def f2j(j,N,jsodd,ajsodd,deltaphi,dxp,pupilRadius): # 2: phij's of matrix A to find a_j even
#Get the jth zernike polynomials values on a circular pupil of radius rad
Zj = Z.calc_zern_j(j,N,dxp,pupilRadius)
#compute the different 2Dfft given in the equations of deltaPSF
cosZj = np.cos(deltaphi)*Zj
sinZj = np.sin(deltaphi)*Zj
FFTcosZj = scaledfft2(cosZj,dxp)
FFTsinZj = scaledfft2(sinZj,dxp)
#odd phase
oddPhasor = ph.phasor(jsodd,ajsodd,N,dxp,pupilRadius)
oddPhase = oddPhasor.phase
pupil = oddPhasor.pupil
cosOddPhase = pupil*np.cos(deltaphi)*oddPhase
sinOddPhase = pupil*np.sin(deltaphi)*oddPhase
FFTcosOddPhase = scaledfft2(cosOddPhase,dxp)
FFTsinOddPhase = scaledfft2(sinOddPhase,dxp)
#2Dfft of pupil function times sin(deltaPhi) and cos(deltaPhi)
pupilSin = pupil*np.sin(deltaphi)
pupilCos = pupil*np.cos(deltaphi)
FFTPupilSin = scaledfft2(pupilSin,dxp)
FFTPupilCos = scaledfft2(pupilCos,dxp)
FFTsinZjOddPhase = scaledfft2(sinZj*oddPhase,dxp)
FFTcosZjOddPhase = scaledfft2(cosZj*oddPhase,dxp)
return np.ravel(2*np.imag(np.conj(FFTcosZj) * FFTsinOddPhase + FFTsinZj * np.conj(FFTcosOddPhase)
- np.conj(FFTPupilCos) * FFTsinZjOddPhase + np.conj(FFTPupilSin) * FFTcosZjOddPhase))
def f1j(j,N,dxp,pupilRadius): # 1: phij's of matrix A to find a_j odd
Zj = Z.calc_zern_j(j,N,dxp,pupilRadius)
FFTZj = scaledfft2(Zj,dxp)
Lp = N*dxp
xp = np.arange(-Lp/2,Lp/2,dxp)
yp = xp
[Xp,Yp]=np.meshgrid(xp,yp)
pupil = np.float64(np.sqrt(Xp**2+Yp**2)<=pupilRadius)
FFTPupil = scaledfft2(pupil,dxp)
return np.ravel(2 * np.real(FFTPupil) * np.imag(FFTZj))
def f2jeven(j,N,deltaphi,dxp,pupilRadius): # 2: phij's of matrix A to find a_j even
#Get the jth zernike polynomials values on a circular pupil of radius rad
Zj = Z.calc_zern_j(j,N,dxp,pupilRadius)
Phasor = ph.phasor([1],[0],N,dxp,pupilRadius)
pupil = Phasor.pupil
#compute the different 2Dfft given in the equations of deltaPSF
cosZj = pupil*np.cos(deltaphi)*Zj
sinZj = pupil*np.sin(deltaphi)*Zj
FFTcosZj = scaledfft2(cosZj,dxp)
FFTsinZj = scaledfft2(sinZj,dxp)
#2Dfft of pupil function times sin(deltaPhi) and cos(deltaPhi)
pupilSin = pupil*np.sin(deltaphi)
pupilCos = pupil*np.cos(deltaphi)
FFTPupilSin = scaledfft2(pupilSin,dxp)
FFTPupilCos = scaledfft2(pupilCos,dxp)
return np.ravel(-4*np.real(np.conj(FFTPupilCos)*FFTsinZj-np.conj(FFTPupilSin)*FFTcosZj))
import fs
import numpy as np
import zernike as Z
import matplotlib.pyplot as plt
#%matplotlib inline
#%config InlineBackend.figure_format = 'svg'
Zj = Z.calc_zern_j(8, 400, 1)
plt.figure()
plt.subplot(3, 2, 1)
plt.imshow(Zj)
plt.subplot(3, 2, 2)
plt.imshow(fs.flipMatrix(Zj))
plt.subplot(3, 2, 3)
plt.imshow(fs.cleanZeros((Zj + fs.flipMatrix(Zj)) / 2., 1e-2))
plt.subplot(3, 2, 4)
plt.imshow(fs.cleanZeros((Zj - fs.flipMatrix(Zj)) / 2., 1e-2))
plt.subplot(3, 2, 5)
plt.imshow(fs.cleanZeros(
Zj - ((Zj + fs.flipMatrix(Zj)) / 2. + (Zj - fs.flipMatrix(Zj)) / 2.),
1e-13),
vmin=1e-16,
vmax=1e-12)
C = np.array([[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15],
[16, 17, 18, 19, 20]])
M = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]])
print(M + fs.flipMatrix(M)) / 2. + (M - fs.flipMatrix(M)) / 2.
