Slope and curvature measurement by a double-frequency-grating shearing interferometer
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This paper describes a shearing interferometer capable of the direct measurement of the slopes and curvatures of reflecting plates. The wavefront shear is produced by a double-frequency grating which is simply a grating containing two closely spaced frequencies. The first-order waves associated with each frequency form the interferogram, the contours of which are related to the model's slope or curvature depending upon system arrangement and recording procedure.
Four arrangements are described: two for slope and two for curvature. In one, the slope contours are obtained directly and in real time. In the second slope arrangement, an extra spatial-filtering step is necessary to obtain the slope contours. However, this arrangement, as opposed to the first, measures the slope only due to the loading, compensating for initial model slope and optical-system aberrations.
The two curvature techniques can be described as double-shearing interferometers having a primary and secondary shear. The primary shear for both arrangements is provided by the double-frequency grating. In one technique, the secondary shear is provided by a translation of the recording film between two exposures during the recording step. A subsequent spatialfiltering step displays the curvature fringes. The second technique requires only a single exposure and places a beam splitter at the location of one of the first-order diffraction spectra during the filtering step. The field equations defining the fringe values are derived for all four arrangements with experimental results also being given.
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