- Last Updated: Friday, 06 October 2017 13:52
- Written by Chavdar Slavov
Lifetime density analysis
Lifetime density analysis (LDA) is the most common analysis technique for time-resolved data (for details see the Data analysis page). This module of OPTIMUS is capable of performing LDA, using the method of Tikhonov regularization, in combination with direct analysis of a number of experimental artifacts typically encountered in ultrafast spectroscopy (see Artifact analysis and Artifact analysis module module).
Please note that the use of the LDA module is not limited to ultrafast time-resolved data, but it can also be used with time-resolved data recorded on longer timescales (e.g. ns, μs, ms, s).
For the Lifetime density analysis' module of OPTIMUS the experimental data files should be supplied in the form of .ana file format.
Important for beginners!
Note 1: The LDA module of OPTIMUS is in beta version and certain features may not perform as expected. Please report bugs!
Note 2: LDA is not a universal remedy for bad experimental data! It will reveal any experimental artifacts, thus please do not try to hide such artifacts by selecting a lifetime density map that is not well regularized. This will compromise the interpretation of your data and may lead to wrong conclusions. If you feel you do not have sufficient experience to interpret the maps, please contact a more experienced user.
Please request the L-curve plot if LDMs are being presented in an article. If the selection of the map does not correspond to the corner of the L-curve, ask the authors to explain their selection and provide the map corresponding to the corner of the L-curve for comparison.
The 'LDA' module is very intuitive and self-explanatory. Nevertheless, here are provided some tips on how to use it.
- analyze your data with GLA to obtain the initial idea of the lifetime range of the examined kinetics.
- For ultrafast data, determine well the dispersion parameters and the width of the IRF either within the CA or the GLA module. Save the results in a .wirf file.
- In the LDA module, load the .wirf file and fix the dispersion parameters and the IRF width.
- For ultrafast experiments the quality of the lifetime density maps (LDMs) in the short lifetime ranges will depend crucially on the quality of the parameters in the .wirf file. If the IRF and the dispersion parameters are not well determined, misfitting of the early (<500 fs) may occur.
- Use a large number of regularization factors (at least 50) spanning the range 0.01-5. (Note: The time for the computation of the maps will depend on whether the IRF widths and the dispersion factors are constrained or not.)
- Select the LDM depending on the L-curve criterion allowing for some deviation from the L-curve corner depending on the presence of experimental artifacts in the data.
- For publications show the L-curve and specify the value of the selected regularization parameter for which the LDM is presented and its location on the L-curve.
The operation of the module is similar to the other modules of OPTIMUS
- The lower (lb) and upper (ub) boundary as well as the starting value (start) of each fit parameter in the LDA module of OPTIMUS are specified using a series of edit boxes. The fit value is given in a text box or push button located next to the corresponding start value edit box.
- Panel - Specify general settings
- Edit box: Wavelength range (nm) and Exclude wavelength ranges (nm) - Specify a wavelength range of interest. Dismiss wavelength regions where no relevant signal is present (Format: e.g. 310:350, 420:460, meaning dismiss wavelength regions 310-350 nm and 420-450 nm).
- Edit box - Time range - Specify the time range (typically you can use the complete time range of your measurement).
- Edit box - Sweep period (ps) - An option is included to be used for analysis of fluorescence time-resolved data from Streak camera measurements where long lifetimes contribute to the signal due to the so-called back sweep (for details see van Stokkum et al. 2008; Slavov, 2009). However, this part of the analysis is not yet fully tested and may not work as expected.
- Edit box - # of start points - This option is not necessary for the LDA module and thus is not available.
- Edit box - Max # of iterations - Specify the maximum number of iterations that will be performed during the optimization.
- Popup menu - Background offset - Background offset option is included in case the data contains a background offset. However, this is rarely the case, thus typically this option is not used.
- Panel - Specify IRF and artifact settings
- Popup menu - IRF with variable FWHMs - Specify whether the IRF FWHM should be varied over the selected wavelength range and if so what kind of variation should be used: i) independent for each wavelength (Option: yes); ii) dispersed (Option: dispersed).
- Pushbuttons - Load and Save - The fitted widths of the IRF can be save in a text file (.wirf), which then can be loaded again. This option allows estimating the IRF widths on a solvent measurements and then use these widths as fixed (option in the Popup menu - IRF with variable FWHMs ) in the analysis of the sample measurements. Note, the .wirf file contains only IRF widths for the analyzed wavelength channels.
- Edit boxes - IRF FWHM (ps) - specifying lower (lb) and upper (ub) boundary and starting value (start) for the IRF width. Note the wavelength dependence of the IRF widths can be viewed as a separate figure by pressing the push button indicating the result of the fit.
- Popup menu - # of artifact components - Specify the number of artifact components to be used in approximating the CA (for details see Artifact analysis). Typically, setting '3' is used.
- Push button- Relative shift - An option is included to allow variation between the center position in time of the different artifact components. Typically the three components should have the same position in time coinciding with the position of the IRF maximum. Thus, this option is almost never used but is included as an option in case it is needed.
- Panel - Specify fit parameters for 'time 0' dispersion
- Popup menu - Dispersion order - Specify the dispersion order to be used for apporximaing the chirp polynomial (for details see Artifact analysis). Order '2' is typically sufficient, while in rare case, e.g. where the chirp is relatively large, also order '3' might be used.
- Edit boxes - Center (nm) - specifying lower (lb) and upper (ub) boundary and starting value (start) for the center position of the polynomial approximating the chirp. This boxes are typically automatically set using the wavelength information from the loaded dataset.
- Edit boxes - Time offset (ps) - specifying lower (lb) and upper (ub) boundary and starting value (start) for the time zero offset. The starting value should be roughly assigned to the time point of the rise of the signal at the center wavelength (Center (nm)). The boundaries should be set wider enough to allow the program to find the time zero offset.
- Edit boxes - Dispersion - specifying lower (lb) and upper (ub) boundary and starting value (start) for the coefficients of the chirp polynomial (should be between -1 and 1).
- Please note that if in Panel: Specify IRF and artifact settings the option dispersed is selected for the varying the IRF FWHM in dependence of the wavelength, a pushbutton will appear in the Panel: Specify fit parameters for 'time 0' dispersion that will allow setting up dispersion fit parameters also for the IRF width.
- Panel - Specify regularization parameters
- Popup menu - regularization - Simple search of the best regularization factor by least square fitting is not straightforward and may lead to erroneous interpretations. Thus, to simplify the analysis in the LDA module a fixed range of regularization factors is scanned and for each factor a lifetime density map (LDM) is obtained.
- Edit boxes - Number of reg. factors - specifying the total number of reg. factors to be scanned.
- Pushbutton - Reg. factor range - specifying the range of reg. factors to be used. Typically the optimal reg. factor is between 0.01 and 5. The range can be adjusted to better visualize the corner of the L-curve for selection of the optimal reg. factor (see below and Slavov et al., 2015)
- Panel - Specify expected lifetimes
- Edit box - Start lifetime - give the expected minimum resolvable (as defined by the time-resolution of the experiment) lifetime in the dataset.
- Edit box - End lifetime - give the expected maximum lifetime in the dataset. In case the signal does not decay on the timescale of the experiment treat this entry as the infinit limit (similar to GLA).
- Edit box - Number of lifetimes - In LDA the data is numerically transformed from the time domain to the lifetime domain using a quasi-continuous distribution of lifetimes (Slavov et al., 2015). Typically 100 lifetimes spread on a log10 scale are sufficient for the analysis of the time-resolved data sets. The use of larger number of lifetimes will significantly reduce the calculation speed, while too few lifetimes may not be sufficient to account for all the features in the dataset.
- Pushbutton - Analyze data - starts the data analysis
- Pushbutton - Save results - For consistency, GLA-OPTIMUS saves the complete analysis results before allowing other figures or data to be saved. The file saved after pressing this pushbutton can later be loaded in OPTIMUS-GLA via the Pushbutton: Load results in the Panel: Load datasets for analysis. Please note, all files saved from OPTIMUS are given automatic name related to the name of the original dataset (for details see Files in OPTIMUS).
- Optimization progress plot - shows the optimization progress for the fitting parameters, e.g. IRF width, chirp etc. Even when the IRF widths option is selected as 'fix' and the boundaries of the chirp parameters are set tightly certain optimization will occur.
- L-curve criterion - the selection of the optimal LDM is done based on the L-curve criterion (see Slavov et al., 2015). In short, for each regularization term a LDM, the residual and the smoothing norms are calculated. The optimal LDM corresponds to the regularization parameter with smallest trade off between the goodness of fit (residual norm) and the solution smoothness (smoothing norm). This optimal condition is located at the corner of the L-curve. Please note that in certain case (e.g. experimental artifacts present in the data, poor S/N ratio, etc.) the corner of the L-curve is not very pronounced. In such cases the selection of the best LDM is not obvious and may require additional examination of the fit quality and the overall LDM look. If the LDM corresponding to the corner of the L-curve shows strong amplitude oscillations a solution with lower smoothing norm should be selected.
- 3D plot and 2D plot pushbuttons - at the top-center of the GUI for this module act as tabs for switching between viewing the 3D plots for the dataset and the fit and the 2D plots comparing data and fit traces.
- Additional push buttons are provided for saving the presented figures in a variety of file formats (please explore the options). Push buttons: Save 3D data, Save 3D fit, Residuals, Save 2D plots.
- Pressing 'Save 3D data', 'Save 3D fit' or 'Residuals' push button brings up a new GUI with enlarged 3D plot.
- Pressing 'Save 2D plots' push button brings up a new GUI for exploring the rests.
- Pushbuttons 'Save LDM', 'Transient spectra' and 'Transient spectra, expanded' bring popup windows with settings for saving those type of figures.