A practical method for determining minimum detectable values in pulse-counting measurements.

Area of Science:

• Analytical Chemistry
• Metrology
• Statistical Physics

Background:

• Pulse-counting detectors in X-ray, electron, and ion spectroscopy generate data following a Poisson distribution.
• Existing methodologies for determining minimum detectable values often require complex statistical treatments.
• Standardization bodies like IUPAC and ISO 11843 recommend specific statistical approaches for measurement uncertainty.

Purpose of the Study:

• To propose a novel statistical method for determining minimum detectable values (MDVs) in pulse-counting measurements.
• To adapt Poisson-distributed detector outputs to a Normal distribution for simplified analysis.
• To ensure the proposed method aligns with established international metrological standards.

Main Methods:

• The study approximates the Poisson distribution of pulse counts with a Normal distribution.
• Two approximation methods are detailed: a Simple approximation and a Square Root approximation.
• Key statistical parameters such as variance, critical values, and detection capability criteria are defined.

Main Results:

• The proposed statistical method provides a framework for calculating MDVs.
• Both Simple and Square Root approximations were evaluated for their theoretical limitations.
• Experimental data validated the accuracy and practical applicability of the developed methodology.

Conclusions:

• The statistical method for determining MDVs in pulse-counting measurements is accurate for practical applications.
• The Normal distribution approximation simplifies the analysis of spectroscopy detector data.
• The methodology adheres to international standards, enhancing its reliability and acceptance.