def plot_delay_spectrum():
x1, y1 = np.loadtxt("data/pm1_delay.txt", unpack=True)
x2, y2 = np.loadtxt("data/pm2_delay.txt", unpack=True)
time = np.hstack((-x1, x2))
count = np.hstack((y1, y2))
error_count = np.sqrt(count + 1)
plt.clf()
plt.errorbar(time, count, yerr=error_count, fmt='s', color="black")
func = lambda x, offset, mu, sigma, A: offset + GAUSS(x, mu, sigma, A)
fit = Fit(func)
fit.offset = 0
fit.mu = -45
fit.sigma = 60
fit.fit(time, count, error_count)
fit.plot(box="tr", units={"mu": "ns", "sigma": "ns"}, color="red")
print(fit)
plt.xlabel(r"$\Delta T / \textrm{ns}$")
plt.ylabel("Count")
plt.savefig("out/delay_fit." + SAVETYPE)
plt.clf()
fit.plot_residual(time,
count,
error_count,
fmt="s",
box="br",
color="black")
plt.xlabel(r"$\Delta T / \textrm{ns}$")
plt.ylabel("Count")
plt.savefig("out/delay_residual." + SAVETYPE)
def fit_radium_calib():
energies = [3.953, 5.332, 7.02] # MeV
error_energies = np.array([0.001, 0.001, 0.01]) / math.sqrt(12)
channels = [240, 815, 1495]
error_channels = [10, 10, 8]
fit = Fit(LINEAR)
fit.set_data(xdata=channels,
xerrors=error_channels,
ydata=energies,
yerrors=error_energies)
fit.set_labels(xlabel="Kanal", ylabel="Energie / MeV")
fit.iterative_fit(5)
plt.clf()
plt.minorticks_on()
fit.plot(box="tl",
units={
"slope": "keV/Kanal",
"offset": "MeV"
},
factors={"slope": 1000})
plt.savefig("out/radium_calib_fit." + SAVETYPE)
plt.clf()
plt.minorticks_on()
fit.plot_residual(box="bl")
plt.savefig("out/radium_calib_residual." + SAVETYPE)
def plot_caesium_absorber():
depth, events, slabs = np.loadtxt("data/caesium_bleiabschirmung.txt",
unpack=True)
error_depth = np.sqrt(slabs) * 0.1
error_events = np.sqrt(events + 1)
plt.clf()
plt.minorticks_on()
plt.errorbar(depth, events, xerr=error_depth, yerr=error_events, fmt=',')
plt.xlabel("Tiefe / mm")
plt.ylabel("ln(Anzahl)")
plt.savefig("out/caesium_absorber_nolog." + SAVETYPE)
ln_events = np.log(events)
error_ln_events = np.abs(1 / events) * error_events
depth /= 10 # mm=>cm
error_depth /= 10
plt.clf()
plt.minorticks_on()
func = lambda x, mu, lnI0: -x * mu + lnI0
fit = Fit(func)
fit.set_data(xdata=depth,
ydata=ln_events,
xerrors=error_depth,
yerrors=error_ln_events)
fit.set_labels(xlabel="Tiefe / cm", ylabel="ln(Anzahl)")
fit.iterative_fit(5)
fit.plot(box="tr", units={"mu": "1/cm"})
plt.savefig("out/caesium_absorber_fit." + SAVETYPE)
plt.clf()
plt.minorticks_on()
fit.plot_residual(box="tr")
plt.savefig("out/caesium_absorber_residual." + SAVETYPE)
plt.clf()
plt.minorticks_on()
fit = fit.filtered(depth <= 2)
fit.iterative_fit(5)
fit.plot(box="tr", units={"mu": "1/cm"})
plt.savefig("out/caesium_absorber_fit2." + SAVETYPE)
plt.clf()
plt.minorticks_on()
fit.plot_residual(box="tr")
plt.savefig("out/caesium_absorber_residual2." + SAVETYPE)
mu = fit.uvalue("mu")
print("Absorptionskoeffizient:", mu, "1/cm")
mu1 = mu / ufloat(11.342, 0.001)
print("Massenabsorptionskoeffizient:", mu1, "cm^2/g")
def plot_coincidence_na():
for spalte in (1, 2):
columns = np.loadtxt("data/natrium_winkel.txt", unpack=True)
angle = columns[0]
count = columns[spalte]
error_angle = 0.3
error_count = np.sqrt(count + 1)
plt.clf()
plt.errorbar(angle,
count,
xerr=error_angle,
yerr=error_count,
fmt=',',
color="black")
fit = Fit(GAUSS)
fit.mu = 0
fit.sigma = 10
for i in range(5):
errors = fit.combine_errors(angle, error_angle, error_count)
fit.fit(angle, count, errors)
fit.plot(fit.mu - 5 * fit.sigma,
