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Digital Detector

Detectors that convert ion abundance into digital signals, enabling quantitative analysis and high-resolution mass spectra acquisition.
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The statement of the theorem

Let Iion(t)I_{ion}(t) be the instantaneous ion current (Amperes) detected at time tt. The detector converts this current into a measurable voltage signal Vout(t)V_{out}(t) via a transimpedance amplifier (TIA) with a gain GG: \nVout(t)=−Iion(t)⋅RfeedbackV_{out}(t) = -I_{ion}(t) \cdot R_{feedback} \nFor quantitative analysis, the measured signal SS is the integral of the ion current over the acquisition time Δt\Delta t: \nS=∫t0t0+ΔtIion(t)dtS = \int_{t_0}^{t_0 + \Delta t} I_{ion}(t) dt \nIf the detector response is modeled by a Gaussian function R(t)\mathcal{R}(t) centered at tpeakt_{peak}, the peak signal amplitude SpeakS_{peak} is proportional to the ion abundance NN: \nSpeak=k⋅N⋅e−(t−tpeak)22σdet2S_{peak} = k \cdot N \cdot e^{-\frac{(t - t_{peak})^2}{2\sigma_{det}^2}} \nwhere kk is the detector sensitivity constant.
Source: Wikipedia