Curve fitting by computer

A similar method uses an optical interferometer as illustrated in Fig. 2.12b [78]. The motion of the small prism, which is attached to the drive, causes a time-dependent interference which is again converted to pulses and registered in the analyser. Neither method is widely applicable because of the prohibitive cost of the precision optical equipment. 

Calibration in terms of a known frequency has also been accomplished by mounting the absorber on a quartz crystal and calculating the velocity scale from the spectrum sidebands produced by frequency modulation [79]. 

Much of the Mossbauer spectroscopic data which is published comes from institutions which also have large computer facilities. Since the raw data of a spectrum are already digitised, it is in a very convenient form for automated analysis by digital computer. The majority of multichannel analysers have output signals which are either directly compatible with or easily adapted for appropriate types of punched paper tape or magnetic tape units, so that accumulated spectra can be printed out in a form which is compatible with the computer installation. 

The information which may be required from the computer analysis of the data are the parameters of a selected function which are the best possible fit to the observed spectrum. In the simplest cdses this function will be one or more Lorentzian curves. However, more complex types of function may sometimes be required, for example when fitting multi-line spectra which are subject to motional narrowing (see p. 72). 

The general problem can be described as follows. The data comprise N digitised values F. The function which is to be fitted contains n variables, represented by the vector V, and will give a calculated value at data point i of A(F)i. The error thereby incurred is 

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