1 # calibcant - tools for thermally calibrating AFM cantilevers
3 # Copyright (C) 2008-2012 W. Trevor King <wking@drexel.edu>
5 # This file is part of calibcant.
7 # calibcant is free software: you can redistribute it and/or modify it under
8 # the terms of the GNU General Public License as published by the Free Software
9 # Foundation, either version 3 of the License, or (at your option) any later
12 # calibcant is distributed in the hope that it will be useful, but WITHOUT ANY
13 # WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
14 # A PARTICULAR PURPOSE. See the GNU General Public License for more details.
16 # You should have received a copy of the GNU General Public License along with
17 # calibcant. If not, see <http://www.gnu.org/licenses/>.
19 """Calculate `k` from arrays of bumps, temperatures, and vibrations.
21 Separate the more general `calib_analyze()` from the other `calib_*()`
22 functions in calibcant.
24 The relevent physical quantities are :
25 Vzp_out Output z-piezo voltage (what we generate)
26 Vzp Applied z-piezo voltage (after external ZPGAIN)
27 Zp The z-piezo position
28 Zcant The cantilever vertical deflection
29 Vphoto The photodiode vertical deflection voltage (what we measure)
30 Fcant The force on the cantilever
31 T The temperature of the cantilever and surrounding solution
32 (another thing we measure)
33 k_b Boltzmann's constant
35 Which are related by the parameters:
37 zp_sensitivity Zp / Vzp
38 photo_sensitivity Vphoto / Zcant
45 >>> from h5config.storage.hdf5 import HDF5_Storage, pprint_HDF5
46 >>> from .config import CalibrationConfig
48 >>> fd,filename = tempfile.mkstemp(suffix='.h5', prefix='calibcant-')
51 >>> calibration_config = CalibrationConfig(storage=HDF5_Storage(
52 ... filename=filename, group='/calib/config/'))
53 >>> bumps = numpy.array((15.9e6, 16.9e6, 16.3e6))
54 >>> temperatures = numpy.array((295, 295.2, 294.8))
55 >>> vibrations = numpy.array((2.20e-5, 2.22e-5, 2.21e-5))
57 >>> k,k_s = calib_analyze(bumps=bumps, temperatures=temperatures,
58 ... vibrations=vibrations)
59 >>> (k, k_s) # doctest: +ELLIPSIS
60 (0.0493..., 0.00248...)
62 Most of the error in this example comes from uncertainty in the
63 photodiode sensitivity (bumps).
65 >>> k_s/k # doctest: +ELLIPSIS
67 >>> bumps.std()/bumps.mean() # doctest: +ELLIPSIS
69 >>> temperatures.std()/temperatures.mean() # doctest: +ELLIPSIS
71 >>> vibrations.std()/vibrations.mean() # doctest: +ELLIPSIS
74 >>> calib_save(filename=filename, group='/calib/',
75 ... bumps=bumps, temperatures=temperatures, vibrations=vibrations,
76 ... calibration_config=calibration_config, k=k, k_s=k_s)
77 >>> pprint_HDF5(filename) # doctest: +ELLIPSIS, +REPORT_UDIFF
81 <HDF5 dataset "bump": shape (), type "|S1">
83 <HDF5 dataset "num-bumps": shape (), type "<i4">
85 <HDF5 dataset "num-temperatures": shape (), type "<i4">
87 <HDF5 dataset "num-vibrations": shape (), type "<i4">
89 <HDF5 dataset "temperature": shape (), type "|S1">
91 <HDF5 dataset "temperature-sleep": shape (), type "<i4">
93 <HDF5 dataset "vibration": shape (), type "|S1">
95 <HDF5 dataset "vibration-spacing": shape (), type "<f8">
98 /calib/processed/spring-constant
99 <HDF5 dataset "data": shape (), type "<f8">
101 <HDF5 dataset "standard-deviation": shape (), type "<f8">
103 <HDF5 dataset "units": shape (), type "|S3">
106 /calib/raw/photodiode-sensitivity
107 <HDF5 dataset "data": shape (3,), type "<f8">
108 [ 15900000. 16900000. 16300000.]
