Abstract

We present a new Point Diffraction Interferometer (PDI). Binary adaptive optics (BAO) and Quaternary Adaptive Optics (QAO) can be performed with the help of this PDI as a wavefront sensor. The PDI interferogram, once binarized, is used in two consecutive steps to produce a quaternary mask with phase values 0, π/2, π and 3π/2. The addition of the quaternary mask compensates for the aberrated wavefront and allows us to reach a Strehl ratio of about 0.81. We have verified through computer simulations that the use of QAO depends on the number of actuators of the compensating device to achieve effective compensation. The technique was successfully validated through an experiment.

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

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References

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  1. G.D. Love, R. Myers, A. Purvis, and R. Sharples, “A new approach to adaptive wavefront correction using a liquid crystal half-wave phase shifter,” inICO-16 Conference on Active and Adaptive Optics (European Southern Observatory, 1993), pp. 295–300.
  2. G. D. Love, N. Andrews, P. Birch, D. Buscher, P. Doel, C. Dunlop, J. Major, R. Myers, A. Purvis, R. Sharples, A. Vick, A. Zadrozny, S. R. Restaino, and A. Glindemann, “Binary adaptive optics: atmospheric wave-front correction with a half-wave phase shifter,” Appl. Opt. 34(27), 6058–6066 (1995).
    [Crossref]
  3. J. Osborn, R. M. Myers, and G. D. Love, “PSF halo reduction in adaptive optics using dynamic pupil masking,” Opt. Express 17(20), 17279–17292 (2009).
    [Crossref]
  4. P. Crabtree, C. L. Woods, J. Khoury, and M. Goda, “Binary phase-only filtering for turbulence compensation in fiber-coupled free-space laser communication systems,” Appl. Opt. 46(34), 8335–8345 (2007).
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    [Crossref]
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  12. F. Bai and C. Rao, “Experimental validation of closed-loop adaptive optics based on a self-referencing interferometer wavefront sensor and a liquid-crystal spatial light modulator,” Opt. Commun. 283(14), 2782–2786 (2010).
    [Crossref]
  13. T. Vettenburg and A. R. Harvey, “Correction of optical phase aberrations using binary-amplitude modulation,” J. Opt. Soc. Am. A 28(3), 429–433 (2011).
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2013 (1)

2011 (1)

2010 (1)

F. Bai and C. Rao, “Experimental validation of closed-loop adaptive optics based on a self-referencing interferometer wavefront sensor and a liquid-crystal spatial light modulator,” Opt. Commun. 283(14), 2782–2786 (2010).
[Crossref]

2009 (1)

2007 (1)

2006 (2)

2001 (1)

1998 (2)

1995 (1)

1975 (1)

R. N. Smartt and W. H. Steel, “Theory and application of point diffraction interferometers,” Jpn. J. Appl. Phys. 14(S1), 351–355 (1975).
[Crossref]

Acosta, E.

Andrews, N.

Bai, F.

F. Bai and C. Rao, “Experimental validation of closed-loop adaptive optics based on a self-referencing interferometer wavefront sensor and a liquid-crystal spatial light modulator,” Opt. Commun. 283(14), 2782–2786 (2010).
[Crossref]

Bashkansky, M.

Birch, P.

Birch, P. M.

Blendowske, R.

Booth, M.

Buscher, D.

Chamadoira, S.

Crabtree, P.

Crespo, J.

Cuevas, F. J.

Doel, P.

Dunlop, C.

Fatemi, F.

Glindemann, A.

Goda, M.

Gourlay, J.

Harvey, A. R.

Ip, E.

Khoury, J.

Liñares, J.

Love, G. D.

Love, G.D.

G.D. Love, R. Myers, A. Purvis, and R. Sharples, “A new approach to adaptive wavefront correction using a liquid crystal half-wave phase shifter,” inICO-16 Conference on Active and Adaptive Optics (European Southern Observatory, 1993), pp. 295–300.

Major, J.

Malacara, D.

D. Malacara, M. Servin, and Z. Malacara, Interferogram analysis for optical testing (Marcel Dekker, 1998).

Malacara, Z.

