Abstract

We propose an approach for implementing a modal wavefront sensor using a binary phase-only multiplexed computer-generated hologram (BPMCGH). To simplify the coding and fabricating processes, a model based on tilt plane reference waves and an effective coding scheme for BPMCGH have been developed. The necessary number of subholograms to be recorded or coded is significantly reduced, from two or even more to just one per aberration mode, accordingly. The numerical and experimental demonstration results are presented and discussed and show that this approach is convenient for producing a BPMCGH and efficient for sensing the aberration modes.

© 2010 Optical Society of America

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References

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2009 (4)

G. P. Anderson, L. Dussan, F. Ghebremichael, and K. Chen, “Holographic wavefront sensor,” Opt. Eng. 48, 085801 (2009).
[CrossRef]

L. Changhai and J. Zongfu, “Holographic modal wavefront sensor: theoretical analysis and simulation,” Chin. J. Lasers 36, 147–152 (2009).

C. Liu, Z. Jiang, F. Xi, and S. Huang, “Simulation of the computer-generated holographic modal wave front sensor,” Proc. SPIE 7508, 750809 (2009).
[CrossRef]

S. K. Mishra, R. Bhatt, and D. Mohan, “Differential modal Zernike wavefront sensor employing a computer-generated hologram: a proposal,” Appl. Opt. 48, 6458–6465 (2009).
[CrossRef] [PubMed]

2008 (2)

F. Ghebremichael, G. P. Andersen, and K. S. Gurley, “Holography-based wavefront sensing,” Appl. Opt. 47, A62–A70 (2008).
[CrossRef] [PubMed]

R. Bhatt, S. K. Mishra, D. Mohan, and A. K. Gupta, “Direct amplitude detection of Zernike modes by computer-generated holographic wavefront sensor: modeling and simulation,” Opt. Lasers Eng. 46, 428–439 (2008).
[CrossRef]

2007 (1)

2006 (1)

G. P. Andersen, “Fast holographic wavefront sensor: sensing without computing,” Proc. SPIE 6272, 6272E (2006).
[CrossRef]

2005 (1)

G. Andersen and R. Reibel, “Holographic wavefront sensor,” Proc. SPIE 5894, 58940O (2005).
[CrossRef]

2003 (1)

J. Primot, “Theoretical description of Shack—Hartmann wavefront sensor,” Opt. Commun. 222, 81–92 (2003).
[CrossRef]

2000 (3)

1988 (1)

1976 (1)

Andersen, G.

G. Andersen and R. Reibel, “Holographic wavefront sensor,” Proc. SPIE 5894, 58940O (2005).
[CrossRef]

Andersen, G. P.

F. Ghebremichael, G. P. Andersen, and K. S. Gurley, “Holography-based wavefront sensing,” Appl. Opt. 47, A62–A70 (2008).
[CrossRef] [PubMed]

G. P. Andersen, “Fast holographic wavefront sensor: sensing without computing,” Proc. SPIE 6272, 6272E (2006).
[CrossRef]

Anderson, G. P.

G. P. Anderson, L. Dussan, F. Ghebremichael, and K. Chen, “Holographic wavefront sensor,” Opt. Eng. 48, 085801 (2009).
[CrossRef]

Bhatt, R.

S. K. Mishra, R. Bhatt, and D. Mohan, “Differential modal Zernike wavefront sensor employing a computer-generated hologram: a proposal,” Appl. Opt. 48, 6458–6465 (2009).
[CrossRef] [PubMed]

R. Bhatt, S. K. Mishra, D. Mohan, and A. K. Gupta, “Direct amplitude detection of Zernike modes by computer-generated holographic wavefront sensor: modeling and simulation,” Opt. Lasers Eng. 46, 428–439 (2008).
[CrossRef]

Booth, M. J.

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Publishing House of Electronics Industry, 2006) (in Chinese).

Changhai, L.

L. Changhai and J. Zongfu, “Holographic modal wavefront sensor: theoretical analysis and simulation,” Chin. J. Lasers 36, 147–152 (2009).

Chen, K.

G. P. Anderson, L. Dussan, F. Ghebremichael, and K. Chen, “Holographic wavefront sensor,” Opt. Eng. 48, 085801 (2009).
[CrossRef]

Chen, S.

Dussan, L.

G. P. Anderson, L. Dussan, F. Ghebremichael, and K. Chen, “Holographic wavefront sensor,” Opt. Eng. 48, 085801 (2009).
[CrossRef]

Ghebremichael, F.

G. P. Anderson, L. Dussan, F. Ghebremichael, and K. Chen, “Holographic wavefront sensor,” Opt. Eng. 48, 085801 (2009).
[CrossRef]

F. Ghebremichael, G. P. Andersen, and K. S. Gurley, “Holography-based wavefront sensing,” Appl. Opt. 47, A62–A70 (2008).
[CrossRef] [PubMed]

Gupta, A. K.

