Abstract

We demonstrate a photonics-based self-heterodyne electro-optic field imaging technique at terahertz (THz) frequency. An optical intensity beat generated by mixing two frequency-detuned free-running lasers is used for both the generation and the detection. The frequency of the beat for detection is shifted by an optical frequency shifter to realize coherent heterodyne measurement with free-running lasers. Neither mechanical delay lines nor phase-locked synthesizers are required for the amplitude and the phase imaging of the THz field, and the system simplicity is thus improved. The amplitude and phase of the THz field (125 GHz) radiated from a horn antenna are simultaneously imaged, and the standard deviation of the phase measurement is found to be 0.18 rad.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Valdmanis, G. Mourou, and C. W. Gabel, Appl. Phys. Lett. 41, 211 (1982).
    [CrossRef]
  2. K. Kamogawa, I. Toyoda, K. Nishikawa, and T. Tokumitsu, IEEE Microwave Guided Wave Lett. 4, 414 (1994).
    [CrossRef]
  3. T. Pfeifer, T. Loffler, H. G. Roskos, H. Kurz, M. Singer, and E. M. Biebl, IEEE Trans. Antennas Propag. 46, 284 (1998).
    [CrossRef]
  4. K. Yang, L. P. B. Katehi, and J. F. Whitaker, IEEE Microw. Wirel. Compon. Lett. 11, 164 (2001).
    [CrossRef]
  5. J. R. Knab, A. J. L. Adam, M. Nagel, E. Shaner, M. A. Seo, D. S. Kim, and P. C. M. Planken, Opt. Express 17, 15072 (2009).
    [CrossRef]
  6. R. Mueckstein and O. Mitrofanov, Opt. Express 19, 3212 (2011).
    [CrossRef]
  7. T. Kleine-Ostmann and T. Nagatsuma, J. Infrared Millim. Terahz. Waves 32, 143 (2011).
    [CrossRef]
  8. T. Hasebe, S. Kawabe, H. Matsui, and H. Tabata, J. Appl. Phys. 112, 094702 (2012).
    [CrossRef]
  9. Q. Wu and X.-C. Zhang, Appl. Phys. Lett. 68, 1604 (1996).
    [CrossRef]
  10. H. Togo, D. Morendo-Dominguez, and N. Kukutsu, IEICE Trans. Electron. E96.C, 227 (2013).
    [CrossRef]
  11. K. Sasagawa, A. Kanno, and M. Tsuchiya, in Proceedings of PIERS, 2009 (2009), pp. 48–51.
  12. H. Ito, T. Furuta, F. Nakajima, K. Yoshino, and T. Ishibashi, J. Lightwave Technol. 23, 4016 (2005).
    [CrossRef]
  13. T. Nagatsuma, H. Ito, and T. Ishibashi, Laser Photon. Rev. 3, 123 (2009).
  14. A. Nahata, J. T. Yardley, and T. F. Heinz, Appl. Phys. Lett. 81, 963 (2002).
    [CrossRef]
  15. A. Nahata, J. T. Yardley, and T. F. Heinz, Appl. Phys. Lett. 75, 2524 (1999).
    [CrossRef]
  16. S. Hisatake, G. Kitahara, K. Ajito, Y. Fukada, N. Yoshimoto, and T. Nagatsuma, IEEE Sens. J. 13, 31 (2013).
    [CrossRef]
  17. T. Okoshi, K. Kikuchi, and A. Nakayama, Electron. Lett. 16, 630 (1980).
    [CrossRef]
  18. A. Garzarella, S.B. Qadri, and D. H. Wu, J. Electron. Mater. 39, 811 (2010).
    [CrossRef]
  19. S. Hisatake and T. Nagatsuma, Appl. Phys. Express 5, 012701 (2012).
    [CrossRef]
  20. H. Togo, N. Kukutsu, N. Shimizu, and T. Nagatsuma, J. Lightwave Technol. 26, 2700 (2008).
    [CrossRef]
  21. A. Sasaki and T. Nagatsuma, IEICE Trans. Electron. E86-C, 1345 (2003).
  22. K. Nishikata, Y. Kimura, Y. Takai, T. Ikuta, and R. Shimizu, Rev. Sci. Instrum. 74, 1393 (2003).
    [CrossRef]
  23. H. Togo, H. Uchida, H. Yokota, A. Izumi, T. Nagatsuma, and N. Fukasaku, J. Eur. Microwave Assoc. 4, 294 (2008).

