Abstract

We investigate the range of application of single-beam homodyne spectral phase interferometry for direct electric field reconstruction (SPIDER) for multiphoton microscopy. Simulations and experimental studies performed on model spectral phase profiles show that the phase reconstruction technique used in this method makes the phase retrieval quality highly sensitive to the complexity of the profile. In addition, we show that the use of iterative processes is likely to deteriorate the phase retrieval quality, especially for strongly varying phase profiles. These effects are illustrated and quantified for sinusoidal and quadratic spectral phase profiles.

© 2011 Optical Society of America

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P. Schön, M. Behrndt, D. Ait-Belkacem, H. Rigneault, and S. Brasselet, Phys. Rev. A 81, 013809 (2010).
[CrossRef]

N. Forget, V. Crozatier, and T. Oksenhendler, J. Opt. Soc. Am. B 27, 742 (2010).
[CrossRef]

2009 (2)

2008 (1)

2007 (1)

2006 (1)

2005 (1)

2003 (3)

2002 (1)

N. Dudovich, D. Oron, and Y. Silberberg, Nature 418, 512 (2002).
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2001 (1)

1998 (2)

1997 (1)

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Ait-Belkacem, D.

P. Schön, M. Behrndt, D. Ait-Belkacem, H. Rigneault, and S. Brasselet, Phys. Rev. A 81, 013809 (2010).
[CrossRef]

Bartels, R. A.

Barty, C. P. J.

Beaurepaire, E.

Behrndt, M.

P. Schön, M. Behrndt, D. Ait-Belkacem, H. Rigneault, and S. Brasselet, Phys. Rev. A 81, 013809 (2010).
[CrossRef]

Boudoux, C.

Brasselet, S.

P. Schön, M. Behrndt, D. Ait-Belkacem, H. Rigneault, and S. Brasselet, Phys. Rev. A 81, 013809 (2010).
[CrossRef]

Chen, B.-C.

Crozatier, V.

Cruz, J. M. D.

Dantus, M.

Dela Cruz, J. M.

DeLong, K. W.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Dorrer, C.

Dudovich, N.

N. Dudovich, D. Oron, and Y. Silberberg, Nature 418, 512 (2002).
[CrossRef] [PubMed]

Farge, E.

Fittinghoff, D. N.

D. N. Fittinghoff, J. A. Squier, C. P. J. Barty, J. N. Sweetser, R. Trebino, and M. Müller, Opt. Lett. 23, 1046 (1998).
[CrossRef]

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Forget, N.

Gunn, J. M.

Herzog, R.

Iaconis, C.

Joffre, M.

Kane, D. J.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Kaplan, D.

Krumbügel, M. A.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

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Lim, S.-H.

Londero, P.

Lozovoy, V. V.

Masihzadeh, O.

Monmayrant, A.

Müller, M.

Oksenhendler, T.

Olivier, N.

Oron, D.

Pastirk, I.

Pillai, R. S.

Richman, B. A.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Rigneault, H.

P. Schön, M. Behrndt, D. Ait-Belkacem, H. Rigneault, and S. Brasselet, Phys. Rev. A 81, 013809 (2010).
[CrossRef]

Schlup, P.

Schön, P.

P. Schön, M. Behrndt, D. Ait-Belkacem, H. Rigneault, and S. Brasselet, Phys. Rev. A 81, 013809 (2010).
[CrossRef]

Shane, J. C.

Silberberg, Y.

Squier, J. A.

Sung, J.

Sweetser, J. N.

D. N. Fittinghoff, J. A. Squier, C. P. J. Barty, J. N. Sweetser, R. Trebino, and M. Müller, Opt. Lett. 23, 1046 (1998).
[CrossRef]

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Tal, E.

Tournois, P.

Trebino, R.

D. N. Fittinghoff, J. A. Squier, C. P. J. Barty, J. N. Sweetser, R. Trebino, and M. Müller, Opt. Lett. 23, 1046 (1998).
[CrossRef]

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

Veilleux, I.

