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@rfrazier716
Last active February 2, 2023 18:56
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Imager Optimization"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Function Imports and Definitions"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import pyrayt\n",
"from pyrayt import components\n",
"import pyrayt.materials as matl\n",
"from pyrayt.utils import lensmakers_equation\n",
"import numpy as np\n",
"import matplotlib\n",
"import matplotlib.pyplot as plt\n",
"import scipy\n",
"import scipy.optimize\n",
"from typing import Tuple\n",
"from tinygfx.g3d import ObjectGroup\n",
"import pandas as pd\n",
"from tinygfx.g3d.renderers import draw\n",
"\n",
"font = {'family' : 'sans',\n",
" 'size' : 14}\n",
"\n",
"matplotlib.rc('font', **font)\n",
"\n",
"def init_figure() -> Tuple[plt.Figure, plt.Axes]:\n",
" \"\"\"\n",
" Convenience Function for generating figure with gridlines\n",
" \"\"\"\n",
" \n",
" fig = plt.figure(figsize = (12,8))\n",
" axis = plt.gca()\n",
" axis.grid()\n",
" return fig, axis"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## System Constants"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"# All spatial units are mm\r\n",
"lens_diameter = 25.4\r\n",
"lens_thickness = 5\r\n",
"system_focus = 50 # The focus of the system\r\n",
"p_sys = 1/system_focus\r\n",
"f_num = 2.4"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## A Single Lens Imager"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Creating a simple Lens \r\n",
"lens_material = matl.glass[\"BK7\"]\r\n",
"lens_radius = 2*(lens_material.index_at(0.532)-1)/p_sys\r\n",
"lens = pyrayt.components.thick_lens(\r\n",
" r1=lens_radius, \r\n",
" r2=-lens_radius,\r\n",
" thickness=lens_thickness,\r\n",
" aperture=lens_diameter,\r\n",
" material=lens_material)\r\n",
"\r\n",
"draw(lens)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"# Creating the Imager\r\n",
"imager = components.baffle((lens_diameter, lens_diameter)).move_x(system_focus)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"# Creating the Aperture\r\n",
"aperture_position = system_focus / 2 # place it half way between the lens and the imager\r\n",
"aperture_diameter = aperture_position / f_num\r\n",
"aperture = components.aperture(\r\n",
" size=(lens_diameter, lens_diameter), \r\n",
" aperture_size=aperture_diameter\r\n",
" ).move_x(aperture_position)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Create a Parallel ray set\r\n",
"source = components.LineOfRays(0.8*lens_diameter, wavelength = 0.633).move_x(-10)\r\n",
"\r\n",
"tracer = pyrayt.RayTracer(source, [lens, aperture, imager])\r\n",
"tracer.set_rays_per_source(11)\r\n",
"results = tracer.trace()\r\n",
"fig, axis = init_figure()\r\n",
"\r\n",
"tracer.show(\r\n",
" #color_function=\"source\",\r\n",
" ray_width=0.2,\r\n",
" axis=axis,\r\n",
" view='xy')\r\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Spherical Aberrations"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"def spherical_aberration(system, ray_origin: float, max_radius:float, sample_points=11):\r\n",
"\r\n",
" # the souce is a line of rays only on the +y axis. It's slightly shifted so zero is not a point\r\n",
" # as it would focus at infinity\r\n",
" source = pyrayt.components.LineOfRays(0.9*max_radius).move_x(ray_origin).move_y(max_radius/2)\r\n",
"\r\n",
"\r\n",
" tracer = pyrayt.RayTracer(source, system)\r\n",
" tracer.set_rays_per_source(sample_points)\r\n",
" results = tracer.trace()\r\n",
"\r\n",
" # Since we don't have the actual imager as a variable in the function\r\n",
" # assume it is the last thing a ray intersect with, meaning the rays that hit it have the \r\n",
" # highest generation\r\n",
" imager_rays = results.loc[results['generation'] == np.max(results['generation'])]\r\n",
" \r\n",
" # Intercept is calculated using the tilt for each ray, with is a normalized vector representing\r\n",
" # the direction the ray is travelling\r\n",
" intercept = -imager_rays['x_tilt']*imager_rays['y0']/imager_rays['y_tilt'] + imager_rays['x0']\r\n",
"\r\n",
" # the original radii \r\n",
" radii = results.loc[np.logical_and(results['generation']==0, results['id'].isin(imager_rays['id']))]['y0']\r\n",
"\r\n",
" # create a new dataframe with the aberration metrics\r\n",
