Abstract

A new technique for determining the surface figure of large submillimeter wavelength telescopes is presented, which is based on measuring the telescope’s focal plane diffraction pattern with a shearing interferometer. In addition to the instrumental theory, results obtained using such an interferometer on the 10.4-m diam telescope of the Caltech Submillimeter Observatory are discussed. Using wavelengths near 1 mm, a measurement accuracy of 9 μm, or λ/115, has been achieved, and the rms surface accuracy has been determined to be just under 30 μm. The distortions of the primary reflector with changing elevation angle have also been measured and agree well with theoretical predictions of the dish deformation.

© 1991 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. Sweet, “New Radiotelescopes Open Era of Submillimeter Astronomy,” Phys. Today 40, 65–67 (1987).
    [CrossRef]
  2. J. C. Bennett, A. P. Anderson, P. A. McInnes, “Microwave Holographic Metrology of Large Reflector Antennas,” IEEE Trans. Antennas Propag. AP-24, 295–303 (1976).
    [CrossRef]
  3. P. F. Scott, M. Ryle, “A Rapid Method for Measuring the Figure of a Radio Telescope Reflector,” Mon. Not. R. Astron. Soc. 178, 539–545 (1976).
  4. D. Morris, “Telescope Testing by Radio Holography,” in Proceedings, U.R.S.I. International Symposium on Millimeter and Submillimeter Wave Radio Astronomy, Granada, Spain (1984), pp. 29–50.
  5. R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1986).
  6. M. P. Godwin, E. P. Schoessow, B. H. Grahl, “Improvement of the Effelsberg 100 Meter Telescope Based on Holographic Reflector Surface Measurement,” Astron. Astrophys. 167, 390–394 (1986).
  7. C. E. Mayer, J. H. Davis, W. L. Peters, W. J. Vogel, “A Holographic Surface Measurement of the Texas 4.9-m Antenna at 86 GHz,” IEEE Trans. Antennas Propag. AP-32, 102–109 (1983).
  8. D. Morris, J. W. M. Baars, H. Hein, H. Steppe, C. Thum, R. Wohlleben, “Radio-Holographic Reflector Measurement of the 30-m Millimeter Radio Telescope at 22 GHz with a Cosmic Signal Source,” Astron. Astrophys. 203, 399–406 (1988).
  9. R. Hills, A. Lasenby, “Millimetre-Wave Metrology of the James Clerk Maxwell Telescope,” in Proceedings, Eleventh Estec Workshop on Antenna Measurements, Gothenburg, Sweden (1988).
  10. D. Morris, “Phase Retrieval in the Radio Holography of Reflector Antennas and Radio Telescopes,” IEEE Trans. Antennas Propag. AP-33, 749–755 (1985).
    [CrossRef]
  11. P. F. Goldsmith, “Quasi-Optical Techniques at Millimeter and Submillimeter Wavelengths,” Infrared Millimeter Waves 6, 277–344 (1982).
  12. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).
  13. J. D. Kraus, Radio Astronomy (Cygnus-Quasar, Powell, OH, 1986).
  14. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  15. P. W. Hannan, “Microwave Antennas Derived from the Cassegrain Telescope,” IRE Trans. Antennas Propag. 9, 140–153 (1961).
    [CrossRef]
  16. J. F. James, R. S. Sternberg, Design of Optical Spectrometers (Chapman & Hall, London, 1969).
  17. T. G. Phillips, “Techniques of Submillimeter Astronomy,” in Millimetre and Submillimetre Astronomy, R. D. Wolstencroft, W. B. Burton, Eds. (Kluwer, Dordrecht, The Netherlands, 1988), pp. 1–25.
    [CrossRef]
  18. W. L. Wolfe, G. J. Zissis, Eds., The Infrared Handbook (Office of Naval Research, Washington, DC, 1978).
  19. H. W. Schnopper, R. I. Thompson, “Fourier Spectrometers,” Methods Exp. Phys. 12A, 491–529 (1974).
    [CrossRef]
  20. R. R. Treffers, “Signal-to-Noise Ratio in Fourier Spectroscopy,” Appl. Opt. 16, 3103–3106 (1977).
    [CrossRef] [PubMed]
  21. D. Malacara, Optical Shop Testing (Wiley, New York, 1978).
  22. D. K. Lambert, P. L. Richards, “New Results in the Theory of a Plane Mirror Interferometer,” J. Opt. Soc. Am. 68, 1124–1130 (1978).
    [CrossRef]
  23. S. von Hoerner, “Telescope Surface Measurement with Two Feeds,” IEEE Trans. Antennas Propag. AP-26, 857–860 (1978).
    [CrossRef]
  24. C. E. Mayer, “Microwave Antenna Metrology by Holographic Means,” Ph.D. thesis, U. Texas (1983).
  25. M. S. Zarghamee, J. Antebi, “Surface Accuracy of Cassegrain Antennas,” IEEE Trans. Antennas Propag. AP-33, 828–837 (1985).
    [CrossRef]
  26. D. H. Martin, “Polarizing (Martin-Pupplett) Interferometric Spectrometers for the Near- and Submillimeter Spectra,” Infrared Millimeter Waves 6, 66–149 (1982).
  27. Infrared Laboratories, Inc., Tucson, AZ.
  28. D. A. Harper, R. H. Hildebrand, R. Stiening, R. Winston, “Heat Trap: An Optimized Far Infrared Field Optics System,” Appl. Opt. 15, 53–60 (1976).
    [CrossRef] [PubMed]
  29. S. E. Whitcomb, J. Keene, “Low Pass Interference Filters for Submillimeter Astronomy,” Appl. Opt. 19, 197–198 (1980).
    [CrossRef] [PubMed]
  30. M. Halpern, H. P. Gush, E. Wishnow, V. De Cosmo, “Far Infrared Transmission of Dielectrics at Cryogenic and Room Temperatures: Glass, Fluorogold, Eccosorb, Stycast, and Various Plastics,” Appl. Opt. 25, 565–570 (1986).
    [CrossRef] [PubMed]
  31. E. E. Russell, E. E. Bell, “Measurement of the Optical Constants of Crystal Quartz in the Far-Infrared with the Asymmetric Fourier-Transform Method,” J. Opt. Soc. Am. 57, 341–348 (1967).
    [CrossRef]
  32. AT, atmospheric transmission software, Airhead Software, Boulder, CO.
  33. D. P. Woody, “Gravitational Deflection of the Leighton Telescopes,” in Submillimetre Astronomy, G. D. Watt, A. S. Webster, Eds. (Kluwer, Dordrecht, The Netherlands, 1990), pp. 43–44.
  34. D. P. Woody, Owens Valley Radio Observatory, Caltech; private communication.

