High efficient superresolution combination filter with twin LCD spatial light modulators

Phanindra Narayan Gundu; Erwin Hack; Pramod Rastogi

doi:10.1364/OPEX.13.002835

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.

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References

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Year
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Author
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Publication

T.R.M. Sales and G.M. Morris, “Diffractive superresolution elements,” J. Opt. Soc. Am. A 14, 1637–1646(1997).
[Crossref]
D.M. de Juana, J.E. Oti, V.F. Canales, and M.P. Cagigal, “Transverse or axial superresolution in a 4Pi-confocal microscope by phase-only filters,” J. Opt. Soc. Am. A 20, 2172–2178(2003).
[Crossref]
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]
V.F. Canales, D.M. de Juana, and M.P. Cagigal, “Superresolution in compensated telescopes,” Opt. Lett. 29, 935–937(2004).
[Crossref] [PubMed]
T.R.M. Sales and G. M. Morris, “Fundamental limits of optical superresolution,” Opt. Lett. 9, 582–584 (1997).
[Crossref]
P.N. Gundu, E. Hack, and P. Rastogi, “‘Apodized superresolution’ - concept and simulations,” Opt. Comm. (to be published).
C.J.R. Sheppard and Z.S. Hegedus, “Axial behavior of pupil-plane filters,” J. Opt. Soc. Am. A 5, 643–647(1988).
[Crossref]
D.M. de Juana, J.E. Oti, V.F. Canales, and M.P. Cagigal, “Design of superresolving continuous phase filters,” Opt. Lett. 28, 607–609(2003).
[Crossref] [PubMed]
http://www.mathworks.com/
S. Zhou and C. Zhou, “Discrete continuous-phase superresolution filters,” Opt. Lett. 29, 2746–2748 (2004).
[Crossref] [PubMed]
M. Yun, L. Liu, J. Sun, and D. Liu, “Three-dimensional superresolution by three-zone complex pupil filters,” J. Opt. Soc. Am. A 22, 272–277(2005).
[Crossref]
J.L. Pezzaniti and R.A. Chipaman, “Phase-only modulation of a twisted nematic liquid-crystal TV by use of the eigenpolarization states,” Opt. Lett. 18, 1567–1569 (1993).
[Crossref] [PubMed]
J.A. Davis, I. Moreno, and P. Tsai, “Polarization eigenstates for twisted-nematic liquid crystal displays,” Appl. Opt. 37, 937–945 (1998).
[Crossref]
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]

2005 (1)

M. Yun, L. Liu, J. Sun, and D. Liu, “Three-dimensional superresolution by three-zone complex pupil filters,” J. Opt. Soc. Am. A 22, 272–277(2005).
[Crossref]

2004 (3)

V.F. Canales, D.M. de Juana, and M.P. Cagigal, “Superresolution in compensated telescopes,” Opt. Lett. 29, 935–937(2004).
[Crossref] [PubMed]

S. Zhou and C. Zhou, “Discrete continuous-phase superresolution filters,” Opt. Lett. 29, 2746–2748 (2004).
[Crossref] [PubMed]

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]

2003 (2)

D.M. de Juana, J.E. Oti, V.F. Canales, and M.P. Cagigal, “Design of superresolving continuous phase filters,” Opt. Lett. 28, 607–609(2003).
[Crossref] [PubMed]

D.M. de Juana, J.E. Oti, V.F. Canales, and M.P. Cagigal, “Transverse or axial superresolution in a 4Pi-confocal microscope by phase-only filters,” J. Opt. Soc. Am. A 20, 2172–2178(2003).
[Crossref]

1998 (2)

J.A. Davis, I. Moreno, and P. Tsai, “Polarization eigenstates for twisted-nematic liquid crystal displays,” Appl. Opt. 37, 937–945 (1998).
[Crossref]

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]

1997 (2)

T.R.M. Sales and G.M. Morris, “Diffractive superresolution elements,” J. Opt. Soc. Am. A 14, 1637–1646(1997).
[Crossref]

T.R.M. Sales and G. M. Morris, “Fundamental limits of optical superresolution,” Opt. Lett. 9, 582–584 (1997).
[Crossref]

1993 (1)

J.L. Pezzaniti and R.A. Chipaman, “Phase-only modulation of a twisted nematic liquid-crystal TV by use of the eigenpolarization states,” Opt. Lett. 18, 1567–1569 (1993).
[Crossref] [PubMed]

1988 (1)

C.J.R. Sheppard and Z.S. Hegedus, “Axial behavior of pupil-plane filters,” J. Opt. Soc. Am. A 5, 643–647(1988).
[Crossref]

Allison, D.B.

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]

D’Nelly, K.G.

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]

Davis, J.A.

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]

J.A. Davis, I. Moreno, and P. Tsai, “Polarization eigenstates for twisted-nematic liquid crystal displays,” Appl. Opt. 37, 937–945 (1998).
[Crossref]

de Juana, D.M.

