Abstract

We present a new technique for the simultaneous measurement of refractive index and wedge angle of optical windows using Fizeau interferometry and a cyclic path optical configuration (CPOC). Two laterally separated beams are obtained from an expanded collimated beam using an aperture containing two rectangular openings. The test wedge plate is placed in one of the two separated beams. Using CPOC, these two beams are made to overlap and interfere, producing interference fringes in the overlapping region. The beams reflected from the front and back surfaces of the test wedge plate interfere and produce Fizeau fringes. The refractive index is related to the spacing of the above two beam fringes. The wedge angle is determined from the evaluated values of the refractive index and Fizeau fringe spacing. The results obtained for a BK-7 optical window are presented.

© 2009 Optical Society of America

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References

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2007 (2)

A. Styk and K. Patorski, “Derivation of quasi-parallel glass plate parameters tested in a Fizeau interferometer,” Proc. SPIE 6616, 66161W (2007).
[CrossRef]

J. Heil, T. Bauer, S. Schmax, T. Sure, and J. Wesner, “Phase shifting Fizeau interferometry of front and back surfaces of optical flats,” Appl. Opt. 46, 5282-5292 (2007).
[CrossRef] [PubMed]

2006 (1)

B. Kimbrough, J. Millerd, J. Wyant, and J. Hayes, “Low-coherence vibration insensitive Fizeau interferometer,” Proc. SPIE 6292, 62920F (2006).

2004 (1)

2003 (1)

2002 (1)

D. Battacharyya, A. Ray, B. K. Dutta, and P. N. Gosh, “Direct measurement on transparent plates by using Fizeau interferometry,” Opt. Laser Technol. 34, 93-96 (2002).
[CrossRef]

2000 (1)

1999 (1)

Y. R. Wang, X. M. Qu, L. Z. Cai, B. M. Ma, and D. L. Sun, “Simultaneous determination of the refractive index and wedge angle of an optical wedge plate using a photorefractive holographic interferometer,” J. Mod. Opt. 46, 1369-1376 (1999).

1994 (1)

1988 (1)

Battacharyya, D.

D. Battacharyya, A. Ray, B. K. Dutta, and P. N. Gosh, “Direct measurement on transparent plates by using Fizeau interferometry,” Opt. Laser Technol. 34, 93-96 (2002).
[CrossRef]

Bauer, T.

Burke, J.

Cai, L. Z.

Y. R. Wang, X. M. Qu, L. Z. Cai, B. M. Ma, and D. L. Sun, “Simultaneous determination of the refractive index and wedge angle of an optical wedge plate using a photorefractive holographic interferometer,” J. Mod. Opt. 46, 1369-1376 (1999).

De Groot, P.

Dutta, B. K.

D. Battacharyya, A. Ray, B. K. Dutta, and P. N. Gosh, “Direct measurement on transparent plates by using Fizeau interferometry,” Opt. Laser Technol. 34, 93-96 (2002).
[CrossRef]

El-Ghazaly, I.

El-Kashef, H.

Fairman, P. S.

Gosh, P. N.

D. Battacharyya, A. Ray, B. K. Dutta, and P. N. Gosh, “Direct measurement on transparent plates by using Fizeau interferometry,” Opt. Laser Technol. 34, 93-96 (2002).
[CrossRef]

Hassan, G. E.

Hayes, J.

B. Kimbrough, J. Millerd, J. Wyant, and J. Hayes, “Low-coherence vibration insensitive Fizeau interferometer,” Proc. SPIE 6292, 62920F (2006).

Heil, J.

Hibino, K.

Kafri, O.

Keren, E.

Kerske, K. M.

Kimbrough, B.

B. Kimbrough, J. Millerd, J. Wyant, and J. Hayes, “Low-coherence vibration insensitive Fizeau interferometer,” Proc. SPIE 6292, 62920F (2006).

Ma, B. M.

Y. R. Wang, X. M. Qu, L. Z. Cai, B. M. Ma, and D. L. Sun, “Simultaneous determination of the refractive index and wedge angle of an optical wedge plate using a photorefractive holographic interferometer,” J. Mod. Opt. 46, 1369-1376 (1999).

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, 2007).
[CrossRef]

Millerd, J.

B. Kimbrough, J. Millerd, J. Wyant, and J. Hayes, “Low-coherence vibration insensitive Fizeau interferometer,” Proc. SPIE 6292, 62920F (2006).

Oreb, B. F.

Patorski, K.

A. Styk and K. Patorski, “Derivation of quasi-parallel glass plate parameters tested in a Fizeau interferometer,” Proc. SPIE 6616, 66161W (2007).
[CrossRef]

Qu, X. M.

Y. R. Wang, X. M. Qu, L. Z. Cai, B. M. Ma, and D. L. Sun, “Simultaneous determination of the refractive index and wedge angle of an optical wedge plate using a photorefractive holographic interferometer,” J. Mod. Opt. 46, 1369-1376 (1999).

Ray, A.

D. Battacharyya, A. Ray, B. K. Dutta, and P. N. Gosh, “Direct measurement on transparent plates by using Fizeau interferometry,” Opt. Laser Technol. 34, 93-96 (2002).
[CrossRef]

Schmax, S.

Styk, A.

A. Styk and K. Patorski, “Derivation of quasi-parallel glass plate parameters tested in a Fizeau interferometer,” Proc. SPIE 6616, 66161W (2007).
[CrossRef]

Sun, D. L.

Y. R. Wang, X. M. Qu, L. Z. Cai, B. M. Ma, and D. L. Sun, “Simultaneous determination of the refractive index and wedge angle of an optical wedge plate using a photorefractive holographic interferometer,” J. Mod. Opt. 46, 1369-1376 (1999).

Sure, T.

Wang, Y. R.

Y. R. Wang, X. M. Qu, L. Z. Cai, B. M. Ma, and D. L. Sun, “Simultaneous determination of the refractive index and wedge angle of an optical wedge plate using a photorefractive holographic interferometer,” J. Mod. Opt. 46, 1369-1376 (1999).

Wesner, J.

Wyant, J.

B. Kimbrough, J. Millerd, J. Wyant, and J. Hayes, “Low-coherence vibration insensitive Fizeau interferometer,” Proc. SPIE 6292, 62920F (2006).

Appl. Opt. (6)

J. Mod. Opt. (1)

Y. R. Wang, X. M. Qu, L. Z. Cai, B. M. Ma, and D. L. Sun, “Simultaneous determination of the refractive index and wedge angle of an optical wedge plate using a photorefractive holographic interferometer,” J. Mod. Opt. 46, 1369-1376 (1999).

Opt. Laser Technol. (1)

D. Battacharyya, A. Ray, B. K. Dutta, and P. N. Gosh, “Direct measurement on transparent plates by using Fizeau interferometry,” Opt. Laser Technol. 34, 93-96 (2002).
[CrossRef]

Proc. SPIE (2)

A. Styk and K. Patorski, “Derivation of quasi-parallel glass plate parameters tested in a Fizeau interferometer,” Proc. SPIE 6616, 66161W (2007).
[CrossRef]

B. Kimbrough, J. Millerd, J. Wyant, and J. Hayes, “Low-coherence vibration insensitive Fizeau interferometer,” Proc. SPIE 6292, 62920F (2006).

Other (1)

D. Malacara, Optical Shop Testing (Wiley, 2007).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of the experimental setup.

Fig. 2
Fig. 2

Illustration of the shear introduced in beam 1 and beam 2 as M 1 is translated: (a) zero shear condition, (b) shear introduced as M 1 is translated, and (c)  M 1 translated such that sheared beams 1 and 2 overlap.

Fig. 3
Fig. 3

Vector representation of the wedge directions of DW and WP.

Fig. 4
Fig. 4

Initially set CPOC fringes with DW.

Fig. 5
Fig. 5

Interference fringes formed by the overlapping beams, 1 and 2 , due to introduction of WP in the path of beam 1 with its wedge direction parallel to the wedge direction of DW.

Fig. 6
Fig. 6

Interference fringes formed by the overlapping beams, 1 and 2 , as WP is rotated by 180 ° .

Fig. 7
Fig. 7

Fizeau fringes formed due to the interference of front and back reflected beams from WP.

Fig. 8
Fig. 8

Interferograms obtained using a fused quartz wedge plate: (a) Fizeau fringes, (b) quartz plate wedge direction parallel to the wedge direction of DW, and (c) wedge direction opposite to the wedge direction of DW.

Equations (11)

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ω P = ( n 1 ) α ,
( n 1 ) α = λ d WP ,
2 n α = λ d F ,
n = ( d WP d WP 2 d F ) .
ω DW + ω P = λ d 1 ,
ω DW ω P = λ d 2 ,
n = [ 1 ( d 2 d 1 d 2 d 1 ) d F ] 1 .
d n = [ ( δ n δ d 1 ) 2 ( d d 1 ) 2 + ( δ n δ d 2 ) 2 ( d d 2 ) 2 + ( δ n δ d F ) 2 ( d d F ) 2 ] 1 / 2 ,
d α = [ ( δ α δ n ) 2 ( d n ) 2 + ( δ α δ d F ) 2 ( d d F ) 2 ] 1 / 2 ,
d n = n [ ( d F d 1 2 ) 2 ( d d 1 ) 2 + ( d F d 2 2 ) 2 ( d d 2 ) 2 + ( 1 d 1 1 d 2 ) 2 ( d d F ) 2 ] 1 / 2 ,
d α = α [ ( 1 n 2 ) ( d n ) 2 + ( 1 d F 2 ) ( d d F ) 2 ] 1 / 2 .

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