Abstract

We present an enhanced version of the Zernike wavefront sensor (WFS), which simultaneously measures phase and amplitude aberrations. The “vector-Zernike” WFS consists of a patterned liquid-crystal mask, which imposes a ±π/2 phase on the point spread function core through the achromatic geometric phase acting with the opposite sign on opposite circular polarizations. After splitting circular polarization, the ensuing pupil intensity images are used to reconstruct the phase and the amplitude of the incoming wavefront. We demonstrate reconstruction of the complex wavefront with monochromatic lab measurements and show in simulation the high accuracy and sensitivity over a bandwidth up to 100%.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  1. F. Zernike, Mon. Not. R. Astron. Soc. 94, 377 (1934).
    [Crossref]
  2. F. Zernike, Physica 9, 686 (1942).
    [Crossref]
  3. F. Zernike, Physica 9, 974 (1942).
    [Crossref]
  4. J. Goodman, Introduction to Fourier Optics, Electrical Engineering Series (McGraw-Hill, 1996).
  5. M. N’Diaye, K. Dohlen, T. Fusco, and B. Paul, Astron. Astrophys. 555, A94 (2013).
    [Crossref]
  6. O. Guyon, Astrophys. J. 629, 592 (2005).
    [Crossref]
  7. A. Vigan, M. N’Diaye, K. Dohlen, J. Milli, Z. Wahhaj, J.-F. Sauvage, J.-L. Beuzit, R. Pourcelot, D. Mouillet, and G. Zins, “On-sky compensation of non-common path aberrations with the ZELDA wavefront sensor in VLT/SPHERE, ”arXiv:1806.06158 (2018).
  8. F. Shi, B.-J. Seo, E. Cady, B. Kern, R. Lam, D. Marx, K. Patterson, C. M. Prada, J. Shaw, C. Shelton, J. Shields, H. Tang, and T. Truong, Proc. SPIE 10698, 106982O (2018).
    [Crossref]
  9. C. Paterson, J. Phys. Conf. Ser. 139, 012021 (2008).
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    [Crossref]
  13. E. Bloemhof, Proc. SPIE 8999, 89991k (2014).
    [Crossref]
  14. M. J. Escuti, J. Kim, and M. W. Kudenov, Opt. Photonics News 27(2), 22 (2016).
    [Crossref]
  15. M. N. Miskiewicz and M. J. Escuti, Opt. Express 22, 12691 (2014).
    [Crossref]
  16. R. K. Komanduri, K. F. Lawler, and M. J. Escuti, Opt. Express 21, 404 (2013).
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  17. C. Oh and M. J. Escuti, Opt. Lett. 34, 3637 (2009).
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  18. E. H. Por, S. Y. Haffert, V. M. Radhakrishnan, D. S. Doelman, M. Van Kooten, and S. P. Bos, Proc. SPIE 10703, 1070342 (2018).
    [Crossref]

2018 (2)

F. Shi, B.-J. Seo, E. Cady, B. Kern, R. Lam, D. Marx, K. Patterson, C. M. Prada, J. Shaw, C. Shelton, J. Shields, H. Tang, and T. Truong, Proc. SPIE 10698, 106982O (2018).
[Crossref]

E. H. Por, S. Y. Haffert, V. M. Radhakrishnan, D. S. Doelman, M. Van Kooten, and S. P. Bos, Proc. SPIE 10703, 1070342 (2018).
[Crossref]

2016 (1)

M. J. Escuti, J. Kim, and M. W. Kudenov, Opt. Photonics News 27(2), 22 (2016).
[Crossref]

2015 (1)

2014 (2)

2013 (2)

R. K. Komanduri, K. F. Lawler, and M. J. Escuti, Opt. Express 21, 404 (2013).
[Crossref]

M. N’Diaye, K. Dohlen, T. Fusco, and B. Paul, Astron. Astrophys. 555, A94 (2013).
[Crossref]

2011 (1)

J. K. Wallace, S. Rao, R. M. Jensen-Clem, and G. Serabyn, Proc. SPIE 8126, 81260F (2011).
[Crossref]

2009 (1)

2008 (1)

C. Paterson, J. Phys. Conf. Ser. 139, 012021 (2008).
[Crossref]

2005 (1)

O. Guyon, Astrophys. J. 629, 592 (2005).
[Crossref]

1999 (1)

1942 (2)

F. Zernike, Physica 9, 686 (1942).
[Crossref]

F. Zernike, Physica 9, 974 (1942).
[Crossref]

1934 (1)

F. Zernike, Mon. Not. R. Astron. Soc. 94, 377 (1934).
[Crossref]

Beuzit, J.-L.

