Summary of Calibration Procedures
In order to share good practice and information about different procedures the following page provides summaries as to how small-angle scattering instruments are calibrated as regards wavelength, intensity, momentum transfer and other quantities, We encourage people to fill in details and make comments on this page. In order to simplify finding information, we encourage everyone to use similiar sub-headings where appropriate.
This project to gather information is new and we hope to have some information soon.
A comprehensive review discussing all possible data correction steps (in particular for X-ray scattering instrumentation) is available here: http://dx.doi.org/10.1088/0953-8984/25/38/383201
Quokka - Bragg Institute, ANSTO
40 m Small-angle neutron scattering instrument
Data is put on an absolute scale using the direct beam measurement with a calibrated attenuator, using the NIST macros for Igor Pro with Quokka specific modifications, (S.R. Kline, J Appl Crystallogr, 2006, 39, 895-900). As per the help file accessible in the NIST macros, the absolute intensity is calculated as: I_abs=I_cor/(κ d T_sam ) Where I_cor is the measured data corrected for the instrument background, detector sensitivity and nornalised to monitor counts, d is the sample thickness and T_sam is the sample transmission.κ is a scaling factor, calculated from the attenuated direct beam measurement taken in the same configuration as the sample measurement: κ=Totcnts_DB/(Moncnts_DB×Attfactor_DB )×∆Ω Where Totcnts_DB is the number of counts in the direct beam, Moncnts_DB the monitor counts for the direct beam measurement, Attfactor_DB the attenuation factor for the attenuator used and ∆Ω is the solid angle subtended by one pixel.
Calculation of attenuation factors on Quokka (thanks to discussions with John Barker, NIST):
On Quokka, a wheel of 25 mm thick plexiglas is used to attenuate the beam, where different thicknesses of plexiglas have been milled out around the wheel, leaving 12 attenuators of different thickness, from 25mm down to 0. Attenuation factors for the 12 attenuators were measured with the detector to sample position of 20m, a 50mm diameter source aperture and 20m source to sample distance. Attenuation factors are calculated by taking the ratio of counts in the direct beam with and without the attenuator in the beam. To avoid over-exposing the detector, this is done with various sized apertures at the sample position, and the values are normalised by the ratio of the same attenuation value measured with different aperture sizes. On Quokka four different aperture sizes were found to be necessary to cover all attenuation values. The factors have been calculated for different wavelengths (5, 6, 7, 8Å) and interpolations are performed if data is measured at an intermediate wavelength.
The error on the attenuator factors for the plexiglas attenuators is less than 2%. Generally transmission measurements and direct beam measurements are performed so that the error is less than 1% (120 seconds counting time with appropriate attenuator in the beam). The errors are given taking into account counting statistics on the instrument detector only.
--Katy wood 01:35, 17 June 2013 (CDT)
Detector Response/Flat Field
Comments about advantages/problems
ESRF ID02 Time-resolved SAXS/WAXS/USAXS/ASAXS
Monochromatic X-ray pinhole camera with 10 m vacuum flight tube (distances 0.8 m to 10 m). Setup optimized for 12.6 keV.
see also http://www.esrf.fr/UsersAndScience/Experiments/SoftMatter/ID02/BeamlineDescription for more details.
Global calibration of the monochromator (over the whole energy range, the actually available monochromatic energy range is restricted to energies below 20 keV due to the mirror) at different absorption edges and least square refinement of dBragg and thetaOffset over all scanned edges: Fe K-edge, Cu K-edge, Au LIII-edge, Zr K-edge, Mo K-edge, Rh K-edge (error DeltaE/E < 10^-4).
We are using the small angle scattering of water to determine a normalization factor that adjusts the online corrected intensity. This calibration factor supersedes any other calibration factor, e.g. the intensity calibration of the beam intensity monitors and the detector efficiency.
Detector Response/Flat Field
The detector uniformity is determined with fluorescence radiation. The detector is placed in 1 m - 2 m distance from the fluorescent sample. The remaining non-uniformity of the field (<0.25% for a 10 cm x 10 cm active area) is corrected by normalizing the intensity pattern to the spherical angle (software). For calibrations around 12 keV we use the K-alpha radiation of bromine at 11.9 keV (solution of HBr in water filled into a 3 mm thick glass capillary). The average value of the resulting flat-field pattern is normalized to unity (for convenience).
The pixel size is measured with a calibration grid in front of the detector. The grid is also used to determine and to correct image distortions, e.g. when using fiber optically coupled CCD detectors.
Sample to Detector Distance
The movement of the detector is encoded. To calibrate the distance of a reference position from the detector a sample is placed there (e.g. silverbehenate or any other sample showing well defined rings, the d-spacing is not needed here). Then a series of scattering patterns is taken for different detector positions and the rings are extrapolated to zero diameter (accuracy <10^-3) which gives the position of the reference sample. The distance of any sample from the detector is measured relative to the reference position with a ruler (typically 1 mm accuracy). The center is determined with a scattering sample that is permanently present in the setup and that can be inserted into the beam path.
PBBA (para-brome benzoic acid) is used as scatterer at the sample position (e.g. in a capillary or as powder on a film). Calibration of the beam center, distance and detector inclinations is done by a least square refinement. This refinement can also be used for SAXS.
