{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github"
},
"source": [
"![\"Open](\"https://colab.research.google.com/assets/colab-badge.svg\")
"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "tYZjdh8TvE7-"
},
"source": [
".![\"Licencia](\"https://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png\")
The following notes written by Sergio Gutiérrez Rodrigo () . Distributed under License Creative Commons Atribución-NoComercial-CompartirIgual 4.0 Internacional"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "j2H5UHGe1Uf8"
},
"source": [
"```\n",
"Departamento de Física Aplicada\n",
"Universidad de Zaragoza\n",
"Instituto de Nanociencia y Materiales de Aragón (INMA)\n",
"C/ Pedro Cerbuna, 12, 50009, Zaragoza, España\n",
"```\n",
"\n",
"\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "D7vYGeB21ZQU"
},
"source": [
"---\n",
"# **Optics - Chapter 7: Optical imaging**\n",
"\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "3su-Kos-AGZ6"
},
"source": [
"# Image calculation and lateral magnification by Gauss's law (coupling of diopters)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "3MiBtTXGAWz6"
},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "rcf99pwoAjsK"
},
"source": [
"*Note that here we use $a,a'$ instead of $s,s'$ for the object-image locations*"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "fOtzUm1DECgR"
},
"source": [
"# Definición de las leyes de la óptica paraxial mediante las leyes de Gauss (se derivan de las invariantes de Abbe y Lagrange-Helmoltz)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "GMyTZzjZ6eND"
},
"outputs": [],
"source": [
"class Sistema_optico_gauss(object):\n",
" '''\n",
" Clase Sistema_optico_gauss\n",
" -------------------------\n",
" Cálculo de la imagen y el aumento de un sistema\n",
" compuesto.\n",
" --------------------------------------------------------------------\n",
" Inputs=Parámetros de la lente\n",
" a1= posición respecto del primer vértice del objeto\n",
" Para cada dioptrio:\n",
" n=[] # Lista con los índices de refracción relativos de los N+1 medios\n",
" # donde se incluye el primer medio (incidencia): [n1,n2,...nN+1]\n",
" R=[] # Lista de los radios de los N dioptrios en mm: [R1,R2,...RN]\n",
" e=[] # Lista de los N-1 distancias entre dióptrios en mm: [e12,e23,...eN-1,N]\n",
"\n",
" Longitud focal del vértice trasero/dorsal (último vértice)\n",
" Se corresponde con la Thickness de la capa IMS en OSLO\n",
" '''\n",
" def __init__(self,nombre,n,R,e): # Función especial\n",
" from math import inf\n",
" self.nombre=nombre\n",
" self.a1=-inf\n",
" self.n=n[:]\n",
" self.R=R[:]\n",
" self.e=e[:]\n",
" self.focal_img_v2=self.calc_lente_compuesta(self.a1)[0] # Se inician valores con a1=-inf\n",
"\n",
" def __str__(self): # Función especial\n",
" print(\"\\n --------------------------------\")\n",
" print(\"Parámetros sistema óptico: \"+self.nombre)\n",
" print(\"n=\",self.n)\n",
" print(\"R=\",self.R)\n",
" print(\"e=\",self.e)\n",
" return '{nombre}'.format(nombre=self.nombre)\n",
"\n",
