Pixel to λ
Exclude Scattering Compare Scans Background Subtraction
Remove Coherent
Artefacts Chirp Correction
Kinetic Cross Validation with TCSPC ΔA(Scans, Pixel , Δt(λ))
Experiment, Data Processing, Quality Control, Data Analysis
ΔA(λ, Δt)
Figure 2.7: Flowchart of steps required prior data analysis in a transient absorption measurement. After the experiment the data has to be processed and its quality has to be validated.
2.4.2 ps- µ s
The ps-µs pumping was described in detail in ref. 9. Excitation is performed at 532 or 355 nm using a passively Q-switched, frequency doubled Nd:YAG laser (Teem Photonics Powerchip) producing pulses with a 500 Hz repetition rate, ap-proximately 20µJ energy per pulse and 300 ps duration.
2.5 Data processing
Before analysis of the TA data, several steps of data processing and quality control are necessary to rule out systematic errors and convert the raw data matrix to TA spectra, which should not depend on the instrument on which they are measured (Figure 2.7). In a standard experiment, 200 spectra are averaged at each timestep before the delay line is moved. This procedure is repeated 4-8 times whereas the data of the different scans are saved separately and are averaged during the data processing after the experiment.
2.5.1 Pixel to λ
The raw experimental output, ∆A(Scans,P ixel, ∆t(λ)), has to be converted to
∆A(λ, ∆t). Since in the UV-Vis and NIR instruments a grating and prism based spectrograph are used, respectively, the pixel toλconversion differs.
Grating spectrograph in the UV-Vis
For a grating spectrograph, the pixel-to-λ conversion depends on a scaling and shifting parameter:
λ(pixel) = (pixel·scale) +shif t (2.3) The two parameters are found by comparing the absorption spectrum of a holmium oxide glass filter, measured with the steady state absorption spectrometer, to the
absorption spectrum of the same filter measured with the TA instrument (Figure 2.8a).d A least squares fitting algorithm (python scipy) is used to find the scale and shifting parameter.
Prism spectrograph in the NIR
The pixel-to-wavelength conversion for for the NIR instrument is given by com-paring the exit angle,φout(λ), from the prism with respect to the exit angle at a reference wavelength,φout(λ0):
pixel(λ) =f
p ·sin φout(λ)−φout(λ0)
+shif t (2.4) wheref is the focal length of the spherical mirror M4,pis the pitch of the detector andshif tis the the pixel offset. φout(λ) is given by Snellius’s law:
φout(λ) =sin−1
n(λ)·sin A−sin−1 φin
n(λ)
(2.5)
whereAis the apex angle of the prism,φinis the angle of incidence on the prism andn(λ) is the refractive index of the prism material, which is obtained from the Sellmeier equation. Even though the focal length is known, it is, together with the shif t, used as a fitting parameter due to the astigmatism as discussed in section 2.3.2. If the spectrograph is not used at the angle of minimal deviation,φin can be used as an additional fitting parameter. For the fit the steady state absorption spectrum of the NIST 2065 is converted topixel and compared to the spectrum obtained from the TA instrument (Figure 2.8b). After determining the fitting parameters, the required function λ(pixel) is obtained by numerically inverting the monotonic functionpixel(λ).
TA
Steady State
a) b)
Holmium Oxide
NIST 2065
Figure 2.8: Pixel to wavelength conversion by comparing the absorption spectrum of rare earth elements recorded with the steady state spectrometer and the transient absorption spectrometer. For the UV-Vis detection a holmium oxide filter is used (a), whereas a mix of rare earth metals is used for the NIR-detection (b, NIST-2065)
dObtained by measuring the intensity with and without the Holmium oxide filter in the collimated beam path.
