Introduction of the Impulse Response Function in Common-Path Interferometers with Fourier Plane Filters

In the present paper it will be shown how the introduction of a Fourier plane filter can create various types of common-path interferometers for measuring changes in surface tilt or curvature of an object surface. This is obtained by placing a holographic optical element in the Fourier plane of a 4-f optical system. The interferometers are analysed by using the paraxial approximation of the Huygens-Fresnel integral formalism, and the interferometer functions are given by a novel formalism using impulse response functions. Based on this technique, an interferometer for measuring dedicated changes in surface deflection is presented. This interferometer is insensitive to rigid surface rotations and displacements. The interferometer can be embedded in systems based on single point measurement of a time dependent deflection, i.e. vibrometers, as well as in full-field measurements such as electronic speckle interferometers.