def local_energy_dispersion(spectra, n=1, order=2, correctE=True, \
refname=None, ret_data=False, verbosity=0, **kwargs):
"""
calculate the position-dependent energy dispersion from
the shift of the ZLP with a change in beam energy
spectra ... file containing the spectrum image (Nspectra, Npx)
n ... (opt) use ZLP shift between spectrum i and i+n
order ... (opt) order of the fitting polynomial for the distances
correctE ... (opt) if True, beam energy is corrected using BeamEnergy
refname ... (opt) filename of reference spectrum for second peak,
which will be used instead of the ZLP
ret_data ... (opt) return (pos, diff)-points used for the fit
verbosity... (opt) verbosity (0=silent, 2=plotting fit, 3=debug)
RETURNS - function object returning the energy dispersion for any
position on the detector
- if ret_data is True, data used to create this function object
"""
# set up beam energy correction
Beam = BeamEnergy()
data = []
pos = []
diff = []
dE = []
for filename in spectra:
# determine zlp position for each beam energy
if refname is not None:
Eref, d, zl = get_peak_pos(filename,
refname=refname,
verbosity=verbosity - 1,
**kwargs)
else:
Eref, zl = get_peak_pos(filename,
verbosity=verbosity - 1,
**kwargs)
# correct BeamEnergy
E = Beam.En(Eref) if correctE else Eref
# remove NaN's in zl (fit failed) and E (no correction available)
ind = ~np.isnan(zl[:, 0] + E)
E = E[ind]
zl = zl[ind]
assert np.allclose(Eref[ind][1:] - Eref[ind][:-1], Eref[1] - Eref[0])
# only even spacing in ZLP energy shifts allowed so far
# calculate energy dispersion from difference in adjacent spectra
data.append([Eref[ind], zl])
# zl[:,0]=mean pos
pos.append((zl[n:, 0] + zl[:-n, 0]) / 2)
# average position on detector
diff.append(-(zl[n:, 0] - zl[:-n, 0]))
# distance between ZLP i and i+n
dE.append(E[n:] - E[:-n])
# corresponding energy distance
# TODO: allow for many spectra with uneven energy spacing
dEref = Eref[n] - Eref[0]
# nominal energy difference
# plotting
if verbosity > 1:
fig = plt.figure()
ax = plt.gca()
plt.title("Position-dependent peak distance"+\
" (n=%d, $\Delta E_{ref}$=%4.1f eV)"%(n,dEref))
for i in range(len(pos)):
ax.plot(pos[i],
diff[i],
'ko',
alpha=0.1,
label="uncorrected" if i == 0 else "")
ax.plot(pos[i],
diff[i] * dEref / dE[i],
'o',
markersize=6,
label="%s" % spectra[i].split('/')[-1].split('.dm3')[0])
# flatten lists (one level)
pos = np.asarray(sum(map(list, pos), []))
diff = np.asarray(sum(map(list, diff), []))
dE = np.asarray(sum(map(list, dE), []))
# fitting polynomial to the Energy-corrected appearent size of the scale
ind = ~np.isnan(pos)
# index for outliers
diff_corr = diff * dEref / dE
disp = np.poly1d(np.polyfit(pos[ind], diff_corr[ind], order))
if verbosity > 1:
plt.gca().plot(pos[~ind], diff[~ind], 'rx', label="outliers")
plt.gca().plot(disp(np.arange(4096)), 'k-', label="fit")
ax.set_xlabel("position on detector [px]")
if correctE:
ax.set_ylabel(
"corrected ZLP distance $ \Delta x * (\Delta E_{ref} / \Delta E)$ [px]"
)
else:
ax.set_ylabel("ZLP distance dx [px]")
#ax.set_ylim(460,475);
ax.legend(loc=0)
# calculate energy dispersion dE/dy
e2x = trafo.NonlinearDispersion(disp, scale=dEref, xrange=(0, 4096))
#
# DEBUG: test energy calibration for positions of ZLP:
if verbosity > 2:
