Abstract

A new calibration method for a photoelastic modulator is proposed. The calibration includes a coarse calibration and a fine calibration. In the coarse calibration, the peak retardation of the photoelastic modulator is set near 1.841rad. In the fine calibration, the value of the zeroth Bessel function is obtained. The zeroth Bessel function is approximated as a linear equation to directly calculate the peak retardation. In experiments, the usefulness of the calibration method is verified and the calibration error is less than 0.014rad. The calibration is immune to the intensity fluctuation of the light source and independent of the circuit parameters. The method specially suits the calibration of a photoelastic modulator with a peak retardation of less than a half-wavelength.

© 2007 Optical Society of America

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References

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    [CrossRef]
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2005 (1)

2004 (1)

M. W. Wang, F. H. Tsai, and Y. F. Chao, "In-situ calibration technique for photoelastic modulator in ellipsometry," Thin Solid Films 455- 456, 78-83 (2004).
[CrossRef]

2001 (2)

2000 (1)

T. C. Oakberg, J. Trunk, and J. C. Sutherland, "Calibration of photoelastic modulators in the vacuum UV," in Polarization Analysis, Measurement, and Remote Sensing III, D. B. Chenault, M. J. Duggin, W. G. Egan, and D. H. Goldstein, eds., Proc. SPIE 4133, 101-112 (2000).
[CrossRef]

1998 (1)

H. L. Maynard, N. Layadi, and J. T. C. Lee, "Plasma etching of submicron devices: in situ monitoring and control by multi-wavelength ellipsometry," Thin Solid Films 313- 314, 398-405 (1998).
[CrossRef]

1995 (2)

Y. Shindo, "Application of polarized modulation technique in polymer science," Opt. Eng. 34, 3369-3384 (1995).
[CrossRef]

J. C. Cheng, L. A. Nafie, S. D. Allen, and A. I. Braunstein, "Photoelastic modulator for the 0.55-13 μm range," Appl. Opt. 15, 1960-1965 (1995).
[CrossRef]

1993 (1)

R. A. Cline, W. B. Westerveld, and J. S. Risley, "A new method for measuring the retardation of a photoelastic modulator using single photon counting techniques," Rev. Sci. Instrum. 64, 1169-1174 (1993).
[CrossRef]

1990 (1)

1983 (1)

Allen, S. D.

Badoz, J.

Braunstein, A. I.

Canit, J. C.

Chao, Y. F.

M. W. Wang, F. H. Tsai, and Y. F. Chao, "In-situ calibration technique for photoelastic modulator in ellipsometry," Thin Solid Films 455- 456, 78-83 (2004).
[CrossRef]

Cheng, J. C.

Cline, R. A.

R. A. Cline, W. B. Westerveld, and J. S. Risley, "A new method for measuring the retardation of a photoelastic modulator using single photon counting techniques," Rev. Sci. Instrum. 64, 1169-1174 (1993).
[CrossRef]

Dogariu, A.

Dubois, A.

Hawkes, N. C.

Kuldkepp, M.

Layadi, N.

H. L. Maynard, N. Layadi, and J. T. C. Lee, "Plasma etching of submicron devices: in situ monitoring and control by multi-wavelength ellipsometry," Thin Solid Films 313- 314, 398-405 (1998).
[CrossRef]

Lee, J. T. C.

H. L. Maynard, N. Layadi, and J. T. C. Lee, "Plasma etching of submicron devices: in situ monitoring and control by multi-wavelength ellipsometry," Thin Solid Films 313- 314, 398-405 (1998).
[CrossRef]

Maynard, H. L.

H. L. Maynard, N. Layadi, and J. T. C. Lee, "Plasma etching of submicron devices: in situ monitoring and control by multi-wavelength ellipsometry," Thin Solid Films 313- 314, 398-405 (1998).
[CrossRef]

Mujat, M.

Nafie, L. A.

Oakberg, T. C.

T. C. Oakberg, J. Trunk, and J. C. Sutherland, "Calibration of photoelastic modulators in the vacuum UV," in Polarization Analysis, Measurement, and Remote Sensing III, D. B. Chenault, M. J. Duggin, W. G. Egan, and D. H. Goldstein, eds., Proc. SPIE 4133, 101-112 (2000).
[CrossRef]

Rachlew, E.

Risley, J. S.

R. A. Cline, W. B. Westerveld, and J. S. Risley, "A new method for measuring the retardation of a photoelastic modulator using single photon counting techniques," Rev. Sci. Instrum. 64, 1169-1174 (1993).
[CrossRef]

Schunke, B.

Shindo, Y.

Y. Shindo, "Application of polarized modulation technique in polymer science," Opt. Eng. 34, 3369-3384 (1995).
[CrossRef]

Silverman, M. P.

Sutherland, J. C.

T. C. Oakberg, J. Trunk, and J. C. Sutherland, "Calibration of photoelastic modulators in the vacuum UV," in Polarization Analysis, Measurement, and Remote Sensing III, D. B. Chenault, M. J. Duggin, W. G. Egan, and D. H. Goldstein, eds., Proc. SPIE 4133, 101-112 (2000).
[CrossRef]

Trunk, J.

