find the last point around i 1 where χ 2 ( i 2 ) < χ mean 2 and redefine i 1 as this point i 1 = i 2 stretching or shrinking the fitting range to a reasonable maximum) 4.
define the data range using indices i 0 = 0 and i 1 = i(t 0), containing at least 4 data points; fit function from i 0…i 1, calculate the squared error of each point and estimate the average error; find the last point around i 1 where χ 2 ( i 2 ) < χ mean 2 and redefine i 1 as this point i 1 = i 2 stretching or shrinking the fitting range to a reasonable maximum).
The analysis and parametric imaging algorithms may be improved by further optimization, such as increasing the number of averaged A-scans for greater speckle reduction, or altering the fitting range based on the expected homogeneity of selected regions.
The procedure is designed to run automatically being controlled only by selecting the start interval of the data and a scaler, which defines how fast the fitting range should increase with time.
For the objective selection of a fitting scale range, we examined the influence of the choice of threshold values (Fig. 3) and data resolutions (Fig. 4).
In an independent study [8], this choice of fitting range for the mono-exponential method has been shown to yield optimal results.
As it is shown for a series of materials, the application of the slope-background provides excellent fits, is transparent to the operator, and is much more independent of the fitting range than other background methods.
It is demonstrated that extrapolation is in particular questionable if the gas phase composition is outside the fitting range.
otherwise, define the new fitting range, using the scaler parameter (by default use i 0…scaler × i 0) 7.
As expected, the SNR improves with increased averages and allows the extension of the fitting range.
The fitting range starts from 65 kHz and ends up at the frequencies where the corresponding intensities are around 20% of the peak intensity.
