Abstract

A digital holographic technique is implemented in a microscope for three-dimensional imaging reconstruction. The setup is a Mach–Zehnder interferometer that uses an incoherent light source to remove the coherent noise that is inherent in the laser sources. A phase-stepping technique determines the optical phase in the image plane of the microscope. Out-of-focus planes are refocused by digital holographic computations, thus considerably enlarging the depth of investigation without the need to change the optical focus mechanically. The technique can be implemented in transmission for various magnification ratios and can cover a wide range of applications. Performances and limitations of the microscope are theoretically evaluated. Experimental results for a test target are given, and examples of two applications in particle localization and investigation of biological sample are provided.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Gabor, “A new microscope principle,” Nature (London) 161, 777–778 (1948).
    [CrossRef]
  2. U. Schnars, W. Jüptner, “Direct recording of holograms by a CCD target and numeral reconstruction,” Appl. Opt. 33, 179–181 (1994).
    [CrossRef] [PubMed]
  3. T. M. Kreis, W. P. O. Jüptner, “Principle of digital holography,” in Proceedings of the Third International Workshop on Automatic Processing of Fringe Patterns (Fringe ’97), Vol. 3 of the Akademie Verlag Series in Optical Metrology (Akademie Verlag, Berlin, 1997), pp. 353–363.
  4. B. Nilsson, T. E. Carlsson, “Direct three-dimensional shape measurement by digital light-in-flight holography,” Appl. Opt. 37, 7954–7959 (1998).
    [CrossRef]
  5. E. Cuche, F. Bevilacqua, C. Depeursinge, “Digital holography for quantitative phase contrast imaging,” Opt. Lett. 24, 291–293 (1999).
    [CrossRef]
  6. I. Yamaguchi, T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
    [CrossRef] [PubMed]
  7. T. Zhang, I. Yamaguchi, “Three-dimensional microscopy with phase-shifting digital holography,” Opt. Lett. 23, 1221–1223 (1998).
    [CrossRef]
  8. D. O. Hogenboom, C. A. Dimarzio, T. J. Gaudette, A. J. Devaney, S. C. Lindberg, “Three-dimensional images generated by quadrature interferometry,” Opt. Lett. 23, 783–785 (1998).
    [CrossRef]
  9. M. Adams, T. M. Kreis, W. P. O. Jüptner, “Particle size and position measurement with digital holography,” in Optical Inspection and Micromeasurements, C. Gorecki, ed., Proc. SPIE3098, 234–240 (1998).
    [CrossRef]
  10. P. Chavel, “Optical noise and temporal coherence,” J. Opt. Soc. Am. 70, 935–943 (1980).
    [CrossRef]
  11. M. Nazarathy, J. Shamir, “Fourier optics described by operator algebra,” J. Opt. Soc. Am. 70, 150–159 (1980).
    [CrossRef]

1999 (1)

1998 (3)

1997 (1)

1994 (1)

1980 (2)

1948 (1)

D. Gabor, “A new microscope principle,” Nature (London) 161, 777–778 (1948).
[CrossRef]

Adams, M.

M. Adams, T. M. Kreis, W. P. O. Jüptner, “Particle size and position measurement with digital holography,” in Optical Inspection and Micromeasurements, C. Gorecki, ed., Proc. SPIE3098, 234–240 (1998).
[CrossRef]

Bevilacqua, F.

Carlsson, T. E.

Chavel, P.

Cuche, E.

Depeursinge, C.

Devaney, A. J.

Dimarzio, C. A.

Gabor, D.

D. Gabor, “A new microscope principle,” Nature (London) 161, 777–778 (1948).
[CrossRef]

Gaudette, T. J.

Hogenboom, D. O.

Jüptner, W.

Jüptner, W. P. O.

M. Adams, T. M. Kreis, W. P. O. Jüptner, “Particle size and position measurement with digital holography,” in Optical Inspection and Micromeasurements, C. Gorecki, ed., Proc. SPIE3098, 234–240 (1998).
[CrossRef]

T. M. Kreis, W. P. O. Jüptner, “Principle of digital holography,” in Proceedings of the Third International Workshop on Automatic Processing of Fringe Patterns (Fringe ’97), Vol. 3 of the Akademie Verlag Series in Optical Metrology (Akademie Verlag, Berlin, 1997), pp. 353–363.

Kreis, T. M.

T. M. Kreis, W. P. O. Jüptner, “Principle of digital holography,” in Proceedings of the Third International Workshop on Automatic Processing of Fringe Patterns (Fringe ’97), Vol. 3 of the Akademie Verlag Series in Optical Metrology (Akademie Verlag, Berlin, 1997), pp. 353–363.

M. Adams, T. M. Kreis, W. P. O. Jüptner, “Particle size and position measurement with digital holography,” in Optical Inspection and Micromeasurements, C. Gorecki, ed., Proc. SPIE3098, 234–240 (1998).
[CrossRef]

Lindberg, S. C.

Nazarathy, M.

Nilsson, B.

Schnars, U.

Shamir, J.

Yamaguchi, I.

Zhang, T.

