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Extended source pyramid wave-front sensor for the human eye

Ignacio Iglesias, Roberto Ragazzoni, Yves Julien, and Pablo Artal

Open Access Open Access

Abstract

We describe a new wave-front sensor based on the previously proposed pyramid sensor. This new sensor uses an extended source instead of a point-like source avoiding in this manner the oscillation of the pyramid. After an introductory background the sensor functioning is described. Among other possible optical testing uses, we apply the sensor to measure the wave-front aberration of the human eye. An experimental system built to test this specific application is described. Results obtained both in an articficial eye and in a real eye are presented. A discussion about the sensor characteristics, the experimental results and future work prospects is also included.

©2002 Optical Society of America

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Supplementary Material (2)

Media 1: GIF (1827 KB)     
Media 2: GIF (518 KB)     

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Figures (7)
Fig. 1.
Fig. 1. (a) Schematics of the wave-front sensor where L1 states for the lens used to form the Fourier transform of the probed field at its focal length where the pyramid is placed. A second lens, L2, is placed behind the pyramid to focus the exit pupil of the optical system under study on an intensity detector. (b) The glass pyramid. (c) A different view of the sensor; A, B, C and D indexes the four re-imaged pupils.

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Fig. 2.
Fig. 2. (a) A simple linear oscillation path in the Fourier plane. The pyramid vertex, marked with a crosshair, follows the dotted line around the origin. In (b) it is drawn a simple extended emitter with binary intensity (white area means light, black means no light) modeled (see text) as an infinite collection of oscillation paths, as the one in Figure (a), with different amplitudes. The doted line on the graph in panel (c) represents the sensor normalized response for the path of Figure (a). The solid line on the same graph represents the response for the extended source of Figure (b).

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Fig. 3.
Fig. 3. Schematics of the wave-front measuring apparatus. S electronic shutter; SF Spatial filter; RD rotating diffusers; A1 A2, apertures; L1, L2, L3, L4, L5, L6 lenses. M1, M2, M3, M4 mirrors (M1, M2 on a translation stage). BS beam splitter. CCD charged coupled device.

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Fig. 4.
Fig. 4. (1.8 Mb) Movie of the acquired data, (a), the gradient in both orthogonal directions, (b), and the computed phase of the pupil function represented modulus 2π obtained by moving the translation stage.

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Fig. 5.
Fig. 5. Variation of the different Zernike coefficients moving the translation stage in the artificial eye experiment. One centimeter of displacement introduces 0.97 diopters of refractive defocus (0.52 μm of Z4).

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Fig. 6.
Fig. 6. (518 KB) Movie of the acquired data, (a), the gradient in both orthogonal directions, (b), and the phase of the pupil function represented modulus 2π obtained by moving the translation stage.

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Fig. 7.
Fig. 7. Variation of the different Zernike coefficients moving the translation stage in the living eye experiment.

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Equations (7)

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ξ ζ = f ( ∂ w ∂ x , ∂ w ∂ y ) = f ∇ → w ,
∂ w ∂ x | i , j ∝ c i , j + d i , j − ( a i , j + b i , j ) a i , j + b i , j + c i , j + d i , j , ∂ w ∂ y | i , j ∝ a i , j + c i , j − ( b i , j + d i , j ) a i , j + b i , j + c i , j + d i , j
a i , j = b i , j = { 0 ξ > Δ 2 ( Δ − ξ ) − Δ ≤ ξ ≤ Δ 2 2 Δ ξ < − Δ c i , j = d i , j = { 2 2 Δ ξ > Δ 2 ( Δ + ξ ) − Δ ≤ ξ ≤ Δ 0 ξ < − Δ
ξ = { 1 ξ > Δ ξ / Δ − Δ ≤ ξ ≤ Δ − 1 ξ < − Δ
a i , j = b i , j = { 0 ξ > Δ 1 2 ( Δ − ξ ) 2 − Δ ≤ ξ ≤ Δ 2 Δ 2 ξ < − Δ c i , j = d i , j = { 2 Δ 2 ξ > Δ 1 2 ( Δ 2 + 2 ξΔ − ξ 2 ) Δ ≤ ξ ≤ Δ 0 ξ > Δ
ξ = { 1 ξ > Δ ( 2 Δ − ξ ) ξ / Δ 2 − Δ ≤ ξ ≤ Δ − 1 ξ < − Δ
ξ = { 1 ξ > Δ 2 ξ / Δ − Δ ≤ ξ ≤ Δ − 1 ξ < − Δ ,
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