Phase modulation fluorometry

The least-squares method is also widely applied to curve fitting in phase-modulation fluorometry the main difference with data analysis in pulse fluorometry is that no deconvolution is required curve fitting is indeed performed in the frequency domain, i.e. directly using the variations of the phase shift I and the modulation ratio M as functions of the modulation frequency. Phase data and modulation data can be analyzed separately or simultaneously. In the latter case the reduced chi squared is given by 

Data analysis in phase fluorometry requires knowledge of the sine and cosine of the Fourier transforms of the b-pulse response. This of course is not a problem for the most common case of multi-exponential decays (see above), but in some cases the Fourier transforms may not have analytical expressions, and numerical calculations of the relevant integrals are then necessary. 

In the case of a single exponential decay, the decay time can be determined 

The values measured in these two ways should of course be identical and independent of the modulation frequency. This provides two criteria to check whether an instrument is correctly tuned by using a lifetime standard whose fluorescence decay is known to be a single exponential. Note that a significant difference between values obtained by means of the above equations is a compelling evidence of nonexponentiality of the fluorescence decay. 

A single frequency suffices for measuring the decay time of a single exponential decay but the frequency should be chosen such that cot is not too different from 1, i.e. f 1/(27it). Therefore, for decay times of 10 ps, 1 ns, 100 ns, the optimum frequencies are about 16 GHz, 160 MHz, 1.6 MHz, respectively. 

1 Phase Fluorometers using a Continuous Light Source and an Electro-optic Modulator 

A schematic diagram of such instruments is given in Fig. 7.6. The light source can be a xenon lamp associated with a monochromator. The optical configuration 

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Szmacinski, H. Lacowicz, J. R. Lifetime-based Sensing Using Phase-Modulation Fluorometry. In Fluorescent Chemosensor for Ion and Molecule Recognition. ACS Symposium Series 538, 1993. 

Beechem, J. M., Knutson, J. R., Ross, B. A., Turner, B. W. and Brand, L. (1983). Global resolution of heterogeneous decay by phase/modulation fluorometry Mixtures and proteins. Biochemistry 22, 6054-8. 

Knowledge of the dynamics of excited states is of major importance in understanding photophysical, photochemical and photobiological processes. Two time-resolved techniques, pulse fluorometry and phase-modulation fluorometry, are commonly used to recover the lifetimes, or more generally the parameters characterizing the S-pulse response of a fluorescent sample (i.e. the response to an infinitely short pulse of light expressed as the Dirac function S). 

Pulse fluorometry uses a short exciting pulse of light and gives the d-pulse response of the sample, convoluted by the instrument response. Phase-modulation fluorometry uses modulated light at variable frequency and gives the harmonic response of the sample, which is the Fourier transform of the d-pulse response. The first technique works in the time domain, and the second in the frequency domain. Pulse fluorometry and phase-modulation fluorometry are theoretically equivalent, but the principles of the instruments are different. Each technique will now be presented and then compared. 

General principles of pulse and phase-modulation fluorometries... 

The principles of pulse and phase-modulation fluorometries are illustrated in Figures 6.5 and 6.6. The d-pulse response I(t) of the fluorescent sample is, in the simplest case, a single exponential whose time constant is the excited-state lifetime, but more often it is a sum of discrete exponentials, or a more complicated function sometimes the system is characterized by a distribution of decay times. For any excitation function E(t), the response R(t) of the sample is the convolution product of this function by the d-pulse response ... 

Phase-modulation fluorometry The sample is excited by a sinusoidally modulated light at high frequency. The fluorescence response, which is the convolution product (Eq. 6.9) of the pulse response by the sinusoidal excitation function, is sinusoidally... 

Fig. 6.6. Principles of pulse fluorometry and multi-frequency phase-modulation fluorometry.

An efficient way of overcoming this difficulty is to use a reference fluorophore (instead of a scattering solution) (i) whose fluorescence decay is a single exponential, (ii) which is excitable at the same wavelength as the sample, and (iii) which emits fluorescence at the observation wavelength of the sample. In pulse fluorometry, the deconvolution of the fluorescence response can be carried out against that of the reference fluorophore. In phase-modulation fluorometry, the phase shift and the relative modulation can be measured directly against the reference fluorophore. 

To answer the question as to whether the fluorescence decay consists of a few distinct exponentials or should be interpreted in terms of a continuous distribution, it is advantageous to use an approach without a priori assumption of the shape of the distribution. In particular, the maximum entropy method (MEM) is capable of handling both continuous and discrete lifetime distributions in a single analysis of data obtained from pulse fluorometry or phase-modulation fluorometry (Brochon, 1994) (see Box 6.1). 

In phase-modulation fluorometry, it is convenient to use the fractional contributions f instead of the fractional amplitudes, as shown in Eqs (6.30) and (6.31). The above equation is thus rewritten as... 

In phase-modulation fluorometry, it is worth noting that the transfer rate constant can be determined from the phase shift between the fluorescence of the acceptor excited directly and via donor excitation. 