" def aj_p(self,aj,Rj,nj,nj1):\n",
" '''\n",
" Ley de Gauss: Cálculo de la imagen para un solo dióptrio\n",
" '''\n",
" num=nj1\n",
" den=nj/aj+(nj1-nj)/Rj\n",
" return num/den\n",
"\n",
" def calc_img(self,a1):\n",
" self.a1=a1\n",
" '''\n",
" Imagen y el aumento de un sistema\n",
" compuesto\n",
" '''\n",
" print(\"Cálculo posición respecto vértice posterior \", len(self.R),\" de la imagen y aumento para objeto a1=\",a1,\"mm\")\n",
" n=self.n\n",
" R=self.R\n",
" e=self.e\n",
" aj=a1 # Objeto\n",
" bjp=1.0\n",
" for i in range(0,len(R)):\n",
" ajp=self.aj_p(aj,R[i],n[i],n[i+1])\n",
" bjp=(n[i]/n[i+1])*(ajp/aj)*bjp\n",
" try:\n",
" aj=ajp-e[i]\n",
" except:\n",
" pass\n",
" return ajp,bjp\n",
"\n",
" def calc_lente_compuesta(self,a1):\n",
" '''\n",
" Cálculo de:\n",
" - Poder refractor y focal de cada dióptrio\n",
" - Imagen y el aumento de un sistema\n",
" compuesto\n",
" '''\n",
" '''\n",
" Longitud focal del vértice trasero/dorsal (último vértice)\n",
" Se corresponde con la Thickness de la capa IMS en OSLO\n",
" '''\n",
" self.a1=a1\n",
" n=self.n\n",
" R=self.R\n",
" e=self.e\n",
" aj=a1 # Objeto\n",
" bjp=1.0\n",
" self.poder_refractor =[]\n",
" self.focal=[]\n",
" self.objeto=[]\n",
" self.imagen=[]\n",
" self.aumento=[]\n",
" for i in range(0,len(R)):\n",
" # Poder refractor de cada dioptrio\n",
" self.poder_refractor.append((n[i+1]-n[i])/R[i])\n",
" self.focal.append(n[i+1]*R[i]/(n[i+1]-n[i]))\n",
" self.objeto.append(aj)\n",
" ajp=self.aj_p(aj,R[i],n[i],n[i+1])\n",
" self.imagen.append(ajp)\n",
" bjp=(n[i]/n[i+1])*(ajp/aj)*bjp\n",
" self.aumento.append(bjp)\n",
" try:\n",
" aj=ajp-e[i]\n",
" except:\n",
" pass\n",
" return ajp,bjp\n",
"\n",
" def info_por_dioptrios(self,**kwargs):\n",
" sentido_menos_inf=kwargs.get('menos_inf',True) # ¿De dónde viene la luz?\n",
" if(sentido_menos_inf==True):\n",
" print(\"\\nEspacio IMAGEN (luz sentido -inf a +inf)\")\n",
" poderref_nombre=\"F'\"\n",
" focal_nombre=\"f'\"\n",
" potencia_nombre=\"P'\"\n",
" else:\n",
" print(\"\\nEspacio OBJETO (luz sentido +inf a -inf)\")\n",
" print(\"OJO: los vértices se corresponden con la lente girada 180º\")\n",
" poderref_nombre=\"F\"\n",
" focal_nombre=\"f\"\n",
" potencia_nombre=\"P\"\n",
"\n",
" for i in range(0,len(self.focal)):\n",
" print(\"vértice\",i+1)\n",
" print(\"\\t Poder refractor (\"+poderref_nombre+str(i+1)+\"):\"\n",
" ,self.poder_refractor[i]*1e3,\"m-1\")\n",
" print(\"\\t Focal (\"+focal_nombre+str(i+1)+\"):\",self.focal[i],\"mm\")\n",
" print(\"\\t Potencia (\"+potencia_nombre+str(i+1)+\"):\",1.0/self.focal[i]*1e3,\"m-1\")\n",
" print(\"\\t objeto:\",self.objeto[i],\"mm\")\n",
" print(\"\\t imagen:\",self.imagen[i],\"mm\")\n",
" print(\"\\t aumento:\",self.aumento[i])\n",
" print(\"\\n*distancias respecto del vértice correspondiente\")\n",
" pass"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "zdZ8OrIf_ibr"
},
"source": [
"# Funciones disponibles en la clase *Sistema Óptico Gauss*"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"executionInfo": {
"elapsed": 380,
"status": "ok",
