Abstract

Using a gradient optimization method with objective functions formulated in terms of a signal-to-noise ratio (SNR) calculated at given values of the prescribed spatial ground resolution, optimization problems of geometrical parameters of a distributed optical system and a charge-coupled device of a space-based optical-electronic system are solved for samples of the optical systems consisting of two and three annular subapertures. The modulation transfer function (MTF) of the distributed aperture is expressed in terms of an average MTF taking residual image alignment (IA) and optical path difference (OPD) errors into account. The results show optimal solutions of the optimization problems depending on diverse variable parameters. The information on the magnitudes of the SNR can be used to determine the number of the subapertures and their sizes, while the information on the SNR decrease depending on the IA and OPD errors can be useful in design of a beam combination control system to produce the necessary requirements to its accuracy on the basis of the permissible deterioration in the image quality.

© 2008 Optical Society of America

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  1. L. M. Stepp, L. G. Daggert, and P. E. Gillett, “Estimating the cost of extremely large telescopes,” Proc. SPIE 4840, 309-321 (2003).
  2. R. Goullioud and J. H. Catanzarite, “Looking for Earth-like planets with the SIM Planet Quest Light Mission,” in Aerospace Conference (IEEE, 2008), pp. 1-9, doi: 10.1109/AERO.2008.4526409.
    [CrossRef]
  3. Technology Plan for the Terrestrial Planet Finder Interferometer, P. R. Lawson and J. A. Dooley, eds. (California Institute of Technology, 2005).
  4. J. E. Harvey, A. B. Wissinger, and A. N. Bunner, “A parametric study of various synthetic aperture telescope configurations for coherent imaging applications,” Proc. SPIE 643, 194-207(1986).
  5. S. M. Watson, J. P. Mills, and S. K. Rogers, “Two-point resolution criterion for multiaperture optical telescopes,” J. Opt. Soc. Am. A 5, 893-903 (1988).
  6. ESO/VLT Interferometry Panel, “The VLT interferometer implementation plan,” VLT Report 59b (European Southern Observatory, 1989).
  7. M. Faucherre, F. Merkle, and F. Vakili, “Beam combination in aperture synthesis from space: field of view limitations and (u,v) plane coverage optimization,” Proc. SPIE 1130, 138-145(1989).
  8. J. P. Fitch and T. W. Lawrence, “Placement of multiple apertures for imaging telescopes,” Proc. SPIE 1237, 61-69(1990).
  9. R. Barakat, “Dilute aperture diffraction imagery and object reconstruction,” Opt. Eng. 29, 131-139 (1990).
  10. L. Damé and T.-D. Guyenne, “Study of an optimized configuration for interferometric imaging of complex and extended solar structures,” in Targets for Space-Based Interferometry, Vol. SP-354, pp. 201-208 (European Space Agency, 1992).
  11. J. L. Flores, M. Strojnik, and G. Paez, “Diluted-aperture mirror with a constraint on the cut-off frequency,” Proc. SPIE 3437, 416-423 (1998).
  12. J. L. Flores, G. Paez, and M. Strojnik, “Design of a diluted aperture by use of the practical cutoff frequency,” Appl. Opt. 38, 6010-6018 (1999).
    [CrossRef]
  13. I. Tcherniavski and M. Kahrizi, “Optimization of the optical sparse array configuration,” Opt. Eng. 44, 103201 (2005).
  14. F. Roddier, “Redundant versus nonredundant beam recombination in an aperture synthesis with coherent optical arrays,” J. Opt. Soc. Am. A 4, 1396-1401 (1987).
  15. J. R. Fienup, “MTF and integration time versus fill factor for sparse-aperture imaging systems,” Proc. SPIE 4091, 43-47(2000).
  16. R. B. Hindsley and D. Mozurkewich, “Signal to noise in sparse aperture imaging,” in Proceedings of IEEE Conference on Aerospace (IEEE, 2001), pp. 1429-1443.
  17. J. R. P. Angel, “Sensitivity of optical interferometers with coherent image combination,” Proc. SPIE 4838, 126-133 (2003).
  18. I. Tcherniavski and M. Kahrizi, “Influence of the random image alignment and optical path difference errors of a beam combination system on the optical transfer function of the optical sparse array,” Opt. Eng. 45, 093202 (2006).
  19. J. M. Irvine, “National Imagery Interpretability Rating Scale (NIIRS),” in Encyclopedia of Optical Engineering, R. G. Driggers, ed. (Marcel Dekker, 2003), pp. 1442-1456.
  20. J. C. Leachtenauer, “Image quality equations and NIIRS,” in Encyclopedia of Optical Engineering, R. G. Driggers, ed. (Marcel Dekker, 2003), pp. 794-811.
  21. R. D. Fiete and Th. Tantalo, “Comparison of SNR image quality metrics for remote sensing systems,” Opt. Eng. 40, 574-585 (2001).
  22. F. A. Rosell and R. H. Willson, “Recent psychophysical experiments and the display signal-to-noise ratio concept,” in Perception of Displayed Information, L. M. Biberman, ed. (Plenum, 1973), pp. 167-232.
  23. J. A. Hall, “Signal and noise in the display of images,” in Solid State Imaging, P. G. Jespers, F. Van de Wiele, and M. H. White, eds. (Noordhoff, 1976), pp. 637-658.
  24. R. E. Hufnagel and N. R. Stanley, “Modulation transfer function associated with image transmission through turbulent media,” J. Opt. Soc. Am. 54, 52-61 (1964).
  25. D. L. Fried, “Optical resolution through a randomly inhomogeneous medium for very long and very short exposures,” J. Opt. Soc. Am. 56, 1372-1379 (1966).
  26. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, 1961).
  27. D. L. Fried, “Limiting resolution looking down through the atmosphere,” J. Opt. Soc. Am. 56, 1380-1384 (1966).
  28. D. L. Fried, “Statistics of a geometric representation of wavefront distortion,” J. Opt. Soc. Am. 55, 1427-1435 (1965).
  29. D. F. Barbe, “Time delay and integration image sensors,” in Solid State Imaging, P. G. Jespers, F. Van de Wiele, and M. H. White, eds. (Noordhoff, 1976), pp. 659-671.
  30. M. H. White, “Design of solid-state imaging arrays,” in Solid State Imaging, P. G. Jespers, F. Van de Wiele, and M. H. White, eds (Noordhoff, 1976), pp. 485-522.
  31. “ASTER spectral library,” http://speclib.jpl.nasa.gov.
  32. R. A. Schowengerdt, Remote Sensing: Models and Methods for Image Processing (Elsevier, 2007), Chap. 2.
  33. A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction,” Proc. SPIE 3756, 348-353 (1999).
  34. Fairchild Imaging, CCD 525 Data Sheet: “CCD525 Time Delay Integration Line Scan Sensor,” http://www.fairchildimaging.com/main/documents/CCD525DataSheetRevA.pdf.
  35. Surrey Satellite Technology Ltd. “Surrey Missions: TopSat,” http://microsat.sm.bmstu.ru/e-library/SSTL/Mission_Topsat.pdf.
  36. DigitalGlobe “QuickBird,” http://www.digitalglobe.com/index.php/85/QuickBird.
  37. DigitalGlobe “WorldView-1,” http://www.digitalglobe.com/index.php/86/WorldView-1.
  38. GeoEye “GeoEye-1,” http://www.geoeye.com/CorpSite/products/imagery-sources/Default.aspx#geoeye1.

