Abstract

We develop a heterodyne polariscope for measuring the two-dimensional principal axis and phase retardation in a linear birefringence material using novel three-frame and two-frame integrating-bucket methods and a CCD. By using a complex programmable logic device to provide an external trigger to the CCD, integrating buckets with multiple frames are achieved. The advantages of the proposed three-frame and two-frame integrating-bucket methods include a simpler signal processing algorithm based on fewer frames and the elimination of flyback error caused by a sawtooth modulation signal at higher frequencies.

© 2006 Optical Society of America

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  1. F. L. Clerc, L. Collot, and M. Gross, "Numerical heterodyne holography with two-dimensional photodetector arrays," Opt. Lett. 25, 716-718 (2000).
    [CrossRef]
  2. M. Akiba, K. P. Chan, and N. Tanno, "Real-time, micrometer depth resolved imaging by low-coherence reflectometry and a two-dimensional heterodyne detection technique," Jpn. J. Appl. Phys. Part 2 39, L1194-L1196 (2000).
    [CrossRef]
  3. T. Suzuki, T. Maki, X. Zhao, and O. Sasaki, "Disturbance-free high-speed sinusoidal phase-modulating laser diode interferometer," Appl. Opt. 41, 1949-1953 (2002).
    [CrossRef] [PubMed]
  4. O. Sasaki, H. Okazaki, and M. Sakai, "Sinusoidal phase modulating interferometer using the integrating-bucket method," Appl. Opt. 26, 1089-1093 (1987).
    [CrossRef] [PubMed]
  5. T. Spirig, P. Seitx, O. Vietze, and F. Heitger, "The lock-in CCD two-dimensional synchronous detection of light," IEEE J. Quantum Electron. 31, 1705-1708 (1995).
    [CrossRef]
  6. A. Dubois, "Phase-map measurements by interferometry with sinusoidal phase modulation and four integrating buckets," J. Opt. Soc. Am. A 18, 1972-1979 (2001).
    [CrossRef]
  7. Y.-L. Lo, C.-H. Lai, J.-F. Lin, and P.-F. Hsu, "Simultaneous absolute measurements of principal angle and phase retardation with a new common-path heterodyne interferometer," Appl. Opt. 43, 2013-2022 (2004).
    [CrossRef] [PubMed]
  8. T. Suzuki, T. Yazawa, and O. Sasaki, "Two-wavelength laser diode interferometer with time-sharing sinusoidal phase modulation," Appl. Opt. 41, 1972-1976 (2002).
    [CrossRef] [PubMed]
  9. T. Suzuki, O. Sasaki, J. Kaneda, and T. Maruyama, "Real-time two-dimensional surface profile measurement in sinusoidal phase modulating laser diode interferometer," Opt. Eng. 33, 2754-2759 (1994).
    [CrossRef]
  10. C. Chou, J.-C. Shyu, Y. C. Huang, and C. K. Yuan, "Common-path optical heterodyne profilometer: a configuration," Appl. Opt. 37, 4137-4142 (1998).
    [CrossRef]
  11. M. V. Aguanno, F. Lakestani, M. P. Whelan, and M. J. Connelly, "Single-pixel carrier-based approach for full-field laser interferometry using a CMOS-DSP camera," in Detectors and Associated Signal Processing, J.-P. Chatard and P. N. Dennis, eds., Proc. SPIE , 5251, 304-312 (2004).
    [CrossRef]
  12. P. Hariharan, B. F. Orbel, and T. Eiju, "Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm," Appl. Opt. 26, 2504-2505 (1987).
    [CrossRef] [PubMed]
  13. Y. L. Lo, S. Y. Lee, and J. F. Lin, "The new circular polariscope and the Senarmont setup with electro-optic modulation for measuring the optical linear birefringent media properties," Opt. Commun. 237, 267-273 (2004).
    [CrossRef]
  14. K. D. Stumpf, "Real-time interferometer," Opt. Eng. 18, 648-653 (1979).
  15. I. L. Lee, "Design and construction of a full-field three-dimensional transient strain metrology system," Master's thesis (Institute of Applied Mechanics, National Taiwan University, 2004).
  16. C. P. Brophy, "Effect of intensity error correlation on the computed phase of phase-shifting interferometry," J. Opt. Soc. Am. A. 7, 537-541 (1990).
    [CrossRef]
  17. K. B. Rochford, A. H. Rose, and C. M. Wang, "NIST study investigates retardance uncertainty," Laser Focus World 33(5), 223-227 (1997).
  18. Y. L. Lo and T. C. Yu, "A polarimetric glucose sensor using a liquid-crystal polarization modulator driven by a sinusoidal signal," Opt. Commun. 259, 40-48 (2006).
    [CrossRef]

2006 (1)

