Validity of diffraction tomography based on the first Born and the first Rytov approximations

Abstract

Using computer simulations we examine the ranges of validity of the first Born and first Rytov approximations employed in diffraction tomography. To that end we apply the filtered backpropagation (FBP) algorithm in conjunction with the first Born approximation and the hybrid FBP algorithm in conjunction with the first Rytov approximation. We find that the range of validity of the first Born approximation is approximately 3 times smaller than that of the first Rytov approximation and that the range of validity of each approximation can be expressed in terms of the product of the refractive-index difference between the object and the background and the size of the object. Also, we establish precise criteria for the validity of diffraction tomography within each of these two approximations. For the first Rytov approximation the validity of the hybrid FBP algorithm is found to be limited by phase-unwrapping problems.