Digital holographic microscopy for live cell applications and technical inspection

doi:10.1364/AO.47.000A52

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Digital holographic microscopy for live cell applications and technical inspection

Björn Kemper and Gert von Bally »View Author Affiliations

Applied Optics, Vol. 47, Issue 4, pp. A52-A61 (2008)
http://dx.doi.org/10.1364/AO.47.000A52

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Abstract

Digital holographic microscopy enables a quantitative phase contrast metrology that is suitable for the investigation of reflective surfaces as well as for the marker-free analysis of living cells. The digital holographic feature of (subsequent) numerical focus adjustment makes possible applications for multifocus imaging. An overview of digital holographic microscopy methods is described. Applications of digital holographic microscopy are demonstrated by results obtained from livings cells and engineered surfaces.

1. Introduction

Holography was proposed by Gabor [1

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

] as a new lensless imaging method in electron microscopy. The main progress in practical applications of holographic methods for the reconstruction of wavefronts in amplitude and phase came about with the invention of the laser as a powerful coherent light source [2

T. H. Maiman, “Stimulated optical radiation in ruby,” Nature 187, 493–494 (1960). [CrossRef]

]. The in-line arrangement that was proposed by Gabor [1

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

] originally causes object and reference waves to propagate in the same direction. This effect results in a superposition of the reconstructed object wavefront with a conjugated wavefront (virtual twin image) and the intensity of the reference wave (zero-order intensity). The separation of the real image from the twin image and the zero-order intensity by a tilt of the reference wave (off-axis geometry) proposed by Leith and Upatnieks [3

E. N. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Am. 52, 1123–1130 (1962). [CrossRef]

, 4

E. N. Leith and J. Upatnieks, “Wavefront reconstruction with continuous-tone objects,” J. Opt. Soc. Am. 53, 1377–1381 (1963). [CrossRef]

, 5

E. N. Leith and J. Upatnieks, “Wavefront reconstruction with diffused illumination and three-dimensional objects,” J. Opt. Soc. Am. 54, 1295–1301 (1964). [CrossRef]

] was the breakthrough of holography for three-dimensional imaging and represents the basics of holographic interferometric metrology [6

R. L. Powell and K. A. Stetson, “Interferometric vibration analysis by wavefront reconstruction,” J. Opt. Soc. Am. 55, 1593–1608 (1965). [CrossRef]

]. Holography and related speckle interferometric metrology are well-established tools for industrial nondestructive testing and quality control. The techniques are usually utilized by the detection of object displacements while applying static stress, temperature changes, shock waves, or vibration monitoring [7

, Interferometry by Holography , Springer Series in Optical Sciences (Springer, 1980).

, 8

, Holographic Interferometry in Experimental Mechanics , Springer Series in Optical Sciences (Springer, 1991).

, 9

M.-A. Beeck and W. Hentschel, “Laser metrology—a diagnostic tool in automotive development processes,” Opt. Lasers Eng. 34, 101–120 (2000). [CrossRef]

, 10

, Strain and Stress Analysis by Holographic and Speckle Interferometry (Wiley, 1996).

, 11

, Holographic Interferometry: Principles and Methods (Akademie Publishing, 1996).

]. Since the 1970s, holographic techniques based on Leith's off-axis arrangements have also been applied in the interdisciplinary fields of biomedicine and life sciences [12

, ed., Holography in Medicine and Biology , Springer Series in Optical Sciences (Springer, 1979).

, 13

, eds., Optics in Biomedical Sciences , Springer Series in Optical Sciences (Springer, 1982).

, 14

, “Coherent Imaging Metrology in Life Sciences and Clinical Diagnostics,” in International Trends in Applied Optics , A. H. Guenther, ed., Spie Press Monograph, Vol. PM119 (SPIE, 2002), pp. 571–608.

] as well as in new research areas such as biophotonics [15

, “New methods for marker-free live cell and tumor analysis (MIKROSO),” in Biophotonics: Visions for Better Health Care , J. Popp and M. Strehle, eds. (Wiley, 2006), pp. 301–360.

]. For biomedical applications holographic and speckle interferometric metrology opens up new perspectives for the visualization and detection of displacements and movements as these techniques can be applied nondestructively, marker free, full field (no scanning required), and online (video repetition rate). Here, e.g., for the early diagnosis of malignant tumors, it is of special interest to distinguish between different tissue elasticities, particularly in combination with endoscopic cavity inspection [16

B. Kemper, D. Dirksen, W. Avenhaus, A. Merker, and G. von Bally, “Endoscopic double-pulse electronic-speckle-pattern interferometer for technical and medical intracavity inspection,” Appl. Opt. 39, 3899–3905 (2000). [CrossRef]

, 17

S. Schedin, G. Pedrini, and H. J. Tiziani, “Pulsed digital holography for deformation measurements on biological tissues,” Appl. Opt. 39, 2853–2857 (2000). [CrossRef]

, 18

W. Avenhaus, B. Kemper, G. von Bally, and W. Domschke, “Gastric wall elasticity assessed by dynamic holographic endoscopy: ex vivo investigations in the porcine stomach,” Gastrointest. Endosc. 54, 496–500 (2001). [CrossRef] [PubMed]

]. In combination with microscopy, modern CCD sensor technology, and image processing systems, digital holography [19

, Digital Holography (Springer, 2004).

