def lt(z, v, znbins, zrange, vnbins, vrange, plot=True):
""" compute the lifetime of v-variable (S2e, Se1, E) vs Z
"""
zbins = np.linspace(*zrange, znbins + 1)
vbins = np.linspace(*vrange, vnbins + 1)
x, y, yu = fitf.profileX(z, v, znbins, zrange)
seed = expo_seed(x, y)
f = fitf.fit(fitf.expo, x, y, seed, sigma=yu)
if (not plot): return f
#print('energy_0', f.values[0], ' +- ', f.errors[0] )
#print('lifetime', f.values[1], ' +- ', f.errors[1] )
frame_data = plt.gcf().add_axes((.1, .3, .8, .6))
plt.hist2d(z, v, (zbins, vbins))
x, y, yu = fitf.profileX(z, v, znbins, zrange)
plt.errorbar(x, y, yu, np.diff(x)[0] / 2, fmt="kp", ms=7, lw=3)
plt.plot(x, f.fn(x), "r-", lw=4)
frame_data.set_xticklabels([])
labels("", "Energy (pes)", "Lifetime fit")
lims = plt.xlim()
frame_res = plt.gcf().add_axes((.1, .1, .8, .2))
plt.errorbar(x, (f.fn(x) - y) / yu, 1, np.diff(x)[0] / 2, fmt="p", c="k")
plt.plot(lims, (0, 0), "g--")
plt.xlim(*lims)
plt.ylim(-5, +5)
labels("Drift time (µs)", "Standarized residual")
return f
def conditional_labels(with_title=True):
"""
Wrapper around the labels function that allows removing
the title by changing one parameter.
"""
with_ = lambda *args: labels(*args)
without_ = lambda *args: labels(*args[:2], "")
return with_ if with_title else without_
def lifetime_calculation(z, zrange, energy, erange, elim, slope, axes):
"""
Measure the lifetime for the given events and plots the raw energy distribution and the energy vs drift time in a separate axes instance.
Parameters:
z = Array of events' drift time
zrange = Range in drift time for the fit.
energy = Array of events' energy.
erange = Range in energy for plotting.
elim = Limits for the energy at z=0.
slope = slope of the exponential, used in the selection of the events, should be the inverse of the expected lifetime (1/[expected lifetime])
axes = Axes object from a subplot, should have length >= 2.
"""
axes[0].hist(energy, 50, erange, rasterized=True)
histFun.labels("S2 energy (pes)", "Entries",
"Fiducialized energy spectrum")
low_cut = elim[0] * np.exp(-slope * z)
high_cut = elim[1] * np.exp(-slope * z)
sel = coref.in_range(energy, low_cut,
high_cut) # remove low and high E background
axes[1].hist2d(z,
energy, (100, 50),
range=(zrange, erange),
rasterized=True)
x, y, u_y = fitf.profileX(z[sel],
energy[sel],
100,
xrange=zrange,
yrange=erange)
axes[1].plot(x, y, "--k", rasterized=True)
axes[1].plot(z[z < 500], low_cut[z < 500], "k.", rasterized=True)
axes[1].plot(z[z < 500], high_cut[z < 500], "k.", rasterized=True)
Zrange_LT = zrange
seed = np.max(y), (x[15] - x[5]) / np.log(y[15] / y[5])
f = fitf.fit(fitf.expo, x, y, seed, fit_range=Zrange_LT, sigma=u_y)
axes[1].plot(x, f.fn(x), "r", lw=3, rasterized=True)
print("Energy at z=0 = {:.1f} +- {:.1f}".format(f.values[0], f.errors[0]))
print("Lifetime = {:.1f} +- {:.1f}".format(-f.values[1], f.errors[1]))
print("Chi2 = {:.2f} \n".format(f.chi2))
# axes[1].text(zrange[0] + 0.05*(zrange[1]-zrange[0]), erange[0] + 1000, \
# "Lifetime = {:.1f} $\pm$ {:.1f}".format(-f.values[1], f.errors[1]), color = "white")#, fontsize = 14)
histFun.labels("Drift time ($\mu$s)", "S2 energy (pes)", "")
return np.array([-f.values[1], f.errors[1]
]), corrf.LifetimeCorrection(-f.values[1], f.errors[1])
def _decorator(*args, **kargs):
if ('canvas' in kargs):
kargs['new_figure'] = False
del kargs['canvas']
has_xylabels, xylabels = 'xylabels' in kargs, ()
if (has_xylabels):
xylabels = kargs['xylabels']
del kargs['xylabels']
response = fun(*args, **kargs)
if (len(xylabels) > 0):
hst.labels(*xylabels)
return response
def _decorator(*args, **kargs):
if ('canvas' in kargs):
kargs['new_figure'] = False
del kargs['canvas']
has_xylabels, xylabels = 'xylabels' in kargs, ()
if (has_xylabels):
xylabels = kargs['xylabels']
del kargs['xylabels']
if (len(xylabels) > 0):
hst.labels(*xylabels)
has_title, () = 'title' in kargs, ()
if (has_title):
title = kargs['title']
del kargs['title']
hst.labels('', '', title)
if ('ylog' in kargs):
plt.yscale('log')
del kargs['ylog']
response = fun(*args, **kargs)
return response
def radialCuts(R, Z, E, ZCorr, elim, run_number=0, fPlot=False):
"""
Returns a R-dependent lower and a higher cut to the Z-corrected energy of the event.
