(OT?) Pulsed NMR phase.

Den onsdag den 7. september 2016 kl. 15.26.02 UTC+2 skrev George Herold:

because your stimulation and demodulation are from the same LO ?

-Lasse

Hmm OK. My asynchronous gate pulse is a red herring? If I think about this in the rotating reference frame, there is no problem. There the RF pulse is divided into two counter rotating circular polarizations, one of which is constant* and torques the spins. (The phase info seems to vanish in the rotating frame...?)

George H.

*the other polarization is spinning about at twice the resonant frequency and does nothing.

clarify the question,

the "phase" of the FID is always the same ___relative to what___?

relative to the LO or relative to the gate pulse?

m

The phase of the LO... the gate pulse has no phase. It's just a digital gate that turn the RF on for a set time. (Getting the RF to turn off nicely can be an issue... but that's another topic.)

George H.

If the spins are waving around (spinning around?) in synchrony with the RF, then the fact that the on/off isn't coordinated with the RF wouldn't matter.

For that matter -- if the RF is at all bandlimited, then turn-on and turn- off will happen over more than one cycle anyway, so the nominal time of the turn-on or turn-off won't be terribly important.

--
Tim Wescott 
Control systems, embedded software and circuit design 
I'm looking for work!  See my website if you're interested 
http://www.wescottdesign.com

Precessing is the right term.. like a gyroscope, As in a gyro there is angular momentum and a torque. (torque comes from the B field and the magnetic moment.)

Well at the start there is no RF, but right, the spins are precessing at the resonant frequency (determined by the magnetic field.)

And like you say when the gate happens doesn't matter. (The data proves it!) I got myself confused though, and I just need a model of what it looks like. I think the answer is that there are a whole bunch of spins, pointing (and precessing) in all different directions. so on average the gate time doesn't matter.

If I happened to have just one big spin, pointing in only one direction (at the start of the gate pulse.) Then I think the gate timing would matter.

(anyway that's the story I'm going to tell myself. :^)

George H.

Yeah it takes a few cycles to turn on and off at the edges. But I wasn't really thinking about edge effects. Typical RF/ resonant frequency is ~20 MHz, typical gating time is ~3 us. So it takes several cycles to cause a 90 degree rotation of the magnetization.

You're not alone!

The short answer is that the first pulse "labels" the spin system with a particular phase. As long as coherence remains (T2 - spin-spin relaxation has not homogeneously dephased the system) any subsequent system response will be relative to the phase of the initial pulse. Since there is no coherence (no free precession in the XY plane) established prior to the first pulse the timing of that pulse has no meaning.

There's a lot more to this which is pretty well wrapped up in the Bloch equations (at least in the classical interpretation) but if you wait long enough between pulses for polarization (T1 - longitudinal relaxation - alignment with the B0 field) to complete and for T2 to dephase the system, any phase, related to the pulse boundaries or not, will yield the same FID/pulse relationship in phase and amplitude.

There are reasons to have a coherent relationship between the pulse envelope and the RF when the pulses are very short (only a few cycles of RF fit in) because of "truncation effects" however the bandwidth of the tuned circuit of the probe generally filters out such effects so you won't see them unless you're pretty far off the beaten path of spectroscopy (extremely broad excitation bandwidth, B1 field comparable to the B0 field).

--
Grizzly H.

Hmm.. OK that seems like an excellent answer! I guess I'm trying to "see" how that happens. I've got all these various pictures with precessing spins and such, A semi-classical picture. (A little QM mixed in.)

Do you know if Slichter talks about it?

I haven't had that off my shelf in years... decades...

OK thanks, Truncation effects sounds like what we can see if the coil is tuned "way off" (... ~1%) from the resonant/ LO frequency. Then you can't get a good 180 deg. pulse*. The coil is ringing down at the "wrong" frequency.

Thanks, George H.

*(a little x-y magnetization remains, by an amount that varies shot to shot. Hey that might be a phase effect, I've never understood the pulse to pulse variation.)

He does. The problem with any book of that caliber is finding and assembling enough of the pieces to answer your particular question.

I've had it out several times recently - beginning of a project involving an area of NMR that hasn't been close to my center of gravity.

If your recycle time is a a bit shorter than a few times T2, there's coherence left and you'll see variations that depend on the exact time relationship between the spin state and the current acquisition. One either has to destroy coherence with a "homospoil gradient" or run through a phase permutation process such that the leftover coherence is averaged away.

"Real" NMR systems use a "phase cycling" technique with quadrature detection to cancel DC offsets, average away small differences in gain and phase response of the electronics and remove the effects of leftover coherence.

Transmit Phase Receiver Phase (degrees) I channel Q channel X (0) +Real +Imag Y (90) +Imag -Real

-X (180) -Real -Imag

-Y (270) -Imag -Real

Usually these phases are permuted forward and backward to give full "correction" in 8 shots. The receiver does not have phase shifters - the averaging arithmetic switches from add/subtract into the real or imaginary array according to the table.

If your electronics are stable, most of the experiment to experiment variation will go away even if you're squeezing timing a bit.

--
Grizzly H.

Grin, yeah it's a very dense book. I did ESR as a grad student, and we did Slichter in a weekly group book club. Every week was a new section, with a different group member leading the discussion at the chalk board. That is one of my favorite ways to do a book!

Whatcha doing? I was going to post a link to some (more recent) optical pumping data. Where I did these field reversal experiments, and it was all about the spins being able to "follow the field." The interesting part was when the spins didn't all get there and dropped out along the way.

Or tune up the coil so it's closer to being "on resonance". :^)

OK I sorta understand that, but we'd have to draw pictures for me to really get it.. When you are pushing the signal to noise limit you pull out all the stops.

The heart of the NMR spectrometer was done by this brilliant guy (well smarter than me) at Princeton. I'm not sure what he's doing now but AIUI he did a lot of the critical work on WMAP... balancing microwave spectrometers.

George H.

[...]

Boltzmann, lattice irregularities and field inhomogeneities (both B0 and B1) have a way of scrambling things. One should remember that the excess population of spins in the low energy "spin up" state (e.g. for spin 1/2 - 1H) is only a few ppm at room temperature. Unless you're near absolute zero with great care taken to maintain homogeneity, you're not going to keep everybody marching coherently. It would be interesting if you identified a mechanism that didn't come out of experimental "loose ends".

I'm working with a startup on a handheld NMR for point-of-care medical diagnostics. Sort of a cell-phone scale widget with a small magnet that will tolerate environmental difficulties and give unambiguous results in a few minutes. Lots of biology and chemistry involved as well as shrinking a spectrometer by a factor of 100 or so.

Maybe this will help with visualizing what the spins are up to:

There are links to youtube and written driving instructions.

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Grizzly H.

Permanent magnets? (Beware the temperature dependence.)

Hmm well my boss built this,

Which is a single big fat "proton". You can even do a spin flip... (Well 90 degrees) but you have to get the phase right!

George H.

Some decades ago I had a ball bearing ball about 4" diameter with a hemispherical air bearing supporting it. Spin it up with your fingers and it would keep going for close to an hour (maybe by canting a hole or two to provide some viscous drive, it might have kept going indefinitely). We drilled and tapped a hole in the ball to support an aluminum rod to which I attached an LED flasher firing about 5 Hz. One could ding the rod with a finger and induce precession which would decay slowly (gravity being the restoring force). In a very dark room with a polaroid camera suspended above you could see the dots slowly relaxing to vertical equilibrium. NMR wasn't in my mind at the time but I can imagine magnetizing the ball, setting up vertical field and pulsing a transverse field at the precession frequency to flip the "spin".

--
Grizzly H.