I don't know if you'll get a good flat field without the flattener. To answer your question about what flatteners do, yes they do reduce the focal length and they do speed up the F ratio. However, this cannot be treated by the same F ratio rules as govern camera lenses because in camera lenses you add aperture (more light) to reduce F ratio/exposure times while keeping focal length the same. You do not do this with a reducer, you change the F ratio by changing the focal length without addin
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