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# HB3AIntegrateDetectorPeaks v1¶

## Summary¶

Integrate four-circle rocking-scan peak in detector space from HB3A

## Properties¶

Name

Direction

Type

Default

Description

InputWorkspace

Input

str list

Mandatory

Workspace or comma-separated workspace list containing input MDHisto scan data.

Method

Input

string

Fitted

Integration method to use. Allowed values: [‘Counts’, ‘CountsWithFitting’, ‘Fitted’]

NumBackgroundPts

Input

number

3

Number of background points from beginning and end of scan to use for background estimation

WidthScale

Input

number

2

Controls integration range (+/- WidthScale/2*FWHM) defined around motor positions for CountsWithFitting method

LowerLeft

Input

long list

128,128

Region of interest lower-left corner, in detector pixels

UpperRight

Input

long list

384,384

Region of interest upper-right corner, in detector pixels

StartX

Input

number

Optional

The start of the scan axis fitting range in degrees, either omega or chi axis.

EndX

Input

number

Optional

The end of the scan axis fitting range in degrees, either omega or chi axis.

ScaleFactor

Input

number

1

scale the integrated intensity by this value

ChiSqMax

Input

number

10

Fitting resulting in chi-sqaured higher than this won’t be added to the output

SignalNoiseMin

Input

number

1

Minimum Signal/Noice ratio (Intensity/SigmaIntensity) of peak to be added to the output

ApplyLorentz

Input

boolean

True

If to apply Lorentz Correction to intensity

OutputFitResults

Input

boolean

False

This will output the fitting result workspace and a ROI workspace

OptimizeQVector

Input

boolean

True

This will convert the data to q and optimize the peak location using CentroidPeaksdMD

OutputWorkspace

Output

IPeaksWorkspace

Mandatory

Output Peaks Workspace

## Description¶

The input to this algorithm is intended as part of the DEMAND data reduction workflow, using HB3AAdjustSampleNorm with OutputType=Detector which can be seen below in the example usage.

This will reduce the input workspace using the region of interest provided to create a 1-dimension workspace with an axis that is the detector scan, either omega or chi in degrees.

An optional fitting range of the scan axis can be provided with StartX and EndX in degrees, which is applicable for the CountsWithFitting and Fitted methods.

The OptimizeQVector option will convert the input data into Q and use CentroidPeaksdMD to find the correct Q-vector starting from the known HKL and UB matrix of the peaks. This will not effect the integration of the peak but allows the UB matrix to be refined afterwards.

### Integration Methods¶

There are three different methods for integrating the input workspace: simple counts summation, simple counts summation with fitted background, and a fitted model.

#### Counts¶

This method uses the simple cuboid integration to approximate the integrated peak intensity.

$I = \sum_i (C_i - B_i) \times \Delta X$
where
• $$C_i$$ is the normalized detector counts in ROI of measurement i

• $$\Delta X$$ is the motor step

• $$B_i$$ is the estimated background

The error is calculated as

$\sigma = \sum_i \sqrt{C_i} \cdot \Delta X$

The background is estimated by averaging data from the first and last scans:

$B = \frac{\sum_i^{<pt>}C_i}{|<pt>|}$

where $$<pt>$$ is the number of scans to include in the background estimation and is specified with the NumBackgroundPts option.

#### CountsWithFitting¶

For Method=CountsWithFitting, the input is fit to a Gaussian with a flat background, just like Method=Fitting. However, the peak intensity is instead approximated by summing the detector counts over a specific set of measurements that are defined by the motor positions in the range of $$\pm \frac{N}{2} \text{FWHM}$$, where N is controlled with the WidthScale option. The background is removed over the same range using the fitted flat background.

$I = \sum_i^{<pt>} (C_i - B) \times \Delta X$
where
• $$C_i$$ is the normalized detector counts in ROI of measurement i

• $$\Delta X$$ is the motor step

• $$B_i$$ is the estimated background

• the set of measurements <pt> is defined by the motor positions in the range of $$x_0 \pm \frac{N}{2}FWHM$$.

• usually the default value of N is set to 2.

• $$FWHM = 2\sqrt{2\ln2}s \approx 2.3548s$$

The error is calculated as

$\sigma = \sum_i \sqrt{C_i} \cdot \Delta X$

#### Fitted¶

For Method=Fitted, the reduced workspace is fitted using Fit with a flat background and a Gaussian, then the area of the Gaussian is used as the peak intensity:

$I = A\times s\times\sqrt{2\pi}$

The error of the intensity is calculated by the propagation of fitted error of A and s.

$\sigma_I^2 = 2\pi (A^2\cdot \sigma_s^2 + \sigma_A^2\cdot s^2 + 2\cdot A\cdot s\cdot \sigma_{As})$

## Usage¶

Example - DEMAND single detector peak integration

data = HB3AAdjustSampleNorm(Filename='HB3A_data.nxs', OutputType='Detector')
peaks = HB3AIntegrateDetectorPeaks(data,
ChiSqMax=100,
OutputFitResults=True,
LowerLeft=[200, 200],
UpperRight=[312, 312])
print('HKL={h:.0f}{k:.0f}{l:.0f} λ={Wavelength}Å Intensity={Intens:.3f}'.format(**peaks.row(0)))

HKL=... λ=...Å Intensity=...


To check the ROI and peak fitting you can plot the results

import matplotlib.pyplot as plt
fig = plt.figure(figsize=(9.6, 4.8))
ax1.pcolormesh(mtd['peaks_data_ROI'], transpose=True)
ax1.set_title("ROI")
ax2.plot(mtd['peaks_data_Workspace'], wkspIndex=0, label='data')
ax2.plot(mtd['peaks_data_Workspace'], wkspIndex=1, label='calc')
ax2.plot(mtd['peaks_data_Workspace'], wkspIndex=2, label='diff')
ax2.legend()
ax2.set_title("Fitted integrated peak")
fig.tight_layout()
fig.show()


Example - DEMAND multiple files, indexing with modulation vector

IPTS = 24855
exp = 755
scans = range(28, 96)
filename = '/HFIR/HB3A/IPTS-{}/shared/autoreduce/HB3A_exp{:04}_scan{:04}.nxs'

data = HB3AAdjustSampleNorm(','.join(filename.format(IPTS, exp, scan) for scan in scans), OutputType="Detector")
peaks = HB3AIntegrateDetectorPeaks(data)
IndexPeaks(peaks, ModVector1='0,0,0.5', MaxOrder=1, SaveModulationInfo=True)
SaveReflections(peaks, Filename='peaks.hkl')


Categories: AlgorithmIndex | Crystal\Integration