Validity criterion for the Born approximation convergence in microscopy imaging.
The need for the reconstruction and quantification of visualized objects from light microscopy images requires an image formation model that adequately describes the interaction of light waves with biological matter. Differential interference contrast (DIC) microscopy, as well as light microscopy, uses the common model of the scalar Helmholtz equation. Its solution is frequently expressed via the Born approximation. A theoretical bound is known that limits the validity of such an approximation to very small objects. We present an analytic criterion for the validity region of the Born approximation. In contrast to the theoretical known bound, the suggested criterion considers the field at the lens, external to the object, that corresponds to microscopic imaging and extends the validity region of the approximation. An analytical proof of convergence is presented to support the derived criterion. The suggested criterion for the Born approximation validity region is described in the context of a DIC microscope, yet it is relevant for any light microscope with similar fundamental apparatus.
Trattner
Sigal
S
Department of BioMedical Engineering, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel. trattner@post.tau.ac.il
Feigin
Micha
M
Greenspan
Hayit
H
Sochen
Nir
N
D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008857:Microscopy, Interference / Q000379:methods*; D015203:Reproducibility of Results