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

Femtosecond laser micromachining can be used either to remove materials or to change a material's properties, and can be applied to both absorptive and transparent substances. Over the past decade, this technique has been used in a broad range of applications, from waveguide fabrication to cell ablation. This review describes the physical mechanisms and the main experimental parameters involved in the femtosecond laser micromachining of transparent materials, and important emerging applications of the technology. Interactions between laser and matter are fascinating and have found a wide range of applications. This article gives an overview of the fundamental physical mechanisms in the processing of transparent materials using ultrafast lasers, as well as important emerging applications of the technology.

Femtosecond laser micromachining in transparent materials

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

Fringe projection techniques: Whither we are?

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

Interferometric technique for the determination of thermal nonlinearities in semiconductor glasses

We present and discuss a technique to measure concurrently the temperature dependence of quartz refractive indices in the thermal range 25–300° C. The magnitude of both indices is found to decrease slightly with increasing temperature in the thermal range considered.

Measurement of the temperature dependence of quartz refractive indices : a technique

We present a method for in-situ visualization of electric field domain reversal in congruent lithium niobate (LN) through an electro-optic interferometric technique. The crystal refractive index n changes by the linear electro-optic and piezoelectric effects along the z crystal axis, due to the external electric field. This variation depends on the domain orientation so that two adjacent antiparallel domains present a refractive index difference equal to 2Dn which is used for in-situ visualization of the reversed domain pattern during formation. A digital holographic (DH) technique is employed for a two-dimensional (2D) reconstruction of the wavefield transmitted by the sample in amplitude and phase during the process. The corresponding amplitude-map and phase-map movies are presented. The amplitude-map gives qualitative information about the spatial evolution of the domain boundaries while the phase-map provides measurement of the 2D distribution of the phase shift induced along the z axis. The phase-map movies provide unequivocal information about the spatial distribution of the reversed domain regions. This technique can be used as in-situ monitoring method alternative to the measurement of the poling current which provides information only about the amount of charge delivered to the sample, ignoring the spatial distribution of the domain boundaries.

Real-time phase-contrast analysis of domain switching in lithium niobate by digital holography

A third-order aberration analysis for a reflective grating interferometer (RGI) is developed for a noncollimated configuration. In such a configuration the RGI is still a folded and reversing interferometer that is sensitive only to coma aberration, as it is in the collimated configuration. However, for an unaberrated input beam converging on a plane grating, the reflective grating of the interferometer introduces self-aberrations. Consequently, a nonnull fringe pattern is obtained. Nevertheless, a RGI in the noncollimated configuration has the potential to be applied for isolating and measuring coma, and a possible configuration for this application is proposed. As an example of the application, the coma of a large mirror could be isolated and measured by use of a converged configuration to avoid the main limitation in using the RGI in a configuration with a nearly collimated beam.

Reflective grating interferometer in a noncollimated configuration

Accurate measurement of the refractive index of solids is of great importance in various field of industrial processes. We present and discuss a method based on digital holographic interferometry for measuring refractive indices of transparent materials. Two recorded digital holograms are added producing a digital double exposure hologram. The numerical reconstruction of the interferogram intensity enables to determine the index of refraction of the sample under investigation. Advantages and limitations of the prosed approach are discussed.

Giovanni Pierattini

Papers

Interferometric technique for the determination of thermal nonlinearities in semiconductor glasses

Measurement of the temperature dependence of quartz refractive indices : a technique

Real-time phase-contrast analysis of domain switching in lithium niobate by digital holography

Reflective grating interferometer in a noncollimated configuration

Digital holographic interferometry for characterization of transparent materials