Abstract

Far-infrared bolometric detectors are used extensively in ground-based and space-borne astronomy, and thus it is important to understand their optical behavior precisely. We have studied the intensity and polarization response of free-space bolometers and shown that when the size of the absorber is reduced below a wavelength, the response changes from being that of a classical optical detector to that of a few-mode antenna. We have calculated the modal content of the reception patterns and found that for any volumetric detector having a side length of less than a wavelength, three magnetic and three electric dipoles characterize the behavior. The size of the absorber merely determines the relative strengths of the contributions. The same formalism can be applied to thin-film absorbers, where the induced current is forced to flow in a plane. In this case, one magnetic and two electric dipoles characterize the behavior. The ability to model easily the intensity, polarization, and straylight characteristics of electrically small detectors will be of great value when designing high-performance polarimetric imaging arrays.

© 2010 Optical Society of America

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2010

C. Thomas and S. Withington, “Electromagnetic simulations of the partially coherent optical behaviour of resistive film TES detectors,” presented at the 21st International Symposium on Space Terahertz Technology, Oxford, UK, 23–25 March 2010.

2009

2008

J. Staguhn, C. Allen, D. Benford, E. Sharp, T. Ames, R. Arendt, D. Chuss, E. Dwek, A. Kovacs, S. Maher, C. Marx, T. Miller, S. Harvey Moseley, S. Navarro, A. Sievers, G. Voellmer, and E. Wollack, “GISMO, a 2 mm bolometer camera optimized for the study of high redshift galaxies,” J. Low Temp. Phys. 151, 709–714 (2008).
[CrossRef]

D. Chuss, E. Wollack, S. Moseley, S. Withington, and G. Saklatvala, “Diffraction considerations for planar detectors in the few-mode limit,” Publ. Astron. Soc. Pac. 120, 430–438 (2008).
[CrossRef]

2007

S. Dicker, B. Mason, P. Korngut, J. Abrahams, P. Ade, J. Aguirre, T. Ames, D. Benford, T. Chen, J. Chervenak, W. Cotton, M. Devlin, E. Figuero-Feliciano, K. Irwin, S. Maher, M. Mello, S. Moseley, J. Staguhn, R. Norrod, D. Tally, C. Tucker, B. Werner, and S. White, “MUSTANG. First light and current status,” in Infrared and Millimeter Waves, 2007, and the 2007 15th International Conference on Terahertz Electronics IRMMW-THz. Joint 32nd International Conference (IEEE, 2007), pp. 331–332.

S. Withington and G. Saklatvala, “Characterizing the behavior of partially coherent detectors through spatio-temporal modes,” J. Opt. A, Pure Appl. Opt. 9, 626–633 (2007).
[CrossRef]

G. Saklatvala, S. Withington, and M. Hobson, “Coupled-mode theory for infrared and submillimeter wave detectors,” J. Opt. Soc. Am. A 24, 764–775 (2007).
[CrossRef]

2006

M. Audley, R. Barker, M. Crane, R. Dace, D. Glowacka, D. Goldie, A. Lasenby, H. Stevenson, V. Tsaneva, S. Withington, P. Grimes, B. Johnson, G. Yassin, L. Piccirillo, G. Pisano, W. Duncan, G. Hilton, K. Irwin, C. Reintsema, and M. Halpern, “TES imaging array technology for CLOVER,” Proc. SPIE 6275, 24–32 (2006).

2004

J. Ruhl, P. Ade, J. Carlstrom, H. Cho, T. Crawford, M. Dobbs, C. Greer, W. Holzapfel, T. Lanting, A. Lee, N. Halverson, E. Leitch, J. Leong, W. Lu, M. Lueker, J. Mehl, S. Meyer, J. Mohr, S. Padin, T. Plagge, C. Pryke, M. Runyan, D. Schwan, M. Sharp, H. Spieler, Z. Staniszewski, and A. Stark, “The south pole telescope,” Proc. SPIE 5498, 11–29 (2004).
[CrossRef]

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

H. Eom, Electromagnetic Wave Theory for Boundary-Value Problems: An Advanced Course on Analytical Methods (Springer Verlag, 2004).
[PubMed]

2003

S. Withington, C. Tham, and G. Yassin, “Theoretical analysis of planar bolometric arrays for thz imaging systems,” Proc. SPIE 4855, 49–62 (2003).
[CrossRef]

1995

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, 1995).

1986

J. Krauss, Radio Astronomy, 2nd ed. (Cygnus-Quasar Books, 1986).

1985

M. Ney, “Method of moments as applied to electromagnetic problems,” IEEE Trans. Microwave Theory Tech. 33, 972–980 (1985).
[CrossRef]

1981

Abrahams, J.

S. Dicker, B. Mason, P. Korngut, J. Abrahams, P. Ade, J. Aguirre, T. Ames, D. Benford, T. Chen, J. Chervenak, W. Cotton, M. Devlin, E. Figuero-Feliciano, K. Irwin, S. Maher, M. Mello, S. Moseley, J. Staguhn, R. Norrod, D. Tally, C. Tucker, B. Werner, and S. White, “MUSTANG. First light and current status,” in Infrared and Millimeter Waves, 2007, and the 2007 15th International Conference on Terahertz Electronics IRMMW-THz. Joint 32nd International Conference (IEEE, 2007), pp. 331–332.

Ade, P.

S. Dicker, B. Mason, P. Korngut, J. Abrahams, P. Ade, J. Aguirre, T. Ames, D. Benford, T. Chen, J. Chervenak, W. Cotton, M. Devlin, E. Figuero-Feliciano, K. Irwin, S. Maher, M. Mello, S. Moseley, J. Staguhn, R. Norrod, D. Tally, C. Tucker, B. Werner, and S. White, “MUSTANG. First light and current status,” in Infrared and Millimeter Waves, 2007, and the 2007 15th International Conference on Terahertz Electronics IRMMW-THz. Joint 32nd International Conference (IEEE, 2007), pp. 331–332.

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

J. Ruhl, P. Ade, J. Carlstrom, H. Cho, T. Crawford, M. Dobbs, C. Greer, W. Holzapfel, T. Lanting, A. Lee, N. Halverson, E. Leitch, J. Leong, W. Lu, M. Lueker, J. Mehl, S. Meyer, J. Mohr, S. Padin, T. Plagge, C. Pryke, M. Runyan, D. Schwan, M. Sharp, H. Spieler, Z. Staniszewski, and A. Stark, “The south pole telescope,” Proc. SPIE 5498, 11–29 (2004).
[CrossRef]

Aguirre, J.

S. Dicker, B. Mason, P. Korngut, J. Abrahams, P. Ade, J. Aguirre, T. Ames, D. Benford, T. Chen, J. Chervenak, W. Cotton, M. Devlin, E. Figuero-Feliciano, K. Irwin, S. Maher, M. Mello, S. Moseley, J. Staguhn, R. Norrod, D. Tally, C. Tucker, B. Werner, and S. White, “MUSTANG. First light and current status,” in Infrared and Millimeter Waves, 2007, and the 2007 15th International Conference on Terahertz Electronics IRMMW-THz. Joint 32nd International Conference (IEEE, 2007), pp. 331–332.

Allen, C.

J. Staguhn, C. Allen, D. Benford, E. Sharp, T. Ames, R. Arendt, D. Chuss, E. Dwek, A. Kovacs, S. Maher, C. Marx, T. Miller, S. Harvey Moseley, S. Navarro, A. Sievers, G. Voellmer, and E. Wollack, “GISMO, a 2 mm bolometer camera optimized for the study of high redshift galaxies,” J. Low Temp. Phys. 151, 709–714 (2008).
[CrossRef]

Ames, T.

J. Staguhn, C. Allen, D. Benford, E. Sharp, T. Ames, R. Arendt, D. Chuss, E. Dwek, A. Kovacs, S. Maher, C. Marx, T. Miller, S. Harvey Moseley, S. Navarro, A. Sievers, G. Voellmer, and E. Wollack, “GISMO, a 2 mm bolometer camera optimized for the study of high redshift galaxies,” J. Low Temp. Phys. 151, 709–714 (2008).
[CrossRef]

S. Dicker, B. Mason, P. Korngut, J. Abrahams, P. Ade, J. Aguirre, T. Ames, D. Benford, T. Chen, J. Chervenak, W. Cotton, M. Devlin, E. Figuero-Feliciano, K. Irwin, S. Maher, M. Mello, S. Moseley, J. Staguhn, R. Norrod, D. Tally, C. Tucker, B. Werner, and S. White, “MUSTANG. First light and current status,” in Infrared and Millimeter Waves, 2007, and the 2007 15th International Conference on Terahertz Electronics IRMMW-THz. Joint 32nd International Conference (IEEE, 2007), pp. 331–332.

Arendt, R.

J. Staguhn, C. Allen, D. Benford, E. Sharp, T. Ames, R. Arendt, D. Chuss, E. Dwek, A. Kovacs, S. Maher, C. Marx, T. Miller, S. Harvey Moseley, S. Navarro, A. Sievers, G. Voellmer, and E. Wollack, “GISMO, a 2 mm bolometer camera optimized for the study of high redshift galaxies,” J. Low Temp. Phys. 151, 709–714 (2008).
[CrossRef]

Atkinson, D.

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

Audley, M.

M. Audley, R. Barker, M. Crane, R. Dace, D. Glowacka, D. Goldie, A. Lasenby, H. Stevenson, V. Tsaneva, S. Withington, P. Grimes, B. Johnson, G. Yassin, L. Piccirillo, G. Pisano, W. Duncan, G. Hilton, K. Irwin, C. Reintsema, and M. Halpern, “TES imaging array technology for CLOVER,” Proc. SPIE 6275, 24–32 (2006).