Y. L. Lo and T. C. Yu, "A polarimetric glucose sensor using a liquid-crystal polarization modulator driven by a sinusoidal signal," Opt. Commun. 259, 40-48 (2006).
[CrossRef]

2004 (3)

M. V. Aguanno, F. Lakestani, M. P. Whelan, and M. J. Connelly, "Single-pixel carrier-based approach for full-field laser interferometry using a CMOS-DSP camera," in Detectors and Associated Signal Processing, J.-P. Chatard and P. N. Dennis, eds., Proc. SPIE , 5251, 304-312 (2004).
[CrossRef]

Y. L. Lo, S. Y. Lee, and J. F. Lin, "The new circular polariscope and the Senarmont setup with electro-optic modulation 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 principal angle and phase retardation with a new common-path heterodyne interferometer," Appl. Opt. 43, 2013-2022 (2004).
[CrossRef] [PubMed]

2002 (2)

2001 (1)

2000 (2)

M. Akiba, K. P. Chan, and N. Tanno, "Real-time, micrometer depth resolved imaging by low-coherence reflectometry and a two-dimensional heterodyne detection technique," Jpn. J. Appl. Phys. Part 2 39, L1194-L1196 (2000).
[CrossRef]

F. L. Clerc, L. Collot, and M. Gross, "Numerical heterodyne holography with two-dimensional photodetector arrays," Opt. Lett. 25, 716-718 (2000).
[CrossRef]

1998 (1)

1997 (1)

K. B. Rochford, A. H. Rose, and C. M. Wang, "NIST study investigates retardance uncertainty," Laser Focus World 33(5), 223-227 (1997).

1995 (1)

T. Spirig, P. Seitx, O. Vietze, and F. Heitger, "The lock-in CCD two-dimensional synchronous detection of light," IEEE J. Quantum Electron. 31, 1705-1708 (1995).
[CrossRef]

1994 (1)

T. Suzuki, O. Sasaki, J. Kaneda, and T. Maruyama, "Real-time two-dimensional surface profile measurement in sinusoidal phase modulating laser diode interferometer," Opt. Eng. 33, 2754-2759 (1994).
[CrossRef]

1990 (1)

C. P. Brophy, "Effect of intensity error correlation on the computed phase of phase-shifting interferometry," J. Opt. Soc. Am. A. 7, 537-541 (1990).
[CrossRef]

1987 (2)

1979 (1)

K. D. Stumpf, "Real-time interferometer," Opt. Eng. 18, 648-653 (1979).

Aguanno, M. V.

M. V. Aguanno, F. Lakestani, M. P. Whelan, and M. J. Connelly, "Single-pixel carrier-based approach for full-field laser interferometry using a CMOS-DSP camera," in Detectors and Associated Signal Processing, J.-P. Chatard and P. N. Dennis, eds., Proc. SPIE , 5251, 304-312 (2004).
[CrossRef]

Akiba, M.

M. Akiba, K. P. Chan, and N. Tanno, "Real-time, micrometer depth resolved imaging by low-coherence reflectometry and a two-dimensional heterodyne detection technique," Jpn. J. Appl. Phys. Part 2 39, L1194-L1196 (2000).
[CrossRef]

Brophy, C. P.

C. P. Brophy, "Effect of intensity error correlation on the computed phase of phase-shifting interferometry," J. Opt. Soc. Am. A. 7, 537-541 (1990).
[CrossRef]

Chan, K. P.

M. Akiba, K. P. Chan, and N. Tanno, "Real-time, micrometer depth resolved imaging by low-coherence reflectometry and a two-dimensional heterodyne detection technique," Jpn. J. Appl. Phys. Part 2 39, L1194-L1196 (2000).
[CrossRef]

Chou, C.

Clerc, F. L.

Collot, L.

Connelly, M. J.

M. V. Aguanno, F. Lakestani, M. P. Whelan, and M. J. Connelly, "Single-pixel carrier-based approach for full-field laser interferometry using a CMOS-DSP camera," in Detectors and Associated Signal Processing, J.-P. Chatard and P. N. Dennis, eds., Proc. SPIE , 5251, 304-312 (2004).
[CrossRef]

Dubois, A.

Eiju, T.

Gross, M.

Hariharan, P.

Heitger, F.

T. Spirig, P. Seitx, O. Vietze, and F. Heitger, "The lock-in CCD two-dimensional synchronous detection of light," IEEE J. Quantum Electron. 31, 1705-1708 (1995).
[CrossRef]

Hsu, P.-F.

Huang, Y. C.

Kaneda, J.

T. Suzuki, O. Sasaki, J. Kaneda, and T. Maruyama, "Real-time two-dimensional surface profile measurement in sinusoidal phase modulating laser diode interferometer," Opt. Eng. 33, 2754-2759 (1994).
[CrossRef]

Lai, C.-H.

