Abstract

The Fourier transform based interferogram analysis technique of Takeda et al. is reviewed, and it is shown that the digitization of the interferogram can act to seriously distort the recovered phase object. An algorithm for dealing with this problem is proposed. The recovered phase object may also be seriously distorted if the response of the recording medium is nonlinear. An algorithm for calibrating the film response is proposed which uses only the data in the interferogram and which can be used to correct the effects of the film nonlinearity. The technique is demonstrated on an experimental inteferogram obtained in a study of laser-produced plasmas.

© 1985 Optical Society of America

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References

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  1. A. Raven, O. Willi, “Electron Density Profiles in Laser-Produced Plasmas at High Irradiances,” Phys. Rev. Lett. 43, 278 (1979).
    [CrossRef]
  2. R. Fedosejevs, “Critical Density Profiles of Plasmas Produced by Nasosecond Gigawatt CO2 Laser Pulses,” Ph.D. Thesis, U. Toronto (1979), unpublished.
  3. M. Takeda, H. Ina, S. Kobayashi, “Fourier-Transform Method of Fringe-Pattern Analysis for Computer-Based Topography and Interferometry,” J. Opt. Soc. Am. 72, 156 (1982).
    [CrossRef]
  4. R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).
  5. W. H. Steel, Interferometry (Cambridge U.P., London, 1967).
  6. M. D. J. Burgess, B. Luther-Davies, K. A. Nugent, “An Experimental Study of Magnetic Fields in Plasmas Created by High Intensity 1 μm Laser Radiation,” Phys. Fluids, in press.

1982 (1)

1979 (1)

A. Raven, O. Willi, “Electron Density Profiles in Laser-Produced Plasmas at High Irradiances,” Phys. Rev. Lett. 43, 278 (1979).
[CrossRef]

Bracewell, R.

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).

Burgess, M. D. J.

M. D. J. Burgess, B. Luther-Davies, K. A. Nugent, “An Experimental Study of Magnetic Fields in Plasmas Created by High Intensity 1 μm Laser Radiation,” Phys. Fluids, in press.

Fedosejevs, R.

R. Fedosejevs, “Critical Density Profiles of Plasmas Produced by Nasosecond Gigawatt CO2 Laser Pulses,” Ph.D. Thesis, U. Toronto (1979), unpublished.

Ina, H.

Kobayashi, S.

Luther-Davies, B.

M. D. J. Burgess, B. Luther-Davies, K. A. Nugent, “An Experimental Study of Magnetic Fields in Plasmas Created by High Intensity 1 μm Laser Radiation,” Phys. Fluids, in press.

Nugent, K. A.

M. D. J. Burgess, B. Luther-Davies, K. A. Nugent, “An Experimental Study of Magnetic Fields in Plasmas Created by High Intensity 1 μm Laser Radiation,” Phys. Fluids, in press.

Raven, A.

A. Raven, O. Willi, “Electron Density Profiles in Laser-Produced Plasmas at High Irradiances,” Phys. Rev. Lett. 43, 278 (1979).
[CrossRef]

Steel, W. H.

W. H. Steel, Interferometry (Cambridge U.P., London, 1967).

Takeda, M.

Willi, O.

A. Raven, O. Willi, “Electron Density Profiles in Laser-Produced Plasmas at High Irradiances,” Phys. Rev. Lett. 43, 278 (1979).
[CrossRef]

J. Opt. Soc. Am. (1)

Phys. Rev. Lett. (1)

A. Raven, O. Willi, “Electron Density Profiles in Laser-Produced Plasmas at High Irradiances,” Phys. Rev. Lett. 43, 278 (1979).
[CrossRef]

Other (4)

R. Fedosejevs, “Critical Density Profiles of Plasmas Produced by Nasosecond Gigawatt CO2 Laser Pulses,” Ph.D. Thesis, U. Toronto (1979), unpublished.

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).

W. H. Steel, Interferometry (Cambridge U.P., London, 1967).

M. D. J. Burgess, B. Luther-Davies, K. A. Nugent, “An Experimental Study of Magnetic Fields in Plasmas Created by High Intensity 1 μm Laser Radiation,” Phys. Fluids, in press.

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Figures (8)

Fig. 1
Fig. 1

Simulated phase object used in this study. The contour interval is 0.03 fringes.

Fig. 2
Fig. 2

Interferogram generated by the object in Fig. 1.

Fig. 3
Fig. 3

Slice through the Fourier transform of a digitized interferogram. The arrows indicate the spatial frequency of the fringes.

Fig. 4
Fig. 4

Reconstruction obtained from the interferogram in Fig. 2.

Fig. 5
Fig. 5

Reconstruction obtained from the interferogram recorded by a nonlinear recording medium.

Fig. 6
Fig. 6

Reconstruction from the corrected interferogram.

Fig. 7
Fig. 7

Experimental interferogram.

Fig. 8
Fig. 8

(a) Phase object recovered from data in Fig. 7. The contour interval is 0.015 fringes. (b) Abel inversion of data in (a). The contour interval is 0.005 times the critical density of the laser light.

Equations (6)

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I ( x , y ) = B ( x , y ) + V ( x , y ) cos [ 2 π ( ω 0 x + ν 0 y ) + ϕ ( x , y ) ] ,
I ( x , y ) = B ( x , y ) + V ( x , y ) exp [ 2 π i ( ω 0 x + ν 0 y ) ] + V * ( x , y ) exp [ 2 π i ( ω 0 x + ν 0 y ) ] ,
i ( ω , ν ) = b ( ω , ν ) + υ ( ω ω 0 , ν ν 0 ) + υ * ( ω + ω 0 , ν + ν 0 ) .
log [ V ( x , y ) ] = log [ V ( x , y ) / 2 ] + i ϕ ( x , y ) .
ϕ ( x , y ) = exp [ 2 π i ( x δ ω + y δ ν ) ] ϕ ( x , y ) ,
ϕ ( x , y ) = exp [ 2 π i ( x δ ω + y δ ν ) ] ϕ ( x , y ) ,

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