How Do Polygonal Mirrors Affect Scan Systems Without Lenses?

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A polygonal mirror with six facets can achieve a total angular scan of 4*pi/6, with the beam scanning at a constant angular frequency. The rotation axis not passing through a surface causes the scanned beam to both translate and pivot, affecting the scan system's performance. For systems without lenses, understanding the scan angle, distance to the scan plane, and total scan line length is crucial. Resources like "Building Electro-Optical Systems" by Phil Hobbs may provide some geometric insights, though specific formulas may be harder to find. Proper optical design considerations are essential for optimizing scan systems using polygonal mirrors.
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Hello Forum , i have a Polygonal mirror with 6 facets of mirrors , i am working in a project for a scan system without lens . I would like to ask you about a document or books to find the formulas of : Scan Angle,The distance between the polygon and the scan plane in a system without a scan lens,The total length of the scan line in the scan plane.
Thank you in advance,
Anita
 
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I don't know of a succinct reference- maybe there's an optical design book in a library near you with a relevant chapter. All I have is a few sections in "Building Electro-Optical Systems", by Phil Hobbs.

He treats the problem purely geometrically- a 6-facet mirror gives a total angular scan of 4*pi/6, and the beam scans at constant angular frequency.

Moreover, he notes that becasue the rotation axis does not pass through a surface, the scanned beam translates as well as pivots during a line. So-called f-\theta lenses are used to convert constant angular velocity scans to constant linear velocity scans by use of distortion.
 

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