Fit Sub-Menu

The FIT sub-menu contains commands for model fitting to 2-D data, and also a number of other commands not particularly related to fitting. The common feature of the other commands is the possibility to ``mask-off'' areas of the data. Thus, commands related to powder diffraction are included in the FIT sub-menu.

Model fitting can range from a relatively simple to a very complicated process, owing to the problems of local minima, poor initialisation, saddle points on the fit surface, etc. This sub-menu contains commands which allow initialisation of a fit model, minimisation, inspection of results, and the setting of constraints of model parameters. Novice users should seek advice from users more experienced with fitting if attempting more than the simplest operations [5].

The basic commands for fitting are:

INPUT PARAMETERS: Initialisation of a fit model by graphical and keyboard input.

MINIMISATION: Optimisation of fit model by the maximum descent method

RESULTS: View fitted parameters

The memory is used to calculate the fit model, so at the end of MINIMISATION it is possible to exit the FIT sub-menu and use EXCHANGE so that fit model can be examined. (EXCHANGE is the default command after exiting.) Similarly SUBTRACT can be used to create the residuals.

Additionally, there are many other commands which support the fitting process and allow other forms of fitting. The commands are:

CHANGE SCALE: Change the typical parameter variation sizes

CLEAR MASK: Eliminate all masked-off ``bad'' data points

CONSTRAIN: Set constraints, change parameters values

COVARIANCE: Output covariance matrix

DEFINE MASK: Mask-off ``bad'' data prior to fitting

DISPLAY MASK: Display masked-off data as a two level image

EXIT: Exit fit sub-menu

INPUT PARAMETERS: Initialisation of fit model

MASK STATISTICS: Statistics of mask

MINIMISE: Search for better fit by maximum descent method

MODEL: Create fit model (in memory) from current parameter values

NORMALISATION: Uni-directional flat-field normalisation

OUTPUT PARAMETERS: Output fit parameters to a file

POWDER DIFFRACTION: Convert 2-D data into a 1-D ``scan''⁵⁴

QUIT: Exit fit sub-menu

R/THETA RE-BINNING: Radial/Angular (polar) re-binning of ROI

RADIAL PROFILE: Calculate 1-D radial profile in memory

RESULTS: View results of fitting

SET MASK COLOUR User choice of colour to draw masked pixels

SET UP: Alter fit control parameters

SURFACE POLYNOMIAL: Fit data using 2-D Chebyshev polynomial

THRESHOLD MASKING Mask elements depending on the ROI data values

TILT/BEAM CENTRE Determine tilt and beam centre from powder rings

TRANSFER MASK TO MEMORY Set masked elements to 1.0 in memory

All the available commands are described in detail in the following sub-sections, but first some very important general concepts are introduced.