T. C. Oakberg, J. Trunk, and J. C. Sutherland, "Calibration of photoelastic modulators in the vacuum UV," in Polarization Analysis, Measurement, and Remote Sensing III, D. B. Chenault, M. J. Duggin, W. G. Egan, and D. H. Goldstein, eds., Proc. SPIE 4133, 101-112 (2000).
[CrossRef]

Tsai, F. H.

M. W. Wang, F. H. Tsai, and Y. F. Chao, "In-situ calibration technique for photoelastic modulator in ellipsometry," Thin Solid Films 455- 456, 78-83 (2004).
[CrossRef]

Wang, M. W.

M. W. Wang, F. H. Tsai, and Y. F. Chao, "In-situ calibration technique for photoelastic modulator in ellipsometry," Thin Solid Films 455- 456, 78-83 (2004).
[CrossRef]

Westerveld, W. B.

R. A. Cline, W. B. Westerveld, and J. S. Risley, "A new method for measuring the retardation of a photoelastic modulator using single photon counting techniques," Rev. Sci. Instrum. 64, 1169-1174 (1993).
[CrossRef]

Appl. Opt. (4)

J. Opt. Soc. Am. A (2)

Opt. Eng. (1)

Y. Shindo, "Application of polarized modulation technique in polymer science," Opt. Eng. 34, 3369-3384 (1995).
[CrossRef]

Proc. SPIE (1)

T. C. Oakberg, J. Trunk, and J. C. Sutherland, "Calibration of photoelastic modulators in the vacuum UV," in Polarization Analysis, Measurement, and Remote Sensing III, D. B. Chenault, M. J. Duggin, W. G. Egan, and D. H. Goldstein, eds., Proc. SPIE 4133, 101-112 (2000).
[CrossRef]

Rev. Sci. Instrum. (1)

R. A. Cline, W. B. Westerveld, and J. S. Risley, "A new method for measuring the retardation of a photoelastic modulator using single photon counting techniques," Rev. Sci. Instrum. 64, 1169-1174 (1993).
[CrossRef]

Thin Solid Films (2)

H. L. Maynard, N. Layadi, and J. T. C. Lee, "Plasma etching of submicron devices: in situ monitoring and control by multi-wavelength ellipsometry," Thin Solid Films 313- 314, 398-405 (1998).
[CrossRef]

M. W. Wang, F. H. Tsai, and Y. F. Chao, "In-situ calibration technique for photoelastic modulator in ellipsometry," Thin Solid Films 455- 456, 78-83 (2004).
[CrossRef]

Other (1)

PEM-90 Photoelastic Modulator Systems User Manual (Hinds Instruments Inc., Hillsboro, Oreg., 1998).

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Figures (4)

Fig. 1
Fig. 1

Optical arrangement for the coarse calibration of the PEM.

Fig. 2
Fig. 2

Plots of Bessel functions versus the peak retardation.

Fig. 3
Fig. 3

Optical arrangements for the fine calibration of the PEM (a) before and (b) after the analyzer is rotated.

Fig. 4
Fig. 4

Peak retardation error caused by linear approximation of the zeroth Bessel function around 1.841 r a d .

Tables (2)

Tables Icon

Table 1 Results of the Coarse Calibration

Tables Icon

Table 2 Results of the Fine Calibrations

Equations (17)

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ϕ ( t ) = α 0 sin ( ω t ) ,
I C = I 0 [ 1 cos ( β + α 0 sin ω t ) ] / 2 ,
I = I 0 [ 1 cos β J 0 ( α 0 ) + 2 sin β J 1 ( α 0 ) sin ω t 2 cos β J 2 ( α 0 ) cos 2 ω t + ] / 2 ,
I 1 f = I 0 sin β J 1 ( α 0 ) .
J 0 ( α 0 ) = J 1 ( α 0 ) .
I F 1 = I 0 [ 1 J 0 ( α 0 max ) 2 J 2 ( α 0 max ) cos 2 ω t + ] / 2 ,
I F 2 = I 0 [ 1 + J 0 ( α 0 max ) + 2 J 2 ( α 0 max ) cos 2 ω t + ] / 2 ,
I d c 1 = I 0 [ 1 J 0 ( α 0 max ) ] / 2 ,
I 2 f 1 = I 0 J 2 ( α 0 max ) .
I d c 2 = I 0 [ 1 + J 0 ( α 0 max ) ] / 2 ,
I 2 f 2 = I 0 J 2 ( α 0 max ) .
R 1 = I d c 1 I 2 f 1 = 1 J 0 ( α 0 max ) 2 J 2 ( α 0 max ) ,
R 2 = I d c 2 I 2 f 2 = 1 + J 0 ( α 0 max ) 2 J 2 ( α 0 max ) .
J 0 ( α 0 max ) = R 2 R 1 R 2 + R 1 .
J 0 ( α 0 ) = 0.5787 α 0 + 1.3816 .
α 0 max = [ 1.3816 J 0 ( α 0 max ) ] / 0.5787 .
α e r r o r = [ 1.3816 J 0 ( α 0 ) ] / 0.5787 α 0 .

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