Abstract

A design formalism is presented for transmission-type phase holograms for use in a submillimeter-wave compact radar-cross-section (RCS) measurement range. The design method is based on rigorous electromagnetic grating theory combined with conventional hologram synthesis. Hologram structures consisting of a curved groove pattern on a 320  mm×280   mm Teflon plate are designed to transform an incoming spherical wave at 650   GHz into an output wave generating a 100   mm diameter planar field region (quiet zone) at a distance of 1   m. The reconstructed quiet-zone field is evaluated by a numerical simulation method. The uniformity of the quiet-zone field is further improved by reoptimizing the goal field. Measurement results are given for a test hologram fabricated on Teflon.

© 2007 Optical Society of America

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2006 (1)

A. Lönnqvist, J. Mallat, and A. V. Räisänen, "Phase-hologram-based compact RCS test range at 310 GHz for scale models," IEEE Trans. Microwave Theory Tech. 54, 2391-2397 (2006).
[CrossRef]

2005 (3)

A. Lönnqvist, T. Koskinen, J. Häkli, J. Säily, J. Ala-Laurinaho, J. Mallat, V. Viikari, J. Tuovinen, and A. V. Räisänen, "Hologram-based compact range for submillimeter-wave antenna testing," IEEE Trans. Antennas Propag. 53, 3151-3159 (2005).
[CrossRef]

J. Häkli, T. Koskinen, A. Lönnqvist, J. Säily, V. Viikari, J. Mallat, J. Ala-Laurinaho, J. Tuovinen, and A. V. Räisänen, "Testing of a 1.5 m reflector antenna at 322 GHz in a CATR based on a hologram," IEEE Trans. Antennas Propag. 53, 3142-3150 (2005).
[CrossRef]

T. Koskinen, J. Ala-Laurinaho, J. Säily, A. Lönnqvist, J. Häkli, J. Mallat, J. Tuovinen, and A. V. Räisänen, "Experimental study on a hologram-based compact antenna test range at 650 GHz," IEEE Trans. Microwave Theory Tech. 53, 2999-3006 (2005).
[CrossRef]

2003 (2)

J. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Millimeter-wave beam shaping using holograms," IEEE Trans. Microwave Theory Tech. 51, 1274-1280 (2003).
[CrossRef]

J. Säily, P. Eskelinen, and A. V. Räisänen, "Pilot signal based real-time measurement and correction of phase errors caused by microwave cable flexing in planar near-field tests," IEEE Trans. Antennas Propag. 51, 195-200 (2003).
[CrossRef]

2002 (1)

J. Salo, J. Meltaus, E. Noponen, M. M. Salomaa, A. Lönnqvist, T. Koskinen, V. Viikari, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Holograms for shaping radio-wave fields," J. Opt. A 4, S161-S167 (2002).
[CrossRef]

2001 (1)

J. Ala-Laurinaho, T. Hirvonen, P. Piironen, A. Lehto, J. Tuovinen, A. V. Räisänen, and U. Frisk, "Measurement of the Odin telescope at 119 GHz with a hologram-type CATR," IEEE Trans. Antennas Propag. 49, 1264-1270 (2001).
[CrossRef]

2000 (1)

J. Säily, J. Ala-Laurinaho, J. Häkli, J. Tuovinen, A. Lehto, and A. V. Räisänen, "Test results of 310 GHz hologram compact antenna test range," Electron. Lett. 36, 111-112 (2000).
[CrossRef]

1999 (1)

T. Sehm, J. Ala-Laurinaho, T. Hirvonen, and A. V. Räisänen, "Antenna measurements using a hologram CATR," Electron. Lett. 35, 757-758 (1999).
[CrossRef]

1997 (3)

T. Hirvonen, J. Ala-Laurinaho, J. Tuovinen, and A. V. Räisänen, "A compact antenna test range based on a hologram," IEEE Trans. Antennas Propag. 45, 1270-1276 (1997).
[CrossRef]

J. Ala-Laurinaho, T. Hirvonen, J. Tuovinen, and A. V. Räisänen, "Numerical modeling of a nonuniform grating with FDTD," Microwave Opt. Technol. Lett. 15, 134-139 (1997).
[CrossRef]

V. Kettunen, P. Vahimaa, J. Turunen, and E. Noponen, "Zeroth-order coding of complex amplitude in two dimensions," J. Opt. Soc. Am. A 14, 808-815 (1997).
[CrossRef]

1996 (2)

E. Noponen and J. Turunen, "Complex-amplitude modulation by high-carrier-frequency diffractive elements," J. Opt. Soc. Am. A 13, 1422-1428 (1996).
[CrossRef]

J. Turunen, P. Vahimaa, M. Honkanen, O. Salminen, and E. Noponen, "Zeroth-order complex-amplitude modulation with dielectric Fourier-type diffractive elements," J. Mod. Opt. 43, 1389-1398 (1996).
[CrossRef]

1994 (1)

1992 (2)

1991 (1)

A. Vasara, E. Noponen, J. Turunen, J. M. Miller, M. R. Taghizadeh, and J. Tuovinen, "Rigorous diffraction theory of binary optical interconnects," in Holographic Optics III: Principles and Applications, Proc. SPIE 1507, 224-238 (1991).
[CrossRef]

1989 (1)

1978 (1)

1977 (1)

G. Tricoles and N. H. Farhat, "Microwave holography: applications and techniques," Proc. IEEE 65, 108-121 (1977).
[CrossRef]

1975 (1)

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. 23, 123-133 (1975).
[CrossRef]

1967 (2)

Ala-Laurinaho, J.

J. Häkli, T. Koskinen, A. Lönnqvist, J. Säily, V. Viikari, J. Mallat, J. Ala-Laurinaho, J. Tuovinen, and A. V. Räisänen, "Testing of a 1.5 m reflector antenna at 322 GHz in a CATR based on a hologram," IEEE Trans. Antennas Propag. 53, 3142-3150 (2005).
[CrossRef]

A. Lönnqvist, T. Koskinen, J. Häkli, J. Säily, J. Ala-Laurinaho, J. Mallat, V. Viikari, J. Tuovinen, and A. V. Räisänen, "Hologram-based compact range for submillimeter-wave antenna testing," IEEE Trans. Antennas Propag. 53, 3151-3159 (2005).
[CrossRef]

T. Koskinen, J. Ala-Laurinaho, J. Säily, A. Lönnqvist, J. Häkli, J. Mallat, J. Tuovinen, and A. V. Räisänen, "Experimental study on a hologram-based compact antenna test range at 650 GHz," IEEE Trans. Microwave Theory Tech. 53, 2999-3006 (2005).
[CrossRef]

J. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Millimeter-wave beam shaping using holograms," IEEE Trans. Microwave Theory Tech. 51, 1274-1280 (2003).
[CrossRef]

J. Salo, J. Meltaus, E. Noponen, M. M. Salomaa, A. Lönnqvist, T. Koskinen, V. Viikari, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Holograms for shaping radio-wave fields," J. Opt. A 4, S161-S167 (2002).
[CrossRef]

J. Ala-Laurinaho, T. Hirvonen, P. Piironen, A. Lehto, J. Tuovinen, A. V. Räisänen, and U. Frisk, "Measurement of the Odin telescope at 119 GHz with a hologram-type CATR," IEEE Trans. Antennas Propag. 49, 1264-1270 (2001).
[CrossRef]

J. Säily, J. Ala-Laurinaho, J. Häkli, J. Tuovinen, A. Lehto, and A. V. Räisänen, "Test results of 310 GHz hologram compact antenna test range," Electron. Lett. 36, 111-112 (2000).
[CrossRef]

T. Sehm, J. Ala-Laurinaho, T. Hirvonen, and A. V. Räisänen, "Antenna measurements using a hologram CATR," Electron. Lett. 35, 757-758 (1999).
[CrossRef]

T. Hirvonen, J. Ala-Laurinaho, J. Tuovinen, and A. V. Räisänen, "A compact antenna test range based on a hologram," IEEE Trans. Antennas Propag. 45, 1270-1276 (1997).
[CrossRef]

J. Ala-Laurinaho, T. Hirvonen, J. Tuovinen, and A. V. Räisänen, "Numerical modeling of a nonuniform grating with FDTD," Microwave Opt. Technol. Lett. 15, 134-139 (1997).
[CrossRef]

E. Noponen, J. Häkli, T. Koskinen, A. Lönnqvist, V. Viikari, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Synthesis of reflection-type phase hologram for compact antenna test range at 310 GHz," in Proceedings of 4th ESA Workshop on Millimetre-Wave Technology and Applications (European Space Agency, 2006), Vol. WPP-258, pp. 391-396.

J. Mallat, J. Ala-Laurinaho, E. Noponen, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Meltaus, and A. V. Räisänen, "A phase hologram RCS range for scale model measurements," in Digest of Technical Papers, URSI/IEEE XXVII Convention on Radio Science, Vol. S 257 of Helsinki University of Technology Radio Laboratory Publications (TKK Helsinki University of Technology, 2002), pp. 143-145.

