Abstract

This paper theoretically analyzes the axial intensity distribution of an optical imaging system with a low-frequency binary phase mask. Based on the derivation, a novel but simple one-step phase mask is designed to extend the depth of field. A comparison is made between the novel phase mask and the one designed in previous research [Opt. Express 14, 2631 (2006)]. Both masks are numerically tested in an achromatic doublet system. The numerical results show that two phase masks have comparable performance in depth of field extension. However, the phase mask designed in this paper has a simpler structure because it has only one step while the previous one has two. Consequently, the easy fabrication of the novel phase mask leads to cost reduction. This novel low-frequency binary phase mask provides a new choice to design depth-of-field-extended optical systems without digital image processing.

© 2014 Optical Society of America

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References

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2014 (1)

2013 (1)

M. Liu, L. Dong, Y. Zhao, M. Hui, and W. Jia, “Stationary phase analysis of generalized cubic phase mask wavefront coding,” Opt. Commun. 298, 67–74 (2013).
[CrossRef]

2012 (2)

T. Zhao and F. Yu, “Point spread function analysis of a cubic phase wavefront coding system with a circular pupil,” Opt. Express 20, 2408–2419 (2012).
[CrossRef]

H. Wang, C. J. R. Sheppard, K. Ravi, S. T. Ho, and G. Vienne, “Fighting against diffraction: apodization and near field diffraction structures,” Laser Photon. Rev. 6, 354–392 (2012).
[CrossRef]

2011 (1)

2010 (2)

2009 (2)

2007 (4)

2006 (1)

2001 (1)

1998 (1)

W. D. Furlan, G. Saavedra, E. Silvestre, and M. Martinez-Corral, “On-axis irradiance for spherically aberrated optical systems with obscured rectangular apertures: a study using Wigner distribution function,” J. Mod. Opt. 45, 69–77 (1998).
[CrossRef]

1996 (1)

C. J. R. Sheppard, “Synthesis of filters for specified axial properties,” J. Mod. Opt. 43, 525–536 (1996).
[CrossRef]

1995 (1)

1989 (1)

Andersson, M.

Belkin, M.

Castaneda, J. O.

Cathey, W. T.

Chen, S.

Cisotto, L.

Diaz, A.

Dong, L.

M. Liu, L. Dong, Y. Zhao, M. Hui, and W. Jia, “Stationary phase analysis of generalized cubic phase mask wavefront coding,” Opt. Commun. 298, 67–74 (2013).
[CrossRef]

Dowski, E. R.

Eliezer, E. B.

Fan, Z.

Filho, L. C. C. P.

Furlan, W. D.

W. D. Furlan, G. Saavedra, E. Silvestre, and M. Martinez-Corral, “On-axis irradiance for spherically aberrated optical systems with obscured rectangular apertures: a study using Wigner distribution function,” J. Mod. Opt. 45, 69–77 (1998).
[CrossRef]

Gan, F.

Harvey, A. R.

Ho, S. T.

H. Wang, C. J. R. Sheppard, K. Ravi, S. T. Ho, and G. Vienne, “Fighting against diffraction: apodization and near field diffraction structures,” Laser Photon. Rev. 6, 354–392 (2012).
[CrossRef]

Huckridge, D.

Hui, M.

M. Liu, L. Dong, Y. Zhao, M. Hui, and W. Jia, “Stationary phase analysis of generalized cubic phase mask wavefront coding,” Opt. Commun. 298, 67–74 (2013).
[CrossRef]

Jia, W.

M. Liu, L. Dong, Y. Zhao, M. Hui, and W. Jia, “Stationary phase analysis of generalized cubic phase mask wavefront coding,” Opt. Commun. 298, 67–74 (2013).
[CrossRef]

Konijnenberg, A. P.

Kumar, N.

Li, G.

Li, Y.

Liu, L.

