Alejandro Cornejo-Rodriguez

Caustics of diffraction fields

Abstract Caustics of diffraction fields are described for radiation passing through a binary screen with amplitude transmittance of the form t(x,y) = δ[y−f(x)]. The description is based on the geometrical properties of the function f(x). Experimental results are presented.

Polynomial fitting of interferograms with Gaussian errors on fringe coordinates. I: Computer simulations

A series of simulations were made for an ideal Twyman-Green interferogram of equally spaced straight fringes having tilt only about x. It was found that fitting polynomials to the interferometric data resulted in biased estimates of some of the fitting coefficients to the optical path difference. The acceptance of the Seidel aberrations grows with the noise level and diminishes when the number of fringes is increased.

Binary grating with variable bar/space ratio following a geometrical progression

Abstract Apodizing the apertures of a binary grating with a variable opening ratio, the diffraction produced by the pupil is eliminated from its spectrum. We study the behavior of a unidimensional binary grating whose bar/space ratio is expressed as a geometrical progression. The experimental and simulation results of Frauhofer diffraction patterns produced by this type of grating are compared with the spectrum of a Ronchi type ruling showing the elimination of the diffraction pupil in one dimension.

Profile measurement of a conic surface, using a He-Ne laser and a nodal bench.

A method of measuring the profile along one diameter of a conic surface is presented. Using some well-known formulas for the conic sections, useful mathematical relations are derived that, together with a simple experimental setup can be used for comparing theoretical and real values of the sagitta of the surface.

Cyclic interferometers for optical testing

In this paper, we describe two compact cyclic interferometers which can be used for the testing of right-angle prisms; with some modifications they can also be used for testing convergent wave fronts.

Analysis of the joint Fourier spectrum for dual-input single-channel rotation

We present a study of the intensity variations of the joint Fourier spectrum when one of two input objects is rotated while the other remains fixed by determining the average contrast as a function of the angle of rotation. The visibility behavior is explained in a theoretical and experimental way for simple test objects whose fine analog rotations are acquired with an optomechanical system that uses a high precision rotatory stage.

Sensing a wave front by use of a diffraction grating.

A method is presented to sense the wave front at the exit of an optical surface. This method uses a set of diffracted rays generated when a He-Ne laser impinges on a rectangular diffraction grating. The grating was placed near the curvature center of the surface to be tested. After they are reflected in the test surface, the diffracted rays have the information of the slopes of the wave front, like in the Hartmann test. The Hartmann pattern was registered near the curvature center and captured with a CCD camera. The slopes for each ray are measured from the experimental pattern, and they are compared with the ideal ones simulated in a computer. The evaluation was carried out by use of Seidel polynomials to obtain the information of the aberrations of a mirror 53 cm in diameter.

Design of projective zone plates and their focusing properties.

Transmittances are designed by generation of a family of curves whose local geometry is similar to that of zone plates. The family is obtained by means of projective mapping in the normal direction of an initial curve, so that all the curves of the family have a common evolute. This property allows the prediction of the geometry of the focusing region of the transmittance. Experimental results with an ellipse as the initial curve are shown. We show that the proposed zone plates can be considered a generalization of conventional zone plates.

Two-dimensional average contrast analysis of the joint Fourier spectrum under rotation of an input object

We present a detailed study of the intensity variations of the joint Fourier spectrum of two input objects when one of them is rotated while the other remains fixed by determining the 2-D average contrast of the spectrum as a function of the angle of rotation. The contrast is found to be object dependent, decreases rapidly for small rotations, and has an almost flat response for larger rotations. We explain this behavior in both theoretical and numerical ways for two simple rectangular objects and only numerically using the fast Fourier transform, for binary and grayscale test objects whose analog rotations are acquired with an optomechanical system that uses a high-precision rotatory stage. As an application of the 2-D average contrast analysis a pair of similar cross section images of a biological organ are used, to obtain the lowest rotation angle between them, and as a consequence a quantitative aligning method for fine angular movements is presented that uses a 2 f optical-digital coherent processor to obtain the Fourier transform of the input objects. Experimental results are presented.

Polynomial fitting of interferograms with Gaussian errors on fringe coordinates. III. Nonlinear solution

Assuming that the measured coordinates of the fringes of an interferogram have random errors and that they are considered Gaussian, the system of normal equations that is obtained on application of the least-squares method is converted into a nonlinear set of equations. We present an algorithm to estimate the coefficients of the nonlinear system by applying the Newton-Raphson method and starting the iteration from the standard classic solution. This algorithm is applied to a pattern of straight and equally spaced fringes, obtaining not only the right coefficients but also the adequate election of the terms to be included in the model, to show the contrast with the results of the classic method.