Passive interferometric array optimization based on redundant spacing calibration

doi:10.1364/OE.17.021598

Passive interferometric array optimization based on redundant spacing calibration

Yuntao He, Yuesong Jiang, Li Liu, and Changwei Wang »View Author Affiliations

Optics Express, Vol. 17, Issue 24, pp. 21598-21607 (2009)
http://dx.doi.org/10.1364/OE.17.021598

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Abstract
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Abstract

An optimization of passive interferometric circular arrays for redundant spacing calibration (RSC) is advanced to eliminate phase errors of the array system. The principle of RSC is presented to solve corresponded constraints for passive interferometric circular arrays. The simulated annealing algorithm (SAA) is introduced to settle the array optimization with a criterion of maximizing the distance between u-v points. The optimized circular arrays with element numbers of 8 to 16 antennas are laid out, and RSC is used for the optimized ten-element passive interferometric circular array.

OCIS Codes
(040.1240) Detectors : Arrays
(100.5070) Image processing : Phase retrieval
(110.3175) Imaging systems : Interferometric imaging

ToC Category:
Imaging Systems

History
Original Manuscript: July 28, 2009
Revised Manuscript: October 27, 2009
Manuscript Accepted: November 1, 2009
Published: November 11, 2009

Citation
Yuntao He, Yuesong Jiang, Li Liu, and Changwei Wang, "Passive interferometric array optimization based on redundant spacing calibration," Opt. Express 17, 21598-21607 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-24-21598

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References

W. T. Rhodes and J. W. Goodman, “Interferometric technique for recording and restoring images degraded by unknown aberrations,” J. Opt. Soc. Am. 63(6), 647–657 (1973). [CrossRef]
J. E. Noordam and A. G. de Bruyn, “High dynamic range mapping of strong radio sources with application to 3C84,” Nature 299(5884), 597–600 (1982). [CrossRef]
J. E. Baldwin, C. A. Haniff, C. D. Mackay, and P. J. Warner, “Closure phase in high-resolution optical imaging,” Nature 320(6063), 595–597 (1986). [CrossRef]
T. J. Cornwell, “The applications of closure phase to astronomical imaging,” Science 245(4915), 263–269 (1989). [CrossRef] [PubMed]
A. Lannes, “Remarkable algebraic structures of phase closure imaging and their algorithmic implications in aperture synthesis,” J. Opt. Soc. Am. A 7(3), 500–512 (1990). [CrossRef]
P. M. Blanchard, A. H. Greenaway, A. R. Harvey, and K. Webster, “Coherent Optical Beam Forming with Passive Millimeter-Wave Arrays,” J. Lightwave Technol. 17(3), 418–425 (1999). [CrossRef]
C. S. Ruf, C. T. Swift, A. B. Tanner, and ., “Interferometric synthetic aperture microwave radiometry for the remote sensing of the earth,” IEEE Trans. On GRS 26, 597–611 (1988).
M. Peichl, H. Suess, M. Suess, and S. Kern, “Microwave imaging of the brightness temperature distribution of extended areas in the near and far field using two-dimensional aperture synthesis with high spatial resolution,” Radio Sci. 33(3), 781–801 (1998). [CrossRef]
A. T. Moffet, “Minimum-Redundancy Linear Arrays,” IEEE Trans. Antenn. Propag. 16(2), 172–175 (1968). [CrossRef]
M. J. E. Golay, “Point Arrays Having Compact, Nonredundant Autocorrelations,” J. Opt. Soc. Am. 61(2), 272–273 (1971). [CrossRef]
T. J. Cornwell, “A novel principle for optimization of the instantaneous Fourier plane coverage of correlation arrays,” IEEE Trans. Antenn. Propag. 36(8), 1165–1167 (1988). [CrossRef]
A. Lannes, E. Anterrieu, L. Koechlin, and ., “Concept of field-to-resolution ratio in aperture synthesis,” in Space Optics 1994: Earth Observation and Astronomy, M. G. Cerutti-Maori ed. Proc. SPIE 2209, 402–412 (1994). [CrossRef]
M. Faucherre, F. Merkle, and F. Vakili, “Beam combination in aperture synthesis from space: Field of view limitations and (u, v) plane coverage optimization” in New Technologies for Astronomy, J. P. Swings, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1130, 138–145 (1989).
J. P. Fitch, and T. W. Lawrence, “Placement of multiple apertures for imaging telescopes,” in Amplitude and Intensity Spatial Interferometry,Jim B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1237, 61–69 (1990).
L. M. Mugnier, G. Rousset, and F. Cassaing, “Aperture configuration optimality criterion for phased arrays of optical telescopes,” J. Opt. Soc. Am. A 13(12), 2367–2374 (1996). [CrossRef]
M. A. Holdaway, Helfer, Tamara T. “Interferometric Array Design,” in Synthesis Imaging in Radio Astronomy II, Proc. ASP Conference 180, 537–563 (1999).
L. Kogan, “Optimizing a large array configuration to minimize the sidelobes,” IEEE Trans. Antenn. Propag. 48(7), 1075–1078 (2000). [CrossRef]
O. Guyon and F. Roddier, “Aperture rotation synthesis: Optimization of the (u, v)-plane coverage for a rotating phased array of telescopes,” The Astronomical Society of the Pacific 113(779), 98–104 (2001). [CrossRef]
Y. Su, R. D. Nan, B. Peng, N. Roddis, and J. F. Zhou, “Optimization of interferometric array configurations by “sieving” u - v points,” Astron. Astrophys. 414(1), 389–397 (2004). [CrossRef]
I. Tcherniavski and M. Kahrizi, “Optimization of the optical sparse array configuration,” Opt. Eng. 44(10), 103201 (2005). [CrossRef]
I. Tcherniavski and M. Kahrizi, “Optimization of design and operating parameters of a space-based optical-electronic system with a distributed aperture,” Appl. Opt. 47(33), 6159–6176 (2008). [CrossRef] [PubMed]
P. Armand, J. Benoist, E. Bousquet, L. Delage, S. Olivier, and F. Reynaud, “Optimization of a one dimensional hypertelescope for a direct imaging in astronomy,” Eur. J. Oper. Res. 195(2), 519–527 (2009). [CrossRef]
A. H. Greenaway, “Self-calibrating dilute-aperture optics”, in Digital image synthesis and inverse optics Proc. SPIE 1351, 738–748 (1990). [CrossRef]
A. Lannes and E. Anterrieu, “Redundant spacing calibration: phase restoration methods,” J. Opt. Soc. Am. A 16(12), 2866–2879 (1999). [CrossRef]
Y. Li, B. Braker, F. Schlottau, D. Gu, M. Colice, and K. H. Wagner, “Broadband RF imaging and spectrum analysis using spatial-spectral hole-burning in an inhomogeneously broadened absorber,” in Photonic Applications in Nonlinear Optics, Nanophotonics, and Microwave Photonics Proc. SPIE 5971, 597122 (2005). [CrossRef]
R. J. Eastwood, A. M. Johnson, and A. H. Greenaway, “Calculation and correction of piston phase aberration in synthesis imaging,” J. Opt. Soc. Am. A 26(1), 195–205 (2009). [CrossRef]
P. M. Blanchard, A. H. Greenaway, R. N. Anderton, and R. Appleby, “Phase calibration of arrays at optical and millimeter wavelengths,” J. Opt. Soc. Am. A 13(7), 1593–1600 (1996). [CrossRef]
A. Bandyopadhyay, A. Stepanov, B. Schulkin, M. D. Federici, A. Sengupta, D. Gary, J. F. Federici, R. Barat, Z.-H. Michalopoulou, and D. Zimdars, “Terahertz interferometric and synthetic aperture imaging,” J. Opt. Soc. Am. A 23(5), 1168–1178 (2006). [CrossRef]
C. S. Ruf, “Numerical annealing of low-redundant linear arrays,” IEEE Trans. Antenn. Propag. 41(1), 85–90 (1993). [CrossRef]
S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220(4598), 671–680 (1983). [CrossRef] [PubMed]
P. J. M. Laarhoven, and E. H. L. Aarts, Simulated annealing: theory and applications. (D. Reidel Publishing Company, Dordrecht, (1987).