2013 (2)

H. Togo, D. Morendo-Dominguez, and N. Kukutsu, IEICE Trans. Electron. E96.C, 227 (2013).
[CrossRef]

S. Hisatake, G. Kitahara, K. Ajito, Y. Fukada, N. Yoshimoto, and T. Nagatsuma, IEEE Sens. J. 13, 31 (2013).
[CrossRef]

2012 (2)

T. Hasebe, S. Kawabe, H. Matsui, and H. Tabata, J. Appl. Phys. 112, 094702 (2012).
[CrossRef]

S. Hisatake and T. Nagatsuma, Appl. Phys. Express 5, 012701 (2012).
[CrossRef]

2011 (2)

R. Mueckstein and O. Mitrofanov, Opt. Express 19, 3212 (2011).
[CrossRef]

T. Kleine-Ostmann and T. Nagatsuma, J. Infrared Millim. Terahz. Waves 32, 143 (2011).
[CrossRef]

2010 (1)

A. Garzarella, S.B. Qadri, and D. H. Wu, J. Electron. Mater. 39, 811 (2010).
[CrossRef]

2009 (2)

2008 (2)

H. Togo, N. Kukutsu, N. Shimizu, and T. Nagatsuma, J. Lightwave Technol. 26, 2700 (2008).
[CrossRef]

H. Togo, H. Uchida, H. Yokota, A. Izumi, T. Nagatsuma, and N. Fukasaku, J. Eur. Microwave Assoc. 4, 294 (2008).

2005 (1)

2003 (2)

A. Sasaki and T. Nagatsuma, IEICE Trans. Electron. E86-C, 1345 (2003).

K. Nishikata, Y. Kimura, Y. Takai, T. Ikuta, and R. Shimizu, Rev. Sci. Instrum. 74, 1393 (2003).
[CrossRef]

2002 (1)

A. Nahata, J. T. Yardley, and T. F. Heinz, Appl. Phys. Lett. 81, 963 (2002).
[CrossRef]

2001 (1)

K. Yang, L. P. B. Katehi, and J. F. Whitaker, IEEE Microw. Wirel. Compon. Lett. 11, 164 (2001).
[CrossRef]

1999 (1)

A. Nahata, J. T. Yardley, and T. F. Heinz, Appl. Phys. Lett. 75, 2524 (1999).
[CrossRef]

1998 (1)

T. Pfeifer, T. Loffler, H. G. Roskos, H. Kurz, M. Singer, and E. M. Biebl, IEEE Trans. Antennas Propag. 46, 284 (1998).
[CrossRef]

1996 (1)

Q. Wu and X.-C. Zhang, Appl. Phys. Lett. 68, 1604 (1996).
[CrossRef]

1994 (1)

K. Kamogawa, I. Toyoda, K. Nishikawa, and T. Tokumitsu, IEEE Microwave Guided Wave Lett. 4, 414 (1994).
[CrossRef]

1982 (1)

A. Valdmanis, G. Mourou, and C. W. Gabel, Appl. Phys. Lett. 41, 211 (1982).
[CrossRef]

1980 (1)

T. Okoshi, K. Kikuchi, and A. Nakayama, Electron. Lett. 16, 630 (1980).
[CrossRef]

Adam, A. J. L.

Ajito, K.

S. Hisatake, G. Kitahara, K. Ajito, Y. Fukada, N. Yoshimoto, and T. Nagatsuma, IEEE Sens. J. 13, 31 (2013).
[CrossRef]

Biebl, E. M.

T. Pfeifer, T. Loffler, H. G. Roskos, H. Kurz, M. Singer, and E. M. Biebl, IEEE Trans. Antennas Propag. 46, 284 (1998).
[CrossRef]

Fukada, Y.

S. Hisatake, G. Kitahara, K. Ajito, Y. Fukada, N. Yoshimoto, and T. Nagatsuma, IEEE Sens. J. 13, 31 (2013).
[CrossRef]

Fukasaku, N.

H. Togo, H. Uchida, H. Yokota, A. Izumi, T. Nagatsuma, and N. Fukasaku, J. Eur. Microwave Assoc. 4, 294 (2008).

Furuta, T.