How can phase-modulation fluorometry contribute to this health-care need It now seems possible to construct a lifetime-based blood gas catheter (Figure 1.3), or alternatively, an apparatus to read the blood gas in the freshly drawn blood at the patient s bedside. To be specific, fluorophores are presently known to accomplish the task using a 543-nm Green Helium-Neon laser,(18 19) and it seems likely that the chemistries will be identified for a laser diode source. The use of longer wavelengths should minimize the problems of light absorption and autofluorescence of the samples, and the use of phase or modulation sensing should provide the robustness needed in a clinical environment. For the more technically oriented researcher, we note that the... 

Noninvasive glucose measurements can potentially be performed with phase-modulation fluorometry. The blood gas application described above requires drawing the blood, i.e., an invasive as well as an unpleasant procedure. Similarly, present measurements of blood glucose also require fresh blood. Insulin-dependent diabetics... 

H. Szmacinski and J. R. Lakowicz, Optical measurements of pH using fluorescence lifetimes and phase-modulation fluorometry, Anal. Chem. 65, 1668-1674(1993). 

K. W. Bemdt, I. Gryczynski, andJ. R. Lakowicz, Phase-modulation fluorometry using afrequency-doubled pulsed laser diode light source, Rev. Sci. Instrum. 61, 2331-2337 (1990). 

J. R. Lakowicz and B. P. Maliwal, Optical sensing of glucose using phase-modulation fluorometry, Anal. Chim. Acta 271, 155-164(1993). 

The use of high-speed modulated excitation (f> kr + knr) combined with coherent detection methods has resulted in the popular techniques of frequency domain fluorometry, also known as phase-modulation fluorometry. These techniques can be used to determine the temporal characteristics of both fluorescence and phosphorescence and will also be addressed later in this chapter. 

In phase-modulation fluorometry, the pulsed light source typical of time-domain measurements is replaced with an intensity-modulated source (Figure 10.5). Because of the time lag between absorption and emission, the emission is delayed in time relative to the modulated excitation. At each modulation frequency (to = 2nf) this delay is described as the phase shift (0, ), which increases from 0 to 90° with increasing modulation frequency. The finite time response of the sample also results in demodulation to the emission by a factor m which decreases from 1.0 to 0.0 with increasing modulation frequency. The phase angle (Ow) and the modulation (m, ) are separate... 

J. R. Lakowicz, B. Maliwal, A. Ozinskas, and R. B. Thompson, Fluorescence lifetime energy-transfer immunoassay quantified by phase-modulation fluorometry. Sensors and Actuators... 

It will be seen that, as in the case of the LED, control of the bias voltage gives simple modulation of the laser output intensity. This is particularly useful in phase-modulation fluorometry. However, a measure of the late awareness of the advantages of IR techniques in fluorescence is that only recently has this approach been applied to the study of aromatic fluorophores. Thompson et al.(51) have combined modulated diode laser excitation at 670 and 791 nm with a commercial fluorimeter in order to measure the fluorescence lifetimes of some common carbocyanine dyes. Modulation frequencies up to 300 MHz were used in conjunction with a Hamamatsu R928 photomultipler for detecting the fluorescence. Figure 12.18 shows typical phase-modulation data taken from their work, the form of the frequency response curves is as shown in Figure 12.2 which describes the response to a monoexponential fluorescence decay. 

The helium-neon (HeNe) laser immediately comes to mind, having a very useful spectral line at 633 nm for steady-state red/near-IR fluorescence studies. Kessler and Wolfbeis have demonstrated the fluorescence assay of the protein human serum albumin using the probe albumin blue excited with a red HeNe laser.(71) Another useful wavelength available from the green HeNe laser is at 543.5 nm and this has been used with phase-modulation fluorometry by Lakowicz etal. to study probes such as carboxy seminaphtorhodafluor-6 (SNARF-6) as a means of measuring pH.(72)... 

Phase-modulation fluorometry has been performed with APDs to a lesser extent than has single-photon timing, but nevertheless there are some reports of this combination006, 107)... 

J. R. Lakowicz, H. Szmacinski, and M. Karakelle, Optical sensing of pH and pC02 using phase-modulation fluorometry and resonance energy transfer, Analytica Chim. Acta 272, 179-186 (1993). 

Figure 14.11. Diagram of phase-modulation fluorometry with sinusoidally modulated excitation, with demodulated and delayed, or phase-shifted emission. (From Ref. 31 with permission.)...

The mathematical basis for the exponential series method is Eq. (5.3), the use of which has recently been criticized by Phillips and Lyke.(19) Based on their analysis of the one-sided Laplace transform of model excited-state distribution functions, it is concluded that a small, finite series of decay constants cannot be used to represent a continuous distribution. Livesey and Brouchon(20) described a method of analysis using pulse fluorometry which determines a distribution using a maximum entropy method. Similarly to Phillips and Lyke, they viewed the determination of the distribution function as a problem related to the inversion of the Laplace transform of the distribution function convoluted with the excitation pulse. Since Laplace transform inversion is very sensitive to errors in experimental data,(21) physically and nonphysically realistic distributions can result from the same data. The latter technique provides for the exclusion of nonrealistic trial solutions and the determination of a physically realistic solution. These authors noted that this technique should be easily extendable to data from phase-modulation fluorometry. 

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