fig = plt.figure()
ax = fig.add_subplot(111)
# reference curve for beam energy
Beam = BeamEnergy()
ax.plot(Beam.E, Beam.E_corr, 'k-', label='reference')
# beam energy from ZLP position and energy dispersion
for i, (Eref, zl) in enumerate(data):
E, _ = e2x.inverse(zl[:, 0], zl[:, 0])
dE = -(E - E[0])
# shift of ZLP from calibrated E-axis
E_corr = dE + Beam.En(Eref[0])
# corrected Beam energy for each ZLP
ax.plot(Eref, E_corr - Eref, 'x', label=spectra[i].split('/')[-1])
ax.set_xlabel("nominal beam energy offset $E_0$ [eV]")
ax.set_ylabel("estimated deviation $E - E_0$ [eV]")
ax.set_ylim(-0.3, 0.3)
ax.legend(loc=0)
# output transformation
if verbosity > 1:
print "Transformation to linear energy axis e2x: \n", e2x.info(3)
return e2x if not ret_data else (e2x, np.vstack(
(pos[ind], diff_corr[ind])))
def get_dispersion(spectra, refname, DE=None, order=2, \
ret_data=False, verbosity=0, **kwargs):
"""
calculate the position-dependent energy dispersion from
the distance between two peaks (ZLP and plasmon reference)
spectra ... file containing the spectrum image (Nspectra, Npx)
refname ... filename of reference spectrum for second peak
DE ... (opt) use energy width of shifted scale to calibrate
the absolute energy axis, otherwise we use the nominal
distance of two ZLPs
order ... (opt) order of the fitting polynomial for the distances
ret_data ... (opt) return (pos, diff)-points used for the fit
verbosity... (opt) verbosity (0=silent, 2=plotting fit, 3=debug)
RETURNS function object returning the energy dispersion for any
position on the detector
"""
pos = []
diff = []
data = []
for filename in spectra:
Eref, zl, pl = get_peak_pos(filename,
refname,
verbosity=verbosity,
**kwargs)
# order zl and pl (zl should be left peak)
if np.nansum(pl[:, 0] - zl[:, 0]) < 0: zl, pl = pl, zl
# remove NaN's in zl (fit failed) and BeamEnergy (no correction available)
ind = ~np.isnan(zl[:, 0] + BeamEnergy().En(Eref))
Eref = Eref[ind]
zl = zl[ind]
pl = pl[ind]
# determine position-dependent peak distance
data.append([Eref, zl, pl])
# zl[:,0]=mean pos
pos.append((zl[:, 0] + pl[:, 0]) / 2)
# average position on detector
diff.append(pl[:, 0] - zl[:, 0])
# distance between peaks dy
# plotting
if verbosity > 1:
fig = plt.figure()
ax = plt.gca()
plt.title("Position-dependent peak distance")
for i in range(len(pos)):
ax.plot(pos[i],
diff[i],
'x',
label="%s" % spectra[i].split('/')[-1].split('.dm3')[0])
# flatten lists (one level)
pos = np.asarray(sum(map(list, pos), []))
diff = np.asarray(sum(map(list, diff), []))
# fitting polynomial to the appearent size of the scale
ind = ~np.isnan(pos)
# index for outliers
disp = np.poly1d(np.polyfit(pos[ind], diff[ind], order))
if verbosity > 1:
plt.gca().plot(pos[~ind], diff[~ind], 'rx', label="outliers")
plt.gca().plot(disp(np.arange(4096)), 'k-', label="fit")
ax.set_xlabel("position on detector [px]")
ax.set_ylabel("distance between ZLP and plasmon [px]")
#ax.set_ylim(460,475);
ax.legend(loc=0)
# Calculate energy width of scale from the linear shift of the ZLP
# with (corrected) beam energy
if DE is None:
# for each data series with N shifted spectra, we calculate the
# missing scaling factor DE from the expected shift of the ZLPs
DE = []
for Eref, zl, pl in data: # data[series][quantity][Nspectra]
