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lens_model.py
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lens_model.py
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# -*- coding: utf-8 -*-
"""
Created on Mon Apr 4 23:02:09 2022
@author: Tanmay Ganguli
"""
import numpy as np
import matplotlib.pyplot as plt
import math,cmath
from scipy.fftpack import fft,ifft,fft2,ifft2,fftshift,ifftshift
def Le_polar(m_x,m_y):
#returns polar coordinates given cartesian ones
r = np.sqrt(m_x*m_x+m_y*m_y)
theta = np.arctan2(m_y,m_x)
return r,theta
def Le_delta_phase(coefficients_st, m_r, m_t):
#calculate change of phase at given point (r,theta)
#use zernike polynomials with given coeff
#input is in form of an array of rad,theta for all points under consideration
a = coefficients_st
Z1 = a[0] * 1*(np.cos(m_t)**2+np.sin(m_t)**2)
Z2 = a[1] * 2*m_r*np.cos(m_t)
Z3 = a[2] * 2*m_r*np.sin(m_t)
Z4 = a[3] * np.sqrt(3)*(2*m_r**2-1)
Z5 = a[4] * np.sqrt(6)*m_r**2*np.sin(2*m_t)
Z6 = a[5] * np.sqrt(6)*m_r**2*np.cos(2*m_t)
Z7 = a[6] * np.sqrt(8)*(3*m_r**2-2)*m_r*np.sin(m_t)
Z8 = a[7] * np.sqrt(8)*(3*m_r**2-2)*m_r*np.cos(m_t)
Z9 = a[8] * np.sqrt(8)*m_r**3*np.sin(3*m_t)
Z10 = a[9] * np.sqrt(8)*m_r**3*np.cos(3*m_t)
Z11 = a[10] * np.sqrt(5)*(1-6*m_r**2+6*m_r**4)
Z12 = a[11] * np.sqrt(10)*(4*m_r**2-3)*m_r**2*np.cos(2*m_t)
Z13 = a[12] * np.sqrt(10)*(4*m_r**2-3)*m_r**2*np.sin(2*m_t)
Z14 = a[13] * np.sqrt(10)*m_r**4*np.cos(4*m_t)
Z15 = a[14] * np.sqrt(10)*m_r**4*np.sin(4*m_t)
Z16 = a[15] * np.sqrt(12)*(10*m_r**4-12*m_r**2+3)*m_r*np.cos(m_t)
Z17 = a[16] * np.sqrt(12)*(10*m_r**4-12*m_r**2+3)*m_r*np.sin(m_t)
Z18 = a[17] * np.sqrt(12)*(5*m_r**2-4)*m_r**3*np.cos(3*m_t)
Z19 = a[18] * np.sqrt(12)*(5*m_r**2-4)*m_r**3*np.sin(3*m_t)
Z20 = a[19] * np.sqrt(12)*m_r**5*np.cos(5*m_t)
Z21 = a[20] * np.sqrt(12)*m_r**5*np.sin(5*m_t)
Z22 = a[21] * np.sqrt(7)*(20*m_r**6-30*m_r**4+12*m_r**2-1)
Z23 = a[22] * np.sqrt(14)*(15*m_r**4-20*m_r**2+6)*m_r**2*np.sin(2*m_t)
Z24 = a[23] * np.sqrt(14)*(15*m_r**4-20*m_r**2+6)*m_r**2*np.cos(2*m_t)
Z25 = a[24] * np.sqrt(14)*(6*m_r**2-5)*m_r**4*np.sin(4*m_t)
Z26 = a[25] * np.sqrt(14)*(6*m_r**2-5)*m_r**4*np.cos(4*m_t)
Z27 = a[26] * np.sqrt(14)*m_r**6*np.sin(6*m_t)
Z28 = a[27] * np.sqrt(14)*m_r**6*np.cos(6*m_t)
Z29 = a[28] * 4*(35*m_r**6-60*m_r**4+30*m_r**2-4)*m_r*np.sin(m_t)
Z30 = a[29] * 4*(35*m_r**6-60*m_r**4+30*m_r**2-4)*m_r*np.cos(m_t)
Z31 = a[30] * 4*(21*m_r**4-30*m_r**2+10)*m_r**3*np.sin(3*m_t)
Z32 = a[31] * 4*(21*m_r**4-30*m_r**2+10)*m_r**3*np.cos(3*m_t)
Z33 = a[32] * 4*(7*m_r**2-6)*m_r**5*np.sin(5*m_t)
Z34 = a[33] * 4*(7*m_r**2-6)*m_r**5*np.cos(5*m_t)