R. Bhatt, S. K. Mishra, D. Mohan, and A. K. Gupta, “Direct amplitude detection of Zernike modes by computer-generated holographic wavefront sensor: modeling and simulation,” Opt. Lasers Eng. 46, 428–439 (2008).
[CrossRef]

Gurley, K. S.

Hardy, J. W.

J. W. Hardy, Adaptive Optics for Astronomical Telescopes(Oxford U. Press, 1998).

Huang, S.

C. Liu, Z. Jiang, F. Xi, and S. Huang, “Simulation of the computer-generated holographic modal wave front sensor,” Proc. SPIE 7508, 750809 (2009).
[CrossRef]

Jiang, Z.

C. Liu, Z. Jiang, F. Xi, and S. Huang, “Simulation of the computer-generated holographic modal wave front sensor,” Proc. SPIE 7508, 750809 (2009).
[CrossRef]

Li, S. S.

Liu, C.

C. Liu, Z. Jiang, F. Xi, and S. Huang, “Simulation of the computer-generated holographic modal wave front sensor,” Proc. SPIE 7508, 750809 (2009).
[CrossRef]

Mishra, S. K.

S. K. Mishra, R. Bhatt, and D. Mohan, “Differential modal Zernike wavefront sensor employing a computer-generated hologram: a proposal,” Appl. Opt. 48, 6458–6465 (2009).
[CrossRef] [PubMed]

R. Bhatt, S. K. Mishra, D. Mohan, and A. K. Gupta, “Direct amplitude detection of Zernike modes by computer-generated holographic wavefront sensor: modeling and simulation,” Opt. Lasers Eng. 46, 428–439 (2008).
[CrossRef]

Mohan, D.

S. K. Mishra, R. Bhatt, and D. Mohan, “Differential modal Zernike wavefront sensor employing a computer-generated hologram: a proposal,” Appl. Opt. 48, 6458–6465 (2009).
[CrossRef] [PubMed]

R. Bhatt, S. K. Mishra, D. Mohan, and A. K. Gupta, “Direct amplitude detection of Zernike modes by computer-generated holographic wavefront sensor: modeling and simulation,” Opt. Lasers Eng. 46, 428–439 (2008).
[CrossRef]

Neil, M. A. A.

Noll, R. J.

Notaras, J.

Paterson, C.

Primot, J.

J. Primot, “Theoretical description of Shack—Hartmann wavefront sensor,” Opt. Commun. 222, 81–92 (2003).
[CrossRef]

Reibel, R.

G. Andersen and R. Reibel, “Holographic wavefront sensor,” Proc. SPIE 5894, 58940O (2005).
[CrossRef]

Roddier, F.

Tyson, R. K.

R. K. Tyson, Principles of Adaptive Optics (Academic, 1991), pp. 213–255.

Wilson, T.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Publishing House of Electronics Industry, 2006) (in Chinese).

Xi, F.

C. Liu, Z. Jiang, F. Xi, and S. Huang, “Simulation of the computer-generated holographic modal wave front sensor,” Proc. SPIE 7508, 750809 (2009).
[CrossRef]

Yan, H. X.

Zhang, D. L.

Zongfu, J.

L. Changhai and J. Zongfu, “Holographic modal wavefront sensor: theoretical analysis and simulation,” Chin. J. Lasers 36, 147–152 (2009).

Appl. Opt. (4)

Chin. J. Lasers (1)

L. Changhai and J. Zongfu, “Holographic modal wavefront sensor: theoretical analysis and simulation,” Chin. J. Lasers 36, 147–152 (2009).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

J. Primot, “Theoretical description of Shack—Hartmann wavefront sensor,” Opt. Commun. 222, 81–92 (2003).
[CrossRef]

Opt. Eng. (1)

G. P. Anderson, L. Dussan, F. Ghebremichael, and K. Chen, “Holographic wavefront sensor,” Opt. Eng. 48, 085801 (2009).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (1)

R. Bhatt, S. K. Mishra, D. Mohan, and A. K. Gupta, “Direct amplitude detection of Zernike modes by computer-generated holographic wavefront sensor: modeling and simulation,” Opt. Lasers Eng. 46, 428–439 (2008).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (3)

G. Andersen and R. Reibel, “Holographic wavefront sensor,” Proc. SPIE 5894, 58940O (2005).
[CrossRef]

G. P. Andersen, “Fast holographic wavefront sensor: sensing without computing,” Proc. SPIE 6272, 6272E (2006).
[CrossRef]

C. Liu, Z. Jiang, F. Xi, and S. Huang, “Simulation of the computer-generated holographic modal wave front sensor,” Proc. SPIE 7508, 750809 (2009).
[CrossRef]

Other (3)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Publishing House of Electronics Industry, 2006) (in Chinese).