Gabel, C. W.

A. Valdmanis, G. Mourou, and C. W. Gabel, Appl. Phys. Lett. 41, 211 (1982).
[CrossRef]

Garzarella, A.

A. Garzarella, S.B. Qadri, and D. H. Wu, J. Electron. Mater. 39, 811 (2010).
[CrossRef]

Hasebe, T.

T. Hasebe, S. Kawabe, H. Matsui, and H. Tabata, J. Appl. Phys. 112, 094702 (2012).
[CrossRef]

Heinz, T. F.

A. Nahata, J. T. Yardley, and T. F. Heinz, Appl. Phys. Lett. 81, 963 (2002).
[CrossRef]

A. Nahata, J. T. Yardley, and T. F. Heinz, Appl. Phys. Lett. 75, 2524 (1999).
[CrossRef]

Hisatake, S.

S. Hisatake, G. Kitahara, K. Ajito, Y. Fukada, N. Yoshimoto, and T. Nagatsuma, IEEE Sens. J. 13, 31 (2013).
[CrossRef]

S. Hisatake and T. Nagatsuma, Appl. Phys. Express 5, 012701 (2012).
[CrossRef]

Ikuta, T.

K. Nishikata, Y. Kimura, Y. Takai, T. Ikuta, and R. Shimizu, Rev. Sci. Instrum. 74, 1393 (2003).
[CrossRef]

Ishibashi, T.

T. Nagatsuma, H. Ito, and T. Ishibashi, Laser Photon. Rev. 3, 123 (2009).

H. Ito, T. Furuta, F. Nakajima, K. Yoshino, and T. Ishibashi, J. Lightwave Technol. 23, 4016 (2005).
[CrossRef]

Ito, H.

T. Nagatsuma, H. Ito, and T. Ishibashi, Laser Photon. Rev. 3, 123 (2009).

H. Ito, T. Furuta, F. Nakajima, K. Yoshino, and T. Ishibashi, J. Lightwave Technol. 23, 4016 (2005).
[CrossRef]

Izumi, A.

H. Togo, H. Uchida, H. Yokota, A. Izumi, T. Nagatsuma, and N. Fukasaku, J. Eur. Microwave Assoc. 4, 294 (2008).

Kamogawa, K.

K. Kamogawa, I. Toyoda, K. Nishikawa, and T. Tokumitsu, IEEE Microwave Guided Wave Lett. 4, 414 (1994).
[CrossRef]

Kanno, A.

K. Sasagawa, A. Kanno, and M. Tsuchiya, in Proceedings of PIERS, 2009 (2009), pp. 48–51.

Katehi, L. P. B.

K. Yang, L. P. B. Katehi, and J. F. Whitaker, IEEE Microw. Wirel. Compon. Lett. 11, 164 (2001).
[CrossRef]

Kawabe, S.

T. Hasebe, S. Kawabe, H. Matsui, and H. Tabata, J. Appl. Phys. 112, 094702 (2012).
[CrossRef]

Kikuchi, K.

T. Okoshi, K. Kikuchi, and A. Nakayama, Electron. Lett. 16, 630 (1980).
[CrossRef]

Kim, D. S.

Kimura, Y.

K. Nishikata, Y. Kimura, Y. Takai, T. Ikuta, and R. Shimizu, Rev. Sci. Instrum. 74, 1393 (2003).
[CrossRef]

Kitahara, G.

S. Hisatake, G. Kitahara, K. Ajito, Y. Fukada, N. Yoshimoto, and T. Nagatsuma, IEEE Sens. J. 13, 31 (2013).
[CrossRef]

Kleine-Ostmann, T.

T. Kleine-Ostmann and T. Nagatsuma, J. Infrared Millim. Terahz. Waves 32, 143 (2011).
[CrossRef]

Knab, J. R.

Kukutsu, N.

H. Togo, D. Morendo-Dominguez, and N. Kukutsu, IEICE Trans. Electron. E96.C, 227 (2013).
[CrossRef]

H. Togo, N. Kukutsu, N. Shimizu, and T. Nagatsuma, J. Lightwave Technol. 26, 2700 (2008).
[CrossRef]

Kurz, H.