A. Lönnqvist, J. Mallat, E. Noponen, J. Ala-Laurinaho, J. Säily, T. Koskinen, J. Häkli, and A. V. Räisänen, "A phase hologram compact RCS-range for scale model measurements," in Proceedings of 3rd ESA Workshop on Millimetre-Wave Technology and Applications (European Space Agency, 2003), Vol. WPP-212, pp. 511-516.

J. Ala-Laurinaho, T. Koskinen, J. Häkli, A. Karttunen, A. Lönnqvist, E. Noponen, J. Mallat, M. Vaaja, V. Viikari, A. Räisänen, J. Heinonen, P. Hautala, and J. Lemanczyk, "Development of a hologram-based CATR for testing a very high gain antenna at 650 GHz," presented at the European Conference on Antennas and Propagation, EuCAP 2006, Nice, France, 6-10 November 2006.

J. Häkli, T. Koskinen, J. Ala-Laurinaho, A. Karttunen, M. Vaaja, V. Viikari, A. Lönnqvist, J. Heinonen, J. Mallat, E. Noponen, P. Hautala, J. Lemanczyk, and A. V. Räisänen, "Development of a 650 GHz hologram based CATR for testing a 1.5 m reflector antenna," in Proceedings of AMTA Europe Symposium 2006 (Antenna Measurement Techniques Association, 2006), pp. 83-88.

Aoki, Y.

Bertoni, H. L.

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. 23, 123-133 (1975).
[CrossRef]

Eskelinen, P.

J. Säily, P. Eskelinen, and A. V. Räisänen, "Pilot signal based real-time measurement and correction of phase errors caused by microwave cable flexing in planar near-field tests," IEEE Trans. Antennas Propag. 51, 195-200 (2003).
[CrossRef]

Farhat, N. H.

G. Tricoles and N. H. Farhat, "Microwave holography: applications and techniques," Proc. IEEE 65, 108-121 (1977).
[CrossRef]

Friberg, A. T.

Frisk, U.

J. Ala-Laurinaho, T. Hirvonen, P. Piironen, A. Lehto, J. Tuovinen, A. V. Räisänen, and U. Frisk, "Measurement of the Odin telescope at 119 GHz with a hologram-type CATR," IEEE Trans. Antennas Propag. 49, 1264-1270 (2001).
[CrossRef]

Goodman, J. W.

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

Häkli, J.

A. Lönnqvist, T. Koskinen, J. Häkli, J. Säily, J. Ala-Laurinaho, J. Mallat, V. Viikari, J. Tuovinen, and A. V. Räisänen, "Hologram-based compact range for submillimeter-wave antenna testing," IEEE Trans. Antennas Propag. 53, 3151-3159 (2005).
[CrossRef]

T. Koskinen, J. Ala-Laurinaho, J. Säily, A. Lönnqvist, J. Häkli, J. Mallat, J. Tuovinen, and A. V. Räisänen, "Experimental study on a hologram-based compact antenna test range at 650 GHz," IEEE Trans. Microwave Theory Tech. 53, 2999-3006 (2005).
[CrossRef]

J. Häkli, T. Koskinen, A. Lönnqvist, J. Säily, V. Viikari, J. Mallat, J. Ala-Laurinaho, J. Tuovinen, and A. V. Räisänen, "Testing of a 1.5 m reflector antenna at 322 GHz in a CATR based on a hologram," IEEE Trans. Antennas Propag. 53, 3142-3150 (2005).
[CrossRef]

J. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Millimeter-wave beam shaping using holograms," IEEE Trans. Microwave Theory Tech. 51, 1274-1280 (2003).
[CrossRef]

J. Salo, J. Meltaus, E. Noponen, M. M. Salomaa, A. Lönnqvist, T. Koskinen, V. Viikari, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Holograms for shaping radio-wave fields," J. Opt. A 4, S161-S167 (2002).
[CrossRef]

J. Säily, J. Ala-Laurinaho, J. Häkli, J. Tuovinen, A. Lehto, and A. V. Räisänen, "Test results of 310 GHz hologram compact antenna test range," Electron. Lett. 36, 111-112 (2000).
[CrossRef]

E. Noponen, J. Häkli, T. Koskinen, A. Lönnqvist, V. Viikari, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Synthesis of reflection-type phase hologram for compact antenna test range at 310 GHz," in Proceedings of 4th ESA Workshop on Millimetre-Wave Technology and Applications (European Space Agency, 2006), Vol. WPP-258, pp. 391-396.

J. Mallat, J. Ala-Laurinaho, E. Noponen, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Meltaus, and A. V. Räisänen, "A phase hologram RCS range for scale model measurements," in Digest of Technical Papers, URSI/IEEE XXVII Convention on Radio Science, Vol. S 257 of Helsinki University of Technology Radio Laboratory Publications (TKK Helsinki University of Technology, 2002), pp. 143-145.

J. Ala-Laurinaho, T. Koskinen, J. Häkli, A. Karttunen, A. Lönnqvist, E. Noponen, J. Mallat, M. Vaaja, V. Viikari, A. Räisänen, J. Heinonen, P. Hautala, and J. Lemanczyk, "Development of a hologram-based CATR for testing a very high gain antenna at 650 GHz," presented at the European Conference on Antennas and Propagation, EuCAP 2006, Nice, France, 6-10 November 2006.

A. Lönnqvist, J. Mallat, E. Noponen, J. Ala-Laurinaho, J. Säily, T. Koskinen, J. Häkli, and A. V. Räisänen, "A phase hologram compact RCS-range for scale model measurements," in Proceedings of 3rd ESA Workshop on Millimetre-Wave Technology and Applications (European Space Agency, 2003), Vol. WPP-212, pp. 511-516.

J. Häkli, T. Koskinen, J. Ala-Laurinaho, A. Karttunen, M. Vaaja, V. Viikari, A. Lönnqvist, J. Heinonen, J. Mallat, E. Noponen, P. Hautala, J. Lemanczyk, and A. V. Räisänen, "Development of a 650 GHz hologram based CATR for testing a 1.5 m reflector antenna," in Proceedings of AMTA Europe Symposium 2006 (Antenna Measurement Techniques Association, 2006), pp. 83-88.

Hautala, P.

J. Häkli, T. Koskinen, J. Ala-Laurinaho, A. Karttunen, M. Vaaja, V. Viikari, A. Lönnqvist, J. Heinonen, J. Mallat, E. Noponen, P. Hautala, J. Lemanczyk, and A. V. Räisänen, "Development of a 650 GHz hologram based CATR for testing a 1.5 m reflector antenna," in Proceedings of AMTA Europe Symposium 2006 (Antenna Measurement Techniques Association, 2006), pp. 83-88.

J. Ala-Laurinaho, T. Koskinen, J. Häkli, A. Karttunen, A. Lönnqvist, E. Noponen, J. Mallat, M. Vaaja, V. Viikari, A. Räisänen, J. Heinonen, P. Hautala, and J. Lemanczyk, "Development of a hologram-based CATR for testing a very high gain antenna at 650 GHz," presented at the European Conference on Antennas and Propagation, EuCAP 2006, Nice, France, 6-10 November 2006.

Heinonen, J.

J. Ala-Laurinaho, T. Koskinen, J. Häkli, A. Karttunen, A. Lönnqvist, E. Noponen, J. Mallat, M. Vaaja, V. Viikari, A. Räisänen, J. Heinonen, P. Hautala, and J. Lemanczyk, "Development of a hologram-based CATR for testing a very high gain antenna at 650 GHz," presented at the European Conference on Antennas and Propagation, EuCAP 2006, Nice, France, 6-10 November 2006.

J. Häkli, T. Koskinen, J. Ala-Laurinaho, A. Karttunen, M. Vaaja, V. Viikari, A. Lönnqvist, J. Heinonen, J. Mallat, E. Noponen, P. Hautala, J. Lemanczyk, and A. V. Räisänen, "Development of a 650 GHz hologram based CATR for testing a 1.5 m reflector antenna," in Proceedings of AMTA Europe Symposium 2006 (Antenna Measurement Techniques Association, 2006), pp. 83-88.

Hirvonen, T.

J. Ala-Laurinaho, T. Hirvonen, P. Piironen, A. Lehto, J. Tuovinen, A. V. Räisänen, and U. Frisk, "Measurement of the Odin telescope at 119 GHz with a hologram-type CATR," IEEE Trans. Antennas Propag. 49, 1264-1270 (2001).
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J. Ala-Laurinaho, T. Hirvonen, J. Tuovinen, and A. V. Räisänen, "Numerical modeling of a nonuniform grating with FDTD," Microwave Opt. Technol. Lett. 15, 134-139 (1997).
[CrossRef]

Honkanen, M.

