Octavio Cardona-Nunez

Ronchi and Hartmann tests with the same mathematical theory.

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 degrees 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.

Conic that best fits an off-axis conic section

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.

Null Hartmann and Ronchi-Hartmann tests.

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.

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.

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.

Cylindrical lenses: testing and radius of curvature measurement.

Using a technique that was previously developed for measuring the radius of curvature of spherical surfaces, an alternative method for testing cylindrical as well as toric lenses is presented. The basic equipment required is a nodal bench and a low power He–Ne laser.

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.

Polynomial fitting of interferograms with Gaussian errors on the fringe coordinates. II: Analytical study

We consider an ideal Twyman-Green interferogram with equally spaced straight fringes parallel to the x axis and fringe coordinates that are affected by Gaussian errors. We adjust the data points by polynomial fitting to the interferograms. We use a statistical analysis to obtain analytical formulas for the expected values of the aberration coefficients. The result of the analysis shows that the expected coefficients are zero, except for tilt about x and for the comatic term, and that such deviation increases with the noise level and decreases with the number of fringes. Formulas are also obtained for the expected values of the sum of squares of the residuals. We show that the problem of choosing the wrong polynomial order is a consequence of erroneous adjustment of the data points.

Comparison between toroidal and conic surfaces that best fit an off-axis conic section.

A mathematical treatment is developed to establish the difference in the sagitta between toroidal and off-axis conic surfaces. The best fit betwen these surfaces is found by optimizing the curvatures of the toroid, and a comparison is made between these results and those obtained previously.

Tilted conic fitting to an off-axis conic surface.

A better fitting to an off-axis conic section can be obtained if a tilted conic is used. The mathematical equation for the tilting angle is obtained as well as the influence over some of the aberration coefficients.