From 03a3c68d6e3c2a8b38f022d1b2769b078a3b89c7 Mon Sep 17 00:00:00 2001 From: "W. Trevor King" Date: Thu, 21 Apr 2011 22:21:42 -0400 Subject: [PATCH] Actually, avoid dollars in code (entities escaped when writing the HTML). --- posts/calibcant.mdwn_itex | 17 +++++++++-------- 1 file changed, 9 insertions(+), 8 deletions(-) diff --git a/posts/calibcant.mdwn_itex b/posts/calibcant.mdwn_itex index aeb4c6c..05581d6 100644 --- a/posts/calibcant.mdwn_itex +++ b/posts/calibcant.mdwn_itex @@ -8,9 +8,10 @@ The `README` is posted on the [PyPI page][pypi], and you might also be interested in the [[package dependency graph|calibcant.svg]] generated with Yu-Jie Lin's [PDepGraph.py][]: - $ IGNORED=matplotlib,scipy,numpy,pyyaml,h5py,python,eselect-python - $ python PDepGraph.py -o calibcant.dot -D "$IGNORED" calibcant - $ dot -T svg -o calibcant.svg calibcant.dot + # python PDepGraph.py -o calibcant.dot \ + -D matplotlib,scipy,numpy,pyyaml,h5py,python,eselect-python \ + calibcant + # dot -T svg -o calibcant.svg calibcant.dot Thermal calibration requires three separate measurements: photodiode sensitivity (via surface bumps), fluid temperature (estimated, or via @@ -19,14 +20,14 @@ in far from the surface). The calibcant package takes repeated measurements ([[!ltio statistics.png]]) of each of these parameters to allow estimation of statistical uncertainty: - $ calibcant-analyze.py calibcant/examples/calibration.h5 + # calibcant-analyze.py calibcant/examples/calibration.h5 ... ... variable (units) : mean +/- std. dev. (relative error) ... cantilever k (N/m) : 0.0629167 +/- 0.00439057 (0.0697838) ... photo sensitivity (V/m) : 2.4535e+07 +/- 616119 (0.0251118) ... T (K) : 295.15 +/- 0 (0) ... vibration variance (V^2) : 3.89882e-05 +/- 1.88897e-06 (0.0484497) - ... + ... While this cannot account for systematic errors, calibration numbers are fairly meaninless without at least statistical error estimates. @@ -53,9 +54,9 @@ well as white noise from the measurement equipment. \[ \text{PSD}(x, \omega) = - \frac{2 k_BT \beta} + \frac{2 k_{B} T \beta} { \pi m \left[{(\omega_0^2-\omega^2)^2 + \beta^2\omega^2}\right] } - + N \;. + + W \;. \] where $\beta$ and $\omega_0$ come from the damped-forced harmonic @@ -65,7 +66,7 @@ oscillator equation of motion \ddot{x} + \beta \dot{x} + \omega_0^2 x = \frac{F(t)}{m} \;, \] -$m$ is the cantilever's effective mass, and $N$ is an optional +the cantilever's effective mass is $m$, and $W$ is an optional white-noise offset. Here is an example of a one-second thermal vibration fit with the -- 2.26.2