A. Vigan, M. N’Diaye, K. Dohlen, J. Milli, Z. Wahhaj, J.-F. Sauvage, J.-L. Beuzit, R. Pourcelot, D. Mouillet, and G. Zins, “On-sky compensation of non-common path aberrations with the ZELDA wavefront sensor in VLT/SPHERE, ”arXiv:1806.06158 (2018).

Bloemhof, E.

E. Bloemhof, Proc. SPIE 8999, 89991k (2014).
[Crossref]

Bos, S. P.

E. H. Por, S. Y. Haffert, V. M. Radhakrishnan, D. S. Doelman, M. Van Kooten, and S. P. Bos, Proc. SPIE 10703, 1070342 (2018).
[Crossref]

Cady, E.

F. Shi, B.-J. Seo, E. Cady, B. Kern, R. Lam, D. Marx, K. Patterson, C. M. Prada, J. Shaw, C. Shelton, J. Shields, H. Tang, and T. Truong, Proc. SPIE 10698, 106982O (2018).
[Crossref]

Cuche, E.

Depeursinge, C.

Doelman, D. S.

E. H. Por, S. Y. Haffert, V. M. Radhakrishnan, D. S. Doelman, M. Van Kooten, and S. P. Bos, Proc. SPIE 10703, 1070342 (2018).
[Crossref]

Dohlen, K.

M. N’Diaye, K. Dohlen, T. Fusco, and B. Paul, Astron. Astrophys. 555, A94 (2013).
[Crossref]

A. Vigan, M. N’Diaye, K. Dohlen, J. Milli, Z. Wahhaj, J.-F. Sauvage, J.-L. Beuzit, R. Pourcelot, D. Mouillet, and G. Zins, “On-sky compensation of non-common path aberrations with the ZELDA wavefront sensor in VLT/SPHERE, ”arXiv:1806.06158 (2018).

Escuti, M. J.

Fusco, T.

M. N’Diaye, K. Dohlen, T. Fusco, and B. Paul, Astron. Astrophys. 555, A94 (2013).
[Crossref]

Goodman, J.

J. Goodman, Introduction to Fourier Optics, Electrical Engineering Series (McGraw-Hill, 1996).

Guyon, O.

O. Guyon, Astrophys. J. 629, 592 (2005).
[Crossref]

Haffert, S. Y.

E. H. Por, S. Y. Haffert, V. M. Radhakrishnan, D. S. Doelman, M. Van Kooten, and S. P. Bos, Proc. SPIE 10703, 1070342 (2018).
[Crossref]

Imada, H.

Jensen-Clem, R. M.

J. K. Wallace, S. Rao, R. M. Jensen-Clem, and G. Serabyn, Proc. SPIE 8126, 81260F (2011).
[Crossref]

Kern, B.

F. Shi, B.-J. Seo, E. Cady, B. Kern, R. Lam, D. Marx, K. Patterson, C. M. Prada, J. Shaw, C. Shelton, J. Shields, H. Tang, and T. Truong, Proc. SPIE 10698, 106982O (2018).
[Crossref]

Kim, J.

M. J. Escuti, J. Kim, and M. W. Kudenov, Opt. Photonics News 27(2), 22 (2016).
[Crossref]

Kino, M.

Komanduri, R. K.

Kudenov, M. W.

M. J. Escuti, J. Kim, and M. W. Kudenov, Opt. Photonics News 27(2), 22 (2016).
[Crossref]

Lam, R.

F. Shi, B.-J. Seo, E. Cady, B. Kern, R. Lam, D. Marx, K. Patterson, C. M. Prada, J. Shaw, C. Shelton, J. Shields, H. Tang, and T. Truong, Proc. SPIE 10698, 106982O (2018).
[Crossref]

Lawler, K. F.

Marquet, P.

Marx, D.

F. Shi, B.-J. Seo, E. Cady, B. Kern, R. Lam, D. Marx, K. Patterson, C. M. Prada, J. Shaw, C. Shelton, J. Shields, H. Tang, and T. Truong, Proc. SPIE 10698, 106982O (2018).
[Crossref]

Matsuo, T.

Milli, J.

