Abstract

A radially symmetric phase mask composed of several annular zones with equal area (called APM) was designed based on the incoherent imaging theory from Fourier Optics. The phase of any ring equals minus of the phase function caused by certain defocus. Another circularly symmetric phase mask similar to the APM (called MQPM) was proposed, except for the different phase function deriving from the quartic phase mask (QPM). For MQPM, there are two differences from an existing phase mask: the selection of the phase parameters and the method to divide the phase mask. An optimization model was developed to obtain optimized parameters of the phase masks. Numerical evaluations show that both APM and MQPM are less insensitive to defocus than QPM, and the defocused optical transfer functions with two phase masks are symmetric about the in-focus plane in the axial direction.

© 2012 Optical Society of America

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References

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[CrossRef]

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George, N.

Gracht, J. v. d.

R. Narayanswamy, P. E. X. Silveira, H. Setty, V. P. Pauca, and J. v. d. Gracht, Proc. SPIE 5779, 41 (2005).
[CrossRef]

Hacka, E.

D. Iwaniuka, E. Hacka, and P. Rastogi, J. Mod. Opt. 57, 2141 (2010).
[CrossRef]

Harvey, A. R.

Huckridge, D.

Iwaniuka, D.

D. Iwaniuka, E. Hacka, and P. Rastogi, J. Mod. Opt. 57, 2141 (2010).
[CrossRef]

Li, G.

Li, Y.

Liu, L.

Q. Yang, L. Liu, and J. Sun, Opt. Commun. 272, 56 (2007).
[CrossRef]

Mezouari, S.

Muyo, G.

Narayanswamy, R.

R. Narayanswamy, P. E. X. Silveira, H. Setty, V. P. Pauca, and J. v. d. Gracht, Proc. SPIE 5779, 41 (2005).
[CrossRef]

Pauca, V. P.

R. Narayanswamy, P. E. X. Silveira, H. Setty, V. P. Pauca, and J. v. d. Gracht, Proc. SPIE 5779, 41 (2005).
[CrossRef]

Rastogi, P.

D. Iwaniuka, E. Hacka, and P. Rastogi, J. Mod. Opt. 57, 2141 (2010).
[CrossRef]

Setty, H.

R. Narayanswamy, P. E. X. Silveira, H. Setty, V. P. Pauca, and J. v. d. Gracht, Proc. SPIE 5779, 41 (2005).
[CrossRef]

Sherif, S. S.

Sicre, E. E.

Silveira, P. E. X.

R. Narayanswamy, P. E. X. Silveira, H. Setty, V. P. Pauca, and J. v. d. Gracht, Proc. SPIE 5779, 41 (2005).
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Singh, A.

Sun, J.

Q. Yang, L. Liu, and J. Sun, Opt. Commun. 272, 56 (2007).
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Wood, A.

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Q. Yang, L. Liu, and J. Sun, Opt. Commun. 272, 56 (2007).
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Ye, R.

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Zhang, H.

Zhao, H.

Zhou, F.

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Figures (4)

Fig. 1.
Fig. 1.

Phase profile curves of APM, QPM, MQPM corresponding to the optimum parameters on condition [10, 0.8].

Fig. 2.
Fig. 2.

Defocused MTF curves of (a) CA, (b) QPM, (c) APM, (d) MQPM. The left side curved lines of each figure represent negative defocus, and the right ones represent positive defocus.

Fig. 3.
Fig. 3.

MTF density maps of (a) CA, (b) QPM, (c) APM, (d) MQPM. The upper part of each figure represents original MTF density map, and the lower represents binary MTF density map.

Fig. 4.
Fig. 4.

Simulated imaging of spoke target without image restoration {(a) CA, (b) QPM, (c) APM, (d) MQPM, the defocus parameters from left to right for each phase mask: φ=10, 0, 10}.

Tables (1)

Tables Icon

Table 1. Optimized Parameters for QPM, APM, MQPM

Equations (6)

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P˜(x,y)=P(x,y)exp[jkW20(x2+y2)]exp[jϕ(x,y)],
ϕ(x,y)=kW20(x2+y2)
ϕAPM(ρ)={mαρ2(mNρ2<2m+12N)mαρ2(2m+12Nρ2<m+1N),
ϕMQPM(ρ)={αρ4+βρ2(mNρ2<2m+12N)αρ4βρ2(2m+12Nρ2<m+1N),
ϕQPM(ρ)=αρ4+βρ2.
{minpara,umax,φmax12φmaxumaxφmaxφmax0umax[|H(u,φ)|H(u)¯]2dudφsubject to:|H(u,φ)|thH(u)¯=12φmaxφmaxφmax|H(u,φ)|dφ,

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