Abstract

The utilization of microscope objectives (MOs) in digital holographic microscopy (DHM) has associated effects that are not present in conventional optical microscopy. The remaining phase curvature, which can ruin the quantitative phase imaging, is the most evident and analyzed. As phase imaging is considered, this interest has made possible the development of different methods of overcoming its undesired consequences. Additionally to the effects in phase imaging, there exist a set of less obvious conditions that have to be accounted for as MOs are utilized in DHM to achieve diffraction-limit operation. These conditions have to be considered even in the case in which only amplitude or intensity imaging is of interest. In this paper, a thorough analysis of the physical parameters that control the appropriate utilization of MOs in DHM is presented. A regular DHM system is theoretically modeled on the basis of the imaging theory. The Fourier spectrum of the recorded hologram is analyzed to evaluate the performance of the DHM. A set of the criteria that consider the microscope features and the recording parameters to achieve DHM operation at the diffraction limit is derived. Numerical modeling and experimental results are shown to validate our findings.

© 2014 Optical Society of America

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References

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2014

2013

2012

2011

2010

2009

2008

P. Picart and J. Leval, “General theoretical formulation of image formation in digital Fresnel holography,” J. Opt. Soc. Am. A 25, 1744–1761 (2008).
[CrossRef]

S. Seo, T. W. Su, A. Erlinger, and A. Ozcan, “Multi-color LUCAS: lensfree on-chip cytometry using tunable monochromatic illumination and digital noise reduction,” Cell. Molec. Bioeng. 1, 146–156 (2008).

2006

2005

2004

2003

2002

T. M. Kreis, “Frequency analysis of digital holography,” Opt. Eng. 41, 771–778 (2002).
[CrossRef]

2000

1999

Alfieri, D.

Andrés, P.

Aspert, N.

Asundi, A.

Atlan, M.

Bourquin, S.

Carl, D.

Charrière, F.

Cheong, F. C.

Choi, Y. S.

Claus, D.

Colomb, T.

Coppola, G.

Cuche, E.

De Nicola, S.

Depeursinge, C.

Doblas, A.

Erlinger, A.

S. Seo, T. W. Su, A. Erlinger, and A. Ozcan, “Multi-color LUCAS: lensfree on-chip cytometry using tunable monochromatic illumination and digital noise reduction,” Cell. Molec. Bioeng. 1, 146–156 (2008).

Ferraro, P.

Finizio, A.

Garcia-Sucerquia, J.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts, 2005).

Grier, D. G.

Grilli, S.

Guo, Z.

Healy, J. J.

D. P. Kelly, J. J. Healy, B. M. Hennelly, and J. T. Sheridan, “Quantifying the 2.5D imaging performance of digital holographic systems,” J. Eur. Opt. Soc. Rapid Pub. 6, 11034 (2011).
[CrossRef]

Hennelly, B. M.

D. P. Kelly, J. J. Healy, B. M. Hennelly, and J. T. Sheridan, “Quantifying the 2.5D imaging performance of digital holographic systems,” J. Eur. Opt. Soc. Rapid Pub. 6, 11034 (2011).
[CrossRef]

Iliescu, D.

Kelly, D. P.

D. P. Kelly, J. J. Healy, B. M. Hennelly, and J. T. Sheridan, “Quantifying the 2.5D imaging performance of digital holographic systems,” J. Eur. Opt. Soc. Rapid Pub. 6, 11034 (2011).
[CrossRef]

Kemper, B.

Kim, M.

Kim, M. K.

Kreis, T.

T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley-VCH, 2005).

Kreis, T. M.

T. M. Kreis, “Frequency analysis of digital holography,” Opt. Eng. 41, 771–778 (2002).
[CrossRef]

Krishnatreya, B. J.

Kühn, J.

Lee, S. J.

Leval, J.

Lo, C.-M.

Magro, C.

Mann, C.

Marian, A.

Marquet, P.

Martínez-Corral, M.

Miao, J.

Montfort, F.

Ozcan, A.

S. Seo, T. W. Su, A. Erlinger, and A. Ozcan, “Multi-color LUCAS: lensfree on-chip cytometry using tunable monochromatic illumination and digital noise reduction,” Cell. Molec. Bioeng. 1, 146–156 (2008).

Pavillon, N.

Peng, X.

Picart, P.

Pierattini, G.

Saavedra, G.

Sánchez-Ortiga, E.

Seelamantula, C. S.

Seo, E. S.

Seo, K. W.

Seo, S.

S. Seo, T. W. Su, A. Erlinger, and A. Ozcan, “Multi-color LUCAS: lensfree on-chip cytometry using tunable monochromatic illumination and digital noise reduction,” Cell. Molec. Bioeng. 1, 146–156 (2008).

Sheridan, J. T.

D. P. Kelly, J. J. Healy, B. M. Hennelly, and J. T. Sheridan, “Quantifying the 2.5D imaging performance of digital holographic systems,” J. Eur. Opt. Soc. Rapid Pub. 6, 11034 (2011).
[CrossRef]

Su, T. W.

S. Seo, T. W. Su, A. Erlinger, and A. Ozcan, “Multi-color LUCAS: lensfree on-chip cytometry using tunable monochromatic illumination and digital noise reduction,” Cell. Molec. Bioeng. 1, 146–156 (2008).

Unser, M.

Verrier, N.

von Bally, G.

Wernicke, G.

Xu, L.

Yu, L.

Appl. Opt.

E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994–7001 (1999).
[CrossRef]

E. Cuche, P. Marquet, and C. Depeursinge, “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography,” Appl. Opt. 39, 4070–4075 (2000).
[CrossRef]

P. Ferraro, S. De Nicola, A. Finizio, G. Coppola, S. Grilli, C. Magro, and G. Pierattini, “Compensation of the inherent wave front curvature in digital holographic coherent microscopy for quantitative phase-contrast imaging,” Appl. Opt. 42, 1938–1946 (2003).
[CrossRef]

D. Carl, B. Kemper, G. Wernicke, and G. von Bally, “Parameter-optimized digital holographic microscope for high-resolution living-cell analysis,” Appl. Opt. 43, 6536–6544 (2004).
[CrossRef]

T. Colomb, E. Cuche, F. Charrière, J. Kühn, N. Aspert, F. Montfort, P. Marquet, and C. Depeursinge, “Automatic procedure for aberration compensation in digital holographic microscopy and applications to specimen shape compensation,” Appl. Opt. 45, 851–863 (2006).
[CrossRef]

N. Pavillon, C. S. Seelamantula, J. Kühn, M. Unser, and C. Depeursinge, “Suppression of the zero-order term in off-axis digital holography through nonlinear filtering,” Appl. Opt. 48, H186–H195 (2009).
[CrossRef]

N. Verrier and M. Atlan, “Off-axis digital hologram reconstruction: some practical considerations,” Appl. Opt. 50, H136–H146 (2011).
[CrossRef]

D. Claus and D. Iliescu, “Optical parameters and space-bandwidth product optimization in digital holographic microscopy,” Appl. Opt. 52, A410–A422 (2013).
[CrossRef]

Cell. Molec. Bioeng.

S. Seo, T. W. Su, A. Erlinger, and A. Ozcan, “Multi-color LUCAS: lensfree on-chip cytometry using tunable monochromatic illumination and digital noise reduction,” Cell. Molec. Bioeng. 1, 146–156 (2008).

J. Eur. Opt. Soc. Rapid Pub.

D. P. Kelly, J. J. Healy, B. M. Hennelly, and J. T. Sheridan, “Quantifying the 2.5D imaging performance of digital holographic systems,” J. Eur. Opt. Soc. Rapid Pub. 6, 11034 (2011).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

T. M. Kreis, “Frequency analysis of digital holography,” Opt. Eng. 41, 771–778 (2002).
[CrossRef]

Opt. Express

Opt. Lett.

Other

J. W. Goodman, Introduction to Fourier Optics (Roberts, 2005).

M. Martínez-Corral and G. Saavedra, “The resolution challenge in 3D optical microscopy,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2009), Chap. 1, pp. 1–67.

T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley-VCH, 2005).

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Figures (7)

Fig. 1.
Fig. 1.

Scheme of the off-axis DHM setup in transmission mode used in this work.

Fig. 2.
Fig. 2.

Fourier transform of the digital hologram. The sizes and shapes of diffraction orders are illustrated. The DC diffraction order is placed at the center of the Fourier spectrum of the digital hologram; its size indicates the achievable resolution of the DHM. The shape and size of the +1 and 1 diffraction orders are controlled by the value of the wavefront curvature C. The solid lines correspond to the TM operation. The dotted/dashed lines are both for the nontelecentric mode (NTM) with different values of C.

Fig. 3.
Fig. 3.

Spectrum of modeled digital holograms of a USAF test target for (a) telecentric mode, C, and (b) NTM, spherically phase distorted case for C=266mm (d=50mm and fTL=200mm). See text for further details.

Fig. 4.
Fig. 4.

Spreading of the +1 diffraction orders as the value of C changes. (a) shows the results from computer modeling. The experimental results are shown in (b). The behavior is identical for the 1 diffraction order.

Fig. 5.
Fig. 5.

Variation of ρNTM/ρTM as a function of 1/C. The plot is illustrated for λ=632.8nm and different numbers of pixels and pixel sizes.

Fig. 6.
Fig. 6.

DHM operating at diffraction limit for different modes of operation. Fourier spectrum of the recorded hologram at the left-hand side and a zoomed view of the corresponding reconstruction image at the right-hand side. (a) corresponds to TM. (b) and (c) are for nontelecentric operation of the DHM.

Fig. 7.
Fig. 7.

DHM operating at diffraction limit applied to a biological sample. Fourier spectrum of the recorded hologram at the left-hand side and the corresponding reconstruction image at the right-hand side. (a) corresponds to TM. (b) and (c) are for nontelecentric operation of the DHM.

Equations (22)

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Up(x)=exp(i2kfMO)iλfMOO˜(xλfMO)p(x),
U(x)=1λ2fMOfTLexp(ikL0)exp(ik1d/fTL2fTL(|x|2))R2dxO˜(x0λfMO)p(x0)exp(i2πλfTL(x0x)),
U(x)=1Mexp(ikL0)exp(ik2C|x|2){O(xM)p˜(xλfTL)},
Iz(x)=|Uz(x)|2+|R(x)|2+Uz(x)R*(x)+Uz*(x)R(x),
Uz(x)=iλzexp(ikz)U(x)exp[ik2z|x|2].
I˜z(u)=DC(u)+U˜z(u)δ(u+k)+U˜z*(u)δ(uk),
DC(u)=I{|Uz(x)|2+|R(x)|2}
ϕmax=λ2Δp,
U˜z(u)=U˜(u)exp[iπλz|u|2],
U˜(u)=[exp(iπλC|u|2){O˜(Mu)p(λfTLu)}].
DC(u)=δ(u)+{O˜(Mu)p(λf2u)}{O˜(Mu)p(λf2u)}*,
U˜z(u,C)={O˜(Mu)p(λf2u)}exp[iπλz|u|2].
p(λfTLu)=circ(λfTLr|u|).
D=2ρTM(3+2).
ρTM12(2+3)Δp,
NAMλ2(2+3)Δp.
NAM22π3sinϕ,
sin1(322πNAM)ϕλ2Δp.
U˜z(u)=exp(iπλ(C+z)|u|2)I(rect(u0/Δu)exp(iπλC|u0|2))u0=λCu.
Δu=N2Δp2(C+z)λC2Δu0.
Δu=N2Δp2λCΔu0.
|kNTM|22(1ΔpNΔpλC).

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