V.F. Canales, D.M. de Juana, and M.P. Cagigal, “Superresolution in compensated telescopes,” Opt. Lett. 29, 935–937(2004).
[Crossref] [PubMed]

D.M. de Juana, J.E. Oti, V.F. Canales, and M.P. Cagigal, “Design of superresolving continuous phase filters,” Opt. Lett. 28, 607–609(2003).
[Crossref] [PubMed]

D.M. de Juana, J.E. Oti, V.F. Canales, and M.P. Cagigal, “Transverse or axial superresolution in a 4Pi-confocal microscope by phase-only filters,” J. Opt. Soc. Am. A 20, 2172–2178(2003).
[Crossref]

Ding, H.

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]

Gundu, P.N.

P.N. Gundu, E. Hack, and P. Rastogi, “‘Apodized superresolution’ - concept and simulations,” Opt. Comm. (to be published).

Hack, E.

P.N. Gundu, E. Hack, and P. Rastogi, “‘Apodized superresolution’ - concept and simulations,” Opt. Comm. (to be published).

Hegedus, Z.S.

C.J.R. Sheppard and Z.S. Hegedus, “Axial behavior of pupil-plane filters,” J. Opt. Soc. Am. A 5, 643–647(1988).
[Crossref]

Li, Q.

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]

Liu, D.

M. Yun, L. Liu, J. Sun, and D. Liu, “Three-dimensional superresolution by three-zone complex pupil filters,” J. Opt. Soc. Am. A 22, 272–277(2005).
[Crossref]

Liu, L.

M. Yun, L. Liu, J. Sun, and D. Liu, “Three-dimensional superresolution by three-zone complex pupil filters,” J. Opt. Soc. Am. A 22, 272–277(2005).
[Crossref]

Moreno, I.

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]

J.A. Davis, I. Moreno, and P. Tsai, “Polarization eigenstates for twisted-nematic liquid crystal displays,” Appl. Opt. 37, 937–945 (1998).
[Crossref]

Morris, G. M.

T.R.M. Sales and G. M. Morris, “Fundamental limits of optical superresolution,” Opt. Lett. 9, 582–584 (1997).
[Crossref]

Morris, G.M.

T.R.M. Sales and G.M. Morris, “Diffractive superresolution elements,” J. Opt. Soc. Am. A 14, 1637–1646(1997).
[Crossref]

Oti, J.E.

D.M. de Juana, J.E. Oti, V.F. Canales, and M.P. Cagigal, “Design of superresolving continuous phase filters,” Opt. Lett. 28, 607–609(2003).
[Crossref] [PubMed]

D.M. de Juana, J.E. Oti, V.F. Canales, and M.P. Cagigal, “Transverse or axial superresolution in a 4Pi-confocal microscope by phase-only filters,” J. Opt. Soc. Am. A 20, 2172–2178(2003).
[Crossref]

Pezzaniti, J.L.

J.L. Pezzaniti and R.A. Chipaman, “Phase-only modulation of a twisted nematic liquid-crystal TV by use of the eigenpolarization states,” Opt. Lett. 18, 1567–1569 (1993).
[Crossref] [PubMed]

Rastogi, P.

P.N. Gundu, E. Hack, and P. Rastogi, “‘Apodized superresolution’ - concept and simulations,” Opt. Comm. (to be published).

Sales, T.R.M.

T.R.M. Sales and G. M. Morris, “Fundamental limits of optical superresolution,” Opt. Lett. 9, 582–584 (1997).
[Crossref]

T.R.M. Sales and G.M. Morris, “Diffractive superresolution elements,” J. Opt. Soc. Am. A 14, 1637–1646(1997).
[Crossref]

Sheppard, C.J.R.

C.J.R. Sheppard and Z.S. Hegedus, “Axial behavior of pupil-plane filters,” J. Opt. Soc. Am. A 5, 643–647(1988).
[Crossref]

Sun, J.

M. Yun, L. Liu, J. Sun, and D. Liu, “Three-dimensional superresolution by three-zone complex pupil filters,” J. Opt. Soc. Am. A 22, 272–277(2005).
[Crossref]

Tsai, P.

J.A. Davis, I. Moreno, and P. Tsai, “Polarization eigenstates for twisted-nematic liquid crystal displays,” Appl. Opt. 37, 937–945 (1998).
[Crossref]

Yun, M.

M. Yun, L. Liu, J. Sun, and D. Liu, “Three-dimensional superresolution by three-zone complex pupil filters,” J. Opt. Soc. Am. A 22, 272–277(2005).
[Crossref]

Zhou, C.

S. Zhou and C. Zhou, “Discrete continuous-phase superresolution filters,” Opt. Lett. 29, 2746–2748 (2004).
[Crossref] [PubMed]

Zhou, S.

S. Zhou and C. Zhou, “Discrete continuous-phase superresolution filters,” Opt. Lett. 29, 2746–2748 (2004).
[Crossref] [PubMed]

Zou, W.

