The diffraction-based optical frequency response characteristic of a birefringent crystal lens sandwiched between two linear polarizers has been studied analytically using the autocorrelation of the pupil function over the lens aperture. The optical transfer function (oTf) of this proposed system depends on the material as well as design parameters of the crystal lens, along with the orientations of the transmission axes of the two polarizers relative to each other and to the optic axis of the birefringent lens. Naturally, the OTF of such a system can be varied at the lens fabrication stage like other lenses. An online variation of the OTF is also possible just by rotating any of the two polarizers included in the system. It has been shown that the proposed system can be adapted either for apodization or for super-resolution simply by rotating any of the two polarizers. This system may be designed for obtaining high depth of focus without significant image degradation, as well as for image processing operations like high frequency enhancement. The response of the system is studied at the Gaussian image plane as a function of the line frequencies in the object for different values of the birefringent lens parameters, and also for two different settings of the analyzer. The results are compared with the response of an ideal lens.