The beam center and/or point of normal incidence is determined with a reference sample showing a circular scattering pattern (see above).
Comments about advantages/problems
Usually, the standard calibration is sufficient. If needed, additional fine adjustments can be done with reference samples.
D33 - Institut Laue Langevin, Grenoble, France
The calibration of wavelength in both Monochromatic and Time-of-Flight modes of operation on D33 all originate from an accurate calibration of the sample-detector distance, in particular an accurate calibration of relative detector distances (position encoder calibration).
Detector Distance : Estimated Precision ~0.05%
Define a nominal sample 'zero-position'. Arbitrary, but close (within mm) of the instrument engineering designs.
Measure detector distance relative to defined sample 'zero-position' directly, at a number of positions, using Laser distance measure (accuracy ~1mm). This works well where the position of the neutron detection plane is well known, i.e. multi tube detectors. In the case of D33, distance is measured up to the detector surface and then 5mm added to take into account the aluminium front window. An additional uncertainty in detection position comes from the detector tube gas thickness. Overall precision in Sample to detector position is of the order ~few(5) mm (in 10's m, i.e. 0.05%) , dominated by the detection position uncertainty with the detector itself.
TOF Distances – Chopper → Sample → Detector : Estimated Precision ~0.05%
Using the nominal sample 'zero-position' measure sample – choppers(1,2,3,4) distances using a combination of Laser distance measure, theodolite, rulers etc. Distances measured between nominal 'zero-position' and centre of chopper disc housing. Estimated precision ~few(5) mm in 10's m, i.e. 0.05%
Wavelength : Monochromatic, i.e. Velocity Selector (Astrium) : Estimated Precision ~0.5%
Install a small beam chopper at the sample position. Accuracy in positioning or delay angle of the trigger pickup are not important. Spin the chopper at a frequency sufficiently slow as to allow neutrons of a given wavelength to reach the furthest detector position.
Measure the TOF profile of the monochromatic beam at two different detector positions, ideally separated by many meters. The TOF profile of the beam from a velocity selector is ideally triangular due to finite selector resolution but may become non-triangular due to beam divergence, finite beam size, finite chopper opening, and the underlying intensity spectrum
From the two TOF profiles use a triangular fit function or numerical centre of mass to estimate the time-centre of the pulsed monochromatic beam for both detector distances
The difference in time-centre, dt, for difference in detector positions, dD allows the real incoming wavelength to be calculated
Repeat the above for different wavelengths given by the selector
A plot of real wavelength vs. selector speed allows should be (almost – due to incoming spectrum) linear, passing though the origin, and allows the selector constant to be calculated
Repeat the above for different selector angles (resolutions) if available
Selector resolution, dlambda/lambda, may also be determined from the TOF profiles from the triangular fit or numerical standard deviation
Wavelength : Time-of-Flight (TOF), i.e. Optically-blind double-chopper (Astrium) : Estimated Precision ~?%
D33 possess 4 choppers with spacings between choppers 1 & 2 of 2.8m, choppers 2 & 3 of 1.4m and choppers 3 & 4 of 0.7m. All choppers have a window opening of 110 degrees with electronic trigger pickup located on the opening edge of the window when turning anti-clockwise looking downstream. In principle only two choppers are required at any one time operating in the 'optically blind' mode, i.e. the upstream chopper of the pair closes a the same moment the downstream chopper opens. The spacing between the chopper pair, dD, relative to the total flight distance, mid-chopper-pair to detector, D, determines the wavelength resolution, dl/l. It is the calibration of the chopper delay angle, i.e. when the trigger signal arrives relative to the window cutting the mid-point of the neutron guide, OR the relative phasing of chopper pair also determined by the pickup 'zero' angle that is required to accurately calibrate neutron wavelengths in TOF mode to ensure a well calibrated 'optically blind', 'over-' or 'under-closed' chopper operation.
Method 1: (Dewhurst D33 method)
By this point all distances, Chopper → Sample → Detector, and monochromatic wavelengths (velocity selector) are well known and calibrated. By using the monochromatic mode with a well calibrated wavelength the chopper delay angle, f, can be measured for each of the choppers 1 to 4 in turn
Set the detector at some arbitrary distance. Calculate the TOF for the chosen wavelength and chopper → detector distance, convert to frequency & RPM. Set the chosen chopper to this speed
Calculate the nominal TOF, t, for the given wavelength to reach the detector. Since the time resolved detector acquisition is triggered close to the opening edge of the chopper the detector should see a 'rising edge' of neutron arriving at the detector close to the nominal TOF
The above rising edge function is actually a convolution of the time it takes the chopper edge to cut the neutron guide (linear slope function) convoluted with the wavelength spread (triangular function) from the velocity selector and results in a linear step function with 'rounded edges'. Fitting such a function to the opening edge of the intensity vs. time measured on the detector allows the actual time, t', between chopper electronic trigger and arrival at the detector. The difference between t'-t is the chopper delay time, easily converted to the physical chopper delay angle using the chopper speed
When all chopper delay angles have been measured the detector acquisition and chopper phasing can be adjusted accordingly
Method 2: (Cubitt D17 & Figaro method)