Parameters:
R = R position of the event.
Z = Drift time of the event.
E = Energy of th event.
ZCorr = Lifetime Correction object.
elim = Limits for the energy at R=0.
fPlot = If true, draw the E vs R distribution and the selection (between the two black lines).
"""
low_cut = elim[0] * rfun(R, 205, 20) #(1/(1 + np.exp((R-205)/20)))
high_cut = elim[1] * rfun(R, 220, 20) #(1/(1 + np.exp((R-220)/20)))
if fPlot:
fig = plt.figure(figsize=(8, 6))
ax1 = fig.add_subplot(111)
plt.axes(ax1)
histFun.hist2d(R,
ZCorr(Z).value * E, (100, 50),
range=([0, 150], [elim[0] - 3000, elim[1] + 3000]),
new_figure=False,
rasterized=True)
histFun.labels("Radial position (mm)", "S2 energy (pes)", "")
plt.plot(R, low_cut, "k.", rasterized=True)
plt.plot(R, high_cut, "k.", rasterized=True)
fig.tight_layout()
extent = ax1.get_tightbbox(fig.canvas.get_renderer()).transformed(
fig.dpi_scale_trans.inverted())
fig.savefig("ECorrvsR_R{}.pdf".format(run_number), bbox_inches=extent)
plt.close(fig)
return low_cut, high_cut
def selection_in_band(E,
Z,
Erange,
Zrange,
Zfitrange,
nsigma=3.5,
Znbins=50,
Enbins=100,
plot=True):
""" This returns a selection of the events that are inside the Kr E vz Z
returns: np.array(bool)
If plot=True, it draws E vs Z and the band
"""
Zfit = Zfitrange
Zbins = np.linspace(*Zrange, Znbins + 1)
Ebins = np.linspace(*Erange, Enbins + 1)
Zcenters = shift_to_bin_centers(Zbins)
Zerror = np.diff(Zbins) * 0.5
sel_e = in_range(E, *Erange)
mean, sigma, chi2, ok = fit_slices_1d_gauss(Z[sel_e],
E[sel_e],
Zbins,
Ebins,
min_entries=5e2)
ok = ok & in_range(Zcenters, *Zfit)
def _line_cut(sign):
x = Zcenters[ok]
y = mean.value[ok] + sign * nsigma * sigma.value[ok]
yu = mean.uncertainty[ok]
seed = expo_seed(x, y)
efit = fitf.fit(fitf.expo, x, y, seed, sigma=yu)
assert np.all(efit.values != seed)
return efit.fn
lowE_cut = _line_cut(-1.)
highE_cut = _line_cut(+1.)
