## Bug #2416

### Polarization: Fix treatment of imperfect analyzers

Status: | Backlog | Start date: | 20 Nov 2019 | |
---|---|---|---|---|

Priority: | Normal | Due date: | ||

Assignee: | - | % Done: | 0% | |

Category: | - | |||

Target version: | - |

**Description**

Currently the analyzer operator used in BornAgain is written (in latex notation) as

a = t (1 + \xi \sigma p).

Here t is the transmission, \xi - efficiency, p - vector of analyzer direction, \sigma - vector of Pauli matrices.

However, only the combination of t = 1/2, \xi = 1 and |p| = 1 is meaningful and corresponds

to a perfect analyzer (i.e. the one always selecting a particular polarization state).

According to the section 4 of this internal report

(note that login to jugit is required to access the document), the analyzer operator should look like

a = \frac{t}{2} (2 - |p| + \sigma p).

Then |p| <= 1 corresponds to the efficiency of the analyzer and 0 <= t <= 1 - to the transmission.

The formula above for sure works for specular reflectivity, but before modifying the code it is necessary

to check that it holds true in the case of GISAS. The description of polarized DWBA by Walter Van Herck can provide some insight in how DWBA is applied in BornAgain.

The analyzer operator is computed in **DetectionProperties::analyzerOperator**.

One will also need to change the signature of the method **setAnalyzerProperties** in **Simulation** class, and correspondingly amend polarization-related classes in the GUI.

**Related issues**

### History

#### #2 Updated by dmitry 8 months ago

**Related to***Envelope task #2419: Polarized reflectivity*added

#### #5 Updated by rbeerwerth 9 days ago

After a first discussion with Artur, he wasn't happy with this operator at all.

He also pointed me to https://doi.org/10.1063/1.1150060, this is the standard paper for treating imperfect instruments.

I will study that and the rethink this problem. For the moment I leave the implemented operator in BornAgain untouched (NOT the one described in the documents).

Also, we need to pay attention to the case polarized beam + no polarization analysis, this is actually the experimental standard case. This corresponds to p = 0, but we might want to provide it as a default if no analyzer is specified.