Abstract

A multimode-laser reflectometer that detects an interference spectrum by use of a multichannel wavelength detector was developed and its characteristics evaluated experimentally. A spatial resolution of 24 µm and a maximum detectable length of 510 µm were achieved. Thickness mapping of a coverglass was attempted as an application and was compared with an interference fringe between the surface and the back. Good results that reflected the tendency of an interference fringe were obtained.

© 1997 Optical Society of America

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  1. J. J. Fauntaine, J. C. Diels, C. Y. Wang, H. Sallaba, “Subpicosecond time-domain reflectometry,” Opt. Lett. 6, 405–407 (1981).
    [CrossRef]
  2. R. C. Youngquist, S. Carr, D. E. N. Davis, “Optical coherence-domain reflectometry: a new optical evaluation technique,” Opt. Lett. 12, 158–160 (1987).
    [CrossRef] [PubMed]
  3. X. Clivaz, F. Marquis-Weible, R. P. Salathe, R. P. Novak, H. H. Gligen, “High-resolution reflectometry in biological tissues,” Opt. Lett. 17, 4–6 (1992).
    [CrossRef] [PubMed]
  4. E. A. Swanson, D. Huang, M. R. Hee, J. G. Fujimoto, C. P. Puliafito, “High-speed optical coherence domain reflectometry,” Opt. Lett. 17, 151–153 (1992).
    [CrossRef] [PubMed]
  5. O. Kamatani, K. Hotate, “Optical coherence domain reflectometry by synthesis of coherence function with nonlinearity compensation in frequency modulation of a laser light,” J. Lightwave Technol. 11, 1854–1862 (1993).
    [CrossRef]
  6. P. Lambelet, R. P. Salathe, M. H. Garrett, D. Rytz, “Characterization of a photorefractive phase conjugator by optical low-coherence reflectometry,” Appl. Phys. Lett. 64, 1079–1081 (1994).
    [CrossRef]
  7. K. Kasaya, Y. Yoshikuni, H. Ishii, “Measurements of a semiconductor waveguide using a low-coherence interferometric reflectometer,” IEEE. Photon. Technol. Lett. 8, 251–253 (1996).
    [CrossRef]
  8. W. Eickhoff, R. Ulrich, “Optical frequency domain reflectometry in single-mode fiber,” Appl. Phys. Lett. 39, 693–695 (1981).
    [CrossRef]
  9. S. A. Kingsley, D. E. N. Davis, “OFDR diagnostics for fiber and integrated-optic system,” Electron. Lett. 21, 434–435 (1985).
    [CrossRef]
  10. P. Passy, N. Gisin, J. P. von der Weid, H. H. Gligen, “Experimental and theoretical investigations of coherent OFDR with semiconductor laser sources,” J. Lightwave Technol. 12, 1622–1630 (1994).
    [CrossRef]
  11. X. Zhou, K. Iiyama, K. Hayashi, “Extended-range FMCW reflectometry using an optical loop with a frequency shifter,” IEEE Photon. Technol. Lett. 8, 248–250 (1996).
    [CrossRef]
  12. K. Iizuka, Y. Imai, A. P. Freundorfer, R. James, R. Wong, S. Fujii, “Optical step frequency reflectometor,” J. Appl. Phys. 68, 932–936 (1990).
    [CrossRef]
  13. S. Fujii, K. Iizuka, “Neural network step-frequency fault locator,” Opt. Eng. 34, 1441–1449 (1995).
    [CrossRef]
  14. N. Tanno, T. Ichimura, T. Funaba, N. Anndo, Y. Odagiri, “Optical multimode frequency-domain reflectometer,” Opt. Lett. 19, 587–589 (1994).
    [CrossRef]
  15. T. Ichimura, N. Anndo, T. Funaba, S. Endo, Y. Odagiri, N. Tanno, “High-resolution reflectometry by optical multidigitized coherence,” Opt. Rev. 3, 38–46 (1996).
    [CrossRef]
  16. T. Funaba, S. Endou, T. Ichimura, N. Tanno, “Multimode laser reflectometry using a multi-channel analyzer,” in 1995 International Laser, Lightwave and Microwave Conference Proceedings (Shanghai World Publishing, Shanghai, 1995), pp. 308–311.
  17. M. Hashimoto, S. Kawata, “Signal to noise ratio of multi-channel Fourier-transform spectroscopy,” J. Spectrosc. Soc. Jpn. 41, 317–326 (1992).
    [CrossRef]

