Analog computing has emerged as a promising candidate for real-time and parallel continuous data processing. This paper presents a reciprocal way for realizing asymmetric optical transfer functions (OTFs) in the reflection side of the on-axis processing channels. It is rigorously demonstrated that the presence of Cross-polarization Exciting Normal Polarizabilities (CPENP) of a reciprocal metasurface circumvents the famous challenge of Greens function approach in implementation of on-axis reflective optical signal processing while providing dual computing channels under orthogonal polarizations. Following a comprehensive theoretical discussion and as a proof of concept, an all-dielectric optical metasurface is elaborately designed to exhibit the desired surface polarizabilities, thereby reflecting the first derivative and extracting the edges of images impinging from normal direction. The proposed study offers a flexible design method for on-axis metasurface-based optical signal processing and also, dramatically facilitates the experimental setup required for ultrafast analog computation and image processing.
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