How Do Polygonal Mirrors Affect Scan Systems Without Lenses?

[anita1984]

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

 

[Andy Resnick]

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.

 

[astrokreng]

Hello Anita,

Thank you for your question. Polygonal mirrors are a very interesting topic in optics, and it sounds like you are working on a challenging project. I would be happy to provide some information and resources that may be helpful to you.

Firstly, the scan angle of a polygonal mirror can be calculated using the formula θ = 2π/n, where n is the number of facets on the mirror. In your case, since you have 6 facets, the scan angle would be θ = 2π/6 = π/3 radians.

The distance between the polygon and the scan plane in a system without a scan lens can be calculated using the formula d = r tan(θ/2), where r is the radius of the polygonal mirror. This distance is important because it determines the size of the scan field and the resolution of the system.

As for the total length of the scan line in the scan plane, this can be calculated by multiplying the distance between the polygon and the scan plane by the scan angle. So, in your case, the total length would be d * θ = r tan(θ/2) * θ.

In terms of resources, there are many books and articles that discuss the principles and applications of polygonal mirrors in optical systems. Some recommended titles are "Optics" by Eugene Hecht, "Introduction to Optics" by Frank L. Pedrotti and Leno M. Pedrotti, and "Handbook of Optical Engineering" by Daniel Malacara. You may also find helpful information in academic journals such as Optics Letters and Optics Express.

I hope this information helps you in your project. Good luck!