J. Turunen, P. Vahimaa, M. Honkanen, O. Salminen, and E. Noponen, "Zeroth-order complex-amplitude modulation with dielectric Fourier-type diffractive elements," J. Mod. Opt. 43, 1389-1398 (1996).
[CrossRef]

Ichikawa, H.

Jaakkola, T.

Karttunen, A.

J. Ala-Laurinaho, T. Koskinen, J. Häkli, A. Karttunen, A. Lönnqvist, E. Noponen, J. Mallat, M. Vaaja, V. Viikari, A. Räisänen, J. Heinonen, P. Hautala, and J. Lemanczyk, "Development of a hologram-based CATR for testing a very high gain antenna at 650 GHz," presented at the European Conference on Antennas and Propagation, EuCAP 2006, Nice, France, 6-10 November 2006.

J. Häkli, T. Koskinen, J. Ala-Laurinaho, A. Karttunen, M. Vaaja, V. Viikari, A. Lönnqvist, J. Heinonen, J. Mallat, E. Noponen, P. Hautala, J. Lemanczyk, and A. V. Räisänen, "Development of a 650 GHz hologram based CATR for testing a 1.5 m reflector antenna," in Proceedings of AMTA Europe Symposium 2006 (Antenna Measurement Techniques Association, 2006), pp. 83-88.

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T. Koskinen, J. Ala-Laurinaho, J. Säily, A. Lönnqvist, J. Häkli, J. Mallat, J. Tuovinen, and A. V. Räisänen, "Experimental study on a hologram-based compact antenna test range at 650 GHz," IEEE Trans. Microwave Theory Tech. 53, 2999-3006 (2005).
[CrossRef]

A. Lönnqvist, T. Koskinen, J. Häkli, J. Säily, J. Ala-Laurinaho, J. Mallat, V. Viikari, J. Tuovinen, and A. V. Räisänen, "Hologram-based compact range for submillimeter-wave antenna testing," IEEE Trans. Antennas Propag. 53, 3151-3159 (2005).
[CrossRef]

J. Häkli, T. Koskinen, A. Lönnqvist, J. Säily, V. Viikari, J. Mallat, J. Ala-Laurinaho, J. Tuovinen, and A. V. Räisänen, "Testing of a 1.5 m reflector antenna at 322 GHz in a CATR based on a hologram," IEEE Trans. Antennas Propag. 53, 3142-3150 (2005).
[CrossRef]

J. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Millimeter-wave beam shaping using holograms," IEEE Trans. Microwave Theory Tech. 51, 1274-1280 (2003).
[CrossRef]

J. Salo, J. Meltaus, E. Noponen, M. M. Salomaa, A. Lönnqvist, T. Koskinen, V. Viikari, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Holograms for shaping radio-wave fields," J. Opt. A 4, S161-S167 (2002).
[CrossRef]

J. Ala-Laurinaho, T. Koskinen, J. Häkli, A. Karttunen, A. Lönnqvist, E. Noponen, J. Mallat, M. Vaaja, V. Viikari, A. Räisänen, J. Heinonen, P. Hautala, and J. Lemanczyk, "Development of a hologram-based CATR for testing a very high gain antenna at 650 GHz," presented at the European Conference on Antennas and Propagation, EuCAP 2006, Nice, France, 6-10 November 2006.

A. Lönnqvist, J. Mallat, E. Noponen, J. Ala-Laurinaho, J. Säily, T. Koskinen, J. Häkli, and A. V. Räisänen, "A phase hologram compact RCS-range for scale model measurements," in Proceedings of 3rd ESA Workshop on Millimetre-Wave Technology and Applications (European Space Agency, 2003), Vol. WPP-212, pp. 511-516.

J. Häkli, T. Koskinen, J. Ala-Laurinaho, A. Karttunen, M. Vaaja, V. Viikari, A. Lönnqvist, J. Heinonen, J. Mallat, E. Noponen, P. Hautala, J. Lemanczyk, and A. V. Räisänen, "Development of a 650 GHz hologram based CATR for testing a 1.5 m reflector antenna," in Proceedings of AMTA Europe Symposium 2006 (Antenna Measurement Techniques Association, 2006), pp. 83-88.

E. Noponen, J. Häkli, T. Koskinen, A. Lönnqvist, V. Viikari, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Synthesis of reflection-type phase hologram for compact antenna test range at 310 GHz," in Proceedings of 4th ESA Workshop on Millimetre-Wave Technology and Applications (European Space Agency, 2006), Vol. WPP-258, pp. 391-396.

J. Mallat, J. Ala-Laurinaho, E. Noponen, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Meltaus, and A. V. Räisänen, "A phase hologram RCS range for scale model measurements," in Digest of Technical Papers, URSI/IEEE XXVII Convention on Radio Science, Vol. S 257 of Helsinki University of Technology Radio Laboratory Publications (TKK Helsinki University of Technology, 2002), pp. 143-145.

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Lehto, A.

J. Ala-Laurinaho, T. Hirvonen, P. Piironen, A. Lehto, J. Tuovinen, A. V. Räisänen, and U. Frisk, "Measurement of the Odin telescope at 119 GHz with a hologram-type CATR," IEEE Trans. Antennas Propag. 49, 1264-1270 (2001).
[CrossRef]

J. Säily, J. Ala-Laurinaho, J. Häkli, J. Tuovinen, A. Lehto, and A. V. Räisänen, "Test results of 310 GHz hologram compact antenna test range," Electron. Lett. 36, 111-112 (2000).
[CrossRef]

Lemanczyk, J.

J. Häkli, T. Koskinen, J. Ala-Laurinaho, A. Karttunen, M. Vaaja, V. Viikari, A. Lönnqvist, J. Heinonen, J. Mallat, E. Noponen, P. Hautala, J. Lemanczyk, and A. V. Räisänen, "Development of a 650 GHz hologram based CATR for testing a 1.5 m reflector antenna," in Proceedings of AMTA Europe Symposium 2006 (Antenna Measurement Techniques Association, 2006), pp. 83-88.

J. Ala-Laurinaho, T. Koskinen, J. Häkli, A. Karttunen, A. Lönnqvist, E. Noponen, J. Mallat, M. Vaaja, V. Viikari, A. Räisänen, J. Heinonen, P. Hautala, and J. Lemanczyk, "Development of a hologram-based CATR for testing a very high gain antenna at 650 GHz," presented at the European Conference on Antennas and Propagation, EuCAP 2006, Nice, France, 6-10 November 2006.

Lohmann, A. W.

Lönnqvist, A.

A. Lönnqvist, J. Mallat, and A. V. Räisänen, "Phase-hologram-based compact RCS test range at 310 GHz for scale models," IEEE Trans. Microwave Theory Tech. 54, 2391-2397 (2006).
[CrossRef]

J. Häkli, T. Koskinen, A. Lönnqvist, J. Säily, V. Viikari, J. Mallat, J. Ala-Laurinaho, J. Tuovinen, and A. V. Räisänen, "Testing of a 1.5 m reflector antenna at 322 GHz in a CATR based on a hologram," IEEE Trans. Antennas Propag. 53, 3142-3150 (2005).
[CrossRef]

T. Koskinen, J. Ala-Laurinaho, J. Säily, A. Lönnqvist, J. Häkli, J. Mallat, J. Tuovinen, and A. V. Räisänen, "Experimental study on a hologram-based compact antenna test range at 650 GHz," IEEE Trans. Microwave Theory Tech. 53, 2999-3006 (2005).
[CrossRef]

A. Lönnqvist, T. Koskinen, J. Häkli, J. Säily, J. Ala-Laurinaho, J. Mallat, V. Viikari, J. Tuovinen, and A. V. Räisänen, "Hologram-based compact range for submillimeter-wave antenna testing," IEEE Trans. Antennas Propag. 53, 3151-3159 (2005).
[CrossRef]

J. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Millimeter-wave beam shaping using holograms," IEEE Trans. Microwave Theory Tech. 51, 1274-1280 (2003).
[CrossRef]

J. Salo, J. Meltaus, E. Noponen, M. M. Salomaa, A. Lönnqvist, T. Koskinen, V. Viikari, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Holograms for shaping radio-wave fields," J. Opt. A 4, S161-S167 (2002).
[CrossRef]

J. Ala-Laurinaho, T. Koskinen, J. Häkli, A. Karttunen, A. Lönnqvist, E. Noponen, J. Mallat, M. Vaaja, V. Viikari, A. Räisänen, J. Heinonen, P. Hautala, and J. Lemanczyk, "Development of a hologram-based CATR for testing a very high gain antenna at 650 GHz," presented at the European Conference on Antennas and Propagation, EuCAP 2006, Nice, France, 6-10 November 2006.

A. Lönnqvist, J. Mallat, E. Noponen, J. Ala-Laurinaho, J. Säily, T. Koskinen, J. Häkli, and A. V. Räisänen, "A phase hologram compact RCS-range for scale model measurements," in Proceedings of 3rd ESA Workshop on Millimetre-Wave Technology and Applications (European Space Agency, 2003), Vol. WPP-212, pp. 511-516.