sel_inband = in_range(E, lowE_cut(Z), highE_cut(Z))
if (plot == False): return sel_inband
plt.hist2d(Z, E, (Zbins, Ebins), cmap=default_cmap)
plt.errorbar(Zcenters[ok],
mean.value[ok],
sigma.value[ok],
Zerror[ok],
"kp",
label="Kr peak energy $\pm 1 \sigma$")
f = fitf.fit(fitf.expo, Zcenters[ok], mean.value[ok], (1e4, -1e3))
plt.plot(Zcenters, f.fn(Zcenters), "r-")
print(f.values)
plt.plot(Zbins,
lowE_cut(Zbins),
"m",
lw=2,
label="$\pm " + str(nsigma) + " \sigma$ region")
plt.plot(Zbins, highE_cut(Zbins), "m", lw=2)
plt.legend()
labels("Drift time (µs)", "S2 energy (pes)", "Energy vs drift")
return sel_inband
def dst_compare_vars(dst1, dst2):
dst = dst1
subdst = dst2
plt.figure(figsize=(20, 15))
plt.subplot(3, 4, 1)
double_hist(dst.nS2, subdst.nS2, np.linspace(0, 5, 6))
plt.yscale("log")
labels("Number of S2s", "Entries", "# S2")
plt.subplot(3, 4, 2)
double_hist(dst.S1e, subdst.S1e, np.linspace(0, 50, 51))
labels("S1 integral (pes)", "Entries", "S1 energy")
plt.subplot(3, 4, 3)
double_hist(dst.S1w, subdst.S1w, np.linspace(0, 600, 25))
labels("S1 width (ns)", "Entries", "S1 width")
plt.subplot(3, 4, 4)
double_hist(dst.S1h, subdst.S1h, np.linspace(0, 15, 31))
labels("S1 height (pes)", "Entries", "S1 height")
plt.subplot(3, 4, 5)
double_hist(dst.Nsipm, subdst.Nsipm, np.linspace(0, 100, 51))
labels("Number of SiPMs", "Entries", "# SiPMs")
plt.subplot(3, 4, 6)
double_hist(dst.S2e, subdst.S2e, np.linspace(0, 25e3, 101))
labels("S2 integral (pes)", "Entries", "S2 energy")
plt.subplot(3, 4, 7)
double_hist(dst.S2w, subdst.S2w, np.linspace(0, 50, 26))
labels("S2 width (µs)", "Entries", "S2 width")
plt.subplot(3, 4, 8)
double_hist(dst.S2h, subdst.S2h, np.linspace(0, 1e4, 101))
labels("S2 height (pes)", "Entries", "S2 height")
plt.subplot(3, 4, 9)
double_hist(dst.Z, subdst.Z, np.linspace(0, 600, 101))
labels("Drift time (µs)", "Entries", "Drift time")
plt.subplot(3, 4, 10)
double_hist(dst.X, subdst.X, np.linspace(-200, 200, 101))
labels("X (mm)", "Entries", "X")
plt.subplot(3, 4, 11)
double_hist(dst.Y, subdst.Y, np.linspace(-200, 200, 101))
labels("Y (mm)", "Entries", "Y")
plt.subplot(3, 4, 12)
double_hist(dst.S2q, subdst.S2q, np.linspace(0, 5e3, 101))
labels("Q (pes)", "Entries", "S2 charge")
plt.tight_layout()
def psf_fit(mapDST, DX, DY, groupZ, groupQ, z_int, Ec_conv, sigma_range,
sipm_lim, cut, min_count, run_number):
"""
Calculates (through a data-driven fit) and returns the transverse spread for a given dataset.
Parameters:
mapDST = Full raw DST.
DX = Difference in position between event and sensor in x-dimension.
DY = Difference in position between event and sensor in y-dimension.
groupQ = Charge of the SiPMs.
groupZ = Mean drift time of the event.
z_int = Drift time interval to do the fit.
Ec_conv = Collection (for several sigmas) of PSF+gaussian convolutions (for the fit).
sigma_range = Collection of sigmas considered in the convolution.
sipm_lim = Limit in the distance point-sensor for the fit.
cut = Minimum charge in a bin to be used for the fit.
min_count = Minimum number of events in a bin to be used for the fit.
"""
fig, axes = plt.subplots(1, 3, figsize=(24, 6))
chimin = 1e20
sipm_xyrange = (-sipm_lim, sipm_lim)
binfactor = 2.
sigmamin = 0.
bin_lim_min = -50.
sipm_lim_min = -50.
nbins = int(binfactor * sipm_lim)
# Plot the distribution to be fitted.
base_selection = ((np.sqrt(DX**2 + DY**2) < 50.) & (mapDST.Q > 0.) &
(mapDST.Q.values / groupQ < 1.))