A. Vigan, M. N’Diaye, K. Dohlen, J. Milli, Z. Wahhaj, J.-F. Sauvage, J.-L. Beuzit, R. Pourcelot, D. Mouillet, and G. Zins, “On-sky compensation of non-common path aberrations with the ZELDA wavefront sensor in VLT/SPHERE, ”arXiv:1806.06158 (2018).

Miskiewicz, M. N.

Mouillet, D.

A. Vigan, M. N’Diaye, K. Dohlen, J. Milli, Z. Wahhaj, J.-F. Sauvage, J.-L. Beuzit, R. Pourcelot, D. Mouillet, and G. Zins, “On-sky compensation of non-common path aberrations with the ZELDA wavefront sensor in VLT/SPHERE, ”arXiv:1806.06158 (2018).

N’Diaye, M.

M. N’Diaye, K. Dohlen, T. Fusco, and B. Paul, Astron. Astrophys. 555, A94 (2013).
[Crossref]

A. Vigan, M. N’Diaye, K. Dohlen, J. Milli, Z. Wahhaj, J.-F. Sauvage, J.-L. Beuzit, R. Pourcelot, D. Mouillet, and G. Zins, “On-sky compensation of non-common path aberrations with the ZELDA wavefront sensor in VLT/SPHERE, ”arXiv:1806.06158 (2018).

Oh, C.

Paterson, C.

C. Paterson, J. Phys. Conf. Ser. 139, 012021 (2008).
[Crossref]

Patterson, K.

F. Shi, B.-J. Seo, E. Cady, B. Kern, R. Lam, D. Marx, K. Patterson, C. M. Prada, J. Shaw, C. Shelton, J. Shields, H. Tang, and T. Truong, Proc. SPIE 10698, 106982O (2018).
[Crossref]

Paul, B.

M. N’Diaye, K. Dohlen, T. Fusco, and B. Paul, Astron. Astrophys. 555, A94 (2013).
[Crossref]

Por, E. H.

E. H. Por, S. Y. Haffert, V. M. Radhakrishnan, D. S. Doelman, M. Van Kooten, and S. P. Bos, Proc. SPIE 10703, 1070342 (2018).
[Crossref]

Pourcelot, R.

A. Vigan, M. N’Diaye, K. Dohlen, J. Milli, Z. Wahhaj, J.-F. Sauvage, J.-L. Beuzit, R. Pourcelot, D. Mouillet, and G. Zins, “On-sky compensation of non-common path aberrations with the ZELDA wavefront sensor in VLT/SPHERE, ”arXiv:1806.06158 (2018).

Prada, C. M.

F. Shi, B.-J. Seo, E. Cady, B. Kern, R. Lam, D. Marx, K. Patterson, C. M. Prada, J. Shaw, C. Shelton, J. Shields, H. Tang, and T. Truong, Proc. SPIE 10698, 106982O (2018).
[Crossref]

Radhakrishnan, V. M.

E. H. Por, S. Y. Haffert, V. M. Radhakrishnan, D. S. Doelman, M. Van Kooten, and S. P. Bos, Proc. SPIE 10703, 1070342 (2018).
[Crossref]

Rao, S.

J. K. Wallace, S. Rao, R. M. Jensen-Clem, and G. Serabyn, Proc. SPIE 8126, 81260F (2011).
[Crossref]

Sauvage, J.-F.

A. Vigan, M. N’Diaye, K. Dohlen, J. Milli, Z. Wahhaj, J.-F. Sauvage, J.-L. Beuzit, R. Pourcelot, D. Mouillet, and G. Zins, “On-sky compensation of non-common path aberrations with the ZELDA wavefront sensor in VLT/SPHERE, ”arXiv:1806.06158 (2018).

Seo, B.-J.

F. Shi, B.-J. Seo, E. Cady, B. Kern, R. Lam, D. Marx, K. Patterson, C. M. Prada, J. Shaw, C. Shelton, J. Shields, H. Tang, and T. Truong, Proc. SPIE 10698, 106982O (2018).
[Crossref]

Serabyn, G.

J. K. Wallace, S. Rao, R. M. Jensen-Clem, and G. Serabyn, Proc. SPIE 8126, 81260F (2011).
[Crossref]

Shaw, J.

F. Shi, B.-J. Seo, E. Cady, B. Kern, R. Lam, D. Marx, K. Patterson, C. M. Prada, J. Shaw, C. Shelton, J. Shields, H. Tang, and T. Truong, Proc. SPIE 10698, 106982O (2018).
[Crossref]

Shelton, C.

