Abstract

A detailed investigation is presented on the tunable extended depth of field (EDOF) method, proposed recently by Klapp et al. [Opt. Lett. 39, 1414 (2014)]. This method is based on temporal multiplexing of phase masks, using an annular liquid crystal spatial light modulator possessing a small number of rings. Examples of 3D simulations used to determine the phase profiles in the pupil plane are presented, as well as more detailed experimental results. Both the experimental and numerical results include comprehensive analysis of contrast dependence on both the spatial spectrum of the object and the amount of defocus. In addition, for the first time, we present the EDOF order inversion in the experimental and simulated data. The results show a profound performance of the proposed system and method.

© 2014 Optical Society of America

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References

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    [CrossRef]
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  10. R. Kingslake, Optics in Photography (SPIE, 1992), Chap. 5.
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    [CrossRef]
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    [CrossRef]
  14. I. Abdulhalim, “Non-display bio-optic applications of liquid crystals,” Liq. Cryst. Today 20(2), 44–60 (2011).
    [CrossRef]
  15. I. Abdulhalim, R. Moses, and R. Sharon, “Biomedical optical applications of liquid crystal devices,” Acta Physica Polonica A 112, 715–722 (2007).
  16. A. Solodar, I. Klapp, and I. Abdulhalim, “Annular liquid crystal spatial light modulator for beam shaping and extended depth of focus,” Opt. Commun. 323, 167–173 (2014).
    [CrossRef]
  17. D.-K. Yang and S.-T. Wu, Fundamentals of Liquid Crystal Devices (Wiley, 2006), Chap. 6.7.
  18. I. C. Khoo and S.-T. Wu, Optics and Nonlinear Optics of Liquid Crystals (World Scientific, 1993).
  19. H. Wang, T. X. Wu, X. Zhu, and S.-T. Wu, “Correlations between liquid crystal director reorientation and optical response time of a homeotropic cell,” J. Appl. Phys. 95, 5502–5508 (2004).
    [CrossRef]
  20. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
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    [CrossRef]
  22. P. Křížek and G. M. Hagen, “Spatial light modulators in fluorescence microscopy,” in Microscopy: Science, Technology, Applications and Education, Vol. 2 of Microscopy Book Series (Formatex, 2010), pp. 1366–1377.
  23. N. S. Kopeika, A System Engineering Approach to Imaging (SPIE, 1998), pp. 517–520.

2014

A. Solodar, I. Klapp, and I. Abdulhalim, “Annular liquid crystal spatial light modulator for beam shaping and extended depth of focus,” Opt. Commun. 323, 167–173 (2014).
[CrossRef]

I. Klapp, A. Solodar, and I. Abdulhalim, “Tunable extended depth of field using a liquid crystal annular spatial filter,” Opt. Lett. 39, 1414–1417 (2014).
[CrossRef]

2012

2011

I. Abdulhalim, “Non-display bio-optic applications of liquid crystals,” Liq. Cryst. Today 20(2), 44–60 (2011).
[CrossRef]

2010

Y. A. Zlotnik, L. Liraz, I. Abdulhalim, and Z. Zalevsky, “Improved extended depth of focus full field spectral domain optical coherence tomography,” Opt. Commun. 283, 4963–4968 (2010).
[CrossRef]

2009

2008

G. Carlesa, G. Muyo, S. Boscha, and A. R. Harvey, “Implementation of a wavefront coded imaging system using a spatial light modulator,” Proc. SPIE 7100, 71000X (2008).
[CrossRef]

2007

2006

2004

H. Wang, T. X. Wu, X. Zhu, and S.-T. Wu, “Correlations between liquid crystal director reorientation and optical response time of a homeotropic cell,” J. Appl. Phys. 95, 5502–5508 (2004).
[CrossRef]

2003

2001

1995

1978

1972

G. Hausler, “A method to increase the depth of focus by two step image processing,” Opt. Commun. 6, 38–42 (1972).
[CrossRef]

Abdulhalim, I.

