Spontaneous parametric down-conversion (SPDC) is a reliable source for generating two-photon entangled states and is recently employed in many quantum optical applications, e.g. quantum cryptography, quantum teleportation, quantum lithography, etc. There are several theoretical studies and experiments of this have been approved. It is briefly described as follows: One photon (signal) of a two-photon pair generated from SPDC of a nonlinear optical crystal (NLC) travels through an optical system, while the other (idler) travels through a different optical system. The location of idler photons is recorded by a scanning detector, while signal photons are registered by a fixed “bucket” detector. Then an image is extracted from certain coincidence statistics, called second-order correlation functions, at the scanning detector of idler photons. Note that the bucket detector can serve as a “gating” signal for the scanning detector. There is another point of view of the quantum image in the framework of Klyshko’s concept of advanced waves: A point source located at the bucket detector emits waves traveling backward through the optical system of signal photons, and then interacting with the pump beam in the NLC. While the two-photon entangled source of SPDC in the NLC serves as a special reflector, treated as a mirror, the waves converted through the optical system of idler photons create an image on the plane of the scanning detector. The quantum image was also named “ghost image” due to the fact that the image of the object is reconstructed by photons that never actually pass through the object. Another interesting subject of quantum mechanics is about Berry phase. In general, Berry phase is defined as a topological (geometric) phase that is acquired by a quantum mechanical system while following a closed circuit in parameter space of the corresponding Hamiltonian, e.g. the well known Aharonov-Bohm effect of electrons. This phase is non-integrable, and in particular is not single-valued going around a closed circuit. In optical systems, the phase acquired by an optical beam depends on the “geometry” of the path, not on the optical path length. Some manifestations of Berry phase for photons, including a quantum level and a classical level, have been verified. In the thesis, we focus on analyzing an optical system bearing Berry phase via orbital angular momentum (OAM) modes, i.e. LG modes, especially in the two-photon level. In addition, we also show this phase via wave vectors. On our best knowledge, effects of Berry phase are always appeared by the first-order correlation (interference), and no one discusses these in the second-order correlation.