2006 (1)

I. Tcherniavski and M. Kahrizi, “Influence of the random image alignment and optical path difference errors of a beam combination system on the optical transfer function of the optical sparse array,” Opt. Eng. 45, 093202 (2006).

2005 (1)

I. Tcherniavski and M. Kahrizi, “Optimization of the optical sparse array configuration,” Opt. Eng. 44, 103201 (2005).

2003 (2)

J. R. P. Angel, “Sensitivity of optical interferometers with coherent image combination,” Proc. SPIE 4838, 126-133 (2003).

L. M. Stepp, L. G. Daggert, and P. E. Gillett, “Estimating the cost of extremely large telescopes,” Proc. SPIE 4840, 309-321 (2003).

2001 (1)

R. D. Fiete and Th. Tantalo, “Comparison of SNR image quality metrics for remote sensing systems,” Opt. Eng. 40, 574-585 (2001).

2000 (1)

J. R. Fienup, “MTF and integration time versus fill factor for sparse-aperture imaging systems,” Proc. SPIE 4091, 43-47(2000).

1999 (2)

J. L. Flores, G. Paez, and M. Strojnik, “Design of a diluted aperture by use of the practical cutoff frequency,” Appl. Opt. 38, 6010-6018 (1999).
[CrossRef]

A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction,” Proc. SPIE 3756, 348-353 (1999).

1998 (1)

J. L. Flores, M. Strojnik, and G. Paez, “Diluted-aperture mirror with a constraint on the cut-off frequency,” Proc. SPIE 3437, 416-423 (1998).

1990 (2)

J. P. Fitch and T. W. Lawrence, “Placement of multiple apertures for imaging telescopes,” Proc. SPIE 1237, 61-69(1990).

R. Barakat, “Dilute aperture diffraction imagery and object reconstruction,” Opt. Eng. 29, 131-139 (1990).

1989 (1)

M. Faucherre, F. Merkle, and F. Vakili, “Beam combination in aperture synthesis from space: field of view limitations and (u,v) plane coverage optimization,” Proc. SPIE 1130, 138-145(1989).

1988 (1)

1987 (1)

1986 (1)

J. E. Harvey, A. B. Wissinger, and A. N. Bunner, “A parametric study of various synthetic aperture telescope configurations for coherent imaging applications,” Proc. SPIE 643, 194-207(1986).

1966 (2)

1965 (1)

1964 (1)

Acharya, P. K.

A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction,” Proc. SPIE 3756, 348-353 (1999).

Adler-Golden, S. M.

A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction,” Proc. SPIE 3756, 348-353 (1999).

Allred, C. L.

A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction,” Proc. SPIE 3756, 348-353 (1999).

Anderson, G. P.

A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction,” Proc. SPIE 3756, 348-353 (1999).

