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Update Exercise 2

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Ceres 2025-12-01 18:01:35 +00:00
parent d28aae39d9
commit ed96bc6c0d
Signed by: ceres-sees-all
GPG key ID: 9814758436430045
6 changed files with 200 additions and 43 deletions
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Exercise 2/exercise2.py
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@ -1,6 +1,7 @@
import matplotlib.pyplot as plt
import numpy as np
from scipy import integrate
from tqdm import tqdm
def Fresnel2dreal(yp, xp, y, x, k, z):
kernel = np.cos((k/(2*z))*((x-xp)**2+(y-yp)**2))
@ -13,63 +14,72 @@ def Fresnel2dimag(yp, xp, y, x, k, z):
c = 3e8
e0 = 8.85e-12
def plot1D():
def genData(aperture, z, k, screen_range):
def plot1D(aperture, z, k, screen_range, resolution):
def genData(aperture, z, k, screen_range, resolution):
y = 0
xp1=yp1=-aperture/2
xp2=yp2=aperture/2
xs = np.linspace(-screen_range/2, screen_range/2, num=1000)
xs = np.linspace(-screen_range/2, screen_range/2, num=resolution)
intensities = []
for x in xs:
realpart, realerror = integrate.dblquad(Fresnel2dreal, xp1, xp2, yp1, yp2, args=(y, x, k, z))
imagpart, imagerror = integrate.dblquad(Fresnel2dimag, xp1, xp2, yp1, yp2, args=(y, x, k, z))
constant = k/2*np.pi*z
completion = 0
for x in tqdm(xs):
realpart, realerror = integrate.dblquad(Fresnel2dreal, xp1, xp2, yp1, yp2, args=(y, x, k, z), epsabs=1e-10, epsrel=1e-10)
imagpart, imagerror = integrate.dblquad(Fresnel2dimag, xp1, xp2, yp1, yp2, args=(y, x, k, z), epsabs=1e-10, epsrel=1e-10)
I = c*e0*(realpart**2+imagpart**2)
I = c*e0*((realpart*constant)**2+(imagpart*constant)**2)
intensities.append(I)
completion = completion + 100/resolution
print(completion)
return xs, intensities
ax = plt.axes()
xs, intensities = genData(2e-4, 0.005, 8.377e6, 0.002)
xs, intensities = genData(aperture, z, k, screen_range, resolution)
ax.plot(xs, intensities)
# xs, intensities = genData(2e-5, 0.05, 8.377e6, 0.015)
# ax.plot(xs, intensities)
plt.show()
def plot2Drectangular():
def genData(aperture, z, k, screen_range):
def plot2Drectangular(aperture, z, k, screen_range, resolution):
def genData(aperture, z, k, screen_range, resolution):
xp1=yp1=-aperture/2
xp2=yp2=aperture/2
xs = np.linspace(-screen_range/2, screen_range/2, num=40)
ys = np.linspace(-screen_range/2, screen_range/2, num=40)
xs = np.linspace(-screen_range/2, screen_range/2, num=resolution)
ys = np.linspace(-screen_range/2, screen_range/2, num=resolution)
intensities = []
for y in ys:
constant = k/2*np.pi*z
completion = 0
for y in tqdm(ys):
xIntensities = []
for x in xs:
realpart, realerror = integrate.dblquad(Fresnel2dreal, xp1, xp2, yp1, yp2, args=(y, x, k, z))
imagpart, imagerror = integrate.dblquad(Fresnel2dimag, xp1, xp2, yp1, yp2, args=(y, x, k, z))
realpart, realerror = integrate.dblquad(Fresnel2dreal, xp1, xp2, yp1, yp2, args=(y, x, k, z), epsabs=1e-10, epsrel=1e-10)
imagpart, imagerror = integrate.dblquad(Fresnel2dimag, xp1, xp2, yp1, yp2, args=(y, x, k, z), epsabs=1e-10, epsrel=1e-10)
I = c*e0*(realpart**2+imagpart**2)
I = c*e0*((realpart*constant)**2+(imagpart*constant)**2)
xIntensities.append(I)
completion = completion + 100/resolution**2
print(completion)
intensities.append(xIntensities)
intensities = np.array(intensities)
return intensities
intensity = genData(2e-4, 0.005, 8.377e6, 0.002)
extents = (-0.01,0.01,-0.01,0.01)
intensity = genData(aperture, z, k, screen_range, resolution)
extents = (-screen_range/2,screen_range/2,-screen_range/2,screen_range/2)
plt.imshow(intensity,vmin=0.0,vmax=1.0*intensity.max(),extent=extents,origin="lower",cmap="nipy_spectral_r")
plt.colorbar()
plt.show()
def plot2Dcircular():
def genData(aperture, z, k, screen_range):
def plot2Dcircular(aperture, z, k, screen_range, resolution):
def genData(aperture, z, k, screen_range, resolution):
xp1=-aperture/2
xp2=aperture/2
@ -79,41 +89,43 @@ def plot2Dcircular():
def yp2func(xp):
return np.sqrt((aperture/2)**2-(xp**2))
xs = np.linspace(-screen_range/2, screen_range/2, num=50)
ys = np.linspace(-screen_range/2, screen_range/2, num=50)
xs = np.linspace(-screen_range/2, screen_range/2, num=resolution)
ys = np.linspace(-screen_range/2, screen_range/2, num=resolution)
intensities = []
for y in ys:
constant = k/2*np.pi*z
for y in tqdm(ys):
xIntensities = []
for x in xs:
realpart, realerror = integrate.dblquad(Fresnel2dreal, xp1, xp2, yp1func, yp2func, args=(y, x, k, z))
imagpart, imagerror = integrate.dblquad(Fresnel2dimag, xp1, xp2, yp1func, yp2func, args=(y, x, k, z))
I = c*e0*(realpart**2+imagpart**2)
I = c*e0*((realpart*constant)**2+(imagpart*constant)**2)
xIntensities.append(I)
intensities.append(xIntensities)
intensities = np.array(intensities)