1988 (1)

D. Morris, J. W. M. Baars, H. Hein, H. Steppe, C. Thum, R. Wohlleben, “Radio-Holographic Reflector Measurement of the 30-m Millimeter Radio Telescope at 22 GHz with a Cosmic Signal Source,” Astron. Astrophys. 203, 399–406 (1988).

1987 (1)

W. Sweet, “New Radiotelescopes Open Era of Submillimeter Astronomy,” Phys. Today 40, 65–67 (1987).
[CrossRef]

1986 (2)

M. P. Godwin, E. P. Schoessow, B. H. Grahl, “Improvement of the Effelsberg 100 Meter Telescope Based on Holographic Reflector Surface Measurement,” Astron. Astrophys. 167, 390–394 (1986).

M. Halpern, H. P. Gush, E. Wishnow, V. De Cosmo, “Far Infrared Transmission of Dielectrics at Cryogenic and Room Temperatures: Glass, Fluorogold, Eccosorb, Stycast, and Various Plastics,” Appl. Opt. 25, 565–570 (1986).
[CrossRef] [PubMed]

1985 (2)

M. S. Zarghamee, J. Antebi, “Surface Accuracy of Cassegrain Antennas,” IEEE Trans. Antennas Propag. AP-33, 828–837 (1985).
[CrossRef]

D. Morris, “Phase Retrieval in the Radio Holography of Reflector Antennas and Radio Telescopes,” IEEE Trans. Antennas Propag. AP-33, 749–755 (1985).
[CrossRef]

1983 (1)

C. E. Mayer, J. H. Davis, W. L. Peters, W. J. Vogel, “A Holographic Surface Measurement of the Texas 4.9-m Antenna at 86 GHz,” IEEE Trans. Antennas Propag. AP-32, 102–109 (1983).