Angel, J. R. P.

J. R. P. Angel, “Sensitivity of optical interferometers with coherent image combination,” Proc. SPIE 4838, 126-133 (2003).

Barakat, R.

R. Barakat, “Dilute aperture diffraction imagery and object reconstruction,” Opt. Eng. 29, 131-139 (1990).

Barbe, D. F.

D. F. Barbe, “Time delay and integration image sensors,” in Solid State Imaging, P. G. Jespers, F. Van de Wiele, and M. H. White, eds. (Noordhoff, 1976), pp. 659-671.

Berk, A.

A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction,” Proc. SPIE 3756, 348-353 (1999).

Bernstein, L. S.

A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction,” Proc. SPIE 3756, 348-353 (1999).

Bunner, A. N.

J. E. Harvey, A. B. Wissinger, and A. N. Bunner, “A parametric study of various synthetic aperture telescope configurations for coherent imaging applications,” Proc. SPIE 643, 194-207(1986).

Catanzarite, J. H.

R. Goullioud and J. H. Catanzarite, “Looking for Earth-like planets with the SIM Planet Quest Light Mission,” in Aerospace Conference (IEEE, 2008), pp. 1-9, doi: 10.1109/AERO.2008.4526409.
[CrossRef]

Chetwynd, J. H.

A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction,” Proc. SPIE 3756, 348-353 (1999).

Daggert, L. G.

L. M. Stepp, L. G. Daggert, and P. E. Gillett, “Estimating the cost of extremely large telescopes,” Proc. SPIE 4840, 309-321 (2003).

Damé, L.

L. Damé and T.-D. Guyenne, “Study of an optimized configuration for interferometric imaging of complex and extended solar structures,” in Targets for Space-Based Interferometry, Vol. SP-354, pp. 201-208 (European Space Agency, 1992).

Dothe, H.

A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction,” Proc. SPIE 3756, 348-353 (1999).

Faucherre, M.

M. Faucherre, F. Merkle, and F. Vakili, “Beam combination in aperture synthesis from space: field of view limitations and (u,v) plane coverage optimization,” Proc. SPIE 1130, 138-145(1989).

Fienup, J. R.

J. R. Fienup, “MTF and integration time versus fill factor for sparse-aperture imaging systems,” Proc. SPIE 4091, 43-47(2000).

Fiete, R. D.

R. D. Fiete and Th. Tantalo, “Comparison of SNR image quality metrics for remote sensing systems,” Opt. Eng. 40, 574-585 (2001).

Fitch, J. P.

J. P. Fitch and T. W. Lawrence, “Placement of multiple apertures for imaging telescopes,” Proc. SPIE 1237, 61-69(1990).

Flores, J. L.

J. L. Flores, G. Paez, and M. Strojnik, “Design of a diluted aperture by use of the practical cutoff frequency,” Appl. Opt. 38, 6010-6018 (1999).
[CrossRef]

J. L. Flores, M. Strojnik, and G. Paez, “Diluted-aperture mirror with a constraint on the cut-off frequency,” Proc. SPIE 3437, 416-423 (1998).

Fried, D. L.

Gillett, P. E.

L. M. Stepp, L. G. Daggert, and P. E. Gillett, “Estimating the cost of extremely large telescopes,” Proc. SPIE 4840, 309-321 (2003).

Goullioud, R.

R. Goullioud and J. H. Catanzarite, “Looking for Earth-like planets with the SIM Planet Quest Light Mission,” in Aerospace Conference (IEEE, 2008), pp. 1-9, doi: 10.1109/AERO.2008.4526409.
[CrossRef]

Guyenne, T.-D.

L. Damé and T.-D. Guyenne, “Study of an optimized configuration for interferometric imaging of complex and extended solar structures,” in Targets for Space-Based Interferometry, Vol. SP-354, pp. 201-208 (European Space Agency, 1992).

Hall, J. A.

J. A. Hall, “Signal and noise in the display of images,” in Solid State Imaging, P. G. Jespers, F. Van de Wiele, and M. H. White, eds. (Noordhoff, 1976), pp. 637-658.

Harvey, J. E.

J. E. Harvey, A. B. Wissinger, and A. N. Bunner, “A parametric study of various synthetic aperture telescope configurations for coherent imaging applications,” Proc. SPIE 643, 194-207(1986).

Hindsley, R. B.

R. B. Hindsley and D. Mozurkewich, “Signal to noise in sparse aperture imaging,” in Proceedings of IEEE Conference on Aerospace (IEEE, 2001), pp. 1429-1443.

Hoke, M. L.

A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction,” Proc. SPIE 3756, 348-353 (1999).

Hufnagel, R. E.

Irvine, J. M.

J. M. Irvine, “National Imagery Interpretability Rating Scale (NIIRS),” in Encyclopedia of Optical Engineering, R. G. Driggers, ed. (Marcel Dekker, 2003), pp. 1442-1456.

Jeong, L. S.

A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction,” Proc. SPIE 3756, 348-353 (1999).

Kahrizi, M.

I. Tcherniavski and M. Kahrizi, “Influence of the random image alignment and optical path difference errors of a beam combination system on the optical transfer function of the optical sparse array,” Opt. Eng. 45, 093202 (2006).