1996

K. Kasaya, Y. Yoshikuni, H. Ishii, “Measurements of a semiconductor waveguide using a low-coherence interferometric reflectometer,” IEEE. Photon. Technol. Lett. 8, 251–253 (1996).
[CrossRef]

X. Zhou, K. Iiyama, K. Hayashi, “Extended-range FMCW reflectometry using an optical loop with a frequency shifter,” IEEE Photon. Technol. Lett. 8, 248–250 (1996).
[CrossRef]

T. Ichimura, N. Anndo, T. Funaba, S. Endo, Y. Odagiri, N. Tanno, “High-resolution reflectometry by optical multidigitized coherence,” Opt. Rev. 3, 38–46 (1996).
[CrossRef]

1995

S. Fujii, K. Iizuka, “Neural network step-frequency fault locator,” Opt. Eng. 34, 1441–1449 (1995).
[CrossRef]

1994

N. Tanno, T. Ichimura, T. Funaba, N. Anndo, Y. Odagiri, “Optical multimode frequency-domain reflectometer,” Opt. Lett. 19, 587–589 (1994).
[CrossRef]

P. Passy, N. Gisin, J. P. von der Weid, H. H. Gligen, “Experimental and theoretical investigations of coherent OFDR with semiconductor laser sources,” J. Lightwave Technol. 12, 1622–1630 (1994).
[CrossRef]

P. Lambelet, R. P. Salathe, M. H. Garrett, D. Rytz, “Characterization of a photorefractive phase conjugator by optical low-coherence reflectometry,” Appl. Phys. Lett. 64, 1079–1081 (1994).
[CrossRef]

1993

O. Kamatani, K. Hotate, “Optical coherence domain reflectometry by synthesis of coherence function with nonlinearity compensation in frequency modulation of a laser light,” J. Lightwave Technol. 11, 1854–1862 (1993).
[CrossRef]

1992

1990

K. Iizuka, Y. Imai, A. P. Freundorfer, R. James, R. Wong, S. Fujii, “Optical step frequency reflectometor,” J. Appl. Phys. 68, 932–936 (1990).
[CrossRef]

1987

1985

S. A. Kingsley, D. E. N. Davis, “OFDR diagnostics for fiber and integrated-optic system,” Electron. Lett. 21, 434–435 (1985).
[CrossRef]

1981

J. J. Fauntaine, J. C. Diels, C. Y. Wang, H. Sallaba, “Subpicosecond time-domain reflectometry,” Opt. Lett. 6, 405–407 (1981).
[CrossRef]

W. Eickhoff, R. Ulrich, “Optical frequency domain reflectometry in single-mode fiber,” Appl. Phys. Lett. 39, 693–695 (1981).
[CrossRef]

Anndo, N.

T. Ichimura, N. Anndo, T. Funaba, S. Endo, Y. Odagiri, N. Tanno, “High-resolution reflectometry by optical multidigitized coherence,” Opt. Rev. 3, 38–46 (1996).
[CrossRef]

N. Tanno, T. Ichimura, T. Funaba, N. Anndo, Y. Odagiri, “Optical multimode frequency-domain reflectometer,” Opt. Lett. 19, 587–589 (1994).
[CrossRef]

Carr, S.

Clivaz, X.

Davis, D. E. N.

R. C. Youngquist, S. Carr, D. E. N. Davis, “Optical coherence-domain reflectometry: a new optical evaluation technique,” Opt. Lett. 12, 158–160 (1987).
[CrossRef] [PubMed]

S. A. Kingsley, D. E. N. Davis, “OFDR diagnostics for fiber and integrated-optic system,” Electron. Lett. 21, 434–435 (1985).
[CrossRef]

Diels, J. C.

Eickhoff, W.

W. Eickhoff, R. Ulrich, “Optical frequency domain reflectometry in single-mode fiber,” Appl. Phys. Lett. 39, 693–695 (1981).
[CrossRef]

Endo, S.

T. Ichimura, N. Anndo, T. Funaba, S. Endo, Y. Odagiri, N. Tanno, “High-resolution reflectometry by optical multidigitized coherence,” Opt. Rev. 3, 38–46 (1996).
[CrossRef]

Endou, S.

