Equivalence analysis of Fourier ghost imaging and sinusoidal ghost imaging

Ghost imaging, also known as correlation imaging, is one of the research hotspots in the imaging field. Various ghost imaging systems with different basic principles and implementation architectures have emerged, but the correlation between them is weak, showing a diversified trend and recent research progress is slower than before. Studying the essence of ghost imaging theory is a feasible direction to explore the unknown field of ghost imaging. Through research, we find that Fourier ghost imaging and sinusoidal ghost imaging are based on the same type of orthogonal sine speckle and cosine speckle, which have a very high similarity. At the same time, sinusoidal ghost imaging method can give a complete spatial description and spatial imaging process, so we guess that these two imaging methods can reveal the relationship between spatial imaging and Fourier domain imaging. On this basis, it is proved that Fourier ghost imaging and sinusoidal ghost imaging are equivalent in principle. The former can be realized by n-step phase shift, while the latter can be equivalent to two-step phase shift. Considering that both of these methods use sine and cosine fringes as structural speckles. By combining the spatial decomposition characteristics of sine speckle imaging, the relationship between structural speckle imaging and traditional ghost imaging is analyzed, and the principles of some methods constructed on the basis of these two methods are explained. The simulation results applied to edge detection show that the combination of the two methods can simultaneously obtain the better anti-noise performance of Fourier ghost imaging and the higher imaging efficiency of sinusoidal ghost imaging. Since sinusoidal ghost imaging relates the characteristics of image spatial decomposition to traditional ghost imaging, and their expression is equivalent to the expression of orthogonal Fourier transform domain of Fourier ghost imaging, the association of ghost imaging methods in Fourier domain and even in the whole orthogonal transform domain and spatial domain can be generalized. This conclusion may provide a way for associating different kinds of ghost imaging, and it can be hoped that more and more new types of ghost imaging systems will be developed.