Abstract

This Letter develops a framework for digital holography at optical wavelengths by merging phase-shifting interferometry with single-pixel optical imaging based on compressive sensing. The field diffracted by an input object is sampled by Hadamard patterns with a liquid crystal spatial light modulator. The concept of a single-pixel camera is then adapted to perform interferometric imaging of the sampled diffraction pattern by using a Mach–Zehnder interferometer. Phase-shifting techniques together with the application of a backward light propagation algorithm allow the complex amplitude of the object under scrutiny to be resolved. A proof-of-concept experiment evaluating the phase distribution of an ophthalmic lens with compressive phase-shifting holography is provided.

© 2013 Optical Society of America

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2013

2012

M. Mir, B. Bhaduri, R. Wang, R. Zhu, and G. Popescu, Prog. Opt. 57, 133 (2012).
[CrossRef]

P. Clemente, V. Durán, E. Tajahuerce, V. Torres-Company, and J. Lancis, Phys. Rev. A 86, 041803(R) (2012).
[CrossRef]

2011

2009

D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, Opt. Mater. Express 17, 13040 (2009).
[CrossRef]

L. Martínez-León, M. Araiza, B. Javidi, P. Andrés, V. Climent, J. Lancis, and E. Tajahuerce, Opt. Mater. Express 17, 12900 (2009).
[CrossRef]

2008

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, IEEE Signal Process. Mag. 25, 83 (2008).
[CrossRef]

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

2006

D. L. Donoho, IEEE Trans. Inf. Theory 52, 1289 (2006).
[CrossRef]

E. Candes, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 489 (2006).
[CrossRef]

I. Yamaguchi, K. Yamamoto, G. A. Mills, and M. Yokota, Appl. Opt. 45, 975 (2006).
[CrossRef]

1997

1976

Andrés, P.

L. Martínez-León, M. Araiza, B. Javidi, P. Andrés, V. Climent, J. Lancis, and E. Tajahuerce, Opt. Mater. Express 17, 12900 (2009).
[CrossRef]

Araiza, M.

L. Martínez-León, M. Araiza, B. Javidi, P. Andrés, V. Climent, J. Lancis, and E. Tajahuerce, Opt. Mater. Express 17, 12900 (2009).
[CrossRef]

Awatsuji, Y.

Baraniuk, R. G.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, IEEE Signal Process. Mag. 25, 83 (2008).
[CrossRef]

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

Bhaduri, B.

M. Mir, B. Bhaduri, R. Wang, R. Zhu, and G. Popescu, Prog. Opt. 57, 133 (2012).
[CrossRef]

Brady, D. J.

D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, Opt. Mater. Express 17, 13040 (2009).
[CrossRef]

Candes, E.

E. Candes, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 489 (2006).
[CrossRef]

Chan, W. L.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

Charan, K.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

Choi, K.

D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, Opt. Mater. Express 17, 13040 (2009).
[CrossRef]

Clemente, P.

P. Clemente, V. Durán, E. Tajahuerce, V. Torres-Company, and J. Lancis, Phys. Rev. A 86, 041803(R) (2012).
[CrossRef]

Climent, V.

L. Martínez-León, M. Araiza, B. Javidi, P. Andrés, V. Climent, J. Lancis, and E. Tajahuerce, Opt. Mater. Express 17, 12900 (2009).
[CrossRef]

Davenport, M. A.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, IEEE Signal Process. Mag. 25, 83 (2008).
[CrossRef]

Decker, J. A.

Donoho, D. L.

D. L. Donoho, IEEE Trans. Inf. Theory 52, 1289 (2006).
[CrossRef]

Duarte, M. F.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, IEEE Signal Process. Mag. 25, 83 (2008).
[CrossRef]

Durán, V.

P. Clemente, V. Durán, E. Tajahuerce, V. Torres-Company, and J. Lancis, Phys. Rev. A 86, 041803(R) (2012).
[CrossRef]

Harwit, M.

Horisaki, R.

D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, Opt. Mater. Express 17, 13040 (2009).
[CrossRef]

Javidi, B.

Y. Rivenson, A. Stern, and B. Javidi, Appl. Opt. 52, A423 (2013).
[CrossRef]

L. Martínez-León, M. Araiza, B. Javidi, P. Andrés, V. Climent, J. Lancis, and E. Tajahuerce, Opt. Mater. Express 17, 12900 (2009).
[CrossRef]

Kakue, T.

Kelly, K. F.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, IEEE Signal Process. Mag. 25, 83 (2008).
[CrossRef]

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

Kubota, T.

Lancis, J.

P. Clemente, V. Durán, E. Tajahuerce, V. Torres-Company, and J. Lancis, Phys. Rev. A 86, 041803(R) (2012).
[CrossRef]

L. Martínez-León, M. Araiza, B. Javidi, P. Andrés, V. Climent, J. Lancis, and E. Tajahuerce, Opt. Mater. Express 17, 12900 (2009).
[CrossRef]

Laska, J. N.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, IEEE Signal Process. Mag. 25, 83 (2008).
[CrossRef]

Lim, S.

