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The skew ray R¯n on the image plane of an optical system possessing n boundary surfaces has the form of an n-layered deep composite function. It is hence difficult to evaluate the system performance using ray tracing alone. The present study therefore uses the Taylor series expansion to expand R¯n with respect to the source ray variable vector. It is shown that the paraxial ray tracing equations, point spread function, caustic surfaces and modulation transfer function can all be explored using the first-order expansion. Furthermore, the
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