Abstract

A technique is described for the fast recording of the information about both spatial and spectral details of an optical radiator. The recorded information is transformed into a spectral image that is easy to apprehend. The principle of spectral-image formation is based on the Fourier-transform relationship between the three-dimensional spatial coherence function of radiation and the radiator geometry, including its position-dependent spectral contents. Relations to other techniques are mentioned, and a result of a preliminary experiment is presented.

© 1986 Optical Society of America

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  1. K. Itoh, Y. Ohtsuka, “Interferometric spectral imaging,” in Conference Digest of the ICO-13 on Optics in Modern Science and Technology (Organizing Committee of ICO-13, Sapporo, Japan, 1984), pp. 600–601.
  2. K. Itoh, Y. Ohtsuka, “Fourier-transform spectral imaging: retrieval of source information from 3-D spatial coherence,” J. Opt. Soc. Am. A 3, 94–99 (1986).
    [CrossRef]
  3. R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), Sec. 20.3.
  4. G. W. Stroke, A. T. Funkhouser, “Fourier-transform spectroscopy using holographic imaging without computing and with stationary interferometers,” Phys. Lett. 16, 272–274 (1965);H. J. Caulfield, “Spectroscopy,” in Handbook of Optical Holography, H. J. Caulfield, ed. (Academic, New York, 1979), Sec. 10.9.
    [CrossRef]
  5. M. Born, E. Wolf, Principles of Optics, 4th ed. (PergamonLondon, 1970), Chap. 10.
  6. J. W. Goodman, Statistical Optics (Wiley, New York, 1965) Chap. 5.
  7. M. V. R. K. Murty, “Interference between wavefronts rotated or reversed with respect to each other and its relation to spatial coherence,” J. Opt. Soc. Am. 54, 1187–1190 (1964).
    [CrossRef]
  8. L. Mertz, Transformations in Optics (Wiley, New York, 1965), Chap. 4.
  9. D. Kohler, L. Mandel, “Source reconstruction from the modulus of the correlation function: practical approach to the phase problem of optical coherence theory,” J. Opt. Soc. Am. 63, 126–134 (1973).
    [CrossRef]
  10. J. J. Burk, J. B. Breckinridge, “Passive imaging through the turbulent atmosphere: fundamental limit on the spatial frequency resolution of a rotational shearing interferometer,” J. Opt. Soc. Am. 68, 66–77 (1978).
  11. C. Roddier, F. Roddier, “Imaging with a coherence interferometer in optical astronomy,” in Image Formation from Coherence Functions in Astronomy, C. van Schooneveld, ed. (Reidel, Dordrecht, The Netherlands, 1979), pp. 175–178.
    [CrossRef]
  12. K. Itoh, Y. Ohtsuka, “Interferometric image reconstruction through the turbulent atmosphere,” Appl. Opt. 20, 4239–4244 (1981).
    [CrossRef] [PubMed]
  13. O. Bryngdahl, A. W. Lohmann, “Variable magnification in incoherent holography,” Appl. Opt. 9, 231–232 (1970).
    [CrossRef] [PubMed]
  14. E. Wolf, A. J. Devaney, F. Gori, “Relationship between spectral properties and spatial properties in one-dimensional free field,” Opt. Commun. 46, 4–8 (1983).
    [CrossRef]
  15. J. W. O’Byrne, “Interferometric measurements of atmospheric seeing,” Proc. Astron. Soc. Aust. 6, 43–48 (1985).
  16. L. Mertz, Transformations in Optics (Wiley, New York, 1965), Chaps. 1 and 2.
  17. G. A. Vanasse, H. Sakai, “Fourier spectroscopy,” in Progress in Optics VI, E. Wolf, ed. (North-Holland, New York, 1967), pp. 261–327.
  18. S. W. Rowland, “Computer implementation of image reconstruction formulas,” in Image Reconstruction from Projections, G. T. Herman, ed. (Springer-Verlag, Berlin, 1979).
    [CrossRef]
  19. H. M. Smith, ed., Holographic Recording Materials (Springer-Verlag, Berlin, 1977).
    [CrossRef]

1986

1985

J. W. O’Byrne, “Interferometric measurements of atmospheric seeing,” Proc. Astron. Soc. Aust. 6, 43–48 (1985).

1983

E. Wolf, A. J. Devaney, F. Gori, “Relationship between spectral properties and spatial properties in one-dimensional free field,” Opt. Commun. 46, 4–8 (1983).
[CrossRef]

1981

1978

J. J. Burk, J. B. Breckinridge, “Passive imaging through the turbulent atmosphere: fundamental limit on the spatial frequency resolution of a rotational shearing interferometer,” J. Opt. Soc. Am. 68, 66–77 (1978).

