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Alternating minimization algorithm for quantitative differential-interference contrast (DIC) microscopy

A new iterative algorithm for quantitative image reconstruction for differential-interference contrast (DIC) microscopy is presented, along with simulations demonstrating key properties of the algorithm. The algorithm is an alternating minimization (AM) algorithm based on a diffraction imaging model for DIC images. The algorithm computes a specimen's complex transmittance function (magnitude and phase) from the DIC images. This new method extends the rotational diversity (RD) method developed by Preza that is based on the assumption that the specimen does not absorb light (or that its magnitude is constant and can be ignored) and thus only the specimen's phase function is computed from rotationally-diverse DIC images. The AM approach lifts the optimization problem to a higher dimensional space that is intimately tied to the underlying physics. The variables that are introduced in this lifting process are the unknown, unmeasurable phases on the data. The AM algorithm iterates between estimating the image given the phase of the data and estimating the phase given the image. The framework allows constraints and penalties on the magnitude and phase estimates to be incorporated in a principled manner. The performance of the AM method is evaluated using simulated noiseless data. Simulation results compare specimen magnitude (absorption) and phase estimated with the AM method to the true specimen parameters showing good quantitative agreement using the mean square error and difference images. The estimated phase is a significant improvement over the phase estimated with the RD method from the same DIC images as shown in a comparison between the two methods. The AM method provides a novel approach in extracting quantitative phase and amplitude information of the same field of view from a single microscope mode.