Abstract

This paper describes a technique that allows a severely distorted coherent optical array receiver to produce images comparable to conventional monolithic imaging systems. The technique is based on using a phase synchronizing point source as a reference to eliminate phase errors in the array. Once phase corrected, the individual elements in the array can be coherently combined to yield a resolution equal to the overall size of the array, and if Doppler information is available, separation of targets within the diffraction limited spot size of the array is possible. Experimental verification of concepts developed within this paper is presented for array receivers operating at 633 and 514 nm.

© 1991 Optical Society of America

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References

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  1. A. R. Thompson, J. M. Moran, G. W. Swenson, Interferometry and Synthesis in Radio Astronomy (Wiley-Interscience, New York, 1986).
  2. B. D. Steinberg, “Microwave Imaging of Aircraft,” Proc. IEEE 76, 1578–1592 (1989) and references therein.
    [CrossRef]
  3. E. K. Hege, J. M. Beckers, P. A. Strittmatter, D. W. McCarthy, “Multiple Mirror Telescope as a Phased Array Telescope,” Appl. Opt. 24, 2565–2576 (1985).
    [CrossRef] [PubMed]
  4. P. D. Henshaw, D. E. B. Lees, “Electronically Agile Multiple Aperture Image Receiver,” Proc. Soc. Photo-Opt. Instrum. Eng. 828, 134–139 (1987).
  5. R. G. Morton et al., “Coherent Sub-Aperture Ultraviolet Imagery,” Proc. Soc. Photo-Opt. Instrum Eng. 1103, 207–218 (1989).
  6. For a discussion of the effects of phase errors, see M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), Chap. 9.

1989

B. D. Steinberg, “Microwave Imaging of Aircraft,” Proc. IEEE 76, 1578–1592 (1989) and references therein.
[CrossRef]

R. G. Morton et al., “Coherent Sub-Aperture Ultraviolet Imagery,” Proc. Soc. Photo-Opt. Instrum Eng. 1103, 207–218 (1989).

1987

P. D. Henshaw, D. E. B. Lees, “Electronically Agile Multiple Aperture Image Receiver,” Proc. Soc. Photo-Opt. Instrum. Eng. 828, 134–139 (1987).

1985

Beckers, J. M.

Born, M.

For a discussion of the effects of phase errors, see M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), Chap. 9.

Hege, E. K.

Henshaw, P. D.

P. D. Henshaw, D. E. B. Lees, “Electronically Agile Multiple Aperture Image Receiver,” Proc. Soc. Photo-Opt. Instrum. Eng. 828, 134–139 (1987).

Lees, D. E. B.

P. D. Henshaw, D. E. B. Lees, “Electronically Agile Multiple Aperture Image Receiver,” Proc. Soc. Photo-Opt. Instrum. Eng. 828, 134–139 (1987).

McCarthy, D. W.

Moran, J. M.

A. R. Thompson, J. M. Moran, G. W. Swenson, Interferometry and Synthesis in Radio Astronomy (Wiley-Interscience, New York, 1986).

Morton, R. G.

R. G. Morton et al., “Coherent Sub-Aperture Ultraviolet Imagery,” Proc. Soc. Photo-Opt. Instrum Eng. 1103, 207–218 (1989).

Steinberg, B. D.

B. D. Steinberg, “Microwave Imaging of Aircraft,” Proc. IEEE 76, 1578–1592 (1989) and references therein.
[CrossRef]

Strittmatter, P. A.

Swenson, G. W.

A. R. Thompson, J. M. Moran, G. W. Swenson, Interferometry and Synthesis in Radio Astronomy (Wiley-Interscience, New York, 1986).

Thompson, A. R.

A. R. Thompson, J. M. Moran, G. W. Swenson, Interferometry and Synthesis in Radio Astronomy (Wiley-Interscience, New York, 1986).

Wolf, E.

For a discussion of the effects of phase errors, see M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), Chap. 9.

Appl. Opt.

Proc. IEEE

B. D. Steinberg, “Microwave Imaging of Aircraft,” Proc. IEEE 76, 1578–1592 (1989) and references therein.
[CrossRef]

Proc. Soc. Photo-Opt. Instrum Eng.

R. G. Morton et al., “Coherent Sub-Aperture Ultraviolet Imagery,” Proc. Soc. Photo-Opt. Instrum Eng. 1103, 207–218 (1989).

Proc. Soc. Photo-Opt. Instrum. Eng.

P. D. Henshaw, D. E. B. Lees, “Electronically Agile Multiple Aperture Image Receiver,” Proc. Soc. Photo-Opt. Instrum. Eng. 828, 134–139 (1987).

Other

For a discussion of the effects of phase errors, see M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), Chap. 9.

A. R. Thompson, J. M. Moran, G. W. Swenson, Interferometry and Synthesis in Radio Astronomy (Wiley-Interscience, New York, 1986).

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Figures (4)

Fig. 1
Fig. 1

Experimental configuration used for (a) AA imaging; (b) AAD imaging.

Fig. 2
Fig. 2

Results of the 2-D experiments: (a) point source image; (b) Air Force bar chart without phase correction; (c) as in (b) but with phase correction; (d) camera lens image of the area shown in (c); (e) plan view of the area of the bar chart shown in (b) and (c). The difference between images (b) and (c) clearly shows the effect that phase errors and phase correcting have on the ability to image targets.

Fig. 3
Fig. 3

AAD results using a 127-element array so that the separation of the slits is well resolved: (a) generated images; (b) cross-section profiles. The images are A, point source; B, AA image of the two slits; C, AAD image of the 4-Hz bin; D, AAD image of the 8-Hz bin.

Fig. 4
Fig. 4

AAD results using a three-element array so that the separation of the slits is not resolved. The images are arranged as in Fig. 3. From the AA image (B) it is impossible to determine what is in the field of view, whereas, by first sorting the data into Doppler bins (C and D), both the intensity pattern and location of what is in the field of view can be readily found.

Equations (3)

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U ( X ) = exp [ i θ ( X ) ] exp [ i k ( X - x 0 ) 2 ) 2 R 0 ] ,
U ( X ) = source exp [ i θ ( X ) ] u ( x ) exp [ i k ( X - x ) 2 2 R t ] d x .
u ( x ) = exp ( i k x 0 2 2 R 0 ) source u ( x ) exp ( i k x 2 2 R t ) aperture × exp [ i k X ( x - x R t + x 0 R 0 ) ] d X d x .

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