J. Häkli, T. Koskinen, J. Ala-Laurinaho, A. Karttunen, M. Vaaja, V. Viikari, A. Lönnqvist, J. Heinonen, J. Mallat, E. Noponen, P. Hautala, J. Lemanczyk, and A. V. Räisänen, "Development of a 650 GHz hologram based CATR for testing a 1.5 m reflector antenna," in Proceedings of AMTA Europe Symposium 2006 (Antenna Measurement Techniques Association, 2006), pp. 83-88.

E. Noponen, J. Häkli, T. Koskinen, A. Lönnqvist, V. Viikari, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Synthesis of reflection-type phase hologram for compact antenna test range at 310 GHz," in Proceedings of 4th ESA Workshop on Millimetre-Wave Technology and Applications (European Space Agency, 2006), Vol. WPP-258, pp. 391-396.

J. Mallat, J. Ala-Laurinaho, E. Noponen, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Meltaus, and A. V. Räisänen, "A phase hologram RCS range for scale model measurements," in Digest of Technical Papers, URSI/IEEE XXVII Convention on Radio Science, Vol. S 257 of Helsinki University of Technology Radio Laboratory Publications (TKK Helsinki University of Technology, 2002), pp. 143-145.

Mallat, J.

A. Lönnqvist, J. Mallat, and A. V. Räisänen, "Phase-hologram-based compact RCS test range at 310 GHz for scale models," IEEE Trans. Microwave Theory Tech. 54, 2391-2397 (2006).
[CrossRef]

J. Häkli, T. Koskinen, A. Lönnqvist, J. Säily, V. Viikari, J. Mallat, J. Ala-Laurinaho, J. Tuovinen, and A. V. Räisänen, "Testing of a 1.5 m reflector antenna at 322 GHz in a CATR based on a hologram," IEEE Trans. Antennas Propag. 53, 3142-3150 (2005).
[CrossRef]

A. Lönnqvist, T. Koskinen, J. Häkli, J. Säily, J. Ala-Laurinaho, J. Mallat, V. Viikari, J. Tuovinen, and A. V. Räisänen, "Hologram-based compact range for submillimeter-wave antenna testing," IEEE Trans. Antennas Propag. 53, 3151-3159 (2005).
[CrossRef]

T. Koskinen, J. Ala-Laurinaho, J. Säily, A. Lönnqvist, J. Häkli, J. Mallat, J. Tuovinen, and A. V. Räisänen, "Experimental study on a hologram-based compact antenna test range at 650 GHz," IEEE Trans. Microwave Theory Tech. 53, 2999-3006 (2005).
[CrossRef]

J. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Millimeter-wave beam shaping using holograms," IEEE Trans. Microwave Theory Tech. 51, 1274-1280 (2003).
[CrossRef]

J. Salo, J. Meltaus, E. Noponen, M. M. Salomaa, A. Lönnqvist, T. Koskinen, V. Viikari, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Holograms for shaping radio-wave fields," J. Opt. A 4, S161-S167 (2002).
[CrossRef]

J. Ala-Laurinaho, T. Koskinen, J. Häkli, A. Karttunen, A. Lönnqvist, E. Noponen, J. Mallat, M. Vaaja, V. Viikari, A. Räisänen, J. Heinonen, P. Hautala, and J. Lemanczyk, "Development of a hologram-based CATR for testing a very high gain antenna at 650 GHz," presented at the European Conference on Antennas and Propagation, EuCAP 2006, Nice, France, 6-10 November 2006.

A. Lönnqvist, J. Mallat, E. Noponen, J. Ala-Laurinaho, J. Säily, T. Koskinen, J. Häkli, and A. V. Räisänen, "A phase hologram compact RCS-range for scale model measurements," in Proceedings of 3rd ESA Workshop on Millimetre-Wave Technology and Applications (European Space Agency, 2003), Vol. WPP-212, pp. 511-516.

J. Häkli, T. Koskinen, J. Ala-Laurinaho, A. Karttunen, M. Vaaja, V. Viikari, A. Lönnqvist, J. Heinonen, J. Mallat, E. Noponen, P. Hautala, J. Lemanczyk, and A. V. Räisänen, "Development of a 650 GHz hologram based CATR for testing a 1.5 m reflector antenna," in Proceedings of AMTA Europe Symposium 2006 (Antenna Measurement Techniques Association, 2006), pp. 83-88.

E. Noponen, J. Häkli, T. Koskinen, A. Lönnqvist, V. Viikari, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Synthesis of reflection-type phase hologram for compact antenna test range at 310 GHz," in Proceedings of 4th ESA Workshop on Millimetre-Wave Technology and Applications (European Space Agency, 2006), Vol. WPP-258, pp. 391-396.

J. Mallat, J. Ala-Laurinaho, E. Noponen, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Meltaus, and A. V. Räisänen, "A phase hologram RCS range for scale model measurements," in Digest of Technical Papers, URSI/IEEE XXVII Convention on Radio Science, Vol. S 257 of Helsinki University of Technology Radio Laboratory Publications (TKK Helsinki University of Technology, 2002), pp. 143-145.

Meltaus, J.

J. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Millimeter-wave beam shaping using holograms," IEEE Trans. Microwave Theory Tech. 51, 1274-1280 (2003).
[CrossRef]

J. Salo, J. Meltaus, E. Noponen, M. M. Salomaa, A. Lönnqvist, T. Koskinen, V. Viikari, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Holograms for shaping radio-wave fields," J. Opt. A 4, S161-S167 (2002).
[CrossRef]

J. Mallat, J. Ala-Laurinaho, E. Noponen, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Meltaus, and A. V. Räisänen, "A phase hologram RCS range for scale model measurements," in Digest of Technical Papers, URSI/IEEE XXVII Convention on Radio Science, Vol. S 257 of Helsinki University of Technology Radio Laboratory Publications (TKK Helsinki University of Technology, 2002), pp. 143-145.

Miller, J. M.

Noponen, E.

J. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Millimeter-wave beam shaping using holograms," IEEE Trans. Microwave Theory Tech. 51, 1274-1280 (2003).
[CrossRef]

J. Salo, J. Meltaus, E. Noponen, M. M. Salomaa, A. Lönnqvist, T. Koskinen, V. Viikari, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Holograms for shaping radio-wave fields," J. Opt. A 4, S161-S167 (2002).
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V. Kettunen, P. Vahimaa, J. Turunen, and E. Noponen, "Zeroth-order coding of complex amplitude in two dimensions," J. Opt. Soc. Am. A 14, 808-815 (1997).
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J. Turunen, P. Vahimaa, M. Honkanen, O. Salminen, and E. Noponen, "Zeroth-order complex-amplitude modulation with dielectric Fourier-type diffractive elements," J. Mod. Opt. 43, 1389-1398 (1996).
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E. Noponen and J. Turunen, "Complex-amplitude modulation by high-carrier-frequency diffractive elements," J. Opt. Soc. Am. A 13, 1422-1428 (1996).
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E. Noponen and J. Turunen, "Binary high-frequency-carrier diffractive optical elements: electromagnetic theory," J. Opt. Soc. Am. A 11, 1097-1109 (1994).
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E. Noponen, A. Vasara, J. Turunen, J. M. Miller, and M. R. Taghizadeh, "Synthetic diffractive optics in the resonance domain," J. Opt. Soc. Am. A 9, 1206-1213 (1992).
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A. Vasara, M. R. Taghizadeh, J. Turunen, J. Westerholm, E. Noponen, H. Ichikawa, J. M. Miller, T. Jaakkola, and S. Kuisma, "Binary surface-relief gratings for array illumination in digital optics," Appl. Opt. 31, 3320-3336 (1992).
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A. Vasara, E. Noponen, J. Turunen, J. M. Miller, M. R. Taghizadeh, and J. Tuovinen, "Rigorous diffraction theory of binary optical interconnects," in Holographic Optics III: Principles and Applications, Proc. SPIE 1507, 224-238 (1991).
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J. Mallat, J. Ala-Laurinaho, E. Noponen, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Meltaus, and A. V. Räisänen, "A phase hologram RCS range for scale model measurements," in Digest of Technical Papers, URSI/IEEE XXVII Convention on Radio Science, Vol. S 257 of Helsinki University of Technology Radio Laboratory Publications (TKK Helsinki University of Technology, 2002), pp. 143-145.

E. Noponen, J. Häkli, T. Koskinen, A. Lönnqvist, V. Viikari, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Synthesis of reflection-type phase hologram for compact antenna test range at 310 GHz," in Proceedings of 4th ESA Workshop on Millimetre-Wave Technology and Applications (European Space Agency, 2006), Vol. WPP-258, pp. 391-396.

J. Häkli, T. Koskinen, J. Ala-Laurinaho, A. Karttunen, M. Vaaja, V. Viikari, A. Lönnqvist, J. Heinonen, J. Mallat, E. Noponen, P. Hautala, J. Lemanczyk, and A. V. Räisänen, "Development of a 650 GHz hologram based CATR for testing a 1.5 m reflector antenna," in Proceedings of AMTA Europe Symposium 2006 (Antenna Measurement Techniques Association, 2006), pp. 83-88.