R. K. Tyson, Principles of Adaptive Optics (Academic, 1991), pp. 213–255.

J. W. Hardy, Adaptive Optics for Astronomical Telescopes(Oxford U. Press, 1998).

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Figures (10)

Fig. 1
Fig. 1

Schematic diagram of the modal wavefront sensor using a BPMCGH. The aberrated input wave illuminates the assembly of the BPMCGH and Fourier-transforming lens, and then it is received by a detector.

Fig. 2
Fig. 2

Diagram of optical holographic recording. A computer-generated hologram can be produced from the interferogram between an aberrated wave O ( r ) and an off-axis reference wave R ( r ) .

Fig. 3
Fig. 3

(a) Distribution approaches of the reference beam direction, in which the black points denote the specific directions and the white points are the conjugates, accordingly. (b) and (c) Two alternative BPMCGHs coded with four aberration modes. (d) Numerical focal pattern with large diffraction angles. (e) Numerical focal pattern with effective fill factor, tested by plane wave.

Fig. 4
Fig. 4

Cross-sectional plots of the spot pairs in the focal pattern when tested with a plane wave; the first corresponds to Z 2 0 , the second Z 2 2 , the third Z 3 1 , and the last Z 4 0 , from left to right.

Fig. 5
Fig. 5

Numerical test results with single Zernike mode; the mode Z 2 0 is specified as the test mode.

Fig. 6
Fig. 6

Normalization intensity difference of the spot pairs in the focal plane. Choose the single Zernike mode (a) Z 2 0 (dashed curve), (b) Z 2 2 (solid curve), (c) Z 3 1 (dotted curve), and (d) Z 4 0 (dashed-dotted curve) as the test mode, respectively.

Fig. 7
Fig. 7

Normalization intensity difference of spot pairs in the focal plane. Choose multiple Zernike modes (a) Z 2 0 + Z 2 2 , (b) Z 2 0 + Z 2 2 + Z 3 1 , (c) Z 2 0 + Z 2 2 + Z 3 1 + Z 4 0 , and (d) Z 2 0 + Z 2 2 + Z 3 1 + Z 4 0 + Z 2 2 as the test modes, respectively. Here, Z 2 0 corresponds to the dashed curve, Z 2 2 to the solid curve, Z 3 1 to the dotted curve, and Z 4 0 to the dashed-dotted curve.

Fig. 8
Fig. 8

Experiment setup. The expanded and collimated 1064 nm beam, through a beam splitter, is reflected off the phase-only SLM1 with a size of 256 × 256 pixels, which serves as a phase screen. From there, reflected light from SLM1 that passes straight through the same beam splitter illuminates onto SLM2 ( 512 × 512 pixels), on which the BPMCGH is displayed, then the modulated light is Fourier transformed by a lens and received by a CCD camera: BS1, BS2, beam splitters; SLM1, SLM2, spatial light modulators; L1, L2, L3, lenses; and PC1, PC2, PC3, personal computers.

Fig. 9
Fig. 9

Intensity pattern in the detector plane when testing (a) 1.0 rad Z 2 0 , (b) 0.1 rad Z 2 0 , and (c) 1.0 rad Z 2 0 . All the images are enhanced by 5 times to be clearer.

Fig. 10
Fig. 10

(a) Intensity difference, and (b) normalization intensity difference as a function of magnitude of test mode aberration.

Equations (11)

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t ( r ) = exp ( j m sin [ φ ( r ) + τ · r ] ) ,
t binary = { exp ( j m ) if sin [ φ ( r ) + τ · r ] 0 1 otherwise .
t binary = q = a q exp [ j q ( φ ( r ) + τ · r ) ] ,
a q = 1 2 π 0 2 π t binary ( ξ ) exp ( j q ξ ) d ξ = sinc ( q 2 ) cos ( m 2 + q π 2 ) exp [ j ( m 2 q π ) ] ,
a 0 = 0 , a ± 1 = sinc ( 1 2 ) cos ( π 2 ± π 2 ) exp [ j ( π 2 π ) ] .
I = | F { U ( r ) · t binary } | 2 ,
I ± 1 = | q = ± 1 a q F ( exp { j [ q φ ( r ) + ψ ( r ) ] } ) * F [ exp ( j q τ · r ) ] | 2 = | q = ± 1 a q F ( exp { j [ q φ ( r ) + ψ ( r ) ] } ) * δ ( f q τ ) | 2 .
{ I + 1 = 4 π 2 | F ( exp { j [ φ ( r ) + ψ ( r ) ] } ) * δ ( f τ ) | 2 I 1 = 4 π 2 | F ( exp { j [ φ ( r ) ψ ( r ) ] } ) * δ ( f + τ ) | 2 .
S i k = 0 2 π d ξ 0 v ( I + 1 I 1 ) β | β = 0 v d v
S i k = { α 2 v 2 i = k O ( α 3 v 2 ) + O ( α v 4 ) i k , p k p i = odd , p k = p i = 0 0 otherwise ,
β = S i k 1 · ( I + 1 I 1 ) ,

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