Lakestani, F.

M. V. Aguanno, F. Lakestani, M. P. Whelan, and M. J. Connelly, "Single-pixel carrier-based approach for full-field laser interferometry using a CMOS-DSP camera," in Detectors and Associated Signal Processing, J.-P. Chatard and P. N. Dennis, eds., Proc. SPIE , 5251, 304-312 (2004).
[CrossRef]

Lee, I. L.

I. L. Lee, "Design and construction of a full-field three-dimensional transient strain metrology system," Master's thesis (Institute of Applied Mechanics, National Taiwan University, 2004).

Lee, S. Y.

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

Lin, J.-F.

Lo, Y. L.

Y. L. Lo and T. C. Yu, "A polarimetric glucose sensor using a liquid-crystal polarization modulator driven by a sinusoidal signal," Opt. Commun. 259, 40-48 (2006).
[CrossRef]

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

Lo, Y.-L.

Maki, T.

Maruyama, T.

T. Suzuki, O. Sasaki, J. Kaneda, and T. Maruyama, "Real-time two-dimensional surface profile measurement in sinusoidal phase modulating laser diode interferometer," Opt. Eng. 33, 2754-2759 (1994).
[CrossRef]

Okazaki, H.

Orbel, B. F.

Rochford, K. B.

K. B. Rochford, A. H. Rose, and C. M. Wang, "NIST study investigates retardance uncertainty," Laser Focus World 33(5), 223-227 (1997).

Rose, A. H.

K. B. Rochford, A. H. Rose, and C. M. Wang, "NIST study investigates retardance uncertainty," Laser Focus World 33(5), 223-227 (1997).

Sakai, M.

Sasaki, O.

Seitx, P.

T. Spirig, P. Seitx, O. Vietze, and F. Heitger, "The lock-in CCD two-dimensional synchronous detection of light," IEEE J. Quantum Electron. 31, 1705-1708 (1995).
[CrossRef]

Shyu, J.-C.

Spirig, T.

T. Spirig, P. Seitx, O. Vietze, and F. Heitger, "The lock-in CCD two-dimensional synchronous detection of light," IEEE J. Quantum Electron. 31, 1705-1708 (1995).
[CrossRef]

Stumpf, K. D.

K. D. Stumpf, "Real-time interferometer," Opt. Eng. 18, 648-653 (1979).

Suzuki, T.

Tanno, N.

M. Akiba, K. P. Chan, and N. Tanno, "Real-time, micrometer depth resolved imaging by low-coherence reflectometry and a two-dimensional heterodyne detection technique," Jpn. J. Appl. Phys. Part 2 39, L1194-L1196 (2000).
[CrossRef]

Vietze, O.

T. Spirig, P. Seitx, O. Vietze, and F. Heitger, "The lock-in CCD two-dimensional synchronous detection of light," IEEE J. Quantum Electron. 31, 1705-1708 (1995).
[CrossRef]

Wang, C. M.

K. B. Rochford, A. H. Rose, and C. M. Wang, "NIST study investigates retardance uncertainty," Laser Focus World 33(5), 223-227 (1997).

Whelan, M. P.

M. V. Aguanno, F. Lakestani, M. P. Whelan, and M. J. Connelly, "Single-pixel carrier-based approach for full-field laser interferometry using a CMOS-DSP camera," in Detectors and Associated Signal Processing, J.-P. Chatard and P. N. Dennis, eds., Proc. SPIE , 5251, 304-312 (2004).
[CrossRef]

Yazawa, T.

Yu, T. C.

Y. L. Lo and T. C. Yu, "A polarimetric glucose sensor using a liquid-crystal polarization modulator driven by a sinusoidal signal," Opt. Commun. 259, 40-48 (2006).
[CrossRef]

Yuan, C. K.

Zhao, X.

Appl. Opt. (6)

IEEE J. Quantum Electron. (1)

T. Spirig, P. Seitx, O. Vietze, and F. Heitger, "The lock-in CCD two-dimensional synchronous detection of light," IEEE J. Quantum Electron. 31, 1705-1708 (1995).
[CrossRef]

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

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

C. P. Brophy, "Effect of intensity error correlation on the computed phase of phase-shifting interferometry," J. Opt. Soc. Am. A. 7, 537-541 (1990).
[CrossRef]

Jpn. J. Appl. Phys. (1)

M. Akiba, K. P. Chan, and N. Tanno, "Real-time, micrometer depth resolved imaging by low-coherence reflectometry and a two-dimensional heterodyne detection technique," Jpn. J. Appl. Phys. Part 2 39, L1194-L1196 (2000).
[CrossRef]

Laser Focus World (1)

K. B. Rochford, A. H. Rose, and C. M. Wang, "NIST study investigates retardance uncertainty," Laser Focus World 33(5), 223-227 (1997).