I. Tcherniavski and M. Kahrizi, “Optimization of the optical sparse array configuration,” Opt. Eng. 44, 103201 (2005).

Lawrence, T. W.

J. P. Fitch and T. W. Lawrence, “Placement of multiple apertures for imaging telescopes,” Proc. SPIE 1237, 61-69(1990).

Leachtenauer, J. C.

J. C. Leachtenauer, “Image quality equations and NIIRS,” in Encyclopedia of Optical Engineering, R. G. Driggers, ed. (Marcel Dekker, 2003), pp. 794-811.

Matthew, M. W.

A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction,” Proc. SPIE 3756, 348-353 (1999).

Merkle, F.

M. Faucherre, F. Merkle, and F. Vakili, “Beam combination in aperture synthesis from space: field of view limitations and (u,v) plane coverage optimization,” Proc. SPIE 1130, 138-145(1989).

Mills, J. P.

Mozurkewich, D.

R. B. Hindsley and D. Mozurkewich, “Signal to noise in sparse aperture imaging,” in Proceedings of IEEE Conference on Aerospace (IEEE, 2001), pp. 1429-1443.

Paez, G.

J. L. Flores, G. Paez, and M. Strojnik, “Design of a diluted aperture by use of the practical cutoff frequency,” Appl. Opt. 38, 6010-6018 (1999).
[CrossRef]

J. L. Flores, M. Strojnik, and G. Paez, “Diluted-aperture mirror with a constraint on the cut-off frequency,” Proc. SPIE 3437, 416-423 (1998).

Pukall, B.

A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction,” Proc. SPIE 3756, 348-353 (1999).

Richtsmeier, S. C.

A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction,” Proc. SPIE 3756, 348-353 (1999).

Roddier, F.

Rogers, S. K.

Rosell, F. A.

F. A. Rosell and R. H. Willson, “Recent psychophysical experiments and the display signal-to-noise ratio concept,” in Perception of Displayed Information, L. M. Biberman, ed. (Plenum, 1973), pp. 167-232.

Schowengerdt, R. A.

R. A. Schowengerdt, Remote Sensing: Models and Methods for Image Processing (Elsevier, 2007), Chap. 2.

Stanley, N. R.

Stepp, L. M.

L. M. Stepp, L. G. Daggert, and P. E. Gillett, “Estimating the cost of extremely large telescopes,” Proc. SPIE 4840, 309-321 (2003).

Strojnik, M.

J. L. Flores, G. Paez, and M. Strojnik, “Design of a diluted aperture by use of the practical cutoff frequency,” Appl. Opt. 38, 6010-6018 (1999).
[CrossRef]

J. L. Flores, M. Strojnik, and G. Paez, “Diluted-aperture mirror with a constraint on the cut-off frequency,” Proc. SPIE 3437, 416-423 (1998).

Tantalo, Th.

R. D. Fiete and Th. Tantalo, “Comparison of SNR image quality metrics for remote sensing systems,” Opt. Eng. 40, 574-585 (2001).

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, 1961).

Tcherniavski, I.

I. Tcherniavski and M. Kahrizi, “Influence of the random image alignment and optical path difference errors of a beam combination system on the optical transfer function of the optical sparse array,” Opt. Eng. 45, 093202 (2006).

I. Tcherniavski and M. Kahrizi, “Optimization of the optical sparse array configuration,” Opt. Eng. 44, 103201 (2005).

Vakili, F.

M. Faucherre, F. Merkle, and F. Vakili, “Beam combination in aperture synthesis from space: field of view limitations and (u,v) plane coverage optimization,” Proc. SPIE 1130, 138-145(1989).

Watson, S. M.

White, M. H.

J. A. Hall, “Signal and noise in the display of images,” in Solid State Imaging, P. G. Jespers, F. Van de Wiele, and M. H. White, eds. (Noordhoff, 1976), pp. 637-658.

M. H. White, “Design of solid-state imaging arrays,” in Solid State Imaging, P. G. Jespers, F. Van de Wiele, and M. H. White, eds (Noordhoff, 1976), pp. 485-522.

M. H. White, “Design of solid-state imaging arrays,” in Solid State Imaging, P. G. Jespers, F. Van de Wiele, and M. H. White, eds (Noordhoff, 1976), pp. 485-522.

Willson, R. H.

F. A. Rosell and R. H. Willson, “Recent psychophysical experiments and the display signal-to-noise ratio concept,” in Perception of Displayed Information, L. M. Biberman, ed. (Plenum, 1973), pp. 167-232.

Wissinger, A. B.

J. E. Harvey, A. B. Wissinger, and A. N. Bunner, “A parametric study of various synthetic aperture telescope configurations for coherent imaging applications,” Proc. SPIE 643, 194-207(1986).

Appl. Opt. (1)

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (2)

Opt. Eng. (4)

R. Barakat, “Dilute aperture diffraction imagery and object reconstruction,” Opt. Eng. 29, 131-139 (1990).

I. Tcherniavski and M. Kahrizi, “Influence of the random image alignment and optical path difference errors of a beam combination system on the optical transfer function of the optical sparse array,” Opt. Eng. 45, 093202 (2006).

