Abstract

A modified white-light Mach–Zehnder interferometer based on a single beam splitter is described for direct group-delay measurements. The arms of the interferometer are folded in such a manner that a single beam splitter can be used to split the incoming beam and combine the outgoing beams. This method offers a twofold advantage: The measuring range of the interferometer is twice as large as that of the Michelson interferometer, and the systematic error that is associated with the beam splitter is minimized because of the configuration. We report the results of measurements on various optical components performed in the 555–630-nm spectral region and propose a scheme for the processing of the experimental data. We present a comparison of the data analyzed by the proposed processing scheme along with the theoretical calculations.

© 1998 Optical Society of America

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References

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  1. C. Spielmann, P. F. Curley, T. Brabec, F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1114 (1994).
    [CrossRef]
  2. W. H. Knox, “Dispersion measurements for femtosecond-pulse generation and applications,” Appl. Phys. B 58, 225–235 (1994).
    [CrossRef]
  3. S. Diddams, J. C. Diels, “Dispersion measurements with white-light interferometry,” J. Opt. Soc. Am. B 13, 1120–1129 (1996).
    [CrossRef]
  4. M. A. Khashan, “Comparison of group and phase velocities of light using the Michelson interferometer,” Optik 64, 285–297 (1983).
  5. Z. Bor, K. Osvay, B. Racz, G. Szabo, “Group refractive index measurement by Michelson interferometer,” Opt. Commun. 78, 109–112 (1990).
    [CrossRef]
  6. W. H. Knox, N. M. Pearson, K. D. Li, C. A. Hirlimann, “Interferometric measurements of femtosecond group delay in optical components,” Opt. Lett. 13, 574–576 (1988).
    [CrossRef] [PubMed]
  7. K. Naganuma, K. Mogi, 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]
  8. M. Beck, I. A. Walmsley, “Measurement of group delay with high temporal and spectral resolution,” Opt. Lett. 15, 492–494 (1990).
    [CrossRef] [PubMed]
  9. M. Beck, I. A. Walmsley, J. D. Kafka, “Group delay measurements of optical components near 800 nm,” IEEE J. Quantum Electron. 27, 2074–2081 (1991).
    [CrossRef]
  10. C. Sainz, P. Jourdain, R. Escalona, J. Calatroni, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 110, 381–390 (1994).
    [CrossRef]
  11. A. P. Kovacs, K. Osvay, Z. Bor, “Group-delay measurement on laser mirrors by spectrally resolved white-light interferometry,” Opt. Lett. 20, 788–790 (1995).
    [CrossRef] [PubMed]
  12. K. Osvay, G. Kurdi, J. Hebling, A. P. Kovacs, Z. Bor, R. Szipöcs, “Measurement of the group delay of laser mirrors by a Fabry–Perot interferometer,” Opt. Lett. 20, 2339–2341 (1995).
    [CrossRef] [PubMed]
  13. S. Tolansky, Multiple-Beam Interferometry of Surfaces and Films (Dover, New York, 1970), Chap. 8.
  14. I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55, 1205–1209 (1965); Schott Optical Glass Catalog, Schott Glass Technologies Inc., 400 York Avenue, Duryea, Pa. 18642.

1996 (1)

1995 (2)

1994 (3)

C. Sainz, P. Jourdain, R. Escalona, J. Calatroni, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 110, 381–390 (1994).
[CrossRef]

C. Spielmann, P. F. Curley, T. Brabec, F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1114 (1994).
[CrossRef]

W. H. Knox, “Dispersion measurements for femtosecond-pulse generation and applications,” Appl. Phys. B 58, 225–235 (1994).
[CrossRef]

1991 (1)

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

1990 (3)

1988 (1)

1983 (1)

M. A. Khashan, “Comparison of group and phase velocities of light using the Michelson interferometer,” Optik 64, 285–297 (1983).

1965 (1)

Beck, M.

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

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

Bor, Z.

Brabec, T.

C. Spielmann, P. F. Curley, T. Brabec, F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1114 (1994).
[CrossRef]

Calatroni, J.

C. Sainz, P. Jourdain, R. Escalona, J. Calatroni, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 110, 381–390 (1994).
[CrossRef]

Curley, P. F.

C. Spielmann, P. F. Curley, T. Brabec, F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1114 (1994).
[CrossRef]

Diddams, S.

Diels, J. C.

Escalona, R.

C. Sainz, P. Jourdain, R. Escalona, J. Calatroni, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 110, 381–390 (1994).
[CrossRef]

Hebling, J.

Hirlimann, C. A.

Jourdain, P.

C. Sainz, P. Jourdain, R. Escalona, J. Calatroni, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 110, 381–390 (1994).
[CrossRef]

Kafka, J. D.

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

Khashan, M. A.

M. A. Khashan, “Comparison of group and phase velocities of light using the Michelson interferometer,” Optik 64, 285–297 (1983).

Knox, W. H.

Kovacs, A. P.

Krausz, F.

C. Spielmann, P. F. Curley, T. Brabec, F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1114 (1994).
[CrossRef]

Kurdi, G.

Li, K. D.

Malitson, I. H.

Mogi, K.

Naganuma, K.

Osvay, K.

Pearson, N. M.

Racz, B.

Z. Bor, K. Osvay, B. Racz, G. Szabo, “Group refractive index measurement by Michelson interferometer,” Opt. Commun. 78, 109–112 (1990).
[CrossRef]

Sainz, C.

