Abstract

In this paper, we use two point sources to analyze the depth resolution of an optical scanning holography (OSH) system with a single-wavelength source. A dual-wavelength source is then employed to improve it, where this dual-wavelength OSH (DW-OSH) system is modeled with a linear system of equations. Object sectioning in DW-OSH is obtained with the Fourier domain conjugate gradient method. Simulation results show that, with the two source wavelengths at 543 nm and 633 nm, a depth resolution at 2.5 μm can be achieved. Furthermore, an OSH system emulator is provided to demonstrate the performance of DW-OSH compared with a conventional OSH system.

© 2011 Optical Society of America

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References

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  1. T.-C. Poon, Optical Scanning Holography with MATLAB (Springer, 2007).
  2. G. Indebetouw, “Properties of a canning holographic microscope: Improved resolution, extended depth-of-focus, and/or optical sectioning,” J. Mod. Opt. 49, 1479–1500 (2002).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  5. H. Kim, S. Min, B. Lee, and T. Poon, “Optical sectioning for optical scanning holography using phase-space filtering with Wigner distribution functions,” Appl. Opt. 47, D164–D175 (2008).
    [CrossRef]
  6. E. Y. Lam, X. Zhang, H. Vo, T. Poon, and G. Indebetouw, “Three-dimensional microscopy and sectional image reconstruction using optical scanning holography,” Appl. Opt. 48, H113–H119 (2009).
    [CrossRef]
  7. X. Zhang and E. Y. Lam, “Edge-preserving sectional image reconstruction in optical scanning holography,” J. Opt. Soc. Am. A 27, 1630–1637 (2010).
    [CrossRef]
  8. Z. Xin, K. Dobson, Y. Shinoda, and T. Poon, “Sectional image reconstruction in optical scanning holography using a random-phase pupil,” Opt. Lett. 35, 2934–2936 (2010).
    [CrossRef]
  9. X. Zhang and E. Y. Lam, “Edge detection of three-dimensional object by manipulating pupil functions in optical scanning holography system,” in IEEE International Conference on Image Processing (IEEE, 2010), pp. 3661–3664.
  10. J. Ke, P. Shankar, and M. A. Neifeld, “Distributed imaging using an array of compressive cameras,” Opt. Commun. 282, 185–197 (2009).
    [CrossRef]
  11. J. Ke, A. Ashok, and M. A. Neifeld, “Object reconstruction from adaptive compressive measurements in feature-specific imaging,” Appl. Opt. 49, H27–H39 (2010).
    [CrossRef]
  12. M. A. Neifeld and J. Ke, “Optical architectures for compressive imaging,” Appl. Opt. 46, 5293–5303 (2007).
    [CrossRef]
  13. X. Zhang, E. Y. Lam, and T. Poon, “Reconstruction of sectional images in holography using inverse imaging,” Opt. Express 16, 17215–17226 (2008).
    [CrossRef]
  14. X. Zhang and E. Y. Lam, “Sectional image reconstruction in optical scanning holography using compressed sensing, in IEEE International Conference on Image Processing (IEEE, 2010).
  15. S. H. Chan, A. K. Wong, and E. Y. Lam, “Initialization for robust inverse synthesis of phase-shifting masks in optical projection lithography,” Opt. Express 16, 14746–14760(2008).
    [CrossRef]
  16. Z. Bai and Z. Wang, “Restrictive preconditioners for conjugate gradient methods for symmetric positive definite linear systems,” J. Comput. Appl. Math. 187, 202–226 (2006).
    [CrossRef]
  17. X. Zhang, E. Y. Lam, T. Kim, Y. S. Kim, and T.-C. Poon, “Blind sectional image reconstruction for optical scanning holography,” Opt. Lett. 34, 3098–3100 (2009).
    [CrossRef]
  18. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company, 2004).
  19. J. Wilson and J. F. B. Hawkes, Optoelectronics: An Introduction (Prentice Hall, 1993).

2010 (3)

2009 (3)

2008 (3)

2007 (1)

2006 (3)

2002 (1)

G. Indebetouw, “Properties of a canning holographic microscope: Improved resolution, extended depth-of-focus, and/or optical sectioning,” J. Mod. Opt. 49, 1479–1500 (2002).
[CrossRef]

Ashok, A.

Bai, Z.

Z. Bai and Z. Wang, “Restrictive preconditioners for conjugate gradient methods for symmetric positive definite linear systems,” J. Comput. Appl. Math. 187, 202–226 (2006).
[CrossRef]

Chan, S. H.

Dobson, K.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company, 2004).

Hawkes, J. F. B.

J. Wilson and J. F. B. Hawkes, Optoelectronics: An Introduction (Prentice Hall, 1993).

Indebetouw, G.

Ke, J.

Kim, H.

Kim, T.

Kim, Y. S.

Lam, E. Y.

Lee, B.

Min, S.