fit.mu + 5 * fit.sigma,
box="bl",
color="red")
plt.ylim(0, plt.ylim()[1])
plt.xlabel("Winkel / Grad")
plt.ylabel("Count")
plt.savefig("out/coincidence_na_%d_fit." % spalte + SAVETYPE)
plt.clf()
fit.plot_residual(angle,
count,
errors,
fmt="s",
box="br",
color="black")
plt.xlabel("Winkel / Grad")
plt.ylabel("Count")
plt.savefig("out/coincidence_na_%d_residual." % spalte + SAVETYPE)
def plot_yag_lifetime():
time, voltage = _load_oscilloscope_csv("data/ALL0010/F0010CH2.CSV")
time *= 1E6 # us
voltage *= 1000 # mV
error_voltage = voltage[time < 0].std()
print("Fehler:", error_voltage, "mV")
fit = Fit(EXPONENTIAL_DECAY)
fit.set_data(xdata=time, ydata=voltage, yerrors=error_voltage)
fit.set_labels(xlabel="Zeit / us", ylabel="Spannung / mV")
fit = fit.filtered(np.logical_and(time > 0, time < 1500))
fit.set_params(A=0.1, offset=0.20, T=250)
fit.iterative_fit(1)
print("Lebensdauer:", formatUFloat(fit.uvalue("T"), "us"), "- Chi^2:",
fit.chi2, "- ndf:", fit.ndf, "- Chi^2/ndf:", fit.chi2ndf)
plt.clf()
fit.plot(box="tr", units={"T": "us", "A": "mV", "offset": "mV"})
plt.savefig("out/yag_lifetime." + SAVETYPE)
def plot_strontium():
m = {
0: 0,
5: 0.03,
6: 0.04,
7: 0.05,
8: 0.08,
9: 0.10,
10: 0.17,
11: 0.25,
12: 0.37,
13: 0.50,
14: 0.64,
15: 0.83,
16: 1.01,
17: 1.23,
18: 1.39,
19: 1.57,
20: 1.88,
21: 2.29,
22: 2.79,
23: 3.46,
}
nr, count = np.loadtxt("data/strontium_alu.txt", unpack=True)
absorb = np.zeros_like(nr)
for i, x in enumerate(nr):
absorb[i] = m[x] / 10
scale = 1 / count[0]
error_count = np.sqrt(count + 1)
error_absorb = 0.01 / 10
count *= scale
error_count *= scale
func = lambda x, A, mu, offset: A * np.exp(-x * mu) + offset
fit = Fit(func)
fit.set_data(xdata=absorb,
ydata=count,
xerrors=error_absorb,
yerrors=error_count)
fit.set_params(A=1, mu=1, offset=0)
fit.set_labels(xlabel="Dicke / cm", ylabel="Anteil")
fit.iterative_fit(5)
plt.clf()
plt.minorticks_on()
plt.xlim(0, .35)
fit.plot(box="tr", units={"mu": "1/cm"})
plt.savefig("out/strontium_fit." + SAVETYPE)
plt.clf()
plt.minorticks_on()
fit.plot_residual(box="tr")
plt.savefig("out/strontium_residual." + SAVETYPE)
rho = ufloat(2.7, 0.1)
mu = fit.uvalue("mu")
print("Absorptionskoeffizient:", mu, "1/cm")
mu1 = mu / rho
print("Massenabsorptionskoeffizient:", mu1, "cm^2/g")
E = umath.pow(17 / mu1, 1 / 1.14)
print("Maximalenergie:", E, "MeV")
R1 = 0.412 * umath.pow(E, 1.265 - 0.0954 * umath.log(E))
R = R1 / rho
print("Reichweite:", R1, "g/cm^2")
print("Reichweite:", R, "cm")
def plot_ionisation_raw():
distances, voltages, error_voltages = np.loadtxt(
"data/radium_ionisationskammer.txt", unpack=True)
# discard 38.80cm
distances = distances[:-1]
voltages = voltages[:-1]
error_voltages = error_voltages[:-1]
for distance, voltage, error_voltage in zip(distances, voltages,
error_voltages):
distance = ufloat(distance, 0.05)
voltage = ufloat(voltage, error_voltage)
print("$({:L}) \\unit{{cm}}$ & $({:L}) \\unit{{mV}}$ \\\\".format(
distance, voltage))
plt.clf()
plt.minorticks_on()
plt.errorbar(distances, voltages, xerr=0.05, yerr=error_voltages, fmt=',')
plt.xlabel("Distanz / cm")
plt.ylabel("Spannung / mV")
plt.savefig("out/radium_ionisation_raw." + SAVETYPE)
plt.clf()
plt.minorticks_on()
currents = []
error_currents = []
for voltage, error_voltage in zip(voltages, error_voltages):
current = ufloat(voltage, error_voltage) #+ ufloat(5, 3)
currents.append(current.n)
error_currents.append(current.s)
