A linear model for coherent diffractive imaging (CDI) is proposed herein. In this model, CDI is expressed as a system of linear equations in the frequency domain of an object and illumination. The linear system can be directly determined to provide a unique solution for complex samples. The method is analytical and straightforward and does not require any approximation. The simulation results demonstrate that the proposed method is valid for all CDI-related imaging methods, such as traditional CDI, ptychography, coherent modulation imaging, and multiple-plane phase retrieval. The relationship between the method and the convergence of iterative phase retrieval is discussed. This mathematical model provides a direct method for analyzing the underlying physics of CDI and can be used to predict the accuracy and error in CDI applications, such as measurement and metrology.
