Model-fitting perspective on the robustness and speed of CLASS in reflection matrix microscopy

Closed-loop accumulation of single scattering (CLASS) recovers the input and output pupil aberrations from intrinsic tissue reflections, even under strong multiple scattering. Its central principle is to maximize the correlation among the ballistic waves in a measured reflection matrix, so that elements sharing the same momentum transfer add coherently. Here we recast CLASS as the solution of a model-fitting problem. We show that correlation maximization is equivalent to a least-squares fit of the measured matrix to a separable forward model with two specific features. First, variable projection removes the object spectrum from the fitted parameters by folding it into the pupil-aberration update. Second, each group of matrix elements sharing the same momentum transfer is weighted in proportion to its size, so the fit favors higher-fidelity data. We then test this account by comparing CLASS against model fits that lack one or both of these features. For the comparison, we devised an experimental scheme that measures reflection matrices with the aberration and the multiple-scattering background controlled independently on a single target. Under increasing scattering and aberration, a fit that trains the object spectrum matches the reduced fit and CLASS once its object learning rate is scaled to the data; variable projection removes the need to choose this rate. Under reduced angular sampling, the unweighted fits work reliably only up to approximately 24% of the illumination angles removed, whereas CLASS, the multiplicity-weighted fit, keeps working up to 53%. CLASS stays accurate over the widest range and, in our implementation, converges fastest. We release these matrices as benchmark data.