I. Tcherniavski and M. Kahrizi, “Optimization of the optical sparse array configuration,” Opt. Eng. 44, 103201 (2005).

R. D. Fiete and Th. Tantalo, “Comparison of SNR image quality metrics for remote sensing systems,” Opt. Eng. 40, 574-585 (2001).

Proc. SPIE (8)

A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction,” Proc. SPIE 3756, 348-353 (1999).

J. R. P. Angel, “Sensitivity of optical interferometers with coherent image combination,” Proc. SPIE 4838, 126-133 (2003).

J. E. Harvey, A. B. Wissinger, and A. N. Bunner, “A parametric study of various synthetic aperture telescope configurations for coherent imaging applications,” Proc. SPIE 643, 194-207(1986).

J. L. Flores, M. Strojnik, and G. Paez, “Diluted-aperture mirror with a constraint on the cut-off frequency,” Proc. SPIE 3437, 416-423 (1998).

J. R. Fienup, “MTF and integration time versus fill factor for sparse-aperture imaging systems,” Proc. SPIE 4091, 43-47(2000).

M. Faucherre, F. Merkle, and F. Vakili, “Beam combination in aperture synthesis from space: field of view limitations and (u,v) plane coverage optimization,” Proc. SPIE 1130, 138-145(1989).

J. P. Fitch and T. W. Lawrence, “Placement of multiple apertures for imaging telescopes,” Proc. SPIE 1237, 61-69(1990).

L. M. Stepp, L. G. Daggert, and P. E. Gillett, “Estimating the cost of extremely large telescopes,” Proc. SPIE 4840, 309-321 (2003).

Other (19)

R. Goullioud and J. H. Catanzarite, “Looking for Earth-like planets with the SIM Planet Quest Light Mission,” in Aerospace Conference (IEEE, 2008), pp. 1-9, doi: 10.1109/AERO.2008.4526409.
[CrossRef]

Technology Plan for the Terrestrial Planet Finder Interferometer, P. R. Lawson and J. A. Dooley, eds. (California Institute of Technology, 2005).

ESO/VLT Interferometry Panel, “The VLT interferometer implementation plan,” VLT Report 59b (European Southern Observatory, 1989).

L. Damé and T.-D. Guyenne, “Study of an optimized configuration for interferometric imaging of complex and extended solar structures,” in Targets for Space-Based Interferometry, Vol. SP-354, pp. 201-208 (European Space Agency, 1992).

R. B. Hindsley and D. Mozurkewich, “Signal to noise in sparse aperture imaging,” in Proceedings of IEEE Conference on Aerospace (IEEE, 2001), pp. 1429-1443.

J. M. Irvine, “National Imagery Interpretability Rating Scale (NIIRS),” in Encyclopedia of Optical Engineering, R. G. Driggers, ed. (Marcel Dekker, 2003), pp. 1442-1456.

J. C. Leachtenauer, “Image quality equations and NIIRS,” in Encyclopedia of Optical Engineering, R. G. Driggers, ed. (Marcel Dekker, 2003), pp. 794-811.

Fairchild Imaging, CCD 525 Data Sheet: “CCD525 Time Delay Integration Line Scan Sensor,” http://www.fairchildimaging.com/main/documents/CCD525DataSheetRevA.pdf.

Surrey Satellite Technology Ltd. “Surrey Missions: TopSat,” http://microsat.sm.bmstu.ru/e-library/SSTL/Mission_Topsat.pdf.

DigitalGlobe “QuickBird,” http://www.digitalglobe.com/index.php/85/QuickBird.

DigitalGlobe “WorldView-1,” http://www.digitalglobe.com/index.php/86/WorldView-1.

GeoEye “GeoEye-1,” http://www.geoeye.com/CorpSite/products/imagery-sources/Default.aspx#geoeye1.

F. A. Rosell and R. H. Willson, “Recent psychophysical experiments and the display signal-to-noise ratio concept,” in Perception of Displayed Information, L. M. Biberman, ed. (Plenum, 1973), pp. 167-232.

J. A. Hall, “Signal and noise in the display of images,” in Solid State Imaging, P. G. Jespers, F. Van de Wiele, and M. H. White, eds. (Noordhoff, 1976), pp. 637-658.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, 1961).

D. F. Barbe, “Time delay and integration image sensors,” in Solid State Imaging, P. G. Jespers, F. Van de Wiele, and M. H. White, eds. (Noordhoff, 1976), pp. 659-671.

M. H. White, “Design of solid-state imaging arrays,” in Solid State Imaging, P. G. Jespers, F. Van de Wiele, and M. H. White, eds (Noordhoff, 1976), pp. 485-522.

“ASTER spectral library,” http://speclib.jpl.nasa.gov.

R. A. Schowengerdt, Remote Sensing: Models and Methods for Image Processing (Elsevier, 2007), Chap. 2.

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Figures (24)

Fig. 1
Fig. 1

θ R direction of resolution.

