3 # calibcant - tools for thermally calibrating AFM cantilevers
5 # Copyright (C) 2007,2008, William Trevor King
7 # This program is free software; you can redistribute it and/or
8 # modify it under the terms of the GNU General Public License as
9 # published by the Free Software Foundation; either version 3 of the
10 # License, or (at your option) any later version.
12 # This program is distributed in the hope that it will be useful, but
13 # WITHOUT ANY WARRANTY; without even the implied warranty of
14 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
15 # See the GNU General Public License for more details.
17 # You should have received a copy of the GNU General Public License
18 # along with this program; if not, write to the Free Software
19 # Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
22 # The author may be contacted at <wking@drexel.edu> on the Internet, or
23 # write to Trevor King, Drexel University, Physics Dept., 3141 Chestnut St.,
24 # Philadelphia PA 19104, USA.
27 Aquire and analyze cantilever calibration data.
29 W. Trevor King Dec. 2007-Jan. 2008
34 The relevent physical quantities are :
35 Vzp_out Output z-piezo voltage (what we generate)
36 Vzp Applied z-piezo voltage (after external ZPGAIN)
37 Zp The z-piezo position
38 Zcant The cantilever vertical deflection
39 Vphoto The photodiode vertical deflection voltage (what we measure)
40 Fcant The force on the cantilever
41 T The temperature of the cantilever and surrounding solution
42 (another thing we measure or guess)
43 k_b Boltzmann's constant
45 Which are related by the parameters :
47 zpSensitivity Zp / Vzp
48 photoSensitivity Vphoto / Zcant
51 Cantilever calibration assumes a pre-calibrated z-piezo
52 (zpSensitivity) and a amplifier (zpGain). In our lab, the z-piezo is
53 calibrated by imaging a calibration sample, which has features with
54 well defined sizes, and the gain is set with a knob on the Nanoscope.
56 photoSensitivity is measured by bumping the cantilever against the
57 surface, where Zp = Zcant (see bump_aquire() and the bump_analyze
60 k_cant is measured by watching the cantilever vibrate in free solution
61 (see the vib_aquire() and the vib_analyze submodule). The average
62 energy of the cantilever in the vertical direction is given by the
63 equipartition theorem.
64 1/2 k_b T = 1/2 k_cant <Zcant**2>
65 so k_cant = k_b T / Zcant**2
66 but Zcant = Vphoto / photoSensitivity
67 so k_cant = k_b T * photoSensitivty**2 / <Vphoto**2>
69 We measured photoSensitivity with the surface bumps. We can either
70 measure T using an external function (see temperature.py), or just
71 estimate it (see T_aquire() and the T_analyze submodule). Guessing
72 room temp ~22 deg C is actually fairly reasonable. Assuming the
73 actual fluid temperature is within +/- 5 deg, the error in the spring
74 constant k_cant is within 5/273.15 ~= 2%. A time series of Vphoto
75 while we're far from the surface and not changing Vzp_out will give us
76 the average variance <Vphoto**2>.
78 We do all these measurements a few times to estimate statistical
81 The functions are layed out in the families:
82 bump_*(), vib_*(), T_*(), and calib_*()
83 where calib_{save|load|analyze}() deal with derived data, not
86 For each family, * can be any of :
87 aquire get real-world data
88 save store real-world data to disk
89 load get real-world data from disk
90 analyze interperate the real-world data.
91 plot show a nice graphic to convince people we're working :p
93 read a file with a list of paths to previously saved
94 real world data load each file using *_load(), analyze
95 using *_analyze(), and optionally plot using *_plot().
96 Intended for re-processing old data.
97 A family name without any _* extension (e.g. bump()), runs *_aquire(),
98 *_save(), *_analyze(), *_plot().
100 We also define the two positioning functions:
101 move_just_onto_surface() and move_far_from_surface()
102 which make automating the calibration procedure more straightforward.