# expected energy shift for n-th ZLP compared to initial pos.
Ecorr = -BeamEnergy().En(Eref)
# energy scale inversed wrt. E-q map
Y = Ecorr[0] - Ecorr[1:]
# measured energy shift for scale DE=1
e2x = NonlinearDispersion(disp, scale=1)
en = e2x.inverse(zl[:, 0], zl[:, 0])[0]
X = en[0] - en[1:]
#print Ecorr, Eref, Y, zl[:,0], en;
# calculate scaling factor DE which minimizes residuals X*DE-Y
# min(|X*DE-Y|^2) <=> 2(X*DE-Y)*X = 0 <=> DE=X*Y/X*X
DE.append(np.dot(X, Y) / np.dot(X, X))
# ouput
if verbosity > 0:
print "-- estimating scale DE ---------------------------"
if verbosity > 1:
for i in range(len(spectra)):
print " optimal Eplasmon for '%s': %8.5f eV " \
% (spectra[i].split('/')[-1], DE[i])
print "\n Average Eplasmon: (%5.3f +- %5.3f) eV" \
% (np.mean(DE), np.std(DE))
# calculate energy dispersion dE/dy
e2x = NonlinearDispersion(disp, scale=np.mean(DE))
# DEBUG: test energy calibration for positions of ZLP:
if verbosity > 2:
fig = plt.figure()
ax = fig.add_subplot(111)
# reference curve for beam energy
Beam = BeamEnergy()
ax.plot(Beam.E, Beam.E_corr, 'k-', label='reference')
# beam energy from ZLP position and energy dispersion
for i, (Eref, zl, pl) in enumerate(data):
E, _ = e2x.inverse(zl[:, 0], zl[:, 0])
dE = -(E - E[0])
# shift of ZLP from calibrated E-axis
E_corr = dE + Beam.En(Eref[0])
# corrected Beam energy for each ZLP
ax.plot(Eref, E_corr - Eref, 'x', label=spectra[i].split('/')[-1])
ax.set_xlabel("nominal beam energy offset $E_0$ [eV]")
ax.set_ylabel("estimated deviation $E - E_0$ [eV]")
ax.set_ylim(-0.3, 0.3)
ax.legend(loc=0)
# output transformation
if verbosity > 1:
print "Transformation to linear energy axis e2x: \n", e2x.info(3)
return e2x if not ret_data else (e2x, np.vstack((pos[ind], diff[ind])))
from TEMareels.ecal.energy_dispersion import get_dispersion;
from TEMareels.ecal.fit_peak_pos import get_peak_pos;
# calculate dispersion
spectra = ["../tests/Eseries%i.tif" %i for i in range(1,4)];
refname = "../tests/Ereference.msa";
order = 2;
DE = None; # energy width of shifted scale [eV]
e2x = get_dispersion(spectra,refname,verbosity=0,order=order,ampl_cut=0.5);
# calculate energy of ZLP for each of the series
E_ref = []; E_zl = []; E_pl = [];
for i,filename in enumerate(spectra):
E,zl,pl=get_peak_pos(filename, refname, border=100, \
ampl_cut=0.1, verbosity=2); # positions [px]
ind=~np.isnan(pl[:,0]-zl[:,0]); # identify NaN's
E = E[ind]; zl = zl[ind]; pl = pl[ind];
zl = e2x.inverse( zl[:,0], zl[:,0] )[0]; # energies [eV]
pl = e2x.inverse( pl[:,0], pl[:,0] )[0];
s0 = np.nanargmax(zl); # remove offset
E_zl.append( E[s0]+zl[s0]-zl );
plOffset = np.mean(pl-zl) \
if DE is None else DE;
E_pl.append( E[s0]+zl[s0]+plOffset-pl);
E_ref.append( E );
#sE = np.argmin(np.abs(E-0)); # align at Energy E0
#print sE, E_zl[-1][sE];
#E_zl[-1] += E[sE]-E_zl[-1][sE];
#E_pl[-1] += E[sE]-E_pl[-1][sE];
def local_energy_dispersion(spectra, n=1, order=2, correctE=True, \
refname=None, ret_data=False, verbosity=0, **kwargs):
