# Peak Centering

## Peak Centering Calculations

Here is the list of functions related to the peak centering calculations that are provided by the "Neutron Scattering" XOP:

#### PeakCentringLin(Angle1, Rate1a, Rate1b, Angle2, Rate2a, Rate2b )

The PeakCentringLin function uses the linear interpolation method and returns the expected angular position of the detector from the four count rates measured with half-shutters at two angular positions. The angular position of the detector is defined by:
(where Angle1 and Angle2 are the detector positions at which the cout rates (Rate1a, Rate1b) and (Rate2a, Rate2b) are measured.)

#### PeakCentringLinSDev(Angle1, Rate1a, Rate1b, Angle2, Rate2a, Rate2b, AngleSDev, Rate1aSDev, Rate1bSDev, Rate2aSDev, Rate2bSDev )

The PeakCentringLinSDev function returns the standard deviation of the expected angular position of the detector from the four count rates measured with half-shutters at two angular positions (linear interpolation method). The standard deviation of the angular position of the detector is defined by:
(where Angle1 and Angle2 are the detector positions at which the cout rates (Rate1a, Rate1b) and (Rate2a, Rate2b) are measured. The angular precision of the detector shaft if given by AngleSDev.)

#### PeakCentringGauss(Angle1, Rate1a, Rate1b, Angle2, Rate2a, Rate2b )

The PeakCentringGauss function uses the inverse Gaussian interpolation method and returns the expected angular position of the detector from the four count rates measured with half-shutters at two angular positions. The angular position of the detector is defined by:
(where Angle1 and Angle2 are the detector positions at which the cout rates (Rate1a, Rate1b) and (Rate2a, Rate2b) are measured.)

#### PeakCentringGaussSDev(Angle1, Rate1a, Rate1b, Angle2, Rate2a, Rate2b, AngleSDev, Rate1aSDev, Rate1bSDev, Rate2aSDev, Rate2bSDev )

The PeakCentringGaussSDev function returns the standard deviation of the expected angular position of the detector from the four count rates measured with half-shutters at two angular positions (inverse Gaussian interpolation method). The standard deviation of the angular position of the detector is defined by:
(where Angle1 and Angle2 are the detector positions at which the cout rates (Rate1a, Rate1b) and (Rate2a, Rate2b) are measured. The angular precision of the detector shaft if given by AngleSDev .)