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optoelectronic-systems-theo…/assignment.ipynb
2023-03-14 01:30:38 +04:00

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{
"cells": [
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"# Optoelectronic Systems Theory Assignment"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"from scipy import signal, constants\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"sns.set()"
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"## Initial data"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"wavelength = 0.8e-3 # mm\n",
"focus = 90 # mm\n",
"T = 5000 # K\n",
"mu = 0.6e-3 # mm\n",
"sigma = 0.1e-3 # mm"
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"## Utility functions"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def triangle(x):\n",
" return np.where(np.abs(x) <= 1, 1 - np.abs(x), 0)\n",
"\n",
"def rect(x):\n",
" return np.where(np.abs(x) <= 0.5, 1, 0)\n",
"\n",
"def sinc(x):\n",
" return np.where(x == 0, 1, np.sin(x) / x)"
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"## Pupil function"
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"### Pupil variants\n",
"\n",
"![](images/pupil_variants.png)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"def pupil(x):\n",
" return rect((x - 3) / 3) + rect((x + 3) / 3)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.linspace(-5, 5, 1000)\n",
"\n",
"fig, ax = plt.subplots()\n",
"ax.set_title('Pupil transmittance function $P(x)$')\n",
"ax.set_xlabel('$x, mm$')\n",
"ax.set_ylabel('$P(x)$')\n",
"ax.plot(x, pupil(x))\n",
"ax.fill_between(x, pupil(x), alpha=0.3)\n",
"plt.show()"
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"## Part 1\n",
"\n",
"For a cylindrical diffraction-limited optical system, on which a plane monochromatic wave with length $\\lambda$ and amplitude $A=1$ falls, find:\n",
"\n",
"1. A coherent transfer function $\\tilde{h}(\\nu_x)$ and plot its graph\n",
"2. An optical transfer function $\\tilde{H}_N^{OS}(\\nu_x)$ and plot its graph\n",
"\n",
"![](images/optical_system.png)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Max frequency = 138.889 [1/mm]\n"
]
}
],
"source": [
"pupil_diameter = 10\n",
"max_frequency = pupil_diameter / (wavelength * focus)\n",
"print('Max frequency = {:.3f} [1/mm]'.format(max_frequency))"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"def transfer_function(frequencies, wavelength, focus):\n",
" return signal.convolve(pupil(-frequencies * wavelength * focus), pupil(frequencies * wavelength * focus), 'same')\n",
"\n",
"def transfer_function_n(frequencies, wavelength, focus):\n",
" result = transfer_function(frequencies, wavelength, focus)\n",
" return result / np.max(result)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"freq = np.linspace(-max_frequency * 1.5, max_frequency * 1.5, 1000)\n",
"H = transfer_function_n(freq, wavelength, focus)\n",
"\n",
"fig, ax = plt.subplots()\n",
"ax.set_title('Optical transfer function $\\\\tilde{H}_N^{OS}(\\\\nu_x)$')\n",
"ax.set_xlabel('$\\\\nu_x, mm^{-1}$')\n",
"ax.set_ylabel('$\\\\tilde{H}_N^{OS}(\\\\nu_x)$')\n",
"ax.plot(freq, H)\n",
"ax.fill_between(freq, H, alpha=0.3)\n",
"plt.show()"
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"## Part 2\n",
"\n",
"Find a polychromatic transfer function $\\tilde{H}^{PC}(\\nu_x)$ for the radiation of a corresponding blackbody with temperature $T$, if the image is formed in the rear focal plane, and the spectral sensitivity of the radiation receiver is approximated by a Gaussian distribution with a mathematical expectation of 600 nm and a standard deviation of 100 nm."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Blackbody wavelength peak = 0.000579554391 mm\n"
]
}
],
"source": [
"wien = constants.value('Wien wavelength displacement law constant')\n",
"wavelength_peak = wien * 1e3 / T\n",
"print('Blackbody wavelength peak = {:} mm'.format(wavelength_peak))"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"def sensitivity_n(wavelength):\n",
" return np.exp(-(wavelength - mu) ** 2 / (2 * sigma ** 2))\n",
"\n",
"def luminance(wavelength):\n",
" c = constants.c * 1e3 # mm\n",
" numerator = 4 * (c ** 2) * constants.hbar\n",
" exp = np.exp((2 * np.pi * constants.hbar * c) / (wavelength * constants.k * T))\n",
" denominator = (wavelength ** 5) * (exp - 1)\n",
"\n",
" return numerator / denominator\n",
"\n",
"def luminance_n(wavelength):\n",
" return luminance(wavelength) / luminance(wavelength_peak)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"C:\\Users\\Maksim Vinogradov\\AppData\\Local\\Temp\\ipykernel_19260\\2852790975.py:7: RuntimeWarning: divide by zero encountered in divide\n",
" exp = np.exp((2 * np.pi * constants.hbar * c) / (wavelength * constants.k * T))\n",
