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‎tutorials/3-advanced-topics/DTAT399E_backend.mie.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# deeptrack.backend.mie\n",
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"\n",
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"<a href=\"https://colab.research.google.com/github/DeepTrackAI/DeepTrack2/blob/develop/tutorials/3-advanced-topics/DTAT399E_backend.mie.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# !pip install deeptrack # Uncomment if running on Colab/Kaggle."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"This advanced tutorial introduces the backend.mie module."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## 1. What is `mie`?\n",
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"\n",
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"The `mie` module provides functions to perform Mie scattering calculations, including computation of spherical harmonics coefficients and related operations."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## 2. Calculate Mie Coefficients for a Solid Particle\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"from deeptrack.backend import mie\n",
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"\n",
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"\n",
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"particle_radius = 0.5\n",
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"relative_refract_index = 1.5 + 0.01j\n",
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"max_order = 5\n",
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"\n",
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"A, B = mie.coefficients(relative_refract_index, particle_radius, max_order)\n",
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"\n",
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"print(\"A coefficients:\", A)\n",
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"print(\"B coefficients:\", B)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## 2. Calculate Mie Coefficients for a Stratified Particle\n",
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"Here we only need to specify multiple radii for the different shells of the stratified particle."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"particle_radii = [0.5, 0.6, 0.7]\n",
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"relative_refract_index = 1.5 + 0.01j\n",
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"max_order = 5\n",
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"\n",
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"A, B = mie.stratified_coefficients(relative_refract_index, particle_radii, max_order)\n",
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"\n",
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"print(\"A coefficients:\", A)\n",
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"print(\"B coefficients:\", B)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## 3. Calculate Spherical Harmonics of the Mie Field "
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"(5, 100)\n",
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"(5, 100)\n"
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]
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},
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{
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"data": {
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"text/plain": [
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"(-0.5, 99.5, 4.5, -0.5)"
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]
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},
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"execution_count": 21,
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"metadata": {},
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"output_type": "execute_result"
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},
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{
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"data": {
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"image/png": "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",
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"text/plain": [
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"<Figure size 1000x1000 with 2 Axes>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"import numpy as np\n",
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"from matplotlib import pyplot as plt\n",
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"\n",
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"\n",
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"x = np.linspace(-1, 1, 100)\n",
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"L = 5\n",
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"pi, tau = mie.harmonics(x, L)\n",
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"\n",
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"print(pi.shape)\n",
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"print(tau.shape)\n",
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"\n",
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"fig, axes = plt.subplots(1, 2, figsize=(10, 10))\n",
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"\n",
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"axes[0].imshow(tau, cmap='viridis') \n",
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"axes[0].set_title('Tau')\n",
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"axes[0].axis('off') \n",
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"\n",
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"axes[1].imshow(pi, cmap='viridis') \n",
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"axes[1].set_title('Pi')\n",
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"axes[1].axis('off') "
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": ".venv",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.10.12"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}

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