A1. Basic Laser-Induced Fluorescence Imaging
Laser-induced fluorescence (LIF) is a commonly used technique in flow visualisation and investigations [
13‐
16]. It was pioneered more than 40 years ago by Smart and Ford [
13] for the studies of oil films between piston ring and cylinder liner. From the early 2000s, LIF saw its gradual adoption as an experimental method in tribology for thin film investigations in compliant contacts starting with the work of Sugimura et al. [
42] on a ball-on-disc type configuration. In its basic form, a LIF imaging experiment in fluids consists of dissolving a fluorescent dye in a fluid and subjecting the probed volume to photo-excitation; the resulting fluorescence signal is then collected and imaged on an imaging sensor where the fluorescence power emitted per unit area,
SF, is amplified and converted into pixel intensity values.
For a probe volume of excitation spot area,
A, and cross-sectional thickness
l, the fluorescence emission intensity
\({I}_\text{f}\) per unit area is
$${I}_\text{f}\left(l\right)={I}_{0}\phi (1-{e}^{-{\epsilon }_{{\lambda }_\text{ex}}Cl})$$
(1)
The spectral width of fluorescence emission depends the particular dye’s photophysical characteristics, the intensity \({I}_\text{f}\) is a function of the concentration C of the fluorescent species in the fluid, the excitation light intensity I0 at wavelength λex and the probed volume cross-sectional thickness l. The dye’s quantum efficiency, ϕ, is the ratio of photons absorbed to the photons emitted through fluorescence and \({\varepsilon }_{{\lambda }_\text{ex}}\) is the molar extinction coefficient, an intrinsic property of the dye.
The excitation light intensity
I0 decays exponentially as it travels through the probe volume according to Eq. (
2) with
\(\frac{{I}_{0}}{{I}_\text{T}}\) the ratio between the incident (excitation) I
0 and the transmitted
IT light being:
$$\frac{{I}_{0}}{{I}_\text{T}}= {e}^{-{\varepsilon }_{{\lambda }_\text{ex}}Cl}$$
(2)
Equation (
2) is normally expressed as Eq. (
3) which is also known as the Beer–Lambert law [
43]:
$$Abs= \log\frac{{I}_{0}}{I}= {\varepsilon }_{{\lambda }_\text{ex}}Cl,$$
(3)
where
Abs is the probe volume absorbance at wavelength
λex.
For low absorbances, i.e.
\(A\)< < 1, a Taylor series expansion of Eq. (
1) leads to:
$${I}_\text{f}\left(l\right)\approx {I}_{0}\phi {\varepsilon }_{{\lambda }_\text{ex}}Cl$$
(4)
That is the fluorescent intensity is linearly proportional to the film thickness for weakly absorbing, dilute probe volumes. This relationship is valid for a range of excitation intensities as long as the dye saturation intensity
Isat is not exceeded [
37], since:
$${I}_\text{ex}=\frac{{I}_{o}}{1+\frac{{I}_{0}}{{I}_\text{sat}}}$$
(5)
It can be seen from Eq. (
5), that as long as
I0 ≪
Isat, the effective excitation intensity
Iex is equal to
Io and linearity of relationship in Eq. (
4) holds. In LIF experiments, it is critical to always operate in excitation regimes well below the dye’s excitation saturation intensity, especially during the calibration step or when operating at short exposures as discussed previously.
The fluorescence signal
\({S}_\text{f}\) collected by the imaging sensor over an integration time
t and over a range of emission wavelengths between
λ1 and
λ2 (
λ1 <
λ2) can be approximated by:
$$S_{{\text{f}}} \, = \,AKt\int_{{\lambda _{1} }}^{{\lambda _{1} }} {I_\text{f} \left( \lambda \right){\text{d}}\lambda \, = \,KAI_{0} \phi \varepsilon _{{\lambda _\text{{ex}} }} Clt,}$$
(6)
where
K is an experimental constant which takes into account the various losses that might exist in the setup as well as other optical, electronic and photophysical effects.
Film thickness measurements using LIF are made with the assumption that Eq. (
6) is valid i.e. a uniform illumination in space and time with an excitation intensity below
Isat impinging on a dilute and weakly absorbing probe volume. A calibration step involves an experiment whereby
\({S}_\text{f}\) is correlated to known film thicknesses (
h) so that the generated calibration curve can subsequently be used for film thickness determination.
While the validity of this general procedure is well established for a typical ball-on-disc setup, where
I0 is considered constant, this is not the case for the SBR configuration. For the latter, Eq. (
6) cannot be assumed valid since during bearing operation, the excitation light incidence angle on the contact zone will change with the spatial position of the ball; this variability compounds with the one due to the temporal instabilities of light source. A further important aspect specific to the SBR is that because the resident time of the contact in the excitation field changes with bearing speed, to keep the
I0 constant every bearing speed would require an adjustment of the excitation light intensity. These factors introduce variability in the excitation intensity,
I0 and therefore the direct use of Eq. (
6) for film thickness measurements would produce inaccurate values in the present experiments. To address this, an alternative ratiometric fluorescence approach that does not rely on constant excitation intensity,
I0 was adopted for the present SBR set-up.
