Abstract

The technique of Fourier synthesis holography is extended to the spatial domain. A spatially extended source is decomposed into its Fourier components, and a hologram of an object distribution is formed at each spatial frequency and stored in a computer. Upon synthesis in the computer a clear image can be formed of the object without the use of lenses.

© 1996 Optical Society of America

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References

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  1. P. C. Sun, “Mutual-intensity lensless imaging system,” Opt. Lett. 18, 394–396 (1993).
    [CrossRef] [PubMed]
  2. E. Leith, L. Shentu, “Tomographic reconstruction of objects by grating interferometer,” Appl. Opt. 31, 907–913 (1986).
    [CrossRef]
  3. J. C. Marron, K. S. Schroeder, “Three-dimensional lensless imaging using laser frequency diversity,” Appl. Opt. 31, 255–262 (1992).
    [CrossRef] [PubMed]
  4. E. Arons, D. Dilworth, M. Shih, P. C. Sun, “Use of Fourier synthesis holography to image through inhomogeneities,” Opt. Lett. 18, 1852–1854 (1993).
    [CrossRef] [PubMed]
  5. E. Arons, D. Dilworth, “Analysis of Fourier synthesis holography for imaging through scattering materials,” Appl. Opt. 34, 1841–1847 (1995).
    [CrossRef] [PubMed]
  6. J. van der Gracht, W. T. Rhodes, “Source sampling for incoherent imaging and spatial filtering,” J. Opt. Soc. Am. A 6, 1165–1167 (1989).
    [CrossRef]
  7. E. O. Brigham, The Fast Fourier Transform (Prentice-Hall, Englewood Cliffs, N.J., 1974).
  8. P. C. Sun, E. Arons, “A nonscanning confocal ranging system,” Appl. Opt. 34, 1254–1261 (1995).
    [CrossRef] [PubMed]

1995

1993

1992

1989

1986

E. Leith, L. Shentu, “Tomographic reconstruction of objects by grating interferometer,” Appl. Opt. 31, 907–913 (1986).
[CrossRef]

Arons, E.

Brigham, E. O.

E. O. Brigham, The Fast Fourier Transform (Prentice-Hall, Englewood Cliffs, N.J., 1974).

Dilworth, D.

Leith, E.

E. Leith, L. Shentu, “Tomographic reconstruction of objects by grating interferometer,” Appl. Opt. 31, 907–913 (1986).
[CrossRef]

Marron, J. C.

Rhodes, W. T.

Schroeder, K. S.

Shentu, L.

E. Leith, L. Shentu, “Tomographic reconstruction of objects by grating interferometer,” Appl. Opt. 31, 907–913 (1986).
[CrossRef]

Shih, M.

Sun, P. C.

van der Gracht, J.

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Figures (2)

Fig. 1
Fig. 1

Experimental setup for lensless imaging with both broad-source and Fourier synthesis holography.

Fig. 2
Fig. 2

Experimental results showing (a) the Fresnel diffraction pattern of the object, (b) an image reconstructed from full source lensless imaging, and [(c) and (d)] two reconstructions from lensless imaging by Fourier synthesis holography. The center points of (c) and (d) are marked with a cross to demonstrate the image displacement that results from the technique.

Equations (12)

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f s x s F λ ,
u inc = exp ( i 2 π f s x ) exp ( i πλ z f s 2 ) .
u obj ( x , f s ) = −∞ r ( x ) exp [ i π λ d ( x x ) 2 ] × exp ( i 2 π f s x ) exp ( i πλ z f s 2 ) d x ′.
u ref ( x , f s ) = exp ( i 2 π f s x ) exp ( i πλ z f s 2 ) .
I h = u obj + u ref 2 = u obj 2 + u ref 2 + u obj u ref * + u obj * u ref .
Δ x s < λ F w 0 ,
Δ f s < 1 w 0 ,
I ( x ; x i ) = L / 2 F λ L / 2 F λ ( u 0 2 + u r 2 + u 0 u r * + u 0 * u r ) × exp ( i 2 π f s x i ) d f s ,
I ( x ; x i ) = −∞ L / 2 F λ L / 2 F λ r ( x ) exp [ i π λ d ( x x ) 2 ] × exp [ i 2 π f s ( x ′− x ) ] exp ( i 2 π f s x i ) d f s d x
= −∞ r ( x ) exp [ i π λ d ( x x ) 2 ] × sinc [ L F λ ( x ′− x + x i ) ] d x ′.
I ( x ; x i ) = −∞ r ( x ) sinc [ L λ F ( x ′− x + x i ) ] d x
= −∞ r ( x ) h ( x ′− x + x i ) d x ,

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