109 <HDF5 dataset "units": shape (), type "|S3">
111 /calib/raw/temperature
112 <HDF5 dataset "data": shape (3,), type "<f8">
114 <HDF5 dataset "units": shape (), type "|S1">
116 /calib/raw/thermal-vibration-variance
117 <HDF5 dataset "data": shape (3,), type "<f8">
118 [ 2.20...e-05 2.220...e-05 2.210...e-05]
119 <HDF5 dataset "units": shape (), type "|S3">
122 >>> bumps,temperatures,vibrations,calibration_config,k,k_s = calib_load(
123 ... filename=filename, group='/calib/')
124 >>> (k, k_s) # doctest: +ELLIPSIS
125 (0.0493..., 0.00248...)
127 >>> os.remove(filename)
131 import numpy as _numpy
133 from scipy.constants import Boltzmann as _kB # in J/K
135 from scipy.constants import Bolzmann as _kB # in J/K
136 # Bolzmann -> Boltzmann patch submitted:
137 # http://projects.scipy.org/scipy/ticket/1417
138 # Fixed in scipy commit 4716d91, Apr 2, 2011, during work after v0.9.0rc5.
141 import matplotlib as _matplotlib
142 import matplotlib.pyplot as _matplotlib_pyplot
143 import time as _time # for timestamping lines on plots
144 except (ImportError, RuntimeError), e:
146 _matplotlib_import_error = e
148 from h5config.storage.hdf5 import HDF5_Storage as _HDF5_Storage
149 from h5config.storage.hdf5 import h5_create_group as _h5_create_group
151 from . import LOG as _LOG
152 from . import package_config as _package_config
153 from .bump_analyze import bump_analyze as _bump_analyze
154 from .bump_analyze import bump_load as _bump_load
155 from .bump_analyze import bump_save as _bump_save
156 from .config import CalibrationConfig as _CalibrationConfig
157 from .T_analyze import T_analyze as _temperature_analyze
158 from .T_analyze import T_load as _temperature_load
159 from .T_analyze import T_save as _temperature_save
160 from .vib_analyze import vib_analyze as _vibration_analyze
161 from .vib_analyze import vib_load as _vibration_load
162 from .vib_analyze import vib_save as _vibration_save
165 def calib_analyze(bumps, temperatures, vibrations):
166 """Analyze data from `get_calibration_data()`
168 Inputs (all are arrays of recorded data):
169 bumps measured (V_photodiode / nm_tip) proportionality constant
170 temperatures measured temperature (K)
171 vibrations measured V_photodiode variance in free solution (V**2)
173 k cantilever spring constant (in N/m, or equivalently nN/nm)
174 k_s standard deviation in our estimate of k
178 We're assuming vib is mostly from thermal cantilever vibrations
179 (and then only from vibrations in the single vertical degree of
180 freedom), and not from other noise sources.
182 If the error is large, check the relative errors
183 (`x.std()/x.mean()`)of your input arrays. If one of them is
184 small, don't bother repeating that measurment too often. If one
185 is large, try repeating that measurement more. Remember that you
186 need enough samples to have a valid error estimate in the first
187 place, and that none of this addresses any systematic errors.
