Measurement of photon incident at an angle on detector

Let us consider an experiment where photons of some frequency $nu$ are incident on a photo detector. Now, say the photons are incident at some angle $theta$ with the normal, then the component of momentum perpendicular to the surface of the detector will be $hbar nu cos(theta)$.

So, if the detector was completely absorbing the photons, it shall measure the total momentum and thus give a value of frequency as $nu$, but if the detector had a reflective surface, then will it not give the measured value of photon frequency as $nu ‘ = nu Cos(theta)$. Also, is there any real world example of where this effect is seen?(Say photoelectric effect on a shiny metal surface maybe)

PS: To consider a realization of such a detector, consider a surface covered with microscopic pressure sensors that only absorb the momentum perpendicular to them. Such a surface can be used to measure only the component of momentum perpendicular to surface.