Abstract

In lensless digital holography, the comparatively low resolution of the CCD devices that are used to record the digital holograms has to date limited both the maximum linear dimensions of the measurement object and also the minimum possible stand-off distance between the object and the CCD detector. A signal-processing-based technique known as superresolution (SR) image reconstruction can provide an alternative approach that reduces these restrictions. We report on an SR image reconstruction technique that has been introduced by employing a camera with a “microscanning” function to capture SR digital holograms via multiple subpixel movements of the CCD sensor. A detailed description of the approach is given, along with experimental results, which are discussed and evaluated, showing the advantages of using this method. An approach using three-dimensional holographic contouring is also described that may be adopted as a strategy for benchmarking newly developed algorithms at any stage of the lensless digital holographic process.

© 2010 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  3. I. Yamaguchi, J.-I. Kato, and H. Matsuzaki, “Measurement of surface shape and deformation by phase-shifting image digital holography,” Opt. Eng. 42, 1267-1271 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  6. S. Yeom and B. Javidi, “Three-dimensional object feature extraction and classification with computational holographic imaging,” Appl. Opt. 43, 442-451 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  12. V. Mico, Z. Zalevsky, and J. Garcia, “Superresolution optical system by common-path interferometry,” Opt. Express 14, 5168-5169 (2006).
    [CrossRef]
  13. S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2006).
    [CrossRef]
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    [CrossRef]
  15. M. Paturzo, F. Merola, S. Grilli, S. De Nicola, A. Finizio, and P. Ferraro, “Super-resolution in digital holography by a two-dimensional dynamic phase grating,” Opt. Express 16, 17107-17118 (2008).
    [CrossRef]
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    [CrossRef]
  17. A. S. Fruchter and R. N. Hook, “Drizzle: a method for the linear reconstruction of undersampled images,” Publ. Astron. Soc. Pac. 114, 144-152 (2002).
    [CrossRef]
  18. J. Kornis and B. Gombkoto, “Application of super image methods in digital holography,” Proc. SPIE 5856, 245-253(2005).
    [CrossRef]
  19. T. D. Lauer, “Combining undersampled dithered images,” Publ. Astron. Soc. Pac. 111, 227-237 (1999).
    [CrossRef]

2008 (2)

2006 (5)

A. Baldi, “Comparative analysis of super-resolution algorithms for digital holography,” Proc. SPIE 6341, 634114(2006).
[CrossRef]

A. Asundi and V. R. Singh, “Sectioning of amplitude images in digital holography,” Meas. Sci. Technol. 17, 75-78 (2006).
[CrossRef]

V. Mico, Z. Zalevsky, P. Garcia-Martinez, and J. Garcia, “Superresolved imaging in digital holography by superposition of tilted wavefronts,” Appl. Opt. 45, 822-828 (2006).
[CrossRef]

V. Mico, Z. Zalevsky, and J. Garcia, “Superresolution optical system by common-path interferometry,” Opt. Express 14, 5168-5169 (2006).
[CrossRef]

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef]

2005 (2)

X. F. Meng, L. Z. Cai, M. Z. He, G. Y. Dong, and X. X. Shen, “Cross-talk-free double-image encryption and watermarking with amplitude-phase separate modulations,” J. Opt. A Pure Appl. Opt. 7, 624-631 (2005).
[CrossRef]

J. Kornis and B. Gombkoto, “Application of super image methods in digital holography,” Proc. SPIE 5856, 245-253(2005).
[CrossRef]

2004 (1)

2003 (2)

I. Yamaguchi, J.-I. Kato, and H. Matsuzaki, “Measurement of surface shape and deformation by phase-shifting image digital holography,” Opt. Eng. 42, 1267-1271 (2003).
[CrossRef]

S. C. Park, M. K. Park, and M. G. Kang, “Super-resolution image reconstruction: A technical overview,” IEEE Signal Process. Mag. 20, 21-36 (2003).
[CrossRef]

2002 (3)

J. H. Massig, “Digital off-axis holography with a synthetic aperture,” Opt. Lett. 27, 2179-2181 (2002).
[CrossRef]

A. S. Fruchter and R. N. Hook, “Drizzle: a method for the linear reconstruction of undersampled images,” Publ. Astron. Soc. Pac. 114, 144-152 (2002).
[CrossRef]

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81, 3143-3145 (2002).
[CrossRef]

1999 (1)

T. D. Lauer, “Combining undersampled dithered images,” Publ. Astron. Soc. Pac. 111, 227-237 (1999).
[CrossRef]

1966 (1)

1965 (1)

G. W. Stroke, R. Restrick, A. Funkhouser, and D. Brumm, “Resolution-retrieving compensation of source effects by correlation reconstruction in high resolution holography,” Phys. Lett. 18, 274-275 (1965).
[CrossRef]

Alexandrov, S. A.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef]

Asundi, A.

