The key in the quality evaluation of the speckle is to construct model which can describe the relation between speckle pattern feature parameters and measurement error of digital image correlation method. Till date, no theoretical analysis model describing the relation between the speckle pattern and its power spectrum has been reported. To address this issue and considering the perspective of stochastic process analysis, the relations between the auto-correlation function of the binary speckle and parameters of speckle duty, speckle radius, and gray value are investigated herein. Furthermore, the theoretical analytical form of the binary speckle power spectrum is obtained according to the Wiener-Khintchine theorem. Finally, the theoretical analysis results are verified by numerical experiments. It is observed that the theoretically derived results are consistent with the numerical experiment results on the main lobe of the power spectrum and on several side-lobes nearby. Considering the power spectrum, the maximum value of the main spectrum is consistent with the experimental results. This model can be applied to subsequent speckle error analysis studies.