Microwave Speckle Correlation Modeling Under the Coupling of Illumination Angle Change and Object Translation

To apply microwave speckle to marker tracking and displacement measurement like vision-based techniques, its correlation model under object movement is required to be more accurate. However, to obtain the analytical form, the traditional hypothesis of the correlated function of the reflected wave from the rough surface is contradictory. In this article, we use the joint characteristic function to resolve the hypothetical contradictions, and the correlation function is resolved by the characteristics of the microwave speckle and the imaging point spread function. First, the joint characteristic function of two variables on the Gaussian rough surface is used to describe the coupling factor of movement. Then, the inner integral is transformed to the wavenumber domain to utilize the characteristics of the <tex-math notation="LaTeX">sinc(·)</tex-math> . And the outer integrals are approximated by the equivalent scatterers number <tex-math notation="LaTeX">N</tex-math> greater than one. Meanwhile, the approximated error with the <tex-math notation="LaTeX">N</tex-math> is described quantitatively, and the estimation of the upper limit of the model error only by images is proposed. Finally, we have demonstrated that the model is superior to the classical Goodman's theory and product model in both computational electromagnetics (CEMs) and 3-D millimeter-wave imaging experiments. And the model is applied for translation measurement with 0.04-pixel accuracy.