Abstract

A classical Mach–Zehnder two-beam interferometer was modernized using the Wollaston compensator, which allowed obtaining a stable set of specific optical markers—optical vortices. This new interferometer setup that generated optical vortices was used to measure small angle tilt. The theoretical basis of setups behavior has been described. The value of the described setup was confirmed by practical experiments.

© 2007 Optical Society of America

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References

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2007 (5)

2006 (5)

2005 (1)

E. Fra̧czek, W. Fra̧czek, and J. Mroczka, "Experimental method for topological charge determination of optical vortices in a regular net," Opt. Eng. 44, 25601 (2005).
[CrossRef]

2004 (2)

J. Masajada, A. Popiołek-Masajada, E. Fra̧czek, and W. Fra̧czek, "Vortex point localization problem in optical vortices interferometry," Opt. Commun. 234, 23-28 (2004).
[CrossRef]

J. Masajada, "Small-angle rotations measurement using optical vortex interferometer," Opt. Commun. 239, 373-381 (2004).
[CrossRef]

2001 (1)

J. Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21-26 (2001).
[CrossRef]

1999 (1)

J. Masajada, "Synthetics holograms for optical vortices generation--image evaluation," Optik 110, 554-558 (1999).

1998 (1)

1996 (1)

A. V. Mamaev, M. Saffman, and A. A. Zazulya, "Propagation of dark stripe beams in nonlinear media: snake instability and creation of optical vortices," Phys. Rev. Lett. 76, 2262-2265 (1996).
[CrossRef] [PubMed]

1995 (1)

T. Ackemann, E. Kriege, and W. Lange, "Phase singularities via nonlinear beam propagation in sodium vapor," Opt. Commun. 155, 339-346 (1995).
[CrossRef]

1994 (2)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, "Helical-wavefront laser beam produced with a spiral phaseplate," Opt. Commun. 112, 321-327 (1994).
[CrossRef]

I. Freund and N. Shvartsman, "Wave-field phase singularities: the sign principle," Phys. Rev. A 50, 5164-5172 (1994).
[CrossRef] [PubMed]

1992 (1)

S. N. Khonina, V. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, "The phase rotor filter," J. Mod. Opt. 39, 1147-1154 (1992).
[CrossRef]

1974 (1)

J. F. Nye and M. V. Berry, "Dislocation in wave trains," Proc. R. Soc. London Ser. A 336, 165-190 (1974).
[CrossRef]

Appl. Opt. (4)

J. Mod. Opt. (1)

S. N. Khonina, V. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, "The phase rotor filter," J. Mod. Opt. 39, 1147-1154 (1992).
[CrossRef]

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

Meas. Sci. Technol. (1)

A. Popiołek-Masajada, M. Borwińska, and E. Fra̧czek, "Testing a new method for small-angle rotation measurements with the optical vortex interferometer," Meas. Sci. Technol. 17, 653-658 (2006).
[CrossRef]

Opt. Commun. (5)

J. Masajada, "Small-angle rotations measurement using optical vortex interferometer," Opt. Commun. 239, 373-381 (2004).
[CrossRef]

J. Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21-26 (2001).
[CrossRef]

J. Masajada, A. Popiołek-Masajada, E. Fra̧czek, and W. Fra̧czek, "Vortex point localization problem in optical vortices interferometry," Opt. Commun. 234, 23-28 (2004).
[CrossRef]

T. Ackemann, E. Kriege, and W. Lange, "Phase singularities via nonlinear beam propagation in sodium vapor," Opt. Commun. 155, 339-346 (1995).
[CrossRef]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, "Helical-wavefront laser beam produced with a spiral phaseplate," Opt. Commun. 112, 321-327 (1994).
[CrossRef]

Opt. Eng. (2)

E. Fra̧czek, W. Fra̧czek, and J. Mroczka, "Experimental method for topological charge determination of optical vortices in a regular net," Opt. Eng. 44, 25601 (2005).
[CrossRef]