] enables high resolution, multifocus analysis of engineered surfaces, and marker-free quantitative phase contrast imaging of living cells [20

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]

, 21

C. Mann, L. Yu, C.-M. Lo, and M. Kim, “High-resolution quantitative phase-contrast microscopy by digital holography,” Opt. Express 13, 8693–8698 (2005). [CrossRef] [PubMed]

, 22

P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. 30, 468–470 (2005). [CrossRef] [PubMed]

]. With information about the integral cellular refractive index, the cell thickness and, for adherent grown cells, the cell shape can be determined from the obtained phase contrast images [22

, 23

B. Rappaz, P. Marquet, E. Cuche, Y. Emery, C. Depeursinge, and P. Magistretti, “Measurement of the integral refractive index and dynamic cell morphotometry of living cells with digital holographic microscopy,” Opt. Express 13, 9361–9373 (2005). [CrossRef] [PubMed]

, 24

B. Kemper, D. D. Carl, J. Schnekenburger, I. Bredebusch, M. Schäfer, W. Domschke, and G. von Bally, “Investigation of living pancreas tumor cells by digital holographic microscopy,” J. Biomed. Opt. 11, 034005 (2006). [CrossRef]

]. To establish digital holography as a microscopy technique, a combination with established microscopy techniques is of particular advantage [15

, “New methods for marker-free live cell and tumor analysis (MIKROSO),” in Biophotonics: Visions for Better Health Care , J. Popp and M. Strehle, eds. (Wiley, 2006), pp. 301–360.

, 25

B. Kemper, D. Carl, A. Höink, G. von Bally, I. Bredebusch, and J. Schnekenburger, “Modular digital holographic microscopy system for marker-free quantitative phase contrast imaging of living cells,” Proc. SPIE 6191, 61910T (2006). [CrossRef]

]. In connection with robust algorithms for numerical reconstruction of digital holograms and for automated evaluation of the measurement data, adaptable and compact digital holographic microscopy tools for integration into modern microscopy systems are created. In this way, new applications for quantitative live cell imaging and high resolution technical inspection are available. Digital holographic microscopy methods are described. Applications of digital holographic microscopy are illustrated by the results from livings cells and engineered surfaces that were obtained at the Laboratory of Biophysics, University of Muenster.

2. Principles of Digital Holographic Microscopy

2A. Measurement Setup

Digital holographic microscopy in off-axis arrangement is based on the classic holographic principle [3

E. N. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Am. 52, 1123–1130 (1962). [CrossRef]

] with the difference being that the hologram recording is performed by a digital sensor, e.g., a CCD or a complementary metal oxide semiconductor camera. The subsequent reconstruction of the holographic image that contains information about the object wave is carried out numerically by computer [35

U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994). [CrossRef] [PubMed]

, 19

, Digital Holography (Springer, 2004).

]. To enhance the lateral resolution, which is restricted by the pixel pitch of the applied image recording sensor, the object wave is magnified by a microscope lens [27

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]

]. Figure 1 depicts the schematics of two off-axis setups for digital holographic microscopy that are suitable for integration into commercial microscopy systems. The coherent light of a laser (frequency-doubled Nd:YAG laser,

λ = 532 nm

) is divided into object and reference waves by use of single-mode optical fibers for light guidance. The setup in Fig. 1(a) is designed for the investigation of (semi) transparent (phase) objects such as living cell cultures. Figure 1(b) shows an incident light illumination arrangement for the investigation of reflective surfaces. In both cases the coherent laser light for illumination of the sample is coupled into the optical path of the microscope's condenser by a beam splitter [25

]. The reference wave is superimposed in the hologram plane (HP) located at

z = z_{0}

with the light reflected or transmitted by the object with a slight tilt against the object wavefront. Thus, off-axis holograms are generated and recorded by a CCD camera (e.g., Sony XCD-SX900, 1280 × 960 pixels, pixel size of

4.65 μm \times 4.46 μm

or Imaging Source DMK41F02,

1280 \times 960

pixels, pixel size of

4.65 μm \times 4.46 μm

). When the sample is not imaged sharply onto the CCD sensor, the parameter

z_{IP}

denotes the distance from the HP to the image plane. After hologram acquisition the data are transmitted to a digital image processing system.

The described approach provides a modular integration of digital holographic add-on components that do not restrict the conventional functions of commercial microscopy systems. Furthermore, common microscope lenses with a high numerical aperture (NA) (e.g., water and oil immersion) can be used in combination with an optimized (Koehler-like) illumination of the sample.

2B. Amplitude and Phase Retrieval in Digital Holographic Microscopy

In quantitative digital holographic phase contrast microscopy, two aspects are of particular importance: (1) reconstruction of the object wave without zero-order intensity and a twin image and (2) consideration of the phase aberration that is effected by the divergent object wave due to the application of a microscope lens.

