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Imaging in digital holographic microscopy

Shan Shan Kou and Colin J. R. Sheppard

Open Access Open Access

Abstract

We present a theoretical formalism for three dimensional (3D) imaging properties of digital holographic microscopy (DHM). Through frequency analysis and visualization of its 3D optical transfer function, an assessment of the imaging behavior of DHM is given. The results are compared with those from other types of interference microscopy. Digital holographic microscopy does not result in true 3D imaging. The main advantage of holographic microscopy lies in its quick acquisition of a single 2D image. Full 3D imaging can be obtained with DHM using a broad-band source or tomographic reconstruction.

©2007 Optical Society of America

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Figures (8)
Fig. 1.
Fig. 1. 3D Spatial frequency cutoffs in holographic microscopy for (a) transmission mode, and (b) reflection mode. m and s are normalized spatial frequencies in transverse and axial directions respectively as defined in section 3.2.

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Fig. 2.
Fig. 2. Spatial frequency cutoffs in interference microscopes for (a) conventional interference, and (b) confocal interference.

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Fig. 3.
Fig. 3. Spatial frequency cutoffs in holographic microscope for an on-axis configuration (a) and an off-axis configuration (b).

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Fig. 4.
Fig. 4. Basic configuration of the DHM in (a) transmission or (b) reflection mode. BS1, BS2, beam splitters; M1, M2, mirrors; MO, microscope objective; S, sample.

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Fig. 5.
Fig. 5. CTF for holographic microscope at α 0 = π/3 for (a) transmission and (b) reflection mode.

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Fig. 6.
Fig. 6. Spatial frequency cutoffs of low-coherence holographic microscope with a range of k numbers from k2 to k1 in (a) transmission and (b) reflection mode.

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Fig. 7.
Fig. 7. Low-coherence CTF for holographic reflection microscope with (a) Gaussian gating and (b) gating using the modified spectral distribution at α 0 = π/3.

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Fig. 8.
Fig. 8. Spatial frequency coverage representation through tomography. (a) rotation of illumination (b) rotation of object.

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Equations (13)

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t ( r ) = ∣ O ( r ) + R ( r ) ∣ 2
= ∣ O ( r ) ∣ 2 + ∣ R ( r ) ∣ 2 + O ( r ) R * ( r ) + O * ( r ) R ( r ) ,
h ( v , u ) = ∫ 0 α 0 P ( θ ) J 0 ( v sin θ sin α 0 ) exp [ − iu cos θ 4 sin 2 ( α 0 2 ) ] sin θ dθ ,
v = kr sin α 0 ,
u = 4 kz sin 2 ( α 0 2 ) ,
l = ( m 2 + n 2 ) 1 2 .
c ( l , s ) = ∫ − ∞ ∞ ∫ 0 ∞ ∫ 0 α 0 P ( θ ) J 0 ( v sin θ sin α 0 ) exp [ − iu cos θ 4 sin 2 ( α 0 2 ) ] sin θ dθ
× J 0 ( 2 πlr ) exp ( − 2 πizs ) 2 πr d r dz .
c ( l , s ) = δ ( s + k ∓ k 2 − l 2 ) P ( θ ) .
c ( l , s ) = δ ( s + k ∓ k 2 − l 2 ) ( 1 − l 2 k 2 ) 1 4 ,
c poly ( l , s ) = ∫ exp ( − A ( k − k 0 ) 2 ) c ( l , s ) d k .
c poly ( l , s ) = ( k 2 − l 2 k ) 1 2 exp [ − A ( s 2 + l 2 2 s + k 0 ) 2 ] .
f ( k ) = 1 β Γ ( ρ ) ( k − α β ) ρ − 1 exp ( − k − α β ) ,
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