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]

Appl. Opt. (1)

J.A. Davis, I. Moreno, and P. Tsai, “Polarization eigenstates for twisted-nematic liquid crystal displays,” Appl. Opt. 37, 937–945 (1998).
[Crossref]

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

T.R.M. Sales and G.M. Morris, “Diffractive superresolution elements,” J. Opt. Soc. Am. A 14, 1637–1646(1997).
[Crossref]

C.J.R. Sheppard and Z.S. Hegedus, “Axial behavior of pupil-plane filters,” J. Opt. Soc. Am. A 5, 643–647(1988).
[Crossref]

D.M. de Juana, J.E. Oti, V.F. Canales, and M.P. Cagigal, “Transverse or axial superresolution in a 4Pi-confocal microscope by phase-only filters,” J. Opt. Soc. Am. A 20, 2172–2178(2003).
[Crossref]

M. Yun, L. Liu, J. Sun, and D. Liu, “Three-dimensional superresolution by three-zone complex pupil filters,” J. Opt. Soc. Am. A 22, 272–277(2005).
[Crossref]

Opt. Comm. (1)

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]

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)

V.F. Canales, D.M. de Juana, and M.P. Cagigal, “Superresolution in compensated telescopes,” Opt. Lett. 29, 935–937(2004).
[Crossref] [PubMed]

S. Zhou and C. Zhou, “Discrete continuous-phase superresolution filters,” Opt. Lett. 29, 2746–2748 (2004).
[Crossref] [PubMed]

T.R.M. Sales and G. M. Morris, “Fundamental limits of optical superresolution,” Opt. Lett. 9, 582–584 (1997).
[Crossref]

J.L. Pezzaniti and R.A. Chipaman, “Phase-only modulation of a twisted nematic liquid-crystal TV by use of the eigenpolarization states,” Opt. Lett. 18, 1567–1569 (1993).
[Crossref] [PubMed]

D.M. de Juana, J.E. Oti, V.F. Canales, and M.P. Cagigal, “Design of superresolving continuous phase filters,” Opt. Lett. 28, 607–609(2003).
[Crossref] [PubMed]

Other (2)

P.N. Gundu, E. Hack, and P. Rastogi, “‘Apodized superresolution’ - concept and simulations,” Opt. Comm. (to be published).

http://www.mathworks.com/

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Fig. 1. Strehl Ratio S versus relative spot size G for three filter types.

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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.

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

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Fig. 4. Optical scheme for implementation of superresolution using a complex filter.

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Fig. 5. The characteristic behavior of phase-only LCD SLM.

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Fig. 6. The characteristic behavior of amplitude-only LCD SLM.

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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).

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Tables (1)

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

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Equations (7)

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U (υ, u) = 2 \int_{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 \int_{0}^{1} P (ρ) J_{0} (υ ρ) ρ d ρ

P (ρ) = g (ρ) . \exp (if (ρ))

g (ρ) = \sum_{n = 0}^{k} a_{2 n} ρ^{2 n}

0 \leq P (ρ) \leq 1, for each set of a_{2 n} ’ s

G(%)	2 zone phase filters	3 zone phase filters		Continuous amplitude Filters
G(%)	ρ1	ρ1	ρ2	a₀	a₂	a₄	a₆	a₈	a₁₀	a₁₂
94	0.16	0.41	0.47	0.52	2.70	-8.98	9.99	2.34	-8.31	2.67
90	0.23	0.34	0.44	0.40	-0.84	12.12	-28.28	18.87	7.04	-8.30
85	0.29	0.30	0.45	0.32	-0.35	3.37	-4.84	3.16	2.53	-3.34
81	0.34	0.33	0.52	0.57	-4.30	10.00	-0.95	-3.12	-7.11	5.92
76	0.38	0.27	0.51	0.31	-2.00	1.45	8.31	-3.01	-10.00	5.91
72	0.43	0.27	0.55	0.00	0.23	-1.87	1.83	12.04	-15.71	4.42
67	0.48	0.24	0.56	2 zone blocking filter with boundary at ρ1=0.87
61	0.53	0.23	0.60	2 zone blocking filter with boundary at ρ1=0.98
53	0.58	0.23	0.65	Not possible even at Strehl ratio S=10-6

Abstract

References

2005 (1)

2004 (3)

2003 (2)

1998 (2)

1997 (2)

1993 (1)

1988 (1)

Allison, D.B.

Cagigal, M.P.

Canales, V.F.

Chipaman, R.A.

D’Nelly, K.G.

Davis, J.A.

de Juana, D.M.

Ding, H.

Gundu, P.N.

Hack, E.

Hegedus, Z.S.

Li, Q.

Liu, D.

Liu, L.

Moreno, I.

Morris, G. M.

Morris, G.M.

Oti, J.E.

Pezzaniti, J.L.

Rastogi, P.

Sales, T.R.M.

Sheppard, C.J.R.

Sun, J.

Tsai, P.

Yun, M.

Zhou, C.

Zhou, S.

Zou, W.

Appl. Opt. (1)

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

Opt. Comm. (1)

Opt. Eng. (1)

Opt. Lett. (5)

Other (2)

Cited By

Figures (7)

Tables (1)

Equations (7)

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