Calibration#

Instrument calibration procedures provide a refined geometry of the instrument and characterization of detector performance. Detector calibration is performed to update the instrument component positions and orientations, as needed, refining from the “engineering” values described by the standard instrument definition file (.xml). This is done using a reference standard single crystal measurement. Measurements of detector efficiency, background, and, if necessary, spectrum of the incident flux are done at regular intervals at least once-per-cycle or change of sample environment.

Detector calibration#

To calibrate the instrument definition. a single crystal measurement using a calibration standard sample with well-known lattice parameters is performed. The sample is rotated through several (many) goniometer rotations. Peak positions located completely on the detector are extracted and indexed with a best-fitting \(UB\)-matrix. The positions in detector space are related to recirpocal space coordinates by

\[\begin{split}\begin{bmatrix} Q_x \\ Q_y \\ Q_z \end{bmatrix}= \frac{2\pi}{\lambda} \begin{bmatrix} \sin{2\theta}\cos{\phi} \\ \sin{2\theta}\sin{\phi} \\ \cos{2\theta}-1 \end{bmatrix}\end{split}\]

Given detector coordinates \((x,y,z)\), the scattering angle is \(2\theta=\arccos(z/l_2)\) and azimuthal angle is \(\phi=\arctan2(y,x)\). For momochromatic source, the wavelength is fixed. However for white-beam Laue data, the wavelength is \(\lambda=ht/m_n(l_1+l_2)\).

  • Time-of-flight, \(t\)

  • Plank constant, \(h\)

  • Mass of neutron, \(m_n\)

  • Source-to-sample distance, \(l_1\)

  • Sample-to-detector distance, \(l_2=\sqrt{x^2+y^2+z^2}\)

In this case, the time-of-flight is the fixed quantitiy. The residual over \(i=1,2,\dots,N\) peaks is minimized by updating bank/detector position(s)/orientation(s) and incideint flight path to minimize the root-mean-square error.

\[\begin{split} \frac{1}{\lambda_i} \begin{bmatrix} \sin{2\theta_i}\cos{\phi_i} \\ \sin{2\theta_i}\sin{\phi_i} \\ \cos{2\theta_i}-1 \end{bmatrix} - \begin{bmatrix} R_{11,i} & R_{12,i} & R_{13,i} \\ R_{21,i} & R_{22,i} & R_{23,i} \\ R_{31,i} & R_{32,i} & R_{33,i} \end{bmatrix} \begin{bmatrix} UB_{11} & UB_{12} & UB_{13} \\ UB_{21} & UB_{22} & UB_{23} \\ UB_{31} & UB_{32} & UB_{33} \end{bmatrix} \begin{bmatrix} h_i \\ k_i \\ l_i \end{bmatrix}\end{split}\]

The algorithm SCDCalibratePanels is used for this purpose of refining the instrument parameters. After calibration, it produces detector calibration files that shoulde be loaded and applied to a dataset before convert units or to reciprocal space data. This supports the legacy ISAW-style files LoadIsawDetCal and the newer Mantid-style LoadParameterFile.

Loading detector calibration ISAW-style .DetCal file.#
  LoadIsawDetCal(InputWorkspace="data", Filename=det_cal_file)
Loading detector calibration .xml file.#
  LoadParameterFile(Workspace="data", Filename=det_cal_file)

Detector efficiency#

The most commonly practiced calibration procedure is to measure vanadium that is dominated by isotropic incoherent scattering. Although pure vanadium is commonly used, it is advantageous to use a vanadium alloy with a dilution component that suppresses the coherent scattering. A common example is a 5% niobium-substituted vanadium alloy. This flood field-like measurements provides a capacability to directly estimate the detector efficiency. The detection efficiency of a pixelated area detector could be thought as proportional to the product of two components:

  • Intrinsic efficiency

  • Geometric efficiency; solid angle

For monochromatic diffraction, the integrated vanadium counts corrected for absorption mapped onto each pixel is all that is required. An empty background measurement is subtracted from the vanadium then an absorption correction for the rod-like or spherical vanadium shape is applied. Conversely, Laue diffraction must provide some additional analysis of the wavelenth-dependent component after correcting for the background and absorption. This is done by integrating the counts on each bank of detectors and placing that in wavelength (or momentum) bins and normalizing its integral to unity. This provides a characterization of the detectected wavelength-dependent spectrum by assuming the spectrum shape of all pixels on a bank are similar. When it is multiplied by the pixel efficiency mapping, it estimates the wavelength-dependent detection efficiency.