C. Sainz, P. Jourdain, R. Escalona, J. Calatroni, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 110, 381–390 (1994).
[CrossRef]

Spielmann, C.

C. Spielmann, P. F. Curley, T. Brabec, F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1114 (1994).
[CrossRef]

Szabo, G.

Z. Bor, K. Osvay, B. Racz, G. Szabo, “Group refractive index measurement by Michelson interferometer,” Opt. Commun. 78, 109–112 (1990).
[CrossRef]

Szipöcs, R.

Tolansky, S.

S. Tolansky, Multiple-Beam Interferometry of Surfaces and Films (Dover, New York, 1970), Chap. 8.

Walmsley, I. A.

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

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

Yamada, H.

Appl. Phys. B (1)

W. H. Knox, “Dispersion measurements for femtosecond-pulse generation and applications,” Appl. Phys. B 58, 225–235 (1994).
[CrossRef]

IEEE J. Quantum Electron. (2)

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

C. Spielmann, P. F. Curley, T. Brabec, F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1114 (1994).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (1)

Opt. Commun. (2)

C. Sainz, P. Jourdain, R. Escalona, J. Calatroni, “Real time interferometric measurements of dispersion curves,” Opt. Commun. 110, 381–390 (1994).
[CrossRef]

Z. Bor, K. Osvay, B. Racz, G. Szabo, “Group refractive index measurement by Michelson interferometer,” Opt. Commun. 78, 109–112 (1990).
[CrossRef]

Opt. Lett. (5)

Optik (1)

M. A. Khashan, “Comparison of group and phase velocities of light using the Michelson interferometer,” Optik 64, 285–297 (1983).

Other (1)

S. Tolansky, Multiple-Beam Interferometry of Surfaces and Films (Dover, New York, 1970), Chap. 8.

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Figures (7)

Fig. 1
Fig. 1

Optical setup of the modified white-light Mach–Zehnder interferometer based on a single beam splitter. D, beam splitter; G, grating; L1, achromatic collimating lens; L2, achromatic imaging lens; M, aluminum mirror; O, test object; P, pinhole; S, slit; solid line, beams passing through the beam splitter one time; dotted line, beams passing through the beam splitter three times.

Fig. 2
Fig. 2

Interferogram produced by the dispersion of a BK-7 window (thickness, 9.730 ± 0.01 mm) on a CCD camera (1134 pixels on the horizontal, 486 pixels on the vertical) in the Mach–Zehnder configuration.

Fig. 3
Fig. 3

Integrated fringe pattern obtained by adding the signal from pixel 100 to pixel 400 along the vertical axis of the interferogram displayed on the CCD camera. (a) Mach–Zehnder configuration. (b) Michelson configuration.

Fig. 4
Fig. 4

Group-delay measurement of a BK-7 window (thickness, 9.730 ± 0.01 mm). (a) Open circles, group delay obtained from the experimental phase curve by use of Eq. (2) and ten-point adjacent average; solid curve, the second-order polynomial curve fitting on the group-delay data. (b) Open circles, experimental curve-fitted group delay; solid curve, theoretically calculated group delay by use of the Sellmeir equation and Eqs. (2) and (3).

Fig. 5
Fig. 5

Group-delay measurement of a fused-silica window (thickness, 5.928 ± 0.01 mm). (a) Open circles, group delay obtained from the experimental phase curve by use of Eq. (2) and ten-point adjacent average; solid curve, the second-order polynomial curve fitting on the group-delay data. (b) Open circles, experimental curve-fitted group delay; solid curve, theoretically calculated group delay by use of the Sellmeir equation and Eqs. (2) and (3).

Fig. 6
Fig. 6

Group-delay measurements of coated beam splitters. Open circles, experimental curve-fitted group delay; solid curve, theoretically calculated group delay for the substrate by use of the Sellmeir equation and Eqs. (2) and (3). (a) Fused-silica beam splitter (thickness, 6.846 ± 0.01 mm). (b) BK-7 beam splitter (thickness, 9.370 ± 0.01 mm).

Fig. 7
Fig. 7

(a) Interferogram produced by the modified Mach–Zehnder interferometer when no test object is present in either arm. (b) Experimental calibrated group delay for the interferometer. Open circles, group delay determined by use of Eq. (2); each data point corresponds to 10 wavelength points on the interferogram. Solid curve, the third-order polynomial curve fitting on the group-delay data.

Tables (1)

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Table 1 Constants in the Sellmeir Equation for Synthetic Fused-Silica and BK-7 Glass

Equations (8)

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ϕ λ = 2 π λ t n λ - 1 + L 0 ,
GD = d ϕ ω d ω AB = λ 2 2 π c λ B 2 d ϕ λ d λ B - λ A 2 d ϕ λ d λ A = t c n g λ A - n g λ B ,
n g λ = n λ - λ   d n λ d λ .
ϕ = arccos 2 I - I max + I min / I max - I min ,
ϕ 1 λ - ϕ 2 λ = 2 π λ L 1 - L 2 .
n λ 2 = 1 + B 1 λ 2 λ 2 - C 1 + B 2 λ 2 λ 2 - C 2 + B 3 λ 2 λ 2 - C 3 ,
SD = k = 1 m x e - x t 2 m - 1 1 / 2 ,
I y ,   λ = I 1 λ + I 2 λ + 2 I 1 λ I 2 λ 1 / 2 × cos ϕ λ + 2 π λ y - y 0 tan α ,

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