Phase coherent detection

Figure 4.2 Digital modulation strategies for phase-coherent detection. A is the synchronising waveform B C and D E are modulation and detection pairs. For full explanation see text...

For these reasons, it is rarely practical to observe microwave or millimeterwave (mmwave) absorptions by simply following the variation of sample transmission with frequency. Rather, one seeks to modulate the absorption by switching it on and off at an audio- or radiofrequency, and to detect any resulting transmitted modulation by phase coherent detection. 

In the earlier decades of microwave spectroscopy, and in all commercial spectrometers on the market at that time, the method of choice was that of Stark modulation. A uniform electric field was applied to the entire sample and switched off and on, typically at a 33 kHz rate. The resulting phase coherently detected spectral frequency scan (Figure 1) shows a spectral line in phase with the switching voltage and a number of electric-field shifted (Stark) components in antiphase with it. 

Hgure 1 A phase coherently detected Stark modulation spectrum of the 4= 3<-2 transition in OCS at 36488.8130 MHz. Three Stark components (negative) appear at varying distances from the unshifted spectral line (positive). (Reproduced with permission from Hollas JM (1992) High Resolution Spectroscopy, figure 4.13, p. 103. Chichester Wiley John Wiley Sons Ltd.)... 

Figure 2 Afrequency modulation spectrum of K =2, K= 1, and K=0 components of the J=7 6 transition of propyne, CH3CCH, at 119.635 MHz, phase coherently detected at twice the modulation frequency, and obtained with a synchronously tuned Fabry-Perot cavity cell. (Courtesy of Wilks AT, with permission.)...

Unlike thermal detectors, which sense the power of the absorbed radiation, photon detectors respond to the number of photons arriving per unit time. Photon as well as thermal detectors are incoherent transducers, which means that the detection process is independent of the wave properties of the incident radiation field. Incoherent detectors produce an electrical signal proportional to the intensity of the radiation. In contrast, coherent detectors, such as the nonlinear elements in heterodyne receivers discussed in Section 5.9, register the amplitude and phase of the electric field associated with the absorbed radiation. Due to the simultaneous measurement of amplitude and phase, coherent detection is subject to a fundamental noise limit that has its origin in the quantum mechanical uncertainty principle. Incoherent detectors are free of this particular limit. However, as we shall see, they are subject to othernoise sources. 

Several modifications have been proposed for the basic HNN-COSY experiment. For example, frequency separations between amino and aromatic 15N resonances are typically in the range 100-130 ppm and therefore much larger than between imino 15N donor and aromatic 15N acceptor resonances. As has been pointed out by Majumdar and coworkers [33], such 15N frequency separations are too large to be covered effectively by the non-selective 15N pulses of the homonuclear HNN-COSY. They therefore designed a pseudo-heteronuclear H(N)N-COSY experiment, where selective 15N pulses excite the amino and aromatic 15N resonances separately to yield excellent sensitivity [33]. An inconvenience of this experiment is that the resonances corresponding to the amino 15N nuclei are not detected, and a separate spin-echo difference experiment was used to quantify the h2/NN values. A slightly improved version of this pseudo-heteronuclear H(N)N-COSY [35] remedies this problem by the use of phase-coherent 15N pulses such that both amino and aromatic 15N resonances can be detected in a single experiment. 

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. 

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. 

Fig. 8.19. Vector representation of a H-13C HMQC experiment. The first 90° pulse along y rotates the equilibrium magnetization of the proton spin, /H, from the z axis to the x axis. After a time /d = 1/2/Hx, the antiphase coherence 2/J1/ t (see Appendix IX) is at its maximum. A 90° pulse on carbon along y then transforms the antiphase coherence into a MQ (multiple quantum) coherence (the 2/J1/ component is shown). During t the MQ evolves (with a 180 refocusing pulse on proton in the middle), until a further 90 pulse on carbon along x transforms the —2/ / component (shown at its maximum for clarity) into a 2/ /f antiphase coherence. After the time fd, in-phase coherence of the proton spin develops. The latter is detected during h. Its initial intensity is modulated by the carbon Larmor frequency during t (if proton refocusing has been used), thus originating a proton-carbon cross peak.

In conclusion we presented an absolute frequency measurement and a frequency comparison of two iodine stabilized frequency-doubled Nd YAG laser systems, one set up at the Institute of Laser Physics, Novosibirsk, Russia, the other at the Physikalisch-Technische Bundesanstalt, Braunschweig, Germany. The individual frequency stability and the reproducibility of the two laser systems were characterized. It was found that despite fundamental differences as far as frequency generation, signal detection and frequency stabilization techniques are concerned the combined frequency reproducibility of the two laser systems was better than 1.5 0.7 kHz. In a further experiment the absolute frequencies of HFS components of the R(56)32-0 and P(54)32-0 transitions in I2 were determined using a phase-coherent frequency chain. This chain links the frequency of the -stabilized Nd YAG laser to a CH4-stabilized He-Ne laser at 3.39 pm. The He-Ne reference was calibrated before the measurement against an atomic... 

It is not necessary that the evolving 13C coherences be detected immediately. As shown in Section 9.6, they can be allowed to precess until they are in phase, then detected while protons are decoupled to provide a single enhanced signal. Alternatively, the entire INEPT sequence can be treated as the preparation period of a 2D experiment. The coherences then evolve during a period t, and can be manipulated in various ways by further pulses. One of the most commonly used methods is to apply a second INEPT sequence, without the initial 90v pulse, after the evolution period to convert the 13C coherences back into H coherences, which can be observed. As we mentioned in Chapter 10, this method, heteronuclear single quantum coherence (HSQC), is widely employed to obtain... 

In multidimensional NMR experiments that contain several evolution and mixing periods, even more combinations are possible (Griesinger et al., 1987b). In these experiments, Hartmann-Hahn mixing periods with in-phase coherence transfer are of particular advantage, because the resolution is often limited in the indirectly detected frequency dimensions. 

The detection of energy at this transition frequency is the basis of NMR spectroscopy. The actual detection of NMR signals, however, is made possible through the bulk magnetization (AT) of the nuclear system that arises from the resultant of the individual nuclear magnetic moments that are distributed between the various energy levels. The rotating components (x and y) of p transverse to the direction (z) of B0 at nonresonant equilibrium have no phase coherence and A7x = My = 0,... 

---