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Why does the size of the image circle in a Large Format lens change as the lens is stopped down?

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Why does the size of the image circle in a Large Format lens change as the lens is stopped down?

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Well . . . it doesn’t actually. What actually happens is that when the lens is wide open, the center of the image is very bright and the corners of the image are VERY dark. So dark in fact that they do not expose the film (When the film is properly exposed for the center of the image). As the lens is stopped down, uniformity of illumination improves and therefore the circle of usable illumination increases.

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