Abstract

A comparative study of pupil filters for transverse superresolution is presented in this article. We propose to combine the advantages of amplitude and phase filters in one complex filter that performs better than either phase or amplitude filters designed so far. The performance here refers to having a smaller spot size along with higher peak to side lobe intensity ratio. Using numerical simulation the limitations of phase and amplitude filters are assessed. The experimental verification of the designed combination filter is performed with two LCD spatial light modulators used for displaying separately the phase and amplitude part of the filter. Results obtained from this setup confirm the simulation.

© 2005 Optical Society of America

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References

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Appl. Opt. (1)

J. Opt. Soc. Am. A (4)

Opt. Comm. (2)

H. Ding, Q. Li and W. Zou, �??Design and comparison of amplitude-type and phase-only transverse super-resolving pupil filters,�?? Opt. Comm. 229, 117-122(2004).
[CrossRef]

P.N. Gundu, E. Hack and P. Rastogi, �??�??Apodized superresolution�?? �?? concept and simulations,�?? Opt. Comm. (to be published).

Opt. Eng. (1)

I. Moreno, J.A. Davis, K.G. D�??Nelly, and D.B. Allison, �??Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators,�?? Opt. Eng. 37, 3048-3052 (1998).
[CrossRef]

Opt. Lett. (5)

Other (1)

<a href="http://www.mathworks.com/">http://www.mathworks.com/</a>

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Figures (7)

Fig. 1.
Fig. 1.

Strehl Ratio S versus relative spot size G for three filter types.

Fig. 2.
Fig. 2.

Peak to side lobe ratio Γ (in log scale) versus relative spot size G for three filter types corresponding to the Strehl ratio in Fig. 1.

Fig. 3.
Fig. 3.

Point spread functions with 2 zone phase, 3 zone phase and complex combination filter.

Fig. 4.
Fig. 4.

Optical scheme for implementation of superresolution using a complex filter.

Fig. 5.
Fig. 5.

The characteristic behavior of phase-only LCD SLM.

Fig. 6.
Fig. 6.

The characteristic behavior of amplitude-only LCD SLM.

Fig. 7.
Fig. 7.

(a) Diffraction point spread intensity pattern (b) Superresolution point spread intensity pattern with complex filter (c) Profile from Fig. 7(a) and (d) profile of Fig. 7(b). Note the scale difference of intensity in Fig. 7(c) and 7(d).

Tables (1)

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Table 1. Parameter of the filters shown in Fig. 1 and 2

Equations (7)

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U ( υ , u ) = 2 0 1 P ( ρ ) J 0 ( υ ρ ) exp ( i u ρ 2 2 ) ρ d ρ
υ = ( 2 π λ ) r sin α
u = 4 ( 2 π λ ) z sin 2 ( α 2 )
U ( υ , 0 ) = 2 0 1 P ( ρ ) J 0 ( υ ρ ) ρ d ρ
P ( ρ ) = g ( ρ ) . exp ( if ( ρ ) )
g ( ρ ) = n = 0 k a 2 n ρ 2 n
0 P ( ρ ) 1 , for each set of a 2 n s

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