Peak Analysis using Cumulative Peak Fitting: An Approach to get more Information from a C TOF AMS Spectrum Markus Müller 1, Thorsten Titzmann 2, Christian George 1, Barbara D Anna 1 [1] IRCELYON, CNRS, UMR 5256, Université Lyon 1, Lyon, France [2] Institute of Ion Physics, University of Innsbruck, Austria How does a TOF MS measure a Signal? TOF MS Acquisition ADC e - Pulser Detector Timing AMS Vaporizer Signal Detection and Analysis Time of Flight 1
How does SQUIRREL analyze C-TOF spectra Diff Spec = MS Open MS Closed Baseline Panel How does SQUIRREL analyze C-TOF spectra: Example O 2 Diff Spec = MS Open MS Closed Baseline I Open Baseline II Closed O 2 Signal = 6500 cps Diff What s the O 2 signal: sum of all acquisition bins within the Stick Integration Region 2
How does SQUIRREL analyze C-TOF spectra: Multiple Peaks Diff Spec = MS Open MS Closed Baseline I Open Baseline II Closed Total Signal = 2500 cps Diff Signal Result for m/z 44: sum of all acquisition bins within the Stick Integration Region No information about multiple peaks How to get more Information than Signal Intensity? I) Fit of a Probability Density Function: PDF Gaussian Fit: µ = 52 A = 7.07 σ = 7.36 3
How to get more Information than Signal Intensity? II) I) Fit of a Probability Cumulative Density Distribution Function: Function: => Calculate a cumulative sum of the sampled data: CDF CDF Fit: µ = 49.5 A = 5 σ = 9.98 Similar result to SQUIRREL PDF or CDF: Which function should be used? Measured Data Bins Discrete cumulated Histogram PDF CDF Under what conditions are directly measured Data Bins or Cumulated Data Bins valid nodes for an approximation function? OR What happens in between two data acquisition Bins? Rare Signal events MCP peak widths (ns range) Thresholds ADC does not count ions BUT: Ionization Efficiency calculations SQUIRREL Analysis. 4
How does a TOF MS measure a Signal? Assumption 1: A normally distributed Ion Packet arrives at the detector Simulation: µ = 49.5 A = 5 σ = 10 How does a TOF MS measure a Signal? Assumption 2: The ADC samples the Signal with a time resolution of 5 => The ADC system, applied in the TDC Histogram mode, detects all ions that arrive within one acquisition bin! Simulation: µ = 49.5 A = 5 σ = 10 4 5 Data Points contribute to the peak 5
How does a TOF MS measure a Signal? Assumption 3: The sampled data points are valid nodes for a Probability Density Function Simulation: µ = 49.5 A = 5 σ = 10 Gaussian Fit: µ = 52 A = 7.07 σ = 10 σ = 7.36 Problem: Ions did not arrive exactly at the sampling time! => PDF leads to wrong µ, A and σ! Solution for this Problem? Use Cumulative Distribution ib i Functions (CDF) instead of PDF 6
=> Calculate a cumulative sum of the sampled data: Simulation: CDF Fit: µ = 49.5 µ = 49.5 A = 5 A = 5 σ = 10 σ = 9.98 PDF CDF Advantages of the CDF: Remark: 1. Measured data points are valid supporting points of the CDF 2. Exact results for Area, width and center 3. Precise data analysis for low number of data bins 4. More robust to peak shape and temperature shifts (not shown) The more bins are available, the better the approximation of the PDF works! 7
C TOF AMS Data Acquisition: typical extraction frequency: ~ 100 khz ADC acquisition bin width: 1 ns Bins/Spectrum: ~ 10,000 typical mass resolving power: < 1000 Thorstens simulations II 8
A PDF = 114,400 cps A CDF = 83,200 cps Advantages: BUT: area, peak center, peak width peak shape evaluation for signal quantification fitting a single peak is not interesting Thorstens simulations II 9
Iterative Residual Analysis: 1. CDF fit of the highest peak (m/z = 44.0495, C 2 H 6 N + ) Similar to: Müller et al., 2010: First eddy covariance flux measurements by PTR TOF, Atmos. Meas. Tech., 3, 387 395. Residual Analysis: 1. CDF fit of the highest peak 2. CDF fit around the residual maximum Similar to: Müller et al., 2010: First eddy covariance flux measurements by PTR TOF, Atmos. Meas. Tech., 3, 387 395. 10
Residual Analysis: 1. CDF fit of the highest peak 2. CDF fit around the residual maximum 3. CDF fit around the new residual maximum No more significant residual left! Similar to: Müller et al., 2010: First eddy covariance flux measurements by PTR TOF, Atmos. Meas. Tech., 3, 387 395. Three ionic peaks detected: I m/z 43.985 14781 cps [CO 2+, m/z 43.990] II m/z 44.027 3765 cps [C 2 H 4 O +, m/z 44.026] III m/z 44.050 11175 cps [C 2 H 6 N +, m/z 44.049] 11
Timeseries during Photooxidation Experiment: DMA low NOx Experiment n MS closed [ncp s] 40000 35000 30000 25000 20000 15000 m/z 43.990 Thermogram 1 Thermogram 2 m/z 44.026 m/z 44.049 MS ope 10000 5000 0 08:24 09:36 10:48 12:00 13:12 14:24 15:36 16:48 18:00 19:12 time There is a difference between PDF and CDF (= counting) fitting Fitting CDFs Thank work very well You to de-convolute multiple peaks Results are consistent to the Ionization Efficiency Calibration 12
PHD Thesis Titzmann 2010 PHD Thesis Titzmann 2010 13