Optical-geometric effect of matched conicoids intersection on the example of line beam scanning

Канделинский С.Л., Ткаченко В.В. Оптико­-геометрический эффект пересечения согласованных коникоидов на примере строчной развёртки луча // Оптический журнал. 2023. Т. 90. № 10. С. 3–12. http://doi.org/10.17586/1023­-5086­-2023-90-10-03-12

 

Kandelinsky S.V., Tkachenko V.V. Optical-geometric effect of matched conicoids intersection as illustrated by line beam scanning [In Russian] // Opticheskii Zhurnal. 2023. V. 90. № 10. P. 3–12. http://doi.org/10.17586/1023-5086-2023-90-10-03-12

 

S. L. Kandelinskiy and V. V. Tkachenko, "Optical geometric effect of the intersection of matched conicoids as illustrated by line beam scanning," Journal of Optical Technology. 90(10), 563-568 (2023).  https://doi.org/10.1364/JOT.90.000563

Subject of study. Forming of a straight­line scanning of a laser beam using a symmetric off­axis parabolic reflector. Aim of study is to develop a method of application of the optical­-geometric effect observed in a system of matched conicoids for line scanning. Method. The solving, as a geometric one, issue of obtaining of scanning line with a parallel transfer of the laser beam axis and maintaining its incidence along the normal to the scanning plane in the approximations of geometric optics. Main results. A theoretical analysis and numerical simulation of the optical-­geometric effect observed in the system of matched conicoids is carried out. The method of its application for the line beam scanning is proposed. For this purpose, a theorem on the intersection of the 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 the postulates of analytic geometry and the results of numerical simulation has been formulated. According to the theorem, the intersection breaks up into two flat lines that make it up — 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. For the case of the circular paraboloid and cone an optical interpretation of the formulated theorem is presented. For the parabolic component it determines the conditions, under which a telecentric path of rays in the image space is provided, while the line of conicoids intersection and the line of horizontal scanning are in one plane. For the elliptical component the optical interpretation of our theorem covers the well­known elliptical reflectors that form collinear beams from conical beams. These interpretations are the essence of the established optical­geometric effect. A way of forming of the ray cone on the axis of the parent paraboloid with the vertex at its focus is also indicated. 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 using 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 the beam path telecentricity are preserved. Such properties are relevant for widely used equipment with the optical­mechanical scanning systems: devices for input/output of graphic information (photoplotters, printers and scanners), technological equipment for laser microlithography, for making of holographic images and printing forms, for power laser processing (laser cutting, welding, scribing), and in other cases of using scanning wave beams.