def _line_spectrum(data, min, line, dE, width, width_error):
# Draw histogram
n, bins = Analysis.histogram(data, binsize=binsize)
if method in ("cs"):
gn, gbins = Analysis.group_bin(n, bins, min=min)
else:
# No grouping in mle and ls
gn, gbins = n, bins
ngn = gn/(np.diff(gbins))
ngn_sigma = np.sqrt(gn)/(np.diff(gbins))
cbins = (gbins[1:]+gbins[:-1])/2
if plotting:
figure()
if width_error is not None:
label = 'FWHM$=%.2f\pm %.2f$ eV' % (width, width_error)
else:
label = 'FWHM$=%.2f$ eV (Fixed)' % width
if method == "cs":
errorbar(cbins, ngn, yerr=ngn_sigma, xerr=np.diff(gbins)/2, capsize=0, ecolor='k', fmt=None, label=label)
else:
hist(data, bins=gbins, weights=np.ones(len(data))/binsize, histtype='step', ec='k', label=label)
E = np.linspace(bins.min(), bins.max(), 1000)
model = Analysis.normalization(ngn, gbins, dE, width, line=line, shift=shift) \
* Analysis.line_model(E, dE, width, line=line, shift=shift, full=True)
# Plot theoretical model
plot(E, model[0], 'r-')
# Plot fine structures
for m in model[1:]:
plot(E, m, 'b--')
xlabel('Energy$\quad$(eV)')
ylabel('Normalized Count$\quad$(count/eV)')
legend(frameon=False)
ymin, ymax = ylim()
ylim(ymin, ymax*1.1)
tight_layout()
savefig("%s-%s.pdf" % (session, line))
if savedat:
np.savetxt('%s-%s.dat' % (session, line), np.vstack((cbins, gn)).T,
header='Energy (keV), Count', delimiter='\t')
def tesana(t, p, n, lpfc=None, hpfc=None, binsize=1, max_shift=10,
thre=0.4, filt=None, nulldc=False, offset=False, center=False, sigma=3,
gain=None, dsr=None, shift=False, ocmethod="ols", flip=False, atom="Mn",
kbfit=False, ignorekb=False, method="mle",
rshunt=None, tbias=None, ites=None, ka_min=80, kb_min=40,
tex=False, plotting=True, savedat=False, session="Unnamed"):
"""
Perform TES Analysis
Parameters (and their default values):
t: time data (array-like)
p: pulse data (array-like)
n: noise data (array-like)
lpfc: low-pass filter cut-off frequency in bins (Default: None)
hpfc: high-pass filter cut-off frequency in bins (Default: None)
binsize: energy bin size for histograms and fittings (only for ls ans cs) in eV (Default: 1)
max_shift: maximum allowed shifts to calculate maximum cross correlation (Default: 10)
thre: correlation threshold for offset correction (Default: 0.4)
filt: window function (hanning/hamming/blackman/tukey) (Default: None)
nulldc: nullify the DC bin when template generation (Default: False)
offset: subtract DC offset (Default: False)
center: centering pulse rise (Default: False)
sigma: sigmas for median filter (Default: 3)
gain: feedback gain for current-space conversion (Default: None)
dsr: down-sampling rate (Default: None)
shift: treat dE as energy shift instead of scaling (Default: False)
ocmethod: offset correction fitting method (ols/odr) (Default: ols)
flip: flip x and y when offset correction fitting (Default: False)
atom: atom to fit (Default: Mn)
kbfit: fit Kb line (Default: False)
ignorekb: ignore Kb line when linearity correction (Default: False)
method: fitting method (mle/ls/cs) (Default: mle)
rshunt: shunt resistance value for r-space conversion (Default: None)
tbias: TES bias current for r-space conversion (Default: None)
ites: TES current for r-space conversion (Default: None)
ka_min: minimum counts to group bins for Ka line (valid only for ls/cs fittings) (Default: 80)
ka_min: minimum counts to group bins for Kb line (valid only for ls/cs fittings) (Default: 20)
tex: use TeX for plots (Default: False)
plotting: generate and save plots (Default: True)
savedat: save data to files (Default: False)
session: session name for plots and data files (Default: Unnamed)
Note:
- Use offset option when using filt option
- Consider using center option when using filt option
"""
if plotting:
# Import matplotlib
import matplotlib
matplotlib.use('Agg')
matplotlib.rcParams['text.usetex'] = str(tex)