I. Klapp, A. Solodar, and I. Abdulhalim, “Tunable extended depth of field using a liquid crystal annular spatial filter,” Opt. Lett. 39, 1414–1417 (2014).
[CrossRef]

A. Solodar, I. Klapp, and I. Abdulhalim, “Annular liquid crystal spatial light modulator for beam shaping and extended depth of focus,” Opt. Commun. 323, 167–173 (2014).
[CrossRef]

I. Abdulhalim, “Non-display bio-optic applications of liquid crystals,” Liq. Cryst. Today 20(2), 44–60 (2011).
[CrossRef]

Y. A. Zlotnik, L. Liraz, I. Abdulhalim, and Z. Zalevsky, “Improved extended depth of focus full field spectral domain optical coherence tomography,” Opt. Commun. 283, 4963–4968 (2010).
[CrossRef]

I. Abdulhalim, R. Moses, and R. Sharon, “Biomedical optical applications of liquid crystal devices,” Acta Physica Polonica A 112, 715–722 (2007).

Ben-Eliezer, E.

Boscha, S.

G. Carlesa, G. Muyo, S. Boscha, and A. R. Harvey, “Implementation of a wavefront coded imaging system using a spatial light modulator,” Proc. SPIE 7100, 71000X (2008).
[CrossRef]

Carlesa, G.

G. Carlesa, G. Muyo, S. Boscha, and A. R. Harvey, “Implementation of a wavefront coded imaging system using a spatial light modulator,” Proc. SPIE 7100, 71000X (2008).
[CrossRef]

Cathey, T.

Chen, N.

Chi, W.

Cho, H.

Chu, K.

Dowski, E. R.

George, N.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Hagen, G. M.

P. Křížek and G. M. Hagen, “Spatial light modulators in fluorescence microscopy,” in Microscopy: Science, Technology, Applications and Education, Vol. 2 of Microscopy Book Series (Formatex, 2010), pp. 1366–1377.

Harvey, A. R.

G. Carlesa, G. Muyo, S. Boscha, and A. R. Harvey, “Implementation of a wavefront coded imaging system using a spatial light modulator,” Proc. SPIE 7100, 71000X (2008).
[CrossRef]

S. Mezouari and A. R. Harvey, “Phase pupil functions for reduction of defocus and spherical aberrations,” Opt. Lett. 28, 771–773 (2003).
[CrossRef]

Hausler, G.

G. Hausler, “A method to increase the depth of focus by two step image processing,” Opt. Commun. 6, 38–42 (1972).
[CrossRef]

Hong, D.

Howe, W.-C.

Khoo, I. C.

I. C. Khoo and S.-T. Wu, Optics and Nonlinear Optics of Liquid Crystals (World Scientific, 1993).

Kim, M.

Kingslake, R.

R. Kingslake, Optics in Photography (SPIE, 1992), Chap. 5.

Klapp, I.

A. Solodar, I. Klapp, and I. Abdulhalim, “Annular liquid crystal spatial light modulator for beam shaping and extended depth of focus,” Opt. Commun. 323, 167–173 (2014).
[CrossRef]

I. Klapp, A. Solodar, and I. Abdulhalim, “Tunable extended depth of field using a liquid crystal annular spatial filter,” Opt. Lett. 39, 1414–1417 (2014).
[CrossRef]

Konforti, N.

Kopeika, N. S.

N. S. Kopeika, A System Engineering Approach to Imaging (SPIE, 1998), pp. 517–520.

Krížek, P.

P. Křížek and G. M. Hagen, “Spatial light modulators in fluorescence microscopy,” in Microscopy: Science, Technology, Applications and Education, Vol. 2 of Microscopy Book Series (Formatex, 2010), pp. 1366–1377.

Liraz, L.

Y. A. Zlotnik, L. Liraz, I. Abdulhalim, and Z. Zalevsky, “Improved extended depth of focus full field spectral domain optical coherence tomography,” Opt. Commun. 283, 4963–4968 (2010).
[CrossRef]

Liu, C.