J. Ala-Laurinaho, T. Koskinen, J. Häkli, A. Karttunen, A. Lönnqvist, E. Noponen, J. Mallat, M. Vaaja, V. Viikari, A. Räisänen, J. Heinonen, P. Hautala, and J. Lemanczyk, "Development of a hologram-based CATR for testing a very high gain antenna at 650 GHz," presented at the European Conference on Antennas and Propagation, EuCAP 2006, Nice, France, 6-10 November 2006.

A. Lönnqvist, J. Mallat, E. Noponen, J. Ala-Laurinaho, J. Säily, T. Koskinen, J. Häkli, and A. V. Räisänen, "A phase hologram compact RCS-range for scale model measurements," in Proceedings of 3rd ESA Workshop on Millimetre-Wave Technology and Applications (European Space Agency, 2003), Vol. WPP-212, pp. 511-516.

Paris, D. P.

Peng, S. T.

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. 23, 123-133 (1975).
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J. Ala-Laurinaho, T. Hirvonen, P. Piironen, A. Lehto, J. Tuovinen, A. V. Räisänen, and U. Frisk, "Measurement of the Odin telescope at 119 GHz with a hologram-type CATR," IEEE Trans. Antennas Propag. 49, 1264-1270 (2001).
[CrossRef]

Räisänen, A.

J. Ala-Laurinaho, T. Koskinen, J. Häkli, A. Karttunen, A. Lönnqvist, E. Noponen, J. Mallat, M. Vaaja, V. Viikari, A. Räisänen, J. Heinonen, P. Hautala, and J. Lemanczyk, "Development of a hologram-based CATR for testing a very high gain antenna at 650 GHz," presented at the European Conference on Antennas and Propagation, EuCAP 2006, Nice, France, 6-10 November 2006.

J. Tuovinen, A. Vasara, and A. Räisänen, "A new type of compact antenna test range," in Proceedings of the 22nd European Microwave Conference (IEEE, 1992), pp. 503-508.
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A. Lönnqvist, J. Mallat, and A. V. Räisänen, "Phase-hologram-based compact RCS test range at 310 GHz for scale models," IEEE Trans. Microwave Theory Tech. 54, 2391-2397 (2006).
[CrossRef]

J. Häkli, T. Koskinen, A. Lönnqvist, J. Säily, V. Viikari, J. Mallat, J. Ala-Laurinaho, J. Tuovinen, and A. V. Räisänen, "Testing of a 1.5 m reflector antenna at 322 GHz in a CATR based on a hologram," IEEE Trans. Antennas Propag. 53, 3142-3150 (2005).
[CrossRef]

T. Koskinen, J. Ala-Laurinaho, J. Säily, A. Lönnqvist, J. Häkli, J. Mallat, J. Tuovinen, and A. V. Räisänen, "Experimental study on a hologram-based compact antenna test range at 650 GHz," IEEE Trans. Microwave Theory Tech. 53, 2999-3006 (2005).
[CrossRef]

A. Lönnqvist, T. Koskinen, J. Häkli, J. Säily, J. Ala-Laurinaho, J. Mallat, V. Viikari, J. Tuovinen, and A. V. Räisänen, "Hologram-based compact range for submillimeter-wave antenna testing," IEEE Trans. Antennas Propag. 53, 3151-3159 (2005).
[CrossRef]

J. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Millimeter-wave beam shaping using holograms," IEEE Trans. Microwave Theory Tech. 51, 1274-1280 (2003).
[CrossRef]

J. Säily, P. Eskelinen, and A. V. Räisänen, "Pilot signal based real-time measurement and correction of phase errors caused by microwave cable flexing in planar near-field tests," IEEE Trans. Antennas Propag. 51, 195-200 (2003).
[CrossRef]

J. Salo, J. Meltaus, E. Noponen, M. M. Salomaa, A. Lönnqvist, T. Koskinen, V. Viikari, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Holograms for shaping radio-wave fields," J. Opt. A 4, S161-S167 (2002).
[CrossRef]

J. Ala-Laurinaho, T. Hirvonen, P. Piironen, A. Lehto, J. Tuovinen, A. V. Räisänen, and U. Frisk, "Measurement of the Odin telescope at 119 GHz with a hologram-type CATR," IEEE Trans. Antennas Propag. 49, 1264-1270 (2001).
[CrossRef]

J. Säily, J. Ala-Laurinaho, J. Häkli, J. Tuovinen, A. Lehto, and A. V. Räisänen, "Test results of 310 GHz hologram compact antenna test range," Electron. Lett. 36, 111-112 (2000).
[CrossRef]

T. Sehm, J. Ala-Laurinaho, T. Hirvonen, and A. V. Räisänen, "Antenna measurements using a hologram CATR," Electron. Lett. 35, 757-758 (1999).
[CrossRef]

T. Hirvonen, J. Ala-Laurinaho, J. Tuovinen, and A. V. Räisänen, "A compact antenna test range based on a hologram," IEEE Trans. Antennas Propag. 45, 1270-1276 (1997).
[CrossRef]

J. Ala-Laurinaho, T. Hirvonen, J. Tuovinen, and A. V. Räisänen, "Numerical modeling of a nonuniform grating with FDTD," Microwave Opt. Technol. Lett. 15, 134-139 (1997).
[CrossRef]

E. Noponen, J. Häkli, T. Koskinen, A. Lönnqvist, V. Viikari, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Synthesis of reflection-type phase hologram for compact antenna test range at 310 GHz," in Proceedings of 4th ESA Workshop on Millimetre-Wave Technology and Applications (European Space Agency, 2006), Vol. WPP-258, pp. 391-396.

J. Mallat, J. Ala-Laurinaho, E. Noponen, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Meltaus, and A. V. Räisänen, "A phase hologram RCS range for scale model measurements," in Digest of Technical Papers, URSI/IEEE XXVII Convention on Radio Science, Vol. S 257 of Helsinki University of Technology Radio Laboratory Publications (TKK Helsinki University of Technology, 2002), pp. 143-145.

A. Lönnqvist, J. Mallat, E. Noponen, J. Ala-Laurinaho, J. Säily, T. Koskinen, J. Häkli, and A. V. Räisänen, "A phase hologram compact RCS-range for scale model measurements," in Proceedings of 3rd ESA Workshop on Millimetre-Wave Technology and Applications (European Space Agency, 2003), Vol. WPP-212, pp. 511-516.

J. Häkli, T. Koskinen, J. Ala-Laurinaho, A. Karttunen, M. Vaaja, V. Viikari, A. Lönnqvist, J. Heinonen, J. Mallat, E. Noponen, P. Hautala, J. Lemanczyk, and A. V. Räisänen, "Development of a 650 GHz hologram based CATR for testing a 1.5 m reflector antenna," in Proceedings of AMTA Europe Symposium 2006 (Antenna Measurement Techniques Association, 2006), pp. 83-88.

Säily, J.

A. Lönnqvist, T. Koskinen, J. Häkli, J. Säily, J. Ala-Laurinaho, J. Mallat, V. Viikari, J. Tuovinen, and A. V. Räisänen, "Hologram-based compact range for submillimeter-wave antenna testing," IEEE Trans. Antennas Propag. 53, 3151-3159 (2005).
[CrossRef]

T. Koskinen, J. Ala-Laurinaho, J. Säily, A. Lönnqvist, J. Häkli, J. Mallat, J. Tuovinen, and A. V. Räisänen, "Experimental study on a hologram-based compact antenna test range at 650 GHz," IEEE Trans. Microwave Theory Tech. 53, 2999-3006 (2005).
[CrossRef]

J. Häkli, T. Koskinen, A. Lönnqvist, J. Säily, V. Viikari, J. Mallat, J. Ala-Laurinaho, J. Tuovinen, and A. V. Räisänen, "Testing of a 1.5 m reflector antenna at 322 GHz in a CATR based on a hologram," IEEE Trans. Antennas Propag. 53, 3142-3150 (2005).
[CrossRef]

J. Säily, P. Eskelinen, and A. V. Räisänen, "Pilot signal based real-time measurement and correction of phase errors caused by microwave cable flexing in planar near-field tests," IEEE Trans. Antennas Propag. 51, 195-200 (2003).
[CrossRef]

J. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Millimeter-wave beam shaping using holograms," IEEE Trans. Microwave Theory Tech. 51, 1274-1280 (2003).
[CrossRef]

J. Salo, J. Meltaus, E. Noponen, M. M. Salomaa, A. Lönnqvist, T. Koskinen, V. Viikari, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Holograms for shaping radio-wave fields," J. Opt. A 4, S161-S167 (2002).
[CrossRef]

J. Säily, J. Ala-Laurinaho, J. Häkli, J. Tuovinen, A. Lehto, and A. V. Räisänen, "Test results of 310 GHz hologram compact antenna test range," Electron. Lett. 36, 111-112 (2000).
[CrossRef]

J. Mallat, J. Ala-Laurinaho, E. Noponen, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Meltaus, and A. V. Räisänen, "A phase hologram RCS range for scale model measurements," in Digest of Technical Papers, URSI/IEEE XXVII Convention on Radio Science, Vol. S 257 of Helsinki University of Technology Radio Laboratory Publications (TKK Helsinki University of Technology, 2002), pp. 143-145.