z_interval_selection = base_selection & coref.in_range(
groupZ, z_int[0], z_int[1])
xc, Ec, Ece = fitf.profileX(DX[z_interval_selection], mapDST[z_interval_selection].Q/groupQ[z_interval_selection],\
nbins, sipm_xyrange)
try:
x_min = xc[(Ec < cut) & (xc < 0)].max()
x_max = xc[(Ec < cut) & (xc > 0)].min()
except:
x_min = xc.min()
x_max = xc.max()
fig1 = plt.figure()
ax1 = fig.add_subplot(1, 1, 1)
(xc, yc, Ec_m, Ece_m), _, cb = \
histFun.hist2d_profile(DX[z_interval_selection], DY[z_interval_selection], mapDST[z_interval_selection].Q.values / groupQ[z_interval_selection],\
nbins, nbins, sipm_xyrange, sipm_xyrange, new_figure = False, rasterized=True)
cb.set_label("Charge fraction")
histFun.labels("X (mm)", "Y (mm)", "")
ax1.set_xticks(np.linspace(-20., 20., 5))
ax1.set_yticks(np.linspace(-20., 20., 5))
fig1.tight_layout()
fig1.savefig("TransPSF_Z{0}-{1}_R{2}.pdf".format(z_int[0], z_int[1],
run_number))
fig, axes = plt.subplots(1, 3, figsize=(24, 6))
plt.axes(axes[0])
(xc, yc, Ec_m, Ece_m), _, cb = \
histFun.hist2d_profile(DX[z_interval_selection], DY[z_interval_selection], mapDST[z_interval_selection].Q.values / groupQ[z_interval_selection],\
nbins, nbins, sipm_xyrange, sipm_xyrange, new_figure = False, rasterized=True)
cb.set_label("E (pes)")
histFun.labels("X (mm)", "Y (mm)", "")
# Fit.
Ec_fit = 0
Ec = Ec_m
Ece = Ece_m
counts, *_ = np.histogram2d(DX[z_interval_selection], DY[z_interval_selection],\
[np.linspace(-sipm_lim, sipm_lim, nbins+1), np.linspace(-sipm_lim, sipm_lim, nbins+1)])
for lim in np.arange(sipm_lim, sipm_lim + 1, 1.):
bin_lim = [len(xc[xc < x_min]), len(xc[xc < x_max]) + 1]
Ec = Ec_m[bin_lim[0]:bin_lim[1], bin_lim[0]:bin_lim[1]]
Ece = Ece_m[bin_lim[0]:bin_lim[1], bin_lim[0]:bin_lim[1]]
counts_sel = counts[bin_lim[0]:bin_lim[1], bin_lim[0]:bin_lim[1]]
for i, sigma in enumerate(sigma_range):
Ec_c = Ec_conv[i]
Ec_c = Ec_c[bin_lim[0]:bin_lim[1], bin_lim[0]:bin_lim[1]]
Ec_c = Ec_c * Ec.sum() / Ec_c.sum()
sel = counts_sel > min_count
chi = ((Ec[sel] - Ec_c[sel])**2 /
(Ece[sel]**2)).sum() / (len(Ec[sel]) - 1)
if chi < chimin:
chimin = chi
sigmamin = sigma
Ec_fit = Ec_c
# Plot the projection at x = 0 / y = 0
xproj = Ec_m[np.argmax(Ec_m.sum(axis=0))]
yproj = Ec_m[:, np.argmax(Ec_m.sum(axis=0))]
xprojf = Ec_fit[np.argmax(Ec_fit.sum(axis=0))]
yprojf = Ec_fit[:, np.argmax(Ec_fit.sum(axis=1))]
h1d(xc, len(xc), [np.min(xc), np.max(xc)], weights=xproj, ax=axes[1])
axes[1].plot(xc[bin_lim[0]:bin_lim[1]],
xprojf,
"r",
lw=1.25,
rasterized=True)
axes[1].set_xlabel("X (mm)")
axes[1].set_ylabel("Charge fraction")
axes[1].grid(True)
h1d(yc, len(yc), [np.min(yc), np.max(yc)], weights=yproj, ax=axes[2])
axes[2].plot(yc[bin_lim[0]:bin_lim[1]],
yprojf,
"r",
lw=1.25,
rasterized=True)
axes[2].set_xlabel("Y (mm)")
axes[2].set_ylabel("Charge fraction")
axes[2].grid(True)
fig.tight_layout()
extent = axes[0].get_tightbbox(fig.canvas.get_renderer()).transformed(
fig.dpi_scale_trans.inverted())
axes[0].set_xticks(np.linspace(-20., 20., 5))
axes[0].set_yticks(np.linspace(-20., 20., 5))
# fig.savefig("TransPSF_Z{0}-{1}_R{2}.pdf".format(z_int[0], z_int[1], run_number), bbox_inches=extent)
extent = axes[1].get_tightbbox(fig.canvas.get_renderer()).transformed(
fig.dpi_scale_trans.inverted())
fig.savefig("TransPSF_X_Z{0}-{1}_R{2}.pdf".format(z_int[0], z_int[1],
run_number),
bbox_inches=extent)
extent = axes[2].get_tightbbox(fig.canvas.get_renderer()).transformed(
fig.dpi_scale_trans.inverted())
fig.savefig("TransPSF_Y_Z{0}-{1}_R{2}.pdf".format(z_int[0], z_int[1],
run_number),
bbox_inches=extent)
axes[0].set_title("Energy vs XY for Z = [{0},{1}]".format(
z_int[0], z_int[1]))
axes[1].set_title("Charge profile X projection at Y = 0")
axes[2].set_title("Charge profile Y projection at X = 0")
fig.tight_layout()
plt.close(fig)
return sigmamin, chimin
def longitudinalPSF(groupDST, mapDST, run_number = 0, sigma_lim = [0.1,12.1], \
sigma_step = 1., z_step = 25, low_drift_int = [10., 75.], zrange = [0, 550], el_time = [0., 0.], norm=True):
"""
Given a dataset, it divides it by drift time intervals and returns an array
with the longitudinal rms (gaussian sigma) of each interval. This is done using
the PSF along Z (longitudinal point-spread function).