"""
calculate the position-dependent energy dispersion from
the shift of the ZLP with a change in beam energy
spectra ... file containing the spectrum image (Nspectra, Npx)
n ... (opt) use ZLP shift between spectrum i and i+n
order ... (opt) order of the fitting polynomial for the distances
correctE ... (opt) if True, beam energy is corrected using BeamEnergy
refname ... (opt) filename of reference spectrum for second peak,
which will be used instead of the ZLP
ret_data ... (opt) return (pos, diff)-points used for the fit
verbosity... (opt) verbosity (0=silent, 2=plotting fit, 3=debug)
RETURNS - function object returning the energy dispersion for any
position on the detector
- if ret_data is True, data used to create this function object
"""
# set up beam energy correction
Beam = BeamEnergy();
data = []; pos = []; diff = []; dE = [];
for filename in spectra:
# determine zlp position for each beam energy
if refname is not None:
Eref,d,zl=get_peak_pos(filename,refname=refname, verbosity=verbosity-1, **kwargs);
else:
Eref,zl = get_peak_pos( filename, verbosity=verbosity-1, **kwargs);
# correct BeamEnergy
E = Beam.En(Eref) if correctE else Eref;
# remove NaN's in zl (fit failed) and E (no correction available)
ind =~np.isnan(zl[:,0] + E);
E = E[ind]; zl=zl[ind];
assert np.allclose( Eref[ind][1:] - Eref[ind][:-1], Eref[1]-Eref[0] )
# only even spacing in ZLP energy shifts allowed so far
# calculate energy dispersion from difference in adjacent spectra
data.append( [Eref[ind], zl] ); # zl[:,0]=mean pos
pos.append( (zl[n:,0] + zl[:-n,0])/2 ); # average position on detector
diff.append(-(zl[n:,0] - zl[:-n,0]) ); # distance between ZLP i and i+n
dE.append( E[n:] - E[:-n] ); # corresponding energy distance
# TODO: allow for many spectra with uneven energy spacing
dEref = Eref[n]-Eref[0]; # nominal energy difference
# plotting
if verbosity > 1:
fig=plt.figure(); ax=plt.gca();
plt.title("Position-dependent peak distance"+\
" (n=%d, $\Delta E_{ref}$=%4.1f eV)"%(n,dEref));
for i in range(len(pos)):
ax.plot(pos[i], diff[i], 'ko', alpha=0.1, label="uncorrected" if i==0 else "");
ax.plot(pos[i], diff[i]*dEref/dE[i], 'o', markersize=6,
label="%s"%spectra[i].split('/')[-1].split('.dm3')[0]);
# flatten lists (one level)
pos = np.asarray(sum(map(list,pos ),[]));
diff = np.asarray(sum(map(list,diff),[]));
dE = np.asarray(sum(map(list,dE),[]));
# fitting polynomial to the Energy-corrected appearent size of the scale
ind = ~np.isnan(pos); # index for outliers
diff_corr = diff*dEref/dE;
disp= np.poly1d(np.polyfit(pos[ind],diff_corr[ind],order));
if verbosity > 1:
plt.gca().plot(pos[~ind],diff[~ind], 'rx', label="outliers");
plt.gca().plot(disp(np.arange(4096)), 'k-', label="fit");
ax.set_xlabel("position on detector [px]");
if correctE:
ax.set_ylabel("corrected ZLP distance $ \Delta x * (\Delta E_{ref} / \Delta E)$ [px]");
else:
ax.set_ylabel("ZLP distance dx [px]");
#ax.set_ylim(460,475);
ax.legend(loc=0);
