Offset frequency

In quadrature detection, the transmitter offset frequency is posidoned at the center of the F domain (i.e., at F2 = 0 in single-channel detection it is positioned at the left edge). Frequencies to the left (or downfield) of the transmitter offset frequency are positive those to the right (or upheld) of it are negative. 

SWi, which in turn is related to the homonuclear or heteronuclear coupling constants. In homonuclear 2D spectra, the transmitter offset frequency is kept at the center of (i.e., at = 0) and F domains. In heteronuclear-shift-correlated spectra, the decoupler offset frequency is kept at the center (Fi = 0) of thei i domain, with the domain corresponding to the invisible or decoupled nucleus. 

Another approach to obtain spatially selective chemical shift information is, instead of obtaining the entire image, to select only the voxel of interest of the sample and record a spectrum. This method called Volume Selective spectroscopY (VOSY) is a ID NMR method and is accordingly fast compared with a 3D sequence such as the CSI method displayed in Figure 1.25(a). In Figure 1.25(b), a VOSY sequence based on a stimulated echo sequence is displayed, where three slice selective pulses excite coherences only inside the voxel of interest. The offset frequency of the slice selective pulse defines the location of the voxel. Along the receiver axis (rx) all echoes created by a stimulated echo sequence are displayed. The echoes V2, VI, L2 and L3 can be utilized, where such multiple echoes can be employed for signal accumulation. 

An improved RAPT sequence utilizing frequency-switched Gaussian pulses (FSG-RAPT) was later proposed [68], This method also allows for the measurement of Cq values. The dependence of the FSG-RAPT enhancement on offset frequency for nuclei with different CgS has been exploited to design pulse schemes for the selective selection of nuclei with large quadrupole couplings [69-71]. 

For each shaped pulse you must select the pulse width (duration in p,s Brukerpl2,pl3, etc., or Varian selpw), the name of the text file that contains the shape function (Bruker spnaml, spnam2, etc., Varian selshape), the maximum power (B amplitude) at the top of the pulse shape (Bruker spl, sp2, etc., or Varian selpwr), and the offset frequency in hertz... 

Note that as is just the Larmor frequency and, because real numbers are associated with the x axis and imaginary numbers with the y axis, time evolution is simply rotation in the x-y plane at the offset frequency. For double-quantum transitions, > = a> + >s, and for zero-quantum transitions co = coi — cos. For example, a 90° pulse on the y axis followed by a delay r would give... 

The measurement of the frequency offset ay [16,17,18,19] as described below usually yields a value modulo uy so that renumbering the modes will restrict the offset frequency to 0 < uy < ay ... 

Fig. 2. Consecutive pulses of a chirp free pulse train (A(t) real) and the corresponding spectrum. Because the carrier propagates with a different velocity within the laser cavity than the envelope (phase- and group velocity), the electric field does not repeat itself after one round trip. A pulse-to-pulse phase shift Aip results in an offset frequency...

Fig. 3. The offset frequency uv that displaces the modes of an octave spanning frequency comb from being exact harmonics of the repetition rate u>r is measured by frequency doubling some modes at the red side of the comb and beat them with modes at the blue side...

Being able to control u>0 and uir is not sufficient if we don t know their values. The repetition rate u>r is simply measured by a photo detector at the output of either the laser or the fiber. To measure the offset frequency oj0, a mode nu>r + u>0 on the red side of the comb is frequency doubled to 2(nu>r + oj0). If the comb contains more than an optical octave there will be a mode with the mode number 2n oscillating at 2nu>r+u>0. As sketched in Fig. 3 we take advantage of the fact that the offset frequency is common to all modes3 by creating the beat frequency (=difference frequency) between the frequency doubled red mode and the blue mode to obtain u>0. This method allowed the construction of a very simple frequency chain [14,15,16,17,18,19] that eventually operated with a single laser. It occupies only 1 square meter on our optical table with considerable potential for further miniaturization. At the same time it supplies us with a reference frequency grid across much of the visible and infrared spectrum. 

Fig. 5. Experimental setup for locking the offset frequency cja. The femtosecond faser is located inside the shaded box. Solid lines represent optical paths, and dashed lines show electrical paths. The high-reflector mirror is mounted on a transducer to provide both tilt and translation...

Figure 2 The stronger component of the 1S-2S two photon transition in deuterium. The signal is the normalised Lyman-a fluorescence observed as a function of the frequency difference between lasers LI and L2 (fig. 1) when LI is locked to the appropriate transition (b2) in 13°Te2. The measured offset frequency is 20 MHz greater than the true value because of the shift introduced by the acousto-optic modulator. The pressure in the deuterium cell was 270 mtorr...

Spatial localization in imaging is by means of magnetic field gradients, which impose local Larmor frequencies dependent upon position. The resonance offset frequency (in radians per second) of a spin at position x in a field gradient Gx is equal to yxGx. 

FIG. 17. Sirailarspectrum to that shown in Fig. 16 but obtained by the proton flip method and using diflerent offset frequencies. From ref 154. 

All the foregoing experiments depend upon having a means of setting the proton offset frequency with sufficient precision, say +10 Hz or better. On certain low-cost spectrometers this may not be possible. It is then convenient to use (197) equation (14) to relate the residual splitting to yB2/2n. 

Adjust the offset frequency of the H/ F channel until the optimum CP and decoupling is observed. The system may then need to be rematched. 

Fig. 5. (A) Vector picture describing the relationship between the rf field strength and offset frequency in off-resonance experiments such as LGCP and PISEMA. (B) A simple pulse sequence (called LGCP or FFLGCP) to set-up the Lee-Goldburg condition. As explained in the text, this sequence can be used to determine the S-spin-lock field strength that matches ileff./for the effective spin exchange between / and S spins.

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