Walmsley, I. A.

Walowicz, K. A.

Xu, B.

J. Opt. Soc. Am. B (2)

Nature (1)

N. Dudovich, D. Oron, and Y. Silberberg, Nature 418, 512 (2002).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (8)

Phys. Rev. A (1)

P. Schön, M. Behrndt, D. Ait-Belkacem, H. Rigneault, and S. Brasselet, Phys. Rev. A 81, 013809 (2010).
[CrossRef]

Rev. Sci. Instrum. (1)

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, Rev. Sci. Instrum. 68, 3277 (1997).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Phase retrieval simulations. x denotes the variable pa rameter in each series. (a) quadratic phase ϕ 0 = x ( ω ω 0 ) 2 ; (b) sinus with varying amplitude ϕ 0 = x sin ( ω 4 π ) ; inset, sinus with varying period ϕ 0 = π 3 sin ( x ω ) ; (c) quadratic phase and sinus with varying amplitude ϕ 0 = 300 fs 2 ( ω ω 0 ) 2 + x sin ( ω 4 π ) ; inset, zoom of the graph. Left column, phase profile with a phase step of π at ω pr and ω pr + δ ω , and laser spectrum (dashed curve). Right column, σ dependence on x for the corresponding series.

Fig. 2
Fig. 2

Experimentally measured phases using single-beam homodyne SPIDER. Target phase profiles (solid curve), retrieved phases after the fourth iteration (dashed curve), laser spectrum (dotted curve). Sinusoidal phase profiles ϕ 0 = x 1 π sin ( x 2 2 π Δ ω ( ω ω 0 ) ) (where Δ ω corresponds to an interval of Δ λ = 50 nm around λ 0 = 2 π c ω 0 = 800 nm ) are implemented for several amplitudes ( x 1 ) and periods per Δ λ ( x 2 ). (a)  ( x 1 , x 2 ) = ( 0.3 , 1.5 ) ; (b)  ( x 1 , x 2 ) = ( 0.3 , 2 ) ; (c)  ( x 1 , x 2 ) = ( 0.3 , 3 ) ; (d)  ( x 1 , x 2 ) = ( 0.45 , 1.5 ) ; (e)  ( x 1 , x 2 ) = ( 0.5 , 2 ) ; (f)  ( x 1 , x 2 ) = ( 0.6 , 1.5 ) .

Fig. 3
Fig. 3

Measurement and simulation of the iteration process for sinusoidal target phases ϕ 0 = x 1 π sin ( x 2 2 π Δ ω ( ω ω 0 ) ) . (a), (b) ( x 1 , x 2 ) = ( 0.3 , 4 ) ; (a) measurement; (b) simulation. ϕ r n , phase obtained after the nth iteration. (c), (d) Discretization effect; ( x 1 , x 2 ) = ( 0.3 , 2 ) ; solid curve, target phase ϕ 0 ; dotted curve, calculated phase ϕ r ; gray dashed curve, new encoded phase in the SLM at the next iteration; (c) situation after the first iteration; (d) situation after the fourth iteration.

Equations (3)

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tan 1 [ S ( 2 ) ( ω , ϕ pr = π / 2 ) S ( 2 ) ( ω , ϕ pr = π / 2 ) S ( 2 ) ( ω , ϕ pr = 0 ) S ( 2 ) ( ω , ϕ pr = π ) ] tan 1 [ S ( 1 ) ( ω , ϕ pr = π / 2 ) S ( 1 ) ( ω , ϕ pr = π / 2 ) S ( 1 ) ( ω , ϕ pr = 0 ) S ( 1 ) ( ω , ϕ pr = π ) ] θ ( ω ω pr )
ϕ ( ω 0 + n δ ω ) = ϕ ( ω 0 ) + k = 1 n θ ( ω 0 + k δ ω ) ,
σ = Ω ( ϕ 0 ( ω ) ϕ r ( ω ) ) 2 d ω ,

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