Rytov approximation for x-ray phase imaging.

In this study, we check the accuracy of the first-order Rytov approximation with a homogeneous sphere as a candidate for application in x-ray phase imaging of large objects e.g., luggage at the airport, or a human patient. Specifically, we propose a validity condition for the Rytov approximation in terms of a parameter V that depends on the complex refractive index of the sphere and the Fresnel number, for Fresnel numbers larger than 1000. In comparison with the exact Mie solution, we provide the accuracy of the Rytov approximation in predicting the intensity and phase profiles after the sphere. For large objects, where the Mie solution becomes numerically impractical, we use the principle of similarity to predict the accuracy of the Rytov approximation without explicit calculation of the Mie solution. Finally, we provide the maximum radius of the sphere for which the first order Rytov approximation remains valid within 1% accuracy.