F. Shi, B.-J. Seo, E. Cady, B. Kern, R. Lam, D. Marx, K. Patterson, C. M. Prada, J. Shaw, C. Shelton, J. Shields, H. Tang, and T. Truong, Proc. SPIE 10698, 106982O (2018).
[Crossref]

Shi, F.

F. Shi, B.-J. Seo, E. Cady, B. Kern, R. Lam, D. Marx, K. Patterson, C. M. Prada, J. Shaw, C. Shelton, J. Shields, H. Tang, and T. Truong, Proc. SPIE 10698, 106982O (2018).
[Crossref]

Shields, J.

F. Shi, B.-J. Seo, E. Cady, B. Kern, R. Lam, D. Marx, K. Patterson, C. M. Prada, J. Shaw, C. Shelton, J. Shields, H. Tang, and T. Truong, Proc. SPIE 10698, 106982O (2018).
[Crossref]

Tang, H.

F. Shi, B.-J. Seo, E. Cady, B. Kern, R. Lam, D. Marx, K. Patterson, C. M. Prada, J. Shaw, C. Shelton, J. Shields, H. Tang, and T. Truong, Proc. SPIE 10698, 106982O (2018).
[Crossref]

Truong, T.

F. Shi, B.-J. Seo, E. Cady, B. Kern, R. Lam, D. Marx, K. Patterson, C. M. Prada, J. Shaw, C. Shelton, J. Shields, H. Tang, and T. Truong, Proc. SPIE 10698, 106982O (2018).
[Crossref]

Van Kooten, M.

E. H. Por, S. Y. Haffert, V. M. Radhakrishnan, D. S. Doelman, M. Van Kooten, and S. P. Bos, Proc. SPIE 10703, 1070342 (2018).
[Crossref]

Vigan, A.

A. Vigan, M. N’Diaye, K. Dohlen, J. Milli, Z. Wahhaj, J.-F. Sauvage, J.-L. Beuzit, R. Pourcelot, D. Mouillet, and G. Zins, “On-sky compensation of non-common path aberrations with the ZELDA wavefront sensor in VLT/SPHERE, ”arXiv:1806.06158 (2018).

Wahhaj, Z.

A. Vigan, M. N’Diaye, K. Dohlen, J. Milli, Z. Wahhaj, J.-F. Sauvage, J.-L. Beuzit, R. Pourcelot, D. Mouillet, and G. Zins, “On-sky compensation of non-common path aberrations with the ZELDA wavefront sensor in VLT/SPHERE, ”arXiv:1806.06158 (2018).

Wallace, J. K.

J. K. Wallace, S. Rao, R. M. Jensen-Clem, and G. Serabyn, Proc. SPIE 8126, 81260F (2011).
[Crossref]

Yamamoto, K.

Zernike, F.

F. Zernike, Physica 9, 686 (1942).
[Crossref]

F. Zernike, Physica 9, 974 (1942).
[Crossref]

F. Zernike, Mon. Not. R. Astron. Soc. 94, 377 (1934).
[Crossref]

Zins, G.

A. Vigan, M. N’Diaye, K. Dohlen, J. Milli, Z. Wahhaj, J.-F. Sauvage, J.-L. Beuzit, R. Pourcelot, D. Mouillet, and G. Zins, “On-sky compensation of non-common path aberrations with the ZELDA wavefront sensor in VLT/SPHERE, ”arXiv:1806.06158 (2018).

Appl. Opt. (2)

Astron. Astrophys. (1)

M. N’Diaye, K. Dohlen, T. Fusco, and B. Paul, Astron. Astrophys. 555, A94 (2013).
[Crossref]

Astrophys. J. (1)

O. Guyon, Astrophys. J. 629, 592 (2005).
[Crossref]

J. Phys. Conf. Ser. (1)

C. Paterson, J. Phys. Conf. Ser. 139, 012021 (2008).
[Crossref]

Mon. Not. R. Astron. Soc. (1)

F. Zernike, Mon. Not. R. Astron. Soc. 94, 377 (1934).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Opt. Photonics News (1)

M. J. Escuti, J. Kim, and M. W. Kudenov, Opt. Photonics News 27(2), 22 (2016).
[Crossref]

Physica (2)

F. Zernike, Physica 9, 686 (1942).
[Crossref]

F. Zernike, Physica 9, 974 (1942).
[Crossref]

Proc. SPIE (4)