currents = np.array(currents)
error_currents = np.array(error_currents)
distances -= 39
plt.clf()
plt.minorticks_on()
plt.errorbar(distances, currents, xerr=0.05, yerr=error_currents, fmt=',')
plt.xlabel("Distanz / cm")
plt.ylabel("Strom / nA")
plt.savefig("out/radium_ionisation." + SAVETYPE)
plt.clf()
plt.minorticks_on()
x = distances[1:] + np.abs(np.diff(distances) / 2)
y = -np.diff(currents) / np.diff(distances)
plt.plot(x, y, 's-')
plt.xlabel("Distanz / cm")
plt.ylabel("- Änderung des Stromes / nA / cm")
plt.savefig("out/radium_ionisation_diff." + SAVETYPE)
plt.clf()
plt.minorticks_on()
fit = Fit(LINEAR)
fit.set_data(xdata=(7.42, 6.92, 6.42),
ydata=currents[9:12],
xerrors=0.25,
yerrors=error_currents[9:12])
fit.set_labels(xlabel="Distanz / cm", ylabel="Strom / nA")
fit.iterative_fit(5)
fit.plot(box="tr", units={"slope": "nA/cm", "offset": "nA"})
plt.savefig("out/radium_ionisation_po_fit." + SAVETYPE)
plt.clf()
plt.minorticks_on()
fit.plot_residual(box="tl")
plt.savefig("out/radium_ionisation_po_residual." + SAVETYPE)
middle = (ufloat(currents[9], error_currents[9]) +
ufloat(currents[11], error_currents[11])) / 2
print("Middle:", middle, "nA")
r = (middle - fit.uvalue("offset")) / fit.uvalue("slope")
print("Range:", r, "cm")
def calc_radium_range():
peak = {
35: (1100, 1800),
35.5: (1000, 1700),
36: (900, 1600),
36.5: (800, 1500),
37: (600, 1400),
37.5: (500, 1200),
38: (300, 1000),
38.5: (100, 700)
}
distances = []
error_distances = []
integrals = []
error_integrals = []
for distanceStr in ("35_0", "35_5", "36_0", "36_5", "37_0", "37_5", "38_0",
"38_5"):
filename = "data/Radium%s.TKA" % distanceStr
distance = ufloat(float(distanceStr.replace("_", ".")), 0.05)
tka = TkaFile(filename)
lower, upper = peak[distance.n]
data = tka.data[lower:upper]
distance = distance - 35 + ufloat(3.17, 0.17)
integral = ufloat(data.sum(), math.sqrt((data + 1).sum()))
integral_fixed = integral * distance**2
print(
"$({:L}) \\unit{{cm}}$ & {:d} & {:d} & ${:dL}$ & ${:dL} \\unit{{cm^2}}$ \\\\"
.format(distance, lower, upper, integral, integral_fixed))
distances.append(distance.n)
error_distances.append(distance.s)
integrals.append(integral_fixed.n)
error_integrals.append(integral_fixed.s)
distances = np.array(distances)
integrals = np.array(integrals)
error_distances = np.array(error_distances)
error_integrals = np.array(error_integrals)
plt.clf()
plt.minorticks_on()
plt.errorbar(distances,
integrals,
xerr=error_distances,
yerr=error_integrals,
fmt="s")
#plt.plot(distances, integrals, 's')
plt.xlabel("Distanz / cm")
plt.ylabel("korrigierte Summe / cm^2")
plt.ylim(0, plt.ylim()[1])
plt.savefig("out/radium_range." + SAVETYPE)
#plt.show()
plt.clf()
plt.minorticks_on()
scale = 1 / integrals[0:3].mean()
fit = Fit(LINEAR)
fit.set_params(offset=1, slope=-0.5)
fit.set_data(xdata=distances[1:],
ydata=integrals[1:] * scale,
xerrors=error_distances[1:],
yerrors=error_integrals[1:] * scale)
fit.set_labels(xlabel="Distanz / cm", ylabel="Intensität")
fit.iterative_fit(5)
fit.plot(plot_data=True, plot_fit=True, box="bl", units={"slope": "1/cm"})
plt.ylim(0, plt.ylim()[1])
plt.savefig("out/radium_range_fit." + SAVETYPE)
plt.clf()
plt.minorticks_on()
fit.plot_residual(box="tr")
plt.savefig("out/radium_range_residual." + SAVETYPE)
r = (0.5 - fit.uvalue("offset")) / fit.uvalue("slope")
print("Range:", r, "cm")
def radium_calib_2():
E, proj_range = np.loadtxt("ranges.txt", unpack=True)
