A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

This article describes the principles and major applications of digital recording and numerical reconstruction of holograms (digital holography). Digital holography became feasible since charged coupled devices (CCDs) with suitable numbers and sizes of pixels and computers with sufficient speed became available. The Fresnel or Fourier holograms are recorded directly by the CCD and stored digitally. No film material involving wet-chemical or other processing is necessary. The reconstruction of the wavefield, which is done optically by illumination of a hologram, is performed by numerical methods. The numerical reconstruction process is based on the Fresnel–Kirchhoff integral, which describes the diffraction of the reconstructing wave at the micro-structure of the hologram. In the numerical reconstruction process not only the intensity, but also the phase distribution of the stored wavefield can be computed from the digital hologram. This offers new possibilities for a variety of applications. Digital holography is applied to measure shape and surface deformation of opaque bodies and refractive index fields within transparent media. Further applications are imaging and microscopy, where it is advantageous to refocus the area under investigation by numerical methods.

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Digital recording and numerical reconstruction of holograms

Digital holography is an emerging field of new paradigm in general imaging applications. We present a review of a subset of the research and development activities in digital holography, with emphasis on microscopy techniques and applications. First, the basic results from the general theory of holography, based on the scalar diffraction theory, are summarized, and a general description of the digital holographic microscopy process is given, including quantitative phase microscopy. Several numerical diffraction methods are described and compared, and a number of representative configurations used in digital holography are described, including off-axis Fresnel, Fourier, image plane, in-line, Gabor, and phase-shifting digital holographies. Then we survey numerical techniques that give rise to unique capabilities of digital holography, including suppression of dc and twin image terms, pixel resolution control, optical phase unwrapping, aberration compensation, and others. A survey is also given of representative application areas, including biomedical microscopy, particle field holography, micrometrology, and holographic tomography, as well as some of the special techniques, such as holography of total internal reflection, optical scanning holography, digital interference holography, and heterodyne holography. The review is intended for students and new researchers interested in developing new techniques and exploring new applications of digital holography.

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Principles and techniques of digital holographic microscopy

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.

Digital holographic microscopy for live cell applications and technical inspection

An approach is proposed for removing the wave front curvature introduced by the microscope imaging objective in digital holography, which otherwise hinders the phase contrast imaging at reconstruction planes. The unwanted curvature is compensated by evaluating a correcting wave front at the hologram plane with no need for knowledge of the optical parameters, focal length of the imaging lens, or distances in the setup. Most importantly it is shown that a correction effect can be obtained at all reconstruction planes. Three different methods have been applied to evaluate the correction wave front and the methods are discussed in detail. The proposed approach is demonstrated by applying digital holography as a method of coherent microscopy for imaging amplitude and phase contrast of microstructures.

Compensation of the inherent wave front curvature in digital holographic coherent microscopy for quantitative phase-contrast imaging

In microscopy, high magnifications are achievable for investigating micro-objects but the paradigm is that higher is the required magnification, lower is the depth of focus. For an object having a three-dimensional (3D) complex shape only a portion of it appears in good focus to the observer who is essentially looking at a single image plane. Actually, two approaches exist to obtain an extended focused image, both having severe limitations since the first requires mechanical scanning while the other one requires specially designed optics. We demonstrate that an extended focused image of an object can be obtained through digital holography without any mechanical scanning or special optical components. The conceptual novelty of the proposed approach lies in the fact that it is possible to completely exploit the unique feature of DH in extracting all the information content stored in hologram, amplitude and phase, to extend the depth of focus.

Extended focused image in microscopy by digital Holography.

A method for controlling the size of amplitude and phase images reconstructed from digital holograms by the Fresnel-transform method is proposed and demonstrated. The method can provide a constant reconstruction pixel width in the reconstructed image plane, independent of the recording and reconstruction distance. The proposed method makes it possible to maintain the size of an object for a sequence of digital holograms recorded at different distances and, therefore, to subtract phase maps for an object recorded at different distances. Furthermore, the method solves the problem of superimposition in multiwavelength digital holography for color display and holographic interferometry applications.

Controlling image size as a function of distance and wavelength in Fresnel-transform reconstruction of digital holograms

We propose a new method for focus tracking during the recording of a sequence of digital holograms while the sample experiences axial displacement. Corrected reconstruction distances can be automatically calculated, and well-focused amplitude and phase-contrast images can be obtained for each digitized hologram. The method is demonstrated for inspection of microelectromechanical systems subjected to thermal load. The method can be applied as a quasi-real-time procedure.

Digital holographic microscope with automatic focus tracking by detecting sample displacement in real time

Aberrations and the distortions due to the imaging optics can be compensated in quantitative phase microscopy of thin phase objects by digital holography using a single hologram. The reconstructed quantitative phase microscopy phase distribution map can be directly corrected in the reconstructed image plane by a numerical method. To remove this unwanted aberration, in the special case of thin objects, the authors perform a two-dimensional fit with the Zernike polynomials of the reconstructed unwrapped phase. Subtraction of the fitted polynomial from the original phase map gives quantitative phase microscopy phase map free of aberrations.

Sergio De Nicola

Papers

Compensation of the inherent wave front curvature in digital holographic coherent microscopy for quantitative phase-contrast imaging

Extended focused image in microscopy by digital Holography.

Controlling image size as a function of distance and wavelength in Fresnel-transform reconstruction of digital holograms

Digital holographic microscope with automatic focus tracking by detecting sample displacement in real time

Direct full compensation of the aberrations in quantitative phase microscopy of thin objects by a single digital hologram