Update README.md

README.md

@@ -72,10 +72,16 @@ To characterize the use of the AS5013 as a three-dimensional tracking device, we
 <img src='as5013-test/testing2.jpg' width=350px>
 <img src='as5013-test/nrf52-as5013-board.jpg' width=400px>
 
-To maximize resolution (and minimize stroke), we are also considering alternative magnet arrangements.  I wrote a very simple (and slow!) 2D B field finite difference simulation, which is in <a href='as5013-test/sim/'>sim</a>.  It uses successive overrelaxation to compute the spatial distribution of the z component of the magnetic field.  Below we should output of the simulation for a single magnet, as well as for a pair of opposing magnets.  The question is whether we can create a region of high field gradient over each of the four sensors.  I think a central rod magnet in one orientation surrounded by four with the opposite orientation would work nicely for this.
+Below are some preliminary plots of readings from the 5 internal hall effect sensors.  They each run over 800 um with 10 um sample spacing.
+<img src='as5013-test/hall-plots.png' width=1000px>
+If we scan over a broader area, we can start to see deviations from an ideal radially symmetric field (there is also an overflow error in these plots that I haven't fixed yet).
+<img src='as5013-test/hall-plots_full_view_aberrations.png' width=1000px>
 
-<img src='as5013-test/sim/run_single_magnet.png' width=350px>
-<img src='as5013-test/sim/run_double_magnet.png' width=350px>
+This last plot indicates why the magnet spacing is 1.1mm -- from the center of the magnet, this is the approximate distance to the highest gradient in the z component of magnetic field.  This observation leads us to consider if we want to maximize resolution in tracking the magnet, could we make an alternative arrangements of magnet(s) to produce higher field gradients.
 
+To test this, I wrote a very simple (and slow for now!) 2D B field finite difference simulation, which is in <a href='as5013-test/sim/'>sim</a>.  It uses successive overrelaxation to compute the spatial distribution of the z component of the magnetic field (todo: fix the field magnitude bug here).  Below we should output of the simulation for a single magnet, as well as for a pair of opposing magnets.  The first plot roughly confirms the shape and size of the magnetic field funtion from a single rod magnet.  
 
+<img src='as5013-test/sim/run_single_magnet.png' width=350px>
+<img src='as5013-test/sim/run_double_magnet.png' width=350px>
 
+The pair of opposing magnets produces a high field gradient.  We could create such a region of high field gradient over each of the four outer hall effect sensors using a simple arrangement of square magnets (todo: make a drawing).