Retardation effects in laser-Doppler measurements

Abstract

Although the Doppler-effect is well known, some recent publications discuss the necessity of relativistic corrections in the measurements of two-beam interferometers. This is remarkable because sensor and detector are in the same reference frame and, therefore, it is not necessary to employ the Lorentz transformation. The whole consideration can be made in one inertial frame even if one reflector is moving in respect to the frame of source and detector. However, the commonly used equation for the Doppler-effect for a reflection at a moving surface is not correct because this equation is derived as a quasi-static solution by using optical path lengths. If the speed of light is considered as finite a different equation containing effects of wave propagation follows. Retardation effects in interferometers are discussed in this paper and its influences to laser-Doppler measurements are derived.

Laser Doppler Vibrometry Measurements in Structural Dynamics

“…One can use a relativistic approach, which takes into account a transformation of space and time coordinates, as explained in [1]. However, recent studies on retardation effects in laser Doppler measurements [2] demonstrated that it is not necessary to consider relativistic effects in measurements of a two-beam interferometer, since the source and the observer are in the same reference frame. This condition is the one depicted in Fig.…”

“…This holding, when the velocity is much less than the speed of light (v < < c), which is almost always the case in standard applications, it might be possible to expand in a power series in v/c and stop the expansion to the first order, so to obtain the Doppler shift ( f ) as shown below in Eq. (2). The equivalence c = fλ and the prosthaphaeresis formulas were utilized to obtain the well-known expression for the Doppler shift.…”