We demonstrate simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object. Subject to the assumptions explicitly stated in the derivation, the algorithm solves the twin-image problem of in-line holography and is capable of analysing data obtained using X-ray microscopy, electron microscopy, neutron microscopy or visible-light microscopy, especially as they relate to defocus and point projection methods. Our simple, robust, non-iterative and computationally efficient method is applied to data obtained using an X-ray phase contrast ultramicroscope.

Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object

We have developed a digital holographic microscope (DHM), in a transmission mode, especially dedicated to the quantitative visualization of phase objects such as living cells. The method is based on an original numerical algorithm presented in detail elsewhere [
	 Cuche
	 
	, Appl. Opt.38, 6994 (1999)]. DHM images of living cells in culture are shown for what is to our knowledge the first time. They represent the distribution of the optical path length over the cell, which has been measured with subwavelength accuracy. These DHM images are compared with those obtained by use of the widely used phase contrast and Nomarski differential interference contrast techniques.

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Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy.

We report the experimental implementation of optical diffraction tomography for quantitative 3D mapping of refractive index in live biological cells. Using a heterodyne Mach-Zehnder interferometer, we record complex field images of light transmitted through a sample with varying directions of illumination. To quantitatively reconstruct the 3D map of complex refractive index in live cells, we apply optical diffraction tomography based on the Rytov approximation. In this way, the effect of diffraction is taken into account in the reconstruction process and diffraction-free high resolution 3D images are obtained throughout the entire sample volume. The quantitative refractive index map can potentially serve as an intrinsic assay to provide the molecular concentrations without the addition of exogenous agents and also to provide a method for studying the light scattering properties of single cells.

Optical diffraction tomography for high resolution live cell imaging

In visualizing transparent biological cells and tissues, the phase contrast microscope and its related techniques have been a cornerstone of nearly every cell biology laboratory. However, phase contrast methods are inherently qualitative and lack in 3-D imaging capability. We introduce a novel tomographic microscopy for quantitative three-dimensional mapping of refractive index in live cells and tissues using a phase-shifting laser interferometric microscope with variable illumination angle.

Tomographic Phase Microscopy

By use of the Fourier decomposition of a low-coherence optical image field into two spatial components that can be controllably shifted in phase with respect to each other, a new high-transverse-resolution quantitative-phase microscope has been developed. The technique transforms a typical optical microscope into a quantitative-phase microscope, with high accuracy and a path-length sensitivity of lambda/5500, which is stable over several hours. The results obtained on epithelial and red blood cells demonstrate the potential of this instrument for quantitative investigation of the structure and dynamics associated with biological systems without sample preparation.

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F. Zernike

Papers

Phase contrast, a new method for the microscopic observation of transparent objects