In this talk, we present three methods of characterizing the spatial degrees of freedom of heralded single photons and entangled photon pairs. First, we introduce a self-referenced interferometric technique that allows the reconstruction of two-dimensional photonic spatial profile by utilizing a single photon interfering with itself, offering a complete characterization of its spatial probability amplitude.

Second, we characterize spatially entangled photon pairs generated in the process of  spontaneous parametric down-conversion. We use a custom-built hybrid camera setup for observing spatial correlations of photon pairs with a high acquisition rate. In our demonstration of the hybrid camera setup, the number of photons detected within each frame can be controlled by gating an image intensifier adaptively.

Lastly, we discuss a nonlinear Zou-Wang-Mandel interferometer that is a basis of the  technique known as quantum imaging with undetected photons (QIUP). QIUP allows for image formation without requiring the detection of light that has interacted with the object being imaged. This approach enables image formation without detecting light that has interacted with the object being imaged. We utilize this interferometric technique for characterizing transverse momentum correlations of down-converted photon pairs without relying on coincidence measurements.