Ghost imaging through turbulent atmospheres are theoretically studied. Based on the extended Huygens-Fresnel integral, we obtain an analytical imaging formula. The ghost image can be viewed as the convolution of the original object and a point-spread function (PSF). The imaging quality is determined by the size of the PSF. Increasing the turbulence strength and propagation distance, or decreasing the source size, will increase the size of the PSF, and lead to the degradation of the imaging quality.

We show that the image quality of ghost imaging (GI) can be controlled by the use of shaped incoherent sources. The formula for the point-spread function in the GI system has been derived and is determined by the Fourier transform of the source intensity distribution. Compared with the widely used Gaussian Schell-model source, we find that using a cosine-Gaussian Schell-model source can lead to the degradation of GI quality, while the quality of GI can be increased with a cosh-Gaussian Schell-model source. Even under atmospheric turbulence, the image resolution of GI still can be improved by means of the cosh-Gaussian Schell-model source.

Reflective ghost diffraction (GD) for objects with rough surfaces is investigated theoretically and numerically. Using a speckle model to describe the reflectivity of the object with variable rough surfaces, the incident and reflective angle-dependent diffraction condition is obtained, and the analytical expression of the reflective GD is derived. Numerical simulations are given to show how the height variance and correlation length of the object and the reflective angle in the experimental scheme can affect the quality of the reflective GD. Specifically, we find that the changes of diffraction patterns of both the simple objects and the complicated objects are sensitive to parameters such as the reflective angle and the surface fluctuation. Additionally, comparative studies on both reflective GD and ghost imaging (GI) have also been performed. We find that reflective GI is more robust against system parameters than reflective GD. These results may be useful for future experimental works.

We show how quantum entangled biphoton states can be used to realize ghost scattering, a nonlocal scheme to obtain scattering information of an unknown object through the correlation measurement of the scattering photons in two different optical paths. We present a framework to describe the biphoton ghost scattering process from the T-matrix formula of the scattering theory. We find the scattering information of a test object can be retrieved from either the test arm or the reference arm. By adjusting the biphoton states, the ghost scattering patterns may be varied from the scattering pattern of the object in the test arm to the object in the reference arm.

Current ghost imaging phase reconstruction schemes require either complex optical systems, iterative algorithms, Fourier transform steps, or entangled photon pairs. These factors may increase the difficulty of system design, lead to phase retrieval errors, or result in excessive time consumption. To tackle this challenge, we propose a five-step phase-shifting method that eliminates the need for complex optical systems, Fourier transform steps, entangled photon pairs, or iterative algorithms. Using five specifically designed incoherent sources, we can generate five distinct ghost imaging patterns. Subsequently, the phase information of the object can be calculated from these five speckle patterns. Additionally, we offer a detailed theoretical explanation for choosing the five-step phase-shifting method over the more commonly used three-step or four-step phase-shifting methods. We demonstrate the applicability of this theoretical proposal through numerical simulations involving two types of complicated objects. The results illustrate that the phase information of the complex object can be successfully and quantitatively reconstructed.

We generalize the theory of ghost scattering with scalar incoherent light sources to the case of stochastic electromagnetic beams under the first-order Born approximation. We derive the expressions for the correlation of intensity fluctuations of the far-zone scattered fields and use them to study the properties of the scatterers. When the incident beam belongs to the class of electromagnetic Gaussian Schell-model beams, we discuss the dependence of ghost scattering results on the parameters such as the coherence lengths, source widths, polarization amplitudes, and degree of coherence. We find under the condition of linear polarized incident beams the scalar ghost scattering results can be retrieved, while the deviation from linear polarization may significantly distort the electromagnetic ghost scattering results.