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

MUCKE aims to mine a large volume of images, to structure them conceptually and to use this conceptual structuring in order to improve large-scale image retrieval. The last decade witnessed important progress concerning low-level image representations. However, there are a number problems which need to be solved in order to unleash the full potential of image mining in applications. The central problem with low-level representations is the mismatch between them and the human interpretation of image content. This problem can be instantiated, for instance, by the incapability of existing descriptors to capture spatial relationships between the concepts represented or by their incapability to convey an explanation of why two images are similar in a content-based image retrieval framework. We start by assessing existing local descriptors for image classification and by proposing to use co-occurrence matrices to better capture spatial relationships in images. The main focus in MUCKE is on cleaning large scale Web image corpora and on proposing image representations which are closer to the human interpretation of images. Consequently, we introduce methods which tackle these two problems and compare results to state of the art methods. Note: some aspects of this deliverable are withheld at this time as they are pending review. Please contact the authors for a preview.

http://ieeexplore.ieee.org/iel2/4524/12820/00592460.pdf

Image Processing

Publisher Summary This chapter describes the self-imaging phenomenon and its applications. The self-imaging phenomenon requires a highly spatially coherent illumination. It disappears when the lateral dimensions of the light source are increased. When the source is made spatially periodic and is placed at the proper distance in front of the periodic structure, a fringe pattern is formed in the space behind the structure. The chapter discusses the theoretical and applicational aspects of the self-imaging phenomenon—that is, the property of the Fresnel diffraction field of some objects illuminated by a spatially coherent light beam. The applications of self-imaging are summarized in four main groups—namely, (1) image processing and synthesis, (2) technology of optical elements, (3) optical testing, and (4) optical metrology. The chapter describes the double diffraction systems using spatially incoherent illumination. The first periodic structure plays the role of a periodic source composed of a multiple of mutually incoherent slits. Depending on whether the periods of two periodic structures are equal, the Lau or the generalized Lau effect is discussed. Various applications of incoherent double-grating systems are described in the fields of optical testing, image processing, and optical metrology. After examining some cases of coherent and incoherent illumination, the general issue of spatial periodicities of optical fields and its relevance to the replication of partially coherent fields in space is discussed.

I The Self-Imaging Phenomenon and its Applications

(1979). Linear Systems, Fourier Transforms and Optics. Optica Acta: International Journal of Optics: Vol. 26, No. 7, pp. 836-836.

Linear Systems, Fourier Transforms and Optics

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Optical Shop Testing

A common mathematical model is established for the Ronchi and Hartmann tests and for interpretation of the Ronchigrams as level curves of the components of the transversal aberrations. With the same point of view, a Hartmanngram is regarded as two 90° crossed null Ronchi gratings. A simple and direct method is also developed for calculating Ronchigrams for the cases of centered and off-axis conic sections with the point light source at any location.

Ronchi and Hartmann tests with the same mathematical theory

To help in the fabrication of off-axis conic sections, we present a method to approximate this off-axis section by an on-axis conic centered on the portion desired. This method is based on the method of continuum least squares to obtain the vertex’s curvature and conic constant of the fitted conic on-axis, given the curvature at the vertex and the conic constant of the parent conic from where we want the section and the size of that section. Simple analytic expressions for the curvature and conic constant are derived in terms of the parameters of the off-axis section.

Conic that best fits an off-axis conic section.

Assuming the Ronchi and the Hartmann tests to be null tests, we were able to design special screens for each test that produce aligned straight fringes and a square array for the observed patterns. It also became clear that the screen filter and observing planes for both tests can be interchanged.

Null Hartmann and Ronchi-Hartmann tests

This work describes a process for measuring thin film steps, using phase shifting interferometry (PSI). The phase shifts are applied only in the region where the thin film steps are located. The phase shift is achieved by displaying different gray levels on a spatial light modulator (SLM Holoeye LC2012) placed in one arm of a Twyman-Green (T-G) interferometer. Before measuring the thin film steps, it was necessary to quantify the phase shifts achieved with this SLM by measuring the fringe shifts in experimental interferograms. The phase shifts observed in the interference patterns were produced by displaying the different gray levels on the SLM one by one, from 0 to 255. The experimental interferograms and the thicknesses of the thin film steps were successfully quantified, proving that this method can be used to measure thin films by applying the PSI method only on the region occupied by them.

Phase shifting interferometry using a spatial light modulator to measure optical thin films

The conservation equation for a monochromatic field with arbitrary polarization propagating in an inhomogeneous transparent medium is expressed in terms of amplitude and phase variables. The expressions obtained for linearly polarized fields are compared with the results obtained in the eikonal approximation. The electric field wave equation is written in terms of intensity and phase variables. The transport equations for the irradiance and the phase are shown to be particular cases of these derivations. The conservation equation arising from the second-order differential wave equation is shown to be equivalent to that obtained from Poynting's theorem.

/pdf/amplitude-and-phase-representation-of-monochromatic-fields-320xrdjibj.pdf

Alejandro Cornejo-Rodriguez

Papers

Ronchi and Hartmann tests with the same mathematical theory

Conic that best fits an off-axis conic section.

Null Hartmann and Ronchi-Hartmann tests

Phase shifting interferometry using a spatial light modulator to measure optical thin films

Amplitude and phase representation of monochromatic fields in physical optics.