189 ps_m = bumps.mean() # ps for photo-sensitivity
191 T_m = temperatures.mean()
192 T_s = temperatures.std()
193 v2_m = vibrations.mean() # average voltage variance
194 v2_s = vibrations.std()
196 # Vphoto / photo_sensitivity = x
197 # k = kB T / <x**2> = kB T photo_sensitivity**2 / Vphoto_var
199 # units, photo_sensitivity = Vphoto/(Zcant in m),
200 # so Vphoto/photo_sensitivity = Zcant in m
201 # so k = J/K * K / m^2 = J / m^2 = N/m
202 k = _kB * T_m * ps_m**2 / v2_m
204 # propogation of errors
208 dk_ps = 2*k/ps_m * ps_s
210 dk_v = -k/v2_m * v2_s
212 k_s = _numpy.sqrt(dk_T**2 + dk_ps**2 + dk_v**2)
214 _LOG.info('variable (units) : '
215 'mean +/- std. dev. (relative error)')
216 _LOG.info('cantilever k (N/m) : %g +/- %g (%g)' % (k, k_s, k_s/k))
217 _LOG.info('photo sensitivity (V/m) : %g +/- %g (%g)'
218 % (ps_m, ps_s, ps_s/ps_m))
219 _LOG.info('T (K) : %g +/- %g (%g)'
220 % (T_m, T_s, T_s/T_m))
221 _LOG.info('vibration variance (V^2) : %g +/- %g (%g)'
222 % (v2_m, v2_s, v2_s/v2_m))
224 if _package_config['matplotlib']:
225 calib_plot(bumps, temperatures, vibrations)
229 def calib_save(filename, group='/', bumps=None, temperatures=None,
230 vibrations=None, calibration_config=None, k=None, k_s=None):
231 with _h5py.File(filename, 'a') as f:
232 cwg = _h5_create_group(f, group)
233 if calibration_config is not None:
234 config_cwg = _h5_create_group(cwg, 'config')
235 storage = _HDF5_Storage()
236 storage.save(config=calibration_config, group=config_cwg)
237 if bumps is not None:
239 del cwg['raw/photodiode-sensitivity/data']
243 del cwg['raw/photodiode-sensitivity/units']
246 cwg['raw/photodiode-sensitivity/data'] = bumps
247 cwg['raw/photodiode-sensitivity/units'] = 'V/m'
248 if temperatures is not None:
250 del cwg['raw/temperature/data']
254 del cwg['raw/temperature/units']
257 cwg['raw/temperature/data'] = temperatures
258 cwg['raw/temperature/units'] = 'K'
259 if vibrations is not None:
261 del cwg['raw/thermal-vibration-variance/data']
265 del cwg['raw/thermal-vibration-variance/units']
268 cwg['raw/thermal-vibration-variance/data'] = vibrations
269 cwg['raw/thermal-vibration-variance/units'] = 'V^2'
272 del cwg['processed/spring-constant/data']
276 del cwg['processed/spring-constant/units']
279 cwg['processed/spring-constant/data'] = k
280 cwg['processed/spring-constant/units'] = 'N/m'
283 del cwg['processed/spring-constant/standard-deviation']
286 cwg['processed/spring-constant/standard-deviation'] = k_s
288 def calib_load(filename, group='/'):
289 assert group.endswith('/')
290 bumps = temperatures = vibrations = k = k_s = None
292 with _h5py.File(filename, 'a') as f:
294 bumps = f[group+'raw/photodiode-sensitivity/data'][...]
298 temperatures = f[group+'raw/temperature/data'][...]
302 vibrations = f[group+'raw/thermal-vibration-variance/data'][...]
306 k = float(f[group+'processed/spring-constant/data'][...])
311 f[group+'processed/spring-constant/standard-deviation'][...])
314 calibration_config = _CalibrationConfig(storage=_HDF5_Storage(
315 filename=filename, group=group+'config/'))
316 calibration_config.load()
317 return (bumps, temperatures, vibrations, calibration_config, k, k_s)
319 def calib_plot(bumps, temperatures, vibrations):
321 raise _matplotlib_import_error
322 figure = _matplotlib_pyplot.figure()
324 bump_axes = figure.add_subplot(3, 1, 1)
325 T_axes = figure.add_subplot(3, 1, 2)
326 vib_axes = figure.add_subplot(3, 1, 3)
328 timestamp = _time.strftime('%H%M%S')
329 bump_axes.set_title('cantilever calibration %s' % timestamp)
331 bump_axes.plot(bumps, 'g.-')
332 bump_axes.set_ylabel('photodiode sensitivity (V/m)')
333 T_axes.plot(temperatures, 'r.-')
334 T_axes.set_ylabel('temperature (K)')
335 vib_axes.plot(vibrations, 'b.-')
336 vib_axes.set_ylabel('thermal deflection variance (V^2)')
338 if hasattr(figure, 'show'):
342 def calib_load_all(filename, group='/'):
343 "Load all data from a `calib()` run."
344 assert group.endswith('/'), group
345 bumps,temperatures,vibrations,calibration_config,k,k_s = calib_load(
346 filename, group+'calibration/')
348 for i in range(calibration_config['num-bumps']):
349 (raw_bump,bump_config,z_axis_config,deflection_channel_config,
350 processed_bump) = _bump_load(
351 filename=filename, group='%sbump/%d/' % (group, i))
352 bump_details.append({
353 'raw_bump': raw_bump,
354 'bump_config': bump_config,
355 'z_axis_config': z_axis_config,
356 'deflection_channel_config': deflection_channel_config,
357 'processed_bump': processed_bump,
359 temperature_details = []
360 for i in range(calibration_config['num-temperatures']):
361 (raw_temperature,temperature_config,processed_temperature
362 ) = _temperature_load(
363 filename=filename, group='%stemperature/%d/' % (group, i))
364 temperature_details.append({
365 'raw_temperature': raw_temperature,
366 'temperature_config': temperature_config,
367 'processed_temperature': processed_temperature,
369 vibration_details = []
370 for i in range(calibration_config['num-vibrations']):
371 (raw_vibration,vibration_config,deflection_channel_config,
372 processed_vibration) = _vibration_load(
373 filename=filename, group='%svibration/%d/' % (group, i))
374 vibration_details.append({
375 'raw_vibration': raw_vibration,
376 'vibration_config': vibration_config,
377 'deflection_channel_config': deflection_channel_config,
378 'processed_vibration': processed_vibration,
382 'bump_details': bump_details,
383 'temperatures': temperatures,
384 'temperature_details': temperature_details,
385 'vibrations': vibrations,
386 'vibration_details': vibration_details,
387 'calibration_config': calibration_config,
392 def calib_analyze_all(filename, group='/', maximum_relative_error=1e-5,
394 "(Re)analyze all data from a `calib()` run."
395 assert group.endswith('/'), group
396 bumps,temperatures,vibrations,calibration_config,k,k_s = calib_load(
397 filename, group+'calibration/')
399 bumps = _numpy.zeros(
400 (calibration_config['num-bumps'],), dtype=float)
401 if temperatures is None:
402 temperatures = _numpy.zeros(
403 (calibration_config['num-temperatures'],), dtype=float)
404 if vibrations is None:
405 vibrations = _numpy.zeros(
406 (calibration_config['num-vibrations'],), dtype=float)
407 changed_bump = changed_temperature = changed_vibration = False
408 for i in range(calibration_config['num-bumps']):
409 bump_group = '%sbump/%d/' % (group, i)
410 (raw_bump,bump_config,z_axis_config,
411 deflection_channel_config,processed_bump) = _bump_load(
412 filename=filename, group=bump_group)
413 sensitivity = _bump_analyze(
414 data=raw_bump, bump_config=bump_config,
415 z_axis_config=z_axis_config,
416 deflection_channel_config=deflection_channel_config)
417 bumps[i] = sensitivity
418 rel_error = abs(sensitivity - processed_bump)/processed_bump
419 if rel_error > maximum_relative_error:
420 _LOG.warn(("new analysis doesn't match for bump %d: %g -> %g "
421 "(difference: %g, relative error: %g)")
422 % (i, processed_bump, sensitivity,
423 sensitivity-processed_bump, rel_error))
426 _bump_save(filename, bump_group, processed_bump=sensitivity)
427 for i in range(calibration_config['num-temperatures']):
428 temperature_group = '%stemperature/%d/' % (group, i)
429 (raw_temperature,temperature_config,processed_temperature
430 ) = _temperature_load(
431 filename=filename, group=temperature_group)
432 temperature = _temperature_analyze(
433 raw_temperature, temperature_config)
434 temperatures[i] = temperature
435 rel_error = abs(temperature - processed_temperature
436 )/processed_temperature
437 if rel_error > maximum_relative_error:
438 _LOG.warn(("new analysis doesn't match for temperature %d: "
439 "%g -> %g (difference: %g, relative error: %g)")
440 % (i, processed_temperature, temperature,
441 temperature-processed_temperature, rel_error))
442 changed_temperature = True
445 filename, temperature_group,
446 processed_T=temperature)
447 for i in range(calibration_config['num-vibrations']):
448 vibration_group = '%svibration/%d/' % (group, i)
449 (raw_vibration,vibration_config,deflection_channel_config,
450 processed_vibration) = _vibration_load(
451 filename=filename, group=vibration_group)
452 variance = _vibration_analyze(
453 deflection=raw_vibration, vibration_config=vibration_config,
454 deflection_channel_config=deflection_channel_config)
455 vibrations[i] = variance
456 rel_error = abs(variance - processed_vibration)/processed_vibration
457 if rel_error > maximum_relative_error:
458 _LOG.warn(("new analysis doesn't match for vibration %d: %g -> %g "
459 "(difference: %g, relative error: %g)")
460 % (i, processed_vibration, variance,
461 variance-processed_vibration, rel_error))
462 changed_vibration = True
465 filename, vibration_group, processed_vibration=variance)
467 calib_group = '%scalibration/' % group
469 if changed_bump and not dry_run:
470 calib_save(filename, calib_group, bumps=bumps)
471 if changed_temperature and not dry_run:
472 calib_save(filename, calib_group, temperatures=temperatures)
473 if changed_vibration and not dry_run:
474 calib_save(filename, calib_group, vibrations=vibrations)
476 new_k,new_k_s = calib_analyze(
477 bumps=bumps, temperatures=temperatures, vibrations=vibrations)
478 rel_error = abs(new_k-k)/k
479 if rel_error > maximum_relative_error:
480 _LOG.warn(("new analysis doesn't match for k: %g -> %g "
481 "(difference: %g, relative error: %g)")
482 % (k, new_k, new_k-k, rel_error))
484 calib_save(filename, calib_group, k=new_k)
485 rel_error = abs(new_k_s-k_s)/k_s
486 if rel_error > maximum_relative_error:
487 _LOG.warn(("new analysis doesn't match for k_s: %g -> %g "
488 "(difference: %g, relative error: %g)")
489 % (k_s, new_k_s, new_k_s-k_s, rel_error))
491 calib_save(filename, calib_group, k_s=new_k_s)
492 return (new_k, new_k_s)
494 def calib_plot_all(bumps, bump_details, temperatures, temperature_details,
495 vibrations, vibration_details, calibration_config, k, k_s,
496 maximum_relative_error=1e-5):
497 calib_plot(bumps, temperatures, vibrations)
498 for i,bump in enumerate(bump_details):
499 sensitivity = _bump_analyze(
500 data=bump['raw_bump'], bump_config=bump['bump_config'],
501 z_axis_config=bump['z_axis_config'],
502 deflection_channel_config=bump['deflection_channel_config'],
504 rel_error = abs(sensitivity - bump['processed_bump']
505 )/bump['processed_bump']
506 if rel_error > maximum_relative_error:
507 _LOG.warn(("new analysis doesn't match for bump %d: %g != %g "
508 "(difference: %g, relative error: %g)")
509 % (i, sensitivity, bump['processed_bump'],
510 sensitivity-bump['processed_bump'], rel_error))
511 # nothing interesting to plot for temperatures...
512 for i,vibration in enumerate(vibration_details):
513 variance = _vibration_analyze(
514 deflection=vibration['raw_vibration'],
515 vibration_config=vibration['vibration_config'],
516 deflection_channel_config=vibration['deflection_channel_config'],
518 rel_error = abs(variance - vibration['processed_vibration']
519 )/vibration['processed_vibration']
520 if rel_error > maximum_relative_error:
521 _LOG.warn(("new analysis doesn't match for vibration %d: %g != %g "
522 "(difference: %g, relative error: %g)")
523 % (i, variance, vibration['processed_vibration'],
524 variance-vibration['processed_vibration'], rel_error))