Abstract

This paper discusses the potential of the synthetic-aperture method in digital holography to increase the resolution, to perform high accuracy deformation measurement, and to obtain a three-dimensional topology map. The synthetic aperture method is realized by moving the camera with a motorized xy stage. In this way a greater sensor area can be obtained resulting in a larger numerical aperture (NA). A larger NA enables a more detailed reconstruction combined with a smaller depth of field. The depth of field can be increased by applying the extended depth of field method, which yields an in-focus reconstruction of all longitudinal object regions. Moreover, a topology map of the object can be obtained.

© 2010 Optical Society of America

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References

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2009 (2)

2008 (4)

2007 (2)

L. Martinez-Len and B. Javidi, “Improved resolution synthetic aperture holographic imaging,” Proc. SPIE 6778, 7 (2007).

T. Kreis and K. Schlüter, “Resolution enhancement by aperture synthesis in digital holography,” Opt. Eng. 46, 0558031(2007).
[CrossRef]

2006 (1)

2005 (2)

S. Zhang, “Application of super-resolution image reconstruction to digital holography,” EURASIP J. Appl. Signal Process. 2006, 1–7 (2005).

L., Xu, Z. Guo, X. Peng, J. Miao, and A. Asundi, “Imaging analysis of digital holography,” Opt. Express 13, 2444–2552(2005).
[CrossRef] [PubMed]

2002 (1)

2001 (1)

2000 (1)

1992 (1)

Asundi, A.

Baumbach, T.

Borbély, V.

Boyer, K.

Chang, H.

H. Chang, T. Shih, N. Chen, and N. WenPu, “A microscope system based on bevel-axial method auto-focus,” Opt. Lasers Eng. 47, 547–551 (2009).
[CrossRef]

Chen, N.

H. Chang, T. Shih, N. Chen, and N. WenPu, “A microscope system based on bevel-axial method auto-focus,” Opt. Lasers Eng. 47, 547–551 (2009).
[CrossRef]

Collet, L.

Cullen, D.

Czitrovszky, A.

Di, J.

Do, C. M.

C. M. Do and B. Javidi, “Multi-focus holographic 3D image fusion independent component analysis,” Proc. SPIE 6778, 67789P(2007).

Fan, Q.

Füzessy, Z.

Goodman, J. W.

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

Gross, M.

Guo, Z.

Gyímesi, F.

Haddad, W. S.

Harmati, I.

Hennely, B. M.

Itoh, M.

Javidi, B.

L. Martinez-Len and B. Javidi, “Improved resolution synthetic aperture holographic imaging,” Proc. SPIE 6778, 7 (2007).

C. M. Do and B. Javidi, “Multi-focus holographic 3D image fusion independent component analysis,” Proc. SPIE 6778, 67789P(2007).

Jiang, H.

Jueptner, W.

U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).

Jüptner, W.

Kebbel, V.

Kolenovic, E.

Kreis, T.

T. Kreis and K. Schlüter, “Resolution enhancement by aperture synthesis in digital holography,” Opt. Eng. 46, 0558031(2007).
[CrossRef]

T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley-VCH, 2005).

Le Clerc, F.

Lohmann, A. W.

A. W. Lohmann and S. Sinzinger, Optical Information Processing (Universitätsverlag, 2006).

Longworth, J. W.

Lotfi, A.

Martinez-Len, L.

L. Martinez-Len and B. Javidi, “Improved resolution synthetic aperture holographic imaging,” Proc. SPIE 6778, 7 (2007).

Massig, J. H.

Matsushima, K.

McElhinney, C. P.

McPherson, A.

Miao, J.

Molnár, G.

Molnárka, G.

Nagy, A.

Nagy, A. Tibor

Nakatsuji, T.

Naughton, T. J.

Peng, X.

Ráczkevi, B.

Rhodes, C. K.

Schlüter, K.

T. Kreis and K. Schlüter, “Resolution enhancement by aperture synthesis in digital holography,” Opt. Eng. 46, 0558031(2007).
[CrossRef]

Schnars, U.

U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).

Shih, T.

H. Chang, T. Shih, N. Chen, and N. WenPu, “A microscope system based on bevel-axial method auto-focus,” Opt. Lasers Eng. 47, 547–551 (2009).
[CrossRef]

Sinzinger, S.

