The structural evolution of the axial intensity distribution during hot image formation perturbed by a small circular optical obscuration is investigated in detail under different conditions. An analytic expression is derived for the axial intensity distribution around the conjugate plane by assuming the thickness of the nonlinear medium to be infinitely small. In view of the analysis of the axial intensity oscillation, the expression can be extensively utilized to characterize the intensity maxima for a nonlinear medium with a finite thickness. The nonlinear medium thickness and obscuration size both have great influence on the magnitudes and distributed features of the intensity maxima, which initially vary from multiple ones with comparable intensities to ultimately a maximum of one obviously remaining. The reason for this phenomenon is that the nonlinear medium acts like a low-pass filter to the scattering field, and optical interference exists between the scattering and background field. Furthermore, a fixed expression of nonlinear medium thickness and obscuration size is obtained to determine the dividing point of the alterations of the hot image intensity distribution.
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