The calculation of phase shift and optical path difference in birefringent media is related to a wide range of applications and devices. We obtain an explicit formula for the phase shift introduced by an anisotropic uniaxial plane-parallel plate with arbitrary orientation of the optical axis when the incident wave has an arbitrary direction. This allows us to calculate the phase shift introduced by waveplates when considering oblique incidence as well as optical axis misalignments. The expressions were obtained by using Maxwell's equations and boundary conditions without any approximation. They can be applied both to single plane wave and space-limited beams.

The fringe pattern obtained when a divergent (or convergent) beam goes through a sample of birefringent crystal between two crossed polarizers contains information that is inherent to the crystalline sample under study. The formation of fringe patterns is analyzed from distinct approaches and with different degrees of approximation considering cones of light of large numerical aperture. We obtain analytic explicit formulas of the phase shift on the screen and compare them with the exact numerical solution. The results obtained are valid for arbitrary orientation of the optical axis and are not restricted either to low birefringence or to small angles of incidence. Moreover, they enable the extraction of the main features related to the characterization of uniaxial crystal slabs, such as the optical axis tilt angle and the principal refractive indices.

This paper describes the design and performance of a low-noise and high-speed optical sensor that provides two output signals in quadrature from the simultaneous detection of four phase-shifted interferograms. The sensor employs four high-speed photodiodes and high-speed, low-noise transimpedance amplifiers. The optical and electronic design was optimized for high-speed displacement measurement interferometry, over a broad range of operating frequencies. Compared to other experimental schemes, the sensor is simpler and of lower cost. The performance of the sensor is demonstrated by characterizing a piezoelectric transducer for ultrasonic applications. We measured displacements between 38 pm and 32 nm with 6% relative uncertainty, in the frequency range from 1 to 2 MHz.

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