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Requirements for segmented correctors for diffraction-limited performance in the human eye

Donald T. Miller, Larry N. Thibos, and Xin Hong

Open Access Open Access

Abstract

Wavefront correctors have yet to provide diffraction-limited imaging through the human eye’s ocular media for large pupils (≥6 mm). To guide future improvements in corrector designs that might enable such imaging, we have modeled the performance of segmented piston correctors in conjunction with measured wave aberration data of normal human eyes (mean=34.2 yr; stdev=10.6 yr). The model included the effects of pupil size and wavelength in addition to dispersion, phase wrapping, and number and arrangement of facets in the corrector. Results indicate that ≤100×100 facets are needed to reach diffraction-limited performance for pupils up to 8 mm (extrapolated) at 0.6 µm wavelength. Required facet density for the eye was found to be substantially higher at the pupil’s edge than at its center, which is in stark contrast to the requirements for correcting atmospheric turbulence. Substantially more facets are required at shorter wavelengths with performance highly sensitive to facet fill. In polychromatic light, the performance of segmented correctors based on liquid crystal technology was limited by the naturally occurring longitudinal chromatic aberration of the eye rather than phase wrapping and dispersion of the liquid crystal. Required facets to correct defocus alone was found highly sensitive to pupil size and decentration.

©2005 Optical Society of America

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Figures (8)
Fig. 1.
Fig. 1. Log10(wavefront variance) plotted as a function of Zernike order. The 12 red curves represent each of the measured 12 eyes used in this study. The blue diamonds and two dashed curves represent the mean and mean ± two times the standard deviation of the log10(wavefront variance), respectively, for the 200 eyes measured in the IU Aberration Study.

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Fig. 2.
Fig. 2. Compensation of ocular aberrations across a 6 mm circular pupil using two hexagonally-packed correctors with 12 (top row) and 48 (bottom row) facets across their pupil diameter. Wavefront phase is represented by a gray-scale image (black and white tones depict minimum and maximum phase, respectively). (a) shows the measured uncorrected wave aberrations for one subject’s eye with defocus and astigmatism removed. The phase RMS is 0.37λ. (b) shows the desired phase profile across two correctors for compensating the subject’s wave aberrations in (a). (c) shows the residual aberrations after correction of the wave aberrations in (a) with the corrector phase profile in (b). The residual phase RMS is 0.12λ (top) and 0.04λ (bottom). The corresponding corrected point spreads and Strehl values are given in (d) that were computed using scalar diffraction theory that incorporated the residual wave aberrations and a circular pupil. λ is 0.6 µm.

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Fig. 3.
Fig. 3. Subject’s point spread calculated from the measured wave aberration shown in Fig. 2(a)

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Fig. 4.
Fig. 4. Corrected Strehl ratio for (red) hexagonally- and (green) square-packed segmented correctors as a function of facet number. Pupil diameter and λ were set to 6 mm and 0.6 µm, respectively. Top two curves do not include the impact of the residual defocus and astigmatism, which were left uncorrected by trial lenses. Bottom two curves include defocus and astigmatism. Error bars represent ±1 standard deviation across the 12 subjects.

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Fig. 5.
Fig. 5. Number of facets required to achieve diffraction-limited imaging (Strehl=0.8) along two orthogonal axes in D-λ space. The two axes are λ=0.6 µm (left) and D=6 mm (right). Simulation results were fit to λ -6/5 and third-order polynomial functions.

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Fig. 6.
Fig. 6. Corrected Strehl ratio for facet fill of 73.5%, 86%, and 100% as a function of facet number for a square-packed segmented corrector. Pupil diameter and λ were 6 mm and 0.6 µm, respectively. Residual defocus and astigmatism was present. Error bars represent ±1 standard deviation across the 12 subjects

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Fig. 7.
Fig. 7. Average SLM performance on human eyes using polychromatic light for 3 (left) and 6 mm (right) pupils. The color-coded curves represent the performance of four SLM types that correspond to the four possible combinations of dispersion and phase wrapping. Dispersion was that of the liquid crystal material E-7. Phase wrapping was modulo 2π for λdesign =0.6 µm. Facet size was set to a single pixel. The black curves represent the performance of the diffraction-limited eye corrupted only by the eye’s naturally occurring longitudinal chromatic aberration. The design wavelength, λdesign , was 0.6 µm.

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Fig. 8.
Fig. 8. Corrected Strehl for various amounts of defocus (0, 1/16, 1/8, 1/4, 1/2, 1, 2, and 4 diopters) as a function of facet number for 3 mm (left) and 6 mm (right) pupils. Facets were hexagonally-packed with 100% fill, and λ was 0.6 µm.

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Equations (4)

Equations on this page are rendered with MathJax. Learn more.

ϕ residual ( λ ) = ϕ eye ( λ ) − ϕ SLM ( λ ) ,
ϕ eye ( λ ) = ϕ eye ( λ design ) λ design λ − ϕ LCA
ϕ SLM ( λ ) = ϕ SLM ( λ design ) Δ n ( λ ) Δ n ( λ design ) λ design λ ,
Δ n ( λ ) = G ( λ λ * ) 2 λ 2 − λ * 2 ,
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