{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Modeling of the thickness of the sensor\n", "\n", "In this notebook we will re-use the experiment done at ID28 and previously calibrated and model in 3D the detector.\n", "\n", "This detector is a Pilatus 1M with a 450µm thick silicon sensor. Let's first have a look at the absorption coefficients of this sensor material: https://physics.nist.gov/PhysRefData/XrayMassCoef/ElemTab/z14.html\n", "\n", "First we retieve the results of the previous step, then calculate the absorption efficiency:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab nbagg" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "wavelength: 6.968e-11m,\t dist: 2.845e-01m,\t poni1: 8.865e-02m,\t poni2: 8.931e-02m,\t energy: 17.793keV\n" ] } ], "source": [ "import numpy\n", "import fabio, pyFAI, pyFAI.units, pyFAI.detectors, pyFAI.azimuthalIntegrator\n", "import json\n", "with open(\"id28.json\") as f:\n", " calib = json.load(f)\n", "\n", "thickness = 450e-6\n", "wavelength = calib[\"wavelength\"]\n", "dist = calib[\"param\"][calib['param_names'].index(\"dist\")]\n", "poni1 = calib[\"param\"][calib['param_names'].index(\"poni1\")]\n", "poni2 = calib[\"param\"][calib['param_names'].index(\"poni2\")]\n", "energy = pyFAI.units.hc/(wavelength*1e10)\n", "print(\"wavelength: %.3em,\\t dist: %.3em,\\t poni1: %.3em,\\t poni2: %.3em,\\t energy: %.3fkeV\" % \n", " (wavelength, dist, poni1, poni2, energy))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Absorption coeficient at 17.8 keV" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "µ = 1537.024174 m^-1 hence absorption efficiency for 450µm: 49.9 %\n" ] } ], "source": [ "# density from https://en.wikipedia.org/wiki/Silicon\n", "rho = 2.3290 # g/cm^3\n", "\n", "#Absorption from https://physics.nist.gov/PhysRefData/XrayMassCoef/ElemTab/z14.html\n", "# Nota: enegies are in MeV !\n", "Si_abs = \"\"\"\n", " 2.00000E-03 2.777E+03 2.669E+03 \n", " 3.00000E-03 9.784E+02 9.516E+02 \n", " 4.00000E-03 4.529E+02 4.427E+02 \n", " 5.00000E-03 2.450E+02 2.400E+02 \n", " 6.00000E-03 1.470E+02 1.439E+02 \n", " 8.00000E-03 6.468E+01 6.313E+01 \n", " 1.00000E-02 3.389E+01 3.289E+01 \n", " 1.50000E-02 1.034E+01 9.794E+00 \n", " 2.00000E-02 4.464E+00 4.076E+00 \n", " 3.00000E-02 1.436E+00 1.164E+00 \n", " 4.00000E-02 7.012E-01 4.782E-01 \n", " 5.00000E-02 4.385E-01 2.430E-01 \n", " 6.00000E-02 3.207E-01 1.434E-01 \n", " 8.00000E-02 2.228E-01 6.896E-02 \n", " 1.00000E-01 1.835E-01 4.513E-02 \n", " 1.50000E-01 1.448E-01 3.086E-02 \n", " 2.00000E-01 1.275E-01 2.905E-02 \n", " 3.00000E-01 1.082E-01 2.932E-02 \n", " 4.00000E-01 9.614E-02 2.968E-02 \n", " 5.00000E-01 8.748E-02 2.971E-02 \n", " 6.00000E-01 8.077E-02 2.951E-02 \n", " 8.00000E-01 7.082E-02 2.875E-02 \n", " 1.00000E+00 6.361E-02 2.778E-02 \n", " 1.25000E+00 5.688E-02 2.652E-02 \n", " 1.50000E+00 5.183E-02 2.535E-02 \n", " 2.00000E+00 4.480E-02 2.345E-02 \n", " 3.00000E+00 3.678E-02 2.101E-02 \n", " 4.00000E+00 3.240E-02 1.963E-02 \n", " 5.00000E+00 2.967E-02 1.878E-02 \n", " 6.00000E+00 2.788E-02 1.827E-02 \n", " 8.00000E+00 2.574E-02 1.773E-02 \n", " 1.00000E+01 2.462E-02 1.753E-02 \n", " 1.50000E+01 2.352E-02 1.746E-02 \n", " 2.00000E+01 2.338E-02 1.757E-02 \"\"\"\n", "data = numpy.array([[float(i) for i in line.split()] for line in Si_abs.split(\"\\n\") if line])\n", "energy_tab, mu_over_rho, mu_en_over_rho = data.T\n", "abs_18 = numpy.interp(energy, energy_tab*1e3, mu_en_over_rho) \n", "mu = abs_18*rho*1e+2\n", "eff = 1.0-numpy.exp(-mu*thickness)\n", "\n", "print(\"µ = %f m^-1 hence absorption efficiency for 450µm: %.1f %%\"%(mu, eff*100))\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "application/javascript": [ "/* Put everything inside the global mpl namespace */\n", "window.mpl = {};\n", "\n", "\n", "mpl.get_websocket_type = function() {\n", " if (typeof(WebSocket) !== 'undefined') {\n", " return WebSocket;\n", " } else if (typeof(MozWebSocket) !== 'undefined') {\n", " return MozWebSocket;\n", " } else {\n", " alert('Your browser does not have WebSocket support. ' +\n", " 'Please try Chrome, Safari or Firefox ≥ 6. 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But before saving it, it makes sense to spend some time in generating a high quality sparse matrix in throwing thousand rays per pixel in a grid of 32x32." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 3min 51s, sys: 949 ms, total: 3min 52s\n", "Wall time: 3min 50s\n" ] } ], "source": [ "%time pre_csr = thick.calc_csr(32)\n", "hq_csr = csr_matrix(pre_csr)\n", "from scipy.sparse import save_npz\n", "save_npz(\"csr.npz\",hq_csr)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }