## Wednesday, August 27, 2008

### What is Quadrature Detection?

In order to distinguish between negative and positive frequencies relative to the carrier frequency (i.e. the frequency at the center of the spectrum), quadrature detection must be employed. Quadrature detection involves the collection of time domain NMR data on both the x and y axes of the rotating frame of reference. One of these FIDs is called "real" and the other one is called "imaginary". The assignment of the labels "real" and "imaginary" stems from the mathematics of a Fourier transform, which requires a complex input. The Fourier transform in turn produces a "real" spectrum and an "imaginary" spectrum". Having these two signals allows us to phase one of the NMR spectra (eg. the "real" one) entirely in absorption mode after the data have been collected. In an ideal world, it would be nice to have the two FID's collected via separate receiver coils. In this case, with a bit of manipulation, we could improve our signal-to-noise ratio by a factor of the square root of 2 by adding the real and imaginary spectra together. A very nice discussion of this has been presented by Carlos Cobas. In the real world we do not have two receiver coils in quadrature and we must rely on electronic "tricks" to achieve quadrature detection. These "tricks" do not allow us to gain a signal-to-noise advantage by combining the real and imaginary spectra. A simple block diagram of how a spectrometer collects data in quadrature is shown in the figure below. The yellow signal is the intermediate frequency (IF) of the spectrometer. The purple signal is the intermediate frequency of the spectrometer modulated with the NMR spectrum information (IF plus or minus delta nu). Two phase sensitive detectors (PSDs) are used. These devices produce a difference signal between two inputs. The inputs to the first PSD are the IF and the IF plus or minus delta nu. The output is therefore plus or minus delta nu (i.e. the information content of the NMR spectrum). The inputs of the second PSD are identical to the first except the phase of the IF is shifted by 90 degrees. The output is therefore similar to the first PSD except that it has a 90 degree phase difference. The two outputs are the "real" and "imaginary" FID's which provide the input for the Fourier transform.

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## 5 comments:

This was very insightful information. I was wondering if you could answer a question for me. Why does the rf coil in the probe have to be perpendicular to the external magnetic field?

Dear Alisha,

Thank you for your comment. In order to rotate an equilibrium magnetization vector from the z axis into the transverse plane, one must provide a pulse with an oscillating magnetic field transverse the the static field, Bo, at the Larmor frequency of the nucleus being observed. See this post from June 17, 2008 for further discussion:

http://u-of-o-nmr-facility.blogspot.com/2008/06/available-rf-field-for-mas-nmr-probes.html

Glenn

Dear Glenn!

I have a question-how to select quadrature mode when we process our data in NMR Pipe?

Is this parameter selected during aquisition of the spectrum or we can "play" with mode when we processing already obtained FID?

Beforehand thank you!

Zina

Dear Zina.

Thank you for your question. Unfortunately I have absolutely no experience with NMR Pipe so I am unable to answer your question. I have found a manual here:

http://www.nmrscience.com/ref/index.html

Perhaps some other readers can reply.

Glenn

It is interesting that you say 'in the real world we do not have two coils', because when I worked on MRI imaging (1979) we did use two coils. The Wikipedia article on 'quadrature detection' also seems to ignore that you can (and we did) use two physical coils.

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