2.5 Data processing 39
2.5.2 Excluding scattering
The intensity of the scattered light from the pump pulse depends on the pump wavelength, scratches or dirt on the cuvette as well as on possible particles or dust in the sample. To decrease the scattering the cuvette has to be cleaned thor-oughly, a spot has to be found where no scratches are present and the sample should be filtered. If the scattering is small compared to the signal, it can usually be subtracted if enough scans are recorded (see section 2.5.4). However, if particles float through the pumped spot scattering events can occur, at which the scattered intensity is orders or magnitude higher. In this cases, the averaged signal at a certain time step is dominated by the high intensity scattering from a single scan and the pump scattering cannot be excluded by background subtraction. The pump region at this time step will therefore be unusable and has to be truncated.
To exclude those high scattering events, the TA signal around the pump is inte-grated and a moving average (MA) filter is applied to the obtained signal. If the deviation from the signal to the MA exceeds a certain threshold a scattering event is detected and this time step of the scan is discarded. The algorithm works as long as the scattering events are very rare compared to the number of scans and enough spectra are left at each ∆t.
2.5.3 Comparing Scans
Usually at least four scans are measured and averaged to obtain an acceptable signal-to-noise ratio of the kinetics. Before averaging, time traces from the different scans are compared to detect possible sample degradation, solvent evaporation or pointing instabilities. If the traces are not on top of each other, the data should be discarded and the source for the error found. The scans are only averaged if all scans are on top of each other .
2.5.4 Background subtraction
The background signal consists of the scattered light of the pump as well as the spontaneous emission. These contributions to the data matrix can be removed by averaging the signal at negative time delays and subtracting it from the whole data matrix. The scattering can however only be removed under the assumption that these contributions are not a function of ∆t and the fluctuations are small (see section 2.5.7). If this assumption does not hold the pump region is often simply removed.
2.5.5 Removing coherent artefacts
To remove the coherent artefact around ∆t=0, the transient absorption matrix of the solvent is measured under the same conditions as the sample and subtracted from the data. Ideally the same sample cuvette is used and the solvent is measured directly after the sample to avoid changes in the pump power or alignment.
2.5.6 Chirp correction
A positive chirp is present on the white light pulse due to the refractive index dependence onλof all traversed elements before the sample. Therefore the tem-poral pump-probe overlap or time zero of the experiment is dependent on the wavelength of the white light probe pulse. To correct for the chirp, an optical Kerr effect (OKE) measurement of the pure solvent is carried out. The ∆t0(λ) is determined by fitting the time-traces of the OKE at each wavelength with a Gaussian function. ∆t0(λ) is then fitted with a polynomial given in equation 2.6 and the measured time delays ∆(t)(λ) are reassigned by interpolation giving a ∆t valid for allλ.10
∆t0(λ) =a+105b λ2 +106c
λ4 (2.6)
2.5.7 Kinetic cross validation with TCSPC
The pump path is altered regularly due to the need for excitation at different wavelengths. This makes it prone to systematic errors which might be mistaken for dynamics of the studied system. The major sources of systematic errors are the alignment of the delay stage and the collimation of the pump beam. Both leads to the same symptom, which is a pump-probe overlap dependence on ∆t and therefore a systematic error in ∆A(∆t,λ). To detect a possible systematic error on the kinetics, a reference sample with a ns lifetime is measured, followed by measuring the lifetime of the identical sample with time correlated single photon counting (TCSPC). It is crucial to use the exactly same sample directly after the TA measurement was performed to guarantee the same oxygen concentration as well as sample concentration, which might impact the lifetime. Differences in the time traces highlight a systematic error originating from the pump path.
Since the systematic error is the same for all samples, measured with the identical alignment, a correction function can be obtained by comparing the TCSPC and TA traces. Note that even though the application of the correction function gives the correct kinetics for the ESA, GSB and SE, the kinetics in the region of significant background contributions can still be erroneous. If the pump-probe overlap is a function of ∆t, the pump scattering as well as the spontaneous emission will also be a function ∆t, leading to incorrect background correction at long times.