Abstract

We propose a highly stable and single-shot wavefront sensor using vectorial shearing interferometry. We design it using a pair of cascaded Sagnac interferometers that allow spatial frequency multiplexing in the interferogram in order to detect the vector gradients simultaneously and independently. The scheme avoids wavelength dispersion in sheared copies as compared to the vectorial shearing interferometer schemes based on diffractive optical elements. Capability to tune the amount of shear merely through the axial displacement of the imaging sensor, and with the added advantage of adjustable resolution controlled by the spatial frequency introduced, the near common-path geometry opens up its applications in optical testing even in a vibration sensitive environment.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. D. R. Neal, J. Copland, and D. A. Neal, “Shack-Hartmann wavefront sensor precision and accuracy,” Proc. SPIE 4779, Advanced Characterization Techniques for Optical, Semiconductor, and Data Storage Components, (11 November 2002).
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    [Crossref]
  3. N. Gu, L. Huang, Z. Yang, and C. Rao, “A single-shot common-path phase-stepping radial shearing interferometer for wavefront measurements,” Opt. Express 19(5), 4703–4713 (2011).
    [Crossref]
  4. G. Paez, M. Strojnik, and G. G. Torales, “Vectorial shearing interferometer,” Appl. Opt. 39(28), 5172–5178 (2000).
    [Crossref]
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2019 (1)

2011 (1)

2005 (2)

2004 (1)

2002 (1)

2000 (2)

1999 (1)

1998 (1)

1996 (1)

1995 (1)

1993 (1)

1988 (1)

1982 (1)

Bilgeri, L. M.

Blanchard, P. M.

Brase, J. M.

Chanteloup, J. C.

Cohen, M.

Copland, J.

D. R. Neal, J. Copland, and D. A. Neal, “Shack-Hartmann wavefront sensor precision and accuracy,” Proc. SPIE 4779, Advanced Characterization Techniques for Optical, Semiconductor, and Data Storage Components, (11 November 2002).

Dainty, C.

Dong, J.

Dong, X.

Druon, F.

Dubra, A.

Elster, C.

Fisher, D. J.

Gavel, D. T.

Goodman, J.

J. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005).

Greenaway, A. H.

Gu, N.

Guerineau, N.

Huang, L.

Ichikawa, K.

Ina, H.

Jakobi, M.

Kobayashi, S.

Koch, A. W.

Lohmann, A.

Lu, M.

Maksimchuk, A.

Malacara, D.

Marroquin, J. L.

Mourou, G.

Nantel, M.

Neal, D. A.

D. R. Neal, J. Copland, and D. A. Neal, “Shack-Hartmann wavefront sensor precision and accuracy,” Proc. SPIE 4779, Advanced Characterization Techniques for Optical, Semiconductor, and Data Storage Components, (11 November 2002).

Neal, D. R.

D. R. Neal, J. Copland, and D. A. Neal, “Shack-Hartmann wavefront sensor precision and accuracy,” Proc. SPIE 4779, Advanced Characterization Techniques for Optical, Semiconductor, and Data Storage Components, (11 November 2002).

Paez, G.

Paterson, C.

Poller, F.

Poyneer, L. A.

Primot, J.

Rao, C.

Salazar-Bloise, F.

Servin, M.

Sogno, L.

Strojnik, M.

Takeda, M.

Torales, G. G.

Velghe, S.

Wang, S.

Wattellier, B.

Weingärtner, I.

Woods, S. C.

Yang, Z.

Appl. Opt. (8)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Opt. Express (1)

Opt. Lett. (2)

Other (2)

D. R. Neal, J. Copland, and D. A. Neal, “Shack-Hartmann wavefront sensor precision and accuracy,” Proc. SPIE 4779, Advanced Characterization Techniques for Optical, Semiconductor, and Data Storage Components, (11 November 2002).

J. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005).

