Blurred and noisy image pairs in parallel optics

In previous works we have shown that parallel optics (PO) architecture can be used to improve the system matrix condition, which results in improving its immunity to additive noise in the image restoration process. PO is composed of a "main" system and an "auxiliary" system. Previously, we suggested the "trajectories" method to realize PO. In that method, a required auxiliary system is composed from auxiliary optics with a pixel confined response, followed by signal processing. In this paper, we emphasize the important secondary effects of the trajectories method. We show that in such a system, where the postprocessing comes after the detection, the postprocessing acts as a noise filter, hence allowing us to work with noisy data in the auxiliary channel. Roughly speaking, the SNR of an imaging system depends on the numerical aperture (NA). It follows that the main system, which typically has a higher NA, also has a higher SNR. Hence in the PO system, the ratio between the NA values of the main and auxiliary systems is expected to dictate the gap between their SNR values. In this paper, we show that when the system is implemented by the trajectories method, this expectation is too conservative. It is shown that due to the noise filtering, the auxiliary system can be noisier than expected. This claim is proved analytically and verified and exemplified by using experimental measurements.