F. Shi, B.-J. Seo, E. Cady, B. Kern, R. Lam, D. Marx, K. Patterson, C. M. Prada, J. Shaw, C. Shelton, J. Shields, H. Tang, and T. Truong, Proc. SPIE 10698, 106982O (2018).
[Crossref]

E. H. Por, S. Y. Haffert, V. M. Radhakrishnan, D. S. Doelman, M. Van Kooten, and S. P. Bos, Proc. SPIE 10703, 1070342 (2018).
[Crossref]

J. K. Wallace, S. Rao, R. M. Jensen-Clem, and G. Serabyn, Proc. SPIE 8126, 81260F (2011).
[Crossref]

E. Bloemhof, Proc. SPIE 8999, 89991k (2014).
[Crossref]

Other (2)

A. Vigan, M. N’Diaye, K. Dohlen, J. Milli, Z. Wahhaj, J.-F. Sauvage, J.-L. Beuzit, R. Pourcelot, D. Mouillet, and G. Zins, “On-sky compensation of non-common path aberrations with the ZELDA wavefront sensor in VLT/SPHERE, ”arXiv:1806.06158 (2018).

J. Goodman, Introduction to Fourier Optics, Electrical Engineering Series (McGraw-Hill, 1996).

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Figures (5)

Fig. 1.
Fig. 1. Layout of the vZWFS. The intensity distribution of the pupils depends on the incoming phase and sign of the polarization state.
Fig. 2.
Fig. 2. Comparison in the simulated reconstruction of both phase and amplitude between the ZWFS and the vZWFS. The phase aberration is shown in the top row, followed by the residual phase, i.e., the difference between the reconstructed and the input phase. The two bottom rows contain the same with amplitude aberrations. The different columns show the results for different measurement and reconstruction methods.
Fig. 3.
Fig. 3. (a) Layout of the vZWFS setup. We generate a clean beam with a laser (633 nm) and a pinhole. A SLM is operated in the phase-mostly configuration with two polarizers and is used to generate phase aberrations with a complicated pattern (i.e., the Leiden University logo). This configuration also generates some amplitude aberrations. The light is focused on the vector-Zernike mask with a spot diameter of 75 μm, corresponding to 1 λ / D . The liquid-crystal orientation is shown in panel (b), and a parallel polarizer microscopic image is shown in panel (c). The detector image with aberrated pupils is shown in panel (d), showing some pupil overlap because of the splitting angle of the Wollaston.
Fig. 4.
Fig. 4. (a) Reconstructed phase and (b) reconstructed amplitude aberration using the vZWFS.
Fig. 5.
Fig. 5. Residual wavefront aberrations as a function of the bandwidth for both the classical ZWFS and the vZWFS. The “achromatic ZWFS” uses the classical ZWFS reconstruction on one pupil of the vZWFS.

Equations (14)

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

Δ θ ( x , y ) = ± 2 α ( x , y ) .
Ψ A = P e i ϕ = P 0 ( 1 ε ) e i ϕ .
I L = 1 2 ( P 2 + 2 b 2 2 P b [ cos ( ϕ ) + sin ( ϕ ) ] ) ,
I R = 1 2 ( P 2 + 2 b 2 2 P b [ cos ( ϕ ) sin ( ϕ ) ] ) ,
I R + I L = P 2 + 2 b 2 2 P b cos ( ϕ ) ,
I R I L = 2 P b sin ( ϕ ) .
P = I R + I L + 4 b 2 ( I R + I L ) ( I R I L ) 2 4 b 4 ,
ϕ = arcsin ( I R I L 2 P b ) .
ϕ ( I R I L ) 2 b 0 ,
P I R + I L b 0 2 ( 2 cos 2 ( ϕ ) ) b 0 cos ( ϕ ) .
I L , Δ 1 = I L cos 2 ( 1 2 Δ δ HW ) + 1 2 P 2 sin 2 ( 1 2 Δ δ HW ) ,
I L , Δ 2 = I L cos 2 ( 1 2 Δ δ QW ) + 1 2 ( I L + I R ) sin 2 ( 1 2 Δ δ QW ) ,
I L , Δ 3 = I L cos 2 ( Δ θ ) + I R sin 2 ( Δ θ ) .
P = ( I L + I R ) / ( 1 + 2 b 0 2 / P 2 2 b 0 / P ) .

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