Abstract

In this work, an optimum plane selection methodology is reported that can be applied to a wide range of single-beam phase retrieval techniques, based on the contrast transfer function. It is shown that the optimum measurement distances obtained by this method form a geometric series that maximizes the range of spatial frequencies to be recovered using a minimum number of planes. This allows a noise-robust phase reconstruction that does not rely on regularization techniques, i.e., an extensive search for a regularization parameter is avoided. Measurement systems that employ this optimization criteria give an instant deterministic noise-robust phase reconstruction with higher accuracy, and enable the phase retrieval of the entire object spectrum, including lower frequency components.

© 2013 Optical Society of America

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References

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2013 (1)

2010 (1)

M. Langer, P. Cloetens, and F. Peyrin, IEEE Trans. Image Process. 19, 2428 (2010).
[CrossRef]

2007 (2)

2005 (1)

2004 (2)

D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, J. Microsc. 214, 51 (2004).
[CrossRef]

C. E. Towers, D. P. Towers, and J. D. C. Jones, Opt. Lett. 29, 1348 (2004).
[CrossRef]

2002 (1)

A. C. Bovik, IEEE Signal Process. Lett. 9, 81 (2002).
[CrossRef]

1994 (1)

Acosta, E.

Barty, A.

D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, J. Microsc. 214, 51 (2004).
[CrossRef]

Boistel, R.

Bovik, A. C.

A. C. Bovik, IEEE Signal Process. Lett. 9, 81 (2002).
[CrossRef]

Cloetens, P.

M. Langer, P. Cloetens, and F. Peyrin, IEEE Trans. Image Process. 19, 2428 (2010).
[CrossRef]

J. P. Guigay, M. Langer, R. Boistel, and P. Cloetens, Opt. Lett. 32, 1617 (2007).
[CrossRef]

Dong, B. Z.

Ersoy, O. K.

Falaggis, K.

Gu, B. Y.

Guigay, J. P.

Jones, J. D. C.

Kozacki, T.

Kujawinska, M.

Langer, M.

M. Langer, P. Cloetens, and F. Peyrin, IEEE Trans. Image Process. 19, 2428 (2010).
[CrossRef]

J. P. Guigay, M. Langer, R. Boistel, and P. Cloetens, Opt. Lett. 32, 1617 (2007).
[CrossRef]

McMahon, P. J.

D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, J. Microsc. 214, 51 (2004).
[CrossRef]

Nugent, K. A.

D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, J. Microsc. 214, 51 (2004).
[CrossRef]

Osten, W.

Paganin, D.

D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, J. Microsc. 214, 51 (2004).
[CrossRef]

Pedrini, G.

Peyrin, F.

M. Langer, P. Cloetens, and F. Peyrin, IEEE Trans. Image Process. 19, 2428 (2010).
[CrossRef]

Soto, M.

Towers, C. E.

Towers, D. P.

Yang, G. Z.

Zhang, Y.

Zhuang, J. Y.

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Figures (4)

Fig. 1.
Fig. 1.

(a) Value of W(f) and wn for the hierarchical approach with TDn=10n, and (b) the comparison of W(f) for N=4 for the case of the hierarchical approach (100, 794, 6300, and 50 mm, r=166.67, and g=530), and the case of equidistant planes (12.5, 25, 37.5, and 50 mm).

Fig. 2.
Fig. 2.

(a)–(d) Phase reconstructions [rad] of a USAF chart (SNR=10dB) and, (e)–(h) a speckle patterns with an object feature size of 32 μm, M=512, p=8μm (SNR=15dB). Figures (b)–(d) and (f)–(h) correspond to subregions of the ideal phase object in (a) and (e), respectively. Figures (b) and (f) correspond to the ideal phase object; (c) and (g) correspond to the hierarchical approach; and (d) and (h) correspond to the case of equidistant planes. The values of Dn are equal to the case of Fig. 1(b).

Fig. 3.
Fig. 3.

(a) IQI [9] and (b) RMS for the example in Fig. 2(e) for various levels of SNR.

Fig. 4.
Fig. 4.

(a) Reconstructed phase of a random object using the GOMF approach (feature size 128 μm, phase difference π/2, M=512, p=8μm), for SNR=25dB, N=11, and DN=5mm, and (b) DN=50mm. The cross sections (c) show the ideal phase object (green curve) and the cases of DN=5mm (blue) and DN=50mm (red), respectively. Figures (d)–(f) correspond to the cases of (a)–(c), but using ε=0.1. The phases in (a)–(f) were not high-pass filtered and include all low-frequency artifacts.

Equations (5)

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B(x,y)=2π/λβ(x,y,z)dz,φ(x,y)=2π/λδ(x,y,z)dz,
F{I0ϕ(v+1)(x)}=n=1Na(Dn,f)[I˜Dn(f)b(v)(Dn,f)]2W(f)+ε,
W(f)=n=1Nwn(Dn,f),wn(Dn,f)=[a(D,f)]2,a(D,f)=sin(πλDf2),b(v)(D,f)=I˜D(f)|ϕ=0+cos(πλDf2)λD2πF{φ(v)(x)I0}.
TDn=gr(Nn),
g=1/[λDN(Δf)2].

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