Monomorphous decomposition method and its application for phase retrieval and phase-contrast tomography

We show that an arbitrary spatial distribution of complex refractive index decrement inside an object can be exactly represented as a sum of two "monomorphous" complex distributions, i.e., distributions with the ratios of the real part to the imaginary part being constant throughout the object. A 'priori' knowledge of constituent materials can be used to estimate the global lower and upper boundaries for this ratio. This "monomorphous decomposition" approach can be viewed as an extension of the successful phase-retrieval method, based on the transport of intensity equation, that was previously developed for monomorphous (homogeneous) objects, such as, e.g., objects consisting of a single material. We demonstrate that the monomorphous decomposition can lead to more stable methods for phase retrieval using the transport of intensity equation. Such methods may find application in quantitative in-line phase-contrast imaging and phase-contrast tomography.