Abstract

The recording of the volume speckle field from an object at different planes combined with the wave propagation equation allows the reconstruction of the wavefront phase and amplitude without requiring a reference wave. The main advantage of this single-beam multiple-intensity reconstruction (SBMIR) technique is the simple experimental setup because no reference wave is required as in the case of holography. The phase retrieval technique is applied to the investigation of diffusely transmitting and reflecting objects. The effects of different parameters on the quality of reconstructions are investigated by simulation and experiment. Significant enhancements of the reconstructions are observed when the number of intensity measurements is 15 or more and the sequential measurement distance is 0.5  mm or larger. Performing two iterations during the reconstruction process using the calculated phase also leads to better reconstruction. The results from computer simulations confirm the experiments. Analysis of transverse and longitudinal intensity distributions of a volume speckle field for the SBMIR technique is presented. Enhancing the resolution method by shifting the camera a distance of a half-pixel in the lateral direction improves the sampling of speckle patterns and leads to better quality reconstructions. This allows the possibility of recording wave fields from larger test objects.

© 2006 Optical Society of America

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References

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2005 (4)

J. Kornis and B. Gombköto;, "Application of super image methods in digital holography," in Optical Measurement Systems for Industrial Inspection IV, W. Osten, C. Gorecki, and E. L. Novak, eds., Proc. SPIE 5856, 245-253 (2005).
[CrossRef]

J. Wu, U. Weierstall, and J. C. H. Spence, "Diffractive electron imaging of nanoparticles on a substrate," Nat. Mater. 4, 912-916 (2005).
[CrossRef] [PubMed]

G. Pedrini, W. Osten, and Y. Zhang, "Wave-front reconstruction from a sequence of interferograms recorded at different planes," Opt. Lett. 30, 833-835 (2005).
[CrossRef] [PubMed]

E. Kolenovic, "Correlation between intensity and phase in monochromatic light," J. Opt. Soc. Am. A 22, 899-906 (2005).
[CrossRef]

2003 (2)

2002 (1)

1998 (1)

1996 (1)

I. Freund and D. A. Kessler, "Phase autocorrelation of random wave fields," Opt. Commun. 124, 321-332 (1996).
[CrossRef]

1994 (1)

1992 (1)

1987 (1)

1983 (1)

1982 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik (Stuttgart) 35, 237-246 (1972).

Barty, A.

Chiang, F. P.

Dong, B.

Ersoy, O. K.

Fienup, J. R.

Freund, I.

I. Freund and D. A. Kessler, "Phase autocorrelation of random wave fields," Opt. Commun. 124, 321-332 (1996).
[CrossRef]

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik (Stuttgart) 35, 237-246 (1972).

Gombköto;, B.

J. Kornis and B. Gombköto;, "Application of super image methods in digital holography," in Optical Measurement Systems for Industrial Inspection IV, W. Osten, C. Gorecki, and E. L. Novak, eds., Proc. SPIE 5856, 245-253 (2005).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, 1985).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Gu, B.

Kessler, D. A.

I. Freund and D. A. Kessler, "Phase autocorrelation of random wave fields," Opt. Commun. 124, 321-332 (1996).
[CrossRef]

Kolenovic, E.

Kornis, J.

J. Kornis and B. Gombköto;, "Application of super image methods in digital holography," in Optical Measurement Systems for Industrial Inspection IV, W. Osten, C. Gorecki, and E. L. Novak, eds., Proc. SPIE 5856, 245-253 (2005).
[CrossRef]

Li, Q. B.

Liu, G.

Nugent, K. A.

Osten, W.

Paganin, D.

Pedrini, G.

Rastogi, P. K.

P. K. Rastogi, Digital Speckle Pattern Interferometry and Related Techniques (Wiley, 2001).

Roberts, A.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik (Stuttgart) 35, 237-246 (1972).

Scott, P. D.

Sheppard, C. J. R.

Spence, J. C. H.

J. Wu, U. Weierstall, and J. C. H. Spence, "Diffractive electron imaging of nanoparticles on a substrate," Nat. Mater. 4, 912-916 (2005).
[CrossRef] [PubMed]

Teague, M. R.

Tiziani, H.

Weierstall, U.

J. Wu, U. Weierstall, and J. C. H. Spence, "Diffractive electron imaging of nanoparticles on a substrate," Nat. Mater. 4, 912-916 (2005).
[CrossRef] [PubMed]

Wu, J.

J. Wu, U. Weierstall, and J. C. H. Spence, "Diffractive electron imaging of nanoparticles on a substrate," Nat. Mater. 4, 912-916 (2005).
[CrossRef] [PubMed]

Yang, G.

Yaroslavsky, L.

L. Yaroslavsky, Digital Holography and Digital Image Processing: Principles, Methods, Algorithms (Kluwer, 2004).

Zhang, Y.

Zhuang, J.