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

Barker, R.

M. Audley, R. Barker, M. Crane, R. Dace, D. Glowacka, D. Goldie, A. Lasenby, H. Stevenson, V. Tsaneva, S. Withington, P. Grimes, B. Johnson, G. Yassin, L. Piccirillo, G. Pisano, W. Duncan, G. Hilton, K. Irwin, C. Reintsema, and M. Halpern, “TES imaging array technology for CLOVER,” Proc. SPIE 6275, 24–32 (2006).

Bastien, P.

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

Benford, D.

J. Staguhn, C. Allen, D. Benford, E. Sharp, T. Ames, R. Arendt, D. Chuss, E. Dwek, A. Kovacs, S. Maher, C. Marx, T. Miller, S. Harvey Moseley, S. Navarro, A. Sievers, G. Voellmer, and E. Wollack, “GISMO, a 2 mm bolometer camera optimized for the study of high redshift galaxies,” J. Low Temp. Phys. 151, 709–714 (2008).
[CrossRef]

S. Dicker, B. Mason, P. Korngut, J. Abrahams, P. Ade, J. Aguirre, T. Ames, D. Benford, T. Chen, J. Chervenak, W. Cotton, M. Devlin, E. Figuero-Feliciano, K. Irwin, S. Maher, M. Mello, S. Moseley, J. Staguhn, R. Norrod, D. Tally, C. Tucker, B. Werner, and S. White, “MUSTANG. First light and current status,” in Infrared and Millimeter Waves, 2007, and the 2007 15th International Conference on Terahertz Electronics IRMMW-THz. Joint 32nd International Conference (IEEE, 2007), pp. 331–332.

Bintley, D.

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

Carlstrom, J.

J. Ruhl, P. Ade, J. Carlstrom, H. Cho, T. Crawford, M. Dobbs, C. Greer, W. Holzapfel, T. Lanting, A. Lee, N. Halverson, E. Leitch, J. Leong, W. Lu, M. Lueker, J. Mehl, S. Meyer, J. Mohr, S. Padin, T. Plagge, C. Pryke, M. Runyan, D. Schwan, M. Sharp, H. Spieler, Z. Staniszewski, and A. Stark, “The south pole telescope,” Proc. SPIE 5498, 11–29 (2004).
[CrossRef]

Chen, T.

S. Dicker, B. Mason, P. Korngut, J. Abrahams, P. Ade, J. Aguirre, T. Ames, D. Benford, T. Chen, J. Chervenak, W. Cotton, M. Devlin, E. Figuero-Feliciano, K. Irwin, S. Maher, M. Mello, S. Moseley, J. Staguhn, R. Norrod, D. Tally, C. Tucker, B. Werner, and S. White, “MUSTANG. First light and current status,” in Infrared and Millimeter Waves, 2007, and the 2007 15th International Conference on Terahertz Electronics IRMMW-THz. Joint 32nd International Conference (IEEE, 2007), pp. 331–332.

Chervenak, J.

S. Dicker, B. Mason, P. Korngut, J. Abrahams, P. Ade, J. Aguirre, T. Ames, D. Benford, T. Chen, J. Chervenak, W. Cotton, M. Devlin, E. Figuero-Feliciano, K. Irwin, S. Maher, M. Mello, S. Moseley, J. Staguhn, R. Norrod, D. Tally, C. Tucker, B. Werner, and S. White, “MUSTANG. First light and current status,” in Infrared and Millimeter Waves, 2007, and the 2007 15th International Conference on Terahertz Electronics IRMMW-THz. Joint 32nd International Conference (IEEE, 2007), pp. 331–332.

Cho, H.

J. Ruhl, P. Ade, J. Carlstrom, H. Cho, T. Crawford, M. Dobbs, C. Greer, W. Holzapfel, T. Lanting, A. Lee, N. Halverson, E. Leitch, J. Leong, W. Lu, M. Lueker, J. Mehl, S. Meyer, J. Mohr, S. Padin, T. Plagge, C. Pryke, M. Runyan, D. Schwan, M. Sharp, H. Spieler, Z. Staniszewski, and A. Stark, “The south pole telescope,” Proc. SPIE 5498, 11–29 (2004).
[CrossRef]

Chuss, D.

J. Staguhn, C. Allen, D. Benford, E. Sharp, T. Ames, R. Arendt, D. Chuss, E. Dwek, A. Kovacs, S. Maher, C. Marx, T. Miller, S. Harvey Moseley, S. Navarro, A. Sievers, G. Voellmer, and E. Wollack, “GISMO, a 2 mm bolometer camera optimized for the study of high redshift galaxies,” J. Low Temp. Phys. 151, 709–714 (2008).
[CrossRef]

D. Chuss, E. Wollack, S. Moseley, S. Withington, and G. Saklatvala, “Diffraction considerations for planar detectors in the few-mode limit,” Publ. Astron. Soc. Pac. 120, 430–438 (2008).
[CrossRef]

Cliffe, M.

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

Cotton, W.

S. Dicker, B. Mason, P. Korngut, J. Abrahams, P. Ade, J. Aguirre, T. Ames, D. Benford, T. Chen, J. Chervenak, W. Cotton, M. Devlin, E. Figuero-Feliciano, K. Irwin, S. Maher, M. Mello, S. Moseley, J. Staguhn, R. Norrod, D. Tally, C. Tucker, B. Werner, and S. White, “MUSTANG. First light and current status,” in Infrared and Millimeter Waves, 2007, and the 2007 15th International Conference on Terahertz Electronics IRMMW-THz. Joint 32nd International Conference (IEEE, 2007), pp. 331–332.

Crane, M.

M. Audley, R. Barker, M. Crane, R. Dace, D. Glowacka, D. Goldie, A. Lasenby, H. Stevenson, V. Tsaneva, S. Withington, P. Grimes, B. Johnson, G. Yassin, L. Piccirillo, G. Pisano, W. Duncan, G. Hilton, K. Irwin, C. Reintsema, and M. Halpern, “TES imaging array technology for CLOVER,” Proc. SPIE 6275, 24–32 (2006).

Crawford, T.

J. Ruhl, P. Ade, J. Carlstrom, H. Cho, T. Crawford, M. Dobbs, C. Greer, W. Holzapfel, T. Lanting, A. Lee, N. Halverson, E. Leitch, J. Leong, W. Lu, M. Lueker, J. Mehl, S. Meyer, J. Mohr, S. Padin, T. Plagge, C. Pryke, M. Runyan, D. Schwan, M. Sharp, H. Spieler, Z. Staniszewski, and A. Stark, “The south pole telescope,” Proc. SPIE 5498, 11–29 (2004).
[CrossRef]

Dace, R.

M. Audley, R. Barker, M. Crane, R. Dace, D. Glowacka, D. Goldie, A. Lasenby, H. Stevenson, V. Tsaneva, S. Withington, P. Grimes, B. Johnson, G. Yassin, L. Piccirillo, G. Pisano, W. Duncan, G. Hilton, K. Irwin, C. Reintsema, and M. Halpern, “TES imaging array technology for CLOVER,” Proc. SPIE 6275, 24–32 (2006).

Devlin, M.

S. Dicker, B. Mason, P. Korngut, J. Abrahams, P. Ade, J. Aguirre, T. Ames, D. Benford, T. Chen, J. Chervenak, W. Cotton, M. Devlin, E. Figuero-Feliciano, K. Irwin, S. Maher, M. Mello, S. Moseley, J. Staguhn, R. Norrod, D. Tally, C. Tucker, B. Werner, and S. White, “MUSTANG. First light and current status,” in Infrared and Millimeter Waves, 2007, and the 2007 15th International Conference on Terahertz Electronics IRMMW-THz. Joint 32nd International Conference (IEEE, 2007), pp. 331–332.

Dicker, S.

S. Dicker, B. Mason, P. Korngut, J. Abrahams, P. Ade, J. Aguirre, T. Ames, D. Benford, T. Chen, J. Chervenak, W. Cotton, M. Devlin, E. Figuero-Feliciano, K. Irwin, S. Maher, M. Mello, S. Moseley, J. Staguhn, R. Norrod, D. Tally, C. Tucker, B. Werner, and S. White, “MUSTANG. First light and current status,” in Infrared and Millimeter Waves, 2007, and the 2007 15th International Conference on Terahertz Electronics IRMMW-THz. Joint 32nd International Conference (IEEE, 2007), pp. 331–332.

Dobbs, M.

J. Ruhl, P. Ade, J. Carlstrom, H. Cho, T. Crawford, M. Dobbs, C. Greer, W. Holzapfel, T. Lanting, A. Lee, N. Halverson, E. Leitch, J. Leong, W. Lu, M. Lueker, J. Mehl, S. Meyer, J. Mohr, S. Padin, T. Plagge, C. Pryke, M. Runyan, D. Schwan, M. Sharp, H. Spieler, Z. Staniszewski, and A. Stark, “The south pole telescope,” Proc. SPIE 5498, 11–29 (2004).
[CrossRef]

Dunare, C.

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

Duncan, W.

M. Audley, R. Barker, M. Crane, R. Dace, D. Glowacka, D. Goldie, A. Lasenby, H. Stevenson, V. Tsaneva, S. Withington, P. Grimes, B. Johnson, G. Yassin, L. Piccirillo, G. Pisano, W. Duncan, G. Hilton, K. Irwin, C. Reintsema, and M. Halpern, “TES imaging array technology for CLOVER,” Proc. SPIE 6275, 24–32 (2006).