" results = pd.DataFrame({'radius': np.asarray(radii), 'focus': np.asarray(intercept)})\r\n",
" return results\r\n",
"\r\n"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"aberrations = spherical_aberration([lens, aperture, imager], -10, 0.4*lens_diameter, 21)\r\n",
"\r\n",
"fig, axis = init_figure()\r\n",
"axis.set_title(\"Focal Length vs. Beam Radius for a single-lens imager\")\r\n",
"axis.plot(aberrations['radius'], aberrations['focus'])\r\n",
"axis.set_xlabel(\"Beam Radius (mm)\")\r\n",
"axis.set_ylabel(\"Focal Length (mm)\")\r\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Chromatic Aberrations"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"def chromatic_abberation(system, ray_origin: float, test_radius:float, wavelengths: np.ndarray) -> pd.DataFrame:\r\n",
" # create a set of sources for every wavelength of light\r\n",
" sources = [\r\n",
" pyrayt.components.LineOfRays(0, wavelength = wave)\r\n",
" .move_y(test_radius)\r\n",
" .move_x(ray_origin) \r\n",
" for wave in wavelengths]\r\n",
" \r\n",
" # Create the ray tracer and propagate\r\n",
" tracer = pyrayt.RayTracer(sources, system)\r\n",
" tracer.set_rays_per_source(1)\r\n",
" results = tracer.trace()\r\n",
"\r\n",
" #filter the rays that intersect the imager\r\n",
" imager_rays = results.loc[results['generation'] == np.max(results['generation'])]\r\n",
" \r\n",
" # calculate intercept of the imager rays with the x-axis and form into a dataframe\r\n",
" intercept = -imager_rays['x_tilt']*imager_rays['y0']/imager_rays['y_tilt'] + imager_rays['x0']\r\n",
" results = pd.DataFrame({'wavelength': imager_rays['wavelength'], 'focus': intercept})\r\n",
"\r\n",
"\r\n",
" return results\r\n",
"\r\n"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"aberrations = chromatic_abberation([lens, aperture, imager], -10, lens_diameter/4, np.linspace(0.45, 0.75, 11))\r\n",
"\r\n",
"fig, axis = init_figure()\r\n",
"axis.set_title(\"Focal Length vs. wavelength for a single-lens imager\")\r\n",
"axis.plot(1000*aberrations['wavelength'], aberrations['focus'])\r\n",
"axis.set_xlabel(\"Beam Radius (mm)\")\r\n",
"axis.set_ylabel(\"wavelength (nm)\")\r\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Coma Aberration"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"source = pyrayt.components.LineOfRays(0.9 * lens_diameter).move_x(-12)\n",
"tracer = pyrayt.RayTracer(source, [lens, imager])\n",
"tracer.set_rays_per_source(11)\n",
"fig, axis = init_figure()\n",
"axis.set_xlabel(\"(mm)\")\n",
"axis.set_ylabel(\"(mm)\")\n",
"axis.set_title(\"Coma of a Lens shifted by 12 Degrees\")\n",
"\n",
"with pyrayt.pin(lens):\n",
" lens.rotate_z(12)\n",
" tracer.trace()\n",
" tracer.show(\n",
" axis=axis,\n",
" ray_width=0.15\n",
" )"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Create a system \n",
"source = pyrayt.components.LineOfRays(0.9 * lens_diameter).move_x(-10)\n",
"tracer = pyrayt.RayTracer(source, [lens, imager])\n",
"tracer.set_rays_per_source(1001)\n",
"angles = (12,6,0)\n",
"fig, axis = init_figure()\n",
"\n",
"for n,angle in enumerate(angles):\n",
" with pyrayt.pin(lens):\n",
" # pin the lens in place so its rotation resets between iterations\n",
" lens.rotate_z(angle)\n",
" results = tracer.trace()\n",
" imager_rays = results.loc[results['generation'] == np.max(results['generation'])]\n",
" axis.hist(imager_rays['y1'], bins=21, label = f\"{angle}-degree incidence\", density=True, alpha=0.8)\n",
" \n",
"# plot labels\n",
"axis.set_xlabel(\"position along Y-axis (mm)\")\n",
"axis.set_ylabel(\"density (AU)\")\n",
"axis.set_label(\"Focal Spot Distribution vs. Angle of Incidence\")\n",
"axis.set_title(\"Distribution of Angled Rays on Imaging Plane\")\n",
"plt.legend()\n",
"plt.show()"
]
}
],
"metadata": {
"interpreter": {
"hash": "70dfabefa7f0aff4182a552484fa514ba9176249c43f1a51b0f735d1f34674d7"
},
"kernelspec": {
"display_name": "PyRayT (Project Venv)",
"language": "python",
"name": "pyrayt"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.10"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
@rfrazier716
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rfrazier716 commented Aug 24, 2021

Some strange things happened when I was switching between Linux and Windows working on this file, cells would have text rearranged and break evaluation. This should be fixed now though.

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