Abstract

This paper presents results of our detailed theoretical and experimental analysis of the relationship between the spectral resolution and the noise in the group-delay dispersion (GDD) data measured by scanning white-light interferometry. We demonstrate that the practically achievable spectral resolution is limited, because the standard deviation of GDD is proportional to the third power of inverse spectral resolution, and for a specified accuracy the required number of averages scales with the sixth power of inverse spectral resolution. The influence of experimental parameters such as spectral brightness, bandwidth of the light source, and detection noise is examined in detail.

© 2005 Optical Society of America

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    [CrossRef]
  3. G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, "Frontiers in ultrashort pulse generation: pushing the limits in linear and nonlinear optics," Science 286, 1507-1512 (1999).
    [CrossRef] [PubMed]
  4. N. Matuschek, L. Gallmann, D. H. Sutter, G. Steinmeyer, and U. Keller, "Back-side-coated chirped mirrors with ultra-smooth broadband dispersion characteristics," Appl. Phys. B 71, 509-522 (2000).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2005 (1)

2004 (2)

G. Sansone, G. Steinmeyer, C. Vozzi, S. Stagira, M. Nisoli, S. De Silvestri, K. Starke, D. Ristau, B. Schenkel, J. Biegert, A. Gosteva, and U. Keller, "Mirror dispersion control of a hollow fiber supercontinuum," Appl. Phys. B 78, 551-555 (2004).
[CrossRef]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, "Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation," Appl. Phys. B 79, 673-677 (2004).
[CrossRef]

2003 (2)

2002 (3)

A. Baltuska, T. Fuji, and T. Kobayashi, "Visible pulse compression to 4 fs by optical parametric amplification and programmable dispersion control," Opt. Lett. 27, 306-308 (2002).
[CrossRef]

R. Haring, R. Paschotta, A. Aschwanden, E. Gini, F. Morier-Genoud, and U. Keller, "High-power passively mode-locked semiconductor lasers," IEEE J. Quantum Electron. 38, 1268-1275 (2002)
[CrossRef]

L. Gallmann, G. Steinmeyer, G. Imeshev, J.-P. Meyn, M. M. Fejer, and U. Keller, "Sub-6-fs blue pulses generated by quasi-phase-matching second-harmonic generation pulse compression," Appl. Phys. B 74, S237-S243 (2002).
[CrossRef]

2001 (2)

2000 (5)

N. Matuschek, L. Gallmann, D. H. Sutter, G. Steinmeyer, and U. Keller, "Back-side-coated chirped mirrors with ultra-smooth broadband dispersion characteristics," Appl. Phys. B 71, 509-522 (2000).
[CrossRef]

D. H. Sutter, L. Gallmann, N. Matuschek, F. Morier-Genoud, V. Scheuer, G. Angelow, T. Tschudi, G. Steinmeyer, and U. Keller, "Sub-6-fs pulses from a SESAM-assisted Kerr-lens modelocked Ti:sapphire laser: at the frontiers of ultrashort pulse generation," Appl. Phys. B 70, S5-S12 (2000).
[CrossRef]

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller "Techniques for the characterization of sub-10-fs optical pulses: a comparison," Appl. Phys. B 70, S67-S75 (2000).
[CrossRef]

C. Dorrer, N. Belabas, J-P. Likforman, and M. Joffre, "Experimental implementation of Fourier-transform spectral interferometry and its application to the study of spectrometers," Appl. Phys. B 70, S99-S107 (2000).
[CrossRef]

L. Gallmann, G. Steinmeyer, D. H. Sutter, N. Matuschek, and U. Keller, "Collinear type II second-harmonic-generation frequency-resolved optical gating for the characterization of sub-10-fs optical pulses," Opt. Lett. 25, 269-271 (2000).
[CrossRef]

1999 (4)

C. Dorrer, "Influence of the calibration of the detector on spectral interferometry," J. Opt. Soc. Am. B 16, 1160-1168 (1999).
[CrossRef]

M. Kuznetsov, F. Hakimi, R. Sprague, and A. Mooradian, "Design and characteristics of high-power (>0.5-W CW) diode-pumped vertical-external-cavity surface-emitting semiconductor lasers with circular TEM00 beams," IEEE J. Sel. Top. Quantum Electron. 5, 561-573 (1999).
[CrossRef]

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, "Frontiers in ultrashort pulse generation: pushing the limits in linear and nonlinear optics," Science 286, 1507-1512 (1999).
[CrossRef] [PubMed]

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, U. Keller, C. Iaconis, and I. A. Walmsley, "Characterization of sub-6-fs optical pulses with spectral phase interferometry for direct electric-field reconstruction," Opt. Lett. 24, 1314-1316 (1999).
[CrossRef]

1998 (1)

1997 (1)

1996 (2)

S. Diddams and J.-C. Diels, "Dispersion measurements with white-light interferometry," J. Opt. Soc. Am. B 13, 1120-1129 (1996).
[CrossRef]

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, "Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers," IEEE J. Sel. Top. Quantum Electron. 2, 435-453 (1996).
[CrossRef]

1995 (1)

1991 (1)

M. Beck, I. A. Walmsley, and J. D. Kafka, "Group delay measurements of optical components near 800 nm," IEEE J. Quantum Electron. 27, 2074-2081 (1991).
[CrossRef]

1990 (2)

1982 (1)

Angelow, G.

M. Zavelani-Rossi, G. Cerullo, S. De Silvestri, L. Gallmann, N. Matuschek, G. Steinmeyer, U. Keller, G. Angelow, V. Scheuer, and T. Tschudi, "Pulse compression over a 170-THz bandwidth in the visible by use of only chirped mirrors," Opt. Lett. 26, 1155-1157 (2001).
[CrossRef]

D. H. Sutter, L. Gallmann, N. Matuschek, F. Morier-Genoud, V. Scheuer, G. Angelow, T. Tschudi, G. Steinmeyer, and U. Keller, "Sub-6-fs pulses from a SESAM-assisted Kerr-lens modelocked Ti:sapphire laser: at the frontiers of ultrashort pulse generation," Appl. Phys. B 70, S5-S12 (2000).
[CrossRef]

Aschwanden, A.

R. Haring, R. Paschotta, A. Aschwanden, E. Gini, F. Morier-Genoud, and U. Keller, "High-power passively mode-locked semiconductor lasers," IEEE J. Quantum Electron. 38, 1268-1275 (2002)
[CrossRef]

Baltuska, A.

Beck, M.

M. Beck, I. A. Walmsley, and J. D. Kafka, "Group delay measurements of optical components near 800 nm," IEEE J. Quantum Electron. 27, 2074-2081 (1991).
[CrossRef]

M. Beck and I. A. Walmsley, "Measurement of group delay with high temporal and spectral resolution," Opt. Lett. 15, 492-494 (1990).
[CrossRef] [PubMed]

Belabas, N.

C. Dorrer, N. Belabas, J-P. Likforman, and M. Joffre, "Experimental implementation of Fourier-transform spectral interferometry and its application to the study of spectrometers," Appl. Phys. B 70, S99-S107 (2000).
[CrossRef]

Biegert, J.

G. Sansone, G. Steinmeyer, C. Vozzi, S. Stagira, M. Nisoli, S. De Silvestri, K. Starke, D. Ristau, B. Schenkel, J. Biegert, A. Gosteva, and U. Keller, "Mirror dispersion control of a hollow fiber supercontinuum," Appl. Phys. B 78, 551-555 (2004).
[CrossRef]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, "Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation," Appl. Phys. B 79, 673-677 (2004).
[CrossRef]

B. Schenkel, J. Biegert, U. Keller, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, S. De Silvestri, and O. Svelto, "Generation of 3.8-fs pulses from adaptive compression of a cascaded hollow fiber supercontinuum," Opt. Lett. 28, 1987-1989 (2003).
[CrossRef] [PubMed]

Bor, Z.

Braun, B.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, "Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers," IEEE J. Sel. Top. Quantum Electron. 2, 435-453 (1996).
[CrossRef]

Cerullo, G.

Couairon, A.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, "Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation," Appl. Phys. B 79, 673-677 (2004).
[CrossRef]

De Silvestri, S.

der Au, J. Aus

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, "Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers," IEEE J. Sel. Top. Quantum Electron. 2, 435-453 (1996).
[CrossRef]

Diddams, S.

Diels, J.-C.

Dorrer, C.

I. Walmsley, L. Waxer, and C. Dorrer, "The role of dispersion in ultrafast optics," Rev. Sci. Instrum. 72, 1-29 (2001).
[CrossRef]

C. Dorrer, N. Belabas, J-P. Likforman, and M. Joffre, "Experimental implementation of Fourier-transform spectral interferometry and its application to the study of spectrometers," Appl. Phys. B 70, S99-S107 (2000).
[CrossRef]

C. Dorrer, "Influence of the calibration of the detector on spectral interferometry," J. Opt. Soc. Am. B 16, 1160-1168 (1999).
[CrossRef]

C. Dorrer and F. Salin, "Characterization of spectral phase modulation by classical and polarization spectral interferometry," J. Opt. Soc. Am. B 15, 2331-2337 (1998).
[CrossRef]

Fejer, M. M.

L. Gallmann, G. Steinmeyer, G. Imeshev, J.-P. Meyn, M. M. Fejer, and U. Keller, "Sub-6-fs blue pulses generated by quasi-phase-matching second-harmonic generation pulse compression," Appl. Phys. B 74, S237-S243 (2002).
[CrossRef]

Ferencz, K.

Fluck, R.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, "Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers," IEEE J. Sel. Top. Quantum Electron. 2, 435-453 (1996).
[CrossRef]

Fuji, T.

Gallmann, L.

L. Gallmann, G. Steinmeyer, G. Imeshev, J.-P. Meyn, M. M. Fejer, and U. Keller, "Sub-6-fs blue pulses generated by quasi-phase-matching second-harmonic generation pulse compression," Appl. Phys. B 74, S237-S243 (2002).
[CrossRef]

M. Zavelani-Rossi, G. Cerullo, S. De Silvestri, L. Gallmann, N. Matuschek, G. Steinmeyer, U. Keller, G. Angelow, V. Scheuer, and T. Tschudi, "Pulse compression over a 170-THz bandwidth in the visible by use of only chirped mirrors," Opt. Lett. 26, 1155-1157 (2001).
[CrossRef]

N. Matuschek, L. Gallmann, D. H. Sutter, G. Steinmeyer, and U. Keller, "Back-side-coated chirped mirrors with ultra-smooth broadband dispersion characteristics," Appl. Phys. B 71, 509-522 (2000).
[CrossRef]

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller "Techniques for the characterization of sub-10-fs optical pulses: a comparison," Appl. Phys. B 70, S67-S75 (2000).
[CrossRef]

L. Gallmann, G. Steinmeyer, D. H. Sutter, N. Matuschek, and U. Keller, "Collinear type II second-harmonic-generation frequency-resolved optical gating for the characterization of sub-10-fs optical pulses," Opt. Lett. 25, 269-271 (2000).
[CrossRef]

