when no refractive errors were present. Computations indicated that the SLM failed to correct refractive errors greater than 1.5 diopters because insufficient density of control cells under-sampled the desired wavefront. Consequently, the SLM diffracted significant amounts of energy into the higher orders, resulting in a multi-modal point spread function. The net effect was multiple duplication of the visual target in the retinal image with the overlapping of the duplicates leading to deterioration of visual acuity.
Spatial light modulators (SLMs) fabricated from liquid crystals have the potential to correct defocus, astigmatism, and higher order aberrations of human eyes. The advantages of liquid crystal SLMs for ophthalmic applications include low cost, reliability, compactness, low power consumption, ease of control, and the ability to function in transmission mode.5 The disadvantages of currently available devices include low spatial density of control cells and the need for polarized monochromatic light, although reflection-mode devices are less hampered by these factors.2, 4 Previous experiments have demonstrated that a liquid-crystal SLM may be used successfully to correct small amounts of prismatic, focus and astigmatic errors of the eye6 as well as higher order aberrations.7 The emphasis of those experiments was on optical assessment of the SLM when used in conjunction with an eye. Here we evaluate the effectiveness of those corrections for improving visual performance.
The SLM used in this study is the Hex-127 model by Meadowlark,
Inc. which contains 127 cells in an hexagonal array. The edge-to-edge
distance of each cell is 1mm, with a gap of 0.036mm in between cells,
which results in a fill factor of 93%. The cells are confined to a
circular area 12mm in diameter. The manufacturer's calibration of
retardance as a function of applied voltage, obtained at 650 nm, was
assumed to apply at our test wavelength of 580 nm. At this test
wavelength the maximum change of retardance was 1 wavelength, which
allowed us to utilize phase wrapping to implement modulo 2
wavefront shaping.3 The purpose of
wavefront shaping was to mimic the focusing behavior of ophthalmic
lenses. In ophthalmic optics the diopter is the traditional unit of
refractive power, which is defined the inverse of focal length in
meters. Dioptric power is related to wavefront error by the
formula6
 |
|
where D is the power of the lens in diopters, r is the radius of the aperture delineating the wavefront in mm, and W is the retardance in µm. For example, to mimic a +1 diopter lens across a 3 mm pupil would require 1.125 µm of wavefront retardance at the pupil center compared to pupil margin.
The experimental apparatus is shown in Fig. 1. The observer viewed a Bailey Lovie eye chart1 that was projected on a screen with a high-intensity projection monitor (Proxima 5900). A lens collimated light from the screen for transmission through an interference filter, a polarizing filter, the SLM, and a 12 mm diameter aperture to mask the active area in the SLM. A pair of relay lenses imaged the SLM in the eye's pupil plane with a magnification factor of 0.25. This reduced the image of the SLM formed in the eye's entrance pupil to 3mm in diameter.
Fig 1. Schematic diagram of experimental apparatus.
Ophthalmic lenses were placed immediately in front of the eye to optimally correct focus and astigmatic refractive errors. In Experiment #1, the same refractive error was induced with either the SLM or an additional ophthalmic lens so their effects on visual acuity could be compared. In Experiment #2 the power of the SLM was of equal magnitude but opposite sign to that of the added ophthalmic lens. The observer's task was to read the letters of the eye chart, which were calibrated in terms of their angular subtense measured from the center of the eye's pupil. Target luminance as seen by the observer was 20 cd/m2.
The results of Experiment #1, shown in Fig. 2, indicate that visual acuity declines as a result of induced refractive error by about the same amount regardless of the source of the error. Although the absolute levels of acuity achieved by the two observers were slightly different, the level of visual performance that could be achieved when viewing through a blurring lens was nearly the same as when viewing through an SLM programmed to deliver the same amount of defocus.
Fig 2. Effect on visual acuity of refractive error induced by SLM or lens
The results of Experiment #2, shown in Fig. 3, indicate that the SLM effectively neutralizes the refractive error induced by the ophthalmic lens provided that the lens power is no larger than 1.5 diopters. For both subjects acuity remained near the normal level of 20/20 (6/6 metric) when the refractive error induced by the ophthalmic lens was corrected by the SLM. However, when the induced refractive error exceeded 1.5 diopters, acuity fell rapidly.
Fig 3. Effect on visual acuity of residual refractive error following correction by SLM
To investigate the probable cause of the decline in visual acuity that occurs for larger refractive errors, we measured the point spread function (PSF) of the system by replacing the observer's eye with a model eye consisting of a video camera with a high quality photographic lens. The eye chart was replaced by a point source of light placed at the focal point of a collimating lens. This point source was the 25 µm pinhole of a conventional spatial filter illuminated by 580 nm light from a monochromator. As in the previous experiments, an ophthalmic lens was used to induce a refractive error in the model eye and this error was corrected by the SLM. The recorded image of the pinhole for a series of induced refractive errors is shown in Fig. 4. Also shown are computer simulations of the SLM when programmed to correct the induced error. These results show that when the SLM is programmed to produce larger amounts of focusing power the PSF becomes multi-modal as more energy is diffracted into the higher orders. These effects may be traced to undersampling of the desired wavefront due to the low spatial density of the SLM.
Fig 4. Point spreaad functions of model eye (bottom row) when refractive error is corrected by the SLM (upper row)
The effect of a multimodal PSF on the retinal image of the eye chart is shown in Fig. 5. Multiple copies of the image are present, each displaced slightly according to the hexagonal pattern of spots in the PSF. For low power conditions the secondary images are of low contrast and do not interfere greatly with the visibility of the primary image. However, as the SLM power increases so does the contrast of the secondary images and eventually these overlapping secondary images have a strong masking effect which severely limits visual performance.
Fig 5. Simulated retinal image of eye chart.