GELLER Labs "Backyard Science"
Thoughts on a proton precession magnetometer design - a Proton Magnetometer Project. Build an Earth's field magnetometer.
The FDM MAGNETOMETER1 project is a low cost high performance proton magnetometer (a digital magnetometer) kit under development for universities and amateur scientists to be able to accurately measure and monitor changes in the Earth's total magnetic F field and to observe geomagnetic storms. Magnetic storms can cause large excursions in the field and are of concern to interests ranging from electrical power grids, radio communications, and satellite operations, to aurora watchers and amateur radio operators.
1 Filter Diagonalization Method "FDM" (harmonic inversion), see Jan 21 and Jan 23 entries, based on: Vladimir A. Mandelshtam, Howard S. Taylor, Harmonic inversion of time signals and its applications, Journal of Chemical Physics (1997), Volume 107, Issue 17, 1997, Pages 6756-6769
Journal Notes:
Saturday, February 26, 2011
Regarding the now common 77% auto-retry rate PDF, aliasing has been suggested as one possible factor, especially since our 10 kHz sample rate is relatively low for the 2 kHz signal of interest. With the very high Q of the narrow band low noise amplifier, my feeling is that it is unlikely that a higher frequency out of band signal is folding back into our digitized signal (aliasing) (although it is certainly not impossible). More likely, (just a guess) there is some sort of phase relationship issue going on, possibly some sort of interaction with an in-band ambient signal, probably a power line harmonic. It might be possible with our relatively unsynchronized software generated trigggers that we are "sweeping" through some sort of in-band interfering signal or signals in a way that ensures that on average 23% of our measurements are rejected by the auto-retry filters. Also, unlikely, but not impossible, is some sort of systematic error in our supervisory software. The observed auto-retry rates are still very much a mystery!
Beyond the auto-retry rate, other figures of instrument performance include FDM amplitude and FDM figure of merit (FOM). As of 6:33 pm (local), about 6 hours in, so far so good PDF. No apparent significant changes. The mysterious and curious 77% auto-retry rate is back. The "Mode" operation in Excel shows that 2e-7 is our most common figure of merit value (FOM), a typical result for recent days. Other than the 15% increase in our precession (FID) signal amplitude, there are no other apparent changes in the FDM magnetometer perfomance with the morning's work on the snubber capactor (now 33 pF) and the secondary dump resistor (now 2.2 k ohms). Late evening: It should be emphasized that the auto-retry rate has no apparent negative affect on the quality of the successful measurements. If anything, the auto-retry process probably rejects a number of "good" measurements. Also, as we have discussed before, it should never be 100%, since the goal of the auto-retry process is to reject measurements distorted by, for example, passing vehicles or for that matter anything which distorts the field by introducing a significant spacial magnetic gradient across the sensor sample volume or anything that causes a rapid change in time during a measurement cycle. Both spacial and temporal variations during the measurment cycle, particulary during precession and digitization, spread the precession energy over a frequency range, deteriorating the quality of frequency estimation for that measurement cycle. That said, it is almost bizarre the way the record so often converges near 77%. Here is the latest plot, almost needless to say, with an auto-retry success rate of 77%. PDF.
Sunday, February 27, 2011 - A new view of the possible significance of the auto-retry rate!
Overnight: PDF, FOM, Amplitude. (accidently overwrote the overnight TXT file, however the overnight TXT data can be found in this Excel spread sheet XLS). Will run for a while today with the auto-retry figure of merit (FOM) threshold set to 2·10-5 (usually 2·10-6). The most common FOM overnight (the statistical "mode") was 2·10-7, the average was 5·10-7.
Sample Spectra, Log spectra PDF1, PDF1 PDF2, PDF2
Perhaps the auto-retry rate (75% to 78% for an FOM threshold of 2·10-6) is providing a statisitical indication of the FDM magnetometer instrument noise floor. Since our NBLNA noise floor is exceptionally low, the instrument noise floor is possibly dominated by the noise floor of our physical process. This is not amplitude noise per se, however the noise floor of the conversion of the precession free induction decay (FID) signal to a fundamental center frequency by the FD method (FDM). An interesting plot might be to take several sets of data (hours to days long, preferably over similar time spans) over a range of figure of merit FOM auto-retry thresholds. One useful plot would be % success rate on the Y axis versus FOM threshold on the X axis. Multiple measurements over similar time periods for same FOM threshold values could be plotted as averaged points with error bars.
A number or our recent improvements have changed the FID amplitude, but have had little effect on the auto-retry rate. I think it is because these changes, while improving the FID signal (generally as improved amplitude), have not lowered the instrument noise floor.
It is way too early to tell (only 30 plotted measurements), however, after about an hour with the auto-retry FOM threshold increased from 2·10-6 to 2·10-5 we are seeing a 97% auto-retry rate! PDF Approaching 4 hours, 97% success rate. 5 pm local, still at 96%.
Recall that in proper operation, the auto-retry success rate should never be 100%, since the whole purpose of the auto-retry filter is to reject measurements influenced by moving vehicles and momentary high in-band EMI / RFI interference.
A plot of % success rate versus a log plot of FDM FOM is going to take a significant data collection effort, however, it will probably reveal useful statistical information, and directly or indirectly our physics noise floor. This is almost a three dimensional problem, since there might be significance to the time window over which the data is collected (i.e. the number of plotted points for each data point on the graph). Or, perhaps for this first look, it is just a matter of collecting enough plotted measurements for each point on the graph to minimize the error bar at each point (e.g. longer collection simply means better convergence, but not a different performance over a different time window). (Undoubtedly there will be some dependance related time windows of varying length as is the case in almost all physical measurements made over time.)
I might try 6 hour window single data points (so no error bars in round 1) as a first approach.
Monday, February 28, 2011 - Plotting Auto-Retry vs. FOM threshold!
The FDM magnetometer plots only measurements that have a figure of merit (FOM) at least as good as the pre-set FOM threshold. A measurement that results in a FOM higher than the FOM threshold triggers the auto-retry process, which continues to take measurements at an interval much shorter than the regular measurement rate until a measurement returns an acceptable FOM. The auto-retry success rate is the ratio of plotted measurements (those that survive the auto-retry filters) to all measurements made for a give data set.
6 hours FOM threshold 2·10-5 PDF 96%
FOM threshold 2·10-6 know from many past runs to be ~77% (typically ~ +/-1%)
6 hours FOM threshold 6 ·10-6 PDF 91%
6 hours FOM threshold 7 ·10-7 PDF 54%
6 hours FOM threshold 3 ·10-7 PDF 36%
6 hours FOM threshold 1 ·10-7 PDF 26%
Graph of Results to date Linear FOM PDF Log FOM PDF
(Afternote: 3/3/11 - There might be some temperature dependence and/or other parameters related to the curve. For a 12 to 24 hour period of measurements, the error bars at each FOM threshold point are probably on the order of +/- 3%-5%)
Project Documentation, Links and References (very early stages)
QUESTIONS/COMMENTS/notice of typos, etc. send email to joegeller @ gellerlabs dot com
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