108 from splittable_kwargs import splittableKwargsFunction, \
109 make_splittable_kwargs_function
121 @splittableKwargsFunction()
122 def bump_aquire(zpiezo, push_depth=200, npoints=1024, push_speed=1000) :
124 Ramps closer push_depth and returns to the original position.
126 zpiezo an opened zpiezo.zpiezo instance
127 push_depth distance to approach, in nm
128 npoints number points during the approach and during the retreat
129 push_speed piezo speed during approach and retreat, in nm/s
130 Returns the aquired ramp data dictionary, with data in DAC/ADC bits.
132 # generate the bump output
133 nm_per_step = float(push_depth) / npoints
134 freq = push_speed / nm_per_step # freq is sample frequency in Hz
135 start_pos = zpiezo.curPos()
136 pos_dist = zpiezo.pos_nm2out(push_depth) - zpiezo.pos_nm2out(0)
137 close_pos = start_pos + pos_dist
138 appr = numpy.linspace(start_pos, close_pos, npoints)
139 retr = numpy.linspace(close_pos, start_pos, npoints)
140 out = numpy.concatenate((appr, retr))
141 # run the bump, and measure deflection
142 if config.TEXT_VERBOSE :
143 print "Bump %g nm at %g nm/s" % (push_depth, push_speed)
144 data = zpiezo.ramp(out, freq)
147 @splittableKwargsFunction(bump_aquire,
148 (bump_analyze.bump_save, 'data'),
149 (bump_analyze.bump_analyze, 'data'))
152 Wrapper around bump_aquire(), bump_save(), bump_analyze()
154 bump_aquire_kwargs,bump_save_kwargs,bump_analyze_kwargs = \
155 bump._splitargs(bump, kwargs)
156 data = bump_aquire(**bump_aquire_kwargs)
157 bump_analyze.bump_save(data, **bump_save_kwargs)
158 photoSensitivity = bump_analyze.bump_analyze(data, **bump_analyze_kwargs)
159 return photoSensitivity
162 # Fairly stubby, since a one shot Temp measurement is a common thing.
163 # We just wrap that to provide a consistent interface.
165 @splittableKwargsFunction()
166 def T_aquire(get_T=None) :
168 Measure the current temperature of the sample,
169 or, if get_T == None, fake it by returning config.DEFAULT_TEMP
172 if config.TEXT_VERBOSE :
173 print "Fake temperature %g" % config.DEFAULT_TEMP
174 return config.DEFAULT_TEMP
176 if config.TEXT_VERBOSE :
177 print "Measure temperature"
180 @splittableKwargsFunction(T_aquire,
181 (T_analyze.T_save, 'T'),
182 (T_analyze.T_analyze, 'T'))
185 Wrapper around T_aquire(), T_save(), T_analyze(), T_plot()
187 T_aquire_kwargs,T_save_kwargs,T_analyze_kwargs = \
188 T._splitargs(T, kwargs)
189 T_raw = T_aquire(**T_aquire_kwargs)
190 T_analyze.T_save(T_raw, **T_save_kwargs)
191 T_ret = T_analyze.T_analyze(T_raw, **T_analyze_kwargs) # returns array
196 @splittableKwargsFunction()
197 def vib_aquire(zpiezo, time=1, freq=50e3) :
199 Record data for TIME seconds at FREQ Hz from ZPIEZO at it's current position.
201 # round up to the nearest power of two, for efficient FFT-ing
202 nsamps = FFT_tools.ceil_pow_of_two(time*freq)
204 # take some data, keeping the position voltage at it's current value
205 out = numpy.ones((nsamps,), dtype=numpy.uint16) * zpiezo.curPos()
206 if config.TEXT_VERBOSE :
207 print "get %g seconds of data" % time
208 data = zpiezo.ramp(out, freq)
209 data['sample frequency Hz'] = numpy.array([freq])
212 @splittableKwargsFunction(vib_aquire,
213 (vib_analyze.vib_save, 'data'),
214 (vib_analyze.vib_analyze, 'deflection_bits', 'freq'))
217 Wrapper around vib_aquire(), vib_save(), vib_analyze()
219 vib_aquire_kwargs,vib_save_kwargs,vib_analyze_kwargs = \
220 vib._splitargs(vib, kwargs)
221 data = vib_aquire(**vib_aquire_kwargs)
222 vib_analyze.vib_save(data, **vib_save_kwargs)
223 freq = data['sample frequency Hz']
224 deflection_bits = data['Deflection input']
225 Vphoto_var = vib_analyze.vib_analyze(deflection_bits=deflection_bits,
226 freq=freq, **vib_analyze_kwargs)
229 # A few positioning functions, so we can run bump_aquire() and vib_aquire()
230 # with proper spacing relative to the surface.