from pylab import figure, plot, errorbar, hist, axvline, xlim, ylim, loglog, xlabel, ylabel, legend, tight_layout, savefig
print "Session: %s" % session
# Preparation
p = np.asarray(p)
n = np.asarray(n)
t = np.asarray(t)
dt = np.diff(t)[0]
df = (dt * t.shape[-1])**-1
# Subtract offset
if offset:
ofs = np.median(n)
p -= ofs
n -= ofs
# Convert to current-space if needed
if gain:
print "Converting to current-space"
p /= gain
n /= gain
# Convert to resistance-space
Rspace = False
if gain and rshunt and tbias and ites:
print "Converting to resistance-space"
ofs = np.median(n)
p += (ites - ofs)
n += (ites - ofs)
# Convert to resistance
p = (tbias - p) * rshunt / p
n = (tbias - n) * rshunt / n
Rspace = True
# Down-sample
if dsr > 1:
p = p[:,:p.shape[-1]/dsr*dsr].reshape(p.shape[0], -1, dsr).mean(axis=-1)
n = n[:,:n.shape[-1]/dsr*dsr].reshape(n.shape[0], -1, dsr).mean(axis=-1)
dt *= dsr
t = t[::dsr]
# Pulse centering (for filtering)
if center:
# Roll pulse to the center
r = p.shape[-1] / 2 - np.median(abs(p - Filter.offset(p)[:, np.newaxis]).argmax(axis=-1))
p = np.hstack((p[...,-r:], p[...,:-r]))
# Calculate offset (needs to be done before applying filter)
if p.size > 0:
offset = Filter.offset(p)
# Generate Filter
if filt is None:
pass
else:
if filt.lower() == "hanning":
f = np.hanning(p.shape[-1])
elif filt.lower() == "hamming":
f = np.hamming(p.shape[-1])
elif filt.lower() == "blackman":
f = np.blackman(p.shape[-1])
elif filt.lower() == "tukey":
f = tukey(p.shape[-1])
else:
raise ValueError('Unsupported filter: %s' % filt.lower())
print "Window filter function: %s" % filt.lower()
# Amplitude correction
cf = f.sum() / len(f)
p *= (f / cf)
n *= (f / cf)
# Equivalent noise bandwidth correction
enb = len(f)*(f**2).sum()/f.sum()**2
df *= enb
if p.size > 0:
# Calculate averaged pulse
avgp = Filter.average_pulse(p, max_shift=max_shift)
if savedat:
np.savetxt('%s-averagepulse.dat' % session, np.vstack((t, avgp)).T,
header='Time (s), Averaged Pulse (%s)' % ('R' if Rspace else ('A' if gain else 'V')), delimiter='\t')
if plotting:
figure()
plot(t, avgp)
xlabel('Time$\quad$(s)')
ylabel('Averaged Pulse$\quad$(%s)' % ('R' if Rspace else ('A' if gain else 'V')))
tight_layout()
savefig('%s-averagepulse.pdf' % session)
# Calculate averaged pulse spectrum
avgps = np.sqrt(Filter.power(avgp)) / df
if savedat:
np.savetxt('%s-avgpulse-power.dat' % session, np.vstack((np.arange(len(avgps))*df, avgps)).T,
header='Frequency (Hz), Average Pulse Power (%s/srHz)' % ('R' if Rspace else ('A' if gain else 'V')), delimiter='\t')
if plotting:
avgps[0] = 0 # for better plot
figure()
plot(np.arange(len(avgps))*df, avgps)
loglog()
xlabel('Frequency$\quad$(Hz)')
ylabel('Average Pulse Power$\quad$(%s/Hz)' % ('R' if Rspace else ('A' if gain else 'V')))
tight_layout()
savefig('%s-avgpulse-power.pdf' % session)
if n.size > 0:
# Plot noise spectrum
avgns = np.sqrt(Filter.average_noise(n) / df)
if savedat:
np.savetxt('%s-noise.dat' % session, np.vstack((np.arange(len(avgns))*df, avgns)).T,
header='Frequency (Hz), Noise (%s/srHz)' % ('R' if Rspace else ('A' if gain else 'V')), delimiter='\t')
if plotting:
avgns[0] = 0 # for better plot
figure()
plot(np.arange(len(avgns))*df, avgns)
loglog()
xlabel('Frequency$\quad$(Hz)')
ylabel('Noise$\quad$(%s/$\sqrt{\mathrm{Hz}}$)' % ('R' if Rspace else ('A' if gain else 'V')))
tight_layout()
savefig('%s-noise.pdf' % session)
if p.size > 0 and n.size > 0:
# Generate template
tmpl, sn = Filter.generate_template(p, n, lpfc=lpfc, hpfc=hpfc, nulldc=nulldc, max_shift=max_shift)
if savedat:
np.savetxt('%s-template.dat' % session, np.vstack((t, tmpl)).T,
header='Time (s), Template (A.U.)', delimiter='\t')
np.savetxt('%s-sn.dat' % session, np.vstack((np.arange(len(sn))*df, sn/np.sqrt(df))).T,
header='Frequency (Hz), S/N (/srHz)', delimiter='\t')
if plotting:
# Plot template
figure()
plot(t, tmpl)
xlabel('Time$\quad$(s)')
ylabel('Template$\quad$(A.U.)')
