# ScatteringMatrixΒΆ

This post process computes a number of quantities used in ellipsometry and scatterometry from the far field of a simulation. As an input it needs the result from the FourierTransform post process, whose results have to be aligned, such that the z-Axis is the optical axis. This can be achieved by corresponding simulation setup or a `CoordinateRenaming`

in the FourierTransform post process. Further, the sources of the initial project have to be plane waves, and for each incidence direction two non-parallel polarizations have to be defined.

The basis of this post process is the SP-Jones matrix. It defines how the amplitude of an S- or P-polarized incidence wave is scattered or transmitted into the S- and P-direction, defined by the outgoing direction.

There is a large number of different possibilities how to define S- and P-direction. Each physical or engineering community basically has its own. You may use PolarizationConvention to switch to your prefered one.
In `JCMsuite`

the convention described in PlaneWave is used by default. The key properties of this definition are the following:
If a wave propagates in +Z or -Z direction, the S-direction is aligned along +Y and the P-direction along +X. The X- and Y-axis are rotated to give the S- and P-direction according to and of the incidence or outgoing direction. Thereby, is always the angle between the Z-axis and the propagation direction. It is restricted between 0 and 90 degrees. Definition of angle for upward or downward propagating fields can best be understood from the drawing given in PlaneWave.

A number of quantities derived from the Jones matrix are further computed and written into the output table. These are:

- 4x4 Mueller matrix
- Rho:
- Delta and Psi defined by:

Further, all the quantities are defined for SP-directions and Sigma/XY-directions as defined in PlaneWave.

The incoming and outgoing directions of the computed quantities are given by their corresponding incidence and outgoing k-Vectors and and .