1973

1970

1965

G. W. Stroke, A. T. Funkhouser, “Fourier-transform spectroscopy using holographic imaging without computing and with stationary interferometers,” Phys. Lett. 16, 272–274 (1965);H. J. Caulfield, “Spectroscopy,” in Handbook of Optical Holography, H. J. Caulfield, ed. (Academic, New York, 1979), Sec. 10.9.
[CrossRef]

1964

Born, M.

M. Born, E. Wolf, Principles of Optics, 4th ed. (PergamonLondon, 1970), Chap. 10.

Breckinridge, J. B.

J. J. Burk, J. B. Breckinridge, “Passive imaging through the turbulent atmosphere: fundamental limit on the spatial frequency resolution of a rotational shearing interferometer,” J. Opt. Soc. Am. 68, 66–77 (1978).

Bryngdahl, O.

Burckhardt, C. B.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), Sec. 20.3.

Burk, J. J.

J. J. Burk, J. B. Breckinridge, “Passive imaging through the turbulent atmosphere: fundamental limit on the spatial frequency resolution of a rotational shearing interferometer,” J. Opt. Soc. Am. 68, 66–77 (1978).

Collier, R. J.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), Sec. 20.3.

Devaney, A. J.

E. Wolf, A. J. Devaney, F. Gori, “Relationship between spectral properties and spatial properties in one-dimensional free field,” Opt. Commun. 46, 4–8 (1983).
[CrossRef]

Funkhouser, A. T.

G. W. Stroke, A. T. Funkhouser, “Fourier-transform spectroscopy using holographic imaging without computing and with stationary interferometers,” Phys. Lett. 16, 272–274 (1965);H. J. Caulfield, “Spectroscopy,” in Handbook of Optical Holography, H. J. Caulfield, ed. (Academic, New York, 1979), Sec. 10.9.
[CrossRef]

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1965) Chap. 5.

Gori, F.

E. Wolf, A. J. Devaney, F. Gori, “Relationship between spectral properties and spatial properties in one-dimensional free field,” Opt. Commun. 46, 4–8 (1983).
[CrossRef]

Itoh, K.

Kohler, D.

Lin, L. H.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), Sec. 20.3.

Lohmann, A. W.

Mandel, L.

Mertz, L.

L. Mertz, Transformations in Optics (Wiley, New York, 1965), Chaps. 1 and 2.

L. Mertz, Transformations in Optics (Wiley, New York, 1965), Chap. 4.

Murty, M. V. R. K.

O’Byrne, J. W.

J. W. O’Byrne, “Interferometric measurements of atmospheric seeing,” Proc. Astron. Soc. Aust. 6, 43–48 (1985).

Ohtsuka, Y.

Roddier, C.

C. Roddier, F. Roddier, “Imaging with a coherence interferometer in optical astronomy,” in Image Formation from Coherence Functions in Astronomy, C. van Schooneveld, ed. (Reidel, Dordrecht, The Netherlands, 1979), pp. 175–178.
[CrossRef]

Roddier, F.

C. Roddier, F. Roddier, “Imaging with a coherence interferometer in optical astronomy,” in Image Formation from Coherence Functions in Astronomy, C. van Schooneveld, ed. (Reidel, Dordrecht, The Netherlands, 1979), pp. 175–178.
[CrossRef]

Rowland, S. W.

S. W. Rowland, “Computer implementation of image reconstruction formulas,” in Image Reconstruction from Projections, G. T. Herman, ed. (Springer-Verlag, Berlin, 1979).
[CrossRef]

Sakai, H.

G. A. Vanasse, H. Sakai, “Fourier spectroscopy,” in Progress in Optics VI, E. Wolf, ed. (North-Holland, New York, 1967), pp. 261–327.

Stroke, G. W.

G. W. Stroke, A. T. Funkhouser, “Fourier-transform spectroscopy using holographic imaging without computing and with stationary interferometers,” Phys. Lett. 16, 272–274 (1965);H. J. Caulfield, “Spectroscopy,” in Handbook of Optical Holography, H. J. Caulfield, ed. (Academic, New York, 1979), Sec. 10.9.
[CrossRef]

Vanasse, G. A.

G. A. Vanasse, H. Sakai, “Fourier spectroscopy,” in Progress in Optics VI, E. Wolf, ed. (North-Holland, New York, 1967), pp. 261–327.

Wolf, E.

E. Wolf, A. J. Devaney, F. Gori, “Relationship between spectral properties and spatial properties in one-dimensional free field,” Opt. Commun. 46, 4–8 (1983).
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 4th ed. (PergamonLondon, 1970), Chap. 10.

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

E. Wolf, A. J. Devaney, F. Gori, “Relationship between spectral properties and spatial properties in one-dimensional free field,” Opt. Commun. 46, 4–8 (1983).
[CrossRef]

Phys. Lett.