Fig. 2
Fig. 2

Beam combination: (a) ideal ray paths, (b) eventual alignment ( x n , y n ) and phasing [ Δ ˜ n Δ ˜ n ( x n , y n ) ] errors.

Fig. 3
Fig. 3

Layout of the TDI-CCD elements.

Fig. 4
Fig. 4

Spectral reflectance for the “object” (1 and 2) and the “background” (0).

Fig. 5
Fig. 5

Initial aperture configurations.

Fig. 6
Fig. 6

Optimal aperture configurations for H = 400 km , Object 1, Δ λ = 0.40 1.05 μm .

Fig. 7
Fig. 7

Optimal aperture configurations for H = 400 km , Object 1, Δ λ = 0.75 1.05 μm .

Fig. 8
Fig. 8

Optimal aperture configurations for H = 400 km , Object 2, Δ λ = 0.40 1.05 μm .

Fig. 9
Fig. 9

Optimal aperture configurations for H = 400 km , Object 2, Δ λ = 0.40 0.70 μm .

Fig. 10
Fig. 10

Optimal aperture configurations for H = 400 km , Object 1, Δ λ : (a) and (b) 0.40 1.05 μm , (c) and (d) 0.75 1.05 μm .

Fig. 11
Fig. 11

Optimal aperture configurations for H = 400 km , Object 2, Δ λ : (a) and (b) 0.40 1.05 μm , (c) and (d) 0.40 0.70 μm .

Fig. 12
Fig. 12

SNR versus f R x and f R y for the configuration in Fig. 10b: H = 400 km , Object 1, Δ λ = 0.40 1.05 μm .

Fig. 13
Fig. 13

SNR versus f R x and f R y for the configuration in Fig. 11b: H = 400 km , Object 2, Δ λ = 0.40 1.05 μm .

Fig. 14
Fig. 14

Variables for the 3D graphics.

Fig. 15
Fig. 15

Dependence of the objective function (40) on F and d c H = 400 km , Object 1, Δ λ = 0.40 1.05 μm , SNR Th = 10 .

Fig. 16
Fig. 16

Cross section curves of the surface in Fig. 15.

Fig. 17
Fig. 17

Dependence of the objective function (40) on φ A and d c for H = 400 km , Object 1, Δ λ = 0.40 1.05 μm , SNR Th = 10 .

Fig. 18
Fig. 18

Cross section curves of the surface in Fig. 17.

Fig. 19
Fig. 19

Optimal aperture configurations for H = 600 km , Object 1, Δ λ : (a) and (b) 0.40 1.05 μm ; (c) and (d) 0.75 1.05 μm .

Fig. 20
Fig. 20

Optimal aperture configurations for H = 600 km , Object 2, Δ λ : (a) and (b) 0.40 1.05 μm ; (c) and (d) 0.40 0.70 μm .

Fig. 21
Fig. 21

SNR versus f R x and f R y for the configuration in Fig. 19b: H = 600 km , Object 1, Δ λ = 0.40 1.05 μm .

Fig. 22
Fig. 22

SNR versus f R x and f R y for the configuration in Fig. 20b: H = 600 km , Object 2, Δ λ = 0.40 1.05 μm .

Fig. 23
Fig. 23

Dependence of the objective function (40) on the CCD pixel sizes and F for H = 400 km , Object 1, Δ λ = 0.40 1.05 μm , SNR Th = 18 .

Fig. 24
Fig. 24

Dependence of the objective function (40) on M and F for H = 400 km , Object 1, Δ λ = 0.40 1.05 μm , SNR Th = 18 .

Tables (20)

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Table 1 Optimal Values for the Aperture Configurations in Fig. 6

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Table 2 Optimal Values for the Aperture Configurations in Fig. 7

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Table 3 Optimal Values for the Aperture Configurations in Fig. 8

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Table 4 Optimal Values for the Aperture Configurations in Fig. 9

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Table 5 Optimal Values for the Aperture Configurations in Fig. 10

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Table 6 Optimal Values for the Aperture Configurations in Fig. 11

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Table 7 Conditional Comparison Parameters of the OESs with a Distributed and Monolithic Aperture for H = 400 km , F = 13.867 m

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Table 8 Optimal Values for the Aperture Configurations in Fig. 19

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Table 9 Optimal Values for the Aperture Configurations in Fig. 20

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Table 10 Conditional Comparison Parameters of the OESs with a Distributed and Monolithic Aperture for H = 600 km , F = 20.8 m

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Table 11 Characteristics of the OES with Respect to the Standard and Calculated Parameters of the CCD for Objects 1 and 2, SNR Th = 13.0

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Table 12 Optimal Parameters Versus the Object Spectral Reflectance ( H = 600 km , Δ λ = 0.40 1.05 μm )

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Table 13 Optimal Parameters Versus the Altitude H

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Table 14 Optimal Parameters Versus the Angle β V [ ° ] Between V img and V ch

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Table 15 Optimal Parameters Versus the V img and V ch Synchronization Parameter α V

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Table 16 Optimal Parameters Versus the Presence ( + E ) and Absence ( E ) of the IA and OPD Errors (E), and the Presence ( + T ) and Absence ( T ) of the Atmosphere Turbulence (T)

