Abstract

We report the simulation of an adaptive interferometric null test using a high-definition phase-only spatial light modulator (SLM) to measure form and mid spatial frequencies of a freeform mirror with a sag departure of 150 μm from its base sphere. A state-of-the-art commercial SLM is modeled as a reconfigurable phase computer generated hologram (CGH) that generates a nulling phase function with close to an order of magnitude higher amplitude than deformable mirrors. The theoretical uncertainty in form measurement arising from pixelation and phase quantization of the SLM is 50.62 nm RMS. The calibration requirements for hardware implementation are detailed.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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J. Reimers, A. Bauer, K. P. Thompson, and J. P. Rolland, Light Sci. Appl. 6, e17026 (2017).
[Crossref]

X. Wu, G. Jin, and J. Zhu, Appl. Opt. 56, 2405 (2017).
[Crossref]

2016 (3)

2014 (4)

2011 (1)

2010 (2)

M. Ares, S. Royo, I. Sergievskaya, and J. Riu, Appl. Opt. 49, 6201 (2010).
[Crossref]

P. Zhou, J. Burge, and C. Zhao, Proc. SPIE 7790, 77900L (2010).
[Crossref]

2009 (1)

2005 (1)

2004 (2)

P. M. Prieto, E. J. Fernández, S. Manzanera, and P. Artal, Opt. Express 12, 4059 (2004).
[Crossref]

M. C. Knauer, J. Kaminski, and G. Hausler, Proc. SPIE 5457, 366 (2004).
[Crossref]

1987 (1)

M. Stedman, Precis. Eng. 9, 149 (1987).
[Crossref]

1972 (1)

Alieva, T.

Anderson, A.

Ares, M.

Artal, P.

Baer, G.

Bauer, A.

A. Bauer, E. M. Schiesser, and J. P. Rolland, Nat. Commun. 9, 1756 (2018).
[Crossref]

J. Reimers, A. Bauer, K. P. Thompson, and J. P. Rolland, Light Sci. Appl. 6, e17026 (2017).
[Crossref]

A. Bauer and J. P. Rolland, Opt. Express 22, 13155 (2014).
[Crossref]

Bennett, V. P.

Burge, J.

P. Zhou, J. Burge, and C. Zhao, Proc. SPIE 7790, 77900L (2010).
[Crossref]

Campos, J.

Chaudhuri, R.

R. Chaudhuri and J. P. Rolland, “Single-shot, adaptive metrology of rotationally variant optical surfaces using a spatial light modulator,” PCT patent (October2018).

Chen, S.

Chen, X.

B. Yang, Y. Wei, X. Chen, and M. Tang, Proc. SPIE 9272, 927218 (2014).
[Crossref]

Choi, H.

Dainty, C.

Dalimier, E.

Defisher, S.

S. Defisher, in Imaging and Applied Optics, OSA Technical Digest (Optical Society of America, 2015), paper JT5A.6.

Estapé, M.

Fan, Z.

Fernández, E.

Fernández, E. J.

Fienup, J. R.

Fuentes, J. L. M.

Fuerschbach, K.

Geng, J.

Graves, L. R.

Hausler, G.

M. C. Knauer, J. Kaminski, and G. Hausler, Proc. SPIE 5457, 366 (2004).
[Crossref]

Huang, L.

Jesacher, A.

A. Jesacher, “Applications of spatial light modulators for optical trapping and image processing,” Ph.D. dissertation (Leopold-Franzens University, 2007).

Jin, G.

Kaminski, J.

M. C. Knauer, J. Kaminski, and G. Hausler, Proc. SPIE 5457, 366 (2004).
[Crossref]

Kim, D. W.

Knauer, M. C.

M. C. Knauer, J. Kaminski, and G. Hausler, Proc. SPIE 5457, 366 (2004).
[Crossref]

Lemmi, C.

Lizana, A.

Malacara, D.

D. Malacara, Optical Shop Testing, 3rd ed. (Wiley, 2007).

Manzanera, S.

Márquez, A.

Martin, N.

Michalko, A. M.

Moreno, I.

Oh, C. J.

Osten, W.

Prieto, P. M.

Pruss, C.

Reimers, J.

J. Reimers, A. Bauer, K. P. Thompson, and J. P. Rolland, Light Sci. Appl. 6, e17026 (2017).
[Crossref]

Rickenstorff, C.

Riu, J.

Rodrigo, J. A.

Rolland, J. P.