D. H. Sutter, L. Gallmann, N. Matuschek, F. Morier-Genoud, V. Scheuer, G. Angelow, T. Tschudi, G. Steinmeyer, and U. Keller, "Sub-6-fs pulses from a SESAM-assisted Kerr-lens modelocked Ti:sapphire laser: at the frontiers of ultrashort pulse generation," Appl. Phys. B 70, S5-S12 (2000).
[CrossRef]

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, U. Keller, C. Iaconis, and I. A. Walmsley, "Characterization of sub-6-fs optical pulses with spectral phase interferometry for direct electric-field reconstruction," Opt. Lett. 24, 1314-1316 (1999).
[CrossRef]

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, "Frontiers in ultrashort pulse generation: pushing the limits in linear and nonlinear optics," Science 286, 1507-1512 (1999).
[CrossRef] [PubMed]

Gini, E.

R. Haring, R. Paschotta, A. Aschwanden, E. Gini, F. Morier-Genoud, and U. Keller, "High-power passively mode-locked semiconductor lasers," IEEE J. Quantum Electron. 38, 1268-1275 (2002)
[CrossRef]

Gosteva, A.

G. Sansone, G. Steinmeyer, C. Vozzi, S. Stagira, M. Nisoli, S. De Silvestri, K. Starke, D. Ristau, B. Schenkel, J. Biegert, A. Gosteva, and U. Keller, "Mirror dispersion control of a hollow fiber supercontinuum," Appl. Phys. B 78, 551-555 (2004).
[CrossRef]

Hakimi, F.

M. Kuznetsov, F. Hakimi, R. Sprague, and A. Mooradian, "Design and characteristics of high-power (>0.5-W CW) diode-pumped vertical-external-cavity surface-emitting semiconductor lasers with circular TEM00 beams," IEEE J. Sel. Top. Quantum Electron. 5, 561-573 (1999).
[CrossRef]

Haring, R.

R. Haring, R. Paschotta, A. Aschwanden, E. Gini, F. Morier-Genoud, and U. Keller, "High-power passively mode-locked semiconductor lasers," IEEE J. Quantum Electron. 38, 1268-1275 (2002)
[CrossRef]

Hauri, C. P.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, "Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation," Appl. Phys. B 79, 673-677 (2004).
[CrossRef]

Heinrich, A.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, "Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation," Appl. Phys. B 79, 673-677 (2004).
[CrossRef]

Helbing, F. W.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, "Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation," Appl. Phys. B 79, 673-677 (2004).
[CrossRef]

Hönninger, C.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, "Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers," IEEE J. Sel. Top. Quantum Electron. 2, 435-453 (1996).
[CrossRef]

Iaconis, C.

Imeshev, G.

L. Gallmann, G. Steinmeyer, G. Imeshev, J.-P. Meyn, M. M. Fejer, and U. Keller, "Sub-6-fs blue pulses generated by quasi-phase-matching second-harmonic generation pulse compression," Appl. Phys. B 74, S237-S243 (2002).
[CrossRef]

Ina, H.

Joffre, M.

C. Dorrer, N. Belabas, J-P. Likforman, and M. Joffre, "Experimental implementation of Fourier-transform spectral interferometry and its application to the study of spectrometers," Appl. Phys. B 70, S99-S107 (2000).
[CrossRef]

Jung, I. D.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, "Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers," IEEE J. Sel. Top. Quantum Electron. 2, 435-453 (1996).
[CrossRef]

Kafka, J. D.

M. Beck, I. A. Walmsley, and J. D. Kafka, "Group delay measurements of optical components near 800 nm," IEEE J. Quantum Electron. 27, 2074-2081 (1991).
[CrossRef]

Kärtner, F. X.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, "Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers," IEEE J. Sel. Top. Quantum Electron. 2, 435-453 (1996).
[CrossRef]

Keller, U.

B. Schenkel, R. Paschotta, and U. Keller, "Pulse compression with supercontinuum generation in microstructure fibers," J. Opt. Soc. Am. B 22, 687-693 (2005).
[CrossRef]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, "Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation," Appl. Phys. B 79, 673-677 (2004).
[CrossRef]

G. Sansone, G. Steinmeyer, C. Vozzi, S. Stagira, M. Nisoli, S. De Silvestri, K. Starke, D. Ristau, B. Schenkel, J. Biegert, A. Gosteva, and U. Keller, "Mirror dispersion control of a hollow fiber supercontinuum," Appl. Phys. B 78, 551-555 (2004).
[CrossRef]

B. Schenkel, J. Biegert, U. Keller, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, S. De Silvestri, and O. Svelto, "Generation of 3.8-fs pulses from adaptive compression of a cascaded hollow fiber supercontinuum," Opt. Lett. 28, 1987-1989 (2003).
[CrossRef] [PubMed]

L. Gallmann, G. Steinmeyer, G. Imeshev, J.-P. Meyn, M. M. Fejer, and U. Keller, "Sub-6-fs blue pulses generated by quasi-phase-matching second-harmonic generation pulse compression," Appl. Phys. B 74, S237-S243 (2002).
[CrossRef]

R. Haring, R. Paschotta, A. Aschwanden, E. Gini, F. Morier-Genoud, and U. Keller, "High-power passively mode-locked semiconductor lasers," IEEE J. Quantum Electron. 38, 1268-1275 (2002)
[CrossRef]

