Corrections for the response time and delay of mass spectrometers

Computations based on mass spectrometer (MS) outputs will be incorrect unless the delay for drawing the sample into the instrument and response time of the instrument are accounted for. When we changed concentration abruptly in two different mass spectrometers, the responses were sigmoid shaped not exponential, and time constants derived from the main part of the response curves were 43-60 ms; single-exponent corrections using these values caused the corrected waveform to overshoot. For a better correction, we used a two-exponent correction, C₂=C₀+(Υ₁+Υ₂)(dC₀/dt) + Υ₁Υ₂(d²C₀/dt²), where C₀ is MS output as a function of time t, C₂ is corrected concentration, and Υ₁ and Υ₂ are time constants. Assumption of a third exponent was of little value. For a successful correction Υ₂ must be smaller than a measured one-exponent time constant. We used two-thirds of the measured value for Υ₁ and then calculated Υ₂ from the once-corrected response. The second-order correction approximates a square output in response to a square input. To deal with delay time in a way that would give good resolution of dynamic changes and also be compatible with our response-time correction, we corrected for the difference between time of the input event and time that the output reaches 20% of full response. We validated our methods by integrations of amounts of gases drawn into and out of a syringe and in human breaths.