Parameters:
groupDST = Grouped DST (by event id).
mapDST = Full raw DST
sigma_lim = Range of RMS that will be evaluated.
sigma_step = Step between sigmas to be evaluated.
z_step = Width of the drift time intervals.
low_drift_int = Drift time interval to obtain the PSF. Near anode so diffusion is negligible.
zrange = Drift time range to be evaluated.
norm = If true, SiPM charge is normalized to the charge of the SiPM with most charge.
"""
z_scan = np.arange(zrange[0], zrange[1], z_step)
sigmaAll = []
groupE = np.array([1.] * len(mapDST))
if norm:
groupE = groupDST.E.transform('sum').values
groupZ = groupDST.Z.transform("mean") - el_time[0]
nbins = 20
# Obtain the PSF
fig1 = plt.figure(figsize=(4.5, 4.))
ax1 = fig1.add_subplot(111)
plt.axes(ax1)
low_drift_selection = coref.in_range(groupZ, low_drift_int[0],
low_drift_int[1])
Ec_o, xc = h1d(mapDST[low_drift_selection].PosSlice.values, nbins+1, [-nbins/2.-0.5, nbins/2+0.5],\
"Relative time position ($\mu$s)", "Energy fraction",
weights = mapDST[low_drift_selection].E/(len(set(mapDST[low_drift_selection].event))*groupE[low_drift_selection]), ax = ax1)
Ec_o = Ec_o / Ec_o.sum()
extent = ax1.get_tightbbox(fig1.canvas.get_renderer()).transformed(
fig1.dpi_scale_trans.inverted())
fig1.savefig("DiffusionLongPSF_EL_R{0}.pdf".format(run_number),
bbox_inches=extent)
histFun.labels("Relative time position ($\mu$s)",\
"Energy fraction",\
"Energy per slice for Z = [{0},{1}]".format(low_drift_int[0], low_drift_int[1]))
# Obtain the set of PSF+gaussian convolutions to be tested (one per evaluated sigma)
sigma_range = np.arange(sigma_lim[0], sigma_lim[1], sigma_step)
Ec_conv = []
mu = 0.
for sigma in sigma_range:
gaussian = np.exp(-np.power(xc - mu, 2.) / (2 * np.power(sigma, 2.)))
gaussian = gaussian / gaussian.sum()
Ec_c = sci.signal.convolve(Ec_o, gaussian, mode='same')
Ec_c = Ec_c / Ec_c.sum()
Ec_conv.append(Ec_c)
n_row = 4
nrows = len(z_scan) // n_row
if len(z_scan) % n_row > 0:
nrows += 1
fig, axes = plt.subplots(nrows, n_row, figsize=(18, 4 * nrows))
# Loop through the different drift time intervals
for i, z in enumerate(z_scan):
chimin = 1e10
sigmamin = 0.
Ec_fit = Ec_o
z_interval_selection = coref.in_range(groupZ, z, z + z_step)
plt.axes(axes[i // n_row][i % n_row])
Ec, xc, = h1d(mapDST[z_interval_selection].PosSlice, nbins+1, [-nbins/2.-0.5, nbins/2+0.5],\
"Relative time position ($\mu$s)", "Energy fraction",\
weights = mapDST[z_interval_selection].E/(len(set(mapDST[z_interval_selection].event))*groupE[z_interval_selection]), ax = axes[i//n_row][i%n_row])