232 @splittableKwargsFunction()
233 def move_just_onto_surface(stepper, zpiezo, Depth_nm=-50, setpoint=2) :
235 Uses z_piezo_utils.getSurfPos() to pinpoint the position of the
236 surface. Adjusts the stepper position as required to get within
237 stepper_tol nm of the surface. Then set Vzp to place the
238 cantilever Depth_nm onto the surface. Negative Depth_nm values
239 will place the cantilever that many nm _off_ the surface.
241 If getSurfPos() fails to find the surface, backs off (for safety)
242 and steps in (without moving the zpiezo) until Vphoto > setpoint.
244 stepper_tol = 250 # nm, generous estimate of the fullstep stepsize
246 if config.TEXT_VERBOSE :
247 print "moving just onto surface"
249 if config.TEXT_VERBOSE :
250 print "zero the z piezo output"
251 zpiezo.jumpToPos(zpiezo.pos_nm2out(0))
252 # See if we're near the surface already
253 if config.TEXT_VERBOSE :
254 print "See if we're starting near the surface"
256 dist = zpiezo.pos_out2nm( \
257 z_piezo_utils.getSurfPos(zpiezo, zpiezo.def_V2in(setpoint))
259 except (z_piezo_utils.tooClose, z_piezo_utils.poorFit), string :
260 if config.TEXT_VERBOSE :
261 print "distance failed with: ", string
262 print "Back off 200 half steps"
263 # Back away 200 steps
264 stepper.step_rel(-400)
265 stepper.step_rel(200)
266 sp = zpiezo.def_V2in(setpoint) # sp = setpoint in bits
267 zpiezo.updateInputs()
268 cd = zpiezo.curDef() # cd = current deflection in bits
269 if config.TEXT_VERBOSE :
270 print "Single stepping approach"
272 if config.TEXT_VERBOSE :
273 print "deflection %g < setpoint %g. step closer" % (cd, sp)
274 stepper.step_rel(2) # Full step in
275 zpiezo.updateInputs()
277 # Back off two steps (protecting against backlash)
278 if config.TEXT_VERBOSE :
279 print "Step back 4 half steps to get off the setpoint"
280 stepper.step_rel(-200)
281 stepper.step_rel(196)
282 # get the distance to the surface
283 zpiezo.updateInputs()
284 if config.TEXT_VERBOSE :
285 print "get surf pos, with setpoint %g (%d)" % (setpoint, zpiezo.def_V2in(setpoint))
286 for i in range(20) : # HACK, keep stepping back until we get a distance
288 dist = zpiezo.pos_out2nm( \
289 z_piezo_utils.getSurfPos(zpiezo,zpiezo.def_V2in(setpoint)))
290 except (z_piezo_utils.tooClose, z_piezo_utils.poorFit), string :
291 stepper.step_rel(-200)
292 stepper.step_rel(198)
296 print "tried %d times, still too close! bailing" % i
297 print "probably an invalid setpoint."
298 raise Exception, "weirdness"
299 if config.TEXT_VERBOSE :
300 print 'distance to surface ', dist, ' nm'
301 # fine tune the stepper position
302 while dist < -stepper_tol : # step back if we need to
303 stepper.step_rel(-200)
304 stepper.step_rel(198)
305 dist = zpiezo.pos_out2nm( \
306 z_piezo_utils.getSurfPos(zpiezo, zpiezo.def_V2in(setpoint)))
307 if config.TEXT_VERBOSE :
308 print 'distance to surface ', dist, ' nm, step back'
309 while dist > stepper_tol : # and step forward if we need to
311 dist = zpiezo.pos_out2nm( \
312 z_piezo_utils.getSurfPos(zpiezo, zpiezo.def_V2in(setpoint)))
313 if config.TEXT_VERBOSE :
314 print 'distance to surface ', dist, ' nm, step closer'
315 # now adjust the zpiezo to place us just onto the surface
316 target = dist + Depth_nm
317 zpiezo.jumpToPos(zpiezo.pos_nm2out(target))
319 if config.TEXT_VERBOSE :
320 print "We're %g nm into the surface" % Depth_nm
322 @splittableKwargsFunction()
323 def move_far_from_surface(stepper, um_back=50) :
