Abstract

We propose a new configuration for using a triangle-wave signal to drive the electro-optic modulator in an electro-optic heterodyne interferometer system. The new configuration is adapted to measure the phase retardation of a wave plate and the optical rotation angle of a chiral medium. By adding optic elements, the second-harmonic component amplitude of the interferometer photodetector output signal became proportional to the phase retardation or optical rotation angle of the samples being tested.

© 2007 Optical Society of America

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References

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  1. Y. Lin, Z. Zhou, and R. Wang, "Optical heterodyne measurement of the phase retardation of a quarter-wave plate," Opt. Lett. 13, 559-555 (1988).
  2. L. H. Shyu, C. L. Chen, and D. C. Su, "Method for measuring the retardation of a wave plate," Appl. Opt. 32, 4228-4230 (1993).
    [CrossRef] [PubMed]
  3. Y. L. Lo, S. Y. Lee, and J. F. Lin, "The new circular polariscope and the Senarmont setup with electro-optic modulator for measuring the optical linear birefringent media properties," Opt. Commun. 237, 267-273 (2004).
    [CrossRef]
  4. D. C. Su, M. H. Chiu, and C. D. Chen, "A heterodyne interferometer using an electro-optic modulator for measuring small displacements," J. Opt. 27, 19-23 (1996).
    [CrossRef]
  5. Y. L. Lo, C. H. Lai, J. F. Lin, and P. F. Hsu, "Simultaneous absolute measurements of principle angle and phase retardation with a new common-path heterodyne interferometer," Appl. Opt. 43, 2013-2022 (2004).
    [CrossRef] [PubMed]
  6. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 5.
  7. M. H. Chiu, J. Y. Lee, and D. C. Su, "Complex reflective-index measurement based on Fresnel's equations and the uses of heterodyne interferometry," Appl. Opt. 38, 4047-4052 (1999).
    [CrossRef]
  8. A. Lakhtakia, Selected Papers on Natural Optical Activity (SPIE, Bellingham,1990).
  9. R. J. McNichols, B. D. Cameron, and G. L. Cote, "Development of a non-invasive polarimetric glucose sensor," IEEE-LEOS Newsletter 12, 30-31 (1998).
  10. R. C. Weast, ed., Handbook of Chemistry and Physics (CRC Press, Boca Raton, Fla., 1981).
  11. J. Y. Lee and D. C. Su, "Improved common-path optical heterodyne interferometer for measuring small optical rotation angle of chiral medium," Opt. Commun. 256, 337-341 (2005).
    [CrossRef]

2005 (1)

J. Y. Lee and D. C. Su, "Improved common-path optical heterodyne interferometer for measuring small optical rotation angle of chiral medium," Opt. Commun. 256, 337-341 (2005).
[CrossRef]

2004 (2)

Y. L. Lo, S. Y. Lee, and J. F. Lin, "The new circular polariscope and the Senarmont setup with electro-optic modulator for measuring the optical linear birefringent media properties," Opt. Commun. 237, 267-273 (2004).
[CrossRef]

Y. L. Lo, C. H. Lai, J. F. Lin, and P. F. Hsu, "Simultaneous absolute measurements of principle angle and phase retardation with a new common-path heterodyne interferometer," Appl. Opt. 43, 2013-2022 (2004).
[CrossRef] [PubMed]

1999 (1)

M. H. Chiu, J. Y. Lee, and D. C. Su, "Complex reflective-index measurement based on Fresnel's equations and the uses of heterodyne interferometry," Appl. Opt. 38, 4047-4052 (1999).
[CrossRef]

1998 (1)

R. J. McNichols, B. D. Cameron, and G. L. Cote, "Development of a non-invasive polarimetric glucose sensor," IEEE-LEOS Newsletter 12, 30-31 (1998).

1996 (1)

D. C. Su, M. H. Chiu, and C. D. Chen, "A heterodyne interferometer using an electro-optic modulator for measuring small displacements," J. Opt. 27, 19-23 (1996).
[CrossRef]

1993 (1)

L. H. Shyu, C. L. Chen, and D. C. Su, "Method for measuring the retardation of a wave plate," Appl. Opt. 32, 4228-4230 (1993).
[CrossRef] [PubMed]

1988 (1)

Y. Lin, Z. Zhou, and R. Wang, "Optical heterodyne measurement of the phase retardation of a quarter-wave plate," Opt. Lett. 13, 559-555 (1988).

1984 (1)

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 5.

Cameron, B. D.

R. J. McNichols, B. D. Cameron, and G. L. Cote, "Development of a non-invasive polarimetric glucose sensor," IEEE-LEOS Newsletter 12, 30-31 (1998).

Chen, C. D.

D. C. Su, M. H. Chiu, and C. D. Chen, "A heterodyne interferometer using an electro-optic modulator for measuring small displacements," J. Opt. 27, 19-23 (1996).
[CrossRef]

Chen, C. L.