A. Lönnqvist, J. Mallat, E. Noponen, J. Ala-Laurinaho, J. Säily, T. Koskinen, J. Häkli, and A. V. Räisänen, "A phase hologram compact RCS-range for scale model measurements," in Proceedings of 3rd ESA Workshop on Millimetre-Wave Technology and Applications (European Space Agency, 2003), Vol. WPP-212, pp. 511-516.

Salminen, O.

J. Turunen, P. Vahimaa, M. Honkanen, O. Salminen, and E. Noponen, "Zeroth-order complex-amplitude modulation with dielectric Fourier-type diffractive elements," J. Mod. Opt. 43, 1389-1398 (1996).
[CrossRef]

Salo, J.

J. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Millimeter-wave beam shaping using holograms," IEEE Trans. Microwave Theory Tech. 51, 1274-1280 (2003).
[CrossRef]

J. Salo, J. Meltaus, E. Noponen, M. M. Salomaa, A. Lönnqvist, T. Koskinen, V. Viikari, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Holograms for shaping radio-wave fields," J. Opt. A 4, S161-S167 (2002).
[CrossRef]

Salomaa, M. M.

J. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Millimeter-wave beam shaping using holograms," IEEE Trans. Microwave Theory Tech. 51, 1274-1280 (2003).
[CrossRef]

J. Salo, J. Meltaus, E. Noponen, M. M. Salomaa, A. Lönnqvist, T. Koskinen, V. Viikari, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Holograms for shaping radio-wave fields," J. Opt. A 4, S161-S167 (2002).
[CrossRef]

Sehm, T.

T. Sehm, J. Ala-Laurinaho, T. Hirvonen, and A. V. Räisänen, "Antenna measurements using a hologram CATR," Electron. Lett. 35, 757-758 (1999).
[CrossRef]

Shaeffer, J. F.

E. F. Knott, J. F. Shaeffer, and M. T. Tuley, Radar Cross Section, 2nd ed. (Artech House, 1993).

Taghizadeh, M. R.

Tamir, T.

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. 23, 123-133 (1975).
[CrossRef]

Tricoles, G.

G. Tricoles and N. H. Farhat, "Microwave holography: applications and techniques," Proc. IEEE 65, 108-121 (1977).
[CrossRef]

Tuley, M. T.

E. F. Knott, J. F. Shaeffer, and M. T. Tuley, Radar Cross Section, 2nd ed. (Artech House, 1993).

Tuovinen, J.

T. Koskinen, J. Ala-Laurinaho, J. Säily, A. Lönnqvist, J. Häkli, J. Mallat, J. Tuovinen, and A. V. Räisänen, "Experimental study on a hologram-based compact antenna test range at 650 GHz," IEEE Trans. Microwave Theory Tech. 53, 2999-3006 (2005).
[CrossRef]

A. Lönnqvist, T. Koskinen, J. Häkli, J. Säily, J. Ala-Laurinaho, J. Mallat, V. Viikari, J. Tuovinen, and A. V. Räisänen, "Hologram-based compact range for submillimeter-wave antenna testing," IEEE Trans. Antennas Propag. 53, 3151-3159 (2005).
[CrossRef]

J. Häkli, T. Koskinen, A. Lönnqvist, J. Säily, V. Viikari, J. Mallat, J. Ala-Laurinaho, J. Tuovinen, and A. V. Räisänen, "Testing of a 1.5 m reflector antenna at 322 GHz in a CATR based on a hologram," IEEE Trans. Antennas Propag. 53, 3142-3150 (2005).
[CrossRef]

J. Ala-Laurinaho, T. Hirvonen, P. Piironen, A. Lehto, J. Tuovinen, A. V. Räisänen, and U. Frisk, "Measurement of the Odin telescope at 119 GHz with a hologram-type CATR," IEEE Trans. Antennas Propag. 49, 1264-1270 (2001).
[CrossRef]

J. Säily, J. Ala-Laurinaho, J. Häkli, J. Tuovinen, A. Lehto, and A. V. Räisänen, "Test results of 310 GHz hologram compact antenna test range," Electron. Lett. 36, 111-112 (2000).
[CrossRef]

J. Ala-Laurinaho, T. Hirvonen, J. Tuovinen, and A. V. Räisänen, "Numerical modeling of a nonuniform grating with FDTD," Microwave Opt. Technol. Lett. 15, 134-139 (1997).
[CrossRef]

T. Hirvonen, J. Ala-Laurinaho, J. Tuovinen, and A. V. Räisänen, "A compact antenna test range based on a hologram," IEEE Trans. Antennas Propag. 45, 1270-1276 (1997).
[CrossRef]

A. Vasara, E. Noponen, J. Turunen, J. M. Miller, M. R. Taghizadeh, and J. Tuovinen, "Rigorous diffraction theory of binary optical interconnects," in Holographic Optics III: Principles and Applications, Proc. SPIE 1507, 224-238 (1991).
[CrossRef]

J. Tuovinen, A. Vasara, and A. Räisänen, "A new type of compact antenna test range," in Proceedings of the 22nd European Microwave Conference (IEEE, 1992), pp. 503-508.
[CrossRef]

Turunen, J.

V. Kettunen, P. Vahimaa, J. Turunen, and E. Noponen, "Zeroth-order coding of complex amplitude in two dimensions," J. Opt. Soc. Am. A 14, 808-815 (1997).
[CrossRef]

J. Turunen, P. Vahimaa, M. Honkanen, O. Salminen, and E. Noponen, "Zeroth-order complex-amplitude modulation with dielectric Fourier-type diffractive elements," J. Mod. Opt. 43, 1389-1398 (1996).
[CrossRef]

E. Noponen and J. Turunen, "Complex-amplitude modulation by high-carrier-frequency diffractive elements," J. Opt. Soc. Am. A 13, 1422-1428 (1996).
[CrossRef]

E. Noponen and J. Turunen, "Binary high-frequency-carrier diffractive optical elements: electromagnetic theory," J. Opt. Soc. Am. A 11, 1097-1109 (1994).
[CrossRef]

E. Noponen, A. Vasara, J. Turunen, J. M. Miller, and M. R. Taghizadeh, "Synthetic diffractive optics in the resonance domain," J. Opt. Soc. Am. A 9, 1206-1213 (1992).
[CrossRef]

A. Vasara, M. R. Taghizadeh, J. Turunen, J. Westerholm, E. Noponen, H. Ichikawa, J. M. Miller, T. Jaakkola, and S. Kuisma, "Binary surface-relief gratings for array illumination in digital optics," Appl. Opt. 31, 3320-3336 (1992).
[CrossRef] [PubMed]

A. Vasara, E. Noponen, J. Turunen, J. M. Miller, M. R. Taghizadeh, and J. Tuovinen, "Rigorous diffraction theory of binary optical interconnects," in Holographic Optics III: Principles and Applications, Proc. SPIE 1507, 224-238 (1991).
[CrossRef]

A. Vasara, J. Turunen, and A. T. Friberg, "Realization of general nondiffracting beams with computer-generated holograms," J. Opt. Soc. Am. A 6, 1748-1754 (1989).
[CrossRef] [PubMed]

Vaaja, M.

J. Ala-Laurinaho, T. Koskinen, J. Häkli, A. Karttunen, A. Lönnqvist, E. Noponen, J. Mallat, M. Vaaja, V. Viikari, A. Räisänen, J. Heinonen, P. Hautala, and J. Lemanczyk, "Development of a hologram-based CATR for testing a very high gain antenna at 650 GHz," presented at the European Conference on Antennas and Propagation, EuCAP 2006, Nice, France, 6-10 November 2006.

J. Häkli, T. Koskinen, J. Ala-Laurinaho, A. Karttunen, M. Vaaja, V. Viikari, A. Lönnqvist, J. Heinonen, J. Mallat, E. Noponen, P. Hautala, J. Lemanczyk, and A. V. Räisänen, "Development of a 650 GHz hologram based CATR for testing a 1.5 m reflector antenna," in Proceedings of AMTA Europe Symposium 2006 (Antenna Measurement Techniques Association, 2006), pp. 83-88.

Vahimaa, P.

V. Kettunen, P. Vahimaa, J. Turunen, and E. Noponen, "Zeroth-order coding of complex amplitude in two dimensions," J. Opt. Soc. Am. A 14, 808-815 (1997).
[CrossRef]

J. Turunen, P. Vahimaa, M. Honkanen, O. Salminen, and E. Noponen, "Zeroth-order complex-amplitude modulation with dielectric Fourier-type diffractive elements," J. Mod. Opt. 43, 1389-1398 (1996).
[CrossRef]

Vasara, A.