Neifeld, M. A.

Poon, T.

Poon, T.-C.

Shankar, P.

J. Ke, P. Shankar, and M. A. Neifeld, “Distributed imaging using an array of compressive cameras,” Opt. Commun. 282, 185–197 (2009).
[CrossRef]

Shinoda, Y.

Vo, H.

Wang, Z.

Z. Bai and Z. Wang, “Restrictive preconditioners for conjugate gradient methods for symmetric positive definite linear systems,” J. Comput. Appl. Math. 187, 202–226 (2006).
[CrossRef]

Wilson, J.

J. Wilson and J. F. B. Hawkes, Optoelectronics: An Introduction (Prentice Hall, 1993).

Wong, A. K.

Xin, Z.

Zhang, X.

Zhong, W.

Appl. Opt. (5)

J. Comput. Appl. Math. (1)

Z. Bai and Z. Wang, “Restrictive preconditioners for conjugate gradient methods for symmetric positive definite linear systems,” J. Comput. Appl. Math. 187, 202–226 (2006).
[CrossRef]

J. Mod. Opt. (1)

G. Indebetouw, “Properties of a canning holographic microscope: Improved resolution, extended depth-of-focus, and/or optical sectioning,” J. Mod. Opt. 49, 1479–1500 (2002).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

J. Ke, P. Shankar, and M. A. Neifeld, “Distributed imaging using an array of compressive cameras,” Opt. Commun. 282, 185–197 (2009).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Other (5)

T.-C. Poon, Optical Scanning Holography with MATLAB (Springer, 2007).

X. Zhang and E. Y. Lam, “Sectional image reconstruction in optical scanning holography using compressed sensing, in IEEE International Conference on Image Processing (IEEE, 2010).

X. Zhang and E. Y. Lam, “Edge detection of three-dimensional object by manipulating pupil functions in optical scanning holography system,” in IEEE International Conference on Image Processing (IEEE, 2010), pp. 3661–3664.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company, 2004).

J. Wilson and J. F. B. Hawkes, Optoelectronics: An Introduction (Prentice Hall, 1993).

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Figures (12)

Fig. 1.
Fig. 1.

An OSH system diagram.

Fig. 2.
Fig. 2.

Function 1/[λ(z2z1)] versus z2 for λ=0.5,1,2 with z1=0.

Fig. 3.
Fig. 3.

Reconstruction signal at (x,y)=(0,0) versus z. For (a), z1=65mm, z2=75mm, and λ=550nm; for (b), z1=65mm, z2=75mm, and λ=480nm; while for (c), z1=35mm, z2=45mm, and λ=550nm.

Fig. 4.
Fig. 4.

Real part of an OSH system PSF using Eq. (1) when (a) z=35mm, (b) z=75mm. The source wavelength is λ=550nm.

Fig. 5.
Fig. 5.

Original object sections located at (a) z1 and (b) z2 planes. (c) Cosine and (d) sine holograms recorded using a source working at wavelength λ1=543nm when the measurement SNR is 40.35 dB.

Fig. 6.
Fig. 6.

Sectioning results using the conventional method with SW-OSH measurements for (a) z1 and (d) z2 planes, using BJ-RPCG method with SW-OSH measurements for (b) z1 and (e) z2 planes, and using BJ-RPCG method with DW-OSH measurements for (c) z1 and (f) z2 planes. The source wavelength for SW-OSH is λ1=543nm. The source wavelengths for DW-OSH are λ1=543nm and λ2=633nm. The measurement SNR is 40.35 dB for SW-OSH and 31.32 dB for DW-OSH.

Fig. 7.
Fig. 7.

Sectioning results for z1 and z2 planes using BJ-RPCG with DW-OSH measurements. The first row shows the results for z1 while the second row for z2. For (a) and (d), λ1=543nm, λ2=633nm, and z1=60mm; for (b) and (e), λ1=400nm, λ2=700nm, and z1=60mm; while for (c) and (f), λ1=543nm, λ2=633nm, and z1=0.1mm. The measurement SNR is 21The real part of the OSH PSF for z1 plane, where (a) λ1=543nm, λ2=633nm, and z1=60mm, (b) λ1=400nm, λ2=700nm, and z1=60mm; (c) λ1=543nm, λ2=633nm, and z1=10mm.ao-50-34-H285-g008.32 dB.

Fig. 8.
Fig. 8.

The real part of the OSH PSF for z1 plane, where (a) λ1=543nm, λ2=633nm, and z1=60mm, (b) λ1=400nm, λ2=700nm, and z1=60mm; (c) λ1=543nm, λ2=633nm, and z1=10mm.

Fig. 9.
Fig. 9.

The system diagram for one source beam (plane wave or spherical wave) propagating from the source to the detector.

Fig. 10.
Fig. 10.