A. W. Lohmann and S. Sinzinger, Optical Information Processing (Universitätsverlag, 2006).

Smith, S. W.

S. W. Smith, The Scientist and Engineer’s Guide to Digital Signal Processing (California Technical Publications, 2002).

Solem, J. C.

Sun, W.

Szigethy, D.

Tachiki, M. L.

WenPu, N.

H. Chang, T. Shih, N. Chen, and N. WenPu, “A microscope system based on bevel-axial method auto-focus,” Opt. Lasers Eng. 47, 547–551 (2009).
[CrossRef]

Xu, L.

Yatagai, T.

Zhang, P.

Zhang, S.

S. Zhang, “Application of super-resolution image reconstruction to digital holography,” EURASIP J. Appl. Signal Process. 2006, 1–7 (2005).

Zhao, J.

Appl. Opt. (7)

T. Baumbach, E. Kolenovic, V. Kebbel, and W. Jüptner, “Improvement of accuracy in digital holography by use of multiple holograms,” Appl. Opt. 45, 6077–6085 (2006).
[CrossRef] [PubMed]

C. P. McElhinney, B. M. Hennely, and T. J. Naughton, “Extended focused imaging for digital holograms of macroscopic three-dimensional objects,” Appl. Opt. 47, D71–D78(2008).
[CrossRef] [PubMed]

M. L. Tachiki, M. Itoh, and T. Yatagai, “Simultaneous depth determination of multiple objects by focus analysis in digital holography,” Appl. Opt. 47, D144–D153 (2008).
[CrossRef] [PubMed]

T. Nakatsuji and K. Matsushima, “Free-viewpoint images captured using phase-shifting synthetic aperture digital holography,” Appl. Opt. 47, D136–D143 (2008).
[CrossRef] [PubMed]

J. Di, J. Zhao, H. Jiang, P. Zhang, Q. Fan, and W. Sun, “High resolution digital holographic microscopy with a wide field of view based on a synthetic aperature technique and use of linear CCD scanning,” Appl. Opt. 47, 5654–5659 (2008).
[CrossRef] [PubMed]

F. Gyímesi, Z. Füzessy, V. Borbély, B. Ráczkevi, A. Tibor Nagy, G. Molnárka, A. Lotfi, G. Molnár, A. Czitrovszky, A. Nagy, I. Harmati, and D. Szigethy, “Half-magnitude extensions of resolution and field of view in digital holography by scanning and magnification,” Appl. Opt. 48, 6026–6034(2009).
[CrossRef] [PubMed]

W. S. Haddad, D. Cullen, J. C. Solem, J. W. Longworth, A. McPherson, K. Boyer, and C. K. Rhodes, “Fourier transform holographic microscope,” Appl. Opt. 31, 4973–4978(1992).
[CrossRef] [PubMed]

EURASIP J. Appl. Signal Process. (1)

S. Zhang, “Application of super-resolution image reconstruction to digital holography,” EURASIP J. Appl. Signal Process. 2006, 1–7 (2005).

Opt. Eng. (1)

T. Kreis and K. Schlüter, “Resolution enhancement by aperture synthesis in digital holography,” Opt. Eng. 46, 0558031(2007).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (1)

H. Chang, T. Shih, N. Chen, and N. WenPu, “A microscope system based on bevel-axial method auto-focus,” Opt. Lasers Eng. 47, 547–551 (2009).
[CrossRef]

Opt. Lett. (3)

Other (7)

L. Martinez-Len and B. Javidi, “Improved resolution synthetic aperture holographic imaging,” Proc. SPIE 6778, 7 (2007).

U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).

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

A. W. Lohmann and S. Sinzinger, Optical Information Processing (Universitätsverlag, 2006).

S. W. Smith, The Scientist and Engineer’s Guide to Digital Signal Processing (California Technical Publications, 2002).

T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley-VCH, 2005).

C. M. Do and B. Javidi, “Multi-focus holographic 3D image fusion independent component analysis,” Proc. SPIE 6778, 67789P(2007).

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Figures (14)

Fig. 1
Fig. 1

Nomenclature for coordinates in the object plane, hologram plane, and reconstruction plane.