"C:\\Users\\Maksim Vinogradov\\AppData\\Local\\Temp\\ipykernel_19260\\2852790975.py:7: RuntimeWarning: overflow encountered in exp\n",
" exp = np.exp((2 * np.pi * constants.hbar * c) / (wavelength * constants.k * T))\n",
"C:\\Users\\Maksim Vinogradov\\AppData\\Local\\Temp\\ipykernel_19260\\2852790975.py:8: RuntimeWarning: invalid value encountered in multiply\n",
" denominator = (wavelength ** 5) * (exp - 1)\n"
]
},
{
"data": {
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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"wv = np.linspace(0, 1e-3, 1000)\n",
"\n",
"S = sensitivity_n(wv)\n",
"L = luminance_n(wv)\n",
"common_sensitivity = S * L\n",
"\n",
"fig, ax = plt.subplots()\n",
"ax.set_title('Receiver sensitivity to a blackbody radiation')\n",
"ax.set_xlabel('$\\\\lambda, mm$')\n",
"ax.plot(wv, S, label='$S_N(\\\\lambda)$', linestyle='dashed')\n",
"ax.fill_between(wv, S, alpha=0.3)\n",
"ax.plot(wv, L, label='$L_N(\\\\lambda)$', linestyle='dashed')\n",
"ax.fill_between(wv, L, alpha=0.3)\n",
"ax.plot(wv, common_sensitivity, label='$S_N(\\\\lambda) * L_N(\\\\lambda)$')\n",
"ax.fill_between(wv, common_sensitivity, alpha=0.3)\n",
"ax.legend()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Meaningful wavelength interval from 3.3e-04 mm to 8.9e-04 mm\n"
]
}
],
"source": [
"start_index = np.argmax(common_sensitivity >= 0.01)\n",
"end_index = len(common_sensitivity) - np.argmax(common_sensitivity[::-1] >= 0.01)\n",
"\n",
"start_wavelength = wv[start_index]\n",
"end_wavelength = wv[end_index]\n",
"\n",
"print('Meaningful wavelength interval from {:.1e} mm to {:.1e} mm'.format(start_wavelength, end_wavelength))"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"def transfer_function_polychromatic(frequencies, start_wavelength, end_wavelength):\n",
" delta_wavelength = 1e-5\n",
" wavelength_range = np.arange(start_wavelength, end_wavelength, delta_wavelength)\n",
" \n",
" numerator = np.sum([transfer_function_n(frequencies, wv, focus) * sensitivity_n(wv) * luminance_n(wv) * delta_wavelength for wv in wavelength_range], 0)\n",
" denominator = np.sum([sensitivity_n(wv) * luminance_n(wv) * delta_wavelength for wv in wavelength_range])\n",
"\n",
" return numerator / denominator"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"H_pc = transfer_function_polychromatic(freq, start_wavelength, end_wavelength)\n",
"\n",
"fig, ax = plt.subplots()\n",
"ax.set_title('Polychromatic transfer function $\\\\tilde{H}^{PC}(\\\\nu_x)$')\n",
"ax.set_xlabel('$\\\\nu_x, mm^{-1}$')\n",
"ax.plot(freq, H_pc)\n",
"ax.fill_between(freq, H_pc, alpha=0.3)\n",
"plt.show()"
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"## Part 3\n",
"\n",
"Find the time-frequency spectrum of the radiation flux $\\tilde{\\Phi}_t(\\nu_t)$ and the magnitude of the radiation flux $\\Phi_t(t)$ in the image analysis plane of the optical system at the output of the modulator of the image analyzer during its linear scanning and plot their graphs. The optical system is a lens with a normalized scattering function $H_N^{OS}(x', y')=\\delta(x', y')$, the source of radiation is an object in the form of a rectangle with a constant energy brightness $L_0$, the study of which obeys Lambert's law. The modulator of the image analyzer is a lattice with a cosine distribution of the transmission coefficient along the $x$ axis.\n",
"\n",
"![](images/modulator_of_image_analyzer.png)"
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"## Initial data"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"b = 6 # mm\n",
"beta = 0.5\n",
"period_x = 2.5 # mm\n",
"vel_x = 90 # mm/s\n",
"c = 1 # mm\n",
"sigma_aperture = 7 # deg\n",
"tau = 1\n",
"luminance_0 = 0.7e-6 # W / (mm^2 * srad)"
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"## Flux function"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Main flux component 3.919e-07 W\n"
]
}
],
"source": [
"flux_0 = 0.5 * np.pi * tau * np.sin(sigma_aperture * (np.pi / 180)) ** 2 * luminance_0 * 2 * b * 2 * c\n",
"\n",
"def flux(t):\n",
" return flux_0 + flux_0 * sinc(2 * np.pi * b * beta / period_x) * np.cos(2 * np.pi * vel_x / period_x * t)\n",
"\n",
"print('Main flux component {:.3e} W'.format(flux_0))"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"t = np.linspace(0, 0.05, 1000)\n",
"\n",
"fig, ax = plt.subplots()\n",
"ax.set_title('$\\\\Phi_t(t)$')\n",
"ax.set_xlabel('$t, s$')\n",
"ax.set_ylabel('$\\\\Phi_t(t), W$')\n",
"ax.plot(t, flux(t), label='$\\\\Phi_t(t)$')\n",
"ax.hlines(flux_0, t[0], t[-1], linestyles='dashed', label='$\\\\Phi_0$')\n",
"ax.legend()\n",
"plt.show()"
]
}
],
"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": "3.10.5"
},
"orig_nbformat": 4
},
"nbformat": 4,
"nbformat_minor": 2
}