An effective interpretation of defocusing and the corresponding defocus convolution kernel

•The physical cause of defocusing can be explained by the propagation of the focused image in image space.•The conservation of energy in the propagation of wavefront is expressed by a dedicated integral formula for the squared of the light disturbance.•The proposed defocus convolution kernel naturally satisfies the normalization condition and meets all the empirical rules.•The proposed defocus convolution kernel is closer to the actual one than the well-known Gaussian one since overcoming the visible ringing artifact in the restored images. The defocusing phenomenon of an optical system is determined by the defocus convolution kernel (DCK). However, the DCKs in the current defocusing theories fail to match the empirical rules of the actual DCK. In this paper, the physical cause of defocusing is supposed to be the propagation of the focused image in image space. For ensuring the conservation of energy during the propagation, an integral formula for the squared of the light disturbance is deduced. The proposed DCK not only naturally satisfies the normalization condition and meets all empirical rules, but is more accurate than the well-known Gaussian DCK since overcoming the visual ringing artifact when restoring the defocused image. Considering the features of image space, the defocusing mechanism can be taken as the real- and virtual- propagation of the defocus image, resulting in the symmetry of the defocusing about the plane of focus.