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Table 17 Optimal Parameters Versus the Upper Bound F 2 [ m ] of the Effective Focal Length

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Table 18 Optimal Parameters Versus the Upper Bound R 22 [ m ] of the Outer Subaperture Radii

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Table 19 Optimal Parameters Versus the Lower Bound R 11 [ m ] of the Inner Subaperture Radii

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Table 20 Optimal Parameters Versus the Spatial Resolution R [ m ]

Equations (46)

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NIIRS = I ( GSD , MTF , SNR , etc. ) .
MRF A ( f , λ ) = exp [ 0.5 D w ( r , λ ) ] ,
D w ( r , λ ) = 2.91 k 2 r 5 / 3 0 H C n 2 ( x ) ( x / H ) 5 / 3 d x .
C n 2 ( x ) = 6.7 × 10 14 ( 2 x 1 / 2 ) 2 / 3 exp ( x / h 0 ) , h 0 = 3200 ,
D w ( R , λ ) = 2.3 × 10 4 R 5 / 3 λ 1 / 3 γ ( 7 / 3 , H / 3200 ) ,
+ U ( x , y , λ ) U * ( x , y , λ ) exp [ i 2 π ( f u x + f v y ) ] d x d y = E D n = 1 N [ τ n ( λ ) ] 1 / 2 exp [ i α ( x n u f + y n v f ) + i k Δ ˜ n ( x n , y n ) ] × m = 1 N [ τ m ( λ ) ] 1 / 2 × A n A m exp { i α [ ( x n x m ) u + ( y n y m ) v ] i k Δ ˜ m ( x m , y m ) } d u d v ,
Δ ˜ j ( x j , y j ) = [ B 0 P 0 P 1 ] [ B 0 P 0 0 0 ] = [ B 0 P 0 P 1 ] [ B 0 P 0 P 2 ] = δ j ( x j , y j ) + Δ j .
u j = u j 0 + L j / F · x j , v j = v j 0 + L j / F · y j ,
δ j ( x j , y j ) ( 1 L j / F ) ( u j 0 x j + v j 0 y j ) / [ ( u j 0 ) 2 + ( v j 0 ) 2 + F 2 ] 1 / 2 ,
p j ( u u j , v v j ) = 1 π ( arctan { η [ ( u u j ) 2 + ( v v j ) 2 r 1 j 2 ] } arctan { η [ ( u u j ) 2 + ( v v j ) 2 r 2 j 2 ] } ) ,
β j = ( 1 L j / F ) · k / [ ( u j 0 ) 2 + ( v j 0 ) 2 + F 2 ] 1 / 2
+ U ( x , y , λ ) U * ( x , y , λ ) exp [ i 2 π ( f u x + f v y ) ] d x d y = E D + n = 1 N [ τ n ( λ ) ] 1 / 2 + exp { i α [ x n ( u u f ) + y n ( v v f ) ] i β n ( u n 0 x n + v n 0 y n ) } P ( x n , y n ) d x n d y n × + exp ( i k Δ n ) P ( Δ n ) d Δ n × 1 π ( arctan { η [ ( u u n 0 u f ) 2 + ( v v n 0 v f ) 2 r 1 n 2 ] } arctan { η [ ( u u n 0 u f ) 2 + ( v v n 0 v f ) 2 r 2 n 2 ] } ) × m = 1 N [ τ m ( λ ) ] 1 / 2 + exp [ i α ( x m u + y m v ) + i β m ( u m 0 x m + v m 0 y m ) ] P ( x m , y m ) d x m d y m × + exp ( i k Δ m ) P ( Δ m ) d Δ m × 1 π ( arctan { η [ ( u u m 0 ) 2 + ( v v m 0 ) 2 r 1 m 2 ] } arctan { η [ ( u u m 0 ) 2 + ( v v m 0 ) 2 r 2 m 2 ] } ) d u d v .
AOTF η ( f , λ ) = 1 / [ π j = 1 N τ j ( λ ) ( r 2 j 2 r 1 j 2 ) ] × n = 1 N [ τ n ( λ ) / ( A 1 A 2 ) ] 1 / 2 / [ 2 σ x n σ y n ( 1 ρ x n y n 2 ) 1 / 2 ] exp [ ( S x n x ¯ n 2 + S y n y ¯ n 2 ) + S x n y n x ¯ n y ¯ n ] × + ( arctan { η [ ( u u n 0 u f ) 2 + ( v v n 0 v f ) 2 r 1 n 2 ) ] } arctan { η [ ( u u n 0 u f ) 2 + ( v v n 0 v f ) 2 r 2 n 2 ] } ) / π × { m = 1 m n N [ τ m ( λ ) / ( A 3 A 4 ) ] 1 / 2 / [ 2 σ x m σ y m ( 1 ρ x m y m 2 ) 1 / 2 ] × exp [ ( S x m x ¯ m 2 + S y m y ¯ m 2 ) + S x m y m x ¯ m y ¯ m ] × exp [ j = 1 4 ( B j 2 / A j ) / 4 ] exp [ k 2 ( σ Δ n 2 + σ Δ m 2 ) / 2 + i k ( Δ ¯ n Δ ¯ m ) ] × ( arctan { η [ ( u u m 0 ) 2 + ( v v m 0 ) 2 r 1 m 2 ] } arctan { η [ ( u u m 0 ) 2 + ( v v m 0 ) 2 r 2 m 2 ] } ) / π + [ τ n ( λ ) ] 1 / 2 exp [ ( B 5 2 / A 1 + B 6 2 / A 2 ) / 4 ] × ( arctan { η [ ( u u n 0 ) 2 + ( v v n 0 ) 2 r 1 n 2 ] } arctan { η [ ( u u n 0 ) 2 + ( v v n 0 ) 2 r 2 n 2 ] } ) / π } d u d v ,
A 1 = S x n , B 1 = 2 S x n x ¯ n S x n y n y ¯ n + i a ( u u f ) i β n u n 0 , C 1 = S x n y n , A 2 = S y n C 1 2 / ( 4 A 1 ) , B 2 = 2 S y n y ¯ n S x n y n x ¯ n + i a ( v v f ) i β n v n 0 + B 1 C 1 / ( 2 A 1 ) , A 3 = S x m , B 3 = 2 S x m x ¯ m S x m y m y ¯ m i a u + i β m u m 0 , C 3 = S x m y m , A 4 = S y m C 3 2 / ( 4 A 3 ) , B 4 = 2 S y m y ¯ m S x m y m x ¯ m i a v + i β m v m 0 + B 3 C 3 / ( 2 A 3 ) , B 5 = 2 S x n x ¯ n S x n y n y ¯ n i a u f , B 6 = 2 S y n y ¯ n S x n y n x ¯ n i a v f + B 5 C 1 / ( 2 A 1 ) , S x n = [ 2 σ x n 2 ( 1 ρ x n y n 2 ) ] 1 , S x n y n = ρ x n y n [ σ x n σ y n ( 1 ρ x n y n 2 ) ] 1 , S y n = [ 2 σ y n 2 ( 1 ρ x n y n 2 ) ] 1 , S x m = [ 2 σ x m 2 ( 1 ρ x m y m 2 ) ] 1 , S x m y m = ρ x m y m [ σ x m σ y m ( 1 ρ x m y m 2 ) ] 1 , S y m = [ 2 σ y m 2 ( 1 ρ x m y m 2 ) ] 1 .
MTF Δ V , x ( f u ) = sinc [ π p x M ( α V cos β V 1 ) f u ] ,
MTF Δ V , x ( f v ) = sinc ( π p x M α V sin β V f v ) ,
MTF CCD ( f , λ , θ R ) = { [ MTF CCD , x ( f u , λ ) · cos θ R ] 2 + [ MTF CCD , y ( f v , λ ) · sin θ R ] 2 } 1 / 2 .
S ( R , θ R ) = | N ob ( f , θ R ) N bg ( f , θ R ) | .
N ( θ R ) = [ N ob ( 0 , θ R ) + N bg ( 0 , θ R ) + 2 ( N h + MT el N dc + N ro 2 ) ] 1 / 2 ,
J ( R , Ω R ) = Ω R I { SNR ( R , θ R ) } d θ R ,
J ( S R , Ω R ) = S R Ω R I { SNR ( R , θ R ) } d θ R d R .
g n R A { [ ( u n 0 ) 2 + ( v n 0 ) 2 ] 1 / 2 + r 2 n } 0 , n = 1 , , N ,
g n m ( u n 0 u m 0 ) 2 + ( v n 0 v m 0 ) 2 ( r 2 n + r 2 m ) 2 0 , n = 1 , , N 1 , m = n + 1 , , N ,
- R A u n 0 R A , n = 1 , , N ,
- R A v n 0 R A , n = 1 , , N ,
R 11 r 1 n R 12 , n = 1 , , N ,
R 21 r 2 n R 22 , n = 1 , , N ,
F 1 F F 2 ,
F 1 = H max { p x , p y } / ( K N q R ) ,
F 2 = C f H ( R E + H ) 3 / 2 p x / [ R E ( GM E ) 1 / 2 cos β V ] .
0 < π p x M ( α V cos β V 1 ) f u < π ,
0 < π p x M α V sin β V f v < π ,
H max { p x , p y } / ( K N q R ) F ,
F C f H ( R E + H ) 3 / 2 p x / [ R E ( GM E ) 1 / 2 cos β V ] ,
p x 1 p x p x 2 ,
p y 1 p y p y 2 ,
d x 1 d x d x 2 ,
d y 1 d y d y 2 ,
M 1 M M 2 .
J ( R , Ω R ) = j = 1 N R { SNR Th SNR [ R , 180 ° / N R ( j 1 ) ] } 2 / ( N R 1 )
{ N R = 18 Ω R = { θ R θ R = 180 ° / N R ( j 1 ) , j = 1 , , N R } ;
J ( R , Ω R ) = [ SNR Th SNR ( R , θ R ) ] 2
{ N R = 1 Ω R = { θ R θ R = 0 ° } ,
{ N R = 1 , Ω R = { θ R θ R = 90 ° } .
SNR th > θ R Ω R max { SNR ( R , θ R ) } .
d x = p x , d y = p y

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