Liu, L.

Lohmann, A. W.

Marom, E.

Mezouari, S.

Mo, X.

Moses, R.

I. Abdulhalim, R. Moses, and R. Sharon, “Biomedical optical applications of liquid crystal devices,” Acta Physica Polonica A 112, 715–722 (2007).

Muyo, G.

G. Carlesa, G. Muyo, S. Boscha, and A. R. Harvey, “Implementation of a wavefront coded imaging system using a spatial light modulator,” Proc. SPIE 7100, 71000X (2008).
[CrossRef]

Park, K.

Rhodes, W.

Sharon, R.

I. Abdulhalim, R. Moses, and R. Sharon, “Biomedical optical applications of liquid crystal devices,” Acta Physica Polonica A 112, 715–722 (2007).

Sheppard, C. J. R.

Solodar, A.

A. Solodar, I. Klapp, and I. Abdulhalim, “Annular liquid crystal spatial light modulator for beam shaping and extended depth of focus,” Opt. Commun. 323, 167–173 (2014).
[CrossRef]

I. Klapp, A. Solodar, and I. Abdulhalim, “Tunable extended depth of field using a liquid crystal annular spatial filter,” Opt. Lett. 39, 1414–1417 (2014).
[CrossRef]

Wang, H.

H. Wang, T. X. Wu, X. Zhu, and S.-T. Wu, “Correlations between liquid crystal director reorientation and optical response time of a homeotropic cell,” J. Appl. Phys. 95, 5502–5508 (2004).
[CrossRef]

Wu, S.-T.

H. Wang, T. X. Wu, X. Zhu, and S.-T. Wu, “Correlations between liquid crystal director reorientation and optical response time of a homeotropic cell,” J. Appl. Phys. 95, 5502–5508 (2004).
[CrossRef]

D.-K. Yang and S.-T. Wu, Fundamentals of Liquid Crystal Devices (Wiley, 2006), Chap. 6.7.

I. C. Khoo and S.-T. Wu, Optics and Nonlinear Optics of Liquid Crystals (World Scientific, 1993).

Wu, T. X.

H. Wang, T. X. Wu, X. Zhu, and S.-T. Wu, “Correlations between liquid crystal director reorientation and optical response time of a homeotropic cell,” J. Appl. Phys. 95, 5502–5508 (2004).
[CrossRef]

Yang, D.-K.

D.-K. Yang and S.-T. Wu, Fundamentals of Liquid Crystal Devices (Wiley, 2006), Chap. 6.7.

Zalevsky, Z.

Y. A. Zlotnik, L. Liraz, I. Abdulhalim, and Z. Zalevsky, “Improved extended depth of focus full field spectral domain optical coherence tomography,” Opt. Commun. 283, 4963–4968 (2010).
[CrossRef]

E. Ben-Eliezer, E. Marom, N. Konforti, and Z. Zalevsky, “Radial mask for imaging systems that exhibit high resolution and extended depths of field,” Appl. Opt. 45, 2001–2013 (2006).
[CrossRef]

Zhu, X.

H. Wang, T. X. Wu, X. Zhu, and S.-T. Wu, “Correlations between liquid crystal director reorientation and optical response time of a homeotropic cell,” J. Appl. Phys. 95, 5502–5508 (2004).
[CrossRef]

Zlotnik, Y. A.

Y. A. Zlotnik, L. Liraz, I. Abdulhalim, and Z. Zalevsky, “Improved extended depth of focus full field spectral domain optical coherence tomography,” Opt. Commun. 283, 4963–4968 (2010).
[CrossRef]

Acta Physica Polonica A

I. Abdulhalim, R. Moses, and R. Sharon, “Biomedical optical applications of liquid crystal devices,” Acta Physica Polonica A 112, 715–722 (2007).

Appl. Opt.