G. W. Stroke, A. T. Funkhouser, “Fourier-transform spectroscopy using holographic imaging without computing and with stationary interferometers,” Phys. Lett. 16, 272–274 (1965);H. J. Caulfield, “Spectroscopy,” in Handbook of Optical Holography, H. J. Caulfield, ed. (Academic, New York, 1979), Sec. 10.9.
[CrossRef]

Proc. Astron. Soc. Aust.

J. W. O’Byrne, “Interferometric measurements of atmospheric seeing,” Proc. Astron. Soc. Aust. 6, 43–48 (1985).

Other

L. Mertz, Transformations in Optics (Wiley, New York, 1965), Chaps. 1 and 2.

G. A. Vanasse, H. Sakai, “Fourier spectroscopy,” in Progress in Optics VI, E. Wolf, ed. (North-Holland, New York, 1967), pp. 261–327.

S. W. Rowland, “Computer implementation of image reconstruction formulas,” in Image Reconstruction from Projections, G. T. Herman, ed. (Springer-Verlag, Berlin, 1979).
[CrossRef]

H. M. Smith, ed., Holographic Recording Materials (Springer-Verlag, Berlin, 1977).
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 4th ed. (PergamonLondon, 1970), Chap. 10.

J. W. Goodman, Statistical Optics (Wiley, New York, 1965) Chap. 5.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), Sec. 20.3.

C. Roddier, F. Roddier, “Imaging with a coherence interferometer in optical astronomy,” in Image Formation from Coherence Functions in Astronomy, C. van Schooneveld, ed. (Reidel, Dordrecht, The Netherlands, 1979), pp. 175–178.
[CrossRef]

L. Mertz, Transformations in Optics (Wiley, New York, 1965), Chap. 4.

K. Itoh, Y. Ohtsuka, “Interferometric spectral imaging,” in Conference Digest of the ICO-13 on Optics in Modern Science and Technology (Organizing Committee of ICO-13, Sapporo, Japan, 1984), pp. 600–601.

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Figures (4)

Fig. 1
Fig. 1

A wave-front-folding type of interferometer for the spectral imaging. The plane mirror (M) is inclined so as to introduce longitudinal shear displacement. BS, beam splitter; P, prism; L, lens.

Fig. 2
Fig. 2

An optical setup for producing a pointlike object with two spectral components. Light beams from He–Cd (LS1) and He–Ne (LS2) lasers are combined at the beam splitter (BS). L, lens.

Fig. 3
Fig. 3

A reconstructed spectral image (upper pair of spots) of an object occupying a single small point but composed of two distinct spectra. The conjugate image (lower pair of spots) is also reconstructed.

Fig. 4
Fig. 4

A wave-field-folding interferometer proposed for the complete recording of transient optical phenomena. BS, beam splitter; M1 and M2, mirrors; P1 and P2, prisms; R, bulk storage material.

Equations (12)

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J ( x , y , z ) = V ( x , y , z ) V * ( x + x , y + y , z + z ) ,
t = ( t 1 , t 2 , t 3 ) = ( x / c , y / c , z / c ) = r / c ,
J t ( t ) = G s ( s ) exp ( 2 π j t · s ) d s ,
J t ( t ) = J ( c t 1 , c t 2 , c t 3 ) ,
G s ( s ) = ( ν s 3 ) 1 G ( Z s 1 / s 3 , Z s 2 / s 3 , ν ) ,
G s ( s ) = J t ( t ) exp ( 2 π j t · s ) d t ,
I ( x , y ) = | V ( x , y , 0 ) + V ( x , y cos 2 θ , y sin 2 θ ) | 2 / 4 .
I t ( t 1 , t 2 ) = J t ( 0 , 0 , 0 ) / 2 + J t ( 2 t 1 , 0 , 2 θ t 2 ) / 4 + J * ( 2 t 1 , 0 , 2 θ t 2 ) / 4 ,
I ˜ t ( s 1 , s 3 ) = J t ( 0 , 0 , 0 ) δ ( s 1 ) δ ( s 3 ) / 2 + ( 16 θ ) 1 G s ( s 1 / 2 , s 2 , s 3 / 2 θ ) d s 2 + ( 16 θ ) 1 G s ( s 1 / 2 , s 2 , s 3 / 2 θ ) d s 2 .
I t ( t 1 ) = J t ( 0 , 0 , 0 ) / 2 + J t ( 2 t 1 , 0 , 0 ) / 4 + J * ( 2 t 1 , 0 , 0 ) / 4 .
I t ( t 2 ) = J t ( 0 , 0 , 0 ) / 2 + J t ( 0 , 0 , 2 θ t 2 ) / 4 + J * t ( 0 , 0 , 2 θ t 2 ) / 4 .
I 3 ( r ) = | V ( r ) + V ( r ) | 2 = J ( 0 ) / 2 + J ( 2 r ) / 4 + J * ( 2 r ) / 4 .

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