T. Funaba, S. Endou, T. Ichimura, N. Tanno, “Multimode laser reflectometry using a multi-channel analyzer,” in 1995 International Laser, Lightwave and Microwave Conference Proceedings (Shanghai World Publishing, Shanghai, 1995), pp. 308–311.

Fauntaine, J. J.

Freundorfer, A. P.

K. Iizuka, Y. Imai, A. P. Freundorfer, R. James, R. Wong, S. Fujii, “Optical step frequency reflectometor,” J. Appl. Phys. 68, 932–936 (1990).
[CrossRef]

Fujii, S.

S. Fujii, K. Iizuka, “Neural network step-frequency fault locator,” Opt. Eng. 34, 1441–1449 (1995).
[CrossRef]

K. Iizuka, Y. Imai, A. P. Freundorfer, R. James, R. Wong, S. Fujii, “Optical step frequency reflectometor,” J. Appl. Phys. 68, 932–936 (1990).
[CrossRef]

Fujimoto, J. G.

Funaba, T.

T. Ichimura, N. Anndo, T. Funaba, S. Endo, Y. Odagiri, N. Tanno, “High-resolution reflectometry by optical multidigitized coherence,” Opt. Rev. 3, 38–46 (1996).
[CrossRef]

N. Tanno, T. Ichimura, T. Funaba, N. Anndo, Y. Odagiri, “Optical multimode frequency-domain reflectometer,” Opt. Lett. 19, 587–589 (1994).
[CrossRef]

T. Funaba, S. Endou, T. Ichimura, N. Tanno, “Multimode laser reflectometry using a multi-channel analyzer,” in 1995 International Laser, Lightwave and Microwave Conference Proceedings (Shanghai World Publishing, Shanghai, 1995), pp. 308–311.

Garrett, M. H.

P. Lambelet, R. P. Salathe, M. H. Garrett, D. Rytz, “Characterization of a photorefractive phase conjugator by optical low-coherence reflectometry,” Appl. Phys. Lett. 64, 1079–1081 (1994).
[CrossRef]

Gisin, N.

P. Passy, N. Gisin, J. P. von der Weid, H. H. Gligen, “Experimental and theoretical investigations of coherent OFDR with semiconductor laser sources,” J. Lightwave Technol. 12, 1622–1630 (1994).
[CrossRef]

Gligen, H. H.

P. Passy, N. Gisin, J. P. von der Weid, H. H. Gligen, “Experimental and theoretical investigations of coherent OFDR with semiconductor laser sources,” J. Lightwave Technol. 12, 1622–1630 (1994).
[CrossRef]

X. Clivaz, F. Marquis-Weible, R. P. Salathe, R. P. Novak, H. H. Gligen, “High-resolution reflectometry in biological tissues,” Opt. Lett. 17, 4–6 (1992).
[CrossRef] [PubMed]

Hashimoto, M.

M. Hashimoto, S. Kawata, “Signal to noise ratio of multi-channel Fourier-transform spectroscopy,” J. Spectrosc. Soc. Jpn. 41, 317–326 (1992).
[CrossRef]

Hayashi, K.

X. Zhou, K. Iiyama, K. Hayashi, “Extended-range FMCW reflectometry using an optical loop with a frequency shifter,” IEEE Photon. Technol. Lett. 8, 248–250 (1996).
[CrossRef]

Hee, M. R.

Hotate, K.

O. Kamatani, K. Hotate, “Optical coherence domain reflectometry by synthesis of coherence function with nonlinearity compensation in frequency modulation of a laser light,” J. Lightwave Technol. 11, 1854–1862 (1993).
[CrossRef]

Huang, D.

Ichimura, T.

T. Ichimura, N. Anndo, T. Funaba, S. Endo, Y. Odagiri, N. Tanno, “High-resolution reflectometry by optical multidigitized coherence,” Opt. Rev. 3, 38–46 (1996).
[CrossRef]

N. Tanno, T. Ichimura, T. Funaba, N. Anndo, Y. Odagiri, “Optical multimode frequency-domain reflectometer,” Opt. Lett. 19, 587–589 (1994).
[CrossRef]

T. Funaba, S. Endou, T. Ichimura, N. Tanno, “Multimode laser reflectometry using a multi-channel analyzer,” in 1995 International Laser, Lightwave and Microwave Conference Proceedings (Shanghai World Publishing, Shanghai, 1995), pp. 308–311.

Iiyama, K.