real_range = proj_range / 1.184e-3
energy_from_range = interp1d(real_range, E, kind='cubic')
energies = []
error_energies = []
for distance in (0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5):
distance = ufloat(35 + distance, 0.05)
total_distance = (distance - 35) + ufloat(3.17, 0.17)
for peak in (3.52, 4.99, 7.18):
peak = ufloat(peak, 0.01)
rest = peak - total_distance
try:
upper = energy_from_range(rest.n + rest.s)
lower = energy_from_range(rest.n - rest.s)
value = energy_from_range(rest.n)
except ValueError as e:
#print(e)
#print("orig distance:", peak, "cm ", "rest distance:", rest, "cm ")
pass
else:
error = max(upper - value, value - lower)
energy = ufloat(value, error)
#print("orig distance:", peak, "cm ", "total distance:", total_distance, "cm ", "rest distance:", rest, "cm ", "rest energy:", energy, "MeV")
print(
"$({:L}) \\unit{{cm}}$ & $({:L}) \\unit{{cm}}$ & $({:L}) \\unit{{cm}}$ & $({:L}) \\unit{{cm}}$ & $({:L}) \\unit{{MeV}}$ \\\\"
.format(peak, distance, total_distance, rest, energy))
energies.append(value)
error_energies.append(error)
# PART2 !!!
channels = [
220, 780, 1460, 620, 1340, 450, 1260, 150, 1170, 990, 820, 620, 390
]
error_channels = [20, 20, 20, 20, 20, 20, 20, 100, 20, 20, 20, 20, 30]
energies = energies[:len(channels)]
error_energies = error_energies[:len(channels)]
for energy, error_energy, channel, error_channel in zip(
energies, error_energies, channels, error_channels):
e = ufloat(energy, error_energy)
c = ufloat(channel, error_channel)
print("$({:L}) \\unit{{MeV}}$ & ${:L}$ \\\\".format(e, c))
fit = Fit(LINEAR)
fit.set_data(xdata=channels,
xerrors=error_channels,
ydata=energies,
yerrors=error_energies)
fit.set_labels(xlabel="Kanal", ylabel="Energie / MeV")
fit.iterative_fit(5)
plt.clf()
plt.minorticks_on()
fit.plot(box="tl",
units={
"slope": "keV/Kanal",
"offset": "MeV"
},
factors={"slope": 1000})
plt.savefig("out/radium_calib2_fit." + SAVETYPE)
plt.clf()
plt.minorticks_on()
fit.plot_residual(box="tr")
plt.savefig("out/radium_calib2_residual." + SAVETYPE)
def plot_ktp():
current, power, error_power = np.loadtxt("data/ktp_kristall.txt",
unpack=True)
error_current = 1 / math.sqrt(12)
# uW -> mW
power /= 1000
error_power /= 1000
plt.clf()
plt.errorbar(current,
power,
xerr=error_current,
yerr=error_power,
fmt=',',
color="black")
plt.xlabel("Strom / mA")
plt.ylabel("Leistung mit KTP / mW")
plt.xlim(0, 700)
plt.savefig("out/ktp_raw." + SAVETYPE)
lower = np.logical_and(current > 182.10, current < 410)
upper = current >= 410
diode_power, error_diode_power = current2diode_power(
current, error_current)
plt.clf()
plt.errorbar(diode_power,
power,
xerr=error_diode_power,
yerr=error_power,
fmt=',',
color="black")
plt.xlabel("Diodenleistung / mW")
plt.ylabel("Laserleistung mit KTP / mW")
plt.savefig("out/ktp_raw2." + SAVETYPE)
yag_power, error_yag_power = diode_power2yag_power(diode_power,
error_diode_power)
plt.clf()
plt.errorbar(yag_power,
power,
xerr=error_yag_power,
yerr=error_power,
fmt=',',
color="black")
plt.xlabel("Laserleistung ohne KTP / mW")
plt.ylabel("Laserleistung mit KTP / mW")
plt.xlim(0, 10)
plt.savefig("out/ktp_raw3." + SAVETYPE)
plt.clf()
fit = Fit(POLY2)
fit.set_data(xdata=yag_power,
ydata=power,
xerrors=error_yag_power,
yerrors=error_power)
fit.set_labels(xlabel="Laserleistung ohne KTP / mW",
ylabel="Laserleistung mit KTP / mW")
fit = fit.filtered(yag_power > 2)
