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495 Similarities and Differences With Other Interferometers We conceptualized, predicted, and demonstrated the performance of a new type of shearing interferometer, with the signi cant capabilities of controlling the amount and the direction of the displacement shear The vectorial shearing interferometer may be based on the Mach Zehnder con guration by incorporating the displacement shearing system The shearing system is composed of a pair of wedge prisms that modify with a high degree of precision the optical path difference and the tilt between the sheared wavefront and the reference wavefront The use of small apex-angle prisms decreases the number of ghost beams within the interferometer and the amount of straight light incident on the detector plane.

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(8.25)

While it is believed that some limited version of the generalized linear shearing interferometer may be implemented with a single prism, we prefer the implementation with two prisms, due to the enhanced control and the range of wavefront positioning Due to the knowledge of the displacement increments along two perpendicular axes, the measured quantity is indeed a directional derivative of the phase function This allows complete phase recovery in two dimensions The variable shear and tilt, that may be implemented along any other direction, have the particular bene cial characteristics that the number of fringes and their orientation may be controlled with the shear direction and its magnitude Xu et al (2005) proposed an implementation of a compact vectorial shearing interferometer that allows phase shift by moving prisms along the beam normal This represents a signi cant simpli cation of its layout.

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With only four thin prisms, shearing is accomplished along an arbitrary direction, and phase stepping is achieved without incorporating a movable mirror on a piezoelectric mount The range of displacement is also large All the interferometric patterns generated with the vectorial shearing interferometer exhibit the fringe movement out of the center of the reference beam We may de ne the angle of rotation of the fringe pattern to be the angle between the normal to the fringes when the shearing angle y is zero, and when the shearing angle y has a nite value Its algebraic sign is opposite to that of the shearing angle y Fringe density increases as the magnitude of the shearing vector is incremented Figure 463 illustrates that the fringe orientation is under the control of operator.

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This may be accomplished upon changing the orientation of both prisms simultaneously, without changing their separation or relative orientation If part (a) is the reference pattern, the fringes are displaced (b) up, (c) down, (d) left, and (e) right using a pair of prism with an index of refraction n, of 1517, and the apex-angle e 5 Figure 464 presents results of a study between the fringe density and the relative prism orientation Fringe density increases as the difference angle between prism orientation increases from (a) 05 , (b) 07 , (c) 13 , (d) 15 , and (e) 16 Prisms with index of refraction N 1:517 and apex-angle e 5 are used The versatility and adaptability of the vectorial shearing interferometer with variable shear and tilt are best appreciated upon examining the experimental results depicted in Figure 465.