tight_layout()
savefig('%s-template.pdf' % session)
# Plot SNR
figure()
plot(np.arange(len(sn))*df, sn/np.sqrt(df))
loglog()
xlabel('Frequency$\quad$(Hz)')
ylabel('S/N$\quad$(/$\sqrt{\mathrm{Hz}}$)')
tight_layout()
savefig('%s-sn.pdf' % session)
# Calculate baseline resolution
print "Resolving power: %.2f (%.2f eV @ 5.9 keV)" % (np.sqrt((sn**2).sum()*2), Analysis.baseline(sn))
# Perform optimal filtering
pha_p = Filter.optimal_filter(p, tmpl, max_shift=max_shift)
pha_n = Filter.optimal_filter(n, tmpl, max_shift=0)
# Offset correction
(a, b), coef = Analysis.fit_offset(pha_p, offset, sigma=sigma, method=ocmethod, flip=flip)
if coef > thre:
oc_pha_p = Analysis.offset_correction(pha_p, offset, b)
oc_pha_n = Analysis.offset_correction(pha_n, offset, b)
print "Offset correction with: PHA = %f * (1 + %f * Offset)" % (a, b)
if plotting:
figure()
ka = Analysis.ka(np.vstack((pha_p, offset)).T, sigma=sigma)
plot(ka.T[1], ka.T[0], '.', c='k')
x_min, x_max = xlim()
ofs = np.linspace(x_min, x_max)
label = '$\mathrm{PHA}=%.2f\\times(1+%.2f\\times\mathrm{Offset})$' % (a, b)
plot(ofs, a*(1+b*ofs), 'r-', label=label)
xlabel('Offset$\quad$(V)')
ylabel('PHA$\quad$(V)')
legend(frameon=False)
tight_layout()
savefig('%s-offset.pdf' % session)
else:
oc_pha_p = pha_p
oc_pha_n = pha_n
print "Skipped offset correction: correlation coefficient (%f) is too small" % coef
# Check line database
if "%sKa" % atom not in Constants.LE.keys() or "%sKb" % atom not in Constants.LE.keys():
raise ValueError('Unsupported atom: %s' % atom)
# Linearity correction
pha_line_center = np.asarray([ np.median(Analysis.ka(oc_pha_p, sigma=sigma)), np.median(Analysis.kb(oc_pha_p, sigma=sigma)) ])
line_energy = np.asarray([ Constants.LE['%sKa' % atom], Constants.LE['%sKb' % atom] ])
if ignorekb:
a, b = Analysis.fit_linearity([pha_line_center[0]], [line_energy[0]], deg=1)
print "Linearity correction with: PHA = %e * E" % (b)
else:
a, b = Analysis.fit_linearity(pha_line_center, line_energy, deg=2)
print "Linearity correction with: PHA = %e * E^2 + %e * E" % (a, b)
print "MnKb saturation ratio: %.2f %%" % ((pha_line_center[1]/pha_line_center[0])/(line_energy[1]/line_energy[0])*100)
lc_pha_p = Analysis.linearity_correction(oc_pha_p, a, b)
lc_pha_n = Analysis.linearity_correction(oc_pha_n, a, b)
if savedat:
np.savetxt('%s-linearity.dat' % session, array([pha_line_center[0]]) if ignorekb else pha_line_center[np.newaxis,:],
header='%sKa PHA' % atom if ignorekb else '%sKa PHA, %sKb PHA' % (atom, atom), delimiter='\t')
if plotting:
figure()
x = np.linspace(0, 7e3)
if ignorekb:
plot(line_energy[0]/1e3, pha_line_center[0], '+', color='b')
plot(x/1e3, x*b, 'r--')
else:
plot(line_energy/1e3, pha_line_center, '+', color='b')
plot(x/1e3, x**2*a+x*b, 'r--')
xlim((0, 7))
xlabel('Energy$\quad$(keV)')
ylabel('PHA$\quad$(a.u.)')
