Abstract

We consider a wavefront sensor combining scattering pupil with a plenoptic imager. Such a sensor utilizes the same reconstruction principle as the Hartmann-Shack sensor, however it is free from the ambiguity of the spot location caused by the periodic structure of the sensor matrix, and allows for wider range of measured aberrations. In our study, sensor with scattering pupil has demonstrated a good match between the introduced and reconstructed aberrations, both in the simulation and experiment. The concept is expected to be applicable to optical metrology of strongly distorted wavefronts, especially for measurements through dirty, distorted, or scattering windows and pupils, such as cataract eyes.

© 2014 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  10. L. F. Rodrguez-Ramos, I. Montilla, J. J. Fernndez-Valdivia, J. L. Trujillo-Sevilla, J. M. Rodrguez-Ramos, “Concepts, laboratory, and telescope test results of the plenoptic camera as a wavefront sensor,” Proc. SPIE 8447, 1–6 (2012).

2012

L. F. Rodrguez-Ramos, I. Montilla, J. J. Fernndez-Valdivia, J. L. Trujillo-Sevilla, J. M. Rodrguez-Ramos, “Concepts, laboratory, and telescope test results of the plenoptic camera as a wavefront sensor,” Proc. SPIE 8447, 1–6 (2012).

2006

2005

2003

Y. Carmon, E. Ribak, “Phase retrieval by demodulation of a Hartmann Shack sensor,” Opt. Commun. 215, 285 (2003).
[CrossRef]

2001

S. Esposito, A. Riccardi, “Pyramid wavefront sensor behavior in partial correction adaptive optic systems,” Astron. Astrophys. 369, L9–L12 (2001).
[CrossRef]

1992

1990

1977

Carmon, Y.

Y. Carmon, E. Ribak, “Phase retrieval by demodulation of a Hartmann Shack sensor,” Opt. Commun. 215, 285 (2003).
[CrossRef]

Clare, R. M.

Esposito, S.

S. Esposito, A. Riccardi, “Pyramid wavefront sensor behavior in partial correction adaptive optic systems,” Astron. Astrophys. 369, L9–L12 (2001).
[CrossRef]

Fernndez-Valdivia, J. J.

L. F. Rodrguez-Ramos, I. Montilla, J. J. Fernndez-Valdivia, J. L. Trujillo-Sevilla, J. M. Rodrguez-Ramos, “Concepts, laboratory, and telescope test results of the plenoptic camera as a wavefront sensor,” Proc. SPIE 8447, 1–6 (2012).

Fried, D. L.

Geary, J.

J. Geary, Introduction to Wavefront Sensors (SPIE, 1995).
[CrossRef]

Hudgin, R. H.

Lane, R. G.

Montilla, I.

L. F. Rodrguez-Ramos, I. Montilla, J. J. Fernndez-Valdivia, J. L. Trujillo-Sevilla, J. M. Rodrguez-Ramos, “Concepts, laboratory, and telescope test results of the plenoptic camera as a wavefront sensor,” Proc. SPIE 8447, 1–6 (2012).

Ribak, E.

N. Zon, O. Srour, E. Ribak, “Hartmann - Shack analysis errors,” Opt. Express 14, 635–643 (2006).
[CrossRef] [PubMed]

Y. Carmon, E. Ribak, “Phase retrieval by demodulation of a Hartmann Shack sensor,” Opt. Commun. 215, 285 (2003).
[CrossRef]

Riccardi, A.

S. Esposito, A. Riccardi, “Pyramid wavefront sensor behavior in partial correction adaptive optic systems,” Astron. Astrophys. 369, L9–L12 (2001).
[CrossRef]

Roddier, F.

Rodrguez-Ramos, J. M.

L. F. Rodrguez-Ramos, I. Montilla, J. J. Fernndez-Valdivia, J. L. Trujillo-Sevilla, J. M. Rodrguez-Ramos, “Concepts, laboratory, and telescope test results of the plenoptic camera as a wavefront sensor,” Proc. SPIE 8447, 1–6 (2012).