T. Pfeifer, T. Loffler, H. G. Roskos, H. Kurz, M. Singer, and E. M. Biebl, IEEE Trans. Antennas Propag. 46, 284 (1998).
[CrossRef]

Loffler, T.

T. Pfeifer, T. Loffler, H. G. Roskos, H. Kurz, M. Singer, and E. M. Biebl, IEEE Trans. Antennas Propag. 46, 284 (1998).
[CrossRef]

Matsui, H.

T. Hasebe, S. Kawabe, H. Matsui, and H. Tabata, J. Appl. Phys. 112, 094702 (2012).
[CrossRef]

Mitrofanov, O.

Morendo-Dominguez, D.

H. Togo, D. Morendo-Dominguez, and N. Kukutsu, IEICE Trans. Electron. E96.C, 227 (2013).
[CrossRef]

Mourou, G.

A. Valdmanis, G. Mourou, and C. W. Gabel, Appl. Phys. Lett. 41, 211 (1982).
[CrossRef]

Mueckstein, R.

Nagatsuma, T.

S. Hisatake, G. Kitahara, K. Ajito, Y. Fukada, N. Yoshimoto, and T. Nagatsuma, IEEE Sens. J. 13, 31 (2013).
[CrossRef]

S. Hisatake and T. Nagatsuma, Appl. Phys. Express 5, 012701 (2012).
[CrossRef]

T. Kleine-Ostmann and T. Nagatsuma, J. Infrared Millim. Terahz. Waves 32, 143 (2011).
[CrossRef]

T. Nagatsuma, H. Ito, and T. Ishibashi, Laser Photon. Rev. 3, 123 (2009).

H. Togo, N. Kukutsu, N. Shimizu, and T. Nagatsuma, J. Lightwave Technol. 26, 2700 (2008).
[CrossRef]

H. Togo, H. Uchida, H. Yokota, A. Izumi, T. Nagatsuma, and N. Fukasaku, J. Eur. Microwave Assoc. 4, 294 (2008).

A. Sasaki and T. Nagatsuma, IEICE Trans. Electron. E86-C, 1345 (2003).

Nagel, M.

Nahata, A.

A. Nahata, J. T. Yardley, and T. F. Heinz, Appl. Phys. Lett. 81, 963 (2002).
[CrossRef]

A. Nahata, J. T. Yardley, and T. F. Heinz, Appl. Phys. Lett. 75, 2524 (1999).
[CrossRef]

Nakajima, F.

Nakayama, A.

T. Okoshi, K. Kikuchi, and A. Nakayama, Electron. Lett. 16, 630 (1980).
[CrossRef]

Nishikata, K.

K. Nishikata, Y. Kimura, Y. Takai, T. Ikuta, and R. Shimizu, Rev. Sci. Instrum. 74, 1393 (2003).
[CrossRef]

Nishikawa, K.

K. Kamogawa, I. Toyoda, K. Nishikawa, and T. Tokumitsu, IEEE Microwave Guided Wave Lett. 4, 414 (1994).
[CrossRef]

Okoshi, T.

T. Okoshi, K. Kikuchi, and A. Nakayama, Electron. Lett. 16, 630 (1980).
[CrossRef]

Pfeifer, T.

T. Pfeifer, T. Loffler, H. G. Roskos, H. Kurz, M. Singer, and E. M. Biebl, IEEE Trans. Antennas Propag. 46, 284 (1998).
[CrossRef]

Planken, P. C. M.

Qadri, S.B.

A. Garzarella, S.B. Qadri, and D. H. Wu, J. Electron. Mater. 39, 811 (2010).
[CrossRef]

Roskos, H. G.

T. Pfeifer, T. Loffler, H. G. Roskos, H. Kurz, M. Singer, and E. M. Biebl, IEEE Trans. Antennas Propag. 46, 284 (1998).
[CrossRef]

Sasagawa, K.

K. Sasagawa, A. Kanno, and M. Tsuchiya, in Proceedings of PIERS, 2009 (2009), pp. 48–51.

Sasaki, A.

A. Sasaki and T. Nagatsuma, IEICE Trans. Electron. E86-C, 1345 (2003).

Seo, M. A.

Shaner, E.

Shimizu, N.

Shimizu, R.