# calculate energy dispersion dE/dy
e2x=trafo.NonlinearDispersion(disp,scale=dEref,xrange=(0,4096));#
# DEBUG: test energy calibration for positions of ZLP:
if verbosity>2:
fig = plt.figure(); ax=fig.add_subplot(111);
# reference curve for beam energy
Beam= BeamEnergy();
ax.plot(Beam.E,Beam.E_corr,'k-',label='reference');
# beam energy from ZLP position and energy dispersion
for i,(Eref,zl) in enumerate(data):
E,_ = e2x.inverse(zl[:,0],zl[:,0]);
dE =-(E - E[0]); # shift of ZLP from calibrated E-axis
E_corr = dE + Beam.En(Eref[0]); # corrected Beam energy for each ZLP
ax.plot(Eref,E_corr-Eref,'x',label=spectra[i].split('/')[-1]);
ax.set_xlabel("nominal beam energy offset $E_0$ [eV]");
ax.set_ylabel("estimated deviation $E - E_0$ [eV]");
ax.set_ylim(-0.3,0.3);
ax.legend(loc=0);
# output transformation
if verbosity > 1:
print "Transformation to linear energy axis e2x: \n", e2x.info(3);
return e2x if not ret_data else (e2x, np.vstack((pos[ind],diff_corr[ind])));
# calculate dispersion
spectra = ["../tests/Eseries%i.tif" % i for i in range(1, 4)]
refname = "../tests/Ereference.msa"
order = 2
DE = None
# energy width of shifted scale [eV]
e2x = get_dispersion(spectra, refname, verbosity=0, order=order, ampl_cut=0.5)
# calculate energy of ZLP for each of the series
E_ref = []
E_zl = []
E_pl = []
for i, filename in enumerate(spectra):
E,zl,pl=get_peak_pos(filename, refname, border=100, \
ampl_cut=0.1, verbosity=2)
# positions [px]
ind = ~np.isnan(pl[:, 0] - zl[:, 0])
# identify NaN's
E = E[ind]
zl = zl[ind]
pl = pl[ind]
zl = e2x.inverse(zl[:, 0], zl[:, 0])[0]
# energies [eV]
pl = e2x.inverse(pl[:, 0], pl[:, 0])[0]
s0 = np.nanargmax(zl)
# remove offset
E_zl.append(E[s0] + zl[s0] - zl)
plOffset = np.mean(pl-zl) \
if DE is None else DE
E_pl.append(E[s0] + zl[s0] + plOffset - pl)
def get_dispersion(spectra, refname, DE=None, order=2, \
ret_data=False, verbosity=0, **kwargs):
"""
calculate the position-dependent energy dispersion from
the distance between two peaks (ZLP and plasmon reference)
spectra ... file containing the spectrum image (Nspectra, Npx)
refname ... filename of reference spectrum for second peak
DE ... (opt) use energy width of shifted scale to calibrate
the absolute energy axis, otherwise we use the nominal
distance of two ZLPs
order ... (opt) order of the fitting polynomial for the distances
ret_data ... (opt) return (pos, diff)-points used for the fit
verbosity... (opt) verbosity (0=silent, 2=plotting fit, 3=debug)
RETURNS function object returning the energy dispersion for any
position on the detector
"""
pos = []; diff = []; data = [];
for filename in spectra:
Eref,zl,pl = get_peak_pos( filename, refname, verbosity=verbosity, **kwargs);
# order zl and pl (zl should be left peak)
if np.nansum(pl[:,0]-zl[:,0])<0: zl,pl=pl,zl
# remove NaN's in zl (fit failed) and BeamEnergy (no correction available)
ind =~np.isnan(zl[:,0] + BeamEnergy().En(Eref));
Eref=Eref[ind]; zl=zl[ind]; pl=pl[ind];
# determine position-dependent peak distance
data.append( [Eref, zl, pl] ); # zl[:,0]=mean pos
