Quantization effects in radiation spectroscopy based on digital pulse processing

Radiation spectra represent inherently quantization data in the form of stacked channels of equal width. The spectrum is an experimental measurement of the discrete probability density function (PDF) of the detector pulse heights. The quantization granularity of the spectra depends on the total number of channels covering the full range of pulse heights. In analog pulse processing the total number of channels is equal to the total digital values produced by a spectroscopy analog-to-digital converter (ADC). In digital pulse processing each detector pulse is sampled and quantized by a fast ADC producing certain number of quantized numerical values. These digital values are linearly processed to obtain a digital quantity representing the peak of the digitally shaped pulse. Using digital pulse processing it is possible to acquire a spectrum with the total number of channels greater than the number of ADC values. Noise and sample averaging are important in the transformation of ADC quantized data into spectral quantized data. Analysis of this transformation is performed using an area sampling model of quantization. Spectrum differential nonlinearity (DNL) is shown to be related to the quantization at low noise levels and small number of averaged samples. Theoretical analysis and experimental measurements are used to obtain the condition to minimize the DNL due to quantization.