Q. Yang, L. Liu, and J. Sun, “Optimized phase pupil masks for extended depth of field,” Opt. Commun. 272, 56–66 (2007).
[CrossRef]

Liu, M.

M. Liu, L. Dong, Y. Zhao, M. Hui, and W. Jia, “Stationary phase analysis of generalized cubic phase mask wavefront coding,” Opt. Commun. 298, 67–74 (2013).
[CrossRef]

Marom, E.

Martinez-Corral, M.

W. D. Furlan, G. Saavedra, E. Silvestre, and M. Martinez-Corral, “On-axis irradiance for spherically aberrated optical systems with obscured rectangular apertures: a study using Wigner distribution function,” J. Mod. Opt. 45, 69–77 (1998).
[CrossRef]

Muyo, G.

Pereira, S. F.

Raveh, I.

Ravi, K.

H. Wang, C. J. R. Sheppard, K. Ravi, S. T. Ho, and G. Vienne, “Fighting against diffraction: apodization and near field diffraction structures,” Laser Photon. Rev. 6, 354–392 (2012).
[CrossRef]

Saavedra, G.

W. D. Furlan, G. Saavedra, E. Silvestre, and M. Martinez-Corral, “On-axis irradiance for spherically aberrated optical systems with obscured rectangular apertures: a study using Wigner distribution function,” J. Mod. Opt. 45, 69–77 (1998).
[CrossRef]

Shemer, A.

Sheppard, C. J. R.

H. Wang, C. J. R. Sheppard, K. Ravi, S. T. Ho, and G. Vienne, “Fighting against diffraction: apodization and near field diffraction structures,” Laser Photon. Rev. 6, 354–392 (2012).
[CrossRef]

Y. Xu, J. Singh, and C. J. R. Sheppard, “Ultra long high resolution beam by multi-zone rotationally symmetrical complex pupil filter,” Opt. Express 15, 6409–6413 (2007).
[CrossRef]

C. J. R. Sheppard, “Synthesis of filters for specified axial properties,” J. Mod. Opt. 43, 525–536 (1996).
[CrossRef]

Silvestre, E.

W. D. Furlan, G. Saavedra, E. Silvestre, and M. Martinez-Corral, “On-axis irradiance for spherically aberrated optical systems with obscured rectangular apertures: a study using Wigner distribution function,” J. Mod. Opt. 45, 69–77 (1998).
[CrossRef]

Singh, A.

Singh, J.

Sun, J.

Q. Yang, L. Liu, and J. Sun, “Optimized phase pupil masks for extended depth of field,” Opt. Commun. 272, 56–66 (2007).
[CrossRef]

Tepichin, E.

Urbach, H. P.

Vienne, G.

H. Wang, C. J. R. Sheppard, K. Ravi, S. T. Ho, and G. Vienne, “Fighting against diffraction: apodization and near field diffraction structures,” Laser Photon. Rev. 6, 354–392 (2012).
[CrossRef]

Wang, D.

Wang, H.

H. Wang, C. J. R. Sheppard, K. Ravi, S. T. Ho, and G. Vienne, “Fighting against diffraction: apodization and near field diffraction structures,” Laser Photon. Rev. 6, 354–392 (2012).
[CrossRef]

H. Wang and F. Gan, “High focal depth with a pure-phase apodizer,” Appl. Opt. 40, 5658–5662 (2001).
[CrossRef]

Wang, S.

Wei, L.

Wood, A.

Xiao, H.

Xu, Y.

Xu, Z.

Yaish, S. B.

Yang, Q.

Q. Yang, L. Liu, and J. Sun, “Optimized phase pupil masks for extended depth of field,” Opt. Commun. 272, 56–66 (2007).
[CrossRef]

Ye, R.

Yehezkel, O.

Yu, F.

Zalevsky, Z.

Zhang, H.

Zhao, H.

Zhao, T.

Zhao, Y.

