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

We present a modal phase-reconstruction method for analyzing wave front aberrations of rotationally symmetric optical components in two beam shearing interferometry. The optical configuration requires only two mutually coherent off-axis plane wave fronts transmitted through or reflected by the optical component under test. Finite moire beating between the interferograms and the CCD array is used to subtract the linear carrier introduced by defocus and the tilt making the presense of high order aberrations more evident. The difference wave front is described by elliptical Zernike polynomials as a function of the amount of lateral displacement between the two aberrated wave fronts. The method allows for accurate wave front reconstruction inside the quasi-elliptical overlap area between the laterally sheared interfering beams. Results of numerical experiments and applications of the technique for measuring aberrations of simple biconvex spherical lenses are presented.

Wavefront aberration analysis in two-beam reversal shearing interferometry by elliptical Zernike polynomials

Ferroelectric domain micro structuring of bulk Lithium Niobate is very useful for optoelectronic applications such as non-linear optics employing Quasi-Phase-Matching for efficient harmonic and parametric conversion processes or for the fabrication route for production of novel MEMS devices, like micro-cantilever beams. Quasi-Phase-Matching based applications require periodically reversed ferroelectric structures with periods of the order of micrometers. Precise control of the surface quality and of the domain structure of the micro structured materials is required such as in the case of optical MEMS applications. We here report on the application of Digital Holography as metrological tool for the inspection and characterization of the domain structures in bulk Lithium Niobate samples. This technique allows reconstructing both the intensity and the phase of the microstructures under test and it allows determining quantitatively the phase distribution. Several examples of application of the Digital Holography technique for the numerical reconstruction of the micro-topography of domain structure are presented and discussed.

Characterization of microstructures in lithium niobate crystals by digital holography

Profile measurement of a one-dimensional phase boundary sample using a single shot phase-step method

We report an interferometric analysis of 0.5mm thick lithium niobate crystal sample by making use of a reflective grating interferometer and a digital holographic technique. The lithium niobate wafer was subjected to electric field poling in order to obtain two antiparallel ferroelectric domains. The crystal was then mounted into one arm of the interferometer in order to study the phase map and consequently to evaluate the effects of domain reversion at the boundary. Engineering of periodically reversed domains in LN is extensively used for quasi-phase-matching applications while the ferroelectric structure investigated here is suitable for producing electro-optically controlled deflector or switch devices via total internal reflection at the domain interface. The above mentioned applications require deep knowledge of how the domain reversal process affects the optical properties of the ferroelectric crystals.

Giovanni Pierattini

Papers

Wavefront aberration analysis in two-beam reversal shearing interferometry by elliptical Zernike polynomials

Characterization of microstructures in lithium niobate crystals by digital holography

Profile measurement of a one-dimensional phase boundary sample using a single shot phase-step method

Interferometric analysis of a lithium niobate with engineering reversed domains

An interferometric technique based on Fourier fringe analysis for measuring the thermo-optic coefficients of transparent materials