fit.iterative_fit(5)
fit.plot(box="tl", units={"a2": "1/mW", "a0": "mW"})
plt.savefig("out/ktp_fit." + SAVETYPE)
plt.clf()
fit.plot_residual(box="tl")
plt.savefig("out/ktp_residual." + SAVETYPE)
def plot_yag_kennlinie():
current, power, error_power = np.loadtxt("data/kennlinie_yag2.txt",
unpack=True)
error_current = 1 / math.sqrt(12)
plt.clf()
plt.errorbar(current,
power,
xerr=error_current,
yerr=error_power,
fmt=',',
color="black")
plt.xlabel("Strom / mA")
plt.ylabel("Leistung / mW")
plt.xlim(0, 700)
plt.savefig("out/kennlinie_yag_raw." + SAVETYPE)
lower = np.logical_and(current > 182.10, current < 410)
upper = current >= 410
fit_indices_list = []
fit_indices_list.append(power > 0.10)
#fit_indices_list.append(np.logical_and(power > 0.10, lower))
#fit_indices_list.append(np.logical_and(power > 0.10, upper))
diode_power, error_diode_power = current2diode_power(
current, error_current)
zero_power = power[current < 150]
background = zero_power.mean()
print("Background:", background, "mW")
power -= background
plt.clf()
plt.errorbar(diode_power,
power,
xerr=error_diode_power,
yerr=error_power,
fmt=',',
color="black")
plt.xlabel("Diodenleistung / mW")
plt.ylabel("Laserleistung / mW")
plt.savefig("out/kennlinie_yag_raw2." + SAVETYPE)
func = lambda x, slope, threshold: (x - threshold) * slope
fit = Fit(func)
fit.set_params(slope=0.016, threshold=16)
fit.set_data(xdata=diode_power,
ydata=power,
xerrors=error_diode_power,
yerrors=error_power)
fit.set_labels(xlabel="Diodenleistung / mW", ylabel="Laserleistung / mW")
fit.iterative_fit(1)
plt.clf()
fit.plot(plot_data=True, plot_fit=True, box="tr")
plt.savefig("out/kennlinie_yag_linear_fit." + SAVETYPE)
plt.clf()
fit.plot_residual(box="br", fmt="s")
plt.savefig("out/kennlinie_yag_linear_residual." + SAVETYPE)
fit = Fit(POLY2)
fit.set_data(xdata=diode_power,
ydata=power,
xerrors=error_diode_power,
yerrors=error_power)
fit.set_labels(xlabel="Diodenleistung / mW", ylabel="Laserleistung / mW")
fit.iterative_fit(5)
for i, fit_indices in enumerate(fit_indices_list):
plt.clf()
fit.plot(plot_fit=False)
subfit = fit[fit_indices]
subfit.iterative_fit(5)
#zero_power = power[power < 0.03]
#zero = umean(zero_power)
#plt.axhline(zero.n, color="blue")
print(subfit)
x = 200
try:
i_threshold = solve_quadratic(subfit.uvalue("a0"),
subfit.uvalue("a1"),
subfit.uvalue("a2"))
i_slope = 2 * x * subfit.uvalue("a2") + subfit.uvalue("a1")
except ValueError:
print("no solution", i)
else:
print("Threshold:", formatUFloat(i_threshold, unit="mW"))
print("Efficiency:", formatUFloat(i_slope * 100, unit="%"))
lines = "threshold = " + formatUFloat(
i_threshold, unit="mW"
) + "\n" + "efficiency at %d mW = " % x + formatUFloat(
i_slope * 100, unit="%")
info_box(lines, location="tl")
subfit.plot(plot_data=False)
plt.savefig("out/kennlinie_yag_%d_fit." % i + SAVETYPE)
plt.clf()
subfit.plot_residual(box="br", color="black", fmt="s")
plt.savefig("out/kennlinie_yag_%d_residual." % i + SAVETYPE)
plt.clf()
x = diode_power[diode_power > i_threshold.n]
plt.plot(x,
100 * (2 * x * subfit.value("a2") + subfit.value("a1")),
color="black")
#x_new = diode_power - i_threshold.n
#plt.plot(diode_power, 100*(x_new*subfit.value("a2") + subfit.value("a1") + subfit.value("a0")/x_new), color="red")
plt.xlabel("Diodenleistung / mW")
plt.ylabel("Effizienz / %")
plt.savefig("out/kennlinie_yag_%d_efficiency." % i + SAVETYPE)
def plot_energy_spectra():
mus = []