K. Nishikata, Y. Kimura, Y. Takai, T. Ikuta, and R. Shimizu, Rev. Sci. Instrum. 74, 1393 (2003).
[CrossRef]

Singer, M.

T. Pfeifer, T. Loffler, H. G. Roskos, H. Kurz, M. Singer, and E. M. Biebl, IEEE Trans. Antennas Propag. 46, 284 (1998).
[CrossRef]

Tabata, H.

T. Hasebe, S. Kawabe, H. Matsui, and H. Tabata, J. Appl. Phys. 112, 094702 (2012).
[CrossRef]

Takai, Y.

K. Nishikata, Y. Kimura, Y. Takai, T. Ikuta, and R. Shimizu, Rev. Sci. Instrum. 74, 1393 (2003).
[CrossRef]

Togo, H.

H. Togo, D. Morendo-Dominguez, and N. Kukutsu, IEICE Trans. Electron. E96.C, 227 (2013).
[CrossRef]

H. Togo, H. Uchida, H. Yokota, A. Izumi, T. Nagatsuma, and N. Fukasaku, J. Eur. Microwave Assoc. 4, 294 (2008).

H. Togo, N. Kukutsu, N. Shimizu, and T. Nagatsuma, J. Lightwave Technol. 26, 2700 (2008).
[CrossRef]

Tokumitsu, T.

K. Kamogawa, I. Toyoda, K. Nishikawa, and T. Tokumitsu, IEEE Microwave Guided Wave Lett. 4, 414 (1994).
[CrossRef]

Toyoda, I.

K. Kamogawa, I. Toyoda, K. Nishikawa, and T. Tokumitsu, IEEE Microwave Guided Wave Lett. 4, 414 (1994).
[CrossRef]

Tsuchiya, M.

K. Sasagawa, A. Kanno, and M. Tsuchiya, in Proceedings of PIERS, 2009 (2009), pp. 48–51.

Uchida, H.

H. Togo, H. Uchida, H. Yokota, A. Izumi, T. Nagatsuma, and N. Fukasaku, J. Eur. Microwave Assoc. 4, 294 (2008).

Valdmanis, A.

A. Valdmanis, G. Mourou, and C. W. Gabel, Appl. Phys. Lett. 41, 211 (1982).
[CrossRef]

Whitaker, J. F.

K. Yang, L. P. B. Katehi, and J. F. Whitaker, IEEE Microw. Wirel. Compon. Lett. 11, 164 (2001).
[CrossRef]

Wu, D. H.

A. Garzarella, S.B. Qadri, and D. H. Wu, J. Electron. Mater. 39, 811 (2010).
[CrossRef]

Wu, Q.

Q. Wu and X.-C. Zhang, Appl. Phys. Lett. 68, 1604 (1996).
[CrossRef]

Yang, K.

K. Yang, L. P. B. Katehi, and J. F. Whitaker, IEEE Microw. Wirel. Compon. Lett. 11, 164 (2001).
[CrossRef]

Yardley, J. T.

A. Nahata, J. T. Yardley, and T. F. Heinz, Appl. Phys. Lett. 81, 963 (2002).
[CrossRef]

A. Nahata, J. T. Yardley, and T. F. Heinz, Appl. Phys. Lett. 75, 2524 (1999).
[CrossRef]

Yokota, H.

H. Togo, H. Uchida, H. Yokota, A. Izumi, T. Nagatsuma, and N. Fukasaku, J. Eur. Microwave Assoc. 4, 294 (2008).

Yoshimoto, N.

S. Hisatake, G. Kitahara, K. Ajito, Y. Fukada, N. Yoshimoto, and T. Nagatsuma, IEEE Sens. J. 13, 31 (2013).
[CrossRef]

Yoshino, K.

Zhang, X.-C.