tight_layout()
savefig('%s-linearity.pdf' % session)
# Energy Spectrum
if plotting:
figure()
hcount, hbin, hpatch = hist(lc_pha_p[lc_pha_p==lc_pha_p]/1e3, bins=7000/binsize, histtype='stepfilled', color='y')
xlim(0, 7)
xlabel('Energy$\quad$(keV)')
ylabel('Count')
tight_layout()
savefig('%s-spec.pdf' % session)
if savedat:
hcount, hbin = np.histogram(lc_pha_p[lc_pha_p==lc_pha_p]/1e3, bins=7000/binsize)
np.savetxt('%s-spec.dat' % session, np.vstack(((hbin[1:]+hbin[:-1])/2, hcount)).T,
header='Energy (keV), Count', delimiter='\t')
# Line fitting
def _line_fit(data, min, line):
# Fit
(dE, width), (dE_error, width_error), e = Analysis.fit(data, binsize=binsize, min=min, line=line, shift=shift, method=method)
if method == "cs":
chi_squared, dof = e
if method in ("mle", "ls"):
print "%s: %.2f +/- %.2f eV @ Ec%+.2f eV" \
% (line, width, width_error, dE)
elif method == "cs":
print "%s: %.2f +/- %.2f eV @ Ec%+.2f eV (Red. chi^2 = %.1f/%d = %.2f)" \
% (line, width, width_error, dE, chi_squared, dof, chi_squared/dof)
return dE, width, width_error
def _line_spectrum(data, min, line, dE, width, width_error):
# Draw histogram
n, bins = Analysis.histogram(data, binsize=binsize)
if method in ("cs"):
gn, gbins = Analysis.group_bin(n, bins, min=min)
else:
# No grouping in mle and ls
gn, gbins = n, bins
ngn = gn/(np.diff(gbins))
ngn_sigma = np.sqrt(gn)/(np.diff(gbins))
cbins = (gbins[1:]+gbins[:-1])/2
if plotting:
figure()
if width_error is not None:
label = 'FWHM$=%.2f\pm %.2f$ eV' % (width, width_error)
else:
label = 'FWHM$=%.2f$ eV (Fixed)' % width
if method == "cs":
errorbar(cbins, ngn, yerr=ngn_sigma, xerr=np.diff(gbins)/2, capsize=0, ecolor='k', fmt=None, label=label)
else:
hist(data, bins=gbins, weights=np.ones(len(data))/binsize, histtype='step', ec='k', label=label)
E = np.linspace(bins.min(), bins.max(), 1000)
model = Analysis.normalization(ngn, gbins, dE, width, line=line, shift=shift) \
* Analysis.line_model(E, dE, width, line=line, shift=shift, full=True)
# Plot theoretical model
plot(E, model[0], 'r-')
# Plot fine structures
for m in model[1:]:
plot(E, m, 'b--')
xlabel('Energy$\quad$(eV)')
ylabel('Normalized Count$\quad$(count/eV)')
legend(frameon=False)
ymin, ymax = ylim()
ylim(ymin, ymax*1.1)
tight_layout()
savefig("%s-%s.pdf" % (session, line))
if savedat:
np.savetxt('%s-%s.dat' % (session, line), np.vstack((cbins, gn)).T,
header='Energy (keV), Count', delimiter='\t')
## Ka
ka = Analysis.ka(lc_pha_p, sigma=sigma)
dE, width, width_error = _line_fit(ka, ka_min, "%sKa" % atom)
_line_spectrum(ka, ka_min, "%sKa" % atom, dE, width, width_error)
## Kb
kb = Analysis.kb(lc_pha_p, sigma=sigma)
if kbfit:
dE, width, width_error = _line_fit(kb, kb_min, "%sKb" % atom)
else:
width_error = None
_line_spectrum(kb, kb_min, "%sKb" % atom, dE, width, width_error)
## Baseline
f_pha_n = lc_pha_n[Filter.median_filter(lc_pha_n, sigma=sigma)]
baseline = Analysis.sigma2fwhm(np.std(f_pha_n))
print "Baseline resolution: %.2f eV" % baseline
n, bins = Analysis.histogram(f_pha_n, binsize=binsize)
if savedat:
np.savetxt('%s-baseline.dat' % session, np.vstack(((bins[1:]+bins[:-1])/2, n)).T,
header='Energy (keV), Count', delimiter='\t')
if plotting:
figure()
label = 'FWHM$=%.2f$ eV' % baseline
hist(f_pha_n, bins=bins, weights=np.ones(len(f_pha_n))/binsize, histtype='step', ec='k', label=label)
mu, sigma = norm.fit(f_pha_n)
E = np.linspace(bins.min(), bins.max(), 1000)
plot(E, norm.pdf(E, loc=mu, scale=sigma)*len(f_pha_n), 'r-')
xlabel('Energy$\quad$(eV)')
ylabel('Normalized Count$\quad$(count/eV)')
legend(frameon=False)
tight_layout()
savefig('%s-baseline.pdf' % session)