Opt. Commun. (2)

Y. L. Lo and T. C. Yu, "A polarimetric glucose sensor using a liquid-crystal polarization modulator driven by a sinusoidal signal," Opt. Commun. 259, 40-48 (2006).
[CrossRef]

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

Opt. Eng. (2)

K. D. Stumpf, "Real-time interferometer," Opt. Eng. 18, 648-653 (1979).

T. Suzuki, O. Sasaki, J. Kaneda, and T. Maruyama, "Real-time two-dimensional surface profile measurement in sinusoidal phase modulating laser diode interferometer," Opt. Eng. 33, 2754-2759 (1994).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (1)

M. V. Aguanno, F. Lakestani, M. P. Whelan, and M. J. Connelly, "Single-pixel carrier-based approach for full-field laser interferometry using a CMOS-DSP camera," in Detectors and Associated Signal Processing, J.-P. Chatard and P. N. Dennis, eds., Proc. SPIE , 5251, 304-312 (2004).
[CrossRef]

Other (1)

I. L. Lee, "Design and construction of a full-field three-dimensional transient strain metrology system," Master's thesis (Institute of Applied Mechanics, National Taiwan University, 2004).

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Figures (12)

Fig. 1
Fig. 1

Full-field measurement of the principal axis of the birefringent material.

Fig. 2
Fig. 2

Full-field measurement of the phase retardation of the birefringent material.

Fig. 3
Fig. 3

(Color online) Schematic of the integrating-bucket method.

Fig. 4
Fig. 4

Electronic block diagram showing the interface between the CCD and the CPLD.

Fig. 5
Fig. 5

(Color online) Three-dimensional image contours of the principal axis at 50° obtained using the three-frame integrating-bucket method.

Fig. 6
Fig. 6

(Color online) Three-dimensional image contours of the phase retardation at 90° with the principal axis at 0° obtained using the three-frame integrating-bucket method.

Fig. 7
Fig. 7

(Color online) Experimental data for the principal axis at the same pixel of the CCD.

Fig. 8
Fig. 8

(Color online) Experimental data for the phase retardation at the same pixel of the CCD.

Fig. 9
Fig. 9

(Color online) Stability in extracting phase retardation at the same pixel using the three-frame integrating-bucket method and the four-frame integrating-bucket method.

Fig. 10
Fig. 10

(Color online) Three-dimensional image contours of the principal axis at 30° obtained using the two-frame integrating-bucket method.

Fig. 11
Fig. 11

(Color online) Modulated signal obtained by driving a 30   kHz sawtooth signal into the EO modulator.

Fig. 12
Fig. 12

(Color online) Modulated signal obtained by driving a 70   kHz sawtooth signal into the EO modulator.

Equations (14)

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I 1 I dc + R 1   sin ( ω t + Φ 1 ) ,
I 2 I dc + R 2   sin ( ω t + Φ 2 ) ,
α = π 4 Φ 1 2 ,
β = tan - 1 [ tan ( Φ 2 ) cos   2 α ] .
I ( x , y , t ) = I dc ( x , y ) + R ( x , y ) sin [ ω t + Φ ( x , y ) ] .
S 1 = 0 T / 4 I 1 ( x , y , t ) d t = T 4 I dc + R 1 ω  sin   θ 1 + R 1 ω  cos   θ 1 , S 2 = T / 4 2 T / 4 I 2 ( x , y , t ) d t = T 4 I dc + R 1 ω  cos   θ 1 R 1 ω  sin   θ 1 , S 3 = 2 T / 4 3 T / 4 I 3 ( x , y , t ) d t = T 4 I dc R 1 ω  sin   θ 1 R 1 ω  cos   θ 1 , S 4 = 3 T / 4 T I 4 ( x , y , t ) d t = T 4 I dc R 1 ω  cos   θ 1 + R 1 ω  sin   θ 1 .
S 1 S 3 + S 2 S 4 = 4 R ω  cos   Φ ,
S 1 S 3 ( S 2 S 4 ) = 4 R ω  sin   Φ ,
Φ = tan - 1 [ S 1 S 3 ( S 2 S 4 ) S 1 S 3 + S 2 S 4 ) ] .
S 1 S 2 = 2 R 1 ω  sin   Φ ,
S 2 S 3 = 2 R 1 ω  cos   Φ ,
Φ = tan - 1 ( S 1 S 2 S 2 S 3 ) .
S 0 = 0 T / 2 [ I dc ( x , y ) + R ( x , y ) sin ( ω t + π 2 ) ] d t = T 2 I dc .
Φ = tan - 1 ( S 1 S 2 S 1 + S 2 S 0 ) .

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