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Cylindrical Concave Metallic Mirrors

Cylindrical concave metallic mirrors have a concave side with cylindrical curvature (unidirectional bending, similar to a part of a cylinder), and the other side is a flat surface coated with a metal reflective coating (e.g., aluminum, silver, gold, etc.). Unlike spherical mirrors, cylindrical mirrors have the ability to focus or diverge in only one direction (axial) and have no optical focus in the perpendicular direction, making them suitable for special applications such as beam shaping, laser line focusing, and optical imaging correction.
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What are the geometric characteristics of a cylindrical concave metallic mirror?
Concave surfaces are cylindrical (radius of curvature R) and have focusing or divergence capability in only one dimension (e.g., X direction).
Plano surfaces have no optical focus and keep light rays from being deflected in the vertical direction (e.g., Y direction).
Focal length calculation (cylindrical direction): F=R/2
(negative values indicate concave surfaces for beam convergence or divergence)

What are the optical functions of a cylindrical concave metallic mirror?
Incident light type Cylindrical concave mirrors function
Parallel light Focuses into a linear spot in the column plano direction (Y direction remains parallel).
Divergent light Correcting divergence in the column direction (e.g., laser diode fast-axis compression).
Focused light Adjustment of spot shape in the direction of the column (e.g. round spot becomes elliptical).
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