Abstract

A nondestructive measurement system based on a position sensing detector (PSD) and a laser interferometer for determining the thickness and refractive indices of birefringent optical wave plates has been developed. Unlike previous methods presented in the literature, the proposed metrology system allows the refractive index and thickness properties of the optical plate to be measured simultaneously. The experimental results obtained for the e-light and o-light refractive indices of a commercially available birefringent optical wave plate with refractive indices of no=1.542972 and ne=1.552033 are found to be accurate to within 0.004132 and 0.000229, respectively. Furthermore, the experimentally derived value of the wave plate thickness deviates by no more than 0.9μm from the analytically derived value of 453.95μm. Overall, the experimental results confirm that the proposed metrology system provides a simple yet highly accurate means of obtaining simultaneous measurements of the refractive indices and thickness of birefringent optical wave plates.

© 2008 Optical Society of America

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References

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  1. H. B. Serreze and R. B. Goldner, “A phase-sensitive technique for measuring small birefringence changes,” Rev. Sci. Instrum. , 45, 1613-1614 (1974).
    [CrossRef]
  2. Y. Shindo and H. Hanabusa, “Highly sensitive instrument for measuring optical birefringence,” Polym. Commun. 24, 240-244(1983).
  3. Y. C. Huang, C. Chou, and M. Chang, “Direct measurement of refractive indices (ne,no) of a linear birefringent retardation plate,” Opt. Commun. 133, 11-16 (1997).
    [CrossRef]
  4. S. Nemoto, “Measurement of the refractive index of liquid using laser beam displacement,” Appl. Opt. 31, 6690-6694(1992).
    [CrossRef] [PubMed]
  5. F. Docchio, S. Corini, M. Perini, and R. S. Kasana, “A simple and reliable system for measuring the refractive index of liquids using a position-sensitive detector,” IEEE Trans. Instrum. Meas. 44,68-70 (1995).
    [CrossRef]
  6. M.-J. Jang and C.-F. Lu, “A measurement system for determining the thickness of an optical wave plate,” Optic Commun. 253, 2-9 (2005).
    [CrossRef]
  7. http://www.casix.com.
  8. http://www.crystaltechno.com/Materials/Crystal_Quartz.htm.

2005 (1)

M.-J. Jang and C.-F. Lu, “A measurement system for determining the thickness of an optical wave plate,” Optic Commun. 253, 2-9 (2005).
[CrossRef]

1997 (1)

Y. C. Huang, C. Chou, and M. Chang, “Direct measurement of refractive indices (ne,no) of a linear birefringent retardation plate,” Opt. Commun. 133, 11-16 (1997).
[CrossRef]

1995 (1)

F. Docchio, S. Corini, M. Perini, and R. S. Kasana, “A simple and reliable system for measuring the refractive index of liquids using a position-sensitive detector,” IEEE Trans. Instrum. Meas. 44,68-70 (1995).
[CrossRef]

1992 (1)

1983 (1)

Y. Shindo and H. Hanabusa, “Highly sensitive instrument for measuring optical birefringence,” Polym. Commun. 24, 240-244(1983).

1974 (1)

H. B. Serreze and R. B. Goldner, “A phase-sensitive technique for measuring small birefringence changes,” Rev. Sci. Instrum. , 45, 1613-1614 (1974).
[CrossRef]

Chang, M.

Y. C. Huang, C. Chou, and M. Chang, “Direct measurement of refractive indices (ne,no) of a linear birefringent retardation plate,” Opt. Commun. 133, 11-16 (1997).
[CrossRef]

Chou, C.

Y. C. Huang, C. Chou, and M. Chang, “Direct measurement of refractive indices (ne,no) of a linear birefringent retardation plate,” Opt. Commun. 133, 11-16 (1997).
[CrossRef]

Corini, S.

F. Docchio, S. Corini, M. Perini, and R. S. Kasana, “A simple and reliable system for measuring the refractive index of liquids using a position-sensitive detector,” IEEE Trans. Instrum. Meas. 44,68-70 (1995).
[CrossRef]

Docchio, F.

F. Docchio, S. Corini, M. Perini, and R. S. Kasana, “A simple and reliable system for measuring the refractive index of liquids using a position-sensitive detector,” IEEE Trans. Instrum. Meas. 44,68-70 (1995).
[CrossRef]

Goldner, R. B.

H. B. Serreze and R. B. Goldner, “A phase-sensitive technique for measuring small birefringence changes,” Rev. Sci. Instrum. , 45, 1613-1614 (1974).
[CrossRef]

Hanabusa, H.

Y. Shindo and H. Hanabusa, “Highly sensitive instrument for measuring optical birefringence,” Polym. Commun. 24, 240-244(1983).

Huang, Y. C.

Y. C. Huang, C. Chou, and M. Chang, “Direct measurement of refractive indices (ne,no) of a linear birefringent retardation plate,” Opt. Commun. 133, 11-16 (1997).
[CrossRef]

Jang, M.-J.

M.-J. Jang and C.-F. Lu, “A measurement system for determining the thickness of an optical wave plate,” Optic Commun. 253, 2-9 (2005).
[CrossRef]

Kasana, R. S.