A. Asundi and V. R. Singh, “Sectioning of amplitude images in digital holography,” Meas. Sci. Technol. 17, 75-78 (2006).
[CrossRef]

Baldi, A.

A. Baldi, “Comparative analysis of super-resolution algorithms for digital holography,” Proc. SPIE 6341, 634114(2006).
[CrossRef]

Bo, F.

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81, 3143-3145 (2002).
[CrossRef]

Brumm, D.

G. W. Stroke, R. Restrick, A. Funkhouser, and D. Brumm, “Resolution-retrieving compensation of source effects by correlation reconstruction in high resolution holography,” Phys. Lett. 18, 274-275 (1965).
[CrossRef]

Cai, L. Z.

X. F. Meng, L. Z. Cai, M. Z. He, G. Y. Dong, and X. X. Shen, “Cross-talk-free double-image encryption and watermarking with amplitude-phase separate modulations,” J. Opt. A Pure Appl. Opt. 7, 624-631 (2005).
[CrossRef]

De Nicola, S.

Dong, G. Y.

X. F. Meng, L. Z. Cai, M. Z. He, G. Y. Dong, and X. X. Shen, “Cross-talk-free double-image encryption and watermarking with amplitude-phase separate modulations,” J. Opt. A Pure Appl. Opt. 7, 624-631 (2005).
[CrossRef]

Ferraro, P.

Finizio, A.

Fruchter, A. S.

A. S. Fruchter and R. N. Hook, “Drizzle: a method for the linear reconstruction of undersampled images,” Publ. Astron. Soc. Pac. 114, 144-152 (2002).
[CrossRef]

Funkhouser, A.

G. W. Stroke, R. Restrick, A. Funkhouser, and D. Brumm, “Resolution-retrieving compensation of source effects by correlation reconstruction in high resolution holography,” Phys. Lett. 18, 274-275 (1965).
[CrossRef]

Garcia, J.

Garcia-Martinez, P.

Gombkoto, B.

J. Kornis and B. Gombkoto, “Application of super image methods in digital holography,” Proc. SPIE 5856, 245-253(2005).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts, 2005).

Grilli, S.

Gutzler, T.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef]

He, M. Z.

X. F. Meng, L. Z. Cai, M. Z. He, G. Y. Dong, and X. X. Shen, “Cross-talk-free double-image encryption and watermarking with amplitude-phase separate modulations,” J. Opt. A Pure Appl. Opt. 7, 624-631 (2005).
[CrossRef]

Hillman, T. R.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef]

Hook, R. N.

A. S. Fruchter and R. N. Hook, “Drizzle: a method for the linear reconstruction of undersampled images,” Publ. Astron. Soc. Pac. 114, 144-152 (2002).
[CrossRef]

Javidi, B.

Kang, M. G.

S. C. Park, M. K. Park, and M. G. Kang, “Super-resolution image reconstruction: A technical overview,” IEEE Signal Process. Mag. 20, 21-36 (2003).
[CrossRef]

Kato, J.-I.

I. Yamaguchi, J.-I. Kato, and H. Matsuzaki, “Measurement of surface shape and deformation by phase-shifting image digital holography,” Opt. Eng. 42, 1267-1271 (2003).
[CrossRef]

Kemper, B.

Kornis, J.

J. Kornis and B. Gombkoto, “Application of super image methods in digital holography,” Proc. SPIE 5856, 245-253(2005).
[CrossRef]

Lauer, T. D.

T. D. Lauer, “Combining undersampled dithered images,” Publ. Astron. Soc. Pac. 111, 227-237 (1999).
[CrossRef]

Leith, E. N.

Liu, C.

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81, 3143-3145 (2002).
[CrossRef]

Liu, Z.

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81, 3143-3145 (2002).
[CrossRef]

Massig, J. H.

Matsuzaki, H.

I. Yamaguchi, J.-I. Kato, and H. Matsuzaki, “Measurement of surface shape and deformation by phase-shifting image digital holography,” Opt. Eng. 42, 1267-1271 (2003).
[CrossRef]

Meng, X. F.

