Phase shift methods

If multiple scattering processes occur an erroneously long lifetime will be obtained, as for several of the above-mentioned methods. The opposite effect is obtained if, in addition to the fluorescence light, non-shifted stray light from the modulated light source is recorded. If the modulation is not perfectly sinusoidal, the first Fourier component can be isolated and the phase shift for this component will still yield the lifetime. 

If the laser is tuned to the center of an absorbing transition ti) - k) the detected fluorescence intensity Ip monitored on the transition k - m) is proportional to the laser intensity as long as saturation can be neglected. In the phase-shift method the laser intensity is modulated at the frequency f = n/2x (Fig. 11.36a) according to 

Inserting (11.39) with Il(0 = cpl(0 into (11.38) yields the time-dependent population density N,j(t) of the upper level, and therefore also the fluorescence power PpL(t) = Nfc(t)A emitted on the transition k) - m). The result is 

According to (11.35-38) the effective lifetime is determined by the inverse sum of all deactivation processes of the excited level k). In order to obtain the spontaneous lifetime fg (. = l/Aj one has to measure (p.Il) at different pressures p and dif rent laser intensities II, and extrapolate the results towards p - 0 and II — 0. 

The influence of induced emission is a definite drawback of the phase-shift method. 

A comparison with (11.40) shows that the mean lifetime r corresponds to the time constant r = RC with R = RiR2/(Ri+R2) and the laser intensity to the charging current I(t) = (Uo-U)/Ri.  

Equation (6.61) anticipates a pure exponential decay. This is justified if a single upper level k) is selectively populated. If several levels are simultaneously excited the fluorescence power Rpi(t) represents a superposition of decay functions with different decay times x/t. In such cases the phase shifts (f2) and the amplitudes a/(l + have to be measured for different modulation frequencies The 

If the laser is tuned to the center frequency coik of an absorbing transition i) k), the detected fluorescence intensity /pL monitored on the 

The intensity 1 of the incident light which excites the molecular level E. is sinusoidally modulated at a frequency Q v/hich is assumed to be small compared with the light frequency 

The modulation may be achieved for example with a Pockels cell or an ultrasonic light modulator (Fig.11.12). 

The differential equation for the time-dependent density N -(t) of molecules in level E with g. = gj = 1 and 1 = pc is 

The solution of (11.9) is straightforward and yields N. (t). The fluorescence intensity Ip-j = N. (t)A. j is observed perpendicular to the incident light beam where no induced emission can be seen. One obtains 

Equation (11.10) shows that the fluorescence intensity is modulated at the same frequency n as the exciting light, but the modulation amplitude has decreased and its phase is shifted by q against the modulation phase of 

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One advantage of the photon counting teclmique over the phase-shift method is that any non-exponential decay is readily seen and studied. It is possible to detect non-exponential decay in the phase-shift method too by making measurements as a fiinction of tlie modulation frequency, but it is more cumbersome. 

Jablonski (48-49) developed a theory in 1935 in which he presented the now standard Jablonski diagram" of singlet and triplet state energy levels that is used to explain excitation and emission processes in luminescence. He also related the fluorescence lifetimes of the perpendicular and parallel polarization components of emission to the fluorophore emission lifetime and rate of rotation. In the same year, Szymanowski (50) measured apparent lifetimes for the perpendicular and parallel polarization components of fluorescein in viscous solutions with a phase fluorometer. It was shown later by Spencer and Weber (51) that phase shift methods do not give correct values for polarized lifetimes because the theory does not include the dependence on modulation frequency. 

Both the subtractive and the phase shift method are valid as long as the RF waveform remains sinusoidal [184]. For asymmetrical discharges the integral method is to be used. 

Fluorescence Lifetimes. Fluorescence lifetimes were determined by the phase shift method, utilizing a previously-described phase fluorimeter. The emission from an argon laser was frequency doubled to provide a 257 nm band for excitation. Fluorescence lifetimes of anisole and polymer 1 in dichloro-methane solution were 2.2 and 1.4 nsec, respectively. Fluorescence lifetimes of polymer films decreased monotonically with increasing DHB concentration from 1.8 (0) to 0.7 nsec (9.2 x 10 3 MDHB). Since fluorescence lifetimes (in contrast to fluorescence intensities) are unaffected by absorption effects of the stabilizer, these results provide direct evidence in support of the intensity measurements for RET from polymer to stabilizer. 