D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, Opt. Mater. Express 17, 13040 (2009).
[CrossRef]

Marks, D. L.

D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, Opt. Mater. Express 17, 13040 (2009).
[CrossRef]

Martínez-León, L.

L. Martínez-León, M. Araiza, B. Javidi, P. Andrés, V. Climent, J. Lancis, and E. Tajahuerce, Opt. Mater. Express 17, 12900 (2009).
[CrossRef]

Matoba, O.

Mills, G. A.

Mir, M.

M. Mir, B. Bhaduri, R. Wang, R. Zhu, and G. Popescu, Prog. Opt. 57, 133 (2012).
[CrossRef]

Mittleman, D. M.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

Nishio, K.

Paganetti, R.

Popescu, G.

M. Mir, B. Bhaduri, R. Wang, R. Zhu, and G. Popescu, Prog. Opt. 57, 133 (2012).
[CrossRef]

Rivenson, Y.

Romberg, J.

E. Candes, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 489 (2006).
[CrossRef]

Stern, A.

Sun, T.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, IEEE Signal Process. Mag. 25, 83 (2008).
[CrossRef]

Swift, R. D.

Tahara, T.

Tajahuerce, E.

P. Clemente, V. Durán, E. Tajahuerce, V. Torres-Company, and J. Lancis, Phys. Rev. A 86, 041803(R) (2012).
[CrossRef]

L. Martínez-León, M. Araiza, B. Javidi, P. Andrés, V. Climent, J. Lancis, and E. Tajahuerce, Opt. Mater. Express 17, 12900 (2009).
[CrossRef]

Takhar, D.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, IEEE Signal Process. Mag. 25, 83 (2008).
[CrossRef]

Tao, T.

E. Candes, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 489 (2006).
[CrossRef]

Torres-Company, V.

P. Clemente, V. Durán, E. Tajahuerce, V. Torres-Company, and J. Lancis, Phys. Rev. A 86, 041803(R) (2012).
[CrossRef]

Ura, S.

Wang, R.

M. Mir, B. Bhaduri, R. Wang, R. Zhu, and G. Popescu, Prog. Opt. 57, 133 (2012).
[CrossRef]

Wattson, R. B.

Yamaguchi, I.

Yamamoto, K.

Yokota, M.

Yonesaka, R.

Zhang, T.

Zhu, R.

M. Mir, B. Bhaduri, R. Wang, R. Zhu, and G. Popescu, Prog. Opt. 57, 133 (2012).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, Appl. Phys. Lett. 93, 121105 (2008).
[CrossRef]

IEEE Signal Process. Mag.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, IEEE Signal Process. Mag. 25, 83 (2008).
[CrossRef]

IEEE Trans. Inf. Theory

D. L. Donoho, IEEE Trans. Inf. Theory 52, 1289 (2006).
[CrossRef]

E. Candes, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 489 (2006).
[CrossRef]

Opt. Lett.

Opt. Mater. Express

L. Martínez-León, M. Araiza, B. Javidi, P. Andrés, V. Climent, J. Lancis, and E. Tajahuerce, Opt. Mater. Express 17, 12900 (2009).
[CrossRef]

D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, Opt. Mater. Express 17, 13040 (2009).
[CrossRef]

Phys. Rev. A

P. Clemente, V. Durán, E. Tajahuerce, V. Torres-Company, and J. Lancis, Phys. Rev. A 86, 041803(R) (2012).
[CrossRef]

Prog. Opt.

M. Mir, B. Bhaduri, R. Wang, R. Zhu, and G. Popescu, Prog. Opt. 57, 133 (2012).
[CrossRef]

Other

E. Candes, http://www-stat.stanford.edu/~candes/l1magic .

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Figures (3)

Fig. 1.
Fig. 1.

Experimental setup for compressive phase-shifting holography. Light diffracted by the phase object is spatially modulated onto a SLM and, afterward, it interferes with the phase-delayed reference beam. The integrated energy flux of the signal is subsequently recorded with a single-pixel detector.

Fig. 2.
Fig. 2.

Retrieved amplitude (left) and phase (right) of the field diffracted by the ophthalmic lens at the SLM plane.

Fig. 3.
Fig. 3.

(a) Phase map of the lens, (b) Zernike coefficients expansion, and fitted curves for the (c) horizontal and (d) vertical profiles marked in (a).

Equations (9)

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

Uisignal(r⃗)=t(r⃗;z)Hi(r⃗),
Uisignal(r⃗;z)=14[Ii,0(r⃗)Ii,π(r⃗)]+j4[2Ii,π/2(r⃗)Ii,0(r⃗)Ii,π(r⃗)],
Ii,δ(r⃗)=|Uisignal(r⃗;z)+Uδreference|2
yi=Uisignal(r⃗;z)d2r⃗=Uisignal(r⃗)d2r⃗,
yi=14[Ii,0Ii,π]+j4[2Ii,π/2Ii,0Ii,π],
Ii,δ=Ii,δ(r⃗)d2r⃗.
y=Hx,
minx,such thaty=Hx,
t(m,n)=F1{F[t(m,n;z)]exp[jπλzN(Δx)2(u2+v2)]},

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