The main constraint of classical off-axis reflecting systems is the primary astigmatism that has long been a research topic of interest. This astigmatism in off-axis spherical reflective imaging systems can be eliminated by using the proper configuration. These configurations could be derived from the marginal ray fans equation, and they are valid for small angles of incidence. The conditions for the astigmatism compensation in configurations with two and three off-axis mirrors have been derived and analyzed, which have not been reported previously. The expression that defines the conditions for primary astigmatism compensation in a four-mirror system is presented. This shows that the marginal ray fan equation can be used to obtain the condition for astigmatism compensation of a reflective system with any number of mirrors. The developed methodology is verified by ray-tracing analysis of some examples.
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