1982 (2)

P. F. Goldsmith, “Quasi-Optical Techniques at Millimeter and Submillimeter Wavelengths,” Infrared Millimeter Waves 6, 277–344 (1982).

D. H. Martin, “Polarizing (Martin-Pupplett) Interferometric Spectrometers for the Near- and Submillimeter Spectra,” Infrared Millimeter Waves 6, 66–149 (1982).

1980 (1)

1978 (2)

D. K. Lambert, P. L. Richards, “New Results in the Theory of a Plane Mirror Interferometer,” J. Opt. Soc. Am. 68, 1124–1130 (1978).
[CrossRef]

S. von Hoerner, “Telescope Surface Measurement with Two Feeds,” IEEE Trans. Antennas Propag. AP-26, 857–860 (1978).
[CrossRef]

1977 (1)

1976 (3)

D. A. Harper, R. H. Hildebrand, R. Stiening, R. Winston, “Heat Trap: An Optimized Far Infrared Field Optics System,” Appl. Opt. 15, 53–60 (1976).
[CrossRef] [PubMed]

J. C. Bennett, A. P. Anderson, P. A. McInnes, “Microwave Holographic Metrology of Large Reflector Antennas,” IEEE Trans. Antennas Propag. AP-24, 295–303 (1976).
[CrossRef]

P. F. Scott, M. Ryle, “A Rapid Method for Measuring the Figure of a Radio Telescope Reflector,” Mon. Not. R. Astron. Soc. 178, 539–545 (1976).

1974 (1)

H. W. Schnopper, R. I. Thompson, “Fourier Spectrometers,” Methods Exp. Phys. 12A, 491–529 (1974).
[CrossRef]

1967 (1)

1961 (1)

P. W. Hannan, “Microwave Antennas Derived from the Cassegrain Telescope,” IRE Trans. Antennas Propag. 9, 140–153 (1961).
[CrossRef]

Anderson, A. P.

J. C. Bennett, A. P. Anderson, P. A. McInnes, “Microwave Holographic Metrology of Large Reflector Antennas,” IEEE Trans. Antennas Propag. AP-24, 295–303 (1976).
[CrossRef]

Antebi, J.

M. S. Zarghamee, J. Antebi, “Surface Accuracy of Cassegrain Antennas,” IEEE Trans. Antennas Propag. AP-33, 828–837 (1985).
[CrossRef]

Baars, J. W. M.

D. Morris, J. W. M. Baars, H. Hein, H. Steppe, C. Thum, R. Wohlleben, “Radio-Holographic Reflector Measurement of the 30-m Millimeter Radio Telescope at 22 GHz with a Cosmic Signal Source,” Astron. Astrophys. 203, 399–406 (1988).

Bell, E. E.

Bennett, J. C.

J. C. Bennett, A. P. Anderson, P. A. McInnes, “Microwave Holographic Metrology of Large Reflector Antennas,” IEEE Trans. Antennas Propag. AP-24, 295–303 (1976).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Bracewell, R. N.

R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1986).

Davis, J. H.

C. E. Mayer, J. H. Davis, W. L. Peters, W. J. Vogel, “A Holographic Surface Measurement of the Texas 4.9-m Antenna at 86 GHz,” IEEE Trans. Antennas Propag. AP-32, 102–109 (1983).

De Cosmo, V.

Godwin, M. P.

M. P. Godwin, E. P. Schoessow, B. H. Grahl, “Improvement of the Effelsberg 100 Meter Telescope Based on Holographic Reflector Surface Measurement,” Astron. Astrophys. 167, 390–394 (1986).

Goldsmith, P. F.

P. F. Goldsmith, “Quasi-Optical Techniques at Millimeter and Submillimeter Wavelengths,” Infrared Millimeter Waves 6, 277–344 (1982).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Grahl, B. H.

