Detection phase-sensitive

Phase-sensitive detection is used in lock-in amplifiers, which are interfaced with potentiostats. Only a general idea of these measurements will be presented here. In this method the measured signal, Ei, which is proportional to the ac current from the potentiostat, is 

The disadvantage of the lock-in technique is that it retains contributions of the harmonic frequencies (2n + l)C0ref if they are present in the input signal (e.g., harmonics, noise), although their influence is attenuated by 1/3, 1/5, 1/7, etc. with increasing n. For example, when the frequency in Eq. (29) is three times the reference frequency in Eq. (30), the average signal obtained 

Lock-in amplifiers operate in the frequency range from 0.5 (lower limit up to 10 Hz, depending on the manufacturer) to 10 Hz, with a precision of 0.1 to 0.2%. Modem lock-in amplifiers are controlled by a microprocessor and permit automated measurements with automatic range selection. 

Increase in signal-to-noise is also linear in the frequency of the modulation. Again, there is a spectroscopic and an engineering limitation. Let us start with the latter one. Low-frequency waves (cfi, the rumble of an earthquake) penetrate further into matter 

FIGURE 2.7 Overmodulation. The single-line spectrum of the strong pitch calibration sample (g = 2.0028) is recorded at v = 9.77 GHz with modulation amplitudes of 2.5, 10, or 40 gauss and with accordingly adjusted electronic gain such that in the absence of modulation deformation the signal should have constant amplitude. 

Finally, the phase of the modulating held has to be set, but this is duck soup The signal amplitude of an arbitrary sample is experimentally maximized by adjusting the phase. And for a given modulation-coil setup (usually associated with a particular resonator) this has to be done only once in the setup s life time. 

Phase-sensitive detection is not at all specihc for EPR spectroscopy but is used in many different types of experiments. Some readers may be familiar with the electrochemical technique of differential-pulse voltammetry. Here, the potential over the working and reference electrode, E, is varied slowly enough to be considered as essentially static on a short time scale. The disturbance is a pulse of small potential difference, AE, and the in-phase, in-frequency detection of the current affords a very low noise differential of the i-E characteristic of a redox couple. 

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Diffey W M and Beck W F 1997 Rapid-scanning interferometer for ultrafast pump-probe spectroscopy with phase-sensitive detection Rev. Sci. Instrum. 3296-300... 

Circular dichroism employs standard dispersive or interferometric instmmentation, but uses a thermal source that is rapidly modulated between circular polari2ation states using a photoelastic or electro-optic modulator. Using phase-sensitive detection, a difference signal proportional to the absorption difference between left- and right-polari2ed light, AA is recorded as a function of wavenumber. Relative differential absorptions... 

The use of phase sensitive detection with the phase fluorometer to analyze multicomponent systems was first described in 1970 by Veselova and coworkers (76). 

By using phase sensitive detection, the detector phase angle can be adjusted to be exactly out of phase with the phase-delayed emission from any single fluorophore, suppressing its contribution to the total emission signal. Phase sensitive detection, coupled with... 

If the signal decay is a single-exponential curve, equations 16 and 17 result in values for X that are in agreement with each other. Dissimilar values indicate multiexponential decay, which usually means that the sample contains more than one fluorophore. Multiexponential decay can be resolved by using a phase fluorometer with phase sensitive detection. A time-independent, direct-current signal is produced that is proportional to the cosine of the difference between the phase angle of the detector ( D) and the phase angle of the fluorescence ( ) ... 

Both methods obtain the necessary sensitivity by modulating the electrode potential between two values which define two distinct states of the electrode surface thus the chemistry to be observed is directly modulated and may be detected with great sensitivity by an appropriate form of synchronous detection. In the case of EMIRS, the modulation frequency is made sufficiently high compared to the wavelength scanning rate to enable a phase sensitive detection system to be used whereas, for SNIFTIRS, the electrode potential is held for a sufficient period at each potential to accumulate data from several interferometric scans and, after an adequate number, the two sets of data are ratioed. 

The advantage of employing periodic perturbation of light intensity, e.g., using a chopper, and phase-sensitive detection are beyond a simple enhancement of the signal-to-noise ratio. For photoinduced electron-transfer mechanisms, as schematized in Fig. 11, the... 

Resolvable modulation is detected on a three-pulse echo decay spectrum of predeuterated 3-carotene radical (Gao et al. 2005) as a function of delay time, T. The resulting modulation is known as ESEEM. Resolvable modulation will not be detected for nondeuterated P-carotene radical since the proton frequency is six times larger. The modulation signal intensity is proportional to the square root of phase sensitive detection and interfering two-pulse echoes and suppressed by phase-cycling technique (Gao et al. 2005). Analysis of the ESEEM spectrum yields the distance from the radical to the D nucleus, a the deuterium coupling constant, and the number of equivalent interacting nuclei (D). The details related to the analysis of the ESEEM spectrum are presented in Gao et al. 2005. 