theta = np.arctan2(Yp, Xp) plt.figure plt.subplot(2, 1, 1) plt.imshow(r) plt.subplot(2, 1, 2) plt.imshow(theta) pup = np.float64(np.sqrt(Xp**2 + Yp**2) <= pupilRadius) rad = int(np.ceil(pupilRadius / dxp)) phasor = ph.phasor([1], [0], N, rad) plt.figure() plt.imshow(pup) plt.figure() plt.imshow(pup - phasor.pupil) fftpup = np.fft.ifftshift(np.fft.fft2(np.fft.fftshift(pup))) fftpupil = np.fft.ifftshift(np.fft.fft2(np.fft.fftshift(phasor.pupil))) plt.figure() plt.subplot(2, 1, 1) plt.imshow(np.real(fftpup) - np.real(fftpupil)) plt.subplot(2, 1, 2) plt.imshow(np.imag(fftpup) - np.imag(fftpupil)) Zj = Z.calc_zern_j(4, N, dxp, pupilRadius) plt.figure() plt.imshow(Zj)
def deltaPhi(N,deltaZ,F,D,wavelength,dxp):
Zj = Z.calc_zern_j(4,N,dxp,D/2.)
P2Vdephasing = np.pi*deltaZ/wavelength*(D/F)**2/4.
a4defocus = P2Vdephasing/2/np.sqrt(3)
return a4defocus*Zj
#[mm]
dExP = 727.4046
#[mm]
DDM = 32.7
#[mm]
# for OAP0
alpha = np.arctan(dExP * 0.5 / ExP2FP)
#[rad]
PFL_OAP0 = (DDM) / 2 / (-1 / np.tan(theta_OAP0 + alpha) +
(1 / (np.tan(theta_OAP0 + alpha))**2 + 1)**0.5 +
1 / np.tan(theta_OAP0 - alpha) -
(1 / (np.tan(theta_OAP0 - alpha))**2 + 1)**0.5)
#[mm] pour l'OAP0
EFL_OAP0 = 2 * PFL_OAP0 / (1 + np.cos(theta_OAP0))
print('PFL_OAP0 (estim) : ', PFL_OAP0)
#PFL_OAP0 = 445.0;
print('PFL_OAP0 : ', PFL_OAP0)
EFL_OAP0 = 2 * PFL_OAP0 / (1 + np.cos(theta_OAP0))
print('EFL_OAP0 : ', EFL_OAP0)
po = -(PFL_OAP0 + ExP2FP)
pi = po * PFL_OAP0 / (po + PFL_OAP0)
print('pi (DM) : ', pi)
#Aberrations : Wabefront MAP
import zernike as zer
aa = zer.calc_zern_j(4, 200, 0.1, 1)
print(aa)
def constructPhase(self):
phase = np.zeros((self.N, self.N))
for ij, j in enumerate(self.js):
Zj = Z.calc_zern_j(j, self.N, self.dxp, self.pupilRadius)
phase += self.ajs[ij] * Zj
return phase