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Figures (6)

Fig. 1.
Fig. 1. Conceptual diagram for common-path vectorial shearing wavefront sensor
Fig. 2.
Fig. 2. Generation of four copies of the wavefront using two Sagnac interferometer in kept in series.
Fig. 3.
Fig. 3. Wavefront Sensing using vectorial shearing interferometer.
Fig. 4.
Fig. 4. (a) Vectorial sheared fringe pattern, (b) Fourier transform of fringe pattern.
Fig. 5.
Fig. 5. (a) Gradient along X-direction, (b) Gradient along Y-direction (c) Reconstructed Wavefront.
Fig. 6.
Fig. 6. (a), (b), (c), (d), (e) and (f) shows the reconstructed wavefront at different positions of collimating lens along z-direction with step size of 0.5 mm. Red and green colored dashed lines show experimental results and blue colored line shows simulation results. Figure (g), (h), (i), (j) and (l) shows the wavefront deviations when collimating lens moves in forward direction. Figure (m), (n), (o), (p) and (q) shows the wavefront deviations when collimating lens moves in backward direction.

Tables (1)

Tables Icon

Table 1. Shows PV and RMS values of calculated wavefront at different position of collimating lens L.

Equations (9)

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u A ( x , y ) = F ( f 1 ) 1 { F ( f 1 ) [ u o ( x , y ) ] × e x p ( i 2 π z 1 λ 1 x ^ 2 f 1 2 y ^ 2 f 1 2 ) }
U F ( x ^ λ f 1 , y ^ λ f 1 ) = F ( f 1 ) [ u O ( x , y ) ] × e x p ( i 2 π z 1 λ 1 x ^ 2 f 1 2 y ^ 2 f 1 2 )
U F ( x ^ x ^ s , n λ f 1 , y ^ y ^ s , n λ f 1 ) = U O ( x ^ x ^ s , n λ f 1 , y ^ y ^ s , n λ f 1 ) × e x p ( i 2 π z 1 λ 1 ( x ^ x ^ s , n ) 2 f 1 2 ( y ^ y ^ s , n ) 2 f 1 2 )
u B , n ( x , y ) = F ( f 2 ) { U F ( x ^ x ^ s , n λ f 1 , y ^ y ^ s , n λ f 1 ) }
u I , n ( x , y ) = F ( f 2 ) 1 { F ( f 2 ) [ u B , n ( x , y ) ] × exp ( i 2 π z 2 λ 1 x ^ 2 f 2 2 y ^ 2 f 2 2 ) }
u I , n ( x , y ) = F ( f 2 ) 1 [ F ( f 2 ) [ F ( f 2 ) { U F ( x ^ x ^ s , n λ f 1 , y ^ y ^ s , n λ f 1 ) } ] × exp ( i 2 π z 2 λ 1 x ^ 2 f 2 2 y ^ 2 f 2 2 ) ]
u I , n ( x , y ) = F ( f 2 ) 1 [ U O ( ( x ^ x ^ s , n ) λ f 1 , ( y ^ y ^ s , n ) λ f 1 ) × exp ( i 2 π z 1 λ 1 ( x ^ x ^ s , n ) 2 f 1 2 ( y ^ y ^ s , n ) 2 f 1 2 ) × exp ( i 2 π z 2 λ 1 x ^ 2 f 2 2 y ^ 2 f 2 2 ) ]
u I , n ( x , y ) = e x p ( i 2 π z 2 λ ( 1 f 1 2 f 2 2 + x ^ s , n 2 + y ^ s , n 2 2 f 2 2 ) ) e x p ( i 2 π λ f 2 ( x x ^ s , n + y y ^ s , n ) ) × u O ( 1 m ( x x ^ s , n z 2 f 2 ) , 1 m ( y y ^ s , n z 2 f 2 ) )
I I ( x , y ) = | u I , 1 ( x , y ) + u I , 2 ( x , y ) + u I , 3 ( x , y ) | 2