  The evaluation of a photon-pair source employs metrics like photon-pair
generation rate, heralding efficiency, and second-order correlation function,
all of which are determined by the photon number distribution of the source.
These metrics, however, can be altered due to spectral or spatial filtering and
optical losses, leading to changes in the metric characteristics. In this
paper, we theoretically describe these changes in the photon number
distribution and the effect of noise counts. We also review the previous
methods used for estimating these characteristics and the photon number
distribution. Moreover, we introduce an improved methodology for estimating the
photon number distribution, focusing on photon-pair sources, and discuss the
accuracy of the calculated characteristics from the estimated (or
reconstructed) photon number distribution through simulations and experiments.

Quantum Physics