A vectorial diffraction theory that considers light polarization is essential to predict the performance of optical systems that have a high numerical aperture or use engineered polarization or phase. Vectorial diffraction integrals to describe light diffraction typically require boundary fields on aperture surfaces. Estimating such boundary fields can be challenging in complex systems that induce multiple depolarizations, unless vectorial ray tracing using Jones matrices is employed. The tracing method, however, has not been sufficiently detailed to cover complex systems and, more importantly, seems influenced by system geometry (transmission versus reflection). Here, we provide a full tutorial on vectorial diffraction calculation in optical systems. We revisit vectorial diffraction integrals and present our approach of consistent vectorial ray tracing irrespective of the system geometry, where both electromagnetic field vectors and ray vectors are traced. Our method is demonstrated in simple optical systems to better deliver our idea, and then in a complex system where point spread function broadening by a conjugate reflector is studied.
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12 March 2018: A typographical correction was made to the final paragraph of page 527.
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