Fig. 2
Fig. 2

Sketch of setup for recording a Fourier hologram.

Fig. 3
Fig. 3

Hologram at recording distance of 295 mm for (a) 3000 × 3000 pixels, (b) 8000 × 8000 pixels, and their reconstructions (c) and (d), respectively.

Fig. 4
Fig. 4

Region of interest including averaged cross-section for (a) 3000 × 3000 pixel hologram, (b) 8000 × 8000 pixel hologram.

Fig. 5
Fig. 5

Segment of reconstructed intensity and double-exposure phase map including cross-section (a), (b) 3000 × 3000 pixels, (c), (d) 8800 × 8800 pixels, and (e), (f) 3000 × 3000 pixel averaging approach.

Fig. 6
Fig. 6

(a) Diffraction caused by collimated illumination of the sensor, (b) sketch of the axial speckle decorrelation due to camera and/or curved sensor, (c) phase offset caused by axial displacement between the two double-exposure camera positions.

Fig. 7
Fig. 7

Flow chart of the spatial averaging approach applied to double-exposure holography.

Fig. 8
Fig. 8

(a) Phase error for a vertical cross-section of the area under investigation, (b) standard deviation of double-exposure phase maps for adjacent and furthest distant holograms including the trend line.

Fig. 9
Fig. 9

(a) SNR for intensity reconstruction versus number of images and their position, (b) SNR for phase map versus number of images and their position.

Fig. 10
Fig. 10

Sketch of the DOF for a reconstructed hologram.

Fig. 11
Fig. 11

(a) Intensity reconstruction for d = 728 mm , (b) intensity reconstruction for d = 735 mm , (c) variance plot for both boxed areas including Gaussian curve fitting, (d) Gaussian curve fitting for different WS and comparison polynomial fitting for WS of 10 × 10 pixels.

Fig. 12
Fig. 12

(Color online) Topology map.

Fig. 13
Fig. 13

Histograms for obtained topology map with (a) traditional variance approach, (b) polynomial interpolation, (c) bandpass filtered polynomial interpolation.

Fig. 14
Fig. 14

Cross-sections for cut lines shown in Fig. 11, (a) A - A , (b) B - B .

Tables (6)

Tables Icon

Table 1 Theoretical and Practically Achieved Resolution

Tables Icon

Table 2 SBP Comparison

Tables Icon

Table 3 Consequences on Lateral and Axial Alignment

Tables Icon

Table 4 Trend-line Standard Deviation of Phase

Tables Icon

Table 5 SNR Spatial Averaging Method for Intensity and Double-Exposure Phase Map

Tables Icon

Table 6 Gaussian Coefficients and R 2 Values

Equations (20)

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d min 2 Δ x b λ ,
u ( x , y ) = i exp ( i k d ) λ d exp [ i π λ d ( x 2 y 2 ) ] · F { u ( x , y ) u r * ( x , y ) · exp [ i π λ d ( x 2 + y 2 ) ] } ,
u r ( x , y ) exp [ i π λ d ( x 2 + y 2 ) ] .
u ( x , y ) = i exp ( i k d ) λ d exp [ i π λ d ( x 2 y 2 ) ] · F { u ( x , y ) } .
L ( x , y , d r , d o ) = exp [ i π λ d r d o d r d o ( x 2 + y 2 ) ] .
SBP = δ x 1 · δ y 1 · N Δ x · M Δ y ,
FOV = O · O .
δ x = O N and δ y = O M .
SBP on-line = N · M .
SBP = N · M 4 .
η = SBP SBP on-line · 100 % .
SNR = 20 log ( X ¯ σ ) ,
Δ x = λ d N Δ x and Δ y = λ d M Δ y ,
Δ φ ( x , y ) = φ 2 ( x , y ) φ 1 ( x , y ) .
δ φ ( x , y ) = i 2 π λ d ( x δ x + y δ y ) .
f ( x ) = a x b .
f ( x ) = a · ln ( x ) + b .
l df = 2 d N Δ x Δ x N 2 Δ x 2 Δ x 2 .
N r Z obj l d f .
f ( x ) = a exp [ ( ( x b ) / c ) 2 ] ,

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