Preparing to Deconvolve a Data Set

Preparation of data for deconvolution must begin prior to the acquisition of the first data point. Once the resolution of the system is set (in a dispersive spectrometer this is equivalent to setting the slit width), the density of data points per resolution element must be chosen as discussed in Sections III.D and III.E. There are some subtle factors that must be taken into account. For example, for continuous scanning, approximately 10 data points per resolution element are recommended (Blass, 1976a) to capture all of the information required by the data and the noise. On the other hand, the data-point density must be great enough to characterize the spectral lines after 

Under less restrictive noise/bandwidth considerations, one might drop the density to 6 points per resolution element at the risk of some minor noise aliasing. However, deconvolution by a factor of 3 would leave only two points per FWHM of a Gaussian spectrum-a number sufficient to characterize the spectrum, although display and measurement are difficult. 

Returning to the mainstream discussion of data preparation, we note that, for a 6-dB-per-octave-rolloff RC filter network in a lock-in amplifier, the continuous scan rate amounts to approximately one time constant per data point or 10 time constants per resolution element (Blass, 1976a). Some time is saved if only six data points are taken per resolution element. We have tried acquiring in this fashion, with no visible negative effects. 

In our operations, we often establish step-scan parameters as if we were continuously scanning. Because continuous scanning requirements are more demanding, no problems arise using this approach. 

Remember, also, that the signal-to-noise ratio must be high enough to accommodate the desired deconvolution (see Section IV.A). As noted, inadequate signal-to-noise ratio is the major cause of unsatisfactory deconvolution results. 

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