TILT/BEAM CENTRE allows any non-orthogonality of the detector to the direct beam (tilt), and the direct beam centre on the detector to be determined [10]. This is achieved by least squares fitting of powder rings (or rings from other randomly orientated samples e.g. wax).
Below is the log file from FIT2D of the present user interaction. The documentation will be fully written when the algorithm and user inputs are stable:
Fit sub-menu: ENTER COMMAND [INPUT PARAMETERS]:tilt
WARNING: This is a development routine, user prompts are likely to change
SAMPLE TO DETECTOR DISTANCE (MILLIMETRES)
(Range: .10000 to 1.000E+05) [200.000]:
NUMBER OF ANGULAR SECTIONS (Range: 10 to 360) [90]:?
The powder ring is divided into a number of equal angle sections for
calculating the radial centre of each section. From the radial centre
and the average angle two Cartesian coordinates are calculated. These
coordinates are used to fit optimum beam centre and detector plane tilt
angles. Enter required number of sections for calculations.
NUMBER OF ANGULAR SECTIONS (Range: 10 to 360) [90]:
WEIGHTED FITTING [NO]:?
The fitting of tilt angle and beam centre to the estimated ring centres
may be performed using weighted fitting or unweighted fitting. If
weighted fitting is chosen then the average intensity (3 pixels) around
the calculated centre of each radial profile is used to weight the fit.
This means that strong rings and strong angular regions of rings will
have more influence than weaker ones. This should make the fitting more
robust when the data has weak rings and noisy background.
WEIGHTED FITTING [NO]:
REJECT OUTLYING COORDINATES [YES]:?
Outlying coordinate positions which are more than an input number of
standard deviations radially from the fitted ring positions may be
rejected from the coordinate lists. The beam centre/tilt can then be
re-fitted without these coordinates. If erroneous coordinate positions
are influencing the fit, this option may allow them to be removed.
have more influence than weaker ones. This should make the fitting more
robust when the data has weak rings and noisy background.
REJECT OUTLYING COORDINATES [YES]:
REJECT LIMIT (NUMBER OF STANDARD DEVIATIONS)
(Range: 1.00000 to 10.0000) [3.00000]:?
Enter the limit of number of standard deviations after which coordinate
positions are to be rejected from the coordinate lists. A three sigma
limit should be reasonable for less than about 200 coordinates (assuming
they are normally distributed.)
REJECT LIMIT (NUMBER OF STANDARD DEVIATIONS)
(Range: 1.00000 to 10.0000) [3.00000]:
FULL ALGORITHM INFORMATION [YES]:?
YES: if you want step by step diagnostics information
FULL ALGORITHM INFORMATION [YES]:
INPUT METHOD FOR BEAM CENTRE [KEYBOARD]:?
AVERAGED GRAPHICAL: Average of average symmetry centres
CIRCLE COORDINATES: Least squares fit on >=3 coordinates
ELLIPSE COORDINATES: Least squares fit on >=5 coordinates
GRAPHICAL COORDINATE: Single graphical input coordinate
KEYBOARD: Single keyboard entered X/Y coordinate
INPUT METHOD FOR BEAM CENTRE [KEYBOARD]:
X-PIXEL COORDINATE OF BEAM CENTRE [256.5]:256
Y-PIXEL COORDINATE OF BEAM CENTRE [256.5]:255
INFO: The search distance either side of the powder rings (mm) = 1.511
INFO: The search distance either side of the powder rings (X-pixels) = 15.11
GRAPHICAL INPUT: 4.3077289E+02 2.6403860E+02
INFO: Radius of powder ring 1 (mm) = 6.894
INFO: Radius of powder ring 2 (mm) = 17.501
INFO: Radius of powder ring 1 (X-pixels) = 68.940
INFO: Radius of powder ring 2 (X-pixels) = 175.006
REFINE BEAM CENTRE [YES]:?
The entered beam centre position may be kept fixed or may be refined
along with the tilt and powder ring opening angles. If the beam centre
is well known e.g. by using a semi-transparent beam-stop then it is
probably better not to refine the position.
Enter "YES" for the beam centre position to be refined, and "NO" if
the present values are to be kept fixed.
REFINE BEAM CENTRE [YES]:
REFINE SAMPLE DISTANCE [NO]:?
Enter "YES" to refine the sample to detector distance. Normally it is
probably best initially to keep this fixed, so answer "NO". Having
refined all other parameters, on a second iteration the distance can
also be simultaneously refined.
