Abstract

Subject of study. Straight-line scanning of a laser beam using a symmetric off-axis parabolic reflector is studied. Aim of study. A method for application of the optical geometric effect observed in a system of matched conicoids to line scanning is developed. Method. The problem of obtaining a scanning line with a parallel transfer of the laser beam axis while maintaining its incidence along the normal to the plane to be scanned in the approximations of geometric optics is solved geometrically. Main results. The optical geometric effect observed in a system of matched conicoids is theoretically analyzed and numerically simulated. An application method for line beam scanning is proposed. For this method, a theorem related to the intersection of matched conicoids (using the example of the interaction of a paraboloid with a ray cone on its axis and a vertex at its focus) involving postulates of analytic geometry and the results of numerical simulation was formulated. According to this theorem, the intersection breaks up into two flat lines—elliptical for the cavity of the cone facing the pole of the paraboloid and parabolic for the cavity of the cone facing the opening of the paraboloid. Regarding the circular paraboloid and cone, an optical interpretation of the formulated theorem is presented. The parabolic component determines the conditions under which a telecentric path of rays in the image space is provided, while the line of intersection of conicoids and the line of horizontal scanning are in one plane. Concerning the elliptical component, the optical interpretation of our theorem covers the well-known elliptical reflectors that form collinear beams from conical beams. These interpretations are the essence of the established optical geometric effect. An approach to form the ray cone on the axis of the parent paraboloid with the vertex at its focus is also reported. The cone is formed using a deflector with a flat reflector, the axis of rotation of which is inclined to the axis of the parent paraboloid at an angle equal to half of the opening angle of the cone. The design of the deflector depends on whether the beam falls along the axis of the parent paraboloid or along the axis of rotation of the deflector’s reflector. Practical significance. The developed line-scan forming method based on the analyzed effect provides opportunities for improving the constructive geometry of optical scanning systems by increasing the length of the raster line within which its straightness and beam path telecentricity are preserved. Such properties are relevant for equipment widely used with optical-mechanical scanning systems: devices for input/output graphical information (photoplotters, printers, and scanners), technological equipment for laser microlithography, generation of holographic images and printing forms, power laser processing (laser cutting, welding, scribing), and other use cases of scanning wave beams.

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