"timestamp": 1699518943657,
"user": {
"displayName": "SERGIO GUTIERREZ RODRIGO",
"userId": "07959720391705098820"
},
"user_tz": -60
},
"id": "7xK7_ntHYmm2",
"outputId": "848d9e8b-db73-4a51-8f19-7bd8d560cf6e"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Funciones disponibles en Sistema_optico_gauss\n",
"Función disponible: aj_p\n",
"Función disponible: calc_img\n",
"Función disponible: calc_lente_compuesta\n",
"Función disponible: info_por_dioptrios\n"
]
}
],
"source": [
"# Conocer los métodos de las distintas librerías\n",
"lib=Sistema_optico_gauss\n",
"method_list = [method for method in dir(lib) if method.startswith('__') is False]\n",
"\n",
"print(\"Funciones disponibles en\",lib.__name__)\n",
"for func in method_list:\n",
" print(\"Función disponible:\",func)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "82UCMV_YNe05"
},
"source": [
"# Ejemplo 0: un único dioptrio"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"executionInfo": {
"elapsed": 10,
"status": "ok",
"timestamp": 1699518999729,
"user": {
"displayName": "SERGIO GUTIERREZ RODRIGO",
"userId": "07959720391705098820"
},
"user_tz": -60
},
"id": "FM42qXRPNe06",
"outputId": "058b47d0-cad5-4fd9-d89a-508fbb5ecebc"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" --------------------------------\n",
"Parámetros sistema óptico: dioptrio\n",
"n= [1.0, 1.5]\n",
"R= [10.0]\n",
"e= [0.0]\n",
"dioptrio\n"
]
}
],
"source": [
"'''\n",
"Longitud focal del vértice trasero/dorsal (último vértice)\n",
"'''\n",
"# Definición de los dióptrios refractivos\n",
"n=[1.0,1.5] # Índices de refracción relativos: [n1,n2,...]\n",
"R=[10.0] # Radios de los dióptrios en mm: [R1,R2,...]\n",
"e=[0.0] # Distancia entre dióptrios en mm: [e12,e23,...]\n",
"\n",
"# Se crea el sistema óptico\n",
"dioptrio=Sistema_optico_gauss('dioptrio',n,R,e)\n",
"\n",
"# Parámetros cargados\n",
"print(dioptrio)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "dFof3gjWOWe1"
},
"source": [
"## Cálculo imagen para objeto a distancia finita"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"executionInfo": {
"elapsed": 400,
"status": "ok",
"timestamp": 1699519026983,
"user": {
"displayName": "SERGIO GUTIERREZ RODRIGO",
"userId": "07959720391705098820"
},
"user_tz": -60
},
"id": "_w9CHmKrOWe1",
"outputId": "416f8892-adfd-4dd8-856b-4352a0ada297"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Cálculo posición respecto vértice posterior 1 de la imagen y aumento para objeto a1= -50.0 mm\n",
"(49.99999999999999, -0.6666666666666665)\n"
]
}
],
"source": [
"'''\n",
"Ejemplo objeto-imagen\n",
"'''\n",
"a1=-50.0 # mm (OJO en OSLO se introducen distancias - quitar el signo)\n",
"print(dioptrio.calc_img(a1))"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "4MeJmphCOWe1"
},
"source": [
"## Caracterización completa (con objeto en menos infinito)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"executionInfo": {
"elapsed": 8,
"status": "ok",
"timestamp": 1699519076856,
"user": {
"displayName": "SERGIO GUTIERREZ RODRIGO",
"userId": "07959720391705098820"
},
"user_tz": -60
},
"id": "-Us6p4VeOWe2",
"outputId": "d87d0b16-507e-4fe9-a002-8ffc11e23445"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Espacio IMAGEN (luz sentido -inf a +inf)\n",
"vértice 1\n",
"\t Poder refractor (F'1): 50.0 m-1\n",
"\t Focal (f'1): 30.0 mm\n",
"\t Potencia (P'1): 33.333333333333336 m-1\n",
"\t objeto: -inf mm\n",
"\t imagen: 30.0 mm\n",
"\t aumento: -0.0\n",
"\n",
"*distancias respecto del vértice correspondiente\n",
"Focal imagen (f'12,v2): 30.0 mm\n"
]
}
],
"source": [
"# Información óptica del sistema\n",
"dioptrio.info_por_dioptrios()\n",
"print(\"Focal imagen (f'12,v2):\",dioptrio.focal_img_v2,\"mm\")"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "ShLGfTyUA1fL"
},
"source": [
"# Ejemplo 1: dos dioptrios acoplados (lente)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"executionInfo": {
"elapsed": 642,
"status": "ok",
"timestamp": 1699348799923,
"user": {
"displayName": "SERGIO GUTIERREZ RODRIGO",
"userId": "07959720391705098820"
},
"user_tz": -60
},
"id": "HALmjY56DkdZ",
"outputId": "f5fe08d3-31d1-4a4b-dc3d-9dc8ceed0a93"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" --------------------------------\n",
"Parámetros sistema óptico: sist_1\n",
"n= [1.0, 1.5, 1.0]\n",
"R= [30.0, -30.0]\n",
"e= [10.0]\n",
"sist_1\n"
]
}
],
"source": [
"'''\n",
"Longitud focal del vértice trasero/dorsal (último vértice)\n",
"'''\n",
"# Definición de los dióptrios refractivos\n",
"n=[1.0,1.5,1.0] # Índices de refracción relativos: [n1,n2,...]\n",
"R=[30.0,-30.0] # Radios de los dióptrios en mm: [R1,R2,...]\n",
"e=[10.0] # Distancia entre dióptrios en mm: [e12,e23,...]\n",
"\n",
"# Se crea el sistema óptico\n",
"sist_1=Sistema_optico_gauss('sist_1',n,R,e)\n",
"\n",
"# Parámetros cargados\n",
"print(sist_1)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "i7eyn5fSDSt5"
},
"source": [
"## Cálculo imagen para objeto a distancia finita"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"executionInfo": {
"elapsed": 4,
"status": "ok",
"timestamp": 1699348801793,
"user": {
"displayName": "SERGIO GUTIERREZ RODRIGO",
"userId": "07959720391705098820"
},
"user_tz": -60
},
"id": "jNqZzcCKwtMq",
"outputId": "c6fe4bfb-b7cf-4e27-816f-170d877b203e"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Cálculo posición respecto vértice posterior 2 de la imagen y aumento para objeto a1= -50.0 mm\n",
"(74.5945945945946, -1.4594594594594594)\n"
]
}
],
"source": [
"'''\n",
"Ejemplo objeto-imagen\n",
"'''\n",
"a1=-50.0 # mm (OJO en OSLO se introducen distancias - quitar el signo)\n",
"print(sist_1.calc_img(a1))"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "CpxvIiIrDZYZ"
},
"source": [
"## Caracterización completa (con objeto en menos infinito)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"executionInfo": {
"elapsed": 2,
"status": "ok",
"timestamp": 1699348802415,
"user": {
"displayName": "SERGIO GUTIERREZ RODRIGO",
"userId": "07959720391705098820"
},
"user_tz": -60
},
"id": "ytQ3lZ1r1aLm",
"outputId": "f52c60bd-2133-4f0d-c1ca-1e8b1b33cf59"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Espacio IMAGEN (luz sentido -inf a +inf)\n",
"vértice 1\n",
"\t Poder refractor (F'1): 16.666666666666668 m-1\n",
"\t Focal (f'1): 90.0 mm\n",
"\t Potencia (P'1): 11.11111111111111 m-1\n",
"\t objeto: -inf mm\n",
"\t imagen: 90.0 mm\n",
"\t aumento: -0.0\n",
"vértice 2\n",
"\t Poder refractor (F'2): 16.666666666666668 m-1\n",
"\t Focal (f'2): 60.0 mm\n",
"\t Potencia (P'2): 16.666666666666668 m-1\n",
"\t objeto: 80.0 mm\n",
"\t imagen: 28.235294117647058 mm\n",
"\t aumento: -0.0\n",
"\n",
"*distancias respecto del vértice correspondiente\n",
"Focal imagen (f'12,v2): 28.235294117647058 mm\n"
]
}
],
"source": [
"# Información óptica del sistema\n",
"sist_1.info_por_dioptrios()\n",
"print(\"Focal imagen (f'12,v2):\",sist_1.focal_img_v2,\"mm\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"executionInfo": {
"elapsed": 3,
"status": "ok",
"timestamp": 1699348902714,
"user": {
"displayName": "SERGIO GUTIERREZ RODRIGO",
"userId": "07959720391705098820"
},
"user_tz": -60
},
"id": "8M3KK8GaFmlE",
"outputId": "4ef78180-356e-4a4a-db4a-984734004f2d"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" --------------------------------\n",
"Parámetros sistema óptico: sist_1\n",
"n= [1.0, 1.5, 1.0]\n",
"R= [30.0, -30.0]\n",
"e= [10.0]\n",
"sist_1\n"
]
}
],
"source": [
"print(sist_1)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "9lhDd4-OGoLx"
},
"source": [
"# Ejemplo 1: dos dioptrios acoplados (lente) - cálculo analítico (focal objeto e imagen para una lente)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "gTjVwXsWIUb2"
},
"source": [
"+ Superficie 1 (dioptrio 1):\n",
"$\\dfrac{1}{s'_1}=\\dfrac{n_1}{n_1's_1}+\\dfrac{n_1'-n_1}{n_1'r_1}$ (Eq. 1)\n",
"\n",
"+ Superficie 2 (dioptrio 2) a distancia $e$ del primer dioptrio:\n",
"$\\dfrac{1}{s'_2}=\\dfrac{n_2}{n_2's_2}+\\dfrac{n_2'-n_2}{n_2'r_2}$ (Eq. 2)\n",
"\n",
"El acoplo entre las ecuaciones (1) y (2) es simplemente que $s_2=s_1'-e$\n",
"\n",
"En una lente con índice de refracción en aire $n$ resulta que:\n",
"+ $n_1=n_2'=1$\n",
"+ $n_1'=n_2=n$\n",
"\n",
"Entonces:\n",
"+ Para cálculo de focal objeto respecto del vértice del dioptrio 1 se impone que: $s_2' \\rightarrow \\infty$ (imagen que forma el sistema óptico en infinito)\n",
"\n",
"+ Para cálculo de focal imagen respecto del vértice del dioptrio 2 se impone que: $s_1 \\rightarrow -\\infty$ (objeto del sistema óptico en infinito)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "2Ir9k6TQKHDr"
},
"source": [
"## Cálculo de focal objeto respecto del vértice del dioptrio 1"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"executionInfo": {
"elapsed": 218,
"status": "ok",
"timestamp": 1699350377756,
"user": {
"displayName": "SERGIO GUTIERREZ RODRIGO",
"userId": "07959720391705098820"
},
"user_tz": -60
},
"id": "KHnlGxLdFPM7",
"outputId": "f75669e0-d088-4060-9943-a90b9b64e160"
},
"outputs": [
{
"data": {
"text/plain": [
"-28.235294117647058"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"def focal_objeto_primer_vertice_lente_aire(n,e,r1,r2):\n",
" s1p=e+n*r2/(n-1)\n",
" return r1*s1p/(n*r1+(1-n)*s1p)\n",
"\n",
"focal_objeto_primer_vertice_lente_aire(n=1.5,e=10.0,r1=30.0,r2=-30.0)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "CT6qB-PTHwAh"
},
"source": [
"## Cálculo de focal imagen respecto del vértice del dioptrio 2"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"executionInfo": {
"elapsed": 332,
"status": "ok",
"timestamp": 1699350388113,
"user": {
"displayName": "SERGIO GUTIERREZ RODRIGO",
"userId": "07959720391705098820"
},
"user_tz": -60
},
"id": "_7JlMLTjHwAq",
"outputId": "2c8059d9-5e64-4eb2-811f-a00830c35c8f"
},
"outputs": [
{
"data": {
"text/plain": [
"28.235294117647058"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"def focal_imagen_segundo_vertice_lente_aire(n,e,r1,r2):\n",
" s1p=n*r1/(n-1)\n",
" s2=s1p-e\n",
" return r2*s2/(n*r2+(1-n)*s2)\n",
"\n",
"focal_imagen_segundo_vertice_lente_aire(n=1.5,e=10.0,r1=30.0,r2=-30.0)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "k5onk3yF3mYO"
},
"source": [
"# Ejemplo 2: acoplo de varios dioptrios (e.j. dos lentes acopladas)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"executionInfo": {
"elapsed": 11,
"status": "ok",
"timestamp": 1699264992324,
"user": {
"displayName": "SERGIO GUTIERREZ RODRIGO",
"userId": "07959720391705098820"
},
"user_tz": -60
},
"id": "_lKkeHtw3mL6",
"outputId": "c5c297a0-3aa2-4183-f6d1-0bbce0427401"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" --------------------------------\n",
"Parámetros sistema óptico: Sistema compuesto de 2.0 lentes\n",
"n= [1.0, 1.5, 1.0, 1.5, 1.0]\n",
"R= [30.0, -30.0, 30.0, -30.0]\n",
"e= [10.0, 150.0, 10]\n",
"Sistema compuesto de 2.0 lentes\n"
]
}
],
"source": [
"#2 lentes acopladas\n",
"n=[1.0,1.5,1.0,1.5,1.0] # Índices de refracción relativos: [n1,n2,n2,n3,n4,...]\n",
"R=[30.0,-30.0,30.0,-30.0] # Radios de los dióptrios en mm: [R1,R2,R3...]\n",
"e=[10.0,150.0,10] # Distancia entre dióptrios en mm: [e12,e23,e34,...]\n",
"\n",
"sist_2=Sistema_optico_gauss('Sistema compuesto de '+str(len(R)/2)+ ' lentes',n,R,e)\n",
"print(sist_2)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "tlFU5-3HD9c9"
},
"source": [
"## Cálculo imagen para objeto a distancia finita"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"executionInfo": {
"elapsed": 9,
"status": "ok",
"timestamp": 1699264992325,
"user": {
"displayName": "SERGIO GUTIERREZ RODRIGO",
"userId": "07959720391705098820"
},
"user_tz": -60
},
"id": "VdrOaFg02ftk",
"outputId": "cf2b4f0d-da8e-4ce4-8f7e-b1212e59ac12"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(49.625884732052576, 0.9828109201213345)\n",
"\n",
"Espacio IMAGEN (luz sentido -inf a +inf)\n",
"vértice 1\n",
"\t Poder refractor (F'1): 16.666666666666668 m-1\n",
"\t Focal (f'1): 90.0 mm\n",
"\t Potencia (P'1): 11.11111111111111 m-1\n",
"\t objeto: -50.0 mm\n",
"\t imagen: -449.9999999999999 mm\n",
"\t aumento: 5.999999999999998\n",
"vértice 2\n",
"\t Poder refractor (F'2): 16.666666666666668 m-1\n",
"\t Focal (f'2): 60.0 mm\n",
"\t Potencia (P'2): 16.666666666666668 m-1\n",
"\t objeto: -459.9999999999999 mm\n",
"\t imagen: 74.5945945945946 mm\n",
"\t aumento: -1.4594594594594594\n",
"vértice 3\n",
"\t Poder refractor (F'3): 16.666666666666668 m-1\n",
"\t Focal (f'3): 90.0 mm\n",
"\t Potencia (P'3): 11.11111111111111 m-1\n",
"\t objeto: -75.4054054054054 mm\n",
"\t imagen: 440.52631578947364 mm\n",
"\t aumento: 5.6842105263157885\n",
"vértice 4\n",
"\t Poder refractor (F'4): 16.666666666666668 m-1\n",
"\t Focal (f'4): 60.0 mm\n",
"\t Potencia (P'4): 16.666666666666668 m-1\n",
"\t objeto: 430.52631578947364 mm\n",
"\t imagen: 49.625884732052576 mm\n",
"\t aumento: 0.9828109201213345\n",
"\n",
"*distancias respecto del vértice correspondiente\n",
"None\n"
]
}
],
"source": [
"'''\n",
"Ejemplo objeto-imagen\n",
"'''\n",
"a1=-50.0 # mm (OJO en OSLO se introducen distancias - quitar el signo)\n",
"print(sist_2.calc_lente_compuesta(a1))\n",
"#Muestra el proceso por dioptrios\n",
"#Si no se llama primero a calc_lente_compuesta pinta el resultado para a1=-inf\n",
"print(sist_2.info_por_dioptrios())"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "kLQiEL0qEABz"
},
"source": [
"## Caracterización completa (con objeto en menos infinito)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"executionInfo": {
"elapsed": 7,
"status": "ok",
"timestamp": 1699264992325,
"user": {
"displayName": "SERGIO GUTIERREZ RODRIGO",
"userId": "07959720391705098820"
},
"user_tz": -60
},
"id": "kbswWXJqD5SZ",
"outputId": "ba56889c-7606-4ed7-f058-c56f88da3c93"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Espacio IMAGEN (luz sentido -inf a +inf)\n",
"vértice 1\n",
"\t Poder refractor (F'1): 16.666666666666668 m-1\n",
"\t Focal (f'1): 90.0 mm\n",
"\t Potencia (P'1): 11.11111111111111 m-1\n",
"\t objeto: -50.0 mm\n",
"\t imagen: -449.9999999999999 mm\n",
"\t aumento: 5.999999999999998\n",
"vértice 2\n",
"\t Poder refractor (F'2): 16.666666666666668 m-1\n",
"\t Focal (f'2): 60.0 mm\n",
"\t Potencia (P'2): 16.666666666666668 m-1\n",
"\t objeto: -459.9999999999999 mm\n",
"\t imagen: 74.5945945945946 mm\n",
"\t aumento: -1.4594594594594594\n",
"vértice 3\n",
"\t Poder refractor (F'3): 16.666666666666668 m-1\n",
"\t Focal (f'3): 90.0 mm\n",
"\t Potencia (P'3): 11.11111111111111 m-1\n",
"\t objeto: -75.4054054054054 mm\n",
"\t imagen: 440.52631578947364 mm\n",
"\t aumento: 5.6842105263157885\n",
"vértice 4\n",
"\t Poder refractor (F'4): 16.666666666666668 m-1\n",
"\t Focal (f'4): 60.0 mm\n",
"\t Potencia (P'4): 16.666666666666668 m-1\n",
"\t objeto: 430.52631578947364 mm\n",
"\t imagen: 49.625884732052576 mm\n",
"\t aumento: 0.9828109201213345\n",
"\n",
"*distancias respecto del vértice correspondiente\n",
"None\n"
]
}
],
"source": [
"#Si no se llama primero a calc_lente_compuesta pinta el resultado para a1=-inf\n",
"print(sist_2.info_por_dioptrios())"
]
}
],
"metadata": {
"colab": {
"authorship_tag": "ABX9TyN4dOP0Zb+33ldsRTKG0wNc",
"provenance": [
{
"file_id": "1R0gfjaJhX1O_AuxkVmxSml0gUivo8aj-",
"timestamp": 1698688292021
}
],
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