# Fit to obtain the sigma that best matches the distribution.
for j, sigma in enumerate(sigma_range):
Ec_c = Ec.sum() * Ec_conv[j]
chi = ((Ec - Ec_c)**2 / Ec_c).sum() / (len(Ec) - 1)
if chi < chimin:
chimin = chi
sigmamin = sigma
Ec_fit = Ec_c
plt.plot(xc, Ec_fit, "r", rasterized=True)
sigmaAll.append(sigmamin)
fig.tight_layout()
for zcount, axi in enumerate(np.ravel(axes)):
plt.axes(axi)
extent = axi.get_tightbbox(fig.canvas.get_renderer()).transformed(
fig.dpi_scale_trans.inverted())
fig.savefig("DiffusionLongPSF_Z{0}-{1}_R{2}.pdf".format(
zrange[0] + zcount * z_step, zrange[0] + (zcount + 1) * z_step,
run_number),
bbox_inches=extent)
histFun.labels("Relative time position ($\mu$s)",\
"Energy fraction",\
"Energy per slice for Z = [{0},{1}]".format(zrange[0] + zcount*z_step, zrange[0] + (zcount+1)*z_step))
plt.close(fig)
return np.array(sigmaAll)
def diffFit(sigma, z, zfit, dv, pressure, temp, diff_type, ax, fHisto2D=False):
"""
Calculates (through a linear fit) and returns the transverse diffusion coefficient for a given dataset.
Parameters:
sigma = Longitudinal or transverse spread.
Z = Drift time of the event.
zfit = Drift time interval to do the fit.
dv = Drift velocity under current conditions.
pressure = Pressure in the chamber.
diff_type = Type of spread being considered; if not 'longitudinal', it will be transverse.
ax = Subfigure to plot distributions.
fHisto2D = Flag to plot a 2D distribution.
"""
seed = 0.03, 0.01
sel = coref.in_range(z, zfit[0], zfit[1])
f = fitf.fit(lin, z[sel], sigma[sel]**2, seed=seed)
if fHisto2D:
x, _, _, _ = histFun.hist2d(
z[sel],
sigma[sel]**2,
100, [[zfit[0], zfit[1]], [0., (sigma[sel].max())**2 + 2]],
new_figure=False,
rasterized=True)
histFun.labels("Drift time ($\mu$s)",
"Longitudinal RMS$^2$ ($\mu$s$^2$)", "")
fit_label = "[({:.4f} +- {:.4f})·x + \n ({:.4f} +- {:.4f})]".format(
f.values[0], f.errors[0], f.values[1], f.errors[1])
ax.plot(z[sel],
f.fn(z[sel]),
'r',
label=fit_label if fit_label
not in plt.gca().get_legend_handles_labels()[1] else '',
rasterized=True)
else:
ax.plot(z,
f.fn(z),
'r',
label="[({:.4f} +- {:.4f})·x + \n ({:.4f} +- {:.4f})]".format(
f.values[0], f.errors[0], f.values[1], f.errors[1]),
rasterized=True)
ax.legend(fontsize=12)
const = f.values[0]
const_e = f.errors[0]
D_e_stat = 0.
D_e_syst = 0.
if diff_type == "transverse":
print("Type Trans")
D = const / 2 * 1000000 / 100
D_e_stat = (const_e / 2) * 1000000 / 100
else:
D = dv[0] * dv[0] * const / 2 * 1000000 / 100
D_e_stat = 1000000 / 100 * np.sqrt((dv[0] * dv[0] * const_e / 2)**2 +
(const * dv[0] * dv[1])**2)
D_e_syst = (const * dv[0] * dv[2]) * 1000000 / 100
# Reduced diffusion coefficient (in um/cm^2)
temp0 = 20. + 273.15
D = np.sqrt(1000 * 2 * D * pressure[0] / dv[0] * temp0 / temp[0])
# Error derived from fits (diffusion and drift velocity)
new_D_e_stat = (D_e_stat * (1000*2*pressure[0]/dv[0]*temp0/temp[0]) / (2*np.sqrt(1000*2*D*pressure[0]/dv[0]*temp0/temp[0]))) ** 2 + \
(np.sqrt(1000*2*D*pressure[0]/dv[0]*temp0/temp[0])*dv[1]/(2*dv[0]))**2
D_e_stat = np.sqrt(new_D_e_stat)
# Error derived from systematics (pressure, drift velocity and temperature)
new_D_e_syst = (D_e_syst * (1000*2*pressure[0]/dv[0]*temp0/temp[0]) / (2*np.sqrt(1000*2*D*pressure[0]/dv[0]*temp0/temp[0]))) ** 2 + \
(pressure[1] * (1000*2*D/dv[0]*temp0/temp[0]) / (2*np.sqrt(1000*2*D*pressure[0]/dv[0]*temp0/temp[0]))) ** 2 + \
(temp[1] * np.sqrt(1000*2*D*pressure[0]/dv[0]*temp0/temp[0]) / (2*temp[0])) ** 2 + \
(dv[2] * np.sqrt(1000*2*D*pressure[0]/dv[0]*temp0/temp[0]) / (2*dv[0])) ** 2
D_e_syst = np.sqrt(new_D_e_syst)
c = np.sqrt(np.abs(f.values[1]))
c_e = 0.5 * np.abs(f.errors[1]) / np.sqrt(np.abs(f.values[1]))
print("Diffusion coefficient (um^2/cm^-1/2) = {:.4f} +- {:.4f} +- {:.4f}".