M. Liu, L. Dong, Y. Zhao, M. Hui, and W. Jia, “Stationary phase analysis of generalized cubic phase mask wavefront coding,” Opt. Commun. 298, 67–74 (2013).
[CrossRef]

Zhou, F.

Zlotnik, A.

Zuo, B.

Appl. Opt. (3)

J. Mod. Opt. (2)

C. J. R. Sheppard, “Synthesis of filters for specified axial properties,” J. Mod. Opt. 43, 525–536 (1996).
[CrossRef]

W. D. Furlan, G. Saavedra, E. Silvestre, and M. Martinez-Corral, “On-axis irradiance for spherically aberrated optical systems with obscured rectangular apertures: a study using Wigner distribution function,” J. Mod. Opt. 45, 69–77 (1998).
[CrossRef]

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

Laser Photon. Rev. (1)

H. Wang, C. J. R. Sheppard, K. Ravi, S. T. Ho, and G. Vienne, “Fighting against diffraction: apodization and near field diffraction structures,” Laser Photon. Rev. 6, 354–392 (2012).
[CrossRef]

Opt. Commun. (2)

M. Liu, L. Dong, Y. Zhao, M. Hui, and W. Jia, “Stationary phase analysis of generalized cubic phase mask wavefront coding,” Opt. Commun. 298, 67–74 (2013).
[CrossRef]

Q. Yang, L. Liu, and J. Sun, “Optimized phase pupil masks for extended depth of field,” Opt. Commun. 272, 56–66 (2007).
[CrossRef]

Opt. Express (7)

Opt. Lett. (3)

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Figures (4)

Fig. 1.
Fig. 1.

Schematic representation of the optical setup.

Fig. 2.
Fig. 2.

Schematic sketch of the doublet optical system with the phase mask.

Fig. 3.
Fig. 3.

Cross sections of the binary phase masks. (a) The phase mask designed in this paper (mask 1). (b) The phase mask designed in previous papers (mask 2).

Fig. 4.
Fig. 4.

(a) MTF versus focus shift at the frequency of 70lp/mm. (b)–(f) MTF curves at different object distances when the system is focused at an object distance of 5000 mm, (b) 5470 mm, (c) 5290 mm, (d) 5000 mm, (e) 4785 mm, and (f) 4585 mm.

Equations (16)

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

U(z)=1λf(f+z)02π0P(r,θ)exp[i2πz2λf(f+z)r2]rdrdθ,
U(z)=2W20zλ02π01P(r,θ)exp(i2πλW20r2)rdrdθ.
P(r,θ)={1,r<r1orr2<r1,exp(iΔ),r1rr2,0,r>1,
U(z)=2kW20z{01exp(ikW20r2)rdr[exp(iΔ)1]r1r2exp(ikW20r2)rdr}.
I(z)=|U(z)|2.
I(φ)=(πλf2φ2f)2[sin2φ+4sin2Δ2sin2(φξ)+4sinΔ2sinφsin(φξ)cos(φη+Δ2)],
φ=kW202=πz2λf(f+z),
ξ=r22r12,η=1r12r22.
2sin(Δ/2)sin(φξ)=sinφcos(φη+Δ),
sinφsin(φη+Δ)+cos(Δ/2)sin(φξ)<0.
I(φ)=(πλf2φ2f)2{sin2(φη+Δ2)+[cos(φη+Δ)cos(φη+Δ2)]2}.
I(φ,ξ,η)=(πλf2φ2f)2[4sin2(φξ)+sin2φ4sinφsin(φξ)sin(φη)].
I(φ,0,η)=(πλf2φ2f)2sin2φ.
I(φ,ξ,η)I(φ,0,η)=cos2(φη)+4sin2φ[sin(φξ)sinφsin(φη)2]2.
sin(φξ)sin(φη)=cos(φ(2r221))cos(φ(2r121))2.
maxr2cos[φ(2r221)],minr1cos[φ(2r121)].

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