Furuyama, S., Atkinson, R., Colussi, A.J., Cvetanovic, R.J. (1974) Determination by the phase shift method of the absolute rate constants of reactions of oxygen ( ,P) atoms with olefins at 25°C. Int 7. J. Chem. Kinet. 6, 741. 

Fig. 6. Experimental arrangement for lifetime measurements by the phase-shift method, using laser excitation. The laser beam is amplitude-modulated by a Pockel cell with analysing Nicol prism and a small part of the beam is reflected by a beam splitter B into a water cell, causing Rayleigh scattering. This Rayleigh-scattered light and the fluorescence light from the absorption cell are both focused onto the multiplier cathode PMl, where the difference in their modulation phases is detected. (From Baumgartner, G., Demtroder, W., Stock, M., ref. 122)).

Compared to the phase-shift method, this technique has the advantage that nonexponential decays can also be investigated. 

The nonsteady state methods may be conveniently divided into two categories (A) pulse methods and (B) phase-shift methods. 

B) Phase-shift methods. The phase shift method for determining fluorescence lifetimes is based on the principle that if fluorescence is excited by suitably modulated light source, emitted radiation will also be similarly modulated. With reference to a scattering substance, emission from a fluorescent substance will introduce a time lag due to finite time between absorption and emission. This, by definition is the lifetime of the excited state. The time lag will cause a phase-shift relative to the exciting light. Phase fluorimetry requires a modulated light source and a phase sensitive detector. 

Figure 10.8 A block diagram of phase-shift method for measurement of life-time.

Patemo-Buchi reactions, 238-255 Pauli s exclusion principle, 19,24,31,40 Perturbation, external heavy atom, 145 Perturbation theory time dependent, 53 Phantom triplet, 229 Phase-shift method, 309, 311 a-phosphorescence, 129 -phosphorescence, 157 Phosphorescence... 

Gazdag, J., 1978, Wave equation migration with the phase-shift method Geophysics, 43, No. 7, 1342-1351. 

The phase shift method is based on the observation that nuclear spins moving in the presence of a magnetic field gradient exhibit a phase shift in the transverse magnetization. This phase shift can be associated with a displacement of fluid molecules in the direction of the pulsed-field gradient. Mathematically, if the nuclear spins have translational motion, the space vector r in Eq. (6) becomes dependent on time and can be expanded in terms of its initial state r(0) and time derivatives 34... 

Extension of the phase shift method to provide spatial resolution... 

Methane was the first polyatomic molecule other than CO2 for which vibrational energy-transfer pathways and rates were investigated. This study of methane involved the utilization of the phase-shift method for determining the lifetimes of vibrationally excited states. The asymmetric stretching vibration, v-, of methane at 3010 cm (see Fig. 1) was excited by a chopped He-Ne laser operating on the 2947.9 cm Ne transition. Fluorescence was detected from both the mode and the bending mode of methane at 1306 cm . Rates were extracted from phase-shift measurements, and Ref. 16 provides an excellent discussion of the background for, and use of the phase-shift method. 

The phenomena discussed above can be studied using various techniques, and not all methods are equally suitable in a particular case. Two principally different kinds of methods for measuring fluorescence lifetimes exist, namely, pulse methods and modulation or phase-shift methods. Phase-shift methods, despite the fact that they have been known for a longer time, have not found widespread use during the last decade. However, important technical advances have been made in phase-shift methods which in fact have inspired many researchers to apply them more frequently. Nevertheless, pulse methods are still the most widely used today, in particular for high time resolution. If carried out properly both types of methods must and will give the same result. Details of the measuring problem will determine which method is more appropriate in a particular case. 

This phase-shift method is a general technique and is e.g. also applied to the measurement of lifetimes of excited atoms or molecules (see Sect. 6.3). The combination of CRDS with Fourier-spectroscopy gives for a fixed detection time a better signal-to noise ratio, because now all absorption lines within the covered spectral range are detected simultaneously. In Fig. 1.22 a possible experimental arrangement for this combined spectroscopic technique is schematically depicted. The transmitted laser... 

Fig. 6.87 Phase-shift method for the measurement of excited-state lifetimes (a) experimental arrangement and (b) equivalent electric network...

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