M. Zavelani-Rossi, G. Cerullo, S. De Silvestri, L. Gallmann, N. Matuschek, G. Steinmeyer, U. Keller, G. Angelow, V. Scheuer, and T. Tschudi, "Pulse compression over a 170-THz bandwidth in the visible by use of only chirped mirrors," Opt. Lett. 26, 1155-1157 (2001).
[CrossRef]

N. Matuschek, L. Gallmann, D. H. Sutter, G. Steinmeyer, and U. Keller, "Back-side-coated chirped mirrors with ultra-smooth broadband dispersion characteristics," Appl. Phys. B 71, 509-522 (2000).
[CrossRef]

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller "Techniques for the characterization of sub-10-fs optical pulses: a comparison," Appl. Phys. B 70, S67-S75 (2000).
[CrossRef]

L. Gallmann, G. Steinmeyer, D. H. Sutter, N. Matuschek, and U. Keller, "Collinear type II second-harmonic-generation frequency-resolved optical gating for the characterization of sub-10-fs optical pulses," Opt. Lett. 25, 269-271 (2000).
[CrossRef]

D. H. Sutter, L. Gallmann, N. Matuschek, F. Morier-Genoud, V. Scheuer, G. Angelow, T. Tschudi, G. Steinmeyer, and U. Keller, "Sub-6-fs pulses from a SESAM-assisted Kerr-lens modelocked Ti:sapphire laser: at the frontiers of ultrashort pulse generation," Appl. Phys. B 70, S5-S12 (2000).
[CrossRef]

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, U. Keller, C. Iaconis, and I. A. Walmsley, "Characterization of sub-6-fs optical pulses with spectral phase interferometry for direct electric-field reconstruction," Opt. Lett. 24, 1314-1316 (1999).
[CrossRef]

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, "Frontiers in ultrashort pulse generation: pushing the limits in linear and nonlinear optics," Science 286, 1507-1512 (1999).
[CrossRef] [PubMed]

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, "Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers," IEEE J. Sel. Top. Quantum Electron. 2, 435-453 (1996).
[CrossRef]

Kobayashi, S.

Kobayashi, T.

Kopf, D.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, "Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers," IEEE J. Sel. Top. Quantum Electron. 2, 435-453 (1996).
[CrossRef]

Kornelis, W.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, "Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation," Appl. Phys. B 79, 673-677 (2004).
[CrossRef]

Kovacs, A. P.

Krausz, F.

Kuznetsov, M.

M. Kuznetsov, F. Hakimi, R. Sprague, and A. Mooradian, "Design and characteristics of high-power (>0.5-W CW) diode-pumped vertical-external-cavity surface-emitting semiconductor lasers with circular TEM00 beams," IEEE J. Sel. Top. Quantum Electron. 5, 561-573 (1999).
[CrossRef]

Likforman, J-P.

C. Dorrer, N. Belabas, J-P. Likforman, and M. Joffre, "Experimental implementation of Fourier-transform spectral interferometry and its application to the study of spectrometers," Appl. Phys. B 70, S99-S107 (2000).
[CrossRef]

Matuschek, N.

M. Zavelani-Rossi, G. Cerullo, S. De Silvestri, L. Gallmann, N. Matuschek, G. Steinmeyer, U. Keller, G. Angelow, V. Scheuer, and T. Tschudi, "Pulse compression over a 170-THz bandwidth in the visible by use of only chirped mirrors," Opt. Lett. 26, 1155-1157 (2001).
[CrossRef]

N. Matuschek, L. Gallmann, D. H. Sutter, G. Steinmeyer, and U. Keller, "Back-side-coated chirped mirrors with ultra-smooth broadband dispersion characteristics," Appl. Phys. B 71, 509-522 (2000).
[CrossRef]

L. Gallmann, G. Steinmeyer, D. H. Sutter, N. Matuschek, and U. Keller, "Collinear type II second-harmonic-generation frequency-resolved optical gating for the characterization of sub-10-fs optical pulses," Opt. Lett. 25, 269-271 (2000).
[CrossRef]

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller "Techniques for the characterization of sub-10-fs optical pulses: a comparison," Appl. Phys. B 70, S67-S75 (2000).
[CrossRef]

D. H. Sutter, L. Gallmann, N. Matuschek, F. Morier-Genoud, V. Scheuer, G. Angelow, T. Tschudi, G. Steinmeyer, and U. Keller, "Sub-6-fs pulses from a SESAM-assisted Kerr-lens modelocked Ti:sapphire laser: at the frontiers of ultrashort pulse generation," Appl. Phys. B 70, S5-S12 (2000).
[CrossRef]

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, U. Keller, C. Iaconis, and I. A. Walmsley, "Characterization of sub-6-fs optical pulses with spectral phase interferometry for direct electric-field reconstruction," Opt. Lett. 24, 1314-1316 (1999).
[CrossRef]

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, "Frontiers in ultrashort pulse generation: pushing the limits in linear and nonlinear optics," Science 286, 1507-1512 (1999).
[CrossRef] [PubMed]

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, "Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers," IEEE J. Sel. Top. Quantum Electron. 2, 435-453 (1996).
[CrossRef]

Meyn, J.-P.

L. Gallmann, G. Steinmeyer, G. Imeshev, J.-P. Meyn, M. M. Fejer, and U. Keller, "Sub-6-fs blue pulses generated by quasi-phase-matching second-harmonic generation pulse compression," Appl. Phys. B 74, S237-S243 (2002).
[CrossRef]

Mogi, K.

Mooradian, A.

M. Kuznetsov, F. Hakimi, R. Sprague, and A. Mooradian, "Design and characteristics of high-power (>0.5-W CW) diode-pumped vertical-external-cavity surface-emitting semiconductor lasers with circular TEM00 beams," IEEE J. Sel. Top. Quantum Electron. 5, 561-573 (1999).
[CrossRef]

Morier-Genoud, F.