J. Appl. Phys.

H. Wang, T. X. Wu, X. Zhu, and S.-T. Wu, “Correlations between liquid crystal director reorientation and optical response time of a homeotropic cell,” J. Appl. Phys. 95, 5502–5508 (2004).
[CrossRef]

Liq. Cryst. Today

I. Abdulhalim, “Non-display bio-optic applications of liquid crystals,” Liq. Cryst. Today 20(2), 44–60 (2011).
[CrossRef]

Opt. Commun.

Y. A. Zlotnik, L. Liraz, I. Abdulhalim, and Z. Zalevsky, “Improved extended depth of focus full field spectral domain optical coherence tomography,” Opt. Commun. 283, 4963–4968 (2010).
[CrossRef]

A. Solodar, I. Klapp, and I. Abdulhalim, “Annular liquid crystal spatial light modulator for beam shaping and extended depth of focus,” Opt. Commun. 323, 167–173 (2014).
[CrossRef]

G. Hausler, “A method to increase the depth of focus by two step image processing,” Opt. Commun. 6, 38–42 (1972).
[CrossRef]

Opt. Lett.

Proc. SPIE

G. Carlesa, G. Muyo, S. Boscha, and A. R. Harvey, “Implementation of a wavefront coded imaging system using a spatial light modulator,” Proc. SPIE 7100, 71000X (2008).
[CrossRef]

Other

P. Křížek and G. M. Hagen, “Spatial light modulators in fluorescence microscopy,” in Microscopy: Science, Technology, Applications and Education, Vol. 2 of Microscopy Book Series (Formatex, 2010), pp. 1366–1377.

N. S. Kopeika, A System Engineering Approach to Imaging (SPIE, 1998), pp. 517–520.

R. Kingslake, Optics in Photography (SPIE, 1992), Chap. 5.

D.-K. Yang and S.-T. Wu, Fundamentals of Liquid Crystal Devices (Wiley, 2006), Chap. 6.7.

I. C. Khoo and S.-T. Wu, Optics and Nonlinear Optics of Liquid Crystals (World Scientific, 1993).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

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Figures (13)

Fig. 1.
Fig. 1.

Schematic of the tunable spatial filter: (a) molecule of LC material and its refractive indices, (b) cross section of a typical LC cell, and (c) top view of the proposed annular structures. The filter is divided into eight rings. From top to bottom the LC device is composed of layers in the following order: glass, ITO, polyimide alignment layer, LC material, polyimide alignment layer, ITO, and glass.

Fig. 2.
Fig. 2.

Schematic presentation of the simulated system. The object is a 16-stair “staircase” structure located in the “object space.” The object distance (Sobj) is measured from the top stair. The imaging system is modeled as a thin lens attached to the active annular filter. The imager is located in the “image space” at a constant distance from the imaging lens.

Fig. 3.
Fig. 3.

Simulated through-focus MTF curves under the condition (W20<0). Spatial frequency is normalized to the incoherent cutoff frequency (fc). (a) The filter is “off,” (b) QPM phase profile, and (c) binary phase profile. Each curve represents the systems MTF at different defocus value. (A) W20=0λ, (B) W20=0.181λ, (C) W20=0.545λ, (D) W20=0.914λ, (E) W20=1.288λ, (F) W20=1.666λ, (G) W20=2.049λ, (H) W20=2.437λ, and (I) W20=2.830λ.

Fig. 4.
Fig. 4.

Simulated “databases.” (a)–(c) Simulated “database” of the “smiley” icon (column 1) and “Ronchi-rulings” (column 2) using the masks: (a) off, (b) QPM, and (c) binary. In (d) the object topography following Fig. 2 is shown; the brighter the higher.

Fig. 5.
Fig. 5.

Simulation results of 16-stair object imaged with five different temporal multiplexing combinations. The temporal multiplexing combinations are (a) min EDOF, (b) min-mid EDOF, (c) medium EDOF, (d) maximum EDOF, and (e) maximum EDOF with contrast improvement. Simulations of the “smiley” icon are presented in column 1, while those in column 2 are for the “Ronchi-rulings” case.

