A general framework for vectorial detection PSF analysis for oblique plane microscopy utilizing trans-medium intermediate image coupling.

We present a unified theoretical framework for vectorial detection point spread function (PSF) analysis in oblique plane microscopy (OPM) systems incorporating arbitrary combinations of secondary and tertiary objectives. By modeling the amplitude, polarization, and phase modulation of each refracted ray at the trans-medium interface, we quantitatively evaluate how key parameters-including the oblique plane angle, the refractive index of the immersion medium, and system geometry-affect the size and orientation of the 3D detection PSF under the remote focusing condition and within the Debye approximation. Especially, we show that the differential optical path length, which is central to PSF estimation, is independent of the refractive index of the tertiary objective's working medium. Furthermore, by comparing three representative secondary-to-tertiary objective configurations, we find that the trans-medium intermediate image coupling configuration generally yields a detection PSF that is more closely aligned with the secondary objective's optical axis. This framework provides a generalizable approach for assessing OPM performance under diverse optical configurations and offers practical guidance for system design and optimization.