Gaussian beam rotated

beamtheta.py

+
+import numpy as np
+import matplotlib.pyplot as plt
+import matplotlib.gridspec as gridspec
+from matplotlib import ticker
+
+def norm(data):
+    return(data)/(sum(data))
+
+
+def makeGaussian2(x_center=0, y_center=0, theta=0, sigma_x = 10, sigma_y=10, x_size=640, y_size=640):
+    # x_center and y_center will be the center of the gaussian, theta will be the rotation angle
+    # sigma_x and sigma_y will be the stdevs in the x and y axis before rotation
+    # x_size and y_size give the size of the frame 
+
+    theta = 2*np.pi*theta/360
+    x = np.arange(-x_size,x_size, 1, float)
+    y = np.arange(-y_size,y_size, 1, float)
+    y = y[:,np.newaxis]
+    sx = sigma_x
+    sy = sigma_y
+    x0 = x_center
+    y0 = y_center
+
+    # rotation
+    a=np.cos(theta)*x -np.sin(theta)*y
+    b=np.sin(theta)*x +np.cos(theta)*y
+    a0=np.cos(theta)*x0 -np.sin(theta)*y0
+    b0=np.sin(theta)*x0 +np.cos(theta)*y0
+
+    return np.exp(-(((a-a0)**2)/(2*(sx**2)) + ((b-b0)**2) /(2*(sy**2))))
+
+
+framesize=23
+theta=0
+std = 12/2.
+z=np.zeros((2*framesize,2*framesize))
+radius=18/2.
+
+for angle in np.arange(0,360,1):
+    x0=np.cos(angle)*radius
+    y0=np.sin(angle)*radius
+    z += makeGaussian2(x0, y0, angle, std, std, framesize, framesize)
+
+
+plt.plot(np.arange(0,2*framesize,1),norm(z[framesize,:]))
+plt.ylim(bottom=0)
+
+plt.show()
+plt.imshow(z)
+#plt.pcolor(x,y,z,cmap='seismic',vmin=-3,vmax=3,shading='auto')
+plt.clim(0,100)
+plt.colorbar()
+plt.show()