M. P. Godwin, E. P. Schoessow, B. H. Grahl, “Improvement of the Effelsberg 100 Meter Telescope Based on Holographic Reflector Surface Measurement,” Astron. Astrophys. 167, 390–394 (1986).

Gush, H. P.

Halpern, M.

Hannan, P. W.

P. W. Hannan, “Microwave Antennas Derived from the Cassegrain Telescope,” IRE Trans. Antennas Propag. 9, 140–153 (1961).
[CrossRef]

Harper, D. A.

Hein, H.

D. Morris, J. W. M. Baars, H. Hein, H. Steppe, C. Thum, R. Wohlleben, “Radio-Holographic Reflector Measurement of the 30-m Millimeter Radio Telescope at 22 GHz with a Cosmic Signal Source,” Astron. Astrophys. 203, 399–406 (1988).

Hildebrand, R. H.

Hills, R.

R. Hills, A. Lasenby, “Millimetre-Wave Metrology of the James Clerk Maxwell Telescope,” in Proceedings, Eleventh Estec Workshop on Antenna Measurements, Gothenburg, Sweden (1988).

James, J. F.

J. F. James, R. S. Sternberg, Design of Optical Spectrometers (Chapman & Hall, London, 1969).

Keene, J.

Kraus, J. D.

J. D. Kraus, Radio Astronomy (Cygnus-Quasar, Powell, OH, 1986).

Lambert, D. K.

Lasenby, A.

R. Hills, A. Lasenby, “Millimetre-Wave Metrology of the James Clerk Maxwell Telescope,” in Proceedings, Eleventh Estec Workshop on Antenna Measurements, Gothenburg, Sweden (1988).

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, New York, 1978).

Martin, D. H.

D. H. Martin, “Polarizing (Martin-Pupplett) Interferometric Spectrometers for the Near- and Submillimeter Spectra,” Infrared Millimeter Waves 6, 66–149 (1982).

Mayer, C. E.

C. E. Mayer, J. H. Davis, W. L. Peters, W. J. Vogel, “A Holographic Surface Measurement of the Texas 4.9-m Antenna at 86 GHz,” IEEE Trans. Antennas Propag. AP-32, 102–109 (1983).

C. E. Mayer, “Microwave Antenna Metrology by Holographic Means,” Ph.D. thesis, U. Texas (1983).

McInnes, P. A.

J. C. Bennett, A. P. Anderson, P. A. McInnes, “Microwave Holographic Metrology of Large Reflector Antennas,” IEEE Trans. Antennas Propag. AP-24, 295–303 (1976).
[CrossRef]

Morris, D.

D. Morris, J. W. M. Baars, H. Hein, H. Steppe, C. Thum, R. Wohlleben, “Radio-Holographic Reflector Measurement of the 30-m Millimeter Radio Telescope at 22 GHz with a Cosmic Signal Source,” Astron. Astrophys. 203, 399–406 (1988).

D. Morris, “Phase Retrieval in the Radio Holography of Reflector Antennas and Radio Telescopes,” IEEE Trans. Antennas Propag. AP-33, 749–755 (1985).
[CrossRef]

D. Morris, “Telescope Testing by Radio Holography,” in Proceedings, U.R.S.I. International Symposium on Millimeter and Submillimeter Wave Radio Astronomy, Granada, Spain (1984), pp. 29–50.

Peters, W. L.

C. E. Mayer, J. H. Davis, W. L. Peters, W. J. Vogel, “A Holographic Surface Measurement of the Texas 4.9-m Antenna at 86 GHz,” IEEE Trans. Antennas Propag. AP-32, 102–109 (1983).

Phillips, T. G.

T. G. Phillips, “Techniques of Submillimeter Astronomy,” in Millimetre and Submillimetre Astronomy, R. D. Wolstencroft, W. B. Burton, Eds. (Kluwer, Dordrecht, The Netherlands, 1988), pp. 1–25.
[CrossRef]

Richards, P. L.

Russell, E. E.

Ryle, M.

P. F. Scott, M. Ryle, “A Rapid Method for Measuring the Figure of a Radio Telescope Reflector,” Mon. Not. R. Astron. Soc. 178, 539–545 (1976).