X. Zhou, K. Iiyama, K. Hayashi, “Extended-range FMCW reflectometry using an optical loop with a frequency shifter,” IEEE Photon. Technol. Lett. 8, 248–250 (1996).
[CrossRef]

Iizuka, K.

S. Fujii, K. Iizuka, “Neural network step-frequency fault locator,” Opt. Eng. 34, 1441–1449 (1995).
[CrossRef]

K. Iizuka, Y. Imai, A. P. Freundorfer, R. James, R. Wong, S. Fujii, “Optical step frequency reflectometor,” J. Appl. Phys. 68, 932–936 (1990).
[CrossRef]

Imai, Y.

K. Iizuka, Y. Imai, A. P. Freundorfer, R. James, R. Wong, S. Fujii, “Optical step frequency reflectometor,” J. Appl. Phys. 68, 932–936 (1990).
[CrossRef]

Ishii, H.

K. Kasaya, Y. Yoshikuni, H. Ishii, “Measurements of a semiconductor waveguide using a low-coherence interferometric reflectometer,” IEEE. Photon. Technol. Lett. 8, 251–253 (1996).
[CrossRef]

James, R.

K. Iizuka, Y. Imai, A. P. Freundorfer, R. James, R. Wong, S. Fujii, “Optical step frequency reflectometor,” J. Appl. Phys. 68, 932–936 (1990).
[CrossRef]

Kamatani, O.

O. Kamatani, K. Hotate, “Optical coherence domain reflectometry by synthesis of coherence function with nonlinearity compensation in frequency modulation of a laser light,” J. Lightwave Technol. 11, 1854–1862 (1993).
[CrossRef]

Kasaya, K.

K. Kasaya, Y. Yoshikuni, H. Ishii, “Measurements of a semiconductor waveguide using a low-coherence interferometric reflectometer,” IEEE. Photon. Technol. Lett. 8, 251–253 (1996).
[CrossRef]

Kawata, S.

M. Hashimoto, S. Kawata, “Signal to noise ratio of multi-channel Fourier-transform spectroscopy,” J. Spectrosc. Soc. Jpn. 41, 317–326 (1992).
[CrossRef]

Kingsley, S. A.

S. A. Kingsley, D. E. N. Davis, “OFDR diagnostics for fiber and integrated-optic system,” Electron. Lett. 21, 434–435 (1985).
[CrossRef]

Lambelet, P.

P. Lambelet, R. P. Salathe, M. H. Garrett, D. Rytz, “Characterization of a photorefractive phase conjugator by optical low-coherence reflectometry,” Appl. Phys. Lett. 64, 1079–1081 (1994).
[CrossRef]

Marquis-Weible, F.

Novak, R. P.

Odagiri, Y.

T. Ichimura, N. Anndo, T. Funaba, S. Endo, Y. Odagiri, N. Tanno, “High-resolution reflectometry by optical multidigitized coherence,” Opt. Rev. 3, 38–46 (1996).
[CrossRef]

N. Tanno, T. Ichimura, T. Funaba, N. Anndo, Y. Odagiri, “Optical multimode frequency-domain reflectometer,” Opt. Lett. 19, 587–589 (1994).
[CrossRef]

Passy, P.

P. Passy, N. Gisin, J. P. von der Weid, H. H. Gligen, “Experimental and theoretical investigations of coherent OFDR with semiconductor laser sources,” J. Lightwave Technol. 12, 1622–1630 (1994).
[CrossRef]

Puliafito, C. P.

Rytz, D.

P. Lambelet, R. P. Salathe, M. H. Garrett, D. Rytz, “Characterization of a photorefractive phase conjugator by optical low-coherence reflectometry,” Appl. Phys. Lett. 64, 1079–1081 (1994).
[CrossRef]

Salathe, R. P.

P. Lambelet, R. P. Salathe, M. H. Garrett, D. Rytz, “Characterization of a photorefractive phase conjugator by optical low-coherence reflectometry,” Appl. Phys. Lett. 64, 1079–1081 (1994).
[CrossRef]

X. Clivaz, F. Marquis-Weible, R. P. Salathe, R. P. Novak, H. H. Gligen, “High-resolution reflectometry in biological tissues,” Opt. Lett. 17, 4–6 (1992).
[CrossRef] [PubMed]

Sallaba, H.

Swanson, E. A.

Tanno, N.