(a) Ideal real and imaginary parts of an OSH system PSF using Eq. (1). The result of our simulator using Eq. (20), (b) when ropen=10mm and f=50mm; (c) when ropen=20mm and f=50mm; and (d) when ropen=20mm and f=150mm. The source wavelength is λ=543nm. The object section is located at z=100μm.

Fig. 11.
Fig. 11.

Original two object sections located at (a) z1 and (e) z2 planes with Δz=20μm. Hologram in area 50μmx, y50μm, sampled with Δs=100nm is used for reconstruction. Here shows the estimated two sections using the conventional method with SW-OSH measurements for (b) z1 and (f) z2 planes, using BJ-RPCG method with SW-OSH measurements for (c) z1 and (g) z2 planes, and using BJ-RPCG method with DW-OSH measurements for (d) z1 and (h) z2 planes. The source wavelength for SW-OSH is λ1=543nm. The source wavelengths for DW-OSH are λ1=543nm and λ2=633nm. The measurement SNR is 25.34 dB in SW-OSH and 22.31 dB in DW-OSH.

Fig. 12.
Fig. 12.

Original two object sections located at z1=100μm and z2=105μm planes. Hologram in area 100μmx, y100μm sampled with Δs=200nm is used for reconstruction. Here shows the estimated two sections using the conventional method with SW-OSH measurements for (a) z1 and (d) z2 planes, using BJ-RPCG method with SW-OSH measurements for (b) z1 and (e) z2 planes, and using BJ-RPCG method with DW-OSH measurements for (c) z1 and (f) z2 planes. The source wavelength for SW-OSH is λ1=543nm. The source wavelengths for DW-OSH are λ1=543nm and λ2=633nm. The measurement SNR is 25.29 dB in SW-OSH and 22.36 dB in DW-OSH.

Tables (1)

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Table 1. Functions and Parameters for the OSH System Simulator

Equations (24)

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h(x,y;z)=jk2πzexp{jk2z(x2+y2)},
H(kx,ky;z)=F{h(x,y;z)}=exp{jz2k(kx2+ky2)}.
g(x,y)=|O(x,y;z)|2*h(x,y;z)dz,
g(x,y)=f(x,y;z)*h(x,y;z)dz.
F{fest(x,y;z0)}=F{g(x,y)}H*(kx,ky;z0),
g(x,y)=h(xx1,yy1;z1)+h(xx2,yy2;z2).
h(xx1,yy1;z1)h*(xx2,yy2;z2)dxdy0,
fest(x,y;z1)=δ(xx1,yy1)δ(zz1)jk2π(z2z1)exp{jk2(z2z1)[(xx2)2+(yy2)2]}=δ(xx1,yy1)δ(zz1)+h(xx2,yy2;z2z1),
g(x,y)=i=1M(f(x,y;zi)*h(x,y;zi)),
F{g(x,y)}=i=1M(F{f(x,y;zi)}F{h(x,y;zi)}).
g1=H1f+n1=[H1(z1)H1(z2)H1(zM)][f(z1)f(z2)f(zM)]+n1.
g=[g1g2]=[H1(z1)H1(z2)H1(zM)H2(z1)H2(z2)H2(zM)][f(z1)f(z2)f(zM)]+[n1n2]=Hf+n,
fest=argminfHfg22+ρCf22,
(H+H+ρC+C)fest=H+g,
[i=12Hi+(z1)Hi(z1)i=12Hi+(z1)Hi(z2)i=12Hi+(z2)Hi(z1)i=12Hi+(z2)Hi(z2)]+ρC+C.
Uf(x,y)=1jλftA1(u,v)P(u+x,v+y)exp{j2πλf(ux+vy)}dudv,
Uf(x,y)=tA1(u,v)exp{j2π(uxλf+vyλf)}dudv=rJ1(2πrρ)ρ,
Uz(x,y)=exp{jkz}jλzUf(x,y)*exp{jk2z(x2+y2)}.
F{Uz(x,y)}=exp{jkz}jλzF{Uf(x,y)}F{exp{jk2z(x2+y2)}}=exp{jkz}jλz[(λf)tA1(λfx,λfy)](2πzjk)exp{jz2k[(2πx)2+(2πy)2]}=2πfexp{jkz}ktA1(x,y)exp{jz2k[(2πx)2+(2πy)2]},
tA1(x,y)={1x2+y2<r/λf0otherwise.
F{Uz*(x,y)}=2πfexp{jkz}ktA1(x,y)exp{jz2k[(2πx)2+(2πy)2]}.
OTF(x,y;z)=[F{UP(x,y)}*F{US*(x,y)}]**F{tA2(x,y)}=tP(x,y)exp{jz2k[(2πx)2+(2πy)2]}*tS(x,y)exp{jz2k[(2πx)2+(2πy)2]}*F{tA2(x,y)},
tA1(x,y)={1x2+y2<r0otherwise
tA2(x,y)={1x2+y2<rA20otherwise

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