Schnopper, H. W.

H. W. Schnopper, R. I. Thompson, “Fourier Spectrometers,” Methods Exp. Phys. 12A, 491–529 (1974).
[CrossRef]

Schoessow, E. P.

M. P. Godwin, E. P. Schoessow, B. H. Grahl, “Improvement of the Effelsberg 100 Meter Telescope Based on Holographic Reflector Surface Measurement,” Astron. Astrophys. 167, 390–394 (1986).

Scott, P. F.

P. F. Scott, M. Ryle, “A Rapid Method for Measuring the Figure of a Radio Telescope Reflector,” Mon. Not. R. Astron. Soc. 178, 539–545 (1976).

Steppe, H.

D. Morris, J. W. M. Baars, H. Hein, H. Steppe, C. Thum, R. Wohlleben, “Radio-Holographic Reflector Measurement of the 30-m Millimeter Radio Telescope at 22 GHz with a Cosmic Signal Source,” Astron. Astrophys. 203, 399–406 (1988).

Sternberg, R. S.

J. F. James, R. S. Sternberg, Design of Optical Spectrometers (Chapman & Hall, London, 1969).

Stiening, R.

Sweet, W.

W. Sweet, “New Radiotelescopes Open Era of Submillimeter Astronomy,” Phys. Today 40, 65–67 (1987).
[CrossRef]

Thompson, R. I.

H. W. Schnopper, R. I. Thompson, “Fourier Spectrometers,” Methods Exp. Phys. 12A, 491–529 (1974).
[CrossRef]

Thum, C.

D. Morris, J. W. M. Baars, H. Hein, H. Steppe, C. Thum, R. Wohlleben, “Radio-Holographic Reflector Measurement of the 30-m Millimeter Radio Telescope at 22 GHz with a Cosmic Signal Source,” Astron. Astrophys. 203, 399–406 (1988).

Treffers, R. R.

Vogel, W. J.

C. E. Mayer, J. H. Davis, W. L. Peters, W. J. Vogel, “A Holographic Surface Measurement of the Texas 4.9-m Antenna at 86 GHz,” IEEE Trans. Antennas Propag. AP-32, 102–109 (1983).

von Hoerner, S.

S. von Hoerner, “Telescope Surface Measurement with Two Feeds,” IEEE Trans. Antennas Propag. AP-26, 857–860 (1978).
[CrossRef]

Whitcomb, S. E.

Winston, R.

Wishnow, E.

Wohlleben, R.

D. Morris, J. W. M. Baars, H. Hein, H. Steppe, C. Thum, R. Wohlleben, “Radio-Holographic Reflector Measurement of the 30-m Millimeter Radio Telescope at 22 GHz with a Cosmic Signal Source,” Astron. Astrophys. 203, 399–406 (1988).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Woody, D. P.

D. P. Woody, “Gravitational Deflection of the Leighton Telescopes,” in Submillimetre Astronomy, G. D. Watt, A. S. Webster, Eds. (Kluwer, Dordrecht, The Netherlands, 1990), pp. 43–44.

D. P. Woody, Owens Valley Radio Observatory, Caltech; private communication.

Zarghamee, M. S.

M. S. Zarghamee, J. Antebi, “Surface Accuracy of Cassegrain Antennas,” IEEE Trans. Antennas Propag. AP-33, 828–837 (1985).
[CrossRef]

Appl. Opt. (4)

Astron. Astrophys. (2)

M. P. Godwin, E. P. Schoessow, B. H. Grahl, “Improvement of the Effelsberg 100 Meter Telescope Based on Holographic Reflector Surface Measurement,” Astron. Astrophys. 167, 390–394 (1986).

D. Morris, J. W. M. Baars, H. Hein, H. Steppe, C. Thum, R. Wohlleben, “Radio-Holographic Reflector Measurement of the 30-m Millimeter Radio Telescope at 22 GHz with a Cosmic Signal Source,” Astron. Astrophys. 203, 399–406 (1988).