format(D, D_e_stat, D_e_syst))
print("Constant parameter (mm) = {:.4f} +- {:.4f}\n".format(c, c_e))
D = [D, D_e_stat, D_e_syst]
C = [c, c_e]
return D, C
def transversalPSF(groupDST, mapDST, sipm_lim, run_number = 0, sigma_lim = [0.1,12.1], sigma_step = 1., z_step = 25, \
low_drift_int = [10., 75.], zrange = [0, 550], el_time = [0., 0.], cut = 0.02, min_count = 5, norm=True):
"""
Given a dataset, it divides it by drift time intervals and returns an array
with the transverse rms (gaussian sigma) of each interval and the chi2 of each fit.
This fit is done to the PSF (point-spread function).
Parameters:
groupDST = Grouped DST (by event id).
mapDST = Full raw DST
sipm_lim = Limit in the distance point-sensor for the fit.
sigma_lim = Range of RMS that will be evaluated.
sigma_step = Step between sigmas to be evaluated.
z_step = Width of the drift time intervals.
low_drift_int = Drift time interval to obtain the PSF. Near anode so diffusion is negligible.
zrange = Drift time range to be evaluated.
cut = Minimum charge in a bin to be used for the fit.
min_count = Minimum number of events in a bin to be used for the fit.
norm = If true, SiPM charge is normalized to the charge of the SiPM with most charge.
"""
z_scan = np.arange(zrange[0], zrange[1], z_step)
sigmaAll = []
chiAll = []
# DX = mapDST.Xevt.values - mapDST.X.values
# DY = mapDST.Yevt.values - mapDST.Y.values
DX = mapDST.X.values - mapDST.Xpeak.values
DY = mapDST.Y.values - mapDST.Ypeak.values
#
groupQ = np.array([1.] * len(mapDST))
if norm:
groupQ = groupDST.Q.transform('sum').values
groupZ = groupDST.Z.transform("mean") - el_time[0]
sipm_xyrange = (-sipm_lim, sipm_lim)
binfactor = 2.
# Obtain the PSF
base_selection = (np.sqrt(DX**2 + DY**2) <
50.) & (mapDST.Q > 5.) & (mapDST.Q.values / groupQ < 1.)
low_drift_selection = base_selection & coref.in_range(
groupZ, low_drift_int[0], low_drift_int[1])
fig1 = plt.figure()
ax1 = fig1.add_subplot(111)
(xc, yc, Ec_o, Ece_o), _, cb = \
histFun.hist2d_profile(DX[low_drift_selection], DY[low_drift_selection], mapDST[low_drift_selection].Q.values / groupQ[low_drift_selection], \
int(binfactor*sipm_lim), int(binfactor*sipm_lim), sipm_xyrange, sipm_xyrange, new_figure = False, rasterized=True)
cb.set_label("Charge fraction")
histFun.labels("X (mm)", "Y (mm)", "")
# extent = ax1.get_tightbbox(fig1.canvas.get_renderer()).transformed(fig1.dpi_scale_trans.inverted())
ax1.set_xticks(np.linspace(-20., 20., 5))
ax1.set_yticks(np.linspace(-20., 20., 5))
fig1.tight_layout()
fig1.savefig("TransPSF_EL_R{}.pdf".format(run_number))
histFun.labels(
"X (mm)", "Y (mm)",
"Energy vs XY for Z = [{0},{1}]".format(low_drift_int[0],
low_drift_int[1]))
#Normalize the measured charge distribution
Ec_o = Ec_o / Ec_o.sum()
Ece_o = Ece_o / Ec_o.sum()
# Obtain the set of PSF+gaussian convolutions to be tested (one per evaluated sigma)
sigma_range = np.arange(sigma_lim[0], sigma_lim[1], sigma_step)
Ec_conv = []
mu = 0.
for sigma in sigma_range:
gaussian = np.outer(np.exp(-np.power(xc - mu, 2.) / (2 * np.power(sigma, 2.))), \
np.exp(-np.power(yc - mu, 2.) / (2 * np.power(sigma, 2.))))
