16. Microscopies optiques

PDF : 16 microscopies optiques (6.45 Mo)

CODE :

In [1]:

import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit,leastsq
import numpy.random as npr
import pandas as pd

In [2]:

# Definition de la fonction affine
def f_aff(x, a, b):
    return a*x+b

# Montecarlo
def montecarlo(X, Y, uX, uY, N_mc=100, color1='r', color2='b', mini=None, maxi=None, label1="Mesures", label2="Ajustement"):
    
    sigma_X = uX*np.ones(X.size)
    sigma_Y = uY*np.ones(Y.size)

    param = np.zeros((2,N_mc))
    for i in range(N_mc):
        x_mc = npr.normal(loc=X, scale=sigma_X)
        y_mc = npr.normal(loc=Y, scale=sigma_Y)
        pop, pcov = curve_fit(f_aff, x_mc, y_mc)
        param[0,i] = pop[0]
        param[1,i] = pop[1]
        
    mini = mini if mini else X.min()
    maxi = maxi if maxi else X.max()
    x_th = np.linspace(mini, maxi, 4)
    y_th = f_aff(x_th, *pop)
    for i in range(N_mc):
        y_th = f_aff(x_th, *param[:,i])
        #plt.plot(x_th, y_th, color2, alpha=0.05)  #ligne à décommenter si on veut afficher les 100 droites
    plt.errorbar(X, Y, xerr=uX, yerr=uY, fmt='+', capsize=2, color=color1, label=label1)
    # plt.show()

    a_moy = np.mean(param[0,:])
    b_moy = np.mean(param[1,:])
    x = np.linspace(0.98*min(X),max(X)*1.02,100)
    plt.plot(x,f_aff(x,a_moy,b_moy),'--',color=color2, label=label2)

    #print("La pente moyenne sur les ", N_mc, "mesures est de :", np.round(a_moy,4))
    a_sig = np.std(param[0,:]) #ecart type
    b_sig = np.std(param[1,:]) #ecart type
    #print("L'écart type entre les pentes des", N_mc, "mesures est de :", np.round(a_sig,4))
    #print("Le résultat est donc de :", f"a = {a_moy:.3f} +/- {a_sig:.3f}")
    #print("Cela correspond à une erreur de:", f"a_rel = {a_sig/a_moy*100:.0f} %")
    return (a_moy, a_sig)

Loupe¶

In [3]:

f_ =  # cm prendre f_ plus petite que dm pour avoir un grossicement intéressant
AB =  # cm
dm =  # cm

uf_ = 1
uAB = 0.1
udm = 1

Gc_th = dm/f_
uGc_th = Gc_th*np.sqrt((uf_/f_)**2+(udm/dm)**2)

A_B_ =  #cm
alpha_ = A_B_/dm
alpha = AB/dm

uA_B_ = 0.1

Gc_exp = alpha_/alpha
uGc_exp = Gc_exp*np.sqrt((uA_B_/A_B_)**2+(uAB/AB)**2)

print('Grossicement commercial théorique Gc_th = ',round(Gc_th,2),'+/-',np.round(uGc_th,2),
      '\nGrossicement commercial expériemental Gc_exp = ',round(Gc_exp,2),'+/-',np.round(uGc_th,2))

Grossicement commercial théorique Gc_th =  1.0 +/- 0.05 
Grossicement commercial expériemental Gc_exp =  1.0 +/- 0.05

Microscope¶

In [6]:

df = pd.DataFrame()

f2_ =  
f3_ = 
O1O2 = 
AB = 
alpha = AB/f3_

# Incertitudes
uAB = 0.05e-2
uf = 0.5e-2 # distances focales
uim = 0.1e-2 # mesures des images A_B_ et A__B__
uO1O2 = 0.2e-2
uDelta = uO1O2+2*uf 
ualpha = alpha*np.sqrt((uim/AB)**2+(uf/f3_)**2)