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

Dwek, E.

J. Staguhn, C. Allen, D. Benford, E. Sharp, T. Ames, R. Arendt, D. Chuss, E. Dwek, A. Kovacs, S. Maher, C. Marx, T. Miller, S. Harvey Moseley, S. Navarro, A. Sievers, G. Voellmer, and E. Wollack, “GISMO, a 2 mm bolometer camera optimized for the study of high redshift galaxies,” J. Low Temp. Phys. 151, 709–714 (2008).
[CrossRef]

Ellis, M.

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

Eom, H.

H. Eom, Electromagnetic Wave Theory for Boundary-Value Problems: An Advanced Course on Analytical Methods (Springer Verlag, 2004).
[PubMed]

Fich, M.

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

Figuero-Feliciano, E.

S. Dicker, B. Mason, P. Korngut, J. Abrahams, P. Ade, J. Aguirre, T. Ames, D. Benford, T. Chen, J. Chervenak, W. Cotton, M. Devlin, E. Figuero-Feliciano, K. Irwin, S. Maher, M. Mello, S. Moseley, J. Staguhn, R. Norrod, D. Tally, C. Tucker, B. Werner, and S. White, “MUSTANG. First light and current status,” in Infrared and Millimeter Waves, 2007, and the 2007 15th International Conference on Terahertz Electronics IRMMW-THz. Joint 32nd International Conference (IEEE, 2007), pp. 331–332.

Gannaway, F.

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

Gao, X.

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

Glowacka, D.

M. Audley, R. Barker, M. Crane, R. Dace, D. Glowacka, D. Goldie, A. Lasenby, H. Stevenson, V. Tsaneva, S. Withington, P. Grimes, B. Johnson, G. Yassin, L. Piccirillo, G. Pisano, W. Duncan, G. Hilton, K. Irwin, C. Reintsema, and M. Halpern, “TES imaging array technology for CLOVER,” Proc. SPIE 6275, 24–32 (2006).

Goldie, D.

M. Audley, R. Barker, M. Crane, R. Dace, D. Glowacka, D. Goldie, A. Lasenby, H. Stevenson, V. Tsaneva, S. Withington, P. Grimes, B. Johnson, G. Yassin, L. Piccirillo, G. Pisano, W. Duncan, G. Hilton, K. Irwin, C. Reintsema, and M. Halpern, “TES imaging array technology for CLOVER,” Proc. SPIE 6275, 24–32 (2006).

Gostick, D.

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

Greer, C.

J. Ruhl, P. Ade, J. Carlstrom, H. Cho, T. Crawford, M. Dobbs, C. Greer, W. Holzapfel, T. Lanting, A. Lee, N. Halverson, E. Leitch, J. Leong, W. Lu, M. Lueker, J. Mehl, S. Meyer, J. Mohr, S. Padin, T. Plagge, C. Pryke, M. Runyan, D. Schwan, M. Sharp, H. Spieler, Z. Staniszewski, and A. Stark, “The south pole telescope,” Proc. SPIE 5498, 11–29 (2004).
[CrossRef]

Griffin, M.

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

Grimes, P.

M. Audley, R. Barker, M. Crane, R. Dace, D. Glowacka, D. Goldie, A. Lasenby, H. Stevenson, V. Tsaneva, S. Withington, P. Grimes, B. Johnson, G. Yassin, L. Piccirillo, G. Pisano, W. Duncan, G. Hilton, K. Irwin, C. Reintsema, and M. Halpern, “TES imaging array technology for CLOVER,” Proc. SPIE 6275, 24–32 (2006).

Halpern, M.

M. Audley, R. Barker, M. Crane, R. Dace, D. Glowacka, D. Goldie, A. Lasenby, H. Stevenson, V. Tsaneva, S. Withington, P. Grimes, B. Johnson, G. Yassin, L. Piccirillo, G. Pisano, W. Duncan, G. Hilton, K. Irwin, C. Reintsema, and M. Halpern, “TES imaging array technology for CLOVER,” Proc. SPIE 6275, 24–32 (2006).

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

Halverson, N.

J. Ruhl, P. Ade, J. Carlstrom, H. Cho, T. Crawford, M. Dobbs, C. Greer, W. Holzapfel, T. Lanting, A. Lee, N. Halverson, E. Leitch, J. Leong, W. Lu, M. Lueker, J. Mehl, S. Meyer, J. Mohr, S. Padin, T. Plagge, C. Pryke, M. Runyan, D. Schwan, M. Sharp, H. Spieler, Z. Staniszewski, and A. Stark, “The south pole telescope,” Proc. SPIE 5498, 11–29 (2004).
[CrossRef]

Harvey Moseley, S.

J. Staguhn, C. Allen, D. Benford, E. Sharp, T. Ames, R. Arendt, D. Chuss, E. Dwek, A. Kovacs, S. Maher, C. Marx, T. Miller, S. Harvey Moseley, S. Navarro, A. Sievers, G. Voellmer, and E. Wollack, “GISMO, a 2 mm bolometer camera optimized for the study of high redshift galaxies,” J. Low Temp. Phys. 151, 709–714 (2008).
[CrossRef]

Hilton, G.

M. Audley, R. Barker, M. Crane, R. Dace, D. Glowacka, D. Goldie, A. Lasenby, H. Stevenson, V. Tsaneva, S. Withington, P. Grimes, B. Johnson, G. Yassin, L. Piccirillo, G. Pisano, W. Duncan, G. Hilton, K. Irwin, C. Reintsema, and M. Halpern, “TES imaging array technology for CLOVER,” Proc. SPIE 6275, 24–32 (2006).

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

Hobson, M.

Hodson, T.

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

Holland, W.

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

Holzapfel, W.

J. Ruhl, P. Ade, J. Carlstrom, H. Cho, T. Crawford, M. Dobbs, C. Greer, W. Holzapfel, T. Lanting, A. Lee, N. Halverson, E. Leitch, J. Leong, W. Lu, M. Lueker, J. Mehl, S. Meyer, J. Mohr, S. Padin, T. Plagge, C. Pryke, M. Runyan, D. Schwan, M. Sharp, H. Spieler, Z. Staniszewski, and A. Stark, “The south pole telescope,” Proc. SPIE 5498, 11–29 (2004).
[CrossRef]

Irwin, K.

S. Dicker, B. Mason, P. Korngut, J. Abrahams, P. Ade, J. Aguirre, T. Ames, D. Benford, T. Chen, J. Chervenak, W. Cotton, M. Devlin, E. Figuero-Feliciano, K. Irwin, S. Maher, M. Mello, S. Moseley, J. Staguhn, R. Norrod, D. Tally, C. Tucker, B. Werner, and S. White, “MUSTANG. First light and current status,” in Infrared and Millimeter Waves, 2007, and the 2007 15th International Conference on Terahertz Electronics IRMMW-THz. Joint 32nd International Conference (IEEE, 2007), pp. 331–332.

M. Audley, R. Barker, M. Crane, R. Dace, D. Glowacka, D. Goldie, A. Lasenby, H. Stevenson, V. Tsaneva, S. Withington, P. Grimes, B. Johnson, G. Yassin, L. Piccirillo, G. Pisano, W. Duncan, G. Hilton, K. Irwin, C. Reintsema, and M. Halpern, “TES imaging array technology for CLOVER,” Proc. SPIE 6275, 24–32 (2006).

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

Johnson, B.

M. Audley, R. Barker, M. Crane, R. Dace, D. Glowacka, D. Goldie, A. Lasenby, H. Stevenson, V. Tsaneva, S. Withington, P. Grimes, B. Johnson, G. Yassin, L. Piccirillo, G. Pisano, W. Duncan, G. Hilton, K. Irwin, C. Reintsema, and M. Halpern, “TES imaging array technology for CLOVER,” Proc. SPIE 6275, 24–32 (2006).

Kelly, D.

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

Korngut, P.

S. Dicker, B. Mason, P. Korngut, J. Abrahams, P. Ade, J. Aguirre, T. Ames, D. Benford, T. Chen, J. Chervenak, W. Cotton, M. Devlin, E. Figuero-Feliciano, K. Irwin, S. Maher, M. Mello, S. Moseley, J. Staguhn, R. Norrod, D. Tally, C. Tucker, B. Werner, and S. White, “MUSTANG. First light and current status,” in Infrared and Millimeter Waves, 2007, and the 2007 15th International Conference on Terahertz Electronics IRMMW-THz. Joint 32nd International Conference (IEEE, 2007), pp. 331–332.

Kovacs, A.

J. Staguhn, C. Allen, D. Benford, E. Sharp, T. Ames, R. Arendt, D. Chuss, E. Dwek, A. Kovacs, S. Maher, C. Marx, T. Miller, S. Harvey Moseley, S. Navarro, A. Sievers, G. Voellmer, and E. Wollack, “GISMO, a 2 mm bolometer camera optimized for the study of high redshift galaxies,” J. Low Temp. Phys. 151, 709–714 (2008).
[CrossRef]

Krauss, J.

J. Krauss, Radio Astronomy, 2nd ed. (Cygnus-Quasar Books, 1986).

Lanting, T.

J. Ruhl, P. Ade, J. Carlstrom, H. Cho, T. Crawford, M. Dobbs, C. Greer, W. Holzapfel, T. Lanting, A. Lee, N. Halverson, E. Leitch, J. Leong, W. Lu, M. Lueker, J. Mehl, S. Meyer, J. Mohr, S. Padin, T. Plagge, C. Pryke, M. Runyan, D. Schwan, M. Sharp, H. Spieler, Z. Staniszewski, and A. Stark, “The south pole telescope,” Proc. SPIE 5498, 11–29 (2004).
[CrossRef]

Lasenby, A.