widths = []
energies = []
#leer = TkaFile("data/EnergiespektrumLeer.TKA")
with LatexTable("out/calib_peaks.tex") as peaktable, LatexTable(
"out/rates.tex") as ratetable:
peaktable.header("El.",
"Höhe",
r"Channel $x_\textrm{max}$",
r"Breite $\Delta x$",
r'$\chi^2/\textrm{ndf}$',
"Energie / keV",
lineafter=1)
ratetable.header("El.", "Events", "Messzeit", "Rate")
for filename, meta in energy_spectra.items():
peaktable.hline()
tka = TkaFile("data/" + filename)
x = np.arange(len(tka))
#y = tka.data - leer.data
y = tka.data
#errors = np.sqrt(tka.data + leer.data + 2)
errors = np.sqrt(tka.data + 1)
plt.clf()
plt.plot(x, y, ',', color="black")
for i, (mu0, sigma0, energy,
sigma_energy) in enumerate(meta["peaks"], 1):
fit = local_fit(x, y, errors, mu=mu0, sigma=sigma0)
fit.plot(fit.mu - 5 * fit.sigma,
fit.mu + 5 * fit.sigma,
1000,
zorder=10000,
color="red")
mus.append((fit.mu, fit.error_mu))
if meta["element"] in ("Na", "Cs"):
E_gamma = 0.09863 * fit.mu - 19.056
m_electron = 511 # keV
E_compton = E_gamma / (1 + m_electron / (2 * E_gamma))
c_compton = (E_compton + 19.056) / 0.09863
plt.axvline(c_compton, color="red", linestyle="--")
peaktable.row((meta["element"], len(meta["peaks"])),
formatQuantityLatex(fit.A, fit.error_A),
formatQuantityLatex(fit.mu, fit.error_mu),
formatQuantityLatex(fit.sigma, fit.error_sigma),
"%.2f" % fit.chi2ndf,
formatQuantityLatex(energy, sigma_energy))
widths.append((fit.sigma, fit.error_sigma))
energies.append((energy, sigma_energy))
#print(meta["element"], i, fit)
plt.xlabel("Kanal")
plt.ylabel("Count")
plt.xlim(0, 2**14)
plt.title(meta["title"])
plt.savefig("out/" + clean_filename(filename) + "_all." + SAVETYPE)
N = ufloat(y.sum(), errors.sum())
t = ufloat(tka.real_time, 1 / math.sqrt(12))
m = N / t # Hz/Bq
r = ufloat(91.5, 0.01) # mm
A = ufloat(*meta["activity"]) * 1000 # Bq
I_g = 1
r = ufloat(15, 5)
F_D = ufloat(7.45, 0.05) * ufloat(80.75, 0.05) # mm^2
efficiency = 4 * math.pi * r**2 * m / (F_D * A * I_g)
print("Efficiency:", meta["element"], efficiency)
ratetable.row(meta["element"], formatUFloatLatex(N),
formatUFloatLatex(t, unit="s"),
formatUFloatLatex(m, unit="1/s"))
mus, error_mus = np.array(mus).T
widths, error_widths = np.array(widths).T
energies, error_energies = np.array(energies).T
# Kalibration
plt.clf()
fit = Fit(LINEAR)
fit.slope = 0.1
fit.offset = -20
for i in range(5):
errors = fit.combine_errors(mus, error_mus, error_energies)
fit.fit(mus, energies, errors)
plt.errorbar(mus,
energies,
xerr=error_mus,
yerr=error_energies,
fmt=',',
color="black")
fit.plot(box='tl',
units={
"slope": "eV / Channel",
"offset": "eV"
},
factors={
"slope": 1000,
"offset": 1000
},
color="red")
plt.xlabel("Kanal")
plt.ylabel("Energie / keV")
plt.savefig("out/calib_fit." + SAVETYPE)
plt.clf()
errs = fit.combine_errors(mus, xerr=error_mus, yerr=error_energies)
fit.plot_residual(mus, energies, errs, box='tl', fmt=',', color="black")
plt.xlabel("Kanal")
plt.ylabel("Energie / keV")
plt.savefig("out/calibresiduum." + SAVETYPE)
s = formatQuantityLatex(fit.slope * 1000,
fit.error_slope * 1000,
unit="eV / Kanal",
math=False)
o = formatQuantityLatex(fit.offset * 1000,
fit.error_offset * 1000,
unit="eV",
math=False)
with open('out/calib.tex', 'w') as file:
file.write(
r'Die in diesem Versuch verwendeten Einstellungen f\"uhren zu einer Einteilung von \[ '
+ s + r' \] wobei der erste Kanal die Energie \[ ' + o +
r' \] besitzt.')