R. Haring, R. Paschotta, A. Aschwanden, E. Gini, F. Morier-Genoud, and U. Keller, "High-power passively mode-locked semiconductor lasers," IEEE J. Quantum Electron. 38, 1268-1275 (2002)
[CrossRef]

D. H. Sutter, L. Gallmann, N. Matuschek, F. Morier-Genoud, V. Scheuer, G. Angelow, T. Tschudi, G. Steinmeyer, and U. Keller, "Sub-6-fs pulses from a SESAM-assisted Kerr-lens modelocked Ti:sapphire laser: at the frontiers of ultrashort pulse generation," Appl. Phys. B 70, S5-S12 (2000).
[CrossRef]

Morita, R.

Mysyrowicz, A.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, "Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation," Appl. Phys. B 79, 673-677 (2004).
[CrossRef]

Naganuma, K.

Nisoli, M.

Oka, K.

Osvay, K.

Paschotta, R.

B. Schenkel, R. Paschotta, and U. Keller, "Pulse compression with supercontinuum generation in microstructure fibers," J. Opt. Soc. Am. B 22, 687-693 (2005).
[CrossRef]

R. Haring, R. Paschotta, A. Aschwanden, E. Gini, F. Morier-Genoud, and U. Keller, "High-power passively mode-locked semiconductor lasers," IEEE J. Quantum Electron. 38, 1268-1275 (2002)
[CrossRef]

Ristau, D.

G. Sansone, G. Steinmeyer, C. Vozzi, S. Stagira, M. Nisoli, S. De Silvestri, K. Starke, D. Ristau, B. Schenkel, J. Biegert, A. Gosteva, and U. Keller, "Mirror dispersion control of a hollow fiber supercontinuum," Appl. Phys. B 78, 551-555 (2004).
[CrossRef]

Salin, F.

Sansone, G.

G. Sansone, G. Steinmeyer, C. Vozzi, S. Stagira, M. Nisoli, S. De Silvestri, K. Starke, D. Ristau, B. Schenkel, J. Biegert, A. Gosteva, and U. Keller, "Mirror dispersion control of a hollow fiber supercontinuum," Appl. Phys. B 78, 551-555 (2004).
[CrossRef]

B. Schenkel, J. Biegert, U. Keller, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, S. De Silvestri, and O. Svelto, "Generation of 3.8-fs pulses from adaptive compression of a cascaded hollow fiber supercontinuum," Opt. Lett. 28, 1987-1989 (2003).
[CrossRef] [PubMed]

Sartania, S.

Schenkel, B.

Scheuer, V.

M. Zavelani-Rossi, G. Cerullo, S. De Silvestri, L. Gallmann, N. Matuschek, G. Steinmeyer, U. Keller, G. Angelow, V. Scheuer, and T. Tschudi, "Pulse compression over a 170-THz bandwidth in the visible by use of only chirped mirrors," Opt. Lett. 26, 1155-1157 (2001).
[CrossRef]

D. H. Sutter, L. Gallmann, N. Matuschek, F. Morier-Genoud, V. Scheuer, G. Angelow, T. Tschudi, G. Steinmeyer, and U. Keller, "Sub-6-fs pulses from a SESAM-assisted Kerr-lens modelocked Ti:sapphire laser: at the frontiers of ultrashort pulse generation," Appl. Phys. B 70, S5-S12 (2000).
[CrossRef]

Spielmann, Ch.

Sprague, R.

M. Kuznetsov, F. Hakimi, R. Sprague, and A. Mooradian, "Design and characteristics of high-power (>0.5-W CW) diode-pumped vertical-external-cavity surface-emitting semiconductor lasers with circular TEM00 beams," IEEE J. Sel. Top. Quantum Electron. 5, 561-573 (1999).
[CrossRef]

Stagira, S.

G. Sansone, G. Steinmeyer, C. Vozzi, S. Stagira, M. Nisoli, S. De Silvestri, K. Starke, D. Ristau, B. Schenkel, J. Biegert, A. Gosteva, and U. Keller, "Mirror dispersion control of a hollow fiber supercontinuum," Appl. Phys. B 78, 551-555 (2004).
[CrossRef]

B. Schenkel, J. Biegert, U. Keller, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, S. De Silvestri, and O. Svelto, "Generation of 3.8-fs pulses from adaptive compression of a cascaded hollow fiber supercontinuum," Opt. Lett. 28, 1987-1989 (2003).
[CrossRef] [PubMed]

Starke, K.

G. Sansone, G. Steinmeyer, C. Vozzi, S. Stagira, M. Nisoli, S. De Silvestri, K. Starke, D. Ristau, B. Schenkel, J. Biegert, A. Gosteva, and U. Keller, "Mirror dispersion control of a hollow fiber supercontinuum," Appl. Phys. B 78, 551-555 (2004).
[CrossRef]

Steinmeyer, G.