M. Audley, R. Barker, M. Crane, R. Dace, D. Glowacka, D. Goldie, A. Lasenby, H. Stevenson, V. Tsaneva, S. Withington, P. Grimes, B. Johnson, G. Yassin, L. Piccirillo, G. Pisano, W. Duncan, G. Hilton, K. Irwin, C. Reintsema, and M. Halpern, “TES imaging array technology for CLOVER,” Proc. SPIE 6275, 24–32 (2006).

Lee, A.

J. Ruhl, P. Ade, J. Carlstrom, H. Cho, T. Crawford, M. Dobbs, C. Greer, W. Holzapfel, T. Lanting, A. Lee, N. Halverson, E. Leitch, J. Leong, W. Lu, M. Lueker, J. Mehl, S. Meyer, J. Mohr, S. Padin, T. Plagge, C. Pryke, M. Runyan, D. Schwan, M. Sharp, H. Spieler, Z. Staniszewski, and A. Stark, “The south pole telescope,” Proc. SPIE 5498, 11–29 (2004).
[CrossRef]

Leitch, E.

J. Ruhl, P. Ade, J. Carlstrom, H. Cho, T. Crawford, M. Dobbs, C. Greer, W. Holzapfel, T. Lanting, A. Lee, N. Halverson, E. Leitch, J. Leong, W. Lu, M. Lueker, J. Mehl, S. Meyer, J. Mohr, S. Padin, T. Plagge, C. Pryke, M. Runyan, D. Schwan, M. Sharp, H. Spieler, Z. Staniszewski, and A. Stark, “The south pole telescope,” Proc. SPIE 5498, 11–29 (2004).
[CrossRef]

Leong, J.

J. Ruhl, P. Ade, J. Carlstrom, H. Cho, T. Crawford, M. Dobbs, C. Greer, W. Holzapfel, T. Lanting, A. Lee, N. Halverson, E. Leitch, J. Leong, W. Lu, M. Lueker, J. Mehl, S. Meyer, J. Mohr, S. Padin, T. Plagge, C. Pryke, M. Runyan, D. Schwan, M. Sharp, H. Spieler, Z. Staniszewski, and A. Stark, “The south pole telescope,” Proc. SPIE 5498, 11–29 (2004).
[CrossRef]

Lu, W.

J. Ruhl, P. Ade, J. Carlstrom, H. Cho, T. Crawford, M. Dobbs, C. Greer, W. Holzapfel, T. Lanting, A. Lee, N. Halverson, E. Leitch, J. Leong, W. Lu, M. Lueker, J. Mehl, S. Meyer, J. Mohr, S. Padin, T. Plagge, C. Pryke, M. Runyan, D. Schwan, M. Sharp, H. Spieler, Z. Staniszewski, and A. Stark, “The south pole telescope,” Proc. SPIE 5498, 11–29 (2004).
[CrossRef]

Lueker, M.

J. Ruhl, P. Ade, J. Carlstrom, H. Cho, T. Crawford, M. Dobbs, C. Greer, W. Holzapfel, T. Lanting, A. Lee, N. Halverson, E. Leitch, J. Leong, W. Lu, M. Lueker, J. Mehl, S. Meyer, J. Mohr, S. Padin, T. Plagge, C. Pryke, M. Runyan, D. Schwan, M. Sharp, H. Spieler, Z. Staniszewski, and A. Stark, “The south pole telescope,” Proc. SPIE 5498, 11–29 (2004).
[CrossRef]

MacIntosh, M.

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

Maher, S.

J. Staguhn, C. Allen, D. Benford, E. Sharp, T. Ames, R. Arendt, D. Chuss, E. Dwek, A. Kovacs, S. Maher, C. Marx, T. Miller, S. Harvey Moseley, S. Navarro, A. Sievers, G. Voellmer, and E. Wollack, “GISMO, a 2 mm bolometer camera optimized for the study of high redshift galaxies,” J. Low Temp. Phys. 151, 709–714 (2008).
[CrossRef]

S. Dicker, B. Mason, P. Korngut, J. Abrahams, P. Ade, J. Aguirre, T. Ames, D. Benford, T. Chen, J. Chervenak, W. Cotton, M. Devlin, E. Figuero-Feliciano, K. Irwin, S. Maher, M. Mello, S. Moseley, J. Staguhn, R. Norrod, D. Tally, C. Tucker, B. Werner, and S. White, “MUSTANG. First light and current status,” in Infrared and Millimeter Waves, 2007, and the 2007 15th International Conference on Terahertz Electronics IRMMW-THz. Joint 32nd International Conference (IEEE, 2007), pp. 331–332.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, 1995).

Marx, C.

J. Staguhn, C. Allen, D. Benford, E. Sharp, T. Ames, R. Arendt, D. Chuss, E. Dwek, A. Kovacs, S. Maher, C. Marx, T. Miller, S. Harvey Moseley, S. Navarro, A. Sievers, G. Voellmer, and E. Wollack, “GISMO, a 2 mm bolometer camera optimized for the study of high redshift galaxies,” J. Low Temp. Phys. 151, 709–714 (2008).
[CrossRef]

Mason, B.

S. Dicker, B. Mason, P. Korngut, J. Abrahams, P. Ade, J. Aguirre, T. Ames, D. Benford, T. Chen, J. Chervenak, W. Cotton, M. Devlin, E. Figuero-Feliciano, K. Irwin, S. Maher, M. Mello, S. Moseley, J. Staguhn, R. Norrod, D. Tally, C. Tucker, B. Werner, and S. White, “MUSTANG. First light and current status,” in Infrared and Millimeter Waves, 2007, and the 2007 15th International Conference on Terahertz Electronics IRMMW-THz. Joint 32nd International Conference (IEEE, 2007), pp. 331–332.

McGregor, H.

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

Mehl, J.

J. Ruhl, P. Ade, J. Carlstrom, H. Cho, T. Crawford, M. Dobbs, C. Greer, W. Holzapfel, T. Lanting, A. Lee, N. Halverson, E. Leitch, J. Leong, W. Lu, M. Lueker, J. Mehl, S. Meyer, J. Mohr, S. Padin, T. Plagge, C. Pryke, M. Runyan, D. Schwan, M. Sharp, H. Spieler, Z. Staniszewski, and A. Stark, “The south pole telescope,” Proc. SPIE 5498, 11–29 (2004).
[CrossRef]

Mello, M.

S. Dicker, B. Mason, P. Korngut, J. Abrahams, P. Ade, J. Aguirre, T. Ames, D. Benford, T. Chen, J. Chervenak, W. Cotton, M. Devlin, E. Figuero-Feliciano, K. Irwin, S. Maher, M. Mello, S. Moseley, J. Staguhn, R. Norrod, D. Tally, C. Tucker, B. Werner, and S. White, “MUSTANG. First light and current status,” in Infrared and Millimeter Waves, 2007, and the 2007 15th International Conference on Terahertz Electronics IRMMW-THz. Joint 32nd International Conference (IEEE, 2007), pp. 331–332.

Meyer, S.

J. Ruhl, P. Ade, J. Carlstrom, H. Cho, T. Crawford, M. Dobbs, C. Greer, W. Holzapfel, T. Lanting, A. Lee, N. Halverson, E. Leitch, J. Leong, W. Lu, M. Lueker, J. Mehl, S. Meyer, J. Mohr, S. Padin, T. Plagge, C. Pryke, M. Runyan, D. Schwan, M. Sharp, H. Spieler, Z. Staniszewski, and A. Stark, “The south pole telescope,” Proc. SPIE 5498, 11–29 (2004).
[CrossRef]

Miller, T.

J. Staguhn, C. Allen, D. Benford, E. Sharp, T. Ames, R. Arendt, D. Chuss, E. Dwek, A. Kovacs, S. Maher, C. Marx, T. Miller, S. Harvey Moseley, S. Navarro, A. Sievers, G. Voellmer, and E. Wollack, “GISMO, a 2 mm bolometer camera optimized for the study of high redshift galaxies,” J. Low Temp. Phys. 151, 709–714 (2008).
[CrossRef]

Mitchell, G.

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

Mohr, J.

J. Ruhl, P. Ade, J. Carlstrom, H. Cho, T. Crawford, M. Dobbs, C. Greer, W. Holzapfel, T. Lanting, A. Lee, N. Halverson, E. Leitch, J. Leong, W. Lu, M. Lueker, J. Mehl, S. Meyer, J. Mohr, S. Padin, T. Plagge, C. Pryke, M. Runyan, D. Schwan, M. Sharp, H. Spieler, Z. Staniszewski, and A. Stark, “The south pole telescope,” Proc. SPIE 5498, 11–29 (2004).
[CrossRef]

Moseley, S.

D. Chuss, E. Wollack, S. Moseley, S. Withington, and G. Saklatvala, “Diffraction considerations for planar detectors in the few-mode limit,” Publ. Astron. Soc. Pac. 120, 430–438 (2008).
[CrossRef]

S. Dicker, B. Mason, P. Korngut, J. Abrahams, P. Ade, J. Aguirre, T. Ames, D. Benford, T. Chen, J. Chervenak, W. Cotton, M. Devlin, E. Figuero-Feliciano, K. Irwin, S. Maher, M. Mello, S. Moseley, J. Staguhn, R. Norrod, D. Tally, C. Tucker, B. Werner, and S. White, “MUSTANG. First light and current status,” in Infrared and Millimeter Waves, 2007, and the 2007 15th International Conference on Terahertz Electronics IRMMW-THz. Joint 32nd International Conference (IEEE, 2007), pp. 331–332.