D. Malacara, M. Servin, and Z. Malacara, Interferogram analysis for optical testing (Marcel Dekker, 1998).

Marroquin, J. L.

Mateo, E. F.

Montero-Orille, C.

Moreno, V.

Myers, R.

G. D. Love, N. Andrews, P. Birch, D. Buscher, P. Doel, C. Dunlop, J. Major, R. Myers, A. Purvis, R. Sharples, A. Vick, A. Zadrozny, S. R. Restaino, and A. Glindemann, “Binary adaptive optics: atmospheric wave-front correction with a half-wave phase shifter,” Appl. Opt. 34(27), 6058–6066 (1995).
[Crossref]

G.D. Love, R. Myers, A. Purvis, and R. Sharples, “A new approach to adaptive wavefront correction using a liquid crystal half-wave phase shifter,” inICO-16 Conference on Active and Adaptive Optics (European Southern Observatory, 1993), pp. 295–300.

Myers, R. M.

Neil, M.

Osborn, J.

Prieto-Blanco, X.

Purvis, A.

Rao, C.

F. Bai and C. Rao, “Experimental validation of closed-loop adaptive optics based on a self-referencing interferometer wavefront sensor and a liquid-crystal spatial light modulator,” Opt. Commun. 283(14), 2782–2786 (2010).
[Crossref]

Restaino, S. R.

Servin, M.

Sharples, R.

G. D. Love, N. Andrews, P. Birch, D. Buscher, P. Doel, C. Dunlop, J. Major, R. Myers, A. Purvis, R. Sharples, A. Vick, A. Zadrozny, S. R. Restaino, and A. Glindemann, “Binary adaptive optics: atmospheric wave-front correction with a half-wave phase shifter,” Appl. Opt. 34(27), 6058–6066 (1995).
[Crossref]

G.D. Love, R. Myers, A. Purvis, and R. Sharples, “A new approach to adaptive wavefront correction using a liquid crystal half-wave phase shifter,” inICO-16 Conference on Active and Adaptive Optics (European Southern Observatory, 1993), pp. 295–300.

Smartt, R. N.

R. N. Smartt and W. H. Steel, “Theory and application of point diffraction interferometers,” Jpn. J. Appl. Phys. 14(S1), 351–355 (1975).
[Crossref]

Steel, W. H.

R. N. Smartt and W. H. Steel, “Theory and application of point diffraction interferometers,” Jpn. J. Appl. Phys. 14(S1), 351–355 (1975).
[Crossref]

Vettenburg, T.

Vick, A.

Wilson, T.

Woods, C. L.

Zadrozny, A.

Appl. Opt. (4)

J. Opt. Soc. Am. A (3)

Jpn. J. Appl. Phys. (1)

R. N. Smartt and W. H. Steel, “Theory and application of point diffraction interferometers,” Jpn. J. Appl. Phys. 14(S1), 351–355 (1975).
[Crossref]

Opt. Commun. (1)

F. Bai and C. Rao, “Experimental validation of closed-loop adaptive optics based on a self-referencing interferometer wavefront sensor and a liquid-crystal spatial light modulator,” Opt. Commun. 283(14), 2782–2786 (2010).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Other (2)

G.D. Love, R. Myers, A. Purvis, and R. Sharples, “A new approach to adaptive wavefront correction using a liquid crystal half-wave phase shifter,” inICO-16 Conference on Active and Adaptive Optics (European Southern Observatory, 1993), pp. 295–300.

D. Malacara, M. Servin, and Z. Malacara, Interferogram analysis for optical testing (Marcel Dekker, 1998).

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Figures (11)