Rodrguez-Ramos, L. F.

L. F. Rodrguez-Ramos, I. Montilla, J. J. Fernndez-Valdivia, J. L. Trujillo-Sevilla, J. M. Rodrguez-Ramos, “Concepts, laboratory, and telescope test results of the plenoptic camera as a wavefront sensor,” Proc. SPIE 8447, 1–6 (2012).

Srour, O.

Tallon, M.

Trujillo-Sevilla, J. L.

L. F. Rodrguez-Ramos, I. Montilla, J. J. Fernndez-Valdivia, J. L. Trujillo-Sevilla, J. M. Rodrguez-Ramos, “Concepts, laboratory, and telescope test results of the plenoptic camera as a wavefront sensor,” Proc. SPIE 8447, 1–6 (2012).

Zon, N.

Appl. Opt.

Astron. Astrophys.

S. Esposito, A. Riccardi, “Pyramid wavefront sensor behavior in partial correction adaptive optic systems,” Astron. Astrophys. 369, L9–L12 (2001).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

Y. Carmon, E. Ribak, “Phase retrieval by demodulation of a Hartmann Shack sensor,” Opt. Commun. 215, 285 (2003).
[CrossRef]

Opt. Express

Proc. SPIE

L. F. Rodrguez-Ramos, I. Montilla, J. J. Fernndez-Valdivia, J. L. Trujillo-Sevilla, J. M. Rodrguez-Ramos, “Concepts, laboratory, and telescope test results of the plenoptic camera as a wavefront sensor,” Proc. SPIE 8447, 1–6 (2012).

Other

J. Geary, Introduction to Wavefront Sensors (SPIE, 1995).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Two adjacent lenslets illuminated by a plane (left) and spherical (right) wave.

Fig. 2
Fig. 2

Simulated (Zemax) undistorted spot pattern (left), patterns distorted by a 50 and 100 waves trefoil aberration (middle and right).

Fig. 3
Fig. 3

Optical setup for measurement of the WF tilt in the pupil (left), plenoptic configuration that allows for measurement of local WF tilts in virtual subapertures (center) and scheme of pixel indexing in the image plane(right).

Fig. 4
Fig. 4

Plenoptic WF sensor described in [8] (left), WF sensor with scattering pupil (middle), same with a collective lens (right).

Fig. 5
Fig. 5

Simulated response of the plenoptic sensor for a flat WF (left) and calibration pattern obtained with a strong scattering screen in the pupil (right), with a small part of magnified calibration image shown in the inset.

Fig. 6
Fig. 6

Simulated intensity pattern (1000 × 1000 pixels) and the WF reconstruction over 18 × 18 subapertures for a 50 D defocus (top row) and trefoil with amplitude of 200λ (bottom row).

Fig. 7
Fig. 7

Experimentally registered intensity distributions for unaberrated WF (a), for decentered plano-convex lens with optical power of 10 D introduced in the pupil (b), and reconstructed aberrated WF (c).

Equations (15)

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φ < d 2 f .
( d f R ) 2 + ( 2 λ f d ) 2 + d f R < d
R > 2 d 4 f d 4 4 λ 2 f 2
d > 2 λ f .
R > 2 f
c = I ( ρ ) ρ d ρ / I ( ρ ) d ρ ; t = ( c c 0 ) / F
c S = I S ( ρ ) ρ d ρ / I S ( ρ ) d ρ ; t S = ( c S c S 0 ) / F
1 f = 1 l + 1 F
D F d l
X m , n = i , j x i , j U i , j ; m , n i , j U i , j ; m , n , Y m , n = i , j y i , j U i , j ; m , n i , j U i , j ; m , n .
X m , n = x i , j , Y m , n = y i , j ,
Δ ~ 2 B I J
E ( ρ , z ) = P A U ( r ) e i φ ( r ) e i k 2 z | r ρ | 2 d r
E ( ρ , z ) = P e i k 2 z | ρ | 2 ( A U ( r ) e i φ ( r ) e i k 2 z | r | 2 ) | f = ρ / λ z .
φ < S 2 F

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