325 Step back a specified number of microns.
326 (uses very rough estimate of step distance at the moment)
329 steps = int(um_back*1000/step_nm)
330 print "step back %d steps" % steps
331 stepper.step_rel(-steps)
334 # and finally, the calib family
336 @splittableKwargsFunction((move_just_onto_surface, 'stepper', 'zpiezo'),
337 (bump, 'zpiezo', 'log_dir', 'Vphoto_in2V'),
338 (move_far_from_surface, 'stepper'),
340 (vib, 'zpiezo', 'log_dir', 'Vphoto_in2V'),
341 (analyze.calib_save, 'bumps','Ts','vibs','log_dir'))
342 def calib_aquire(stepper, zpiezo, num_bumps=10, num_Ts=10, num_vibs=20,
343 log_dir=config.LOG_DIR, Vphoto_in2V=config.Vphoto_in2V,
346 Aquire data for calibrating a cantilever in one function.
347 return (bump, T, vib), each of which is an array.
349 stepper a stepper.stepper_obj for coarse Z positioning
350 zpiezo a z_piezo.z_piezo for fine positioning and deflection readin
351 setpoint maximum allowed deflection (in Volts) during approaches
352 num_bumps number of 'a's (see Outputs)
353 push_depth_nm depth of each push when generating a
354 num_temps number of 'T's (see Outputs)
355 num_vibs number of 'vib's (see Outputs)
356 log_dir directory to log data to. Default 'None' disables logging.
357 Outputs (all are arrays of recorded data) :
358 bumps measured (V_photodiode / nm_tip) proportionality constant
359 Ts measured temperature (K)
360 vibs measured V_photodiode variance in free solution
362 move_just_onto_surface_kwargs,bump_kwargs,move_far_from_surface_kwargs, \
363 T_kwargs,vib_kwargs,calib_save_kwargs = \
364 calib_aquire._splitargs(calib_aquire, kwargs)
366 move_just_onto_surface(stepper, zpiezo, **move_just_onto_surface_kwargs)
367 bumps = numpy.zeros((num_bumps,), dtype=numpy.float)
368 for i in range(num_bumps) :
369 bumps[i] = bump(zpiezo=zpiezo, log_dir=log_dir,
370 Vphoto_in2V=Vphoto_in2V, **bump_kwargs)
371 if config.TEXT_VERBOSE :
374 move_far_from_surface(stepper, **move_far_from_surface_kwargs)
377 Ts = numpy.zeros((num_Ts,), dtype=numpy.float)
378 for i in range(num_Ts) :
379 Ts[i] = T(**T_kwargs)
380 time.sleep(1) # wait a bit to get an independent temperature measure
384 vibs = numpy.zeros((num_vibs,), dtype=numpy.float)
385 for i in range(num_vibs) :
386 vibs[i] = vib(zpiezo=zpiezo, log_dir=log_dir, Vphoto_in2V=Vphoto_in2V,
390 analyze.calib_save(bumps, Ts, vibs, log_dir, **calib_save_kwargs)
392 return (bumps, Ts, vibs)
395 @splittableKwargsFunction( \
396 (calib_aquire, 'log_dir'),
397 (analyze.calib_analyze, 'bumps','Ts','vibs'))
398 def calib(log_dir=config.LOG_DIR, **kwargs) :
400 Calibrate a cantilever in one function.
401 The I-don't-care-about-the-details black box version :p.
406 k cantilever spring constant (in N/m, or equivalently nN/nm)
407 k_s standard deviation in our estimate of k
409 See get_calibration_data() for the data aquisition code
410 See analyze_calibration_data() for the analysis code
412 calib_aquire_kwargs,calib_analyze_kwargs = \
413 calib._splitargs(calib, kwargs)
414 a, T, vib = calib_aquire(**calib_aquire_kwargs)
415 k,k_s,ps2_m, ps2_s,T_m,T_s,one_o_Vp2_m,one_o_Vp2_s = \
416 analyze.calib_analyze(a, T, vib, **calib_analyze_kwargs)
417 analyze.calib_save_analysis(k, k_s, ps2_m, ps2_s, T_m, T_s,
418 one_o_Vp2_m, one_o_Vp2_s, log_dir)