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Chapter 10:
Enhancing Regular Interferometric Sensitivity
A technical realization for enhancing regular interferometric sensitivity is shown in Fig. 10.1(a). The errors of a Fizeau beamsplitter T, rear mirror M (usually the sample), and included medium (air) are accumulated both longitudinally (wanted) and, inseparably, laterally (unwanted). The resulting error summation upon each passage of the initially collimated beam is a successive wavefront deformation (Fig. 10.2) and the associated phase shift. The effect of increasing phase shift is demonstrated in the vector diagrams in Figs. 3.5(a) and (b). The depth of an error Dt appears as 2nDt on the nth wavefront. Errors seen in the summation are determined by the relation of the error gradient to the amount of beam walkoff tWn, where W is walkoff. Wn is determined by wedge angle b and by the T-to-M distance t (thought to be small). With small values of 2nDt, multiple beam fringes are seen. Only the contrast profile of the fringes becomes modified. Side lobes develop, and the maximum of the amplitude becomes shifted as a function of increasing angle b. The side lobes indicate the direction away from the zeroth order of the interference. Both the depth and the width of the error zones on a nominally flat problem surface, assumed to be small enough for their representation in the defocal plane, will not extend into the neighboring orders of reflection (see Fig. 8.3). With these qualitative limitations, one may expect to visualize slow slope errors with gradually enhanced sensitivity. In the experimental setup shown in Figs. 10.1(a) and (b), wedge angle b is shown to be large enough to have successive beams defocused in positions clearly separated from each other, allowing beam selection by a slit in the stop. The stop is arranged in the defocal plane, as shown in Fig. 10.1(b).
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