Numerical aperture influences on image speckle fields near a random surface

In order to reveal influences of numerical aperture on image speckle fields near a random surface, we adopt a convenient and practical method to make it. We choose an interference pattern of a reference light and an image speckle field, and then obtain its first-order frequency spectrum by Fourier transform. In inverse Fourier transform, we change the range of the frequency spectrum, and different distributions of speckle intensities, phase and phase vortices are presented. In addition, their statistical properties are also given. It is shown that with a decrease of range of the first-order frequency spectrum, equivalent to numerical aperture reduced, image speckle fields take on different features. Moreover, their statistical properties are distinct from each other. This paper is significant to understand influences caused by numerical aperture on image speckle fields and helpful for applications of speckle fields near a random surface.