Navarro, S.

J. Staguhn, C. Allen, D. Benford, E. Sharp, T. Ames, R. Arendt, D. Chuss, E. Dwek, A. Kovacs, S. Maher, C. Marx, T. Miller, S. Harvey Moseley, S. Navarro, A. Sievers, G. Voellmer, and E. Wollack, “GISMO, a 2 mm bolometer camera optimized for the study of high redshift galaxies,” J. Low Temp. Phys. 151, 709–714 (2008).
[CrossRef]

Naylor, D.

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

Ney, M.

M. Ney, “Method of moments as applied to electromagnetic problems,” IEEE Trans. Microwave Theory Tech. 33, 972–980 (1985).
[CrossRef]

Norrod, R.

S. Dicker, B. Mason, P. Korngut, J. Abrahams, P. Ade, J. Aguirre, T. Ames, D. Benford, T. Chen, J. Chervenak, W. Cotton, M. Devlin, E. Figuero-Feliciano, K. Irwin, S. Maher, M. Mello, S. Moseley, J. Staguhn, R. Norrod, D. Tally, C. Tucker, B. Werner, and S. White, “MUSTANG. First light and current status,” in Infrared and Millimeter Waves, 2007, and the 2007 15th International Conference on Terahertz Electronics IRMMW-THz. Joint 32nd International Conference (IEEE, 2007), pp. 331–332.

Padin, S.

J. Ruhl, P. Ade, J. Carlstrom, H. Cho, T. Crawford, M. Dobbs, C. Greer, W. Holzapfel, T. Lanting, A. Lee, N. Halverson, E. Leitch, J. Leong, W. Lu, M. Lueker, J. Mehl, S. Meyer, J. Mohr, S. Padin, T. Plagge, C. Pryke, M. Runyan, D. Schwan, M. Sharp, H. Spieler, Z. Staniszewski, and A. Stark, “The south pole telescope,” Proc. SPIE 5498, 11–29 (2004).
[CrossRef]

Parkes, W.

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

Peacocke, T.

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

Piccirillo, L.

M. Audley, R. Barker, M. Crane, R. Dace, D. Glowacka, D. Goldie, A. Lasenby, H. Stevenson, V. Tsaneva, S. Withington, P. Grimes, B. Johnson, G. Yassin, L. Piccirillo, G. Pisano, W. Duncan, G. Hilton, K. Irwin, C. Reintsema, and M. Halpern, “TES imaging array technology for CLOVER,” Proc. SPIE 6275, 24–32 (2006).

Pisano, G.

M. Audley, R. Barker, M. Crane, R. Dace, D. Glowacka, D. Goldie, A. Lasenby, H. Stevenson, V. Tsaneva, S. Withington, P. Grimes, B. Johnson, G. Yassin, L. Piccirillo, G. Pisano, W. Duncan, G. Hilton, K. Irwin, C. Reintsema, and M. Halpern, “TES imaging array technology for CLOVER,” Proc. SPIE 6275, 24–32 (2006).

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

Plagge, T.

J. Ruhl, P. Ade, J. Carlstrom, H. Cho, T. Crawford, M. Dobbs, C. Greer, W. Holzapfel, T. Lanting, A. Lee, N. Halverson, E. Leitch, J. Leong, W. Lu, M. Lueker, J. Mehl, S. Meyer, J. Mohr, S. Padin, T. Plagge, C. Pryke, M. Runyan, D. Schwan, M. Sharp, H. Spieler, Z. Staniszewski, and A. Stark, “The south pole telescope,” Proc. SPIE 5498, 11–29 (2004).
[CrossRef]

Pontoppidan, K.

K. Pontoppidan, “GRASP9 technical description,” TICRA Engineering Consultants, www.ticra.com..

Pryke, C.

J. Ruhl, P. Ade, J. Carlstrom, H. Cho, T. Crawford, M. Dobbs, C. Greer, W. Holzapfel, T. Lanting, A. Lee, N. Halverson, E. Leitch, J. Leong, W. Lu, M. Lueker, J. Mehl, S. Meyer, J. Mohr, S. Padin, T. Plagge, C. Pryke, M. Runyan, D. Schwan, M. Sharp, H. Spieler, Z. Staniszewski, and A. Stark, “The south pole telescope,” Proc. SPIE 5498, 11–29 (2004).
[CrossRef]

Reintsema, C.

M. Audley, R. Barker, M. Crane, R. Dace, D. Glowacka, D. Goldie, A. Lasenby, H. Stevenson, V. Tsaneva, S. Withington, P. Grimes, B. Johnson, G. Yassin, L. Piccirillo, G. Pisano, W. Duncan, G. Hilton, K. Irwin, C. Reintsema, and M. Halpern, “TES imaging array technology for CLOVER,” Proc. SPIE 6275, 24–32 (2006).

Robson, I.

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

Ruhl, J.

J. Ruhl, P. Ade, J. Carlstrom, H. Cho, T. Crawford, M. Dobbs, C. Greer, W. Holzapfel, T. Lanting, A. Lee, N. Halverson, E. Leitch, J. Leong, W. Lu, M. Lueker, J. Mehl, S. Meyer, J. Mohr, S. Padin, T. Plagge, C. Pryke, M. Runyan, D. Schwan, M. Sharp, H. Spieler, Z. Staniszewski, and A. Stark, “The south pole telescope,” Proc. SPIE 5498, 11–29 (2004).
[CrossRef]

Runyan, M.

J. Ruhl, P. Ade, J. Carlstrom, H. Cho, T. Crawford, M. Dobbs, C. Greer, W. Holzapfel, T. Lanting, A. Lee, N. Halverson, E. Leitch, J. Leong, W. Lu, M. Lueker, J. Mehl, S. Meyer, J. Mohr, S. Padin, T. Plagge, C. Pryke, M. Runyan, D. Schwan, M. Sharp, H. Spieler, Z. Staniszewski, and A. Stark, “The south pole telescope,” Proc. SPIE 5498, 11–29 (2004).
[CrossRef]

Saklatvala, G.

D. Chuss, E. Wollack, S. Moseley, S. Withington, and G. Saklatvala, “Diffraction considerations for planar detectors in the few-mode limit,” Publ. Astron. Soc. Pac. 120, 430–438 (2008).
[CrossRef]

G. Saklatvala, S. Withington, and M. Hobson, “Coupled-mode theory for infrared and submillimeter wave detectors,” J. Opt. Soc. Am. A 24, 764–775 (2007).
[CrossRef]

S. Withington and G. Saklatvala, “Characterizing the behavior of partially coherent detectors through spatio-temporal modes,” J. Opt. A, Pure Appl. Opt. 9, 626–633 (2007).
[CrossRef]

Schwan, D.

J. Ruhl, P. Ade, J. Carlstrom, H. Cho, T. Crawford, M. Dobbs, C. Greer, W. Holzapfel, T. Lanting, A. Lee, N. Halverson, E. Leitch, J. Leong, W. Lu, M. Lueker, J. Mehl, S. Meyer, J. Mohr, S. Padin, T. Plagge, C. Pryke, M. Runyan, D. Schwan, M. Sharp, H. Spieler, Z. Staniszewski, and A. Stark, “The south pole telescope,” Proc. SPIE 5498, 11–29 (2004).
[CrossRef]

Sharp, E.

J. Staguhn, C. Allen, D. Benford, E. Sharp, T. Ames, R. Arendt, D. Chuss, E. Dwek, A. Kovacs, S. Maher, C. Marx, T. Miller, S. Harvey Moseley, S. Navarro, A. Sievers, G. Voellmer, and E. Wollack, “GISMO, a 2 mm bolometer camera optimized for the study of high redshift galaxies,” J. Low Temp. Phys. 151, 709–714 (2008).
[CrossRef]

Sharp, M.

J. Ruhl, P. Ade, J. Carlstrom, H. Cho, T. Crawford, M. Dobbs, C. Greer, W. Holzapfel, T. Lanting, A. Lee, N. Halverson, E. Leitch, J. Leong, W. Lu, M. Lueker, J. Mehl, S. Meyer, J. Mohr, S. Padin, T. Plagge, C. Pryke, M. Runyan, D. Schwan, M. Sharp, H. Spieler, Z. Staniszewski, and A. Stark, “The south pole telescope,” Proc. SPIE 5498, 11–29 (2004).
[CrossRef]

Sievers, A.

J. Staguhn, C. Allen, D. Benford, E. Sharp, T. Ames, R. Arendt, D. Chuss, E. Dwek, A. Kovacs, S. Maher, C. Marx, T. Miller, S. Harvey Moseley, S. Navarro, A. Sievers, G. Voellmer, and E. Wollack, “GISMO, a 2 mm bolometer camera optimized for the study of high redshift galaxies,” J. Low Temp. Phys. 151, 709–714 (2008).
[CrossRef]

Smith, I.

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

Spieler, H.

J. Ruhl, P. Ade, J. Carlstrom, H. Cho, T. Crawford, M. Dobbs, C. Greer, W. Holzapfel, T. Lanting, A. Lee, N. Halverson, E. Leitch, J. Leong, W. Lu, M. Lueker, J. Mehl, S. Meyer, J. Mohr, S. Padin, T. Plagge, C. Pryke, M. Runyan, D. Schwan, M. Sharp, H. Spieler, Z. Staniszewski, and A. Stark, “The south pole telescope,” Proc. SPIE 5498, 11–29 (2004).
[CrossRef]

Staguhn, J.