L. H. Shyu, C. L. Chen, and D. C. Su, "Method for measuring the retardation of a wave plate," Appl. Opt. 32, 4228-4230 (1993).
[CrossRef] [PubMed]

Chiu, M. H.

M. H. Chiu, J. Y. Lee, and D. C. Su, "Complex reflective-index measurement based on Fresnel's equations and the uses of heterodyne interferometry," Appl. Opt. 38, 4047-4052 (1999).
[CrossRef]

D. C. Su, M. H. Chiu, and C. D. Chen, "A heterodyne interferometer using an electro-optic modulator for measuring small displacements," J. Opt. 27, 19-23 (1996).
[CrossRef]

Cote, G. L.

R. J. McNichols, B. D. Cameron, and G. L. Cote, "Development of a non-invasive polarimetric glucose sensor," IEEE-LEOS Newsletter 12, 30-31 (1998).

Hsu, P. F.

Y. L. Lo, C. H. Lai, J. F. Lin, and P. F. Hsu, "Simultaneous absolute measurements of principle angle and phase retardation with a new common-path heterodyne interferometer," Appl. Opt. 43, 2013-2022 (2004).
[CrossRef] [PubMed]

Lai, C. H.

Y. L. Lo, C. H. Lai, J. F. Lin, and P. F. Hsu, "Simultaneous absolute measurements of principle angle and phase retardation with a new common-path heterodyne interferometer," Appl. Opt. 43, 2013-2022 (2004).
[CrossRef] [PubMed]

Lakhtakia, A.

A. Lakhtakia, Selected Papers on Natural Optical Activity (SPIE, Bellingham,1990).

Lee, J. Y.

J. Y. Lee and D. C. Su, "Improved common-path optical heterodyne interferometer for measuring small optical rotation angle of chiral medium," Opt. Commun. 256, 337-341 (2005).
[CrossRef]

M. H. Chiu, J. Y. Lee, and D. C. Su, "Complex reflective-index measurement based on Fresnel's equations and the uses of heterodyne interferometry," Appl. Opt. 38, 4047-4052 (1999).
[CrossRef]

Lee, S. Y.

Y. L. Lo, S. Y. Lee, and J. F. Lin, "The new circular polariscope and the Senarmont setup with electro-optic modulator for measuring the optical linear birefringent media properties," Opt. Commun. 237, 267-273 (2004).
[CrossRef]

Lin, J. F.

Y. L. Lo, S. Y. Lee, and J. F. Lin, "The new circular polariscope and the Senarmont setup with electro-optic modulator for measuring the optical linear birefringent media properties," Opt. Commun. 237, 267-273 (2004).
[CrossRef]

Y. L. Lo, C. H. Lai, J. F. Lin, and P. F. Hsu, "Simultaneous absolute measurements of principle angle and phase retardation with a new common-path heterodyne interferometer," Appl. Opt. 43, 2013-2022 (2004).
[CrossRef] [PubMed]

Lin, Y.

Y. Lin, Z. Zhou, and R. Wang, "Optical heterodyne measurement of the phase retardation of a quarter-wave plate," Opt. Lett. 13, 559-555 (1988).

Lo, Y. L.

Y. L. Lo, S. Y. Lee, and J. F. Lin, "The new circular polariscope and the Senarmont setup with electro-optic modulator for measuring the optical linear birefringent media properties," Opt. Commun. 237, 267-273 (2004).
[CrossRef]

Y. L. Lo, C. H. Lai, J. F. Lin, and P. F. Hsu, "Simultaneous absolute measurements of principle angle and phase retardation with a new common-path heterodyne interferometer," Appl. Opt. 43, 2013-2022 (2004).
[CrossRef] [PubMed]

McNichols, R. J.

R. J. McNichols, B. D. Cameron, and G. L. Cote, "Development of a non-invasive polarimetric glucose sensor," IEEE-LEOS Newsletter 12, 30-31 (1998).

Shyu, L. H.

L. H. Shyu, C. L. Chen, and D. C. Su, "Method for measuring the retardation of a wave plate," Appl. Opt. 32, 4228-4230 (1993).
[CrossRef] [PubMed]

Su, D. C.

J. Y. Lee and D. C. Su, "Improved common-path optical heterodyne interferometer for measuring small optical rotation angle of chiral medium," Opt. Commun. 256, 337-341 (2005).
[CrossRef]

M. H. Chiu, J. Y. Lee, and D. C. Su, "Complex reflective-index measurement based on Fresnel's equations and the uses of heterodyne interferometry," Appl. Opt. 38, 4047-4052 (1999).
[CrossRef]

D. C. Su, M. H. Chiu, and C. D. Chen, "A heterodyne interferometer using an electro-optic modulator for measuring small displacements," J. Opt. 27, 19-23 (1996).
[CrossRef]

L. H. Shyu, C. L. Chen, and D. C. Su, "Method for measuring the retardation of a wave plate," Appl. Opt. 32, 4228-4230 (1993).
[CrossRef] [PubMed]

Wang, R.