T. Ichimura, N. Anndo, T. Funaba, S. Endo, Y. Odagiri, N. Tanno, “High-resolution reflectometry by optical multidigitized coherence,” Opt. Rev. 3, 38–46 (1996).
[CrossRef]

N. Tanno, T. Ichimura, T. Funaba, N. Anndo, Y. Odagiri, “Optical multimode frequency-domain reflectometer,” Opt. Lett. 19, 587–589 (1994).
[CrossRef]

T. Funaba, S. Endou, T. Ichimura, N. Tanno, “Multimode laser reflectometry using a multi-channel analyzer,” in 1995 International Laser, Lightwave and Microwave Conference Proceedings (Shanghai World Publishing, Shanghai, 1995), pp. 308–311.

Ulrich, R.

W. Eickhoff, R. Ulrich, “Optical frequency domain reflectometry in single-mode fiber,” Appl. Phys. Lett. 39, 693–695 (1981).
[CrossRef]

von der Weid, J. P.

P. Passy, N. Gisin, J. P. von der Weid, H. H. Gligen, “Experimental and theoretical investigations of coherent OFDR with semiconductor laser sources,” J. Lightwave Technol. 12, 1622–1630 (1994).
[CrossRef]

Wang, C. Y.

Wong, R.

K. Iizuka, Y. Imai, A. P. Freundorfer, R. James, R. Wong, S. Fujii, “Optical step frequency reflectometor,” J. Appl. Phys. 68, 932–936 (1990).
[CrossRef]

Yoshikuni, Y.

K. Kasaya, Y. Yoshikuni, H. Ishii, “Measurements of a semiconductor waveguide using a low-coherence interferometric reflectometer,” IEEE. Photon. Technol. Lett. 8, 251–253 (1996).
[CrossRef]

Youngquist, R. C.

Zhou, X.

X. Zhou, K. Iiyama, K. Hayashi, “Extended-range FMCW reflectometry using an optical loop with a frequency shifter,” IEEE Photon. Technol. Lett. 8, 248–250 (1996).
[CrossRef]

Appl. Phys. Lett.

P. Lambelet, R. P. Salathe, M. H. Garrett, D. Rytz, “Characterization of a photorefractive phase conjugator by optical low-coherence reflectometry,” Appl. Phys. Lett. 64, 1079–1081 (1994).
[CrossRef]

W. Eickhoff, R. Ulrich, “Optical frequency domain reflectometry in single-mode fiber,” Appl. Phys. Lett. 39, 693–695 (1981).
[CrossRef]

Electron. Lett.

S. A. Kingsley, D. E. N. Davis, “OFDR diagnostics for fiber and integrated-optic system,” Electron. Lett. 21, 434–435 (1985).
[CrossRef]

IEEE Photon. Technol. Lett.

X. Zhou, K. Iiyama, K. Hayashi, “Extended-range FMCW reflectometry using an optical loop with a frequency shifter,” IEEE Photon. Technol. Lett. 8, 248–250 (1996).
[CrossRef]

IEEE. Photon. Technol. Lett.

K. Kasaya, Y. Yoshikuni, H. Ishii, “Measurements of a semiconductor waveguide using a low-coherence interferometric reflectometer,” IEEE. Photon. Technol. Lett. 8, 251–253 (1996).
[CrossRef]

J. Appl. Phys.

K. Iizuka, Y. Imai, A. P. Freundorfer, R. James, R. Wong, S. Fujii, “Optical step frequency reflectometor,” J. Appl. Phys. 68, 932–936 (1990).
[CrossRef]

J. Lightwave Technol.

O. Kamatani, K. Hotate, “Optical coherence domain reflectometry by synthesis of coherence function with nonlinearity compensation in frequency modulation of a laser light,” J. Lightwave Technol. 11, 1854–1862 (1993).
[CrossRef]

P. Passy, N. Gisin, J. P. von der Weid, H. H. Gligen, “Experimental and theoretical investigations of coherent OFDR with semiconductor laser sources,” J. Lightwave Technol. 12, 1622–1630 (1994).
[CrossRef]

J. Spectrosc. Soc. Jpn.

M. Hashimoto, S. Kawata, “Signal to noise ratio of multi-channel Fourier-transform spectroscopy,” J. Spectrosc. Soc. Jpn. 41, 317–326 (1992).
[CrossRef]

Opt. Eng.

S. Fujii, K. Iizuka, “Neural network step-frequency fault locator,” Opt. Eng. 34, 1441–1449 (1995).
[CrossRef]

Opt. Lett.