J. Staguhn, C. Allen, D. Benford, E. Sharp, T. Ames, R. Arendt, D. Chuss, E. Dwek, A. Kovacs, S. Maher, C. Marx, T. Miller, S. Harvey Moseley, S. Navarro, A. Sievers, G. Voellmer, and E. Wollack, “GISMO, a 2 mm bolometer camera optimized for the study of high redshift galaxies,” J. Low Temp. Phys. 151, 709–714 (2008).
[CrossRef]

S. Dicker, B. Mason, P. Korngut, J. Abrahams, P. Ade, J. Aguirre, T. Ames, D. Benford, T. Chen, J. Chervenak, W. Cotton, M. Devlin, E. Figuero-Feliciano, K. Irwin, S. Maher, M. Mello, S. Moseley, J. Staguhn, R. Norrod, D. Tally, C. Tucker, B. Werner, and S. White, “MUSTANG. First light and current status,” in Infrared and Millimeter Waves, 2007, and the 2007 15th International Conference on Terahertz Electronics IRMMW-THz. Joint 32nd International Conference (IEEE, 2007), pp. 331–332.

Staniszewski, Z.

J. Ruhl, P. Ade, J. Carlstrom, H. Cho, T. Crawford, M. Dobbs, C. Greer, W. Holzapfel, T. Lanting, A. Lee, N. Halverson, E. Leitch, J. Leong, W. Lu, M. Lueker, J. Mehl, S. Meyer, J. Mohr, S. Padin, T. Plagge, C. Pryke, M. Runyan, D. Schwan, M. Sharp, H. Spieler, Z. Staniszewski, and A. Stark, “The south pole telescope,” Proc. SPIE 5498, 11–29 (2004).
[CrossRef]

Stark, A.

J. Ruhl, P. Ade, J. Carlstrom, H. Cho, T. Crawford, M. Dobbs, C. Greer, W. Holzapfel, T. Lanting, A. Lee, N. Halverson, E. Leitch, J. Leong, W. Lu, M. Lueker, J. Mehl, S. Meyer, J. Mohr, S. Padin, T. Plagge, C. Pryke, M. Runyan, D. Schwan, M. Sharp, H. Spieler, Z. Staniszewski, and A. Stark, “The south pole telescope,” Proc. SPIE 5498, 11–29 (2004).
[CrossRef]

Stevenson, H.

M. Audley, R. Barker, M. Crane, R. Dace, D. Glowacka, D. Goldie, A. Lasenby, H. Stevenson, V. Tsaneva, S. Withington, P. Grimes, B. Johnson, G. Yassin, L. Piccirillo, G. Pisano, W. Duncan, G. Hilton, K. Irwin, C. Reintsema, and M. Halpern, “TES imaging array technology for CLOVER,” Proc. SPIE 6275, 24–32 (2006).

Sudiwala, R.

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

Tally, D.

S. Dicker, B. Mason, P. Korngut, J. Abrahams, P. Ade, J. Aguirre, T. Ames, D. Benford, T. Chen, J. Chervenak, W. Cotton, M. Devlin, E. Figuero-Feliciano, K. Irwin, S. Maher, M. Mello, S. Moseley, J. Staguhn, R. Norrod, D. Tally, C. Tucker, B. Werner, and S. White, “MUSTANG. First light and current status,” in Infrared and Millimeter Waves, 2007, and the 2007 15th International Conference on Terahertz Electronics IRMMW-THz. Joint 32nd International Conference (IEEE, 2007), pp. 331–332.

Tham, C.

S. Withington, C. Tham, and G. Yassin, “Theoretical analysis of planar bolometric arrays for thz imaging systems,” Proc. SPIE 4855, 49–62 (2003).
[CrossRef]

Thomas, C.

C. Thomas and S. Withington, “Electromagnetic simulations of the partially coherent optical behaviour of resistive film TES detectors,” presented at the 21st International Symposium on Space Terahertz Technology, Oxford, UK, 23–25 March 2010.

S. Withington and C. Thomas, “Optical theory of partially coherent thin-film energy-absorbing structures for power detectors and imaging arrays,” J. Opt. Soc. Am. A 26, 1382–1392 (2009).
[CrossRef]

Tsaneva, V.

M. Audley, R. Barker, M. Crane, R. Dace, D. Glowacka, D. Goldie, A. Lasenby, H. Stevenson, V. Tsaneva, S. Withington, P. Grimes, B. Johnson, G. Yassin, L. Piccirillo, G. Pisano, W. Duncan, G. Hilton, K. Irwin, C. Reintsema, and M. Halpern, “TES imaging array technology for CLOVER,” Proc. SPIE 6275, 24–32 (2006).

Tucker, C.

S. Dicker, B. Mason, P. Korngut, J. Abrahams, P. Ade, J. Aguirre, T. Ames, D. Benford, T. Chen, J. Chervenak, W. Cotton, M. Devlin, E. Figuero-Feliciano, K. Irwin, S. Maher, M. Mello, S. Moseley, J. Staguhn, R. Norrod, D. Tally, C. Tucker, B. Werner, and S. White, “MUSTANG. First light and current status,” in Infrared and Millimeter Waves, 2007, and the 2007 15th International Conference on Terahertz Electronics IRMMW-THz. Joint 32nd International Conference (IEEE, 2007), pp. 331–332.

Ullom, J.

M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

Voellmer, G.

J. Staguhn, C. Allen, D. Benford, E. Sharp, T. Ames, R. Arendt, D. Chuss, E. Dwek, A. Kovacs, S. Maher, C. Marx, T. Miller, S. Harvey Moseley, S. Navarro, A. Sievers, G. Voellmer, and E. Wollack, “GISMO, a 2 mm bolometer camera optimized for the study of high redshift galaxies,” J. Low Temp. Phys. 151, 709–714 (2008).
[CrossRef]

Walker, I.

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M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

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S. Dicker, B. Mason, P. Korngut, J. Abrahams, P. Ade, J. Aguirre, T. Ames, D. Benford, T. Chen, J. Chervenak, W. Cotton, M. Devlin, E. Figuero-Feliciano, K. Irwin, S. Maher, M. Mello, S. Moseley, J. Staguhn, R. Norrod, D. Tally, C. Tucker, B. Werner, and S. White, “MUSTANG. First light and current status,” in Infrared and Millimeter Waves, 2007, and the 2007 15th International Conference on Terahertz Electronics IRMMW-THz. Joint 32nd International Conference (IEEE, 2007), pp. 331–332.

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S. Dicker, B. Mason, P. Korngut, J. Abrahams, P. Ade, J. Aguirre, T. Ames, D. Benford, T. Chen, J. Chervenak, W. Cotton, M. Devlin, E. Figuero-Feliciano, K. Irwin, S. Maher, M. Mello, S. Moseley, J. Staguhn, R. Norrod, D. Tally, C. Tucker, B. Werner, and S. White, “MUSTANG. First light and current status,” in Infrared and Millimeter Waves, 2007, and the 2007 15th International Conference on Terahertz Electronics IRMMW-THz. Joint 32nd International Conference (IEEE, 2007), pp. 331–332.

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C. Thomas and S. Withington, “Electromagnetic simulations of the partially coherent optical behaviour of resistive film TES detectors,” presented at the 21st International Symposium on Space Terahertz Technology, Oxford, UK, 23–25 March 2010.

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D. Chuss, E. Wollack, S. Moseley, S. Withington, and G. Saklatvala, “Diffraction considerations for planar detectors in the few-mode limit,” Publ. Astron. Soc. Pac. 120, 430–438 (2008).
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M. Audley, W. Holland, W. Duncan, D. Atkinson, M. Cliffe, M. Ellis, X. Gao, D. Gostick, T. Hodson, D. Kelly, M. MacIntosh, H. McGregor, T. Peacocke, I. Robson, I. Smith, K. Irwin, G. Hilton, J. Ullom, A. Walton, C. Dunare, W. Parkes, P. Ade, D. Bintley, F. Gannaway, M. Griffin, G. Pisano, R. Sudiwala, I. Walker, A. Woodcroft, M. Fich, M. Halpern, G. Mitchell, D. Naylor, and P. Bastien, “SCUBA-2: A large-format TES array for submillimetre astronomy,” Nucl. Instrum. Methods Phys. Res. A 520, 479–482 (2004).
[CrossRef]

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M. Audley, R. Barker, M. Crane, R. Dace, D. Glowacka, D. Goldie, A. Lasenby, H. Stevenson, V. Tsaneva, S. Withington, P. Grimes, B. Johnson, G. Yassin, L. Piccirillo, G. Pisano, W. Duncan, G. Hilton, K. Irwin, C. Reintsema, and M. Halpern, “TES imaging array technology for CLOVER,” Proc. SPIE 6275, 24–32 (2006).

S. Withington, C. Tham, and G. Yassin, “Theoretical analysis of planar bolometric arrays for thz imaging systems,” Proc. SPIE 4855, 49–62 (2003).
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J. Staguhn, C. Allen, D. Benford, E. Sharp, T. Ames, R. Arendt, D. Chuss, E. Dwek, A. Kovacs, S. Maher, C. Marx, T. Miller, S. Harvey Moseley, S. Navarro, A. Sievers, G. Voellmer, and E. Wollack, “GISMO, a 2 mm bolometer camera optimized for the study of high redshift galaxies,” J. Low Temp. Phys. 151, 709–714 (2008).
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J. Opt. A, Pure Appl. Opt.