IEEE Trans. Antennas Propag. (5)

C. E. Mayer, J. H. Davis, W. L. Peters, W. J. Vogel, “A Holographic Surface Measurement of the Texas 4.9-m Antenna at 86 GHz,” IEEE Trans. Antennas Propag. AP-32, 102–109 (1983).

J. C. Bennett, A. P. Anderson, P. A. McInnes, “Microwave Holographic Metrology of Large Reflector Antennas,” IEEE Trans. Antennas Propag. AP-24, 295–303 (1976).
[CrossRef]

D. Morris, “Phase Retrieval in the Radio Holography of Reflector Antennas and Radio Telescopes,” IEEE Trans. Antennas Propag. AP-33, 749–755 (1985).
[CrossRef]

S. von Hoerner, “Telescope Surface Measurement with Two Feeds,” IEEE Trans. Antennas Propag. AP-26, 857–860 (1978).
[CrossRef]

M. S. Zarghamee, J. Antebi, “Surface Accuracy of Cassegrain Antennas,” IEEE Trans. Antennas Propag. AP-33, 828–837 (1985).
[CrossRef]

Infrared Millimeter Waves (2)

D. H. Martin, “Polarizing (Martin-Pupplett) Interferometric Spectrometers for the Near- and Submillimeter Spectra,” Infrared Millimeter Waves 6, 66–149 (1982).

P. F. Goldsmith, “Quasi-Optical Techniques at Millimeter and Submillimeter Wavelengths,” Infrared Millimeter Waves 6, 277–344 (1982).

IRE Trans. Antennas Propag. (1)

P. W. Hannan, “Microwave Antennas Derived from the Cassegrain Telescope,” IRE Trans. Antennas Propag. 9, 140–153 (1961).
[CrossRef]

J. Opt. Soc. Am. (2)

Methods Exp. Phys. (1)

H. W. Schnopper, R. I. Thompson, “Fourier Spectrometers,” Methods Exp. Phys. 12A, 491–529 (1974).
[CrossRef]

Mon. Not. R. Astron. Soc. (1)

P. F. Scott, M. Ryle, “A Rapid Method for Measuring the Figure of a Radio Telescope Reflector,” Mon. Not. R. Astron. Soc. 178, 539–545 (1976).

Phys. Today (1)

W. Sweet, “New Radiotelescopes Open Era of Submillimeter Astronomy,” Phys. Today 40, 65–67 (1987).
[CrossRef]

Other (15)

D. Malacara, Optical Shop Testing (Wiley, New York, 1978).

Infrared Laboratories, Inc., Tucson, AZ.

C. E. Mayer, “Microwave Antenna Metrology by Holographic Means,” Ph.D. thesis, U. Texas (1983).

AT, atmospheric transmission software, Airhead Software, Boulder, CO.

D. P. Woody, “Gravitational Deflection of the Leighton Telescopes,” in Submillimetre Astronomy, G. D. Watt, A. S. Webster, Eds. (Kluwer, Dordrecht, The Netherlands, 1990), pp. 43–44.

D. P. Woody, Owens Valley Radio Observatory, Caltech; private communication.

D. Morris, “Telescope Testing by Radio Holography,” in Proceedings, U.R.S.I. International Symposium on Millimeter and Submillimeter Wave Radio Astronomy, Granada, Spain (1984), pp. 29–50.

R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1986).

R. Hills, A. Lasenby, “Millimetre-Wave Metrology of the James Clerk Maxwell Telescope,” in Proceedings, Eleventh Estec Workshop on Antenna Measurements, Gothenburg, Sweden (1988).

J. F. James, R. S. Sternberg, Design of Optical Spectrometers (Chapman & Hall, London, 1969).

T. G. Phillips, “Techniques of Submillimeter Astronomy,” in Millimetre and Submillimetre Astronomy, R. D. Wolstencroft, W. B. Burton, Eds. (Kluwer, Dordrecht, The Netherlands, 1988), pp. 1–25.
[CrossRef]

W. L. Wolfe, G. J. Zissis, Eds., The Infrared Handbook (Office of Naval Research, Washington, DC, 1978).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

J. D. Kraus, Radio Astronomy (Cygnus-Quasar, Powell, OH, 1986).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Schematic layout of the interferometer optics: P1 and P2, off-axis paraboloids; BS, Mylar beam splitter; and M1 and M2, plane mirrors. The double arrow shows the direction of travel of M1, and the small arrow and cross, the rotation axes of M2. The light solid lines indicate the on-axis beam from M1, and the dashed lines the off-axis beam from M2.