Appl. Opt. (5)

J. Opt. Soc. Am. (1)

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

Nat. Mater. (1)

J. Wu, U. Weierstall, and J. C. H. Spence, "Diffractive electron imaging of nanoparticles on a substrate," Nat. Mater. 4, 912-916 (2005).
[CrossRef] [PubMed]

Opt. Commun. (1)

I. Freund and D. A. Kessler, "Phase autocorrelation of random wave fields," Opt. Commun. 124, 321-332 (1996).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Optik (1)

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik (Stuttgart) 35, 237-246 (1972).

Proc. SPIE (1)

J. Kornis and B. Gombköto;, "Application of super image methods in digital holography," in Optical Measurement Systems for Industrial Inspection IV, W. Osten, C. Gorecki, and E. L. Novak, eds., Proc. SPIE 5856, 245-253 (2005).
[CrossRef]

Other (4)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

J. W. Goodman, Statistical Optics (Wiley, 1985).

L. Yaroslavsky, Digital Holography and Digital Image Processing: Principles, Methods, Algorithms (Kluwer, 2004).

P. K. Rastogi, Digital Speckle Pattern Interferometry and Related Techniques (Wiley, 2001).

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Figures (15)

Fig. 1
Fig. 1

Diagram for sequential intensity measurements of volume speckle field.

Fig. 2
Fig. 2

Diagram for wave field reconstruction.

Fig. 3
Fig. 3

(a) Array of reconstructions from multiple intensity measurements at 2   mm interval reconstruction planes. (b) Corresponding array of reconstructions from a single intensity measurement.

Fig. 4
Fig. 4

Correlations of reconstructions at different positions for multiple intensity measurements and a single intensity measurement.

Fig. 5
Fig. 5

Reconstructions of a diffusely transmitting object at 2   mm interval reconstruction planes using (a) multiple intensity measurements and (b) a single intensity measurement.

Fig. 6
Fig. 6

(a) Reconstructions of a diffusely reflecting object at 2   mm interval reconstruction planes. (b) Photographic images obtained using a lens imaging system.

Fig. 7
Fig. 7

Simulations of the effects of number of intensity measurements and iterations on the quality of reconstructions.

Fig. 8
Fig. 8

Correlations of reconstructions for an increasing number of intensity measurements and iterations.

Fig. 9
Fig. 9

Reconstructions of a diffusely transmitting object for increasing number of intensity measurement and iterations.

Fig. 10
Fig. 10

Nonreconstructions obtained from two intensity measurements separated by 0.5 and 1.0 mm, despite the large number of iterations. For comparison, the images at right show good reconstructions when multiple intensity measurements are used.

Fig. 11
Fig. 11

Simulations of the effects of increasing sequential measurement distance (from left to right): Δ z = 0.1   mm , Δ z = 0.2   mm , . . . , Δ z = 1   mm .

Fig. 12
Fig. 12

Correlation as a function of measurement distance ( Δ z ) .

Fig. 13
Fig. 13

Reconstructions for a diffusely transmitting object for increasing measurement distance (from left to right): Δ z = 0.1   mm , Δ z = 0.2   mm , . . . , Δ z = 1   mm .

Fig. 14
Fig. 14

(a) Diagram of volume speckle field; (b) and (c) sections of intensity measurements at transverse planes A and B, respectively; (e) and (f) the corresponding phase distributions; (h) and (i) the corresponding phase autocorrelations. (d) Section of intensity measurements in longitudinal plane C; (g) and (j) longitudinal intensity distributions from 20 measurement planes for Δ z = 0.1   mm and Δ z = 1.0   mm , respectively.

Fig. 15
Fig. 15

Reconstructions using the enhanced resolution method. (a) Zoomed-in image from a 1024 × 1024 pixel intensity measurement. (b) Zoomed-in image from a 2048 × 2048 pixel super image intensity measurement. (c) Reconstruction from a set of 1024 × 1024 pixel intensity measurements. (d) Reconstruction from a set of 2048 × 2048 pixel super image intensity measurements.

Equations (5)

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U ( x , y , z ) = u u ^ ( f x , f y ) exp [ ( - i2 π z / λ ) × ( 1 λ 2 f x 2 λ 2 f y 2 ) 1 / 2 ] exp [ i2 π ( f x x + f y y ) ] × d f x d f y ,
U p + 1 ( k Δ x , l Δ y , z ) = A p + 1 ( k Δ x , l Δ y , z ) × exp i φ p + 1 ( k Δ x , l Δ y , z )
= - 1 ( { [ I p ( m Δ x , n Δ y ) ] 1 / 2 × exp [ i φ p ( m Δ x , n Δ y ) ] } × exp [ ( - i2 π z / λ ) × ( 1 λ 2 m 2 Δ x 2 λ 2 n 2 Δ y 2 ) 1 / 2 ] ) ,
Λ trans 1.22 λ z / D ,
Λ long 8 λ ( z / D ) 2 ,

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