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.

/pdf/principles-and-techniques-of-digital-holographic-microscopy-56tmwltigo.pdf

Principles and techniques of digital holographic microscopy

We describe an interferometric method for measuring effective focal length of lenses. Measurement of the effective focal lengths of macroscopic refractive lenses and of a diffractive microlens are performed within the limit of paraxial approximation. The technique uses a reflective grating interferometer to produce a fringe pattern with a regular pitch. The lens under test is illuminated by the interference pattern and the focal length is obtained by the knowledge of the spatial frequency in a fixed aperture. Three imags of the interference pattern are stored by using a CCD camera: two of them are imaged by the lens under test placed at two different position, an one is the reference pattern with no lens inserted in the set-up. A 1D fast Fourier algorithm is applied to the digitized image and the phase modulo 2 (pi) is reconstructed. The phase is unwrapped and averaged to calculate the spatial fringe frequency inside the chosen aperture. The method has been applied for measuring the focal length of macroscopic refractive lenses and of a 1mm aperture diffractive microlens.

Interferometric method for testing focal lengths using a digital Fourier transform

We present a concept of interferometric testing, believed to be novel, that can be applied to measuring aberrations of optical components that have rotational symmetry. The optical configuration uses two coherent, collimated wave fronts that are tilted to impinge upon the optical component being tested such that one beam is on axis and the other is off axis. For small tilt angles the two aberrated wave fronts can be considered to be carrying the same aberrations. Furthermore, the off-axis beam is displaced along a direction orthogonal to the optical axis of the component. Interference between the two aberrated wave fronts produces a fringe pattern that is similar to a lateral shear interference pattern. Moire fringes are obtained by spatial beating of the interference pattern with a CCD TV camera array. Under such conditions it is possible to subtract most of the linear carrier that is intrinsically present in the resultant fringe pattern owing to the large defocus aberration and tilt.

Two-beam interferometer for measuring aberrations of optical components with axial symmetry.

The temperature field generated by the weak absorption of a gaussian laser beam in an optically and thermally thin film bounded by two transparent plates is discussed. An analytical solution of the problem is presented together with an algorithm for the numerical integration. The influence of the finite thermal conductivity of the plates is shown in an example.

Laser induced thermal profiles in thermally and optically thin films

We describe an optical heterodyne polarization interferometer that can be efficiently used for the precision measurement of the change in the state of polarization of a light wave induced by polarizing optical devices. This technique is used to measure the change with wavelength of the phase retardation of a quarter-wave plate. A theor- etical derivation is presented to permit computation of the wavelength dependence of the phase shift induced by a quarter-wave plate.

http://rd.springer.com/content/pdf/10.1007%2FBF01082277.pdf

Rapid communication Wavelength dependence of the phase retardation of a quarter-wave plate

An automated Fourier-transform method of phase retrieval of moire interferometric fringe pattern is presented. The method is shown to provide fast and accurate determination of the phase information by removing the carrier without shifting in frequency domain the filtered Fourier spectrum of the carrier-modulated moire fringe pattern. The principle of the method is described and moire interferometric measurements with submicron sensitivity of the in-plane displacement fields of thick carbon fiber/graphite-PEEK composite laminates are analyzed as example of application of the technique.

Giovanni Pierattini

Papers

Interferometric method for testing focal lengths using a digital Fourier transform

Two-beam interferometer for measuring aberrations of optical components with axial symmetry.

Laser induced thermal profiles in thermally and optically thin films

Rapid communication Wavelength dependence of the phase retardation of a quarter-wave plate

Fourier transform method of fringe analysis for moire interferometry