arctanS2S1

arctanS2S1 is a notation that does not refer to a single universal mathematical function, but rather to a form of the arctangent applied to two quantities labeled S2 and S1. In practice, it often represents the idea of computing an angle from two components, typically by taking the arctangent of their ratio or by using a two-argument variant such as arctan2(S2, S1). The exact meaning depends on the context, including the definitions of S1 and S2 and the conventions used for angular measurements.

A common mathematical interpretation is arctan(S2/S1), which yields an angle whose tangent equals the ratio S2/S1. This can be ambiguous with respect to the quadrant in which the angle lies, because the ordinary arctangent function has a principal value and loses information about the signs of both arguments. To address this, the two-argument arctangent function, arctan2(S2, S1), is often preferred because it returns an angle in the full range, correctly locating the angle based on the signs of S1 and S2.

In polarization optics and related fields, S1 and S2 may denote components of the Stokes parameters describing linear polarization. In such contexts, the angle of polarization or orientation angle is frequently derived as psi = (1/2) arctan2(S2, S1). This use highlights how arctanS2S1-like expressions connect to practical measurements of direction or phase from two correlated quantities.

Key considerations when using arctanS2S1 ideas include ensuring consistent definitions of S1 and S2, choosing atan2 over arctan for quadrant correctness, and handling edge cases where denominators vanish.