G. Sansone, G. Steinmeyer, C. Vozzi, S. Stagira, M. Nisoli, S. De Silvestri, K. Starke, D. Ristau, B. Schenkel, J. Biegert, A. Gosteva, and U. Keller, "Mirror dispersion control of a hollow fiber supercontinuum," Appl. Phys. B 78, 551-555 (2004).
[CrossRef]

L. Gallmann, G. Steinmeyer, G. Imeshev, J.-P. Meyn, M. M. Fejer, and U. Keller, "Sub-6-fs blue pulses generated by quasi-phase-matching second-harmonic generation pulse compression," Appl. Phys. B 74, S237-S243 (2002).
[CrossRef]

M. Zavelani-Rossi, G. Cerullo, S. De Silvestri, L. Gallmann, N. Matuschek, G. Steinmeyer, U. Keller, G. Angelow, V. Scheuer, and T. Tschudi, "Pulse compression over a 170-THz bandwidth in the visible by use of only chirped mirrors," Opt. Lett. 26, 1155-1157 (2001).
[CrossRef]

N. Matuschek, L. Gallmann, D. H. Sutter, G. Steinmeyer, and U. Keller, "Back-side-coated chirped mirrors with ultra-smooth broadband dispersion characteristics," Appl. Phys. B 71, 509-522 (2000).
[CrossRef]

L. Gallmann, G. Steinmeyer, D. H. Sutter, N. Matuschek, and U. Keller, "Collinear type II second-harmonic-generation frequency-resolved optical gating for the characterization of sub-10-fs optical pulses," Opt. Lett. 25, 269-271 (2000).
[CrossRef]

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller "Techniques for the characterization of sub-10-fs optical pulses: a comparison," Appl. Phys. B 70, S67-S75 (2000).
[CrossRef]

D. H. Sutter, L. Gallmann, N. Matuschek, F. Morier-Genoud, V. Scheuer, G. Angelow, T. Tschudi, G. Steinmeyer, and U. Keller, "Sub-6-fs pulses from a SESAM-assisted Kerr-lens modelocked Ti:sapphire laser: at the frontiers of ultrashort pulse generation," Appl. Phys. B 70, S5-S12 (2000).
[CrossRef]

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, U. Keller, C. Iaconis, and I. A. Walmsley, "Characterization of sub-6-fs optical pulses with spectral phase interferometry for direct electric-field reconstruction," Opt. Lett. 24, 1314-1316 (1999).
[CrossRef]

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, "Frontiers in ultrashort pulse generation: pushing the limits in linear and nonlinear optics," Science 286, 1507-1512 (1999).
[CrossRef] [PubMed]

Suguro, A.

Sutter, D. H.

L. Gallmann, G. Steinmeyer, D. H. Sutter, N. Matuschek, and U. Keller, "Collinear type II second-harmonic-generation frequency-resolved optical gating for the characterization of sub-10-fs optical pulses," Opt. Lett. 25, 269-271 (2000).
[CrossRef]

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller "Techniques for the characterization of sub-10-fs optical pulses: a comparison," Appl. Phys. B 70, S67-S75 (2000).
[CrossRef]

N. Matuschek, L. Gallmann, D. H. Sutter, G. Steinmeyer, and U. Keller, "Back-side-coated chirped mirrors with ultra-smooth broadband dispersion characteristics," Appl. Phys. B 71, 509-522 (2000).
[CrossRef]

D. H. Sutter, L. Gallmann, N. Matuschek, F. Morier-Genoud, V. Scheuer, G. Angelow, T. Tschudi, G. Steinmeyer, and U. Keller, "Sub-6-fs pulses from a SESAM-assisted Kerr-lens modelocked Ti:sapphire laser: at the frontiers of ultrashort pulse generation," Appl. Phys. B 70, S5-S12 (2000).
[CrossRef]

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, U. Keller, C. Iaconis, and I. A. Walmsley, "Characterization of sub-6-fs optical pulses with spectral phase interferometry for direct electric-field reconstruction," Opt. Lett. 24, 1314-1316 (1999).
[CrossRef]

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, "Frontiers in ultrashort pulse generation: pushing the limits in linear and nonlinear optics," Science 286, 1507-1512 (1999).
[CrossRef] [PubMed]

Svelto, O.

Szipcs, R.

Szipocs, R.

Takeda, M.

Tschudi, T.

M. Zavelani-Rossi, G. Cerullo, S. De Silvestri, L. Gallmann, N. Matuschek, G. Steinmeyer, U. Keller, G. Angelow, V. Scheuer, and T. Tschudi, "Pulse compression over a 170-THz bandwidth in the visible by use of only chirped mirrors," Opt. Lett. 26, 1155-1157 (2001).
[CrossRef]

D. H. Sutter, L. Gallmann, N. Matuschek, F. Morier-Genoud, V. Scheuer, G. Angelow, T. Tschudi, G. Steinmeyer, and U. Keller, "Sub-6-fs pulses from a SESAM-assisted Kerr-lens modelocked Ti:sapphire laser: at the frontiers of ultrashort pulse generation," Appl. Phys. B 70, S5-S12 (2000).
[CrossRef]

Vozzi, C.

G. Sansone, G. Steinmeyer, C. Vozzi, S. Stagira, M. Nisoli, S. De Silvestri, K. Starke, D. Ristau, B. Schenkel, J. Biegert, A. Gosteva, and U. Keller, "Mirror dispersion control of a hollow fiber supercontinuum," Appl. Phys. B 78, 551-555 (2004).
[CrossRef]

B. Schenkel, J. Biegert, U. Keller, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, S. De Silvestri, and O. Svelto, "Generation of 3.8-fs pulses from adaptive compression of a cascaded hollow fiber supercontinuum," Opt. Lett. 28, 1987-1989 (2003).
[CrossRef] [PubMed]

Walmsley, I.

I. Walmsley, L. Waxer, and C. Dorrer, "The role of dispersion in ultrafast optics," Rev. Sci. Instrum. 72, 1-29 (2001).
[CrossRef]

Walmsley, I. A.

Waxer, L.