Y. Lin, Z. Zhou, and R. Wang, "Optical heterodyne measurement of the phase retardation of a quarter-wave plate," Opt. Lett. 13, 559-555 (1988).

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 5.

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 5.

Zhou, Z.

Y. Lin, Z. Zhou, and R. Wang, "Optical heterodyne measurement of the phase retardation of a quarter-wave plate," Opt. Lett. 13, 559-555 (1988).

Appl. Opt. (3)

L. H. Shyu, C. L. Chen, and D. C. Su, "Method for measuring the retardation of a wave plate," Appl. Opt. 32, 4228-4230 (1993).
[CrossRef] [PubMed]

Y. L. Lo, C. H. Lai, J. F. Lin, and P. F. Hsu, "Simultaneous absolute measurements of principle angle and phase retardation with a new common-path heterodyne interferometer," Appl. Opt. 43, 2013-2022 (2004).
[CrossRef] [PubMed]

M. H. Chiu, J. Y. Lee, and D. C. Su, "Complex reflective-index measurement based on Fresnel's equations and the uses of heterodyne interferometry," Appl. Opt. 38, 4047-4052 (1999).
[CrossRef]

IEEE-LEOS Newsletter (1)

R. J. McNichols, B. D. Cameron, and G. L. Cote, "Development of a non-invasive polarimetric glucose sensor," IEEE-LEOS Newsletter 12, 30-31 (1998).

J. Opt. (1)

D. C. Su, M. H. Chiu, and C. D. Chen, "A heterodyne interferometer using an electro-optic modulator for measuring small displacements," J. Opt. 27, 19-23 (1996).
[CrossRef]

Opt. Commun. (1)

Y. L. Lo, S. Y. Lee, and J. F. Lin, "The new circular polariscope and the Senarmont setup with electro-optic modulator for measuring the optical linear birefringent media properties," Opt. Commun. 237, 267-273 (2004).
[CrossRef]

Opt. Lett. (1)

Y. Lin, Z. Zhou, and R. Wang, "Optical heterodyne measurement of the phase retardation of a quarter-wave plate," Opt. Lett. 13, 559-555 (1988).

Opt. Commun. (1)

J. Y. Lee and D. C. Su, "Improved common-path optical heterodyne interferometer for measuring small optical rotation angle of chiral medium," Opt. Commun. 256, 337-341 (2005).
[CrossRef]

Other (3)

R. C. Weast, ed., Handbook of Chemistry and Physics (CRC Press, Boca Raton, Fla., 1981).

A. Lakhtakia, Selected Papers on Natural Optical Activity (SPIE, Bellingham,1990).

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 5.

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Figures (10)

Fig. 1
Fig. 1

(Color online) Basic schematic diagram of the new type of EOHI.

Fig. 2
Fig. 2

(Color online) Numerical simulation of (a) the original driving triangle waveform, and PD intensity waveforms corresponding to (b) δ = 0 and (c) δ = π / 6 .

Fig. 3
Fig. 3

(Color online) Numerical simulation results of the second-harmonic component amplitude versus the δ value.

Fig. 4
Fig. 4

(Color online) Experimental PD signal waveforms when VWP was set to have phase retardation values of (a) 0 and (b) π / 6 .

Fig. 5
Fig. 5

(Color online) Experimental result of SH amplitude reading versus retardation.

Fig. 6
Fig. 6

(Color online) EOHI optical setup adapted to perform optical rotation angle measurement.

Fig. 7
Fig. 7

(Color online) Numerical calculations of SH amplitude versus rotation angle β for three different δ values of 178°, 175°, 160°, and 145°.

Fig. 8
Fig. 8

(Color online) Linearity comparison between pure phase detection method and the new SH detection method over an extended rotation angle range.

Fig. 9
Fig. 9

(Color online) Comparison between the new SH detection curve and a linear line for a further extended rotation angle range.

Fig. 10
Fig. 10

(Color online) Measured SH amplitudes for the seven glucose solution samples.

Equations (7)

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I = | E x | 2 + | E y | 2 = 1 2 [ 1 + cos ( π V d V π + δ P ) ]
β = [ α s ] C L
[ E x E y ] = 1 2 [ 1 1 1 1 ] [ e i δ R / 2 0 0 e i δ R / 2 ] [ cos β sin β sin β cos β ] × 1 2 [ 1 1 1 1 ] [ 1 0 0 i ] [ e i ( V d / V π ) / 2 0 0 e i ( V d / V π ) / 2 ] 1 2 [ 1 1 ]
I = | E x | 2 + | E y | 2 = 1 2 [ 1 A cos ( π V d V π + ϕ ) ]
A = sin 2 δ R + ( sin 2 β cos δ R ) 2
ϕ = tan 1 ( tan δ R sin 2 β ) 90 ° .
Δ β tan δ R 2 Δ ϕ .

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