Q. Wu and X.-C. Zhang, Appl. Phys. Lett. 68, 1604 (1996).
[CrossRef]

Appl. Phys. Express (1)

S. Hisatake and T. Nagatsuma, Appl. Phys. Express 5, 012701 (2012).
[CrossRef]

Appl. Phys. Lett. (4)

A. Valdmanis, G. Mourou, and C. W. Gabel, Appl. Phys. Lett. 41, 211 (1982).
[CrossRef]

Q. Wu and X.-C. Zhang, Appl. Phys. Lett. 68, 1604 (1996).
[CrossRef]

A. Nahata, J. T. Yardley, and T. F. Heinz, Appl. Phys. Lett. 81, 963 (2002).
[CrossRef]

A. Nahata, J. T. Yardley, and T. F. Heinz, Appl. Phys. Lett. 75, 2524 (1999).
[CrossRef]

Electron. Lett. (1)

T. Okoshi, K. Kikuchi, and A. Nakayama, Electron. Lett. 16, 630 (1980).
[CrossRef]

IEEE Microw. Wirel. Compon. Lett. (1)

K. Yang, L. P. B. Katehi, and J. F. Whitaker, IEEE Microw. Wirel. Compon. Lett. 11, 164 (2001).
[CrossRef]

IEEE Microwave Guided Wave Lett. (1)

K. Kamogawa, I. Toyoda, K. Nishikawa, and T. Tokumitsu, IEEE Microwave Guided Wave Lett. 4, 414 (1994).
[CrossRef]

IEEE Sens. J. (1)

S. Hisatake, G. Kitahara, K. Ajito, Y. Fukada, N. Yoshimoto, and T. Nagatsuma, IEEE Sens. J. 13, 31 (2013).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

T. Pfeifer, T. Loffler, H. G. Roskos, H. Kurz, M. Singer, and E. M. Biebl, IEEE Trans. Antennas Propag. 46, 284 (1998).
[CrossRef]

IEICE Trans. Electron. (2)

H. Togo, D. Morendo-Dominguez, and N. Kukutsu, IEICE Trans. Electron. E96.C, 227 (2013).
[CrossRef]

A. Sasaki and T. Nagatsuma, IEICE Trans. Electron. E86-C, 1345 (2003).

J. Appl. Phys. (1)

T. Hasebe, S. Kawabe, H. Matsui, and H. Tabata, J. Appl. Phys. 112, 094702 (2012).
[CrossRef]

J. Electron. Mater. (1)

A. Garzarella, S.B. Qadri, and D. H. Wu, J. Electron. Mater. 39, 811 (2010).
[CrossRef]

J. Eur. Microwave Assoc. (1)

H. Togo, H. Uchida, H. Yokota, A. Izumi, T. Nagatsuma, and N. Fukasaku, J. Eur. Microwave Assoc. 4, 294 (2008).

J. Infrared Millim. Terahz. Waves (1)

T. Kleine-Ostmann and T. Nagatsuma, J. Infrared Millim. Terahz. Waves 32, 143 (2011).
[CrossRef]

J. Lightwave Technol. (2)

Laser Photon. Rev. (1)

T. Nagatsuma, H. Ito, and T. Ishibashi, Laser Photon. Rev. 3, 123 (2009).

Opt. Express (2)

Rev. Sci. Instrum. (1)

K. Nishikata, Y. Kimura, Y. Takai, T. Ikuta, and R. Shimizu, Rev. Sci. Instrum. 74, 1393 (2003).
[CrossRef]

Other (1)

K. Sasagawa, A. Kanno, and M. Tsuchiya, in Proceedings of PIERS, 2009 (2009), pp. 48–51.

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 (4)

Fig. 1.
Fig. 1.

Experimental setup. LD, laser diode; FS, electro-optic frequency shifter; EDFA, erbium-doped fiber amplifier; PBS, polarization beam splitter; PD, photodiode; UTC-PD, uni-travelling-carrier PD; AUT, antenna under test.

Fig. 2.
Fig. 2.

EO sensor (ZnTe) and horn antenna. PMF, polarization maintaining fiber. The horn antenna was scanned in the xy, xz, and yz planes. The coordinates are given in millimeter units.

Fig. 3.
Fig. 3.

THz electric field distributions. (a) Normalized amplitude and (b) phase. The frequency of the field was 125 GHz.

Fig. 4.
Fig. 4.

Unwrapped phase distribution in the z direction on the xz plane at y=0 (solid line) and the phase deviation from a fitted line (filled circles).

Equations (3)

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

iIF(t)A(ω)cos[ωst+ϕ(ω)+ωτ+ωsτ+Δφ1n+Δφ2n+Δφf],
I(ω)=A(ω)cos(ϕ(ω)+ϕn),
Q(ω)=A(ω)sin(ϕ(ω)+ϕn),

Metrics