Appl. Opt. (2)

J. Opt. Soc. Am. (2)

Nature (London) (1)

D. Gabor, “A new microscope principle,” Nature (London) 161, 777–778 (1948).
[CrossRef]

Opt. Lett. (4)

Other (2)

T. M. Kreis, W. P. O. Jüptner, “Principle of digital holography,” in Proceedings of the Third International Workshop on Automatic Processing of Fringe Patterns (Fringe ’97), Vol. 3 of the Akademie Verlag Series in Optical Metrology (Akademie Verlag, Berlin, 1997), pp. 353–363.

M. Adams, T. M. Kreis, W. P. O. Jüptner, “Particle size and position measurement with digital holography,” in Optical Inspection and Micromeasurements, C. Gorecki, ed., Proc. SPIE3098, 234–240 (1998).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Coordinates used for computer refocusing.

Fig. 2
Fig. 2

Refocusing resolution in a digital holography microscope as a function of magnification for two numerical apertures (NA’s). The size of pixel Δ is 10 µm.

Fig. 3
Fig. 3

Maximum refocus distance from a single complex optical field distribution as a function of magnification M. Δ = 10 µm, λ = 675 nm, N = 512.

Fig. 4
Fig. 4

Schematic of the microscope implemented in a Mach–Zehnder interferometer with a spatially partial coherent source. Abbreviations are defined in text.

Fig. 5
Fig. 5

Example of refocusing capability with a digital holography microscope on a metric scale (100 divisions/mm): (a) intensity of the defocus, (b) phase of the defocus image, (c) computer-refocused image. The refocus distance is 80 µm.

Fig. 6
Fig. 6

Computer-refocused images obtained from mechanical defocus at (a) 50 µm, (b) 80 µm, (c) 140 µm, (d) 220 µm.

Fig. 7
Fig. 7

Accuracy in the determination of focus position. Evolution of intensity on a line with increasing propagation distance. The object is focused at a propagation distance of 90 µm.

Fig. 8
Fig. 8

Localization of glass spheres in different planes with the digital holography microscope: (a) defocus image, (b) focus on one plane, backpropagation of 40 µm, (c) focus on the other plane, forward propagation of 95 µm.

Fig. 9
Fig. 9

Example of refocusing capability on an urchin larva: (a) recorded image, (b) computer refocus at 12 µm, (c) computer refocus at 40 µm.

Equations (32)

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

uox, y=expikdidλexpik2dx2+y2×Fx,y+1 expik2dx2+y2uix, y×xλd, yλd,
uox, y=expikdFvx,vy-1 exp-ikdλ22vx2+vy2×Fx,y+1uix, yvx, vyx, y,
Fαβ±1gα, βη, ξ=--exp2iπαη+βξgα, βdαdβ.
uosΔ, tΔ=expjkdN2s,t,U,V=0N-1exp-2πjNs-s×U+t-tVexp-jkλ2d2N2Δ2×U2+V2uisΔ, tΔ,
FOV=ΔN/M.
R=Δ/M.
δz=Δ/M2N.A.
kλ2d2N2Δ2Umax2-Umax-12π
kλ2dN2Δ2 Umaxπ,
dmax=±NΔ2/2λ.
ϕx, y=tan-1I4x, y-I2x, yI1x, y-I3x, y.
γx1, y1, x2, y2=I0ax1, y1ax2, y2δx1-x2δy1-y2,
V1θux1, y1=uθx1, θy1,
Q1τux1, y1=expi kτ2x12+y12ux1, y1.
F±1uα, β=Fx1,y1±1ux1, y1α, β.
uoutx1, y1=Q1-1fuinx1, y1.
uoutx1, y1=Luinx1, y1,
LSuinx1, y1=expikdF-1Q-λ2d×F+1uinx1, y1.
γoutx1, y1, x2, y2=L1L2*γinx1, y1, x2, y2.
L=exp2ikf1+f2V-f2f1Pxλf2, yλf2,
γoutx1, y1, x2, y2=Ca2f1x2f2, f1y2f2×Px1λf2, y1λf2Px2λf2, y2λf2×x2-x1, y2-y1,
γsx1, y1, x2, y2=Ca2f3f1x2f4f2, f3f1y2f4f2×Px1λf2, y1λf2Px2λf2, y2λf2×f3x2-x1f4, f3y2-y1f4,
γex1, y1, x2, y2=t*x2, y2tx1, y1×γSx1-x2, y1-y2.
γs,ex1, y1, x2, y2=LS1LS2*γex1, y1, x2, y2.
γs,ex1, y1, x2, y2=F2+1Q2λ2dF2-1F1-1Q1-λ2d×F1+1γex1, y1, x2, y2.
F2-1F1+1γeu1, v1, u2, v2= dεdηTu1-ε, v1-η×T*ε-u2, η-v2Γε, η,
γs,ex1, y1, x2, y2= dεdηΓε, ηexp2πix1-x2×ε+y1-y2η  du1dv1×exp2πix1-λdεu1+y1-λdηv1×exp-i kλ2d2u12+v12×Tu1, v1 du2dv2×exp-2πix2-λdεu2+y2-λdηv2×expi kλ2d2u22+v22Tu2, v2.
wA22λf2/D,
wS2λf2f4/Df3.
WSDf3/2λf2f4.
exp2πix1-λdεu1+y1-λdηv1×exp-2πix2-λdεu2+y2-λdηv2.
d  2f2f4Df3vmax.

Metrics