Fig. 1.
Fig. 1. The PDI sensor consists of a 4-f system, formed by lenses L1 and L2, and a mask placed in the common focus plane (M). A camera placed after lens L2 records the interference pattern produced by the mask.
Fig. 2.
Fig. 2. Scheme of operation of QAO technique. The first step is like in BAO. The binarization of the interferogram produces a binary phase mask, BF1, which added to the distorted wavefront DW produces the BAO compensated wavefront, BCW. This wavefront generates a new interferogram used to create a new binary phase mask, BF2. The QAO compensation consist of the addition of BF1 + BF2 to the DW to create the quaternary compensated wavefront QCW.
Fig. 3.
Fig. 3. Comparison between the direct binarization of the wavefront at the entrance pupil of the optical system (a) and the binary wavefront resulting from the PDI sensor (b). Quaternary function obtained from the direct discretization of the aberrated wavefront into four levels (c) and that obtained after binarizing the two interferograms obtained during the QAO compensation process (d).
Fig. 4.
Fig. 4. Strehl ratio attainable by BAO as a function of the compensating device pixel size expressed in r0 units for D/r0 =40 (blue line), 20 (orange line) and 10 (grey line).
Fig. 5.
Fig. 5. Strehl ratio attained by the BAO and QAO systems as a function of the binning applied to the pixels of the compensating device for different $D/{r_0}$ values. $D/{r_0} = 5 $: light blue and dark blue lines, $D/{r_0} = 20 $: light yellow and dark yellow lines and $D/{r_0} = 40 $: light red and dark red lines.
Fig. 6.
Fig. 6. Experimental set-up.
Fig. 7.
Fig. 7. DIC microscopic image of the 24-µm diameter phase element to be used in the PDI.
Fig. 8.
Fig. 8. (a) Interferogram of the distorted wavefront. (b) Binary function BF1 obtained from Fig. 8(a), (c) Interferogram of the BF1 compensated wavefront, (d) Binary function BF2 obtained from Fig. 8(c), (e) Quaternary function BF1 + BF2 obtained from Fig. 8(b) + 8(d), (e) Interferogram of the QAO compensated wavefront.
Fig. 9.
Fig. 9. (a) Interferogram of the distorted wavefront. (b) Binary function BF1 obtained from Fig. 9(a), (c) Interferogram of the BAO compensated wavefront, (d) Binary function BF2 obtained from Fig. 9(c), (e) Quaternary function BF1 + BF2 obtained from Fig. 9(b) + 9(d), (f) Interferogram of the QAO compensated wavefront.
Fig. 10.
Fig. 10. Transverse cuts of the PSF intensity (in grey level) for the plane (black line), aberrated (yellow line), BAO compensated (green line) and QAO compensated (blue line) wavefronts.
Fig. 11.
Fig. 11. a: Non aberrated PSF. b: Aberrated PSF. c: BAO compensated PSF and d: QAO compensated PSF.

Tables (3)

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Table 1. S and σI for three spherical concave wavefronts with decreasing radii

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Table 2. S and ${\sigma _I}$ for three spherical convex wavefronts with decreasing radii

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Table 3. S and ${\sigma _I}$ for three randomly aberrated wavefronts with increasing aberration degree

Equations (12)

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S = sin c 2 ( Δ ϕ 2 )
I x , y = | A x , y  exp( i ϕ x , y )   +   A 0  exp( i ϕ 0 ) |
cos ( ϕ x , y ϕ 0 ) = I x , y 2 | A x , y | 2 1
BF 1 x , y = { 0 if cos ( ϕ x , y ϕ 0 ) 0 π if cos ( ϕ x , y ϕ 0 ) < 0
SM 1 x , y = { 1 if BF 1 x , y = 0 1 if BF 1 x , y = π
BC W x , y = SM 1 x , y A x , y exp ( i ϕ x , y ) = A x , y exp ( i ϕ x , y )
BF 2 x , y = { 0 if cos ( ϕ x , y ϕ 0 π 2 ) = sin ( ϕ x , y ϕ 0 ) 0 π 2 if cos ( ϕ x , y ϕ 0 π 2 ) = sin ( ϕ x , y ϕ 0 ) < 0
SM 2 x , y = { 1 if BF 2 x , y = 0 i if BF 2 x , y = π 2
QC W x , y = SM 2 x , y SM 1 x , y A x , y exp ( i ϕ x , y ) = A x , y exp ( i ϕ x , y )
I M = | A x , y | 2 + | A 0 | 2 + 2 | A x , y | | A 0 | I m = | A x , y | 2 + | A 0 | 2 2 | A x , y | | A 0 |
I M I m 2 = 2 | A x , y | | A 0 | > σ n
2 | A x , y | | A 0 | > | A x , y | 2 + | A 0 | 2

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