The role of detector position in quantum ghost diffraction

Quantum ghost diffraction enables the measurement of the spatial diffraction pattern of an object without measuring the spatial distribution of the photons that actually interacted with the object [1]. It uses photon pairs generated e.g. by spontaneous parametric down conversion (SPDC) in a nonlinear optical crystal, and relies on the correlation of the generated signal and idler photons in their spatial and temporal degrees of freedom. This measurement scheme is sketched in Fig. 1 (a). After the source, the two photons are separated into two different paths. The object, here we consider a grating, is located only in the signal path and thus interacts only with the signal photons. To measure the diffraction pattern, two detectors of small cross sections are used in the signal and idler arms. The signal detector is usually at a fixed position, collecting photons that interacted with the object. The idler detector can have varying positions, allowing to spatially resolve the collected photons that never interacted with the object. Through measuring the two-photon coincidence counting rate R, there exists the potential for recovering the diffraction pattern of the object, which allows to retrieve the grating period.