Abstract

The technique of Fourier synthesis holography to image through scattering materials is analyzed in detail. A broad spectral source is decomposed into its Fourier components, and a hologram is formed at each wavelength and stored in the computer. Upon synthesis in the computer, a clear image can be formed of the obscured object. Post-data-acquisition processing such as selection of the gating time delay and autocorrelation shaping are also demonstrated.

© 1995 Optical Society of America

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References

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1993 (3)

1992 (2)

1990 (1)

J. C. Hebden, R. A. Kruger, “Transillumination imaging performance: time of flight imaging system,” Med. Phys. 17, 351–356 (1990).
[CrossRef] [PubMed]

1989 (2)

N. H. Abramson, K. G. Spears, “Single pulse light-in-flight recording by holography,” Appl. Opt. 28, 1834–1841 (1989).
[CrossRef] [PubMed]

K. G. Spears, J. Serafin, N. Abramson, X. Zhu, H. Bjelkhagen, “Chronocoherent imaging for medicine,” IEEE Trans. Biomed. Eng. 36, 1210–1214 (1989).
[CrossRef] [PubMed]

1986 (1)

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

1971 (1)

Abramson, N.

K. G. Spears, J. Serafin, N. Abramson, X. Zhu, H. Bjelkhagen, “Chronocoherent imaging for medicine,” IEEE Trans. Biomed. Eng. 36, 1210–1214 (1989).
[CrossRef] [PubMed]

Abramson, N. H.

Alfano, R. R.

Arons, E.

Bjelkhagen, H.

K. G. Spears, J. Serafin, N. Abramson, X. Zhu, H. Bjelkhagen, “Chronocoherent imaging for medicine,” IEEE Trans. Biomed. Eng. 36, 1210–1214 (1989).
[CrossRef] [PubMed]

Chen, C.

Chen, H.

Chen, Y.

Dai, H.

Dilworth, D.

Duguay, M. A.

Fujimoto, J. G.

Hebden, J. C.

J. C. Hebden, R. A. Kruger, “Transillumination imaging performance: time of flight imaging system,” Med. Phys. 17, 351–356 (1990).
[CrossRef] [PubMed]

Hee, M. R.

Ho, P. P.

Izatt, J. A.

Kruger, R. A.

J. C. Hebden, R. A. Kruger, “Transillumination imaging performance: time of flight imaging system,” Med. Phys. 17, 351–356 (1990).
[CrossRef] [PubMed]

Leith, E.

Liang, X.

Lopez, J.

Marron, J. C.

Mattick, A. T.

Rudd, J.

Schroeder, K. S.

Serafin, J.

K. G. Spears, J. Serafin, N. Abramson, X. Zhu, H. Bjelkhagen, “Chronocoherent imaging for medicine,” IEEE Trans. Biomed. Eng. 36, 1210–1214 (1989).
[CrossRef] [PubMed]

Shentu, L.

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

Shih, M.

Spears, K. G.

N. H. Abramson, K. G. Spears, “Single pulse light-in-flight recording by holography,” Appl. Opt. 28, 1834–1841 (1989).
[CrossRef] [PubMed]

K. G. Spears, J. Serafin, N. Abramson, X. Zhu, H. Bjelkhagen, “Chronocoherent imaging for medicine,” IEEE Trans. Biomed. Eng. 36, 1210–1214 (1989).
[CrossRef] [PubMed]

Sun, P. C.

Swanson, E. A.

Valdmanis, J.

Vossler, G.

Wang, L. M.

Zhu, X.

K. G. Spears, J. Serafin, N. Abramson, X. Zhu, H. Bjelkhagen, “Chronocoherent imaging for medicine,” IEEE Trans. Biomed. Eng. 36, 1210–1214 (1989).
[CrossRef] [PubMed]

Appl. Opt. (4)

IEEE Trans. Biomed. Eng. (1)

K. G. Spears, J. Serafin, N. Abramson, X. Zhu, H. Bjelkhagen, “Chronocoherent imaging for medicine,” IEEE Trans. Biomed. Eng. 36, 1210–1214 (1989).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (1)

Med. Phys. (1)

J. C. Hebden, R. A. Kruger, “Transillumination imaging performance: time of flight imaging system,” Med. Phys. 17, 351–356 (1990).
[CrossRef] [PubMed]

Opt. Lett. (3)

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Figures (8)

Fig. 1
Fig. 1

Sampling in the frequency domain produces periodicity in the time domain, giving rise to the concept of an unambiguous range: (a) example frequency spectrum and its Fourier transform, (b) frequency sampling function and its Fourier transform, (c) sampled spectrum and its periodic Fourier transform.

Fig. 2
Fig. 2

Sidelobes in the autocorrelation function act as secondary pulses, drawing in later-arriving light.

Fig. 3
Fig. 3

Discrete Fourier transform produces sampling in the time domain: (a) normalized power spectrum and its autocorrelation function, (b) artificial creation of infinitely narrow autocorrelation function when sampling is carried out before convolution.

Fig. 4
Fig. 4

Experimental setup.

Fig. 5
Fig. 5

Experimental results: (a) object obscured by 6 mm of wax, and reconstructed images at reference beam time delays of (b) 0 fs, (c) 150 fs, (d) 3000 fs.

Fig. 6
Fig. 6

Plots of the spectra and corresponding autocorrelation functions used to demonstrate pulse shaping for null regions in the spectrum of (a) 0 samples, 64 samples, (c) 128 samples, and 192 samples.

Fig. 7
Fig. 7

Four images reconstructed from the spectral profiles shown in (a) Fig. 6(a), (b) Fig. 6(b), (c) Fig. 6(c), (d) Fig. 6(d), respectively.

Fig. 8
Fig. 8

Experimental results: images reconstructed from bandwidths of (a) 0.04 nm, (b) 1.28 nm, (c) 9 nm.

Equations (5)

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G s ( f ) = G ( f ) m = - δ ( m Δ f ) ,
u t = u o + u r = H ( f ) G ( f ) m = - δ ( m Δ f ) + exp ( i 2 π α x ) G ( f ) m = - δ ( m Δ f ) ,
I h = u o + u r 2 = u o 2 + u r 2 + exp ( - i 2 π α x ) H ( f ) G ( f ) G * ( f ) m = - δ ( m Δ f ) + exp ( i 2 π α x ) H * ( f ) G * ( f ) G ( f ) m = - δ ( m Δ f ) ,
I ( m Δ f ) = H ( f ) G ( f ) m = - δ ( m Δ f ) ,
I ( l Δ t ) = [ h ( t ) * g ( t ) * k = - δ ( k Δ T ) ] l = - δ ( l Δ t ) ,

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