# Energieauflösung
error_widths = np.sqrt(
np.power(fit.error_slope * widths, 2) +
np.power(error_widths * fit.slope, 2))
widths = widths * fit.slope
error_energies = np.sqrt(
np.power(fit.error_offset, 2) + np.power(mus * fit.error_slope, 2) +
np.power(fit.slope * error_mus, 2))
energies = fit.slope * mus + fit.offset
X = energies
Y = widths
SX = error_energies
SY = error_widths
func = lambda E, a, b: np.sqrt(np.power(a * E, 2) + np.power(b, 2) * E)
fit = Fit(func)
fit.a = 0.01
fit.b = 0.01
for _ in range(10):
err = fit.combine_errors(X, SX, SY)
fit.fit(X, Y, err)
plt.clf()
plt.errorbar(X, Y, xerr=SX, yerr=SY, fmt=',', color="black")
fit.plot(box='br', units={'b': r'\sqrt{\textrm{keV}}'}, color="red")
plt.xlabel(r"$ E $ / keV")
plt.ylabel(r"$ \Delta E / keV$")
plt.title(
r'Energieauflösung: Fit zu $ \Delta E = \sqrt{\left(a E\right)^2 + b^2 E} $'
)
plt.savefig("out/energyresolution_fit." + SAVETYPE)
print("a =", formatQuantity(fit.a, fit.error_a))
print("b =", formatQuantity(fit.b, fit.error_b))
plt.clf()
err = fit.combine_errors(X, SX, SY)
fit.plot_residual(X, Y, err, box='tr', fmt=",", color="black")
plt.xlabel(r"$ E $ / keV")
plt.ylabel(r"$ \Delta E / keV$")
plt.title("Energieauflösung: Residuen")
plt.savefig("out/energyresolution_residual." + SAVETYPE)
with LatexTable("out/energyresolution.tex") as table:
table.header("Parameter", "Wert")
table.row("$a$", formatQuantityLatex(fit.a, fit.error_a))
table.row("$b$",
formatQuantityLatex(fit.b, fit.error_b, unit="\sqrt{keV}"))
def plot_coincidence_co():
angle, count = np.loadtxt("data/winkel_cobalt3.txt", unpack=True)
error_angle = 0.3
error_count = np.sqrt(count + 1)
plt.clf()
plt.errorbar(angle,
count,
xerr=error_angle,
yerr=error_count,
fmt='s',
color="black")
W = lambda theta, A, a2, a4: A * (1 + a2 * np.power(
np.cos(np.radians(theta)), 2) + a4 * np.power(
np.cos(np.radians(theta)), 4))
fit = Fit(W)
fit.A = count.mean()
fit.a2 = 0
fit.a4 = 0
for i in range(5):
errors = fit.combine_errors(angle, error_angle, error_count)
fit.fit(angle, count, errors)
fit.plot(-90, 90, box="br", color="red")
plt.xlim(-90, 90)
plt.xlabel("Winkel / Grad")
plt.ylabel("Count")
plt.savefig("out/coincidence_co_fit." + SAVETYPE)
plt.clf()
fit.plot_residual(angle, count, errors, fmt="s", box="br", color="black")
plt.xlabel("Winkel / Grad")
plt.ylabel("Count")
plt.savefig("out/coincidence_co_residual." + SAVETYPE)
plt.clf()
plt.errorbar(angle,
count,
xerr=error_angle,
yerr=error_count,
fmt='s',
color="black")
fit = Fit(CONSTANT)
fit.c = count.mean()
for i in range(5):
errors = fit.combine_errors(angle, error_angle, error_count)
fit.fit(angle, count, errors)
fit.plot(-90, 90, box="br", color="red")
plt.xlim(-90, 90)
plt.xlabel("Winkel / Grad")
plt.ylabel("Count")
plt.savefig("out/coincidence_co_fitc." + SAVETYPE)
plt.clf()
fit.plot_residual(angle, count, errors, fmt="s", box="br", color="black")
plt.xlabel("Winkel / Grad")
plt.ylabel("Count")
plt.savefig("out/coincidence_co_residualc." + SAVETYPE)
def energieaufloesung(calibration, plot=True):
print("##### ENERGY RESOLUTION #####")
energies = []
widths = []