S. Withington and G. Saklatvala, “Characterizing the behavior of partially coherent detectors through spatio-temporal modes,” J. Opt. A, Pure Appl. Opt. 9, 626–633 (2007).
[CrossRef]

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J. Opt. Soc. Am. A

Nucl. Instrum. Methods Phys. Res. A

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[CrossRef]

Proc. SPIE

M. Audley, R. Barker, M. Crane, R. Dace, D. Glowacka, D. Goldie, A. Lasenby, H. Stevenson, V. Tsaneva, S. Withington, P. Grimes, B. Johnson, G. Yassin, L. Piccirillo, G. Pisano, W. Duncan, G. Hilton, K. Irwin, C. Reintsema, and M. Halpern, “TES imaging array technology for CLOVER,” Proc. SPIE 6275, 24–32 (2006).

J. Ruhl, P. Ade, J. Carlstrom, H. Cho, T. Crawford, M. Dobbs, C. Greer, W. Holzapfel, T. Lanting, A. Lee, N. Halverson, E. Leitch, J. Leong, W. Lu, M. Lueker, J. Mehl, S. Meyer, J. Mohr, S. Padin, T. Plagge, C. Pryke, M. Runyan, D. Schwan, M. Sharp, H. Spieler, Z. Staniszewski, and A. Stark, “The south pole telescope,” Proc. SPIE 5498, 11–29 (2004).
[CrossRef]

S. Withington, C. Tham, and G. Yassin, “Theoretical analysis of planar bolometric arrays for thz imaging systems,” Proc. SPIE 4855, 49–62 (2003).
[CrossRef]

Publ. Astron. Soc. Pac.

D. Chuss, E. Wollack, S. Moseley, S. Withington, and G. Saklatvala, “Diffraction considerations for planar detectors in the few-mode limit,” Publ. Astron. Soc. Pac. 120, 430–438 (2008).
[CrossRef]

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S. Dicker, B. Mason, P. Korngut, J. Abrahams, P. Ade, J. Aguirre, T. Ames, D. Benford, T. Chen, J. Chervenak, W. Cotton, M. Devlin, E. Figuero-Feliciano, K. Irwin, S. Maher, M. Mello, S. Moseley, J. Staguhn, R. Norrod, D. Tally, C. Tucker, B. Werner, and S. White, “MUSTANG. First light and current status,” in Infrared and Millimeter Waves, 2007, and the 2007 15th International Conference on Terahertz Electronics IRMMW-THz. Joint 32nd International Conference (IEEE, 2007), pp. 331–332.

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Figures (8)

Fig. 1
Fig. 1

Ideal imaging system with a free-space bolometer.

Fig. 2
Fig. 2

(a) Sampling points in the k-domain. (b) Corresponding sampling points in the spatial domain. In each case the total number of points is the same. The gray area in (a) indicates the region of the k-plane where the modes are non-zero.

Fig. 3
Fig. 3

Responsivity, R ( r t ) , of the optical system shown in Fig. 1 to power in the different Stoke’s components of the field for values of p λ in the range 0.25–4.0. In each plot, the positive x-direction is horizontal from left to right, and the positive y-direction vertical from bottom to top. The small black square is the re-imaged pixel. For each value of p λ , all four plots are normalized to the peak value in the corresponding I plot. Each set of U , Q and V plots uses the same color scale, but the scale’s range changes with p λ .  

Fig. 4
Fig. 4

Spectra of mode coefficients for different values of p λ . In (a) and (b) the coefficients, γ n , have been scaled by 1 ( α p 2 ) ; in (c) the coefficients have been scaled by 1 γ n to indicate relative contribution.

Fig. 5
Fig. 5

Contributions from the three coherent modes with the largest eigenvalues to the Stokes parameters of the reception pattern when p λ = 0.25 . The small black square is the re-imaged pixel. All plots are normalized to the peak flux in the Stokes I of the full field. The Stokes parameters are plotted against a single color scale to emphasize their relative contributions.

Fig. 6
Fig. 6

Normalized coefficients, γ n γ n , of the far-field optical modes.

Fig. 7
Fig. 7

Diagonal elements of A m n as a function of p λ for a volumetric absorber. The ratio n A n n m γ m can be calculated for a particular value of p λ by summing the contributions from each line. This ratio provides a measure of how well the dipole model describes the behavior of the absorber, and is equal to unity when the description is complete.

Fig. 8
Fig. 8

Diagonal elements of A m n as a function of p λ for the resistive film absorber.

Equations (66)