I. Walmsley, L. Waxer, and C. Dorrer, "The role of dispersion in ultrafast optics," Rev. Sci. Instrum. 72, 1-29 (2001).
[CrossRef]

Weingarten, K. J.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, "Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers," IEEE J. Sel. Top. Quantum Electron. 2, 435-453 (1996).
[CrossRef]

Yamada, H.

Yamane, K.

Yamashita, M.

Zavelani-Rossi, M.

Zhang, Z. G.

Appl. Phys. B (7)

N. Matuschek, L. Gallmann, D. H. Sutter, G. Steinmeyer, and U. Keller, "Back-side-coated chirped mirrors with ultra-smooth broadband dispersion characteristics," Appl. Phys. B 71, 509-522 (2000).
[CrossRef]

G. Sansone, G. Steinmeyer, C. Vozzi, S. Stagira, M. Nisoli, S. De Silvestri, K. Starke, D. Ristau, B. Schenkel, J. Biegert, A. Gosteva, and U. Keller, "Mirror dispersion control of a hollow fiber supercontinuum," Appl. Phys. B 78, 551-555 (2004).
[CrossRef]

L. Gallmann, G. Steinmeyer, G. Imeshev, J.-P. Meyn, M. M. Fejer, and U. Keller, "Sub-6-fs blue pulses generated by quasi-phase-matching second-harmonic generation pulse compression," Appl. Phys. B 74, S237-S243 (2002).
[CrossRef]

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, "Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation," Appl. Phys. B 79, 673-677 (2004).
[CrossRef]

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller "Techniques for the characterization of sub-10-fs optical pulses: a comparison," Appl. Phys. B 70, S67-S75 (2000).
[CrossRef]

D. H. Sutter, L. Gallmann, N. Matuschek, F. Morier-Genoud, V. Scheuer, G. Angelow, T. Tschudi, G. Steinmeyer, and U. Keller, "Sub-6-fs pulses from a SESAM-assisted Kerr-lens modelocked Ti:sapphire laser: at the frontiers of ultrashort pulse generation," Appl. Phys. B 70, S5-S12 (2000).
[CrossRef]

C. Dorrer, N. Belabas, J-P. Likforman, and M. Joffre, "Experimental implementation of Fourier-transform spectral interferometry and its application to the study of spectrometers," Appl. Phys. B 70, S99-S107 (2000).
[CrossRef]

IEEE J. Quantum Electron. (2)

M. Beck, I. A. Walmsley, and J. D. Kafka, "Group delay measurements of optical components near 800 nm," IEEE J. Quantum Electron. 27, 2074-2081 (1991).
[CrossRef]

R. Haring, R. Paschotta, A. Aschwanden, E. Gini, F. Morier-Genoud, and U. Keller, "High-power passively mode-locked semiconductor lasers," IEEE J. Quantum Electron. 38, 1268-1275 (2002)
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, "Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers," IEEE J. Sel. Top. Quantum Electron. 2, 435-453 (1996).
[CrossRef]

M. Kuznetsov, F. Hakimi, R. Sprague, and A. Mooradian, "Design and characteristics of high-power (>0.5-W CW) diode-pumped vertical-external-cavity surface-emitting semiconductor lasers with circular TEM00 beams," IEEE J. Sel. Top. Quantum Electron. 5, 561-573 (1999).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (4)

Opt. Lett. (10)

A. P. Kovacs, K. Osvay, Z. Bor, and R. Szipocs, "Group-delay measurement on laser mirrors by spectrally resolved white-light interferometry," Opt. Lett. 20, 788-790 (1995).
[CrossRef] [PubMed]

L. Gallmann, G. Steinmeyer, D. H. Sutter, N. Matuschek, and U. Keller, "Collinear type II second-harmonic-generation frequency-resolved optical gating for the characterization of sub-10-fs optical pulses," Opt. Lett. 25, 269-271 (2000).
[CrossRef]

K. Naganuma, K. Mogi, and H. Yamada, "Group-delay measurement using the Fourier transform of an interferometric cross correlation generated by white light," Opt. Lett. 15, 393-395 (1990).
[CrossRef] [PubMed]

M. Beck and I. A. Walmsley, "Measurement of group delay with high temporal and spectral resolution," Opt. Lett. 15, 492-494 (1990).
[CrossRef] [PubMed]

M. Nisoli, S. De Silvestri, O. Svelto, R. Szipcs, K. Ferencz, Ch. Spielmann, S. Sartania, and F. Krausz, "Compression of high-energy laser pulses below 5 fs," Opt. Lett. 22, 522-524 (1997).
[CrossRef] [PubMed]

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, U. Keller, C. Iaconis, and I. A. Walmsley, "Characterization of sub-6-fs optical pulses with spectral phase interferometry for direct electric-field reconstruction," Opt. Lett. 24, 1314-1316 (1999).
[CrossRef]

M. Zavelani-Rossi, G. Cerullo, S. De Silvestri, L. Gallmann, N. Matuschek, G. Steinmeyer, U. Keller, G. Angelow, V. Scheuer, and T. Tschudi, "Pulse compression over a 170-THz bandwidth in the visible by use of only chirped mirrors," Opt. Lett. 26, 1155-1157 (2001).
[CrossRef]

A. Baltuska, T. Fuji, and T. Kobayashi, "Visible pulse compression to 4 fs by optical parametric amplification and programmable dispersion control," Opt. Lett. 27, 306-308 (2002).
[CrossRef]

B. Schenkel, J. Biegert, U. Keller, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, S. De Silvestri, and O. Svelto, "Generation of 3.8-fs pulses from adaptive compression of a cascaded hollow fiber supercontinuum," Opt. Lett. 28, 1987-1989 (2003).
[CrossRef] [PubMed]

