Showing papers by "Alberto Cordero-Dávila published in 1994"
TL;DR: A series of simulations were made for an ideal Twyman-Green interferogram of equally spaced straight fringes having tilt only about x and 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.
Abstract: 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.
13 citations
TL;DR: An ideal Twyman-Green interferogram with equally spaced straight fringes parallel to the x axis and fringe coordinates that are affected by Gaussian errors is considered and it is shown that deviation increases with the noise level and decreases with the number of fringes.
Abstract: 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.
5 citations