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E ̿ D ( r t 1 , r t 2 , ω ) = E D ( r t 1 , ω ) E D * ( r t 2 , ω ) ,
p ( ω ) = D d 2 r t 1 D d 2 r t 2 D ̿ D ( r t 1 , r t 2 , ω ) E ̿ D ( r t 1 , r t 2 , ω ) ,
E ̿ D ( r t 1 , r t 2 , ω ) = n λ ( n ) U ( n ) ( r t 1 , ω ) U ( n ) * ( r t 2 , ω ) .
p ( ω ) = m , n γ ( m ) λ ( n ) | F d 2 r t R ( m ) * ( r t , ω ) U ( n ) ( r t , ω ) | 2 .
p ( ω ) = F d 2 r t 1 F d 2 r t 2 D ̿ F ( r t 1 , r t 2 , ω ) E ̿ P ( r t 1 , r t 2 , ω ) ,
A ( k t , ω ) = 1 2 π S d 2 r t E S ( r t , ω ) exp ( i k t r t ) ,
E P ( r t , ω ) = 1 2 π | k t | < ω c d 2 k t ( I ̿ k ̂ k ̂ ) A ( k t , ω ) exp ( i k t r t ) ,
E ̿ P ( r t 1 , r t 2 , ω ) = 1 ( 2 π ) 2 | k t | < ω c d 2 k t 1 | k t | < ω c d 2 k t 2 exp ( i k t 1 r t 1 ) exp ( i k t 2 r t 2 ) ( I ̿ k ̂ 1 k ̂ 1 ) A ̿ ( k t 1 , k t 2 , ω ) ( I ̿ k ̂ 2 k ̂ 2 ) ,
p ( ω ) = | k t | < ω c d 2 k t 1 | k t | < ω c d 2 k t 2 [ ( I ̿ k ̂ 1 k ̂ 1 ) G ̿ ( k t 1 , k t 2 , ω ) ( I ̿ k ̂ 2 k ̂ 2 ) ] A ̿ ( k t 1 , k t 2 , ω ) .
G ̿ ( k t 1 , k t 2 , ω ) = 1 ( 2 π ) 2 F d 2 r t 1 F d 2 r t 2 D ̿ F ( r t 1 , r t 2 , ω ) exp ( i k t 1 r t 1 ) exp ( + i k t 2 r t 2 ) .
p ( ω ) = S d 2 r t 1 S d 2 r t 2 D ̿ S ( r t 1 , r t 2 , ω ) E ̿ S ( r t 1 , r t 2 , ω ) ,
D ̿ S ( r t 1 , r t 2 , ω ) = 1 ( 2 π ) 2 | k t | < ω c d 2 k t 1 | k t | < ω c d 2 k t 2 ( I ̿ k ̂ 1 k ̂ 1 ) G ̿ ( k t 1 , k t 2 , ω ) ( I ̿ k ̂ 2 k ̂ 2 ) exp ( i k t 1 r t 1 ) exp ( i k t 2 r t 2 ) .
E ̿ S ( r t 1 , r t 2 , ω ) = i , j = 1 2 E i j ( r t 1 , r t 2 , ω ) x ̂ i x ̂ j δ ( r t 1 r t 2 ) ,
p ( ω ) = i , j = 1 2 S d 2 r t D i j * ( r t , r t , ω ) E i j ( r t , r t , ω ) .
{ σ ( 1 ) = ( 1 0 0 1 ) , σ ( 2 ) = ( 1 0 0 1 ) , }
{ σ ( 3 ) = ( 0 1 1 0 ) , σ ( 4 ) = ( 0 i i 0 ) } ,
E i j ( r t , r t , ω ) = 1 2 k = 1 4 χ ( k ) ( r t , ω ) σ i j ( k ) ,
χ ( k ) ( r t , ω ) = i , j = 1 2 E i j ( r t , r t , ω ) σ j i ( k ) .
p ( ω ) = S d 2 r t R * ( r t , ω ) χ ( r t , ω ) ,
R ( k ) ( r t , ω ) = 1 2 i , j = 1 2 D i j ( r t , r t , ω ) σ j i ( k ) ,
D ̿ F ( r t 1 , r t 1 , ω ) = { α I ̿ δ ( r t 1 r t 1 ) , | x 1 | , | x 2 | , | y 1 | , | y 2 | p 2 0 ̿ , elsewhere } .
D ̿ S ( r t 1 , r t 1 , ω ) = 1 ( 2 π ) 2 d 2 k t 1 d 2 k t 2 M ̿ ( k t 1 , k t 2 , ω ) exp ( i k t 1 r t 1 ) exp ( + i k t 2 r t 2 ) ,
M ̿ ( k t 1 , k t 2 , ω ) = H ( ω c | k t 1 | ) H ( ω c | k t 2 | ) α ( I ̿ k ̂ 1 k ̂ 1 ) ( I ̿ k ̂ 2 k ̂ 2 ) S ( k t 1 , k t 2 , ω ) ,
S ( k t 1 , k t 2 , ω ) = 1 ( 2 π ) 2 A d 2 r t exp ( i ( k t 1 k t 2 ) r t )
S ( k t 1 , k t 2 , ω ) = 1 ( 2 π ) 2 [ p 2 p 2 d x exp ( i ( k t 1 k t 2 ) x ̂ x ) ] × [ p 2 p 2 d y exp ( i ( k t 1 k t 2 ) y ̂ y ) ] = ( p 2 π ) 2 sinc [ p 2 π ( k t 2 k t 1 ) x ̂ ] × sinc [ p 2 π ( k t 2 k t 1 ) y ̂ ] ,
M ̿ ( k t 1 , k t 2 , ω ) = n γ ( n ) V ( n ) ( k t 1 , ω ) V ( n ) * ( k t 2 , ω ) ,
d 2 k t 2 M ̿ ( k t 1 , k t 2 , ω ) V ( n ) ( k t 2 , ω ) = γ ( n ) V ( n ) ( k t 1 , ω ) .
D ̿ S ( r t 1 , r t 2 , ω ) = n γ ( n ) U ( n ) ( r t , ω ) U ( n ) * ( r t , ω ) .
U ( n ) ( r t , ω ) = 1 2 π d 2 k t V ( n ) ( k t , ω ) exp ( i k t r t ) .
S d 2 r t D ̿ S ( r t 1 , r t 2 , ω ) U ( n ) ( r t 2 , ω ) = γ ( n ) U ( n ) ( r t 1 , ω ) ,
{ s = 1 N u = 1 3 ( 2 π L ) 2 [ x ̂ q M ̿ ( k t ( r ) , k t ( s ) , ω ) x ̂ u ] [ x ̂ u V ( n ) ( k t ( s ) , ω ) ] = γ ( n ) [ x ̂ q V ( n ) ( k t ( r ) , ω ) ] } ,
j = 1 3 N M i j V j ( n ) = γ ( n ) V i ( n ) ;
E D ( r t , ω ) = 1 2 π d 2 k t W ( k t , ω ) exp ( i k t r t ) ,
p ( ω ) = d 2 k t 1 d 2 k t 2 G ̿ ( k t 1 , k t 2 , ω ) W ̿ ( k t 1 , k t 2 , ω ) ,
W ̿ ( k t 1 , k t 2 , ω ) = W ( k t 1 , ω ) W * ( k t 2 , ω ) .
k t = k ( x ̂ x ̂ + y ̂ y ̂ ) Ω ̂ = k I ̿ t Ω ̂ ;
d 2 k t = k 2 ( z ̂ Ω ̂ ) d Ω .
p ( ω ) = d Ω 1 d Ω 2 A ̿ e ( Ω ̂ 1 , Ω ̂ 2 , ω ) B ̿ ( Ω ̂ 1 , Ω ̂ 2 , ω ) ,
B ̿ ( Ω ̂ 1 , Ω ̂ 2 , ω ) = k 4 ( z ̂ Ω ̂ 1 ) ( z ̂ Ω ̂ 2 ) 2 ( 2 π ) 2 Z 0 W ̿ ( k I ̿ t Ω ̂ 1 , k I ̿ t Ω ̂ 2 , ω ) ,
A ̿ e ( Ω ̂ 1 , Ω ̂ 2 , ω ) = 2 ( 2 π ) 2 Z 0 G ̿ ( k I ̿ t Ω ̂ 1 , k I ̿ t Ω ̂ 2 , ω ) .
B ̿ ( Ω ̂ 1 , Ω ̂ 2 , ω ) = 1 2 ( I ̿ Ω ̂ 1 Ω ̂ 1 ) B ( Ω ̂ 1 , ω ) δ ( Ω ̂ 1 Ω ̂ 2 ) ,
p ( ω ) = 1 2 d Ω [ A ̿ e ( Ω ̂ , Ω ̂ , ω ) ( I ̿ Ω ̂ Ω ̂ ) ] B ( Ω ̂ , ω ) ,
p ( ω ) = d Ω A e ( Ω ̂ , ω ) B ( Ω ̂ , ω ) ,
d Ω 2 A ̿ e ( Ω ̂ 1 ; Ω ̂ 2 , ω ) U ( n ) ( Ω ̂ 2 , ω ) = γ ( n ) U ( n ) ( Ω ̂ 1 , ω ) .
0 π d θ 2 0 2 π d ϕ 2 sin θ 2 A ̿ e ( θ 1 , ϕ 1 ; θ 2 , ϕ 2 ) U ( n ) ( θ 2 , ϕ 2 ) = γ ( n ) U ( n ) ( θ 1 , ϕ 1 ) ,
1 + 1 d u 2 0 2 π d ϕ 2 A ̿ e ( θ ( u 1 ) , ϕ 1 ; θ ( u 2 ) , ϕ 2 ) U ( n ) ( θ ( u 2 ) , ϕ 2 ) = λ ( n ) U ( n ) ( θ ( u 1 ) , ϕ 1 ) .
A ̿ e ( Ω ̂ 1 , Ω ̂ 2 ; ω ) = 2 α p 2 Z 0 I ̿ sinc [ p λ ( Ω ̂ 1 Ω ̂ 2 ) x ̂ ] × sinc [ p λ ( Ω ̂ 1 Ω ̂ 2 ) y ̂ ] ,
A ̿ e ( Ω ̂ 1 , Ω ̂ 2 , ω ) m n A m n ( ω ) D m ( Ω ̂ 1 ) D n * ( Ω ̂ 2 ) ,
A m n ( ω ) = d Ω 1 d Ω 2 D m * ( Ω ̂ 1 ) A ̿ e ( Ω ̂ 1 , Ω ̂ 2 , ω ) D n ( Ω ̂ 2 ) .
m γ m = d Ω I ̿ A ̿ e ( Ω ̂ , Ω ̂ , ω ) = 16 π α p 2 Z 0 .
M x ( θ , ϕ ) = N ( sin ϕ θ ̂ + cos θ cos ϕ ϕ ̂ ) ,
M y ( θ , ϕ ) = N ( cos ϕ θ ̂ + cos θ sin ϕ ϕ ̂ ) ,
M z ( θ , ϕ ) = N sin θ ϕ ̂ ,
E x ( θ , ϕ ) = N ( cos θ cos ϕ θ ̂ sin ϕ ϕ ̂ ) ,
E y ( θ , ϕ ) = N ( cos θ sin ϕ θ ̂ + cos ϕ ϕ ̂ ) ,
E z ( θ , ϕ ) = N sin θ θ ̂ .
T ̿ = ( θ ̂ 1 θ ̂ 1 + ϕ ̂ 1 ϕ ̂ 1 ) ( θ ̂ 2 θ ̂ 2 + ϕ ̂ 2 ϕ ̂ 2 ) = [ cos θ 1 cos θ 2 cos ( ϕ 1 ϕ 2 ) + sin θ 1 sin θ 2 ] θ ̂ 1 θ ̂ 2 + cos θ 1 sin ( ϕ 1 ϕ 2 ) θ ̂ 1 ϕ ̂ 2 + cos θ 2 sin ( ϕ 2 ϕ 1 ) ϕ ̂ 1 θ ̂ 2 + cos ( ϕ 1 ϕ 2 ) ϕ ̂ 1 ϕ ̂ 2 .
A m n ( ω ) = 0 π d θ 1 0 π d θ 2 0 2 π d ϕ 1 0 2 π d ϕ 2 sin θ 1 sin θ 2 D m * ( θ 1 , ϕ 1 ) A ̿ e ( θ 1 , ϕ 1 ; θ 2 , ϕ 2 ; ω ) D n ( θ 2 , ϕ 2 ) .
A m n ( ω ) 16 π α p 2 Z 0 1 8 π 0 π d θ 1 0 π d θ 2 0 2 π d ϕ 1 0 2 π d ϕ 2 sin θ 1 sin θ 2 D m * ( θ 1 , ϕ 1 ) D n ( θ 2 , ϕ 2 ) .
p ( ω ) = 1 2 p 2 p 2 d x p 2 p 2 d y R s | J s ( x , y ) | 2 .
E s ( z ) = ( Z 0 2 ) J s exp ( i k | z | ) .
( R s + Z 0 2 ) | J s | = | E | .
J s ( x , y ) = 1 ( R s + Z 0 2 ) ( I ̿ z ̂ z ̂ ) E ( x , y ) .
p ( ω ) = 1 2 R s ( R s + Z 0 2 ) 2 p 2 p 2 d x 1 p 2 p 2 d y 1 p 2 p 2 d x 2 p 2 p 2 d y 2 [ ( I ̿ z ̂ z ̂ ) ( I ̿ z ̂ z ̂ ) δ ( x 1 x 2 ) δ ( y 1 y 2 ) ] E ( x 1 , y 1 ) E * ( x 2 , y 2 ) ,
D ̿ ( r t 1 ; r t 2 ; ω ) = { 1 2 R s ( R s + Z 0 2 ) 2 ( I ̿ z ̂ 1 z ̂ 1 ) ( I ̿ z ̂ 2 z ̂ 2 ) δ ( r t 1 r t 2 ) , r t 1 and r t 2 on film 0 ̿ , otherwise } .
( I ̿ z ̂ 1 z ̂ 1 ) ( I ̿ z ̂ 2 z ̂ 2 ) = cos θ 1 cos θ 2 cos ( ϕ 1 ϕ 2 ) θ ̂ 1 θ ̂ 2 + cos θ 1 sin ( ϕ 1 ϕ 2 ) θ ̂ 1 ϕ ̂ 2 + cos θ 2 sin ( ϕ 2 ϕ 1 ) ϕ ̂ 1 θ ̂ 2 + cos ( ϕ 1 ϕ 2 ) ϕ ̂ 1 ϕ ̂ 2 ,

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