Abstract

Star-9 is an experimental demonstration of distributed aperture imaging built at the Lockheed Martin Advanced Technology Center. White light from a scene generator enters an array of nine actively controlled telescopes, and is combined at a focused image plane. This paper describes the algorithms used to automatically bring each telescope’s relative tip/tilt and phasing errors to within the operational range of the control system. The algorithms work with point-sources as well as with extended scenes. Experimental results and software algorithms are presented.

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References

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  1. R. L. Kendrick, J.-N. Aubrun, R. Bell, R. Benson, L. Benson, D. Brace, J. Breakwell, L. Burriesci, E. Byler, J. Camp, G. Cross, P. Cuneo, P. Dean, R. Digumerthi, A. Duncan, J. Farley, A. Green, H. H. Hamilton, B. Herman, K. Lauraitis, E. de Leon, K. Lorell, R. Martin, K. Matosian, T. Muench, M. Ni, A. Palmer, D. Roseman, S. Russell, P. Schweiger, R. Sigler, J. Smith, R. Stone, D. Stubbs, G. Swietek, J. Thatcher, C. Tischhauser, H. Wong, V. Zarifis, K. Gleichman, and R. Paxman, “Wide-field Fizeau imaging telescope: experimental results,” Appl. Opt. 45(18), 4235–4240 (2006).
    [Crossref] [PubMed]
  2. V. Zarifis, R. M. Bell, L. R. Benson, P. J. Cuneo, A. L. Duncan, B. J. Herman, B. Holmes, R. D. Sigler, R. E. Stone, and D. M. Stubbs, “The Multi Aperture Imaging Array,” Opt. and IR Interferometry from Ground and Space ASP Conf. Series 194, 278–285 (1999).
  3. R. G. Paxman, T. J. Schulz, and J. R. Fienup, “Joint Estimation of Object and Aberrations by Using Phase Diversity,” J. Opt. Soc. Am. A 9(7), 1072–1085 (1992).
    [Crossref]
  4. J. W. Goodman, Introduction to Fourier Optics. (McGraw Hill, Boston MA, USA, 1968).
  5. G. D. Boreman, Modulation Transfer Function in Optical and Electro-Optical Systems. (SPIE Press, Bellingham WA, USA, 2001).
  6. R. R. Butts, “Analysis of Phase Measurement Algorithms Utilizing Two-Beam Interference,” Proc. SPIE 440, 130–134 (1983).

2006 (1)

1999 (1)

V. Zarifis, R. M. Bell, L. R. Benson, P. J. Cuneo, A. L. Duncan, B. J. Herman, B. Holmes, R. D. Sigler, R. E. Stone, and D. M. Stubbs, “The Multi Aperture Imaging Array,” Opt. and IR Interferometry from Ground and Space ASP Conf. Series 194, 278–285 (1999).

1992 (1)

1983 (1)

R. R. Butts, “Analysis of Phase Measurement Algorithms Utilizing Two-Beam Interference,” Proc. SPIE 440, 130–134 (1983).

Aubrun, J.-N.

Bell, R.

Bell, R. M.

V. Zarifis, R. M. Bell, L. R. Benson, P. J. Cuneo, A. L. Duncan, B. J. Herman, B. Holmes, R. D. Sigler, R. E. Stone, and D. M. Stubbs, “The Multi Aperture Imaging Array,” Opt. and IR Interferometry from Ground and Space ASP Conf. Series 194, 278–285 (1999).

Benson, L.

Benson, L. R.

V. Zarifis, R. M. Bell, L. R. Benson, P. J. Cuneo, A. L. Duncan, B. J. Herman, B. Holmes, R. D. Sigler, R. E. Stone, and D. M. Stubbs, “The Multi Aperture Imaging Array,” Opt. and IR Interferometry from Ground and Space ASP Conf. Series 194, 278–285 (1999).

Benson, R.

Brace, D.

Breakwell, J.

Burriesci, L.

Butts, R. R.

R. R. Butts, “Analysis of Phase Measurement Algorithms Utilizing Two-Beam Interference,” Proc. SPIE 440, 130–134 (1983).

Byler, E.

Camp, J.

Cross, G.

Cuneo, P.

Cuneo, P. J.

V. Zarifis, R. M. Bell, L. R. Benson, P. J. Cuneo, A. L. Duncan, B. J. Herman, B. Holmes, R. D. Sigler, R. E. Stone, and D. M. Stubbs, “The Multi Aperture Imaging Array,” Opt. and IR Interferometry from Ground and Space ASP Conf. Series 194, 278–285 (1999).

de Leon, E.

Dean, P.

Digumerthi, R.

Duncan, A.

Duncan, A. L.

V. Zarifis, R. M. Bell, L. R. Benson, P. J. Cuneo, A. L. Duncan, B. J. Herman, B. Holmes, R. D. Sigler, R. E. Stone, and D. M. Stubbs, “The Multi Aperture Imaging Array,” Opt. and IR Interferometry from Ground and Space ASP Conf. Series 194, 278–285 (1999).

