Software and Calibration for Photothermal Threshold Quantum Yield

This is code used to process and apply calibrations to photothermal threshold quantum yields taken, with our specific spectrometer. The calibrations included will not work for any other optics path or components, but this serves as a guide to calibrate one built in any other lab. This code is written in Matlab2018b. 

Methods
for more information about calibrations included please see: 

www.sciencemag.org/content/363/6432/1199/suppl/DC1

Error Analysis & Propagation

The uncertainty was computed by quantifying as many different sources of uncertainty in the measurement as possible and performing a bootstrap error analysis on each data set. A random Gaussian-distributed perturbation for each source is applied to the data at the beginning of the analysis, and then the entire analysis is carried out. This process is repeated many times to collect adequate statistics. Typically 1,000 random perturbations is sufficient for a good average and standard deviation, and 10,000 perturbations allows a smooth plot of the distribution of resulting PTQY values. This is preferable to simpler error propagation analysis because it captures non-linearities and co-variances in the uncertainties. The sources of error analyzed are: (1) the detection spectrograph wavelength accuracy, (2) the detection spectrograph spectral sensitivity, (3) the average excitation uncertainty, measured by the detection spectrograph, and (4) the statistical uncertainty due to finite averaging of the photoluminescence and photothermal deflection signals. Finite averaging of photoluminescence and photothermal deflection signals, per energy step, depending on the sampling conditions. Our software was set to increase N until standard errors of from were achieved per data point for both photothermal deflection magnitude and EPL. Measurements were done at a variety of chopping frequencies to ensure measurement fidelity. Energy steps 10-50meVwere used to extract a photothermal threshold quantum yield over excitation energies where integrating sphere PLQY was measured to be constant

The total measurement uncertainty budget is calculated by running this bootstrap error analysis on a data set with all four sources of uncertainty enabled. Subsequently, by each source of uncertainty one at a time and then reperforming the bootstrap error analysis, the amount of uncertainty associated with it individually can be determined.