2B1. Elimination of Zero-Order Intensity and Twin Image

For suppression of the zero-order intensity and twin image in digital holography, several reconstruction methods have been proposed. In [28

Y. Zhang, Q. Lü, and B. Ge, “Elimination of zero-order diffraction in digital off-axis holography,” Opt. Commun. 240, 261–267 (2004). [CrossRef]

] a phase-modulated object wave is used to eliminate zero-order intensity. In [29

J. A. Herrera Ramírez and J. Garcia-Sucerquia, “Digital off-axis holography without zero-order diffraction via phase manipulation,” Opt. Commun. 277, 259–263 (2007). [CrossRef]

] a shutter based method is proposed to overcome the zero-order problem. In [30

Y. Takaki, H. Kawai, and H. Ohzu, “Hybrid holographic microscopy free of conjugate and zero-order images,” Appl. Opt. 38, 4990–4996 (1999). [CrossRef]

] shutter based methods and phase modulation techniques are applied to eliminate both zero-order intensity and a twin image. Also phase-shifting in-line holographic methods have been developed [31

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997). [CrossRef] [PubMed]

, 32

I. Yamaguchi, J. Kato, S. Ohta, and J. Mizuno, “Image formation in phase-shifting digital holography and applications to microscopy,” Appl. Opt. 40, 6177–6186 (2001). [CrossRef]

]. All these methods require the acquisition and evaluation of several holograms or intensity images and thus are applicable only restricted for the investigation of dynamic processes such as fluctuating living cells. In [33

C. Liu, Y. Li, X. Cheng, Z. Liu, F. Bo, and J. Zhu, “Elimination of zero-order diffraction in digital holography,” Opt. Eng. 41, 2434–2437 (2002). [CrossRef]

] the Laplacian of a single digitized off-axis hologram is used for suppression of zero-order intensity. Cuche et al. [34

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]

] proposed an efficient spatial filter in the Fourier domain to eliminate zero-order intensity and a twin image from a single digital hologram in combination with subsequent Fresnel propagation. Hence, the reconstructed image covers only a part of the captured data field and the image size depends on the propagation distance.

2B2. Compensation for the Wavefront Aberration between Object and Reference Waves

The setups in Figs. 1(a) and 1(b) effect divergence of the object wave versus the reference wave that has to be considered in the digital holographic reconstruction process. Thus, several methods have been developed to compensate for this aberration. Double exposure with and without an object has been used to compensate for phase aberration [36

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] [PubMed]

, 37

T. Colomb, J. Kühn, F. Charrière, C. Depeursinge, P. Marquet, and N. Aspert, “Total aberrations compensation in digital holographic microscopy with a reference conjugated hologram,” Opt. Express 14, 4300–4306 (2006). [CrossRef] [PubMed]

] and thus require recording to at least two holograms. Another method for aberration compensation by a lateral shear was proposed by Ferraro et al. [38

P. Ferraro, D. Alferi, S. De Nicola, L. De Petrocellis, A. Finizio, and G. Pierattini, “Quantitative phase-contrast microscopy by a lateral shear approach to digital holographic image reconstruction,” Opt. Lett. 31, 1405–1407 (2006). [CrossRef] [PubMed]

]. This method determines the first derivative of the phase data from one hologram and requires for the further interpretation the integration of the phase contrast data. Also polynomial models [36

, 39

L. Miccio, D. Alfieri, S. Grilli, P. Ferraro, A. Finizio, L. De Petrocellis, and S. De Nicola, “Direct full compensation of the aberrations in quantitative phase microscopy of thin objects by a single digital hologram,” Appl. Phys. Lett. 90, 041104 (2007). [CrossRef]

] have been reported to be useful to determine correct sets of reconstruction parameters that overcome even wavefront deviations that are due to lens aberrations [40

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] [PubMed]

, 41

T. Colomb, F. Montfort, J. Kühn, N. Aspert, E. Cuche, A. Marian, F. Charrière, S. Bourquin, P. Marquet, and C. Depeursinge, “Numerical parametric lens for shifting, magnification, and complete aberration compensation in digital holographic microscopy,” J. Opt. Soc. Am. A 23, 3177–3190 (2006). [CrossRef]

2B3. Application of Spatial Phase-Shifting Holography to Digital Off-Axis Holograms

Spatial phase-shifting holography has been found to be particularly suitable for use in the reconstruction of digital holograms that are recorded in off-axis geometry [20

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]

, 42

M. Liebling, T. Blu, and M. Unser, “Complex-wave retrieval from a single off-axis hologram,” J. Opt. Soc. Am. A 21, 367–377 (2004). [CrossRef]

]. This technique offers both the elimination of zero-order intensity and a twin image, as well as the compensation of aberrations of the object wavefront versus the reference wave.

The intensity distribution

I_{HP} (x, y, z_{0})

in the HP, located at

z = z_{0}

[see Figs. 1(a) and 1(b)], is formed by the interference of the object wave

O (x, y, z = z_{0})

and the reference wave

R (x, y, z = z_{0})

I_{HP} (x, y, z_{0}) = O (x, y, z_{0}) O * (x, y, z_{0}) + R (x, y, z_{0}) R * (x, y, z_{0}) + O (x, y, z_{0}) R * (x, y, z_{0}) + R (x, y, z_{0}) O * (x, y, z_{0}) = I_{O} (x, y, z_{0}) + I_{R} (x, y, z_{0}) + 2 \sqrt{I_{O} (x, y, z_{0}) I_{R} (x, y, z_{0})} \times \cos Δ ϕ_{HP} (x, y, z_{0}),

(1)

with

I_{O} = O O * = {| O |}^{2}

and

I_{R} = R R * = {| R |}^{2}

(* denotes the complex conjugate). The parameter

Δ ϕ_{HP} (x, y, z_{0}) = ϕ_{R} (x, y, z_{0}) - ϕ_{O} (x, y, z_{0})

denotes the phase difference between O and R. In the presence of a sample in the optical path of O the phase distribution represents the sum

ϕ_{O} (x, y, z_{0}) = ϕ_{O_{0}} (x, y, z_{0}) + Δ φ_{S} (x, y, z_{0})

where

ϕ_{O_{0}} (x, y, z_{0})

denotes the pure object wave phase and

Δ φ_{s} (x, y, z_{0})

is the optical path length induced by the sample. For areas without a sample,

Δ ϕ_{HP} (x, y, z_{0})

can be approximated by a mathematical model [20

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]

, 42

M. Liebling, T. Blu, and M. Unser, “Complex-wave retrieval from a single off-axis hologram,” J. Opt. Soc. Am. A 21, 367–377 (2004). [CrossRef]

Δ ϕ_{HP} (x, y, z_{0}) = ϕ_{R} (x, y, z_{0}) - ϕ_{O_{0}} (x, y, z_{0}) = 2 π (K_{x} x^{2} + K_{y} y^{2} + L_{x} x + L_{y} y) .