# Mesure en direct
f1_ = 
A_B_ = 
A__B__ = 

df['f1_'] = np.array([,f1_])*1e-2
df['Delta'] = [O1O2-f2_-df['f1_'][i] for i in df.index]

df['A_B_'] = np.array([,A_B_])*1e-2

df['gamma'] = [df['A_B_'][i]/AB for i in df.index]
df['ugamma'] = [df['gamma'][i]*np.sqrt((uim/df['A_B_'][i])**2+(uAB/AB)**2) for i in df.index]

df['A__B__'] = np.array([,A__B__])*1e-2

df['alpha_'] = [df['A__B__'][i]/f3_ for i in df.index]
df['ualpha_'] = [df['alpha_'][i]*np.sqrt((uim/df['A__B__'][i])**2+(uf/f3_)**2) for i in df.index]

df['Gc_exp'] = [df['alpha_'][i]/alpha for i in df.index]
df['uGc_exp'] = [df['Gc_exp'][i]*np.sqrt((df['ualpha_'][i]/df['alpha_'][i])**2+(ualpha/alpha)**2) for i in df.index]

df['Gc_th'] = [df['Delta'][i]*f3_/(df['f1_'][i]*f2_) for i in df.index]
df['uGc_th'] = [df['Gc_th'][i]*np.sqrt((uDelta/df['Delta'][i])**2+(uf/f3_)**2+(uf/df['f1_'][i])**2+(uf/f2_)**2) for i in df.index]

df['P'] = [df['Delta'][i]/(df['f1_'][i]*f2_) for i in df.index]
df['uP'] = [df['P'][i]*np.sqrt((uDelta/df['Delta'][i])**2+(uf/df['f1_'][i])**2+(uf/f2_)**2) for i in df.index]

print(alpha, ualpha)
print(np.sqrt((0.003363/0.06666)**2+(ualpha/alpha)**2))
print(df)

In [7]:

a_moy, a_sig = montecarlo(df['Delta'], df['gamma'], uDelta , df['ugamma'], color1='red', color2='blue')
plt.plot(df['Delta'][len(df)-1],df['gamma'][len(df)-1],"og", markersize = 10, label='Mesure en direct')
plt.xlabel('Delta [m]')
plt.ylabel('gamma')
plt.title('Grandissement de l objectif en fonction de l intervalle optique')
plt.legend()

Out[7]:

<matplotlib.legend.Legend at 0x203833ee690>

In [8]:

a_moy, a_sig = montecarlo(df['Delta'], df['P'], uDelta , df['uP'], color1='red', color2='blue')
plt.plot(df['Delta'][len(df)-1],df['P'][len(df)-1],"og", markersize = 10, label='Mesure en direct')
plt.xlabel('Delta [m]')
plt.ylabel('P [1/m]')
plt.title('Puissance en fonction de l intervalle optique')
plt.legend()

Out[8]:

<matplotlib.legend.Legend at 0x20386c462d0>

In [9]:

a_moy, a_sig = montecarlo(df['Delta'], df['Gc_exp'], uDelta , df['uGc_exp'], color1='red', color2='blue', label1="Gc_exp mesures", label2="Gc_exp ajustement")
a_moy_, a_sig_ = montecarlo(df['Delta'], df['Gc_th'], uDelta , df['uGc_th'], color1='orange', color2='green', label1="Gc_th mesures", label2="Gc_th ajustement")
plt.plot(df['Delta'][len(df)-1],df['Gc_exp'][len(df)-1],"og", markersize = 10)
plt.plot(df['Delta'][len(df)-1],df['Gc_th'][len(df)-1],"ob", markersize = 10)
plt.xlabel('Delta [m]')
plt.ylabel('Grossicement')
plt.title('Grossissement en fonction de l intervalle optique')
plt.legend()

Out[9]:

<matplotlib.legend.Legend at 0x20387789610>

Cercle oculaire¶

$$ -\frac{1}{O_2O_1} + \frac{1}{O_2C} = \frac{1}{f_2'} $$

In [5]:

# Position expérimentale du cercle oculaire
O2C_exp =   # en m
uO2C_exp = 0.5e-2  # en m

# Position théorique du cercle oculaire
O2O1 = -O1O2
O2C_th = 1 / (1 / f2_ - 1 / O2O1)
uO2C_th = O2C_th * np.sqrt((uf/f2_)**2 + (uO1O2/O2O1)**2)

print('O2C_th = {} +- {} cm'.format(np.round(O2C_th*10**2, 2), np.round(uO2C_th*10**2, 2)))
print('O2C_exp = {} +- {} cm'.format(np.round(O2C_exp*10**2, 2), np.round(uO2C_exp*10**2, 2)))

O2C_th = 21.86 +- 0.37 cm
O2C_exp = 17.6 +- 0.5 cm

In [ ]:

Date de dernière mise à jour : 07/06/2025