Opt. Rev.

T. Ichimura, N. Anndo, T. Funaba, S. Endo, Y. Odagiri, N. Tanno, “High-resolution reflectometry by optical multidigitized coherence,” Opt. Rev. 3, 38–46 (1996).
[CrossRef]

Other

T. Funaba, S. Endou, T. Ichimura, N. Tanno, “Multimode laser reflectometry using a multi-channel analyzer,” in 1995 International Laser, Lightwave and Microwave Conference Proceedings (Shanghai World Publishing, Shanghai, 1995), pp. 308–311.

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Figures (12)

Fig. 1
Fig. 1

Model of a multimode-laser Gaussian power spectrum and each spectral width.

Fig. 2
Fig. 2

Measured visibility for a multimode semiconductor laser diode: The center wavelength is 772.5 nm, ΔλG = 13.8 nm, Δλ = 0.29 nm. The dashed curves represent the envelope of the coherence function peaks for δλ = 0.014–0.02 nm.

Fig. 3
Fig. 3

Experimental setup for a multimode-laser reflectometer with a multichannel wavelength detector.

Fig. 4
Fig. 4

Observed spectrum of a multimode semiconductor laser: injection current of 90 mA at 20 °C.

Fig. 5
Fig. 5

Observed interferospectrum measuring two coverglasses (interference spectrum between the surface and the back).

Fig. 6
Fig. 6

Spatialgram (Fourier transformation of Fig. 5) plotted with the first coverglass surface as a reference. The optical thickness of the coverglass was approximately 225 µm.

Fig. 7
Fig. 7

Relation between the peak position and the mirror translation length: The circles represent the peak positions when the mirror is moved in 10-µm steps and the dashed curve is the peak position calculated from Eqs. (7) and (11).

Fig. 8
Fig. 8

Accuracy of the position measurement: The circles represent the peak positions obtained when moving the mirror in 0.5-µm steps. The curve represents the calculated peak positions and stepwise separations of 1.86 µm. The separation is determined with the IFFT.

Fig. 9
Fig. 9

Detection characteristics of the reflection light: Rnorm was plotted versus the normalized reflection power. The dashed curve was calculated from Eq. (14). The vertical dotted–dashed line represents the electrical-noise power normalized by the full scale of the detector. The horizontal dashed line represents the noise floor of the spatialgram normalized by the RIBMD.

Fig. 10
Fig. 10

Relation between the spatial resolution and the spectrum width ΔλG: ΔλG is the FWHM of the Gaussian distribution for a multimode laser. The dots represent data measured by use of MWDS. The dashed curve is the spatial resolution calculated from Eq. (10).

Fig. 11
Fig. 11

Interference-fringe image between the surface and the back of a coverglass illuminated by a mercury-vapor lamp.

Fig. 12
Fig. 12

Thickness mapping of a coverglass measured with a multimode-laser reflectometer with a multichannel wavelength detector: The measured area is 17 mm × 20 mm, scanned in the vertical and horizontal directions in 1-mm steps.

Equations (14)

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

Gf=Am=0Mδfδf/22+f-mΔf2×exp-4 ln 2ΔfM/2-m/ΔfG2,
γGζ=2π ln 21/2ΔfGMΔfA exp-2πδfζ×m=0McosπMΔfζ-m/Δf×exp-π2ΔfGζ-m/Δf2/4 ln 2,
Ereft, f=s0E0gfexpj2πft-jϕf,
Esigt, f=szE0gfexpj2πft-τ-jϕf,
hf=Ereft, f+Esigt, f2=s20+s2zE02gf2+s0szE02gf2expj2πfτ+exp-j2πfτ,
Hζ=12π-hfexpj2πfζdf=s20+s2zE0212π-Gfexpj2πfζdf+s0szE02-Gfexpj2πfζ-τ+expj2πfζ+τdf.
HGζ=s20+s2zE02γGζ+s0sz×E02γGζ-τ+γGζ+τ.
π2ΔfGΔzc214 ln 2+2πδfΔzc-ln 2=0.
Δz=c-4δf ln 2±2 ln22πδf2+ΔfG21/2πΔfG2.
Δz=c2 ln 2πΔfG.
zmax=c/2Δf/2=L/2,
Iscanν=TscanNeηνGνFνΔνDν.
Imultiν=TinteηnνGνFνΔνDν.
Rnorm=s0szs02+sz2,

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