pos.append( (zl[:,0] + pl[:,0])/2 ); # average position on detector
diff.append( pl[:,0] - zl[:,0] ); # distance between peaks dy
# plotting
if verbosity > 1:
fig=plt.figure(); ax=plt.gca();
plt.title("Position-dependent peak distance");
for i in range(len(pos)):
ax.plot(pos[i],diff[i], 'x', label="%s"%spectra[i].split('/')[-1].split('.dm3')[0]);
# flatten lists (one level)
pos = np.asarray(sum(map(list,pos ),[]));
diff = np.asarray(sum(map(list,diff),[]));
# fitting polynomial to the appearent size of the scale
ind = ~np.isnan(pos); # index for outliers
disp= np.poly1d(np.polyfit(pos[ind],diff[ind],order));
if verbosity > 1:
plt.gca().plot(pos[~ind],diff[~ind], 'rx', label="outliers");
plt.gca().plot(disp(np.arange(4096)), 'k-', label="fit");
ax.set_xlabel("position on detector [px]");
ax.set_ylabel("distance between ZLP and plasmon [px]");
#ax.set_ylim(460,475);
ax.legend(loc=0);
# Calculate energy width of scale from the linear shift of the ZLP
# with (corrected) beam energy
if DE is None:
# for each data series with N shifted spectra, we calculate the
# missing scaling factor DE from the expected shift of the ZLPs
DE = [];
for Eref,zl,pl in data: # data[series][quantity][Nspectra]
# expected energy shift for n-th ZLP compared to initial pos.
Ecorr=-BeamEnergy().En(Eref); # energy scale inversed wrt. E-q map
Y =Ecorr[0]-Ecorr[1:];
# measured energy shift for scale DE=1
e2x=NonlinearDispersion(disp,scale=1);
en =e2x.inverse(zl[:,0],zl[:,0])[0];
X = en[0]-en[1:];
#print Ecorr, Eref, Y, zl[:,0], en;
# calculate scaling factor DE which minimizes residuals X*DE-Y
# min(|X*DE-Y|^2) <=> 2(X*DE-Y)*X = 0 <=> DE=X*Y/X*X
DE.append( np.dot(X,Y)/np.dot(X,X) );
# ouput
if verbosity>0:
print "-- estimating scale DE ---------------------------"
if verbosity>1:
for i in range(len(spectra)):
print " optimal Eplasmon for '%s': %8.5f eV " \
% (spectra[i].split('/')[-1], DE[i]);
print "\n Average Eplasmon: (%5.3f +- %5.3f) eV" \
% (np.mean(DE), np.std(DE));
# calculate energy dispersion dE/dy
e2x=NonlinearDispersion(disp,scale=np.mean(DE));
# DEBUG: test energy calibration for positions of ZLP:
if verbosity>2:
fig = plt.figure(); ax=fig.add_subplot(111);
# reference curve for beam energy
Beam= BeamEnergy();
ax.plot(Beam.E,Beam.E_corr,'k-',label='reference');
# beam energy from ZLP position and energy dispersion
for i,(Eref,zl,pl) in enumerate(data):
E,_ = e2x.inverse(zl[:,0],zl[:,0]);
dE =-(E - E[0]); # shift of ZLP from calibrated E-axis
E_corr = dE + Beam.En(Eref[0]); # corrected Beam energy for each ZLP
ax.plot(Eref,E_corr-Eref,'x',label=spectra[i].split('/')[-1]);
ax.set_xlabel("nominal beam energy offset $E_0$ [eV]");
ax.set_ylabel("estimated deviation $E - E_0$ [eV]");
ax.set_ylim(-0.3,0.3);
ax.legend(loc=0);
# output transformation
if verbosity > 1:
print "Transformation to linear energy axis e2x: \n", e2x.info(3);
return e2x if not ret_data else (e2x, np.vstack((pos[ind],diff[ind])));
