Lock-in detection

The dependence of the in-phase and quadrature lock-in detected signals on the modulation frequency is considerably more complicated than for the case of monomolecular recombination. The steady state solution to this equation is straightforward, dN/dt = 0 Nss — fG/R, but there is not a general solution N(l) to the inhomogeneous differential equation. Furthermore, the generation rate will vary throughout the sample due to the Gaussian distribution of the pump intensity and absorption by the sample... 

As we have shown, the polarization force depends not only on the topography [through the f(R z) term] and dielectric constant e, but also on the local contact potential 4). As we shall see now, ac bias modulation and lock-in detection allow these contributions to be separated. 

The cationie dye was assoeiated with the anion (7,8,9,10,11,12 Brg-l-CBnHg) in order to dissolve it in the organie phase. The polarizable window available for photoinduced electron transfer in this system extended over 100 mV for the eonditions specified in Fig. 13. The photoeurrent responses were measured under ehopped light and lock-in detection at 8.4 Hz. Figure 13(b) shows that some photoresponses oeeur only in the presence of the dye speeies, whieh the authors attributed to the transfer of Ru(bpy)3" to the aqueous phase as a result of interfaeial polarization induced by the ehopped light [130]. Upon addition of in the aqueous phase, an inerease in the amplitude of the photo-... 

FIG. 13 Cyclic voltammogram (a) and potential dependence of the photoresponses (b)-(c) to chopped illumination and lock-in detection associated with the photoreaction in Eq. (40). The CV shows that the polarizable window extended to less than 100 mV. The photocurrent measurements carried out were done in the presence (trace 3) and absence (trace 2) of the redox quencher in the organic phase. (Reprinted with permission from Ref 48. Copyright 1989 American Chemical Society.)... 

FIG. 14 On-off photocurrent responses (a) associated with the reaction in Eq. (41) at Ao0 = —0.225 V. In this figure, positive currents correspond to the transfer of a negative charge from water to DCE. The potential dependence of the photocurrent (b) was obtained under chopped illumination and lock-in detection. The maximum in the photocurrent-potential curve contrasts with the small changes in the dark current shown in (c). These responses are developed within the polarizable window described in (d). (From Ref. 49. Reproduced by permission of The Royal Society of Chemistry.)... 

The basic experimental arrangements for photocurrent measurements under periodic square and sinusoidal light perturbation are schematically depicted in Fig. 19. In the previous section, we have already discussed experimental results based on chopped light and lock-in detection. This approach is particularly useful for measurement at a single frequency, generally above 5 Hz. At lower frequencies the performance of lock-in amplifier and mechanical choppers diminishes considerably. For rather slow dynamics, DC photocurrent transients employing optical shutters are more advisable. On the other hand, for kinetic studies of the various reaction steps under illumination, intensity modulated photocurrent spectroscopy (IMPS) has proved to be a very powerful approach [132,133,148-156]. For IMPS, the applied potential is kept constant and the light intensity is sinusoid-... 

FIG. 19 Block diagrams for photocurrent measurements with chopped light and lock-in detection (a) as well as for intensity-modulated photocurrent spectroscopy (b). (Adapted from Ref. 85.)... 

Photocurrent analysis under chopped illumination and lock-in detection is largely complementary to IMPS. While the former provides a simple approach for studying the dependence of the photocurrent on applied potential or illumination wavelength (see examples in Figs. 13, 14, and 16), the latter allows reliable kinetic analysis as a function... 

BRET [31, 32]), lock-in detection techniques exploiting optical switches [33], and schemes for alternating D/A excitation (ALEX [34]). The increased attention to quantitative FRET imaging encompasses the use of polarization [35-39], the perennial issue of calibration and standards [40-44], and practical guides to operational principles and protocols ([45, 46] and other references above). The fundamental distinctions between the requirements for live and fixed cell imaging cannot be overemphasized, as is exemplified in a report of erroneous FRET determinations with visible fluorescent proteins (VFPs) in fixed cells [47],... 

If the crystal is a semiconductor such as Si, it can be used as the working electrode itself and this was the means employed in the early experiments. However, the limited number of suitable electrode materials available was a severe restriction and attempts to use metal-coated crystals suffered severely from the low sensitivity caused by the attenuation of the IR beam by the coating. In addition, lock-in detection is mainly limited to those electrochemical systems capable of responding sufficiently rapidly to the imposed potential modulation. 

In order to employ a lock-in detection technique, as in EMIRS, the modulation frequency of the potential at the electrode would have to be at least an order of magnitude greater than F(v). Thus, the potential modulation would have to be c. 100 kHz too great to allow sufficient relaxation time for most electrochemical processes to respond. Instead, a slow modulation or single-step approach is employed, as follows ... 

Fignre 5.7 presents the experimentally measured values of the FM-CARS microscopy signal versus concentration for two distinctly different lock-in detection... 

Fig. 5.2. Schematic r.f. systems, (a) Simple heterodyne circuit, SI determines the pulse length, S2 switches the lens from transmit to receive, and A1 amplifies the reflected signal (b) quasi-monochromatic circuit the two oscillators and the pulse repetition frequency are phase-locked, and the final signal is lock-in detected (courtesy of John...

This experiment may also be carried out by means of lock-in detection, as schematically illustrated in Fig. 9c. If tp t where ts is the period of the lock-in reference signal, the signal S will be given by... 

Our samples were fabricated with a multistep process described elsewhere [10]. The samples had structure Co(20)/Cu(10)/Co(2.5), where thicknesses are in nm. To minimize dipolar coupling between the Co layers, only the Cu(10)/ Co(2.5) layers were patterned into a nanopillar with approximate dimensions 140 x 70 nm. We measured differential resistance, dV/dl, at 295 K with four-probes and lock-in detection, adding an ac current of amplitude 20 //,A at... 

Analogous to the principal concept of multiplex CARS microspectroscopy (cf. Sect. 6.3.5), in multiplex SRS detection a pair of a broad-bandwidth pulse, eg., white-light femtosecond pulse, and a narrow-bandwidth picosecond pulse that determine the spectral width of the SRS spectrum and its inherent spectral resolution, respectively, is used to simultaneously excite multiple Raman resonances in the sample. Due to SRS, modulations appear in the spectrum of the transmitted broad-bandwidth pulse, which are read out using a photodiode array detector. Unlike SRS imaging, it is difficult to integrate phase-sensitive lock-in detection with a multiplex detector in order to directly retrieve the Raman spectrum from these modulations. Instead, two consecutive spectra, i.e., one with the narrow-bandwidth picosecond beam present and one with that beam blocked, are recorded. Their ratio allows the computation of the linear Raman spectrum that can readily be interpreted in a quantitative manner [49]. Unlike the spectral analysis of a multiplex CARS spectrum, no retrieval of hidden phase information is required to obtain the spontaneous Raman response in multiplex SRS microspectroscopy. 

In this section, more general excitation patterns will be discussed, which allow for tailored deconvolutable excitations with high spectral power densities. Periodic amplitude modulation with a single frequency has been proposed in the literature [73]. It is well suited for noise suppression by lock-in detection, but in practice it suffers from stability problems during the slow frequency sweep. 

Before stochastic TDFRS is treated in detail, periodic amplitude modulation of the grating in combination with phase-sensitive lock-in detection, similar to the procedure proposed by Bloisi [73], will be briefly discussed. With periodic amplitude modulation with a single frequency, which is slowly scanned through the frequency range of interest, the Fourier transform of the TDFRS response function, G([Pg.40]

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