Modeling phase microscopy of transparent three-dimensional objects: a product-of-convolutions approach

We present a product-of-convolutions (POC) model for phase microscopy images. The model was designed to simulate phase images of thick heterogeneous transparent objects. The POC approach attempts to capture phase delays along the optical axis by modeling the imaged object as a stack of parallel slices. The product of two-dimensional convolutions between each slice and the appropriate slice of the point spread function is used to represent the object at the image plane. The total electric field at the image plane is calculated as the product of the object function and the incident field. Phase images from forward models based on the first Born and Rytov approximations are used for comparison. Computer simulations and measured images illustrate the ability of the POC model to represent phase images from thick heterogeneous objects accurately, cases where the first Born and Rytov models have well-known limitations. Finally, measured phase microscopy images of mouse embryos are compared to those produced by the Born, Rytov, and POC models. Our comparisons show that the POC model is capable of producing accurate representations of these more complex phase images.