Fig. 2
Fig. 2

Solid curve, calculated CSO zenith atmospheric transmission for 1.5-mm precipitable water vapor; dashed curve, measured transmission of the filter designed to match the 200–300-GHz atmospheric window. The vertical scaling of this curve is arbitrary.

Fig. 3
Fig. 3

(a) Cross-power interferograms measured on Mars for three orientations of mirror M2. (b) Corresponding cross-power spectra. The solid and dashed lines give the real and imaginary parts of the Fourier transform, respectively. The arrow indicates the frequency for which the first dark Airy ring is 34 sec of arc off-axis.

Fig. 4
Fig. 4

Measured difference map between two telescope aperture plane phase maps, one made with and one without a 250-μm thick piece of Mylar located at the position of the rectangle in the upper right quadrant of the dish. The contour levels are ±25 μm, the grid size 15 × 15, and the spacing of the data points 0.85 × 0.85 m. The small centered circle shows the approximate central obscuration.

Fig. 5
Fig. 5

Measured differences between two 21 × 21 point dish surface maps made over similar zenith angle ranges (10° ± 7° vs 12° ± 8°). For this and all succeeding figures, the solid contours show 10-μm increments in height above the ideal surface, and the dashed contours 10-μm decrements below the ideal surface.

Fig. 6
Fig. 6

The 21 × 21 point dish surface error maps made with Jupiter in the zenith angle range of 10° ± 7° at the frequencies indicated in the upper right-hand corners of the maps.

Fig. 7
Fig. 7

(a) Far field power map made in the zenith angle range of 65° ± 10° on Venus. The contour interval is 3 dB [also for (d) and (e)]. (b) Aperture plane illumination with 2-dB contours. (c) Aperture plane phase with ±10-μm contours. (d) Calculated far field power pattern for a 10.4-m dish with a 70-μm dip over the central 3 m. (e) Calculated pattern with uniform phase over the entire dish, but with a central obscuration of 1.2-m diameter.

Fig. 8
Fig. 8

(a) Measured telescope surface deformations incurred when tipping the telescope from 10° zenith angle to 65°. Grid size = 21 × 21, and spacing of data points on the dish = 0.6 m. Frequency = 290 ± 35 GHz. (b) Theoretical predictions of the same. Contour intervals for both maps are 10 μm. Solid contours indicate an upward (toward the prime focus) displacement of the surface when tipping and dashed contours an opposite movement.

Equations (36)

Equations on this page are rendered with MathJax. Learn more.

