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# FindSatellitePeaks v1¶

## Summary¶

Algorithm for finding satellite peaks in an MDWorkspace in the HKL frame.

## Properties¶

Name

Direction

Type

Default

Description

NuclearPeaks

Input

PeaksWorkspace

Mandatory

Main integer HKL peaks. Q vectors will be calculated relative to these peaks.

SatellitePeaks

Input

PeaksWorkspace

Mandatory

Positions of seed satellite peaks. These will be used to define the modulation (q) vectors for each satellite.

MDWorkspace

Input

Workspace

Mandatory

MD workspace to search for satellites peak in. This data must be in the HKL frame.

OutputWorkspace

Output

PeaksWorkspace

Mandatory

All found satellite peaks. These will be given with satellite coordinates.

NumOfQs

Input

number

-1

The number of satellite peaks to look for. If this option is not set to the default then all the provided satellites will be grouped into exactly this number of modulation (q) vectors

ClusterThreshold

Input

number

1.5

Threshold for automaticallty deciding on the number of modulation (q) vectors to use. If NumOfQs found is set then this is property is ignored.

Input

number

0.1

The peak radius used to integrate the satellite peaks. This is Euclidean distance in HKL space. This is passed directly to IntegratePeaksMD

Input

number

0.1

The inner background radius used to integrate the satellite peaks. This is Euclidean distance in HKL space. This is passed directly to IntegratePeaksMD

Input

number

0.2

The outer background radius used to integrate satellite peaks. This is Euclidean distance in HKL space. his is passed directly to IntegratePeaksMD

IOverSigma

Input

number

2

The I/sigma threshold use to identify if peaks exist. This is passed direclty to FilterPeaks

## Description¶

FindSatellitePeaks can be used to refine the locations of “satellite” peaks occurring at fractional HKL locations in reciprocal space. FindSatellitePeaks takes a MDWorkspace of experimental data, a PeaksWorkspace containing the locations of peaks with integer HKL, and another PeaksWorkspace containing a subset of peaks found at fractional HKL.

For each satellite peak the euclidean distance between the nearest integer peak and satellite are computed in the HKL frame. Peaks are then grouped according to euclidean distance using using the properties NumOfQs and ClusterThreshold. If NumOfQs is specified then each offset will be grouped into exactly k clusters. If ClusterThreshold is specified then offsets will be grouped into clusters separated by no more than a cophenetic distance below this threshold. The centroid of each cluster calculated for each group and is used as the offset to predict the location of fractional peaks everywhere in the MDWorkspace.

For each predicted fractional peak, the local centroid (the radius of which is defined by PeakRadius) in the MD data is found and this is taken as the actual position of the satellite peaks.

Finally the found satellite peaks are integerated using the IntegratePeaksMD algorithm with the parameters PeakRadius, BackgroundInnerRadius, and BackgroundOuterRadius. Satellite peaks are discarded if there I/sigma value is less than the parameter IOverSigma.

The output of the algorithm is a peaks workspace containing all of the satellite peaks found by the algorithm in fractional coordinates. Each of the peaks will have an intensity value from the IntegratePeaksMD algorithm.

Warning

This integration is very approximate and may not produce the best possible values. It is recommended that satellite peaks are reintegrated using one of the many peak integration algorithms and to tune their parameters to obtain the best possible peak integration.

• Van Smaalen, Sander. “An elementary introduction to superspace crystallography.” Zeitschrift für Kristallographie-Crystalline Materials 219, no. 11 (2004): 681-691.

• Van Smaalen, Sander. “Incommensurate crystal structures.” Crystallography Reviews 4, no. 2 (1995): 79-202.

## Usage¶

Note

Example - calling FindSatellitePeaks:

md_workspace = Load(Filename='WISH_md_small.nxs', OutputWorkspace='WISH_md_small')

params = {
"OutputWorkspace": "refined_peaks",
"NumOfQs": 2
}

satellites_refined = FindSatellitePeaks(NuclearPeaks=main_peaks, SatellitePeaks=satellite_peaks, MDWorkspace=md_workspace, **params)

print (len(satellites_refined))


Output:

4


Categories: AlgorithmIndex | Crystal\Peaks

## Source¶

Python: FindSatellitePeaks.py