A. Popiołek-Masajada, M. Borwińska, and B. Dubik, "Reconstruction of a plane wave's tilt and orientation using an optical vortex interferometer," Opt. Eng. 46, 073604 (2007).
[CrossRef]

Opt. Express (4)

Optik (1)

J. Masajada, "Synthetics holograms for optical vortices generation--image evaluation," Optik 110, 554-558 (1999).

Phys. Rev. A (1)

I. Freund and N. Shvartsman, "Wave-field phase singularities: the sign principle," Phys. Rev. A 50, 5164-5172 (1994).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

A. V. Mamaev, M. Saffman, and A. A. Zazulya, "Propagation of dark stripe beams in nonlinear media: snake instability and creation of optical vortices," Phys. Rev. Lett. 76, 2262-2265 (1996).
[CrossRef] [PubMed]

Proc. R. Soc. London Ser. A (1)

J. F. Nye and M. V. Berry, "Dislocation in wave trains," Proc. R. Soc. London Ser. A 336, 165-190 (1974).
[CrossRef]

Other (3)

M. Vasnetsov and K. Staliunas, Optical Vortices (Nova Science, 1999).

L. Allen, M. J. Padgett, and M. Babiker, "The orbital angular momentum of light," in Progress in Optics, Vol. XXXIX, E. Wolf, ed. (Elsevier North-Holland, 1999), Chap. IV.
[CrossRef]

Ch. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, 1998), pp. 332-333.

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Figures (9)

Fig. 1
Fig. 1

Scheme of the interferometer setup and orientation of coordinate axes: P, polarizer; W, Wollaston compensator; A, analyzer; F, transmission filter; GW, glass wedge; BS1, BS2, BS3, BS4, four beam splitters.

Fig. 2
Fig. 2

Simulated phase plot at the output of the presented setup. White and black circles indicate the optical vortices of opposite topological sign; Λ denotes the distance between two fringes generated by W.

Fig. 3
Fig. 3

Experimental results, the intensity at the output of the measurement system for the Wollaston compensator with shearing angle equal to (a) 5°, and (b) 2°; both OVs sets with opposite topological signs are marked using different symbols (circles and crosses).

Fig. 4
Fig. 4

Superposition of both OVs lattices; OVs lattices with different topological sign have the same shape and the same dimensions of all basic cells.

Fig. 5
Fig. 5

Probability density function for all measured values of the quantity A for positive OVs set and 5° W.

Fig. 6
Fig. 6

Mean value of the distance A as a function of recording time.

Fig. 7
Fig. 7

Behavior of the OVs lattice for the tilt of the object wave (experiment): Crosses denote reference lattice (with no tilt), squares, wedge orientation equal to 0°; circles, wedge orientation equal to 90°.

Fig. 8
Fig. 8

Measured wavefront tilt as a function of glass wedge orientation for both Ws (dashed line, the mean value of the wave tilt).

Fig. 9
Fig. 9

Differences between measured and presumed glass wedge orientations (Δδ) as a function of its presumed orientation for both Ws.

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

a A o A r ,
cos δ o = a cos δ r 2 = a , cos δ o = a cos δ r 2 = + a .
b = arccos ( a ) ,
δ r = ± 2 b + 2 m π ,
δ o = π ± b + 2 n π ,
δ r = K x ,
δ o = k x x + k y y ,
Δ x m = 2 π K Δ m = Λ Δ m ,
Δ y m , n = 2 π k y ( Δ n k x K Δ m ) ,
Λ 2 π K .
A ( A x , A y ) P 10 P 00 = ( Λ , Λ k x k y ) ,
B ( B x , B y ) P 01 P 00 = ( 0 , 2 π k y ) .
k x = 2 π B y A y A x ,
k y = 2 π B y .
k x = 2 π B y A y A x ,
k y = 2 π B y .
Δ k x = k x k x ,
Δ k y = k y k y .
φ = arccos ( Δ k x Δ k x 2 + Δ k y 2 ) ,
δ = Δ k x 2 + Δ k y 2 k .

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