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par[0]; + const double n2 = par[1]; + const double deltaTheta = par[2]; + + const double theta1 = (xx[0] - deltaTheta) / 180 * TMath::Pi(); + + const double theta2 = TMath::ASin(n1 / n2 * TMath::Sin(theta1)); + + return (n1 * cos(theta2) - n2 * cos(theta1)) / (n1 * cos(theta2) + n2 * cos(theta1)); +} + +// Ampiezza riflessa con polarizzazione sigma +inline double r_sigma(double *xx,double *par) { + const double n1 = par[0]; + const double n2 = par[1]; + const double deltaTheta = par[2]; + + const double theta1 = (xx[0] - deltaTheta) / 180 * TMath::Pi(); + + const double theta2 = TMath::ASin(n1 / n2 * TMath::Sin(theta1)); + + return (n1 * cos(theta1) - n2 * cos(theta2)) / (n1 * cos(theta1) + n2 * cos(theta2)); +} + +// Intensità riflessa con polarizzazione pi +inline double R_pi(double *xx,double *par) { + const double I_0 = par[3]; + + return I_0 * pow(r_pi(xx, par), 2); +} + +// Ampiezza riflessa con polarizzazione sigma +inline double R_sigma(double *xx,double *par) { + const double I_0 = par[3]; + + return I_0 * pow(r_sigma(xx, par), 2); +} + +//double T_p2(double *xx,double *par) { +// return 1 - R_p2(xx, par); +//} +// +//double T_s2(double *xx,double *par) { +// return 1 - R_s2(xx, par); + +#endif // define FUNCTIONS_HPP diff --git a/code/fitting/ROOT/graphs.hpp b/code/fitting/ROOT/graphs.hpp new file mode 100644 index 0000000..21e8560 --- /dev/null +++ b/code/fitting/ROOT/graphs.hpp @@ -0,0 +1,7 @@ +#ifndef GRAPHS_HPP +#define GRAPHS_HPP + +inline TGraphErrors* R_pi_raw_graph; +inline TGraphErrors* R_sigma_raw_graph; + +#endif // define GRAPHS_HPP diff --git a/code/fitting/ROOT/macro.cpp b/code/fitting/ROOT/macro.cpp new file mode 100644 index 0000000..8d12abe --- /dev/null +++ b/code/fitting/ROOT/macro.cpp @@ -0,0 +1,62 @@ +#include "functions.hpp" +#include "graphs.hpp" + +void macro() { + gStyle->SetOptFit(111111); + + cv = new TCanvas("rawdata", "Raw Data"); + cv->Divide(2, 2); + + cv->cd(1); + R_pi_raw_graph = new TGraphErrors("../../data/pi/run3-adjusted.csv", "%lg %lg %lg %lg", " "); + R_pi_raw_graph->Draw(); + + R_pi_raw_fun = new TF1("R_pi_raw_fun", R_pi, 0, 90, 4); + R_pi_raw_fun->SetParNames("$n_1$", "$n_2$", "$$\\Delta\\theta$$", "$$I_0$$"); + R_pi_raw_fun->SetParameters(1, 1.519, 0, 1000); + R_pi_raw_fun->SetParLimits(0, 1, 1); + R_pi_raw_fun->SetParLimits(2, -0.00001, 0.00001); + R_pi_raw_fun->Draw("same"); + R_pi_raw_graph->Fit(R_pi_raw_fun); + + cv->cd(3); + ifstream ifs("../../data/pi/run3-adjusted.csv"); + int npoints = 38; + double x[npoints]; + double y[npoints]; + for (int i = 0; i < npoints; ++i) { + double _; + ifs >> x[i] >> y[i] >> _ >> _; + y[i] -= R_pi_raw_fun->Eval(x[i]); + } + auto pi_residual = new TGraph(npoints, x, y); + pi_residual->Draw(); + + // Sigma polarisation //////////////////////////////////////////////////////// + cv->cd(2); + R_sigma_raw_graph = new TGraphErrors("../../data/sigma/run1-adjusted.csv", "%lg %lg %lg %lg"); + R_sigma_raw_graph->Draw(); + + R_sigma_raw_fun = new TF1("R_sigma_raw_fun", R_sigma, 0, 90, 4); + R_sigma_raw_fun->SetParNames("$n_1$", "$n_2$", "$$\\Delta\\theta$$", "$$I_0$$"); + R_sigma_raw_fun->SetParameters(1, 1.519, 0, 1000); + R_sigma_raw_fun->SetParLimits(0, 1, 1); + R_sigma_raw_fun->SetParLimits(2, -0.00001, 0.00001); + R_sigma_raw_fun->Draw("same"); + R_sigma_raw_graph->Fit(R_sigma_raw_fun); + + cv->cd(4); + ifs.close(); + ifs.open("../../data/sigma/run1-adjusted.csv"); + for (int i = 0; i < npoints; ++i) { + double _; + ifs >> x[i] >> y[i] >> _ >> _; + y[i] -= R_sigma_raw_fun->Eval(x[i]); + } + auto sigma_resiudal = new TGraph(npoints, x, y); + sigma_resiudal->Draw(); +} + + + + diff --git a/code/fitting/chi-square.py b/code/fitting/chi-square.py new file mode 100644 index 0000000..4f3e1d5 --- /dev/null +++ b/code/fitting/chi-square.py @@ -0,0 +1,55 @@ +from math import pi, cos, asin, sin + +n2_pi = 1.493 +n2_sigma = 1.490 + +I_0pi = 2550 +I_0sigma = 1340 + +a = 0.29 +theta_brewster = 56.8 + +def R_pi(x): + theta1 = x / 180 * pi + theta2 = asin(1 / n2_pi * sin(theta1)) + + r_pi = (1 * cos(theta2) - n2_pi * cos(theta1)) / (1 * cos(theta2) + n2_pi * cos(theta1)) + return I_0pi * (r_pi ** 2) + +def R_sigma(x): + theta1 = x / 180 * pi + theta2 = asin(1 / n2_pi * sin(theta1)) + + r_sigma = (1 * cos(theta1) - n2_sigma * cos(theta2)) / (1 * cos(theta1) + n2_sigma * cos(theta2)) + return I_0sigma * (r_sigma ** 2) + +def D(func, x): + return (func(x+0.0000001) - func(x-0.0000001)) / 0.0000002 + +def parabola(x): + return a*((x - theta_brewster)**2) + +def calc_chisquare(xs, ys, delta_xs, delta_ys, func): + delta_y1s = [delta_xs * D(func, x) for x, delta_xs in zip(xs, delta_xs)] + delta_ys_corrected = [dy + dy1 for dy, dy1 in zip(delta_ys, delta_y1s)] + os = [func(x) for x in xs] + chi_square = sum([((e - o) / dyc)**2 for e, o, dyc in zip(ys, os, delta_ys_corrected)]) + return chi_square + + +datasets = ["./data/pi/run3-adjusted.csv", "./data/sigma/run1-adjusted.csv", "./data/pi/run3-parabola.csv"] +funcs = [R_pi, R_sigma, parabola] +constraints = [2, 2, 2] +for dataset, func, constraints in zip(datasets, funcs, constraints): + xs = [] + ys = [] + delta_xs = [] + delta_ys = [] + with open(dataset) as file: + for line in file: + x, y, dx, dy = line.split() + xs.append(float(x)) + ys.append(float(y)) + delta_xs.append(0) # float(dx)) we don't want to recalculate this. + delta_ys.append(float(dy)) + print(dataset, calc_chisquare(xs, ys, delta_xs, delta_ys, func) / (len(xs) - constraints)) diff --git a/code/fitting/error-estimate.xlsx b/code/fitting/error-estimate.xlsx new file mode 100644 index 0000000..30378c4 Binary files /dev/null and b/code/fitting/error-estimate.xlsx differ diff --git a/code/fitting/fit-parabola.nb b/code/fitting/fit-parabola.nb new file mode 100644 index 0000000..cf02267 --- /dev/null +++ b/code/fitting/fit-parabola.nb @@ -0,0 +1,99 @@ +Notebook[{Cell[ +CellGroupData[{Cell[ 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Data logged with _Python_. Parameters: `step = 5°`. - [run3.csv](pi/run3.csv): third run with lab equipment. Data logged with _Python_. Parameters: `step = 2°`. - [run3-manual.csv](pi/run3-manual.csv): third run with lab equipment. Data logged by hand. Parameters: `step = 2°`. +- [run3-adjusted.csv](pi/run3-adjusted.csv): Adjusted third run, accounting for errors on the y-axis and initial + angle offset (`7°`). Part of this data (tail, from `31°` included) is taken from `run3.csv`. The + rest is taken from `run3-manual.csv`, to account for (most likely) corrupted data. +- [run3-parabola.csv](pi/run3-parabola.csv): Data used for parabolic fit of Brewster's angle. Taken from `run3-adjusted.csv` +- [run3-normalised.csv](pi/run3-normalised.csv): Normalised data from `run3-adjusted.csv` using best fit from Mathematica. ### sigma - [sim.csv](sigma/sim.csv): simulated data with parameters: `n1 = 1`, `n2 = 1.509`, `I_0 = 950`. -- [run1.csv](sigma/run1-manual.csv): first run with lab equipment. Data logged with _Python_. Parameters: `step = 2°`. -- [run3-manual.csv](pisigma/run1-manual.csv): third run with lab equipment. Data logged by hand. Parameters: `step = 2°`. +- [run1.csv](sigma/run1-adjusted.csv): first run with lab equipment. Data logged with _Python_. Parameters: `step = 2°`. +- [run1-manual.csv](sigma/run1-manual.csv): first run with lab equipment. Data logged by hand. Parameters: `step = + 2°`. +- [run1-adjusted.csv](sigma/run1-manual.csv): Adjusted first run, accounting for errors on the y-axis and initial + angle offset (`7°`). +- [run1-normalised.csv](pi/run1-normalised.csv): Normalised data from `run1-adjusted.csv` using best fit from Mathematica. diff --git a/data/pi/run3-adjusted.csv b/data/pi/run3-adjusted.csv new file mode 100644 index 0000000..cb275d3 --- /dev/null +++ b/data/pi/run3-adjusted.csv @@ -0,0 +1,38 @@ +83 934.2 0.5 14.5 +81 708.5 0.5 12.7 +79 518.9 0.5 11.2 +77 399.1 0.5 10.2 +75 278.3 0.5 9.2 +73 194.1 0.5 8.6 +71 134.5 0.5 8.1 +69 76.5 0.5 7.6 +67 50.1 0.5 7.4 +65 20.5 0.5 7.2 +63 12 0.5 7.1 +61 2.2 0.5 7.0 +59 0 0.5 7.0 +57 0 0.5 7.0 +55 2.29 0.5 7.0 +53 6.3 0.5 7.1 +51 8.1 0.5 7.1 +49 18.1 0.5 7.1 +47 22.2 0.5 7.2 +45 28.5 0.5 7.2 +43 33.1 0.5 7.3 +41 40.9 0.5 7.3 +39 45.7 0.5 7.4 +37 51.2 0.5 7.4 +35 53.6 0.5 7.4 +33 58.9 0.5 7.5 +31 64.8 0.5 7.5 +29 70 0.5 7.6 +27 72 0.5 7.6 +25 74 0.5 7.6 +23 76 0.5 7.6 +21 79 0.5 7.6 +19 81 0.5 7.6 +17 85 0.5 7.7 +15 86 0.5 7.7 +13 85 0.5 7.7 +11 87 0.5 7.7 +09 90 0.5 7.7 diff --git a/data/pi/run3-normalised.csv b/data/pi/run3-normalised.csv new file mode 100644 index 0000000..1dba960 --- /dev/null +++ b/data/pi/run3-normalised.csv @@ -0,0 +1,38 @@ +83 0.3661 0.5 0.0057 +81 0.2777 0.5 0.0050 +79 0.2034 0.5 0.0044 +77 0.1564 0.5 0.0040 +75 0.1091 0.5 0.0036 +73 0.0761 0.5 0.0034 +71 0.0527 0.5 0.0032 +69 