REFINE SAMPLE DISTANCE [NO]:
INFO: Calculating centre of gravity coordinates on 1 powder ring
INFO: Number of acceptable coordinates on first ring = 90
INFO: Fitting ellipse to centre of gravity coordinates
INFO: Number of coordinates = 90
INFO: Best fit ellipse centre (X/Y mm) = 25.61649 25.61244
INFO: Best fit ellipse centre (X/Y pixels) = 256.1649 256.1244
INFO: Best fit radius 1, radius 2 (mm) = 7.004938 6.983946
INFO: Best fit radius 1 (X pixels) = 70.04938
INFO: Best fit radius 2 (Y pixels) = 69.83945
INFO: Best fit angle of axis 1 (degrees) = 36.94184
INFO: Estimated coordinate radial position error (mm) = .1446273E-01
INFO: Estimated coordinate radial position error (X pixels) = .1446273
INFO: Calculating centre of gravity coordinates on powder rings
INFO: Fitting powder rings to centre of gravity coordinates
INFO: Number of iterations = 6
INFO: Number of function calls = 64
INFO: Sum of squares = .3310081043632615E-07
INFO: Number of rejected coordinates = 0
INFO: Number of iterations = 4
INFO: Number of function calls = 125
INFO: Sum of squares = .3310080011801160E-07
INFO: Fit of powder ring to inclined detector
INFO: Best fit beam centre (X/Y mm) = 25.59796 25.60419
INFO: Best fit beam centre (X/Y pixels) = 255.9796 256.0420
INFO: Cone 1 best fit 2 theta angle (degrees) = 1.999999
INFO: Cone 2 best fit 2 theta angle (degrees) = 4.999608
INFO: Best fit angle of tilt plane rotation (degrees) = 28.59482
INFO: Best fit angle of tilt (degrees) = 4.826739
INFO: Estimated coordinate radial position error (mm) = .1379255E-01
INFO: Estimated coordinate radial position error (X pixels) = .1379255
INFO: Alternative fit of powder rings to centre of gravity coordinates
INFO: Number of iterations = 5
INFO: Number of function calls = 46
INFO: Sum of squares = .3310209888343639E-07
INFO: Number of rejected coordinates = 0
INFO: Number of iterations = 1
INFO: Number of function calls = 18
INFO: Sum of squares = .3310145134466964E-07
INFO: Fit of powder ring to inclined detector
INFO: Best fit beam centre (X/Y mm) = 25.59794 25.60424
INFO: Best fit beam centre (X/Y pixels) = 255.9794 256.0424
INFO: Cone 1 best fit 2 theta angle (degrees) = 2.000001
INFO: Cone 2 best fit 2 theta angle (degrees) = 4.999619
INFO: Best fit angle of tilt plane rotation (degrees) = 28.54871
INFO: Best fit angle of tilt (degrees) = 4.825097
INFO: Estimated coordinate radial position error (mm) = .1379269E-01
INFO: Estimated coordinate radial position error (X pixels) = .1379269
INFO: In the absence of any other information, there are two equally
valid solutions to the tilt angle and beam centre which could
have formed a powder ring on an inclined detector. Theoretically
these should both give the same goodness of fit, so both solutions
are output. If the position of the beam-stop is known, then the
"correct" solution may be selected.
INFO: SOLUTION 1
INFO: Best fit beam centre (X/Y mm) = 25.59796 25.60419
INFO: Best fit beam centre (X/Y pixels) = 255.9796 256.0420
INFO: Cone 1 best fit 2 theta angle (degrees) = 1.999999
INFO: Cone 2 best fit 2 theta angle (degrees) = 4.999608
INFO: Best fit angle of tilt plane rotation (degrees) = 28.59482
INFO: Best fit angle of tilt (degrees) = 4.826739
INFO: Estimated coordinate radial position error (mm) = .1379255E-01
INFO: Estimated coordinate radial position error (X pixels) = .1379255
INFO: SOLUTION 2
INFO: Best fit beam centre (X/Y mm) = 25.59794 25.60424
INFO: Best fit beam centre (X/Y pixels) = 255.9794 256.0424
INFO: Cone 1 best fit 2 theta angle (degrees) = 2.000001
INFO: Cone 2 best fit 2 theta angle (degrees) = 4.999619
INFO: Best fit angle of tilt plane rotation (degrees) = 28.54871
INFO: Best fit angle of tilt (degrees) = 4.825097
INFO: Estimated coordinate radial position error (mm) = .1379269E-01
INFO: Estimated coordinate radial position error (X pixels) = .1379269
WHICH SOLUTION (Range: 1 to 2) [1]: