Added images

README.md

@@ -1,10 +1,16 @@
 # Optoelectronic Systems Theory Assignment
 
-1. For a cylindrical diffraction-limited optical system (Fig. 1), on which a plane monochromatic wave with length $\lambda$ and amplitude $A=1$ falls, find:
+1. For a cylindrical diffraction-limited optical system, on which a plane monochromatic wave with length $\lambda$ and amplitude $A=1$ falls, find:
 
     1. A coherent transfer function $\tilde{h}(\nu_x)$ and plot its graph
     2. An optical transfer function $\tilde{H}_N^{OS}(\nu_x)$ and plot its graph
 
-2. 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. The pupil function $P(\xi)$ is shown in Figure 2.
+![](images/optical_system.png)
 
-3. 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 (Fig. 3) 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.
+2. 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.
+
+![](images/pupil_variants.png)
+
+3. 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.
+
+![](images/modulator_of_image_analyzer.png)

assignment.ipynb

@@ -10,7 +10,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 1,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -31,7 +31,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 115,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -52,7 +52,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 116,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -74,9 +74,19 @@
     "## Pupil function"
    ]
   },
+  {
+   "attachments": {},
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Pupil variants\n",
+    "\n",
+    "![](images/pupil_variants.png)"
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 117,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -86,7 +96,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 118,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
@@ -119,15 +129,17 @@
    "source": [
     "## Part 1\n",
     "\n",
-    "For a cylindrical diffraction-limited optical system (Fig. 1), on which a plane monochromatic wave with length $\\lambda$ and amplitude $A=1$ falls, find:\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"
+    "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": 119,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [
     {
@@ -146,7 +158,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 120,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -160,7 +172,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 121,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [
     {
@@ -194,12 +206,12 @@
    "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. The pupil function $P(\\xi)$ is shown in Figure 2."
+    "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": 122,
+   "execution_count": 9,
    "metadata": {},
    "outputs": [
     {
@@ -218,7 +230,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 123,
+   "execution_count": 10,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -239,25 +251,19 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 124,
+   "execution_count": 11,
    "metadata": {},
    "outputs": [
     {
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "C:\\Users\\Maksim Vinogradov\\AppData\\Local\\Temp\\ipykernel_10780\\2852790975.py:7: RuntimeWarning:\n",
-      "\n",
-      "divide by zero encountered in divide\n",
-      "\n",
-      "C:\\Users\\Maksim Vinogradov\\AppData\\Local\\Temp\\ipykernel_10780\\2852790975.py:7: RuntimeWarning:\n",
-      "\n",
-      "overflow encountered in exp\n",
-      "\n",
-      "C:\\Users\\Maksim Vinogradov\\AppData\\Local\\Temp\\ipykernel_10780\\2852790975.py:8: RuntimeWarning:\n",
-      "\n",
-      "invalid value encountered in multiply\n",
-      "\n"
+      "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"
      ]
     },
     {
@@ -293,7 +299,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 125,
+   "execution_count": 12,
    "metadata": {},
    "outputs": [
     {
@@ -316,7 +322,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 126,
+   "execution_count": 13,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -332,7 +338,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 127,
+   "execution_count": 14,
    "metadata": {},
    "outputs": [
     {
@@ -364,7 +370,9 @@
    "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 (Fig. 3) 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."
+    "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)"
    ]
   },
   {
@@ -377,7 +385,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 128,
+   "execution_count": 15,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -401,7 +409,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 140,
+   "execution_count": 16,
    "metadata": {},
    "outputs": [
     {
@@ -423,7 +431,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 142,
+   "execution_count": 17,
    "metadata": {},
    "outputs": [
     {