Hidden symmetry of the beam spread function resulting from the reciprocity theorem

- Symmetry properties of beam spread function (BSF) are considered.
- In uniform turbid medium BSF has hidden symmetry property besides axial symmetry.
- The examples of BSF models with and without the required symmetry are given.
- A universal method for BSF symmetry error elimination is proposed.

It is shown that the optical reciprocity theorem imposes certain constraints on the radiation field structure of a unidirectional point source (beam spread function (BSF)) in a turbid medium with spatially uniform optical properties. To satisfy the reciprocal relation, the BSF should have an additional symmetry property along with axial symmetry. This paper mathematically formulates the BSF symmetry condition that follows from the reciprocity theorem and discusses test results of some approximate analytical BSF models for their compliance with the symmetry requirement. A universal method for eliminating symmetry errors of approximate BSF models is proposed.