Analysis of quantization error in high-precision continuous-flow isotope ratio mass spectrometry

High-precision isotope ratio mass spectrometry (IRMS) systems are equipped with digitizers that deliver effective maximum digitization depths of 16 to 24 bits; however, there are no analyses of the proper board depth required to retain high precision in continuous-flow techniques. We report an experimental and theoretical evaluation of quantization error in continuous-flow IRMS (CF-IRMS). CO2 samples (100 pmol-30 nmol) were injected into a gas chromatography combustion IRMS system (GC-CIRMS). The analog signal was digitized by high precision, 24-bit ADC boards at 10 Hz, and was post-processed to simulate 12, 14, and 16-bit data sets. Delta13Cpdh values were calculated for all data sets by the conventional "summation" method or by curve-fitting the chromatographic peaks to the exponentially modified Gaussian (EMG) function. Benchmarks of S.D.(delta13Cpdh) = 0.3, 0.6, and 1.0/1000 were considered to assess precision. In the presence of significant quantization noise, curve-fitting required several-fold less CO2 than the summation method to reach a given benchmark. We derived an equation to describe the theoretical limitations of precision for the summation method as a function of CO2 admitted to the source and the step size of the boards. Theory was in close agreement with the observed lower limit of precision for the simulated 16-bit data set. Curve-fitting achieved a precision of S.D. <0.3/1000 for injections 20-fold smaller than summation for CO2 samples collected on an IRMS with 16-bit resolution. By mitigating the impact of quantization noise, curve-fitting expands the dynamic range within a single run to include lower analyte levels, and effectively reduces the need for high pumping capacities and high precision ADC boards.