To improve the S/N ratio, the modulation signal is processed by amplification with a tuned amplifier using phase-sensitive detection. This means that the detected signal must not only be at the modulation frequency, but must also be in phase with the modulation. Since the amplifier itself can introduce a bit of phase shift, there is a phase control which, in principle, should be adjusted to maximize the signal amplitude. In practice, this control needs to be adjusted only rarely and in most cases the best approach is to leave it alone. 

Since in EPR we usually observe first-derivative spectra as a consequence of phase-sensitive detection (see 2.7) it is relevant to note that the first derivatives of the two distributions are features with a positive and a negative peak. The peak-to-peak separation App in field units for the two distributions is... 

At this point, some mention of the intensity of the lines observed in epr spectra should be made. In the case of a radical having no magnetic nuclei the difference in the energy of the a and 0 levels is of the order of 0.3 cm . At room temperature, kT is c. 200cm and the Boltzmann equation thus gives the ratio of the number of radicals in the lower state to those in the upper, Np/Na, as 1.0015. The absorption intensity is proportional to this difference and as a consequence epr absorptions are very weak. The phase-sensitive detection employed in epr spectrometers is thus a necessity if these weak... 

In order to observe a short-lived species it may be necessary to employ a rapid-scanning spectrometer, such as a diode-array instrument (Sms for a 240nm-800nm spectrum). In addition, the absorbances of electrogenerated species can be very small and signal-averaging or phase-sensitive detection may be necessary to achieve the required signal-to-noise ratio (cf. EMIRS and FTIR). 

In order to study the identity and nature of the intermediate, Aylmer-K.elly et al. (1973) employed modulated specular reflectance spectroscopy. They studied the reduction reaction at a lead cathode in both aqueous and non-aqueous electrolytes. A phase-sensitive detection system was employed by the authors, locked-in to the frequency of the potential modulation. The potential was modulated at 30 Hz between the reference potential of — 1.0 V vs. Ag/AgCl and a more cathodic limit. 

The luminescence lifetime may also be extracted from phase-sensitive detection of the modulated emission that originates from modulated continuous excitation of the indicator dye (equation 9)2 ... 

It is even possible to convert changes of the fluorophore emission intensity as a function of the analyte level into lifetime-based sensing devices using phase-sensitive detection. The technique is called dual lifetime... 

J. R. Lakowicz and S. Heating, Binding of an indole derivative to micelles as quantified by phase-sensitive detection of fluorescence,/. Biol. Chem. 5519-5524(1983). 

By modulating the electric field and using phase-sensitive detection methods, Uehara et al. 8 ) were able to increase the sensitivity considerably and they could even detect Stark splittings of less than the doppler width of the components. Fig. 3 shows the Stark spectrum of HDCO for different electric field strengths. Because of the Stark modulation technique the absorption lines appear differentiated the zero points represent the center of each line. 

EPR spectra were recorded with a Varian E9 X-band spectrometer using field (100 kHz) and light (13 or 83 Hz) modulation with phase-sensitive detection at the modulation frequencies (19). Typically, the field modulation amplitude employed ranged from 20 to 40 gauss, the microwave power from 0.1 to 0.5 mW. Measurements were performed on frozen solutions of the porphyrins at about 100 K using the standard Varian variable temperature accessory or at about 10 R with an Oxford Instruments helium gas cryostat. Light sources used for photoexcitation were a 1000 W Xe arc source powered by a Photochemical Research Associates Supply with electronic modulation... 

We first review the essentials of the phase distribution of the electric fields at the focus of a high numerical aperture lens in Section II. After discussing the phase properties of the emitted signal, in Section HI we zoom in on how the information carried by the emitted held can be detected with phase-sensitive detection methods. Interferometric CARS imaging is presented as a useful technique for background suppression and signal enhancement. In Section IV, the principles of spatial interferometry in coherent microscopy are laid out and applications are discussed. The influence of phase distortions in turbid samples on phase-sensitive nonlinear microscopy is considered in Section V. Finally, in Section VI, we conclude this chapter with a brief discussion on the utility of phase-sensitive approaches to coherent microscopy. 

A number of different modulation techniques can be used to increase the signal-to-noise ratio (e.g., see Schiff et al., 1994a, 1994b and Brassington, 1995). For example, the laser beam can be mechanically chopped and detected using phase-sensitive detection with a lock-in amplifier. A more commonly used method for accurately measuring small absorbances is to modulate... 

For a square-wave-chopped photometer with phase-sensitive detection following a bandpass filter centered on the chopping frequency such that... 

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