Update Exercise 2

Exercise 2/exercise2.py

@@ -13,28 +13,143 @@ def Fresnel2dimag(yp, xp, y, x, k, z):
 c = 3e8
 e0 = 8.85e-12
 
-def plot1D(aperture, z, k, screen_range):
+def plot1D():
+    def genData(aperture, z, k, screen_range):
+        y = 0
 
-    y = 0
-
-    xp1=yp1=-aperture/2
-    xp2=yp2=aperture/2
+        xp1=yp1=-aperture/2
+        xp2=yp2=aperture/2
     
-    xs = np.linspace(-screen_range/2, screen_range/2, num=1000)
-    intensities = []
+        xs = np.linspace(-screen_range/2, screen_range/2, num=1000)
+        intensities = []
 
-    for x in xs:
-        realpart, realerror = integrate.dblquad(Fresnel2dreal, xp1, xp2, yp1, yp2, args=(y, x, k, z), epsabs=1e-11, epsrel=1e-11)
-        imagpart, imagerror = integrate.dblquad(Fresnel2dimag, xp1, xp2, yp1, yp2, args=(y, x, k, z), epsabs=1e-11, epsrel=1e-11)
+        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))
 
-        I = c*e0*(realpart**2+imagpart**2)
-        intensities.append(I)
+            I = c*e0*(realpart**2+imagpart**2)
+            intensities.append(I)
 
-    return xs, intensities
+        return xs, intensities
 
-ax = plt.axes()
-xs, intensities = plot1D(2e-4, 0.005, 8.377e6, 0.002)
-ax.plot(xs, intensities)
-# xs, intensities = plot1D(2e-5, 0.05, 8.377e6, 0.015)
-# ax.plot(xs, intensities)
-plt.show()
+    ax = plt.axes()
+    xs, intensities = genData(2e-4, 0.005, 8.377e6, 0.002)
+    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):
+        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)
+
+        intensities = []
+
+        for y in 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))
+
+                I = c*e0*(realpart**2+imagpart**2)
+                xIntensities.append(I)
+            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)
+
+    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):
+        xp1=-aperture/2
+        xp2=aperture/2
+
+        def yp1func(xp):
+            return -np.sqrt((aperture/2)**2-(xp**2))
+
+        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)
+
+        intensities = []
+
+        for y in 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)
+                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)
+
+    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 doubleInteg(x, y, xp, yp, z, k, aperture):
+        values = []
+        for i in range(len(xp)):
+            if (xp[i]**2+yp[i]**2) > aperture:
+                values.append(0)
+            else:
+                value = np.exp(((1j*k)/(2*z))*((x-xp)**2+(y-yp)**2))
+                values.append(value.real)
+        return np.array(values)
+    
+    def monteCarlo(x, y, z, k, aperture):
+       xp = np.random.uniform(low=(-aperture/2), high=aperture/2, size=N) 
+       yp = np.random.uniform(low=(-aperture/2), high=aperture/2, size=N)
+       values = doubleInteg(x, y, xp, yp, z, k , aperture)
+       mean = values.sum()/N
+       meansq = (values*values).sum()/N
+       integral = aperture*mean
+       error = aperture*np.sqrt((meansq-mean*mean)/N)
+       return integral, error
+         
+    def genData(aperture, z, k, screen_range):
+
+        xs = np.linspace(-screen_range/2, screen_range/2, num=50)
+        ys = np.linspace(-screen_range/2, screen_range/2, num=50)
+
+        constant = k/2*np.pi*z
+
+        intensities = []
+        
+        for y in ys:
+            xIntensities = []
+            for x in xs:
+                integral, error = monteCarlo(x, y, z, k, aperture)
+                I = c*e0*constant*integral
+                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)
+
+    plt.imshow(intensity,vmin=0.0,vmax=1.0*intensity.max(),extent=extents,origin="lower",cmap="nipy_spectral_r")
+    plt.colorbar()
+    plt.show()
+
+monte()