A2. Ratiometric Laser Induced Fluorescence Imaging
The ratiometric LIF imaging approach implemented on the SBR uses two fluorescent dyes (a donor and an acceptor) dissolved in a fluid to take advantage of a fluorescence measurement artefact known as the inner-filter effect. This approach is similar to the one proposed by Hidrovo et al. [
39], termed Emission Reabsorption Laser Induced Fluorescence (ERLIF).
Although the inner filter effect can occur for a single dye system, it is more pronounced in the case of a mixture of two dyes [
38]. This fluorescence quenching effect may occur whenever there is a spectral overlap between the donor dye (D) emission and the acceptor dye (A) absorption spectra so that a radiative transfer process can take place between them whereby a photon emitted by D is absorbed by A. This radiative transfer results in a decrease of the donor quantum efficiency in the region of spectral overlap and hence a decrease in the donor fluorescence signal. The ratiometric imaging consists of separating the donor and acceptor signal and using the ratio as a scalar with no dependence on excitation intensity but only the cross-sectional depth of the probed volume i.e. the oil film thickness in the present case.
Following similar formulation as Valeur [
44], for a given concentration C
A and C
D of donor and acceptor dyes in a fluid, the fraction
a of photons emitted by D and absorbed by A is:
$$a=\frac{1}{{\phi }_\text{D}^{0}}\underset{0}{\overset{\infty }{\int }}{I}_\text{D}\left(\lambda \right)\left[1-{e}^{-{\epsilon }_\text{A}\left(\lambda \right){C}_\text{A}l}\right]d\lambda ,$$
(7)
where
\({\phi }_\text{D}^{0}\) is the fluorescence quantum yield of the donor in the absence of acceptor and
\({I}_\text{D}\left(\lambda \right)\),
\({\epsilon }_\text{A}\left(\lambda \right)\) the donor fluorescence intensity and molar absorption coefficient of the acceptor, respectively.
For dilute and weakly absorbing probe volumes Eq. (
7) can be simplified to:
$$a=\frac{{C}_\text{A}l}{{\phi }_\text{D}^{0}}\underset{0}{\overset{\infty }{\int }}{I}_\text{D}\left(\lambda \right){\epsilon }_\text{A}\left(\lambda \right)d\lambda$$
(8)
With the magnitude of the spectral overlap between D and A represented by the integral in Eq. (
8). The donor fluorescence signal can therefore be expressed as:
$${S}_\text{D}= {S}_\text{D}^{0}\left(1-a\right),$$
(9)
where
\({S}_\text{D}^{0}\) is the donor fluorescence signal in the absence of the acceptor.
Using the expression in Eq. (
6) and assuming a dilute and weakly absorbing probe volume, the ratio, R, of the donor and acceptor fluorescence signals,
\({S}_\text{D} and {S}_\text{A}\) respectively, is:
$$R=\frac{{S}_\text{D}}{{S}_\text{A}}=\frac{{S}_\text{D}^{0}\left(1-a\right)}{{S}_\text{A}}=\frac{{\phi }_\text{D}^{0}{\epsilon }_\text{D}\left(\lambda \right){C}_\text{D}}{{\phi }_\text{A}{\epsilon }_\text{A}\left(\lambda \right){C}_\text{A}}[1-\frac{{C}_\text{A}l}{{\phi }_\text{D}^{0}}\underset{0}{\overset{\infty }{\int }}{I}_\text{D}\left(\lambda \right){\epsilon }_\text{A}\left(\lambda \right)d\lambda ]$$
(10)
If the overlap integral, O, is assumed as invariant for the two fluorescent dyes undergoing radiative transfer, Eq. (
10) can be simplified to:
$$R=\frac{{\phi }_\text{D}^{0}{\epsilon }_\text{D}\left(\lambda \right){C}_\text{D}}{{\phi }_\text{A}{\epsilon }_\text{A}\left(\lambda \right){C}_\text{A}}\left(1-\frac{{OC}_\text{A}}{{\phi }_\text{D}^{0}}l\right)=B-Cl,$$
(11)
where
B and
C are constants.
From (11) it follows that the ratio of the fluorescence signals from the donor and acceptor dyes, D and A, correlates linearly with the film thickness, \(l\), with dependence on the excitation intensity I0 suppressed. This ratiometric approach also has the benefit of suppressing other undesirable setup specific factors that might affect the fluorescence signal such as optical non-linearities and surface reflectivity.