X. F. Meng, L. Z. Cai, M. Z. He, G. Y. Dong, and X. X. Shen, “Cross-talk-free double-image encryption and watermarking with amplitude-phase separate modulations,” J. Opt. A Pure Appl. Opt. 7, 624-631 (2005).
[CrossRef]

Merola, F.

Mico, V.

Park, M. K.

S. C. Park, M. K. Park, and M. G. Kang, “Super-resolution image reconstruction: A technical overview,” IEEE Signal Process. Mag. 20, 21-36 (2003).
[CrossRef]

Park, S. C.

S. C. Park, M. K. Park, and M. G. Kang, “Super-resolution image reconstruction: A technical overview,” IEEE Signal Process. Mag. 20, 21-36 (2003).
[CrossRef]

Paturzo, M.

Restrick, R.

G. W. Stroke, R. Restrick, A. Funkhouser, and D. Brumm, “Resolution-retrieving compensation of source effects by correlation reconstruction in high resolution holography,” Phys. Lett. 18, 274-275 (1965).
[CrossRef]

Sampson, D. D.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef]

Shen, X. X.

X. F. Meng, L. Z. Cai, M. Z. He, G. Y. Dong, and X. X. Shen, “Cross-talk-free double-image encryption and watermarking with amplitude-phase separate modulations,” J. Opt. A Pure Appl. Opt. 7, 624-631 (2005).
[CrossRef]

Singh, V. R.

A. Asundi and V. R. Singh, “Sectioning of amplitude images in digital holography,” Meas. Sci. Technol. 17, 75-78 (2006).
[CrossRef]

Stroke, G. W.

G. W. Stroke, R. Restrick, A. Funkhouser, and D. Brumm, “Resolution-retrieving compensation of source effects by correlation reconstruction in high resolution holography,” Phys. Lett. 18, 274-275 (1965).
[CrossRef]

Upatnieks, J.

Vander Lugt, A.

von Bally, G.

Wang, Y.

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81, 3143-3145 (2002).
[CrossRef]

Yamaguchi, I.

I. Yamaguchi, J.-I. Kato, and H. Matsuzaki, “Measurement of surface shape and deformation by phase-shifting image digital holography,” Opt. Eng. 42, 1267-1271 (2003).
[CrossRef]

Yeom, S.

Zalevsky, Z.

Zhu, J.

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81, 3143-3145 (2002).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. Lett. (1)

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81, 3143-3145 (2002).
[CrossRef]

IEEE Signal Process. Mag. (1)

S. C. Park, M. K. Park, and M. G. Kang, “Super-resolution image reconstruction: A technical overview,” IEEE Signal Process. Mag. 20, 21-36 (2003).
[CrossRef]

J. Opt. A Pure Appl. Opt. (1)

X. F. Meng, L. Z. Cai, M. Z. He, G. Y. Dong, and X. X. Shen, “Cross-talk-free double-image encryption and watermarking with amplitude-phase separate modulations,” J. Opt. A Pure Appl. Opt. 7, 624-631 (2005).
[CrossRef]

Meas. Sci. Technol. (1)

A. Asundi and V. R. Singh, “Sectioning of amplitude images in digital holography,” Meas. Sci. Technol. 17, 75-78 (2006).
[CrossRef]

Opt. Eng. (1)

I. Yamaguchi, J.-I. Kato, and H. Matsuzaki, “Measurement of surface shape and deformation by phase-shifting image digital holography,” Opt. Eng. 42, 1267-1271 (2003).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Lett. (1)

G. W. Stroke, R. Restrick, A. Funkhouser, and D. Brumm, “Resolution-retrieving compensation of source effects by correlation reconstruction in high resolution holography,” Phys. Lett. 18, 274-275 (1965).
[CrossRef]

Phys. Rev. Lett. (1)

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef]

Proc. SPIE (2)

J. Kornis and B. Gombkoto, “Application of super image methods in digital holography,” Proc. SPIE 5856, 245-253(2005).
[CrossRef]

A. Baldi, “Comparative analysis of super-resolution algorithms for digital holography,” Proc. SPIE 6341, 634114(2006).
[CrossRef]

Publ. Astron. Soc. Pac. (2)

A. S. Fruchter and R. N. Hook, “Drizzle: a method for the linear reconstruction of undersampled images,” Publ. Astron. Soc. Pac. 114, 144-152 (2002).
[CrossRef]

T. D. Lauer, “Combining undersampled dithered images,” Publ. Astron. Soc. Pac. 111, 227-237 (1999).
[CrossRef]

Other (1)

J. W. Goodman, Introduction to Fourier Optics (Roberts, 2005).

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Figures (8)

Fig. 1
Fig. 1

Reconstruction results for a die with different resolutions of the CCD sensor: (a)  1024 × 1024 pixels, equivalent to a neighboring pixel distance of 6.45 μm ; (b)  512 × 512 pixels, equivalent to a neighboring pixel distance of 12.9 μm ; and (c)  340 × 340 pixels, equivalent to a neighboring pixel distance of 19.35 μm .