F. Docchio, S. Corini, M. Perini, and R. S. Kasana, “A simple and reliable system for measuring the refractive index of liquids using a position-sensitive detector,” IEEE Trans. Instrum. Meas. 44,68-70 (1995).
[CrossRef]

Lu, C.-F.

M.-J. Jang and C.-F. Lu, “A measurement system for determining the thickness of an optical wave plate,” Optic Commun. 253, 2-9 (2005).
[CrossRef]

Nemoto, S.

Perini, M.

F. Docchio, S. Corini, M. Perini, and R. S. Kasana, “A simple and reliable system for measuring the refractive index of liquids using a position-sensitive detector,” IEEE Trans. Instrum. Meas. 44,68-70 (1995).
[CrossRef]

Serreze, H. B.

H. B. Serreze and R. B. Goldner, “A phase-sensitive technique for measuring small birefringence changes,” Rev. Sci. Instrum. , 45, 1613-1614 (1974).
[CrossRef]

Shindo, Y.

Y. Shindo and H. Hanabusa, “Highly sensitive instrument for measuring optical birefringence,” Polym. Commun. 24, 240-244(1983).

Appl. Opt. (1)

IEEE Trans. Instrum. Meas. (1)

F. Docchio, S. Corini, M. Perini, and R. S. Kasana, “A simple and reliable system for measuring the refractive index of liquids using a position-sensitive detector,” IEEE Trans. Instrum. Meas. 44,68-70 (1995).
[CrossRef]

Opt. Commun. (1)

Y. C. Huang, C. Chou, and M. Chang, “Direct measurement of refractive indices (ne,no) of a linear birefringent retardation plate,” Opt. Commun. 133, 11-16 (1997).
[CrossRef]

Optic Commun. (1)

M.-J. Jang and C.-F. Lu, “A measurement system for determining the thickness of an optical wave plate,” Optic Commun. 253, 2-9 (2005).
[CrossRef]

Polym. Commun. (1)

Y. Shindo and H. Hanabusa, “Highly sensitive instrument for measuring optical birefringence,” Polym. Commun. 24, 240-244(1983).

Rev. Sci. Instrum. (1)

H. B. Serreze and R. B. Goldner, “A phase-sensitive technique for measuring small birefringence changes,” Rev. Sci. Instrum. , 45, 1613-1614 (1974).
[CrossRef]

Other (2)

http://www.casix.com.

http://www.crystaltechno.com/Materials/Crystal_Quartz.htm.

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Figures (7)

Fig. 1
Fig. 1

Configuration of the PSD calibration system.

Fig. 2
Fig. 2

Schematic of proposed optical metrology system.

Fig. 3
Fig. 3

Relationship between optical refractive length difference and rotational angle.

Fig. 4
Fig. 4

Actual thickness of the sample wave plate.

Fig. 5
Fig. 5

PSD calibration test results.

Fig. 6
Fig. 6

Variation of refractive index with wave plate thickness for the e-light component of the laser beam.

Fig. 7
Fig. 7

Variation of refractive index with wave plate thickness for the o-light component of the laser beam.

Tables (2)

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Table 1 Experimental Errors in Refractive Index Measurements

Tables Icon

Table 2 Experimental Errors in Thickness Measurements

Equations (17)

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L = d 1 cos θ 1 × sin θ 2 ,
n 0 a sin θ = n 1 sin θ 1 ,
L = d 1 cos ( sin 1 ( n 0 a sin θ n 1 ) ) × sin ( θ sin 1 ( n 0 a sin θ n 1 ) ) .
L = 2 d f cos ( sin 1 ( n 0 a sin θ n f ) ) × sin [ θ sin 1 ( n 0 a sin θ n f ) ] + d w cos ( sin 1 ( n 0 a sin θ n 1 ) ) × sin [ θ sin 1 ( n 0 a sin θ n 1 ) ] .
EL = [ d 1 cos θ 1 d 1 ] CRYSTAL [ d 1 cos θ 2 cos θ 1 d 1 ] AIR ,
EL = d 1 [ 1 ( 1 α ) 0.5 1 ] CRYSTAL d 1 [ cos β ( 1 α ) 0.5 1 ] AIR ,
α = ( n 0 a sin θ n 1 ) 2 ,
β = θ sin 1 ( n 0 a sin θ n 1 ) .
EL = n 1 d 1 [ 1 ( 1 α ) 0.5 1 ] n 0 a d 1 [ cos β ( 1 α ) 0.5 1 ] .
EL = 0.5 × [ n 1 d ( 1 ( 1 α ) 0.5 1 ) n 0 a d ( cos β ( 1 α ) 0.5 1 ) ] .
EL = d w { [ n 1 ( 1 ( 1 α ) 0.5 1 ) n 0 a ( cos β ( 1 α ) 0.5 1 ) ] } + 2 d f { [ n f ( 1 ( 1 α 1 ) 0.5 1 ) n 0 a ( cos β ( 1 α 1 ) 1 ) ] } ,
S = k · V ,
δ = ( 2 p 2 + 1 ) π ,
δ = 2 π ( Δ n d w / λ ) ,
d W = δ λ 2 π Δ n ,
d f = ( 2 p 1 + 1 ) · λ 4 · n f ,
d total = d w + 2 d f = 453.95 μm + 2 × 5.454 μm = 464.858 μm .

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