POLYNOMIAL FITTING OF INTERFEROGRAMS WITH GAUSSIAN ERRORS ON THE FRINGE COORDINATES .2. ANALYTICAL STUDY

We consider an ideal Twyman-Green interferogram with equally spaced st raight fringes parallel to the x axis and fringe coordinates that are affected by Gaussian errors. We adjust the data points by polynomial f itting to the interferograms. We use a statistical analysis to obtain analytical formulas for the expected values of the aberration coeffici ents. The result of the analysis shows that the expected coefficients are zero, except for tilt about x and for the comatic term, and that s uch deviation increases with the noise level and decreases with the nu mber of fringes. Formulas are also obtained for the expected values of the sum of squares of the residuals. We show that the problem of choo sing the wrong polynomial order is a consequence of erroneous adjustme nt of the data points.