Manuel Servin Guirado

Direct-phase detection of modulated Ronchi rulings using a phase-locked loop

A recently developed technique for fringe analysis based on a digital phase-locked loop is applied to detect the ray aberration of modulated Ronchi rulings. The Ronchi ruling is placed outside the caus- tic, and the shadow of the ruling is imaged directly into a two-dimensional CCD video array for further processing. The CCD array is placed at a

Aspherical wavefront testing with several defocusing steps

A deep aspheric wavefront produces many interference fringes even when the optimum defocusing term is selected. The large number of fringes imposes a limit to the degree of asphericity that may be measured. A procedure using several interferograms with several defocusing values is described.

Spatial carrier analysis of interferograms with aspheric wavefronts

The method of spatial carrier synchronous detection of an interferogram, also called direct interferometry, has been developed by several authors. Besides reviewing this method, we present here two spatial carrier interferometric procedures using a spatial circular carrier and also a phase modulated carrier to compensate the aberration of aspherical surfaces.

Unwrapping of noisy phase maps: a comparison of two methods

The unwrapping of experimental phase maps is not a straightforward process and much research has been devoted recently to the development of robust algorithms that can remove 2ir phase discontinuities in the presence of noise, phase inconsistencies, missing data and holes or shadows. In this paper, the performance of two recently developed phase unwrapping methods are compared. The first uses a least squares minimization formulation whose solution is provided by a fast discrete cosine transform. Areas ofbad data are removed from the differential equation by means of a weighting matrix and the unwrapped phase distribution is evaluated using an iterative approach. The second is a path-independent method based in the Thikonov regularization theory. This theory finds solutions that correspond to minimizers of positive definite quadratic cost functionals. The solution to the unwrapping problem by this method is a generalization of classical least-squares . The introduction of a regularization term permits the reduction of noise and the interpolation over regions with invalid data in a stable and controlled way. The performance ofboth methods are compared in their application to computer generated and experimental phase maps. Their main advantages and limitations are discussed. Keywords: Optical metrology, fringe analysis, cosine transform, regularization methods.

Digitization of interferograms of aspheric wavefronts

When digitizing an interferogram with a detector array, the sampling theorem requires the minimum local fringe spacing or period to be greater than twice the pixel separation. Thus, given a detector, there is a minimum fringe period that may be allowed.1,2 This minimum period, in turn, is set by the wavefront asphericity and the testing method.

Limit to the degree of asphericity when testing wavefronts using digital interferometry

When testing an aspheric wavefront with any digital interferogram evaluation method, like phase shifting interferometry, Fourier interferometry, or with a spatial carrier analysis, there is a limit to the maximum degree of asphericity if a null compensator is not used. An analysis of this limitation using different interferogram interpretation methods are described.

New wavefront representation for large wavefront slopes in radial GRIN rods

The wavefronts in some optical systems like radial Gradient Index (GRIN) rods and aspherical lenses have large radial slopes at the circular edge of the pupil. Then some special mathematical tools are needed to represent these wavefronts. An idea of the mechanisms employed to fabricate the GRIn rods is helpful when designing these tools. In this article we propose the use of a gaussian function to represent these wavefront deformations at the edge of the pupil. This is a compact representation and it is also very convenient for radial GRIN rods. A data fitting is performed with a regularization process introducing the a priori known wavefront characteristics.

Recursive phase estimation with a spatial radar carrier

An interferogram can be demodulated to find the wavefront shape if a radial carrier is introduced. The phase determination is made in the space domain, but the low-pass filter characteristics must be properly chosen. One disadvantage of this method is the possible removal of some frequencies from the central lobe, resulting in a misinterpretation of the true phase. Nevertheless isolating the central order by using a recursive method when a radial carrier reference is used is possible. An example of a recovered phase from a simulated interferogram is shown.

Regularization methods for processing fringe pattern images

A very powerful technique for solving the kind of inverse problems that often arise in the processing of fringe pattern images is based on Bayesian Estimation with prior Markov Random Field models. In this approach, the solution of a processing problem is characterized as the minimizer of a cost function which has two types of terms: terms that specify that the solution should be compatible with the available observations and terms that impose certain constraints on the solution. In this paper we show that by the appropriate choice of these terms, one can use this approach in almost every processing step for accurate interferogram demodulation. Specifically, one can construct: robust smoothing filters that are almost insensitive to edge effects; operators that automatically determine a mask that indicates the shape of the region where valid fringes are available; adaptive quadrature filters for phase recovery from single and multi-phase stepping interferograms and robust phase unwrapping algorithms.

Construction of a phase-shifting interferometer

The construction of a phase shifting interferometer is described. The movable reference mirror is driven by a piezoelectric transducer. This piezoelectric was completely characterized in order to know the range for linear behavior. Besides this, a special voltage source was constructed to feed the piezoelectric through software. Several dephase interferograms were digitized in a PC computer.