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[1] W. T. Rhodes and J. W. Goodman, “Interferometric technique for recording and restoring images degraded by unknown aberrations,” J. Opt. Soc. Am. 63(6), 647–657 (1973). [CrossRef]

[2] J. E. Noordam and A. G. de Bruyn, “High dynamic range mapping of strong radio sources with application to 3C84,” Nature 299(5884), 597–600 (1982). [CrossRef]

[3] J. E. Baldwin, C. A. Haniff, C. D. Mackay, and P. J. Warner, “Closure phase in high-resolution optical imaging,” Nature 320(6063), 595–597 (1986). [CrossRef]

[4] T. J. Cornwell, “The applications of closure phase to astronomical imaging,” Science 245(4915), 263–269 (1989). [CrossRef] [PubMed]

[5] A. Lannes, “Remarkable algebraic structures of phase closure imaging and their algorithmic implications in aperture synthesis,” J. Opt. Soc. Am. A 7(3), 500–512 (1990). [CrossRef]

[6] P. M. Blanchard, A. H. Greenaway, A. R. Harvey, and K. Webster, “Coherent Optical Beam Forming with Passive Millimeter-Wave Arrays,” J. Lightwave Technol. 17(3), 418–425 (1999). [CrossRef]

[7] C. S. Ruf, C. T. Swift, A. B. Tanner, and ., “Interferometric synthetic aperture microwave radiometry for the remote sensing of the earth,” IEEE Trans. On GRS 26, 597–611 (1988).

