Abstract

We describe a technique for a phase-stepping interferometer based on programmable binary phase holograms, particularly useful for optical testing of aspheric or free-form surfaces. It is well-known that binary holograms can be used to generate reference surfaces for interferometry, but a major problem is that cross talk from higher diffraction orders and aliasing can reduce the fidelity of the system. Here, we propose a new encoding technique which improves the accuracy of the technique and demonstrate its implementation using a binary liquid crystal spatial light modulator.

© 2011 Optical Society of America

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References

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2009

2007

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

2003

1998

1995

J. Burge, Proc. SPIE 2576, 258 (1995).
[CrossRef]

1994

1988

K. Creath, Prog. Opt. 26, 349 (1988).
[CrossRef]

Am. J. Phys.

B. R. Boruah, Am. J. Phys. 77, 331 (2009).
[CrossRef]

Appl. Opt.

Opt. Lett.

Proc. SPIE

J. Burge, Proc. SPIE 2576, 258 (1995).
[CrossRef]

Prog. Opt.

K. Creath, Prog. Opt. 26, 349 (1988).
[CrossRef]

Other

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

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Figures (3)

Fig. 1
Fig. 1

Modulo 2 π phases obtained from simulations using a (a) normal binarization algorithm and a (b) random binarization algorithm and 24 holograms for each step.

Fig. 2
Fig. 2

Experimental arrangement to implement the proposed PSI scheme.

Fig. 3
Fig. 3

Modulo 2 π phases obtained experimentally using (a) a normal binarization algorithm and three phase steps, (b) a random binarization algorithm and 24 holograms per step for three phase steps. (c) and (d) Show residual phase for (a) and (b), respectively, after removal of programmed spherical aberration, tilt, and low order system aberrations.

Equations (4)

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I n = ( A o 2 + A r 2 ) + 2 A o A r cos ( ϕ o ϕ r n 2 π N ) .
A o A r exp ( i ( ϕ o ϕ r ) ) = 1 N n = 1 N I n exp ( i 2 n π N ) .
t ( x , y ) = { + 1 if     cos ( Φ ( x , y ) ) 0 1 if     cos ( Φ ( x , y ) ) < 0 .
t ( x , y ) = { + 1 if     cos ( Φ ( x , y ) ) R ( x , y ) 1 if     cos ( Φ ( x , y ) ) < R ( x , y ) ,

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