Fig. 2
Fig. 2

Basic premise for SR methods with four LR images (showing just 4 pixels for simplicity but valid for the whole CCD array, supposing each pixel is square, Δ x is the pixel size, and the arrows indicate the directions of the movements of the CCD sensor between LR exposures). The synthesized SR hologram has four times the effective resolution of the native LR images.

Fig. 3
Fig. 3

Off-axis setup used to record digital holograms (BS, beam splitter; E, objective; L, collimating lens; M, mirror; O, object).

Fig. 4
Fig. 4

Numerical reconstruction results for the case when the recording conditions are such that the angle between the die and the reference wave is bigger than that which the CCD camera can resolve: (a) reconstruction of a hologram at the native resolution of 1024 × 1024 pixels, and (b) reconstruction of a SR hologram with a resolution of 2048 × 2048 pixels captured in four-shot mode.

Fig. 5
Fig. 5

Reconstruction results for a small statuette of a couple obtained from (a) a LR hologram, (b) a SR hologram generated by the SR method using in ProgRes MF scan , (c) a SR hologram generated by the interlace method, and (d) a SR hologram generated by the four-quadrant 2 × 2 drizzle method.

Fig. 6
Fig. 6

Two-source contouring results for the roller produced from SR holograms: (a) phase-difference image, (b) phase-difference image with the linear inclination factor removed, (c) unwrapped phase-difference image, and (d) reconstructed 3D surface of the roller.

Fig. 7
Fig. 7

Two-source contouring results for the roller from the normal holograms: (a) phase-difference image, (b) phase-difference image with the linear inclination factor removed, (c) unwrapped phase-difference image, and (d) reconstructed 3D surface of the roller.

Fig. 8
Fig. 8

Two-source contouring results for the roller from the interlaced holograms: (a) phase-difference image, (b) phase- difference image with the linear inclination factor removed, (c) unwrapped phase-difference image, and (d) reconstructed 3D surface of the roller.

Equations (18)

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

Γ ( ξ , η ) = i λ d exp ( i 2 π λ d ) exp [ i π λ d ( ξ 2 + η 2 ) ] × U r ( x , y ) U h ( x , y ) exp [ i π λ d ( x 2 + y 2 ) ] exp [ i 2 π λ d ( x ξ + y η ) ] d x d y ,
Δ ξ = λ d N Δ x ,
f max = 2 λ sin ( θ max 2 ) .
f max = 1 2 Δ x .
θ max = 2 arcsin ( λ 4 Δ x ) λ 2 Δ x ,
J l = k = 1 N w k , l I k ,
J ( 2 x , 2 y ) = I 1 ( x , y ) ,
J ( 2 x + 1 , 2 y ) = I 2 ( x , y ) ,
J ( 2 x , 2 y + 1 ) = I 3 ( x , y ) ,
J ( 2 x + 1 , 2 y + 1 ) = I 4 ( x , y ) ,
x ( 0 , m 1 ) , y ( 0 , n 1 ) .
W x o y o = a x i y i x o y o W x i y i ,
I x o y o = I x i y i a x i y i x o y o W x i y i s 2 W x o y o ,
J ( 2 x , 2 y ) = [ I 1 ( x , y ) + I 2 ( x 1 , y ) + I 3 ( x , y 1 ) + I 4 ( x 1 , y 1 ) ] / 4 ,
J ( 2 x + 1 , 2 y ) = [ I 1 ( x , y ) + I 2 ( x , y ) + I 3 ( x , y 1 ) + I 4 ( x , y 1 ) ] / 4 ,
J ( 2 x , 2 y + 1 ) = [ I 1 ( x , y ) + I 2 ( x 1 , y ) + I 3 ( x , y ) + I 4 ( x 1 , y ) ] / 4 ,
J ( 2 x + 1 , 2 y + 1 ) = [ I 1 ( x , y ) + I 2 ( x , y ) + I 3 ( x , y ) + I 4 ( x , y ) ] / 4 ,
x ( 0 , m 1 ) , y ( 0 , n 1 ) .

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