Abstract
The paper describes in detail the governing relationships for the electromagnetic field on the surface of the laser beam splitter of a laser interferometer. These expressions are intended for numerical simulation of measuring the displacements of control object surfaces by using a laser interferometer. We consider the cases of perpendicular and parallel polarizations of the radiation source. Moreover, the most relevant particular cases of constructing optical circuits of the interferometer in question are treated. The presented theoretical results have been used in numerical studies of the functional characteristics of promising contactless optical means of measuring displacements. The use of the described results has improved the quality and informativeness of the numerical simulation results of the measurement process of displacements by a laser interferometer.
Highlights
The paper describes in detail the governing relationships for the electromagnetic field on the surface of the laser beam splitter of a laser interferometer
The photodetectors for analyzing the interference field are located in the direction of reflection from the beam splitter of the source radiation, at a certain distance from the beam splitter corresponding to the Fresnel zone
It can be noted that the relationships are obtained for determining the field distribution on the beam splitter surface of the laser interferometer under consideration, which is represented by the tangential components of the electric field intensity vector Ex and Ey expressed in the Cartesian coordinates of the basic system Oxyz, taking into account the polarization of the radiation source and the transmittance of the beam splitter
Summary
The relationships for the spherical components of the field of the source of electromagnetic radiation are sufficiently well-known [9,10,11]. If the beam splitter is flat, has a rectangular shape and is completely illuminated, the field on its surface is convenient to express through the Cartesian components of the vector E, and in the case where the source field is a light spot on the beam splitter surface, it is more convenient to consider the cylindrical components of the vector E. Let us consider the first case when the beam splitter is fully illuminated. It is necessary, by transforming from spherical to Cartesian coordinates, to express the tangential components of this field on the beam splitter surface through the Cartesian components. The coordinate system O”x”y”z” is obtained from the system O’x’y’z’ by mirroring it and changing the direction of the y-axis to the opposite. In the expressions (1)–(3), the values of the parameters x0 , y0 , α0 and α, h determine the position of the radiation source and the reflector in space (see Figure 1)
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