Farley, J.

Fienup, J. R.

Gleichman, K.

Green, A.

Hamilton, H. H.

Herman, B.

Herman, B. J.

V. Zarifis, R. M. Bell, L. R. Benson, P. J. Cuneo, A. L. Duncan, B. J. Herman, B. Holmes, R. D. Sigler, R. E. Stone, and D. M. Stubbs, “The Multi Aperture Imaging Array,” Opt. and IR Interferometry from Ground and Space ASP Conf. Series 194, 278–285 (1999).

Holmes, B.

V. Zarifis, R. M. Bell, L. R. Benson, P. J. Cuneo, A. L. Duncan, B. J. Herman, B. Holmes, R. D. Sigler, R. E. Stone, and D. M. Stubbs, “The Multi Aperture Imaging Array,” Opt. and IR Interferometry from Ground and Space ASP Conf. Series 194, 278–285 (1999).

Kendrick, R. L.

Lauraitis, K.

Lorell, K.

Martin, R.

Matosian, K.

Muench, T.

Ni, M.

Palmer, A.

Paxman, R.

Paxman, R. G.

Roseman, D.

Russell, S.

Schulz, T. J.

Schweiger, P.

Sigler, R.

Sigler, R. D.

V. Zarifis, R. M. Bell, L. R. Benson, P. J. Cuneo, A. L. Duncan, B. J. Herman, B. Holmes, R. D. Sigler, R. E. Stone, and D. M. Stubbs, “The Multi Aperture Imaging Array,” Opt. and IR Interferometry from Ground and Space ASP Conf. Series 194, 278–285 (1999).

Smith, J.

Stone, R.

Stone, R. E.

V. Zarifis, R. M. Bell, L. R. Benson, P. J. Cuneo, A. L. Duncan, B. J. Herman, B. Holmes, R. D. Sigler, R. E. Stone, and D. M. Stubbs, “The Multi Aperture Imaging Array,” Opt. and IR Interferometry from Ground and Space ASP Conf. Series 194, 278–285 (1999).

Stubbs, D.

Stubbs, D. M.

V. Zarifis, R. M. Bell, L. R. Benson, P. J. Cuneo, A. L. Duncan, B. J. Herman, B. Holmes, R. D. Sigler, R. E. Stone, and D. M. Stubbs, “The Multi Aperture Imaging Array,” Opt. and IR Interferometry from Ground and Space ASP Conf. Series 194, 278–285 (1999).

Swietek, G.

Thatcher, J.

Tischhauser, C.

Wong, H.

Zarifis, V.

Appl. Opt. (1)

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

Opt. and IR Interferometry from Ground and Space ASP Conf. Series (1)

V. Zarifis, R. M. Bell, L. R. Benson, P. J. Cuneo, A. L. Duncan, B. J. Herman, B. Holmes, R. D. Sigler, R. E. Stone, and D. M. Stubbs, “The Multi Aperture Imaging Array,” Opt. and IR Interferometry from Ground and Space ASP Conf. Series 194, 278–285 (1999).

Proc. SPIE (1)

R. R. Butts, “Analysis of Phase Measurement Algorithms Utilizing Two-Beam Interference,” Proc. SPIE 440, 130–134 (1983).

Other (2)

J. W. Goodman, Introduction to Fourier Optics. (McGraw Hill, Boston MA, USA, 1968).

G. D. Boreman, Modulation Transfer Function in Optical and Electro-Optical Systems. (SPIE Press, Bellingham WA, USA, 2001).

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Figures (6)

Fig. 1
Fig. 1

Left, a photo of the Star-9 lab; right, the ray trace of Star-9.

Fig. 2
Fig. 2

(a) Progression of operational modes. (b) Data flow of Autoalign and Autophase.

Fig. 3
Fig. 3

The Modulation Transfer Function (MTF) with two apertures. The arrow indicates the height of the MTF side lobe, which can be used as a scalar metric of point-source phasing error.

Fig. 4
Fig. 4

MTF metric as a function of piston between two telescopes. This data was oversampled for illustrative purposes. The piston locations are tighter, and each have 10 MTF metric measurements (dots); solid line is the average.

Fig. 5
Fig. 5

(a) the 2-telescope PSF. The dots on the PSF are markers for locations “O” and “I”, showing which pixels were used in the PSF metric computation. (b) the PSF metric plotted as a function of pathlength difference between two telescopes. Dots are individual measurements; line is the mean.

Fig. 6
Fig. 6

PSF, MTF, and extended scene from start to finish of automatic alignment/phasing program

Equations (5)

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C u v = j k g j k f j u , k v j k g j k 2 j k f j u , k v 2
P N R = f max s t d ( f 1 ) ,
m ( x ) = a 1 e a 3 ( x a 2 ) 2
ln ( m ( x ) ) = a 3 x 2 + 2 a 2 a 3 x a 2 2 a 3 + ln ( a 1 )
x ^ p s f = 0.5 P S F ( I ) P S F ( O ) P S F ( I ) + P S F ( O )

Metrics