sigma_energies = []
sigma_widths = []
for filename, meta in kalib.items():
experiment = Experiment("data/" + filename,
title=meta["title"],
calibration=calibration)
for peak in meta["peaks"]:
mu0, sigma0 = peak[0], peak[1]
fit = experiment.find_peak(mu0, sigma0, plot=False)
energies.append(experiment.channel2energy(fit.mu))
widths.append(experiment.channelwidth2energywidth(fit.sigma))
sigma_energies.append(
experiment.channelwidth2energywidth(fit.sigma_mu))
sigma_widths.append(
experiment.channelwidth2energywidth(fit.sigma_sigma))
for filename, meta in data.items():
experiment = Experiment("data/" + filename,
title=filename,
calibration=calibration)
experiment.subtract_empty("data/G20_Leer.mca", 0.5)
for peak in meta["peaks"]:
mu0, sigma0 = peak[0], peak[1]
fit = experiment.find_peak(mu0, sigma0, plot=False)
energies.append(experiment.channel2energy(fit.mu))
widths.append(experiment.channelwidth2energywidth(fit.sigma))
sigma_energies.append(
experiment.channelwidth2energywidth(fit.sigma_mu))
sigma_widths.append(
experiment.channelwidth2energywidth(fit.sigma_sigma))
energies = np.array(energies)
widths = np.array(widths)
sigma_energies = np.array(sigma_energies)
sigma_widths = np.array(sigma_widths)
X = energies
Y = np.power(widths, 2)
SX = sigma_energies
SY = 2 * widths * sigma_widths
func = lambda x, a0, a1, : a0 + x * a1 #+np.power(x,2)*a2
fit = Fit(func)
fit.a0 = 1
fit.a1 = 1
for _ in range(10):
err = fit.combine_errors(X, SX, SY)
fit.fit(X, Y, err)
if plot:
plt.clf()
plt.errorbar(X, Y, xerr=SX, yerr=SY, fmt=',')
fit.plot(np.min(X),
np.max(X),
box='br',
units={
'a0': 'keV',
'a1': r'\sqrt{keV}'
})
plt.xlabel(r"$ E $ / keV")
plt.ylabel(r"$ \Delta E^2 / keV^2$")
plt.title(r'Energieauflösung: Fit zu $ \Delta E^2 = a_0 + a_1 E $'
) # \oplus \frac{c}{E}
plt.savefig("out/energyresolution_fit." + SAVETYPE)
plt.clf()
err = fit.combine_errors(X, SX, SY)
fit.plot_residuums(X, Y, err, box='tr', fmt=",")
plt.xlabel(r"$ E $ / keV")
plt.ylabel(r"$ \Delta E^2 / keV^2$")
plt.title("Energieauflösung: Residuen")
plt.savefig("out/energyresolution_residuum." + SAVETYPE)
with LatexTable("out/energyresolution.tex") as table:
table.header("Parameter", "Wert")
table.row("$a_0$", format_error(fit.a0, fit.sigma_a0, unit="keV^2"))
table.row("$a_1$", format_error(fit.a1, fit.sigma_a1, unit="keV"))
table.hline()
a = math.sqrt(fit.a0)
b = math.sqrt(fit.a1)
sa = 0.5 * fit.sigma_a0 / a
sb = 0.5 * fit.sigma_a1 / b
table.row("$a$", format_error(a, sa, unit="keV"))
table.row("$b$", format_error(b, sb, unit="\sqrt{keV}"))
with LatexTable("out/energyresolution_examples.tex") as table:
energies = np.linspace(10, 60, 6)
sigmas = np.sqrt(fit.apply(energies))
deltas = sigmas * 2 * math.sqrt(2 * math.log(2))
table.header("Energie",
"Auflösung",
"Relative Auflösung",
"FWHM",
lineafter=0)
table.row("$E$", "$\sigma$", "$\sigma / E$",
"$2 \sqrt{2 \ln{2}} \sigma$")
table.hline(2)
for energy, sigma, delta in zip(energies, sigmas, deltas):
e = "%d keV" % energy
s = _n(sigma * 1000) + " eV"
d = "%d eV" % (delta * 1000)
table.row(e, s, _n(sigma / energy * 100) + r"\%", d)