Z35 = a[34] * 4*m_r**7*np.sin(7*m_t)
Z36 = a[35] * 4*m_r**7*np.cos(7*m_t)
Z37 = a[36] * 3*(70*m_r**8-140*m_r**6+90*m_r**4-20*m_r**2+1)
ans = Z1 + Z2 + Z3+ Z4+ Z5+ Z6+ Z7+ Z8+ Z9+ Z10+ Z11+ Z12+ Z13+ Z14+ Z15+ Z16+ Z17+ Z18+ Z19+Z20+ Z21+ Z22+ Z23+ Z24+ Z25+ Z26+ Z27+ Z28+ Z29+Z30+ Z31+ Z32+ Z33+ Z34+ Z35+ Z36+ Z37
return ans
#define function which returns exit pupil radius
def Le_exit_pupil_radius(aperture, f, wavelength, pixel, side):
theta_pixel = side*pixel/f
theta_screen = wavelength/aperture
radius = int(theta_pixel/2/theta_screen)
return radius
#define pupil function
def Le_pupil_function(l, b, rpupil, r_coefficients_st):
r = 1
m_pupil_matrix = np.zeros([l, b], dtype=complex)
#final array containing value of pupilfunc at each point
#mask function
r_x = np.linspace(-r, r, 2*rpupil)
r_y = np.linspace(-r, r, 2*rpupil)
[m_X, m_Y] = np.meshgrid(r_x, r_y)#store values of x,y coordinates in X,Y
m_rad,m_theta = Le_polar(m_X, m_Y)
m_M = 1*(np.sin(m_theta)**2 + np.cos(m_theta)**2)
m_M[m_rad > 1] = 0
#phase modulation
m_A = np.exp(1*cmath.sqrt(-1)*Le_delta_phase(r_coefficients_st, m_rad, m_theta), dtype=complex)
m_pupil_center = m_M*m_A
m_pupil_matrix[l//2-rpupil+1:l//2+rpupil+1,b//2-rpupil+1:b//2+rpupil+1] = m_pupil_center
return m_pupil_matrix
#define PSF
def Le_PSF(m_pupil):
#fourier transform of pupil function
m_psf = fftshift(fft2(ifftshift(m_pupil)))
m_psf = np.abs(m_psf)**2
return m_psf/m_psf.sum()
#define OTF
def Le_OTF(m_psf):
#fourier transform of psf
m_otf = fftshift(fft2(ifftshift(m_psf)))
m_otf = m_otf/abs(m_otf.max())
return m_otf
#define MTF
def Le_MTF(m_otf):
return np.abs(m_otf)
#__main__
#given variables in metres
APERTURE = 0.08
FOCUS = 0.8
WAVELENGTH = 550*10**(-9)
PIXEL_SIZE = 5*10**(-6)
LENGTH = 1000 #sensor length
BREADTH = 1200 #sensor width
r_coefficients_st = np.zeros(37)#zernike coefficients for phase modulation
r_coefficients_st[0] = 6.54080697
r_coefficients_st[3] = 3.77411473
r_coefficients_st[10] = -0.00172336
r_coefficients_st[21] = -0.00000190
#calculations
pupil_radius = Le_exit_pupil_radius(APERTURE,FOCUS,WAVELENGTH,PIXEL_SIZE,(LENGTH+BREADTH)/2)
m_pupil = Le_pupil_function(LENGTH,BREADTH,pupil_radius,r_coefficients_st)
m_psf = Le_PSF(m_pupil)
m_otf = Le_OTF(m_psf)
m_mtf = Le_MTF(m_otf)
#plot figures
#plot psf
plt.imshow(m_psf)
plt.xlim(500,700)
plt.ylim(400,600)
plt.show()
plt.imshow(m_psf)
plt.xlim(0,1200)
plt.ylim(0,1000)
plt.show()
'''
plt.plot(m_psf[499])
plt.xlim(500,700)
plt.show()
'''
#plot mtf
plt.imshow(m_mtf)
plt.xlim(0,1200)
plt.ylim(0,1000)
plt.show()
'''
plt.plot(m_mtf[499])
plt.xlim(0,1200)
plt.show()
'''