(2)

The parameters

K_{x}

K_{y}

in Eq. (2) describe the divergence of the object wave and the properties of the applied microscopy lens. The factors

L_{x}

L_{y}

denote the linear phase difference between O and R that is due to the off-axis geometry of the experimental setup. For quantitative phase measurements from

I_{HP} (x, y, z_{0})

the complex object wave

O (x, y, z = z_{0})

in the hologram plane is determined pixelwise by solving a set of equations that is obtained from insertion of Eq. (2) into Eq. (1). For that purpose, neighboring intensity values within a square area of, e.g.,

5 \times 5

pixels around a given hologram pixel, are considered by application of a spatial phase-shifting algorithm (for details see [20

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]

] and [42

M. Liebling, T. Blu, and M. Unser, “Complex-wave retrieval from a single off-axis hologram,” J. Opt. Soc. Am. A 21, 367–377 (2004). [CrossRef]

]). The utilized algorithm is based on the assumption that only

Δ ϕ_{HP} (x, y, z_{0}) = ϕ_{R} (x, y, z_{0}) - ϕ_{O_{0}} (x, y, z_{0})

between the object wave

O (x, y, z_{0})

and the reference wave

R (x, y, z_{0})

varies rapidly spatially in the hologram plane. In addition, because of the spatial phase-shifting algorithm, the object wave intensity must be assumed to be constant within an area of approximately 5 × 5 pixels around a given point of interest of the hologram. These requirements can be fulfilled by an adequate relation between the magnification of the microscope lens and the image recording device. Therefore, the magnifications of the microscope lenses in Fig. 1 were chosen in such a way that the smallest imaged structures of the sample, which are restricted by the resolution of the optical imaging system because of the Abbe criterion, are oversampled by the CCD sensor. In this way the lateral resolution of the reconstructed holographic phase contrast images is not decreased by the spatial phase-shifting algorithm [20

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]

The parameters

K_{x}

K_{y}

L_{x}

L_{y}

in Eq. (2) cannot be obtained directly from the geometry of the experimental setups in Figs. 1(a) and 1(b) with adequate accuracy and for this reason are adapted by an iterative fitting process in an area of the hologram without a sample [20

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]

]. As a consequence of the applied algorithms and the parameter model for the phase difference

Δ ϕ_{HP}

in Eq. (2), the resulting reconstructed holographic images do not contain the terms twin image and zero order.

The evaluation of digital holographic phase contrast images requires, corresponding to microscopy with white-light illumination, a sharply focused image of the sample. If the object is imaged sharply during the hologram recording process, spatial phase-shifting holography is similar to Hilbert phase microscopy [43

T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, “Hilbert phase microscopy for investigating fast dynamics in transparent systems,” Opt. Lett. 30, 1165–1167 (2005). [CrossRef] [PubMed]

, 44

G. Popescu, T. Ikeda, C. A. Best, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Erythrocyte structure and dynamics quantified by Hilbert phase microscopy,” J. Biomed. Opt. 10, 060 503 (2005). [CrossRef]

]. However, when the object is not imaged sharply in the HP, e.g., because of object movement, mechanical instability of the experimental setup, or thermal effects, the availability of the complex object wave provides a subsequent focus correction by propagation of

O (x, y, z_{0})

to the image plane.

2B4. Numerical Propagation of the Object Wave

The propagation of

O (x, y, z_{0})

to image plane (IP) that is located at

z_{IP} = z_{0} + Δ z

in the distance Δz to HP is carried out with the Fresnel–Kirchhoff formalism [11

, Holographic Interferometry: Principles and Methods (Akademie Publishing, 1996).

]. For Fresnel transformation based propagation [20

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]

, 22

] the size of the reconstructed holographic image depends on the propagation distance Δz. Thus, the convolution approximation of the Fresnel–Kirchhoff integral [45

T. H. Demetrakopoulos and R. Mittra, “Digital and optical reconstruction of images from suboptical diffraction patterns,” Appl. Opt. 13, 665–670 (1974). [CrossRef] [PubMed]

, 46

T. M. Kreis, M. Adams, and W. P. O. Jüptner, “Methods of digital holography: a comparison,” Proc. SPIE 3098, 224–233 (1997). [CrossRef]

] for propagation of the object wave

O (x, y, z_{0})

is applied:

O (x, y, z_{IP} = z_{0} + Δ z) = F^{- 1} {F {O (x, y, z_{0})}

\times \exp [i π λ Δ z (v^{2} + μ^{2})]} .

(3)

In Eq. (3) λ represents the wavelength, v, μ are the coordinates in the frequency domain, and

F

denotes a Fourier transformation. Equation (3) provides a constant image size during propagation. This feature is particularly suitable for the application of algorithms to determine the image definition, thus enabling digital holographic autofocus [47

F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, “Focus plane detection criteria in digital holography microscopy by amplitude analysis,” Opt. Express 14, 5895–5908 (2006). [CrossRef] [PubMed]

, 48

P. Langehanenberg, B. Kemper, and G. von Bally, “Autofocus algorithms for digital-holographic microscopy,” Proc SPIE 6633, 66330E (2007). [CrossRef]

]. In addition, even the evaluation of image plane holograms that contain sharply focused images of the sample

(Δ z \approx 0)

is possible.

For subsequent refocusing parameter Δz is chosen in such a way that the holographic amplitude image appeared sharply in correspondence to a microscopic image under white-light (bright-field) illumination. A further criterion for a sharp image of the sample is that diffraction effects appear minimized in the reconstructed data. In the special case when the image of the sample is sharply focused in the hologram plane with

Δ z = 0

and thus

z_{IP} = z_{0}

, the reconstruction process is accelerated because no propagation of O by Eq. (3) is required.

2B5. Phase Retrieval and Interpretation

From

O (x, y, z_{IP})

, in addition to the absolute amplitude

| O (x, y, z_{IP}) |

that represents the image of the sample, the phase information

Δ φ_{S} (x, y, z_{IP})

of the sample is reconstructed simultaneously:

Δ φ_{S} (x, y, z_{IP}) = ϕ_{O} (x, y, z_{IP}) - ϕ_{O_{0}} (x, y, z_{IP}) = \arctan \frac{Im {O (x, y, z_{IP})}}{Re {O (x, y, z_{IP})}} (\mod 2 π) .

(4)

After removal of the 2π ambiguity by a phase unwrapping process [11

, Holographic Interferometry: Principles and Methods (Akademie Publishing, 1996).

], the data obtained with Eq. (4) can be applied for quantitative phase contrast microscopy, which is the main topic of interest for the described experiments.

For incident light, as depicted in Fig. 1(b), the topography of specimen z _s can be calculated from the phase distribution

Δ φ_{S} (x, y, z_{IP})

[11

, Holographic Interferometry: Principles and Methods (Akademie Publishing, 1996).

z_{s} (x, y, z_{IP}) = 2 \frac{λ Δ φ_{s} (x, y, z_{IP})}{2 π} = \frac{λ}{π} Δ φ_{s} (x, y, z_{IP}),

(5)

with wavelength λ of the applied laser light.

In transmission mode, as depicted in Fig. 1(a), the measured phase information

Δ φ_{S} (x, y, z_{IP})

of a semitransparent sample is influenced by the sample thickness, by the refractive index of the sample, and by the refractive index of the surrounding medium. For live cell imaging, information about the cellular refractive index is rare. Thus, several interferometric and holographic methods for determination of the refractive index have been proposed. In [24

] a coverslip is pressed onto the cells to ensure uniform cell thickness. Afterward, the integral cellular refractive index is determined in reference to the phase changes that are effected by air inclusions. Lue et al. proposed a similar method [49

N. Lue, G. Popescu, T. Ikeda, R. R. Dasari, K. Badizadegan, and M. S. Feld, “Live cell refractometry using microfluidic devices,” Opt. Lett. 31, 2759–2761 (2006). [CrossRef] [PubMed]

] using microfluidic equipment to ensure a constant cell thickness. In [23

] the integral refractive index is determined by a decoupling procedure in which two cell culture media with slightly different refractive indices are applied. In [50

F. Charrière, A. Marian, F. Montfort, J. Kühn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Cell refractive index tomography by digital holographic microscopy,” Opt. Lett. 31, 178–180 (2006). [CrossRef] [PubMed]

] and [51

F. Charrière, N. Pavillon, T. Colomb, C. Depeursinge, T. J. Heger, E. A. D. Mitchell, P. Marquet, and B. Rappaz, “Living specimen tomography by digital holographic microscopy: morphometry of testate amoeba,” Opt. Express 14, 7005–7013 (2006). [CrossRef] [PubMed]

] a digital holographic microscopy based refractive-index tomography of cellular samples is performed by recording multiple phase contrast images of a rotated sample. However, it is not possible to perform an independent determination of the parameter thickness and refractive index in each measurement case.

For cells in a cell culture medium with refractive index

n_{medium}

and the assumption of a known homogeneously distributed integral cellular refractive index

n_{cell}

, the cell thickness

d_{cell} (x, y, z_{IP})

can be determined by measuring the optical path-length change

Δ φ_{cell}

of the cells to the surrounding medium [22

, 24

d_{cell} (x, y, z_{IP}) = \frac{λ Δ φ_{cell} (x, y, z_{IP})}{2 π} \frac{1}{n_{cell} - n_{medium}} .

(6)

For complete adherently grown cells parameter

d_{cell}

is estimated to describe the shape of single cells. Nevertheless Eq. (6) must be handled critically if, e.g., toxin and osmotically induced reactions of cells are analyzed that could effect dynamic changes of

n_{c e l l}

(see the results in Section 4 and [23

, 24

]).

2B6. Example of Hologram Reconstruction and Evaluation by Spatial Phase-Shifting Digital Holography

Figure 2 illustrates the numerical reconstruction process for the example of a digital hologram [Fig. 2(a)] of human red blood cells, recorded with a

63 \times

microscope lens

(0.75 NA)

with a transmitting light illumination arrangement

(λ = 532 nm)

as depicted in Fig. 1(a). The enlarged area in Fig. 2(a) shows a part of the carrier fringe pattern that is generated by the holographic off-axis arrangement. Figure 2(b) shows the reconstructed and propagated holographic amplitude image

| O (x, y, z_{IP}) |

of the sample. Figure 2(c) shows the simultaneously reconstructed phase information

Δ φ_{S} (x, y, z_{IP})

modulo 2π, coded to 256 gray levels. The phase distribution quantifies the variation of the optical path length that is caused by the sample in comparison with the surrounding medium. For illustrative representation as well as for further quantitative evaluation, a removal of the modulo 2π ambiguity by phase unwrapping is necessary. Figures 2(d) and 2(e) show the unwrapped phase distribution and the corresponding 256 gray level coded pseudo-three-dimensional representation. The quantitative detection of optical path-length changes (in rad) and the corresponding cell thickness, calculated with Eq. (6) for

n_{medium} = 1.337

and approximation

n_{cell} \approx 1.4

[52

P. Marquet, B. Rappaz, F. Charrière, Y. Emery, C. Depeursinge, and P. Magistretti, “Analysis of cellular structure and dynamics with digital holographic microscopy,” Proc SPIE 6633, 66330F (2007). [CrossRef]

], is demonstrated in Fig. 2(e) by a horizontal cross section through the phase data of a cell.

3. Resolution and Numerical Focus

Figure 3(a) shows the reconstructed amplitude of a negative U.S. Air Force 1951 resolution test chart (illumination in transmission), recorded with a

40 \times

microscope lens

(0.6 NA)

. In the magnified image section [Fig. 3(b)] group 9.5 (resolution limit of the test chart) is visible, representing a linewidth of

620 nm

. Comparison with the Abbe criterion shows that the lateral resolution is diffraction limited [20

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]

] (corresponding to bright-field microscopy) and can be increased by use of microscope optics with a higher NA. Figures 3(c) and 3(d) demonstrate the axial resolution for incident light illumination of a reflective metal test chart (nanostructure gold-coated surface), recorded with a

5 \times

microscope lens

(0.1 NA)

. The depicted elements represent a height of

50 nm

and are clearly resolved in the reconstructed phase distribution as well as in the corresponding pseudo-three-dimensional plot [Fig. 3(d)]. From the phase noise and Eq. (5) the axial resolution is determined to be

\approx 5 nm

; see Section 6.

The digital reconstruction of different object planes from a single hologram enables a variable numerical focus of digital holographic images without additional mechanical or optical components. Figure 4 demonstrates the digital holographic microscopy feature of subsequent numerical focus correction by variation of the propagation distance Δz in Eq. (3). Figure 4(a) shows the reconstructed holographic amplitude of a positive U.S. Air Force 1951 test chart that has been recorded slightly out of focus in a transmission mode (40× microscope lens, 0.6 NA) at

Δ z = 0

. The corresponding sharply refocused holographic amplitude is shown in Fig. 4(b). Figures 4(c) and 4(d) present respective results obtained from investigation of a living human pancreas carcinoma cell (Patu8988S, [24

, 53

H. P. Elsässer, U. Lehr, B. Agricola, and H. F. Kern, “Establishment and characterization of two cell lines with different grade of differentiation derived from one primary human pancreatic adenocarcinoma,” Virchows Arch. B. Cell Pathol. Incl. Mol. Pathol. 61, 295–306 (1992). [CrossRef] [PubMed]

, 54

J. Schnekenburger, J. Mayerle, B. Krüger, I. Buchwalow, F. U. Weiss, E. Albrecht, V. E. Samoilova, W. Domschke, and M. M. Lerch, “Protein tyrosine phosphatase κ and SHP-1 are involved in the regulation of cell–cell contacts at adherens junctions in the exocrine pancreas,” Gut 54, 1445–1455 (2005). [CrossRef] [PubMed]

]) (transmission mode, 100× oil immersion microscope lens, 1.3 NA). The nontransparent structures of the U.S. Air Force chart (amplitude object) appear in focus with sharp edges while the cell that represents an almost pure phase object is imaged with minimal contrast. These criteria can be considered for the implementation of digital holographic autofocus functions [47

, 48

P. Langehanenberg, B. Kemper, and G. von Bally, “Autofocus algorithms for digital-holographic microscopy,” Proc SPIE 6633, 66330E (2007). [CrossRef]

, 55

M. Liebling and M. Unser, “Autofocus for digital Fresnel holograms by use of a Fresnelet-sparsity criterion,” J. Opt. Soc. Am. A 21, 2424–2430 (2004). [CrossRef]

]. The advantage of subsequent digital holographic focus correction is the avoidance of a mechanical focus adaptation that is particularly convenient, e.g., for long-term measurements on living cell specimens and for automated measurements.

Figure 5 demonstrates the requirement of a digital holographic focus alignment for the retrieval of optimized phase contrast data for a pancreas tumor cell (Patu8988T, [24

]) in suspension (

63 \times

microscope lens,

0.75 NA

) that was recorded out of focus. The amplitude and phase contrast images in Fig. 5 have been reconstructed for propagation distances in the range from

Δ z = 0

12.9 cm

(left column, amplitude image

| O (x, y, Δ z) |

; middle column, phase contrast image

Δ φ_{S} (x, y, Δ z)

modulo 2π; right column, unwrapped phase data). The unfocused phase contrast images contain unwrapping errors and diffraction artifacts that appear significantly reduced for the refocused image while the corresponding amplitude appears with minimal contrast.

4. Dynamic Live Cell Analysis

In connection with time-lapse recording, digital holographic microscopy facilitates dynamic quantitative phase contrast imaging and analysis of living cells. The hologram capture time depends on the available output power of the laser and the photosensitivity of the CCD image sensor (typically in the millisecond range). The time interval between the acquisition of two digital holograms is restricted by the acquisition rate of the image recording sensor. Investigation of living pancreas tumor cells (Patu8988T) were carried out to demonstrate the potential of digital holographic microscopy for the visualization of drug-induced morphology changes. Therefore, the tumor cells were exposed to an anticancer drug (Taxol). Digital holograms of selected cells were recorded continuously every 120 s over 16 h in a temperature-stabilized environment

(T = 37 ° C)

with an inverse digital holographic microscopy setup as shown in Fig. 1(b). Figure 6 shows the results for the unwrapped digital holographic phase distributions

Δ φ_{S} (x, y, z_{IP})

t = 0

t = 3.5 h

t = 5 h

t = 8.3 h

and

t = 14.2 h

after the addition of Taxol. The temporal dependence of the maximum phase contrast

Δ φ_{S,max}

for the cells denoted A, B, and C in Fig. 6 as well as the corresponding cell thickness obtained from Eq. (6) (

n_{medium} = 1.337

and

n_{cell} = 1.38

[24

λ = 532 nm

) are depicted in Fig. 7. Figure 8 shows cross sections through the measured optical path-length changes for cell C (dashed white lines in Fig. 6) and the corresponding cell thickness

d_{cell}

. From Figs. 6–8 it is clearly obvious, that Taxol first induces morphological changes as well as cell rounding that effects an increase in cell thickness. Afterward, for all the specimens, the final cell collapse is detected precisely by a significant decrease of the phase contrast (see temporal dependence of

Δ φ_{S,max}

in Fig. 7).

5. Characterization of Engineered Surfaces

Figure 9 demonstrates the application of digital holographic microscopy on engineered surfaces. The experiments were carried out in an incident light arrangement [see Fig. 1(b)]. Figures 9(a)–9(c) show the results obtained from the topography detection of the silicon surface of an integrated circuit (

20 \times

microscope lens, 0.4 NA,

λ = 532 nm

). Figure 9(a) depicts the obtained unwrapped phase distribution; Fig. 9(b) represents the corresponding rendered pseudo-three-dimensional representation of the phase data; Fig. 9(c) shows a cross section through the obtained topography data calculated by Eq. (5) along the dashed line in Fig. 9(a). Figures 9(d)–9(f) show, in analogy to Figs. 9(a)–9(c), results from a microstructured silicon surface (

5 \times

microscope lens, 0.1 NA,

λ = 532 nm

). From the noise of the phase data and Eq. (5), corresponding to the results shown in Fig. 3, a mean resolution of

\approx 5 nm

was obtained.

6. Discussion and Conclusions

The results described in Section 3 demonstrate that the subsequent numerical focus adjustment reduces unwrapping artifacts that are caused by diffraction patterns in defocused phase contrast images. For investigation of suspension cells this feature is of particular advantage because cells in different focal planes can be investigated by the evaluation of a single captured hologram.

The results in Section 4 show that digital holographic phase contrast microscopy can be applied for quantitative long-term observation of living cells. Because of the assumption of a constant refractive index of the cells, near and after the cell collapse, the values for cell thickness calculated from the phase measurements in Figs. 7 and 8 must be handled carefully. Here, more precise information can be obtained by refractive-index decoupling as reported by Rappaz et al. [23

]. However, the information shows new ways for marker-free dynamic monitoring of cell morphology changes to access new parameters, e.g., for quantitative observation of the time-dependent reactions of cells to drugs.

The value for the axial resolution on engineered surfaces

(\approx 5 nm)

that is described in Section 5 depends on the phase noise and is typical for the applied measurement setup. The phase noise includes different sources: parasitic interferences caused by internal reflections in the optical setup and the CCD sensor window; shot noise [56

F. Charrière, T. Colomb, F. Montfort, E. Cuche, P. Marquet, and C. Depeursinge, “Shot-noise influence on the reconstructed phase image signal-to-noise ratio in digital holographic microscopy,” Appl. Opt. 45, 7667–7673 (2006). [CrossRef] [PubMed]

], and the electronic pattern of the CCD camera [57

F. Charrière, B. Rappaz, J. Kühn, T. Colomb, P. Marquet, and C. Depeursinge, “Influence of shot noise on phase measurement accuracy in digital holographic microscopy,” Opt. Express 15, 8818–8831 (2007). [CrossRef] [PubMed]

]. In addition, for investigation of cells, the scattering properties of the cell culture medium and the optical quality of the cell handling equipment (e.g., glass carrier, coverslip, or Petri dishes) must be considered. A further decrease of the phase noise is expected by suppression of disturbing interference patterns in the experimental setup that represents the predominant noise in the reconstructed amplitude and phase distributions, e.g., by application of polarization optics or by short coherence length sources.

In summary, the presented results demonstrate that digital holographic microscopy can be applied for noncontact, marker-free, and quantitative phase contrast imaging. The method allows a high resolution multifocus reconstruction of amplitude and phase data from single recorded digital holograms. It enables hologram capture time in the millisecond range. The hologram acquisition rate is limited by a digital recording device. Although the method does not reach the resolution of atomic force microscopy, scanning optical near-field microscopy, or scanning electron microscopy, it does overcome some of the limitations of these techniques, e.g., the scanning process or the requirement of fixed cells in a vacuum.

For technical applications topography detection with nanometer resolution in the axial direction is enabled. Thus new ways for use in the analysis of microelectromechanical systems (MEMS), micro-optoelectromechanical systems (MOEMS), and micro-optics as well as for defect recognition are opened up. In life science applications, e.g., in combination with fluorescence microscopy [15

, “New methods for marker-free live cell and tumor analysis (MIKROSO),” in Biophotonics: Visions for Better Health Care , J. Popp and M. Strehle, eds. (Wiley, 2006), pp. 301–360.

, 26

Y. Park, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Diffraction phase and fluorescence microscopy,” Opt. Express 14, 8263–8268 (2006). [CrossRef] [PubMed]

], new possibilities for multifunctional microscopy systems for imaging and analysis of living cells are available. In conclusion, the digital holographic microscopy techniques represent a useful extension to established microscopy techniques, with the advantage that a simultaneous, dynamic, marker-free, nondestructive and full-field topography or morphology analysis is possible. In this way, the presented methods have the potential to form versatile tools for microscopy applications in the life sciences, biophotonics, and technical surface inspection.

Acknowledgments

The authors acknowledge financial support from the German Federal Ministry of Education and Research (BMBF) within the Biophotonics research program. We are grateful to Carl Zeiss Jena GmbH, Germany, and P.A.L.M. Microlaser Technologies GmbH, Bernried, Germany, for their cooperation. Additionally, the authors particularly acknowledge the support of Patrik Langehanenberg. The authors also thank Jürgen Schnekenburger and Ilona Bredebusch from the Department of Medicine B of the University of Muenster, Germany, for their cooperation during the live cell analysis experiments.

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Fig. 1 (Color online) Schematic of digital holographic microscopy: (a) inverse transmission setup and (b) incident light (reflective) setup; HP at

z = z_{0}

;

z_{IP}

, image plane; Δz, propagation distance.

Fig. 2 (a) Digital hologram of living human erythrocytes (human red blood cells); the enlarged area shows a part of the carrier fringe pattern that is generated by the holographic off-axis arrangement. (b) Reconstructed holographic amplitude image; (c) reconstructed phase contrast image modulo 2π; (d) unwrapped phase distribution; (e) pseudo-three-dimensional representation of the phase distribution with a cross section through a cell.

Fig. 3 (a) Digital holographic reconstructed amplitude image of a negative U.S. Air Force 1951 resolution test chart recorded with a

40 \times

microscope lens

(0.6 NA)

; (b) enlarged area of (a); (c) topography calculated from the phase distribution of a nanostructured gold-coated surface (pure phase object, cooperation: Nano+Bio Center Technical University, Kaiserslautern, Germany); (d) 256 gray level coded pseudo-three-dimensional representation of the phase data in (c).

Fig. 4 (a) Amplitude in the hologram plane reconstructed from a slightly out-of-focus recorded hologram of a semitransparent U.S. Air Force 1951 test chart (illumination in transmission, 40× microscope optic,

0.6 NA

); (b) numerically refocused holographic amplitude reconstructed by variation of the propagation distance; (c), (d) corresponding results obtained from investigation of a living adherent grown human pancreas tumor cell (Patu8988S) in culture medium (

100 \times

oil immersion microscope lens,

1.3 NA

Fig. 5 Reconstruction of a spherical living pancreas tumor cell (Patu8988T) in suspension (

63 \times

microscope lens,

0.75 NA

) for different focal planes and propagation distances Δz. Left column, amplitude images; middle column, phase distributions modulo 2π; right, unwrapped phase contrast images.

Fig. 6 Monitoring of living PaTu8988T cells after the addition of Taxol to the cell culture medium. Gray level coded unwrapped phase distributions at

t = 0

t = 3.5 h

t = 8.3 h

, and

t = 14.2 h

after the addition of Taxol.

Fig. 7 Temporal dependence of the maximum phase contrast

Δ φ_{s, \max}

and related cell thickness

d_{c e l l}

for the cells that are marked in Fig. 6 by A, B, C.

Fig. 8 Cross sections through the phase data

Δ φ_{s}

marked by dashed white lines in Fig. 6 and corresponding cell thickness

d_{cell}

Fig. 9 Characterization of engineered surfaces (incident light arrangement): (a)–(c) topography measurement of a silicon sensor (

25 \times

microscope lens,

0.4 NA

). (a) Unwrapped phase distribution coded to 256 gray levels; (b) rendered pseudo-three-dimensional representation of (a); (c) profile calculated from the cross section that is marked in (a) by a dashed line. (d)–(f) Topography measurement of a reflective microstructured silicon surface: (d) unwrapped phase distribution coded to 256 gray levels; (e) rendered pseudo-three-dimensional representation of (d); (f) profile calculated from the cross section that is marked in (d) by a dotted line.

OCIS Codes
(090.0090) Holography : Holography
(180.6900) Microscopy : Three-dimensional microscopy

History
Original Manuscript: May 8, 2007
Revised Manuscript: September 5, 2007
Manuscript Accepted: September 7, 2007
Published: October 26, 2007

Virtual Issues
Vol. 3, Iss. 3 Virtual Journal for Biomedical Optics

Citation
Björn Kemper and Gert von Bally, "Digital holographic microscopy for live cell applications and technical inspection," Appl. Opt. 47, A52-A61 (2008)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-47-4-A52

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