Fig. 6.
Fig. 6.

Through-focus MTF curves, under the experimental condition (W20>0). Spatial frequency is normalized to the incoherent cutoff frequency (fc). (a) The filter is “off,” (b) QPM phase profile, and (c) binary phase profile. Each curve represents the systems MTF at different defocus value. (A) W20=0λ, (B) W20=0.181λ, (C) W20=0.545λ, (D) W20=0.914λ, (E) W20=1.288λ, (F) W20=1.666λ, (G) W20=2.049λ, (H) W20=2.437λ, and (I) W20=2.830λ.

Fig. 7.
Fig. 7.

Layout of the experimental setup. The USAF1951 target is illuminated by an LED that serves as an object. The imaging system is an assembly of linear polarizer, simple lens, and the tunable spatial filter. To allow defocusing, the camera is mounted on a stage with axial degree of freedom.

Fig. 8.
Fig. 8.

Different scenes of the experimental setup: (A) a general image of the experimental setup. (B) A detailed image of the part of the USAF1951 resolution target used in the experiment. (C) A front view of the SLM, lens, and polarizer assembly.

Fig. 9.
Fig. 9.

Experimental “database.” Each column contains experimental results with a different phase filter in various defocus levels. The value of W20 in each defocus is given to the left of the images. The column order from left to right is filter OFF, filter on with binary phase mask, and filter on with QPM phase mask.

Fig. 10.
Fig. 10.

Measured target contrast versus defocus with various phase masks. The “Ronchi-rulings” targets are with various periods: (a) average, (b) “Ronchi-rulings” with spatial spatial frequency=13cycles/mm, (c) “Ronchi-rulings” with spatial frequency=7.8cycles/mm, and (d) “Ronchi-ruling” with spatial frequency=5.2cycles/mm. Double size width.

Fig. 11.
Fig. 11.

Experimental results of tunable EDOF and EDOF inversion. Columns (a)–(e) present the process of successive extension of the DOF. Column f presents inverting the EDOF order. The green and red lines are visualization of the tunable EDOF and EDOF inversion, respectively.

Fig. 12.
Fig. 12.

Average target contrast versus maximum defocus aberration. The aberration for the various EDOF levels is given in λ [20].

Fig. 13.
Fig. 13.

Inverting EDOF order. Simulation results of inverting the EDOF order, using the same weight vector as in the experiments, for the two cases of (a) “smiley” and (b) “Ronchi-ruling” targets.

Equations (16)

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

δxy=κλΔz,
Φ(i)=2πλneff(V(i),z)dz.
OTF(f;ΦDF)FT2{|FT2{P(x,y)ej(Φn(x,y)+ΦDF(x,y))}|2}.
OTFT(f;ΦDF)n=1NFT2{|FT2{Pn(x,y)ej(Φn(x,y)+ΦDF(x,y))}|2},
OTF(fx,fy;ΦDF(x,y))=1TnTn·OTF(fx,fy;ΦDF(x,y),Φn(x,y)).
iWi·OTF(fx,fy;DFj,Φn(x,y))=1TiTi·OTF(fx,fy;DFj,Φn(x,y)).
OTF=function(fx,fy;DF).
ΦOFF(ri)=0,ΦQPM(ri)=2π·(ari4+bri2),ΦBinary(ri)={πifi=6,80else.
W20(DF)=D28(1SimgDF1Simg),
OTF(fx,fy;ΦDF(x,y))=iWi·OTF(fx,fy;DFj,Φn(x,y)).
PSF(x,y;ΦDF(x,y))=iWi·PSF(x,y;DFj,Φn(x,y)).
IDFj(x,y)=iWi·Ii(x,y,DFj).
0.05i=1NWiC(i,j).
C(j)=j=1MwiC(i,j)|wi{[Wa],[Wb],[Wc],[Wd],[We]}.
err(W)=argminf=1Lj=1Mi=1N(WiC(i,j,f)Ct(j,f))2.
Ct(j,f)=|0j40.05else.

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