Comparison of logarithmic stepping (circles) vs linear stepping (triangles) for a simulated observable. Top trace, displaced by one unit for clarity, shows evenly spaced points while the bottom trace displays points spaced evenly on a logarithmic scale.
Logarithmic stepping value plotted as function of relative index with (0.667 fs), (2 ns), and equal to 50 (circles), 100 (triangles), and 200 (squares). As increases, the number of repeated data points increases. equal to 100 and 200 stepping functions have been offset by 0.005 and 0.01 ps, respectively.
Logarithmic stepping value plotted as a function of the data point index with (50), (0.667 fs) constant, and equal to (a) 2 ns, (b), 2 ps, and (c) 10 fs. Note the increase in repeated delay steps at early delay time as approaches the time scale of .
Uncorrected (upper trace, triangles) vs linear corrected (lower trace, circles) logarithmic stepping values with (200), (0.6667 fs), and (2 ns). The uncorrected values include repeated time delay points while the corrected contains no repeated time delay points. The uncorrected values are displaced by 0.01 ps for clarity.
Linear (a) and logarithmic (b) broadband ultrafast transient absorption spectrograms of HPTS in pH-7 water. Note that the time delay axis is plotted linearly but represents time delay values with (a) variable linear resolution and (b) logarithmic spacing. Both spectrograms contain 200 spectra with final delay equal to 2 ns.
Extracted deprotonation dynamics from HPTS/pH-7 water transient absorption data collected with linear (circles) and logarithmic (triangles) stepping. Comparisons between the two methods show that although linear stepping provides effective resolution, logarithmic stepping smoothly adjusts the time stepping on the tens of (a) picosecond and (b) nanosecond time scales. Logarithmic traces (triangles) are displaced by one unit for clarity.
Extracted Stokes shift dynamics from HPTS/pH-7 water transient absorption data collected with linear (circles) and logarithmic (triangles) stepping. Comparisons between the two methods show that although linear stepping provides effective resolution, logarithmic stepping smoothly adjusts the time stepping. Logarithmic trace (triangles) is displaced by for clarity.
Analysis of the statistical “efficiency” of HPTS/pH-7 water deprotonation fitted parameters.
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