E c ( x c , y c ) = C E f f ( ϕ x , ϕ y ) .
E o ( x o , y o ) = 1 2 F c F o E c ( x c , y c ) ,
E o ( x o , y o ) = 1 2 F c F o [ E c ( x c , y c ) + E c ( x c + 2 f 1 θ x , y c + 2 f 1 θ y ) ] ,
E o ( 0 , 0 ) = 1 2 F c F o [ E c ( 0 , 0 ) + E c ( 2 f 1 θ x , 2 f 1 θ y ) ] .
E o ( 0 , 0 ) = C [ E f f ( 0 , 0 ) + E f f ( ϕ x , ϕ y ) ] ,
n Δ λ D λ 2 D ,
SNR d SNR h = 2 k T n NEP Δ ν d Δ ν h ,
SNR = k T A Δ ν NEP δ t 4 .
SNR = k T A NEP c Δ ν 8 υ ,
E o ( x o = 0 , y o = 0 , δ , k ) = t ( k ) [ E f f ( 0 , 0 , k ) exp ( i k δ ) + E f f ( ϕ x , ϕ y , k ) ] ,
I ( ϕ x , ϕ y , δ ) = 0 T ( k ) | E f f ( 0 , 0 , k ) exp ( i k δ ) + E f f ( ϕ x , ϕ y , k ) | 2 d k ,
I ( ϕ x , ϕ y , δ ) = 0 T ( k ) { | E f f ( 0 , 0 , k ) | 2 + | E f f ( ϕ x , ϕ y , k ) | 2 + 2 R [ E f f * ( 0 , 0 , k ) E f f ( ϕ x , ϕ y , k ) i k δ ] } d k ,
I ( ϕ x , ϕ y , δ ) = P ( 0 , 0 ) + P ( ϕ x , ϕ y ) + T ( k ) E f f * ( 0 , 0 , k ) E f f ( ϕ x , ϕ y , k ) exp ( i k δ ) d k .
I m ( ϕ x , ϕ y , δ ) = T ( k ) E f f * ( 0 , 0 , k ) E f f ( ϕ x , ϕ y , k ) exp ( i k δ ) d k .
S ( k ) = I m ( 0 , 0 , δ ) exp ( i k δ ) d δ .
r ( ϕ x , ϕ y , k ) E f f ( ϕ x , ϕ y , k ) E f f ( 0 , 0 , k ) = 1 S ( k ) I m ( ϕ x , ϕ y , δ ) exp ( i k δ ) d δ .
E a p ( x a p , y a p , k ) = r ( ϕ x , ϕ y , k ) × exp [ i k ( x a p ϕ x + y a p ϕ y ) ] k 2 d ϕ x d ϕ y .
E a p ( x , y , k ) = k 2 S ( k ) I m ( ϕ x , ϕ y , δ ) × exp [ i ( x ϕ x + y ϕ y + k δ ) ] d δ d ϕ x d ϕ y .
g = λ N Δ ϕ s .
r m ( ϕ x , ϕ y , k ) = 1 S ( k ) I m ( ϕ x , ϕ y , δ ) a ( δ ) exp ( i k δ ) d δ ,
r m ( ϕ x , ϕ y , k ) = r ( ϕ x , ϕ y , k ) A ( k k ) d k ,
E a p , m ( x a p , y a p , k ) = [ r ( ϕ x , ϕ y , k ) A ( k k ) d k ] × w ( ϕ x , ϕ y ) exp [ i k ( x a p ϕ x + y a p ϕ y ) ] k 2 d ϕ x d ϕ y .
E a p , m ( x a p , y a p , k ) = d k A ( k k ) r ( ϕ x , ϕ y , k ) × w ( ϕ x , ϕ y ) exp [ i k ( x a p ϕ x + y a p ϕ y ) ] k 2 d ϕ x d ϕ y .
( x a p , y a p ) = k k ( x a p , y a p ) ,
E a p , m ( x a p , y a p , k ) = d k A ( k k ) ( k k ) 2 × r ( ϕ x , ϕ y , k ) w ( ϕ x , ϕ y ) exp [ i k ( x a p ϕ x + y a p ϕ y ) ] k 2 d ϕ x d ϕ y .
E a p , m ( x a p , y a p , k ) = d k A ( k k ) × E a p ( x a p , y a p , k ) W ( x a p x a p , y a p y a p , k ) d x a p d y a p .
E a p , m ( x a p , y a p , k ) = E a p ( x a p , y a p , k ) × W ( x a p x a p , y a p y a p , k ) d x a p d y a p .
E a p , m ( x a p , y a p , k ) = d k E a p ( x a p , y a p , k ) A ( k k ) ,
E a p , m ( x a p , y a p , k ) = d k E a p ( k k x a p , k k y a p , k ) A ( k k ) .
Δ ρ = k ρ k 2 Δ k ,
Δ ρ ρ Δ k k 1 R .
R = N 2 ( Δ ϕ s λ / D ) ( g Δ ρ edge ) .
I m ( ϕ x , ϕ y , δ ) = d ϕ x d ϕ y T ( k ) f ( ϕ x ϕ x , ϕ y ϕ y , k ) × E f f * ( ϕ x ϕ x , ϕ y ϕ y , k ) E f f ( ϕ x , ϕ y , k ) exp ( i k δ ) d k ,
d z = 2 . 44 λ ϕ d ,
ϕ d = 2 . 44 λ D ,
α = 2 . 44 λ D .

Metrics