K. Yamane, Z. G. Zhang, K. Oka, R. Morita, M. Yamashita, and A. Suguro, "Optical pulse compression to 3.4 fs in the monocycle region by feedback phase compensation," Opt. Lett. 28, 2258-2260 (2003).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

I. Walmsley, L. Waxer, and C. Dorrer, "The role of dispersion in ultrafast optics," Rev. Sci. Instrum. 72, 1-29 (2001).
[CrossRef]

Science (1)

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, and U. Keller, "Frontiers in ultrashort pulse generation: pushing the limits in linear and nonlinear optics," Science 286, 1507-1512 (1999).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Scanning Michelson interferometer using a fiber-coupled white-light source with the peak spectral brightness at 1550 nm. M1, M2, and M3 are silver mirrors; SOA = semiconductor optical amplifier (50 nm FWHM, 3 μ W nm ); L = lens ; P = polarizer ; BS = nonpolarizing beam splitter ; PD 1 = silicon photodiode ; PD 2 = InGaAs photodiode ; DM = dichroic mirror .

Fig. 2
Fig. 2

Measured interferogram for a Gaussian source spectrum and low dispersion. The noise floor can be determined from the outer parts of the trace (see inset).

Fig. 3
Fig. 3

Optical power density OPD (right axis) and GDD (left axis) of DUT, measured with three different resolutions (9.1, 5.8, and 4.0 nm) and corresponding number of averages (150, 2 313, and 22 048), scaled with the sixth power of the spectral resolution for equal standard deviations of all measurements.

Fig. 4
Fig. 4

Standard deviation of measured GDD ( σ D 2 ) versus wavelength for a fixed number of averaged traces and two different wavelength resolutions.

Fig. 5
Fig. 5

Experimentally obtained standard deviation of GDD ( σ D 2 ) measured with 4.0, 5.8, and 9.1 nm resolution and corresponding number of averages (22 048, 2 313, and 150).

Fig. 6
Fig. 6

Standard deviation of GDD ( σ D 2 ) . Filled circles, experimentally measured with 5.8 nm resolution and 2 313 averages; crossed circles, theoretically calculated value without noise correction; open circles, theoretically calculated value with correction for residual noise correlations.

Equations (19)

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

E ( t ) + S ( ω ) exp [ i ω t + i φ wl ( ω ) ] d ω .
E 1 ( z 1 , t ) + S ( ω ) r ref ( ω ) exp [ i ω ( t z 1 c ) + i φ wl ( ω ) ] d ω ,
E 2 ( z 2 , t ) + S ( ω ) r sa ( ω ) exp [ i ω ( t z 2 c ) + i φ wl ( ω ) ] d ω ,
I ( Δ z ) E 1 ( z 1 , t ) 2 + E 2 ( z 2 , t ) 2 + E 1 * ( z 1 , t ) E 2 ( z 2 , t ) + E 1 ( z 1 , t ) E 2 * ( z 2 , t ) ,
I int ( Δ z ) Re { E 1 * ( z 1 ) E 2 ( z 2 ) } .
exp ( i ω 1 t i ω 2 t ) = δ ( ω 1 ω 2 ) ,
I int ( Δ z ) Re { + S ( ω ) r ref * ( ω ) r sa ( ω ) exp ( i ω c Δ z ) d ω } = Re { + S ( ω ) r ref r sa exp [ i φ sa ( ω ) i φ ref ( ω ) ] exp ( i ω c Δ z ) d ω } ,
I int ( ω c ) = FT { I int ( Δ z ) } ,
φ ( ω ) = φ sa ( ω ) φ ref ( ω ) = φ DUT ( ω ) + φ sa , balance ( ω ) φ ref ( ω ) ,
D 2 [ ω ] = φ [ ω + δ ω ] 2 φ [ ω ] + φ [ ω δ ω ] δ ω 2 .
σ D 2 2 ( ω ) = [ d D 2 [ ω ] d ( φ [ ω + δ ω ] ) σ φ [ ω + δ ω ] ] 2 + [ d D 2 [ ω ] d ( φ [ ω ] ) σ φ [ ω ] ] 2 + [ d D 2 [ ω ] d ( φ [ ω δ ω ] ) σ φ [ ω δ ω ] ] 2 = 6 σ φ 2 ( ω ) δ ω 4 .
σ a 2 ( ω ) d ω = 1 2 σ s ̃ 2 ( ω ) d ω
σ φ 2 ( ω ) d ω = 1 2 arctan [ σ s ̃ 2 ( ω ) d ω s ̃ 2 ( ω ) ] σ s ̃ 2 ( ω ) d ω 2 s ̃ 2 ( ω ) .
σ s ̃ 2 ( ω ) = ( 2 π ) 2 σ s 2 ( t ) p ( δ ω ) 2 .
SNR = S max 2 σ s 2 ,
S max 1 2 π s ̃ ( ω ) d ω = 1 2 π I ( ω ) d ω
σ D 2 ( ω ) = { 3 [ I ( ω ) d ω ] 2 I 2 ( ω ) 1 SNR p M ( δ ω ) 6 } 1 2 ,
σ D 2 ( ω ) = [ 3 π 4 ln ( 2 ) 1 I n 2 ( ω ) Δ ω 2 SNR p M ( δ ω ) 6 ] 1 2 ,
σ D 2 ( ω ) = [ 3 I n 2 ( ω ) Δ ω 2 SNR p M ( δ ω ) 6 ] 1 2 .

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