return intensities
intensity = genData(2e-5, 0.05, 8.377e6, 0.015)
extents = (-0.01,0.01,-0.01,0.01)
intensity = genData(aperture, z, k, screen_range, resolution)
extents = (-screen_range/2,screen_range/2,-screen_range/2,screen_range/2)
plt.imshow(intensity,vmin=0.0,vmax=1.0*intensity.max(),extent=extents,origin="lower",cmap="nipy_spectral_r")
plt.colorbar()
plt.show()
def monte():
N = 1000
def monte(aperture, z, k, screen_range, resolution, samples):
N = samples
def doubleInteg(x, y, xp, yp, z, k, aperture):
values = []
for i in range(len(xp)):
if (xp[i]**2+yp[i]**2) > aperture:
if (xp[i]**2+yp[i]**2) > (aperture/2)**2:
values.append(0)
else:
value = np.exp(((1j*k)/(2*z))*((x-xp)**2+(y-yp)**2))
values.append(value.real)
value = np.exp(((1j*k)/(2*z))*((x-xp[i])**2+(y-yp[i])**2))
values.append(value.imag)
return np.array(values)
def monteCarlo(x, y, z, k, aperture):
@ -126,30 +138,79 @@ def monte():
error = aperture*np.sqrt((meansq-mean*mean)/N)
return integral, error
def genData(aperture, z, k, screen_range):
def genData(aperture, z, k, resolution, screen_range):
xs = np.linspace(-screen_range/2, screen_range/2, num=50)
ys = np.linspace(-screen_range/2, screen_range/2, num=50)
xs = np.linspace(-screen_range/2, screen_range/2, num=resolution)
ys = np.linspace(-screen_range/2, screen_range/2, num=resolution)
constant = k/2*np.pi*z
intensities = []
completion = 0
for y in ys:
constant = k/(2*np.pi*z)
for y in tqdm(ys):
xIntensities = []
for x in xs:
for x in tqdm(xs):
integral, error = monteCarlo(x, y, z, k, aperture)
I = c*e0*constant*integral
if I < 0.005:
I = 0
# completion = completion + 100/resolution**2
# print(completion)
xIntensities.append(I)
intensities.append(xIntensities)
intensities = np.array(intensities)
return intensities
intensity = genData(2e-4, 0.005, 8.377e6, 0.002)
extents = (-0.001,0.001,-0.001,0.001)
intensity = genData(aperture, z, k, resolution, screen_range)
extents = (-screen_range/2,screen_range/2,-screen_range/2,screen_range/2)
plt.imshow(intensity,vmin=0.0,vmax=1.0*intensity.max(),extent=extents,origin="lower",cmap="nipy_spectral_r")
plt.imshow(intensity,vmin=1.0*intensity.min(),vmax=1.0*intensity.max(),extent=extents,origin="lower",cmap="nipy_spectral_r")
plt.colorbar()
plt.show()
monte()
MyInput = '0'
while MyInput != 'q':
MyInput = input('Enter a choice, "1", "2", "3", "4" or "q" to quit: ')
print('You entered the choice: ',MyInput)
if MyInput == '1':
print('You have chosen part (1): 1D rectangular diffraction')
aperture = input("Please input the desired aperture (m): ")
z = input("Please enter the desired distnce from the screen (m): ")
wl = input("Please enter the desired wavelength of light (m): ")
k = (2*np.pi)/float(wl)
screen_range = input("Please enter the diameter of the screen (m): ")
resolution = input("Please enter the resolution of the plot (pixels): ")
plot1D(float(aperture), float(z), float(k), float(screen_range), int(resolution))
elif MyInput == '2':
print('You have chosen part (2): 2D rectangular diffraction')
aperture = input("Please input the desired aperture (m): ")
z = input("Please enter the desired distnce from the screen (m): ")
wl = input("Please enter the desired wavelength of light (m): ")
k = (2*np.pi)/float(wl)
screen_range = input("Please enter the diameter of the screen (m): ")
resolution = input("Please enter the resolution of the plot (pixels): ")
plot2Drectangular(float(aperture), float(z), float(k), float(screen_range), int(resolution))
elif MyInput == '3':
print('You have chosen part (3): 2D circular diffraction')
aperture = input("Please input the desired aperture (m): ")
z = input("Please enter the desired distnce from the screen (m): ")
wl = input("Please enter the desired wavelength of light (m): ")
k = (2*np.pi)/float(wl)
screen_range = input("Please enter the diameter of the screen (m): ")
resolution = input("Please enter the resolution of the plot (pixels): ")
plot2Dcircular(float(aperture), float(z), float(k), float(screen_range), int(resolution))
elif MyInput == '4':
print('You have chosen part (3): 2D circular diffraction usinf Monte Carlo')
aperture = input("Please input the desired aperture (m): ")
z = input("Please enter the desired distnce from the screen (m): ")
wl = input("Please enter the desired wavelength of light (m): ")
k = (2*np.pi)/float(wl)
screen_range = input("Please enter the diameter of the screen (m): ")
resolution = input("Please enter the resolution of the plot (pixels): ")
samples = input("Please enter the desired nu,ber of samples for the calculation: ")
monte(float(aperture), float(z), float(k), float(screen_range), int(resolution), int(samples))
elif MyInput != 'q':
print('This is not a valid choice')
print('You have chosen to finish - goodbye.')