[8] M. Peichl, H. Suess, M. Suess, and S. Kern, “Microwave imaging of the brightness temperature distribution of extended areas in the near and far field using two-dimensional aperture synthesis with high spatial resolution,” Radio Sci. 33(3), 781–801 (1998). [CrossRef]

[9] A. T. Moffet, “Minimum-Redundancy Linear Arrays,” IEEE Trans. Antenn. Propag. 16(2), 172–175 (1968). [CrossRef]

[10] M. J. E. Golay, “Point Arrays Having Compact, Nonredundant Autocorrelations,” J. Opt. Soc. Am. 61(2), 272–273 (1971). [CrossRef]

[11] T. J. Cornwell, “A novel principle for optimization of the instantaneous Fourier plane coverage of correlation arrays,” IEEE Trans. Antenn. Propag. 36(8), 1165–1167 (1988). [CrossRef]

[12] A. Lannes, E. Anterrieu, L. Koechlin, and ., “Concept of field-to-resolution ratio in aperture synthesis,” in Space Optics 1994: Earth Observation and Astronomy, M. G. Cerutti-Maori ed. Proc. SPIE 2209, 402–412 (1994). [CrossRef]

[13] M. Faucherre, F. Merkle, and F. Vakili, “Beam combination in aperture synthesis from space: Field of view limitations and (u, v) plane coverage optimization” in New Technologies for Astronomy, J. P. Swings, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1130, 138–145 (1989).

[14] J. P. Fitch, and T. W. Lawrence, “Placement of multiple apertures for imaging telescopes,” in Amplitude and Intensity Spatial Interferometry,Jim B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1237, 61–69 (1990).

[15] L. M. Mugnier, G. Rousset, and F. Cassaing, “Aperture configuration optimality criterion for phased arrays of optical telescopes,” J. Opt. Soc. Am. A 13(12), 2367–2374 (1996). [CrossRef]

[16] M. A. Holdaway, Helfer, Tamara T. “Interferometric Array Design,” in Synthesis Imaging in Radio Astronomy II, Proc. ASP Conference 180, 537–563 (1999).

[17] L. Kogan, “Optimizing a large array configuration to minimize the sidelobes,” IEEE Trans. Antenn. Propag. 48(7), 1075–1078 (2000). [CrossRef]

[18] O. Guyon and F. Roddier, “Aperture rotation synthesis: Optimization of the (u, v)-plane coverage for a rotating phased array of telescopes,” The Astronomical Society of the Pacific 113(779), 98–104 (2001). [CrossRef]

[19] Y. Su, R. D. Nan, B. Peng, N. Roddis, and J. F. Zhou, “Optimization of interferometric array configurations by “sieving” u - v points,” Astron. Astrophys. 414(1), 389–397 (2004). [CrossRef]

[20] I. Tcherniavski and M. Kahrizi, “Optimization of the optical sparse array configuration,” Opt. Eng. 44(10), 103201 (2005). [CrossRef]

[21] I. Tcherniavski and M. Kahrizi, “Optimization of design and operating parameters of a space-based optical-electronic system with a distributed aperture,” Appl. Opt. 47(33), 6159–6176 (2008). [CrossRef] [PubMed]

[22] P. Armand, J. Benoist, E. Bousquet, L. Delage, S. Olivier, and F. Reynaud, “Optimization of a one dimensional hypertelescope for a direct imaging in astronomy,” Eur. J. Oper. Res. 195(2), 519–527 (2009). [CrossRef]

[23] A. H. Greenaway, “Self-calibrating dilute-aperture optics”, in Digital image synthesis and inverse optics Proc. SPIE 1351, 738–748 (1990). [CrossRef]

[24] A. Lannes and E. Anterrieu, “Redundant spacing calibration: phase restoration methods,” J. Opt. Soc. Am. A 16(12), 2866–2879 (1999). [CrossRef]

[25] Y. Li, B. Braker, F. Schlottau, D. Gu, M. Colice, and K. H. Wagner, “Broadband RF imaging and spectrum analysis using spatial-spectral hole-burning in an inhomogeneously broadened absorber,” in Photonic Applications in Nonlinear Optics, Nanophotonics, and Microwave Photonics Proc. SPIE 5971, 597122 (2005). [CrossRef]

[26] R. J. Eastwood, A. M. Johnson, and A. H. Greenaway, “Calculation and correction of piston phase aberration in synthesis imaging,” J. Opt. Soc. Am. A 26(1), 195–205 (2009). [CrossRef]

[27] P. M. Blanchard, A. H. Greenaway, R. N. Anderton, and R. Appleby, “Phase calibration of arrays at optical and millimeter wavelengths,” J. Opt. Soc. Am. A 13(7), 1593–1600 (1996). [CrossRef]

[28] A. Bandyopadhyay, A. Stepanov, B. Schulkin, M. D. Federici, A. Sengupta, D. Gary, J. F. Federici, R. Barat, Z.-H. Michalopoulou, and D. Zimdars, “Terahertz interferometric and synthetic aperture imaging,” J. Opt. Soc. Am. A 23(5), 1168–1178 (2006). [CrossRef]

[29] C. S. Ruf, “Numerical annealing of low-redundant linear arrays,” IEEE Trans. Antenn. Propag. 41(1), 85–90 (1993). [CrossRef]

[30] S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by Simulated Annealing,” Science 220(4598), 671–680 (1983). [CrossRef] [PubMed]

[31] P. J. M. Laarhoven, and E. H. L. Aarts, Simulated annealing: theory and applications. (D. Reidel Publishing Company, Dordrecht, (1987).

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Passive interferometric array optimization based on redundant spacing calibration