gaussian = gaussian / gaussian.sum()
Ec_c = sci.signal.convolve2d(Ec_o, gaussian, mode='same')
Ec_conv.append(Ec_c)
# Fit to obtain the sigma that best matches the distribution.
for i, z in enumerate(z_scan):
sigmamin, chi = psf_fit(mapDST, DX, DY, groupZ, groupQ, [z, z+z_step], \
np.array(Ec_conv), sigma_range, sipm_lim, cut, min_count, run_number)
sigmaAll.append(sigmamin)
chiAll.append(chi)
return np.array(sigmaAll), np.array(chiAll)
def measureDriftVelocity(run, drift_field, z, zrange_dv, bins_dv, buffersize,
z_cathode, el_time):
"""
Given a Z distribution, returns the drift velocity with its error.
The drift velocity is obtained through an smooth Heavyside fit or logistic function (https://en.wikipedia.org/wiki/Logistic_function).
Parameters:
run = Run number, to add it to the figure title
drift_field = Drift field of the run, to add it to the figure title.
groupDST = Grouped DST (by event id).
zrange_dv = Range in drift time for the fit.
bins_dv = Bins for plotting the region of interest.
buffersize = Buffersize of the run, to plot the drift time distribution.
z_cathode = Cathode z-position in mm.
"""
fig, axes = plt.subplots(1, 3, figsize=(24, 6))
st = fig.suptitle(
"Run {0} (drift field = {1:.0f} V/cm/bar) Z distribution".format(
run, drift_field[0]),
fontsize=16)
axes[0].hist(z, 100, [0, buffersize], rasterized=True)
axes[0].set_xlabel("Z (mm)")
axes[0].set_ylabel("")
axes[1].hist(z, 100, [0, buffersize], rasterized=True)
axes[1].set_xlabel("Z (mm)")
axes[1].set_ylabel("")
axes[1].set_yscale('log')
plt.axes(axes[2])
y, x = h1d(z, bins_dv, zrange_dv, "Z (mm)", "Number of events", ax=axes[2])
axes[2].set_yscale('log')
sigmoid = lambda x, A, B, C, D: A / (1 + np.exp(-C * (x - B))) + D
seed = np.max(y), np.mean(zrange_dv), np.diff(zrange_dv)[0] / 100, np.min(
y)
f = fitf.fit(sigmoid,
x,
y,
seed,
fit_range=zrange_dv,
sigma=statf.poisson_sigma(y))
plt.plot(x, f.fn(x), "r", lw=1.25, rasterized=True)
histFun.labels("Drift time ($\mu$s)", "Number of events", "")
dv = z_cathode[0] / (f.values[1] - el_time[0])
dv_e_stat = z_cathode[0] / (
(f.values[1] - el_time[0])**
2) * f.errors[1] # Statistic error derived from fit.
dv_e_syst = (z_cathode[0]/((f.values[1] - el_time[0])**2) * 1.)**2 + \
(z_cathode[1]/(f.values[1] - el_time[0]))**2 + \
(z_cathode[0]/((f.values[1] - el_time[0])**2) * el_time[1])**2 # Systematic error derived from drift time measurement (asumed to be 1 mus), drift length and drifted time in EL.
dv_e_syst = np.sqrt(dv_e_syst)
dv = np.array([dv, dv_e_stat, dv_e_syst])
print("Max drift time = {:.3f} +- {:.3f}".format(f.values[1], f.errors[1]))
print(
"Drift velocity = {:.5f} +- {:.5f} (stat.) +- {:.5f} (syst.)".format(
dv[0], dv[1], dv[2]))
print("======================================")
axes[2].annotate("Drift time = \n{:.3f} $\pm$ {:.3f}".format(
f.values[1], f.errors[1]),
xy=(0.665, 0.9),
xycoords='axes fraction',
color="black") #, fontsize = 14)
extent = axes[0].get_tightbbox(fig.canvas.get_renderer()).transformed(
fig.dpi_scale_trans.inverted())
fig.savefig("DriftVel_R{}.pdf".format(run), bbox_inches=extent)
extent = axes[1].get_tightbbox(fig.canvas.get_renderer()).transformed(
fig.dpi_scale_trans.inverted())
fig.savefig("DriftVel_Log_R{}.pdf".format(run), bbox_inches=extent)
extent = axes[2].get_tightbbox(fig.canvas.get_renderer()).transformed(
fig.dpi_scale_trans.inverted())
fig.savefig("DriftVel_LogZoom_R{}.pdf".format(run), bbox_inches=extent)
plt.close(fig)
return dv