A. Bauer, E. M. Schiesser, and J. P. Rolland, Nat. Commun. 9, 1756 (2018).
[Crossref]

J. Yao, A. Anderson, and J. P. Rolland, Opt. Express 26, 10242 (2018).
[Crossref]

J. Reimers, A. Bauer, K. P. Thompson, and J. P. Rolland, Light Sci. Appl. 6, e17026 (2017).
[Crossref]

K. Fuerschbach, K. P. Thompson, and J. P. Rolland, Opt. Lett. 39, 18 (2014).
[Crossref]

A. Bauer and J. P. Rolland, Opt. Express 22, 13155 (2014).
[Crossref]

R. Chaudhuri and J. P. Rolland, “Single-shot, adaptive metrology of rotationally variant optical surfaces using a spatial light modulator,” PCT patent (October2018).

Royo, S.

Schiesser, E. M.

A. Bauer, E. M. Schiesser, and J. P. Rolland, Nat. Commun. 9, 1756 (2018).
[Crossref]

Schindler, J.

Sergievskaya, I.

Siepmann, J.

Stedman, M.

M. Stedman, Precis. Eng. 9, 149 (1987).
[Crossref]

Su, P.

Su, T.

Tang, M.

B. Yang, Y. Wei, X. Chen, and M. Tang, Proc. SPIE 9272, 927218 (2014).
[Crossref]

Thompson, K. P.

J. Reimers, A. Bauer, K. P. Thompson, and J. P. Rolland, Light Sci. Appl. 6, e17026 (2017).
[Crossref]

K. Fuerschbach, K. P. Thompson, and J. P. Rolland, Opt. Lett. 39, 18 (2014).
[Crossref]

Wei, Y.

B. Yang, Y. Wei, X. Chen, and M. Tang, Proc. SPIE 9272, 927218 (2014).
[Crossref]

Wu, X.

Wyant, J. C.

Xue, S.

Yang, B.

B. Yang, Y. Wei, X. Chen, and M. Tang, Proc. SPIE 9272, 927218 (2014).
[Crossref]

Yao, J.

Yzuel, M. J.

Zhai, D.

Zhao, C.

P. Zhou, J. Burge, and C. Zhao, Proc. SPIE 7790, 77900L (2010).
[Crossref]

Zhao, W.

Zhou, P.

P. Zhou, J. Burge, and C. Zhao, Proc. SPIE 7790, 77900L (2010).
[Crossref]

Zhu, J.

Adv. Opt. Photon. (1)

Appl. Opt. (3)

Light Sci. Appl. (1)

J. Reimers, A. Bauer, K. P. Thompson, and J. P. Rolland, Light Sci. Appl. 6, e17026 (2017).
[Crossref]

Nat. Commun. (1)

A. Bauer, E. M. Schiesser, and J. P. Rolland, Nat. Commun. 9, 1756 (2018).
[Crossref]

Opt. Express (9)

Opt. Lett. (4)

Precis. Eng. (1)

M. Stedman, Precis. Eng. 9, 149 (1987).
[Crossref]

Proc. SPIE (3)

P. Zhou, J. Burge, and C. Zhao, Proc. SPIE 7790, 77900L (2010).
[Crossref]

M. C. Knauer, J. Kaminski, and G. Hausler, Proc. SPIE 5457, 366 (2004).
[Crossref]

B. Yang, Y. Wei, X. Chen, and M. Tang, Proc. SPIE 9272, 927218 (2014).
[Crossref]

Other (5)

D. Malacara, Optical Shop Testing, 3rd ed. (Wiley, 2007).

S. Defisher, in Imaging and Applied Optics, OSA Technical Digest (Optical Society of America, 2015), paper JT5A.6.

Holoeye Corporation, https://holoeye.com/gaea-4k-phase-only-spatial-light-modulator/ .

R. Chaudhuri and J. P. Rolland, “Single-shot, adaptive metrology of rotationally variant optical surfaces using a spatial light modulator,” PCT patent (October2018).

A. Jesacher, “Applications of spatial light modulators for optical trapping and image processing,” Ph.D. dissertation (Leopold-Franzens University, 2007).

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Figures (3)

Fig. 1.
Fig. 1. Illustration of the SLM-based null test showing (a) system layout (not drawn to scale), and (b) Stedman diagram (sag range “ z ” versus spatial wavelength “ Λ ”), representing the metrology capability.
Fig. 2.
Fig. 2. Illustrations before optimization of the SLM showing (a) the freeform sag departure of the optic from the base sphere, (b) the null test layout in optical design software with the SLM switched off, and (inset) the corresponding interferogram (scaled 40 × ).
Fig. 3.
Fig. 3. Illustrations after optimization of the SLM: (a) null test showing the separation of diffraction orders and the generated null interferogram, (b) the optimized nulling wavefront, and (c) the wrapped nulling phase function on the SLM with the tilt carrier superposed (scaled 50 × for visibility).

Equations (3)

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2 * p * D optic D SLM 0.2 mm ,
I test = 0.96 I * ( T BE 2 * T WP * R SLM * η * T lens 2 ) 2 * R o ,
ϕ q = Round ( ϕ * 255 2 π ) * 2 p 255 .

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