Impact of the ADC Nonlinearities on X-ray Spectral Analysis and Correction Techniques

Analog-to-digital conversion (ADC) is a key element in spectroscopic systems with low-noise and high dynamic range and the impact of ADC non-linearities must be carefully estimated. Aim of this work is to study the impact of the ADC non-linearity errors and the benefit of suitable correction to experimental X-ray spectra. A simulative study was first conducted on the impact on centroid determination and on the discrimination of two X-ray lines. Correction techniques were applied to experimental X-ray spectra acquired by a ladder (512 x 128 pixels) of the Mini-SDD X-ray imager, featuring a fast 8-bit ADC integrated in the hexagonal pixel (136 μm side) and noise performance down to 40 electrons rms. We measured the individual ADC bin-edges with the 13-bit DAC available at the periphery of the readout ASIC. Fitting the ADC output vs. the DAC code with multiple error-function model returns the bin edges, the sigma of the bin transitions and the goodness-of-fit parameters. The global ADC staircase showed a relative bin-width non-uniformity (mostly differential non-linearity, DNL) in the range 10-50%. The relative bin-width non-uniformity across a full-size sensor (256 x 128) was found about 10% rms in the periphery of the sensor and 3-4 times larger in the internal rows. This spatial pattern had been already observed, e.g. in gain and noise measurements, confirming the relevance of DNL errors.X-ray spectra of Cu target have been compared before and after correction of the ADC bin widths. Both the pedestal and Cu Ka peak as well as the low-energy continuum visually recover a smoother trend. The root-mean-square error (RMSE) of the Cu Ka peak fit shows a marked reduction by a factor 3 after DNL correction. This is also reflected in the marked drop from 4% to 0.5% of the standard error of gain, directly linked to the improved peak fitting, which shows the significant benefit of the correction.