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In [1]:

    
import matplotlib.pyplot as plt
from numpy import pi, sin, cos, linspace, exp, real, imag, abs, conj, angle, unwrap
from numpy.fft import fft, fftshift

import numpy as np



In [2]:

    
%matplotlib inline



In [41]:

    
b=.08*1e-3

a=.25*1e-3

k=2*pi/(795*1e-9)

wt=0

C=1

L=1.9

d=.03

ccdsize = 1300



In [4]:

    
def alpha(y):
    return k*a*y/(2*L)



In [5]:

    
def beta(y):
    return k*b*y/(2*L)



In [6]:

    
def E(y):
    return b*C*(sin(beta(y)) / beta(y)) * (sin(wt-k*L) + sin(wt-k*L+2*alpha(y)))

Import gaussian beam function:



In [7]:

    
import BeamOptics as bopt



In [105]:

    
d=.045

pixwidth = 1e-5  # CCD pixel width

y = linspace(-pixwidth*ccdsize/2,pixwidth*ccdsize/2,ccdsize)



In [106]:

    
#E_lo_gauss = bopt.gaussian_beam(0,y,10*L,E0=0.005,wavelambda=795e-9,w0=0.0030,k=[0,k*d/L,k])
E_lo_gauss = bopt.gaussian_beam(0,y,L,E0=0.005,wavelambda=795e-9,w0=0.0060,k=[0,k*d/L,k])

#TODO: change to normal LO and angled signal



In [107]:

    
plt.plot(y,unwrap(angle(E_lo_gauss)))
#plt.ylim([0,0.005])









    Out[107]:





[<matplotlib.lines.Line2D at 0x1083214e0>]

Interesting, the phase fronts are pretty flat under these conditions. Need to revisit the Zernike model we started?



In [108]:

    
plt.plot(y,abs(E_lo_gauss))
plt.ylim([0,0.005])









    Out[108]:





(0, 0.005)



In [109]:

    
TotalIntensity=(E(y)+E_lo_gauss) * (E(y)+E_lo_gauss).conj()



In [110]:

    
plt.figure(figsize=(14,4))
plt.plot(y,TotalIntensity,".-")

#plt.xlim([-.002,0])









    



/Users/dawe7269/anaconda3/lib/python3.6/site-packages/numpy/core/numeric.py:531: ComplexWarning: Casting complex values to real discards the imaginary part
  return array(a, dtype, copy=False, order=order)






    Out[110]:





[<matplotlib.lines.Line2D at 0x112cd66d8>]



In [111]:

    
plt.plot(abs(fft(TotalIntensity)),".-")

plt.ylim([0,.0005]) # Had to lower the LO power quite a bit, and then zoom way in.

plt.xlim([300,500])









    Out[111]:





(300, 500)

Summary:

With the right scaling (-0.006 to 0.006) the peaks agree fairly well. Next compare to different slit sizes.

Extend this exploration over another dimension vs. gaussian beam parameters:



In [85]:

    
N=15
data = np.zeros((ccdsize,N))
wmin = 0.001
wmax = 0.010

wlist = linspace(wmin,wmax,N)
for i,w in enumerate(wlist):
    E_lo_gauss = bopt.gaussian_beam(0,y,0,E0=0.005,wavelambda=795e-9,w0=w,k=[0,k*d/L,k])
    TotalIntensity=(E(y)+E_lo_gauss) * (E(y)+E_lo_gauss).conj()
    data[:,i] = abs(fft(TotalIntensity))
    #plt.plot(abs(fft(TotalIntensity)),".-")
    
#plt.xlim([150,275])
#plt.ylim([0,0.00003])



In [88]:

    
plt.imshow(data[375:450,:])









    Out[88]:





<matplotlib.image.AxesImage at 0x11243fb38>



In [89]:

    
plt.plot(data[375:450,:])









    Out[89]:





[<matplotlib.lines.Line2D at 0x1127d66d8>,
 <matplotlib.lines.Line2D at 0x1127d6588>,
 <matplotlib.lines.Line2D at 0x1127d6780>,
 <matplotlib.lines.Line2D at 0x1127d6240>,
 <matplotlib.lines.Line2D at 0x1127d67f0>,
 <matplotlib.lines.Line2D at 0x11251b080>,
 <matplotlib.lines.Line2D at 0x1127bf668>,
 <matplotlib.lines.Line2D at 0x1127bf0b8>,
 <matplotlib.lines.Line2D at 0x1127bfb70>,
 <matplotlib.lines.Line2D at 0x1127bfe48>,
 <matplotlib.lines.Line2D at 0x112543630>,
 <matplotlib.lines.Line2D at 0x1127bfa58>,
 <matplotlib.lines.Line2D at 0x1127bf9b0>,
 <matplotlib.lines.Line2D at 0x1127bff28>,
 <matplotlib.lines.Line2D at 0x1127bf198>]



In [100]:

    
Z = data[375:450,:]
xs = wlist
ys = np.linspace(150, 275, Z.shape[0])

X, Y = np.meshgrid(xs, ys)



In [101]:

    
from mpl_toolkits.mplot3d import axes3d



In [103]:

    
fig = plt.figure(figsize=(15,10))
ax = fig.add_subplot(111, projection='3d')
wframe = ax.plot_wireframe(X, Y, data[375:450,:],rstride=100)
plt.ylabel("Mode index")
plt.xlabel("w_0")









    Out[103]:





Text(0.5,0,'w_0')

The spot size effectively determines the resolution. Gaussian blurring takes over for small spot sizes.



In [ ]:

Import gaussian beam function:

Summary:

Next: