Can Born Approximate the Unborn? A New Validity Criterion for the Born Approximation in Microscopic Imaging

The Nomarski differential interference contrast (DIC) microscopy is of widespread use for observing live biological specimens. In fertility clinics the DIC microscope is used for evaluating human embryo cells. An image formation model for DIC imaging is needed for reconstruction and quantification of the visualized specimens. This calls for a complicated analysis of the interaction of light waves with biological matter. Most works express the solution via the first Born approximation, yet a theoretical bound is known that limits the validity of such approximation to very small objects. We show in this work that the theoretical bound is not directly relevant to microscopic imaging and is far too limiting. We derive a more realistic bound and show that it may justify in many cases the use of the Born approximation in biological cell microscopic imaging. It also provides limits on the validity of the Born expansion that several works violate.