0.0300 0.5 0.0030 +67 0.0196 0.5 0.0029 +65 0.0080 0.5 0.0028 +63 0.0047 0.5 0.0028 +61 0.0009 0.5 0.0027 +59 0.0000 0.5 0.0027 +57 0.0000 0.5 0.0027 +55 0.0009 0.5 0.0027 +53 0.0025 0.5 0.0028 +51 0.0032 0.5 0.0028 +49 0.0071 0.5 0.0028 +47 0.0087 0.5 0.0028 +45 0.0112 0.5 0.0028 +43 0.0130 0.5 0.0029 +41 0.0160 0.5 0.0029 +39 0.0179 0.5 0.0029 +37 0.0201 0.5 0.0029 +35 0.0210 0.5 0.0029 +33 0.0231 0.5 0.0029 +31 0.0254 0.5 0.0029 +29 0.0274 0.5 0.0030 +27 0.0282 0.5 0.0030 +25 0.0290 0.5 0.0030 +23 0.0298 0.5 0.0030 +21 0.0310 0.5 0.0030 +19 0.0317 0.5 0.0030 +17 0.0333 0.5 0.0030 +15 0.0337 0.5 0.0030 +13 0.0333 0.5 0.0030 +11 0.0341 0.5 0.0030 +9 0.0353 0.5 0.0030 diff --git a/data/pi/run3-parabola.csv b/data/pi/run3-parabola.csv new file mode 100644 index 0000000..40aea6b --- /dev/null +++ b/data/pi/run3-parabola.csv @@ -0,0 +1,9 @@ +65 20.5 0.5 7.2 +63 12 0.5 7.1 +61 2.2 0.5 7.0 +59 0 0.5 7.0 +57 0 0.5 7.0 +55 2.29 0.5 7.0 +53 6.3 0.5 7.1 +51 8.1 0.5 7.1 +49 18.1 0.5 7.1 diff --git a/data/sigma/run1-adjusted.csv b/data/sigma/run1-adjusted.csv new file mode 100644 index 0000000..72c9534 --- /dev/null +++ b/data/sigma/run1-adjusted.csv @@ -0,0 +1,38 @@ +83 830 0.5 13.6 +81 753 0.5 13.0 +79 705 0.5 12.6 +77 619 0.5 12.0 +75 549 0.5 11.4 +73 483 0.5 10.9 +71 434 0.5 10.5 +69 379 0.5 10.0 +67 344 0.5 9.8 +65 305 0.5 9.4 +63 272 0.5 9.2 +61 237 0.5 8.9 +59 207 0.5 8.7 +57 188 0.5 8.5 +55 172 0.5 8.4 +53 159 0.5 8.3 +51 144 0.5 8.2 +49 129 0.5 8.0 +47 119 0.5 8.0 +45 110 0.5 7.9 +43 103 0.5 7.8 +41 96 0.5 7.8 +39 92 0.5 7.7 +37 88 0.5 7.7 +35 86 0.5 7.7 +33 82 0.5 7.7 +31 77 0.5 7.6 +29 73 0.5 7.6 +27 69 0.5 7.6 +25 65 0.5 7.5 +23 64 0.5 7.5 +21 63 0.5 7.5 +19 63 0.5 7.5 +17 61 0.5 7.5 +15 59 0.5 7.5 +13 58 0.5 7.5 +11 58 0.5 7.5 +09 58 0.5 7.5 diff --git a/data/sigma/run1-normalised.csv b/data/sigma/run1-normalised.csv new file mode 100644 index 0000000..17446fe --- /dev/null +++ b/data/sigma/run1-normalised.csv @@ -0,0 +1,38 @@ +83 0.6156 0.5 0.0101 +81 0.5585 0.5 0.0096 +79 0.5229 0.5 0.0093 +77 0.4591 0.5 0.0089 +75 0.4072 0.5 0.0085 +73 0.3583 0.5 0.0081 +71 0.3219 0.5 0.0078 +69 0.2811 0.5 0.0074 +67 0.2552 0.5 0.0073 +65 0.2262 0.5 0.0070 +63 0.2018 0.5 0.0068 +61 0.1758 0.5 0.0066 +59 0.1535 0.5 0.0065 +57 0.1394 0.5 0.0063 +55 0.1276 0.5 0.0062 +53 0.1179 0.5 0.0062 +51 0.1068 0.5 0.0061 +49 0.0957 0.5 0.0059 +47 0.0883 0.5 0.0059 +45 0.0816 0.5 0.0059 +43 0.0764 0.5 0.0058 +41 0.0712 0.5 0.0058 +39 0.0682 0.5 0.0057 +37 0.0653 0.5 0.0057 +35 0.0638 0.5 0.0057 +33 0.0608 0.5 0.0057 +31 0.0571 0.5 0.0056 +29 0.0541 0.5 0.0056 +27 0.0512 0.5 0.0056 +25 0.0482 0.5 0.0056 +23 0.0475 0.5 0.0056 +21 0.0467 0.5 0.0056 +19 0.0467 0.5 0.0056 +17 0.0452 0.5 0.0056 +15 0.0438 0.5 0.0056 +13 0.0430 0.5 0.0056 +11 0.0430 0.5 0.0056 +9 0.0430 0.5 0.0056 diff --git a/data/sigma/run1.txt b/data/sigma/run1.csv similarity index 100% rename from data/sigma/run1.txt rename to data/sigma/run1.csv