Viikari, V.

J. Häkli, T. Koskinen, A. Lönnqvist, J. Säily, V. Viikari, J. Mallat, J. Ala-Laurinaho, J. Tuovinen, and A. V. Räisänen, "Testing of a 1.5 m reflector antenna at 322 GHz in a CATR based on a hologram," IEEE Trans. Antennas Propag. 53, 3142-3150 (2005).
[CrossRef]

A. Lönnqvist, T. Koskinen, J. Häkli, J. Säily, J. Ala-Laurinaho, J. Mallat, V. Viikari, J. Tuovinen, and A. V. Räisänen, "Hologram-based compact range for submillimeter-wave antenna testing," IEEE Trans. Antennas Propag. 53, 3151-3159 (2005).
[CrossRef]

J. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Millimeter-wave beam shaping using holograms," IEEE Trans. Microwave Theory Tech. 51, 1274-1280 (2003).
[CrossRef]

J. Salo, J. Meltaus, E. Noponen, M. M. Salomaa, A. Lönnqvist, T. Koskinen, V. Viikari, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Holograms for shaping radio-wave fields," J. Opt. A 4, S161-S167 (2002).
[CrossRef]

J. Ala-Laurinaho, T. Koskinen, J. Häkli, A. Karttunen, A. Lönnqvist, E. Noponen, J. Mallat, M. Vaaja, V. Viikari, A. Räisänen, J. Heinonen, P. Hautala, and J. Lemanczyk, "Development of a hologram-based CATR for testing a very high gain antenna at 650 GHz," presented at the European Conference on Antennas and Propagation, EuCAP 2006, Nice, France, 6-10 November 2006.

J. Häkli, T. Koskinen, J. Ala-Laurinaho, A. Karttunen, M. Vaaja, V. Viikari, A. Lönnqvist, J. Heinonen, J. Mallat, E. Noponen, P. Hautala, J. Lemanczyk, and A. V. Räisänen, "Development of a 650 GHz hologram based CATR for testing a 1.5 m reflector antenna," in Proceedings of AMTA Europe Symposium 2006 (Antenna Measurement Techniques Association, 2006), pp. 83-88.

E. Noponen, J. Häkli, T. Koskinen, A. Lönnqvist, V. Viikari, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Synthesis of reflection-type phase hologram for compact antenna test range at 310 GHz," in Proceedings of 4th ESA Workshop on Millimetre-Wave Technology and Applications (European Space Agency, 2006), Vol. WPP-258, pp. 391-396.

J. Mallat, J. Ala-Laurinaho, E. Noponen, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Meltaus, and A. V. Räisänen, "A phase hologram RCS range for scale model measurements," in Digest of Technical Papers, URSI/IEEE XXVII Convention on Radio Science, Vol. S 257 of Helsinki University of Technology Radio Laboratory Publications (TKK Helsinki University of Technology, 2002), pp. 143-145.

Westerholm, J.

Appl. Opt. (3)

Electron. Lett. (2)

T. Sehm, J. Ala-Laurinaho, T. Hirvonen, and A. V. Räisänen, "Antenna measurements using a hologram CATR," Electron. Lett. 35, 757-758 (1999).
[CrossRef]

J. Säily, J. Ala-Laurinaho, J. Häkli, J. Tuovinen, A. Lehto, and A. V. Räisänen, "Test results of 310 GHz hologram compact antenna test range," Electron. Lett. 36, 111-112 (2000).
[CrossRef]

IEEE Trans. Antennas Propag. (5)

J. Ala-Laurinaho, T. Hirvonen, P. Piironen, A. Lehto, J. Tuovinen, A. V. Räisänen, and U. Frisk, "Measurement of the Odin telescope at 119 GHz with a hologram-type CATR," IEEE Trans. Antennas Propag. 49, 1264-1270 (2001).
[CrossRef]

A. Lönnqvist, T. Koskinen, J. Häkli, J. Säily, J. Ala-Laurinaho, J. Mallat, V. Viikari, J. Tuovinen, and A. V. Räisänen, "Hologram-based compact range for submillimeter-wave antenna testing," IEEE Trans. Antennas Propag. 53, 3151-3159 (2005).
[CrossRef]

J. Häkli, T. Koskinen, A. Lönnqvist, J. Säily, V. Viikari, J. Mallat, J. Ala-Laurinaho, J. Tuovinen, and A. V. Räisänen, "Testing of a 1.5 m reflector antenna at 322 GHz in a CATR based on a hologram," IEEE Trans. Antennas Propag. 53, 3142-3150 (2005).
[CrossRef]

T. Hirvonen, J. Ala-Laurinaho, J. Tuovinen, and A. V. Räisänen, "A compact antenna test range based on a hologram," IEEE Trans. Antennas Propag. 45, 1270-1276 (1997).
[CrossRef]

J. Säily, P. Eskelinen, and A. V. Räisänen, "Pilot signal based real-time measurement and correction of phase errors caused by microwave cable flexing in planar near-field tests," IEEE Trans. Antennas Propag. 51, 195-200 (2003).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (4)

J. Meltaus, J. Salo, E. Noponen, M. M. Salomaa, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Millimeter-wave beam shaping using holograms," IEEE Trans. Microwave Theory Tech. 51, 1274-1280 (2003).
[CrossRef]

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides," IEEE Trans. Microwave Theory Tech. 23, 123-133 (1975).
[CrossRef]

A. Lönnqvist, J. Mallat, and A. V. Räisänen, "Phase-hologram-based compact RCS test range at 310 GHz for scale models," IEEE Trans. Microwave Theory Tech. 54, 2391-2397 (2006).
[CrossRef]

T. Koskinen, J. Ala-Laurinaho, J. Säily, A. Lönnqvist, J. Häkli, J. Mallat, J. Tuovinen, and A. V. Räisänen, "Experimental study on a hologram-based compact antenna test range at 650 GHz," IEEE Trans. Microwave Theory Tech. 53, 2999-3006 (2005).
[CrossRef]

J. Mod. Opt. (1)

J. Turunen, P. Vahimaa, M. Honkanen, O. Salminen, and E. Noponen, "Zeroth-order complex-amplitude modulation with dielectric Fourier-type diffractive elements," J. Mod. Opt. 43, 1389-1398 (1996).
[CrossRef]

J. Opt. A (1)

J. Salo, J. Meltaus, E. Noponen, M. M. Salomaa, A. Lönnqvist, T. Koskinen, V. Viikari, J. Säily, J. Häkli, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Holograms for shaping radio-wave fields," J. Opt. A 4, S161-S167 (2002).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (5)

Microwave Opt. Technol. Lett. (1)

J. Ala-Laurinaho, T. Hirvonen, J. Tuovinen, and A. V. Räisänen, "Numerical modeling of a nonuniform grating with FDTD," Microwave Opt. Technol. Lett. 15, 134-139 (1997).
[CrossRef]

Proc. IEEE (1)

G. Tricoles and N. H. Farhat, "Microwave holography: applications and techniques," Proc. IEEE 65, 108-121 (1977).
[CrossRef]

Proc. SPIE (1)

A. Vasara, E. Noponen, J. Turunen, J. M. Miller, M. R. Taghizadeh, and J. Tuovinen, "Rigorous diffraction theory of binary optical interconnects," in Holographic Optics III: Principles and Applications, Proc. SPIE 1507, 224-238 (1991).
[CrossRef]

Other (10)

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

W.-H. Lee, "Computer-generated holograms: techniques and applications," in Progress in Optics, E. Wolf, ed. (North-Holland, 1978), Vol. XVI, pp. 119-232.
[CrossRef]

R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, 1980).
[CrossRef]

J. Tuovinen, A. Vasara, and A. Räisänen, "A new type of compact antenna test range," in Proceedings of the 22nd European Microwave Conference (IEEE, 1992), pp. 503-508.
[CrossRef]

J. Häkli, T. Koskinen, J. Ala-Laurinaho, A. Karttunen, M. Vaaja, V. Viikari, A. Lönnqvist, J. Heinonen, J. Mallat, E. Noponen, P. Hautala, J. Lemanczyk, and A. V. Räisänen, "Development of a 650 GHz hologram based CATR for testing a 1.5 m reflector antenna," in Proceedings of AMTA Europe Symposium 2006 (Antenna Measurement Techniques Association, 2006), pp. 83-88.

J. Ala-Laurinaho, T. Koskinen, J. Häkli, A. Karttunen, A. Lönnqvist, E. Noponen, J. Mallat, M. Vaaja, V. Viikari, A. Räisänen, J. Heinonen, P. Hautala, and J. Lemanczyk, "Development of a hologram-based CATR for testing a very high gain antenna at 650 GHz," presented at the European Conference on Antennas and Propagation, EuCAP 2006, Nice, France, 6-10 November 2006.

E. Noponen, J. Häkli, T. Koskinen, A. Lönnqvist, V. Viikari, J. Ala-Laurinaho, J. Mallat, and A. V. Räisänen, "Synthesis of reflection-type phase hologram for compact antenna test range at 310 GHz," in Proceedings of 4th ESA Workshop on Millimetre-Wave Technology and Applications (European Space Agency, 2006), Vol. WPP-258, pp. 391-396.

E. F. Knott, J. F. Shaeffer, and M. T. Tuley, Radar Cross Section, 2nd ed. (Artech House, 1993).

J. Mallat, J. Ala-Laurinaho, E. Noponen, V. Viikari, A. Lönnqvist, T. Koskinen, J. Säily, J. Häkli, J. Meltaus, and A. V. Räisänen, "A phase hologram RCS range for scale model measurements," in Digest of Technical Papers, URSI/IEEE XXVII Convention on Radio Science, Vol. S 257 of Helsinki University of Technology Radio Laboratory Publications (TKK Helsinki University of Technology, 2002), pp. 143-145.

A. Lönnqvist, J. Mallat, E. Noponen, J. Ala-Laurinaho, J. Säily, T. Koskinen, J. Häkli, and A. V. Räisänen, "A phase hologram compact RCS-range for scale model measurements," in Proceedings of 3rd ESA Workshop on Millimetre-Wave Technology and Applications (European Space Agency, 2003), Vol. WPP-212, pp. 511-516.

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Figures (16)

Fig. 1
Fig. 1

Geometry and the coordinate system.

Fig. 2
Fig. 2

Geometry and notation for the feed field.

Fig. 3
Fig. 3

Amplitude (thick curve) and phase (thin curve) of the goal field along the x axis for a hologram designed by using the parameters of Table 1. The amplitude is shown in the linear scale using the normalization of the quiet-zone amplitude.

Fig. 4
Fig. 4

Amplitude (thick curve) and phase (thin curve) modulation profiles along the x axis for the goal pattern of Fig. 3, assuming a 650 GHz feed field.

Fig. 5
Fig. 5

Local grating structure and the parameters for rigorous optimization.

Fig. 6
Fig. 6

Effect of the reflecting planar input interface in the optimization parameter space. (a) First-order transmission efficiency curves in the real geometry with the reflecting interface for three values of c = w / d . (b) The same in the modified geometry without the reflecting interface. The parameters used are n = 1.44 , d = 1.84 λ , H = 10.84 λ , and θ = 0 .

Fig. 7
Fig. 7

Range of combinations ( d , θ ) in the parameter space of the 650 G H z hologram with the aperture 320 m m × 280 m m .

Fig. 8
Fig. 8

Schematic illustration of the hologram pattern consisting of curved grooves on a rectangular substrate plate. The modulation is cut off at the radius ϱ 0 (defined in the quiet-zone coordinate system).

Fig. 9
Fig. 9

Cross section of the hologram profile at y = 0 designed by using the parameter values of Table 1 (note the different horizontal and vertical scales).

Fig. 10
Fig. 10

(a) Schematic illustration of a section of the actual groove structure. The shaded area represents the grooves. (b) Quantized pixel-formatted groove structure used in the simulation. The local grating elements are depicted by using the bold-line rectangles.

Fig. 11
Fig. 11

Simulation results for the quiet-zone field calculated by using the parameter values of Table 2 (hologram thickness H = 5 m m ): (a) amplitude cross sections along the x axis (black curve) and y axis (gray curve); (b) gray-level plot of amplitude over the quiet-zone; (c), (d) the respective graphs for the phase distribution. The dashed circles indicate the boundaries of the initially targeted quiet zone.

Fig. 12
Fig. 12

Same as Fig. 11, but for a thicker hologram plate with H = 10 m m .

Fig. 13
Fig. 13

Evolution of (a) the amplitude nonuniformity Δ A and (b) the phase nonuniformity Δ ϕ in terms of peak-to-peak ripple (round markers) and standard deviation (square markers) during the reoptimization runs A (open markers) and B (filled markers).

Fig. 14
Fig. 14

Amplitude (thick curve) and phase (thin curve) of the optimized goal field along the x axis after the eighth iteration in the reoptimization run B. The scale is equivalent to Fig. 3.

Fig. 15
Fig. 15

Simulated quiet-zone field for the reoptimized hologram structure B8, corresponding to the goal field of Fig. 14.

Fig. 16
Fig. 16

Measured quiet-zone field for a hologram designed by using the reoptimization algorithm and fabricated on a 5 mm thick Teflon plate. The amplitude and phase distributions are presented analogously to Figs. 11 and 15.

Tables (2)

Tables Icon

Table 1 Design Parameters for the Phase-Hologram-Based Compact Measurement Range at 650 GHz

Tables Icon

Table 2 Parameter Values used in the Simulation of the 650-GHz Hologram

Equations (34)

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x = x cos β z sin β ,
y = y ,
z = x sin β + z cos β .
T ( x , y ) = τ ( x , y ) exp [ i φ ( x , y ) ] = F ( x , y ) I ( x , y ) ,
T ( x , y ) = G ( x , y ) I ( x , y ) .
tan θ 1 = ρ 1 | z F | H ,
tan θ 2 = ρ 0 ρ 1 H .
n = ( n 2 sin 2 θ 1 ) 1 / 2 cos θ 1 = n cos θ 2 cos θ 1 .
ρ 1 = ρ 0 1 + H / [ n ( | z F | H ) ] .
A I ( P ) = A F ( δ ) ( R F / R ) ,
ϕ I ( P ) = k 0 ( R 1 + n R 2 ) Δ ϕ F ( δ ) ,
θ I ( x , y ) = arcsin [ | ϕ I ( x , y ) | n k 0 ] ,
W ( ϱ ) = W ( ϱ , ϱ 1 , ϱ 0 ) = { 1 when   0 ϱ ϱ 1 ( 1 τ ) 2 ( 1 + 2 τ ) when   ϱ 1 < ϱ < ϱ 0 0 when   ϱ ϱ 0 ,
G ( qz ) ( r ) = W ( r , r 1 ( qz ) , r 0 ( qz ) ) ,
G ( qz ) ( x , y , z ) = A 0 ( qz ) ( u , v ) × exp [ i 2 π ( u x + v y + w z ) ] d u d v = A ( qz ) ( u , v ; z ) × exp [ i 2 π ( u x + v y ) ] d u d v ,
A ( qz ) ( u , v ; z ) = A 0 ( qz ) ( u , v ) exp ( i 2 π w z ) .
A 0 ( qz ) ( u , v ) = G ( qz ) ( x , y , 0 ) × exp [ i 2 π ( u x + v y ) ] d x d y .
w = { [ ( 1 / λ ) 2 ( u 2 + v 2 ) ] 1 / 2 when   u 2 + v 2 ( 1 / λ ) 2 i [ ( u 2 + v 2 ) ( 1 / λ ) 2 ] 1 / 2 when   u 2 + v 2 > ( 1 / λ ) 2 .
x m = m Δ x ,   m = M / 2 ,   …   ,   M / 2 1 ,
y n = n Δ y ,   n = N / 2 ,   …   ,   N / 2 1 ,
u j = j Δ u ,   j = M / 2 ,   …   ,   M / 2 1 ,
v k = k Δ v ,   k = N / 2 ,   …   ,   N / 2 1 .
A ˜ ( j , k ) = m = 0 M 1 n = 0 N 1 G ˜ ( qz ) ( m , n ) W M j m W N k n ,
G ˜ ( qz ) ( m , n ; z ) = 1 M N j = 0 M 1 k = 0 N 1 A ˜ ( j , k ; z ) W M j m W N k n ,
ϕ c ( x , y ) = k 0 x sin β ,
d L ( x , y ) = 2 π / | φ ( x , y ) | ,
d c = λ / sin β ,
h = { h opt when   0 φ opt 2 π c opt 0 otherwise .
s = ( 2 r q + q 2 ) 1 / 2 ,
r = sin α x φ opt ( x , y ) + cos α y φ opt ( x , y ) cos 2 α x 2 φ opt ( x , y ) + 2 sin α cos α x y φ opt ( x , y ) + sin 2 α y 2 φ opt ( x , y ) ,
C ( x , y ) = G 0 ( x , y ) F 0 ( x , y ) ,
C i ( x , y ) = 1 + s w ( opt ) ( x , y ) [ G 0 ( x , y ) F i 1 ( x , y ) 1 ] .
| G i ( x , y ) | = | G i 1 ( x , y ) | { 1 + s w ( opt ) ( x , y ) × [ γ i 1 | G 0 ( x , y ) | | F i 1 ( x , y ) | 1 ] } ,
ψ i ( x , y ) = ψ i 1 ( x , y ) + s w ( opt ) ( x , y ) × [ ψ 0 ( x , y ) ϕ i 1 ( x , y ) ] ,

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