def zernikesurface(self, label = True, zlim=[], matrix = False):
"""
------------------------------------------------
zernikesurface(self, label_1 = True):
Return a 3D Zernike Polynomials surface figure
label_1: default show label
------------------------------------------------
"""
theta = __np__.linspace(0, 2*__np__.pi, 100)
rho = __np__.linspace(0, 1, 100)
[u,r] = __np__.meshgrid(theta,rho)
X = r*__cos__(u)
Y = r*__sin__(u)
Z = __zernikepolar__(self.__coefficients__,r,u)
fig = __plt__.figure(figsize=(12, 8), dpi=80)
ax = fig.gca(projection='3d')
surf = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=__cm__.RdYlGn,
linewidth=0, antialiased=False, alpha = 0.6)
if zlim == []:
v = max(abs(Z.max()),abs(Z.min()))
ax.set_zlim(-v*5, v*5)
cset = ax.contourf(X, Y, Z, zdir='z', offset=-v*5, cmap=__cm__.RdYlGn)
else:
ax.set_zlim(zlim[0], zlim[1])
cset = ax.contourf(X, Y, Z, zdir='z', offset=zlim[0], cmap=__cm__.RdYlGn)
ax.zaxis.set_major_locator(__LinearLocator__(10))
ax.zaxis.set_major_formatter(__FormatStrFormatter__('%.02f'))
fig.colorbar(surf, shrink=1, aspect=30)
p2v = round(__tools__.peak2valley(Z),5)
rms1 = round(__tools__.rms(Z),5)
label_1 = self.listcoefficient()[0]+"P-V: "+str(p2v)+"\n"+"RMS: "+str(rms1)
if label == True:
__plt__.title('Zernike Polynomials Surface',fontsize=18)
ax.text2D(0.02, 0.1, label_1, transform=ax.transAxes,fontsize=14)
else:
pass
__plt__.show()
if matrix == True:
return Z
else:
pass
def zernikesurface(self, label = True, zlim=[], matrix = False):
"""
------------------------------------------------
zernikesurface(self, label_1 = True):
Return a 3D Zernike Polynomials surface figure
label_1: default show label
------------------------------------------------
"""
theta = __np__.linspace(0, 2*__np__.pi, 100)
rho = __np__.linspace(0, 1, 100)
[u,r] = __np__.meshgrid(theta,rho)
X = r*__cos__(u)
Y = r*__sin__(u)
Z = __interferometer__.__zernikepolar__(self.__coefficients__,r,u)
fig = __plt__.figure(figsize=(12, 8), dpi=80)
ax = fig.gca(projection='3d')
surf = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=__cm__.RdYlGn,
linewidth=0, antialiased=False, alpha = 0.6)
if zlim == []:
v = max(abs(Z.max()),abs(Z.min()))
ax.set_zlim(-v*5, v*5)
cset = ax.contourf(X, Y, Z, zdir='z', offset=-v*5, cmap=__cm__.RdYlGn)
else:
ax.set_zlim(zlim[0], zlim[1])
cset = ax.contourf(X, Y, Z, zdir='z', offset=zlim[0], cmap=__cm__.RdYlGn)
ax.zaxis.set_major_locator(__LinearLocator__(10))
ax.zaxis.set_major_formatter(__FormatStrFormatter__('%.02f'))
fig.colorbar(surf, shrink=1, aspect=30)
p2v = round(__tools__.peak2valley(Z),5)
rms1 = round(__tools__.rms(Z),5)
label_1 = self.listcoefficient()[0]+"P-V: "+str(p2v)+"\n"+"RMS: "+str(rms1)
if label == True:
__plt__.title('Zernike Polynomials Surface',fontsize=18)
ax.text2D(0.02, 0.1, label_1, transform=ax.transAxes,fontsize=14)
else:
pass
__plt__.show()
if matrix == True:
return Z
else:
pass
def spherical_surf(l1):
R = 1.02
l1 = l1 #surface matrix length
theta = __np__.linspace(0, 2*__np__.pi, l1)
rho = __np__.linspace(0, 1, l1)
[u,r] = __np__.meshgrid(theta,rho)
X = r*__cos__(u)
Y = r*__sin__(u)
Z = __sqrt__(R**2-r**2)-__sqrt__(R**2-1)
v_1 = max(abs(Z.max()),abs(Z.min()))
noise = (__np__.random.rand(len(Z),len(Z))*2-1)*0.05*v_1
Z = Z+noise
fig = __plt__.figure(figsize=(12, 8), dpi=80)
ax = fig.gca(projection='3d')
surf = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=__cm__.RdYlGn,\
linewidth=0, antialiased=False, alpha = 0.6)
v = max(abs(Z.max()),abs(Z.min()))
ax.set_zlim(-1, 2)
ax.zaxis.set_major_locator(__LinearLocator__(10))
ax.zaxis.set_major_formatter(__FormatStrFormatter__('%.02f'))
cset = ax.contourf(X, Y, Z, zdir='z', offset=-1, cmap=__cm__.RdYlGn)
fig.colorbar(surf, shrink=1, aspect=30)
__plt__.title('Test Surface: Spherical surface with some noise',fontsize=16)
__plt__.show()
#Generate test surface matrix from a detector
x = __np__.linspace(-1, 1, l1)
y = __np__.linspace(-1, 1, l1)
[X,Y] = __np__.meshgrid(x,y)
Z = __sqrt__(R**2-(X**2+Y**2))-__sqrt__(R**2-1)+noise
for i in range(len(Z)):
for j in range(len(Z)):
if x[i]**2+y[j]**2>1:
Z[i][j]=0
return Z
def fitting(Z,n,remain3D=False,remain2D=False,barchart=False,interferogram=False,removepiston=True):
"""
------------------------------------------------
fitting(Z,n)
Fitting an aberration to several orthonormal Zernike
polynomials.
Return: n-th Zernike coefficients for a fitting surface aberration
Zernike coefficients barchart
Remaining aberration
Fiting surface plot
Input:
Z: A surface or aberration matrix measure from inteferometer
or something else.
n: How many order of Zernike Polynomials you want to fit
reamin(default==Flase): show the surface after remove fitting
aberrations.
removepiston: if remove piston, default = True
------------------------------------------------
"""
fitlist = []
l = len(Z)
x2 = __np__.linspace(-1, 1, l)
y2 = __np__.linspace(-1, 1, l)
[X2,Y2] = __np__.meshgrid(x2,y2)
r = __np__.sqrt(X2**2 + Y2**2)
u = __np__.arctan2(Y2, X2)
for i in range(n):
C = [0]*i+[1]+[0]*(37-i-1)
ZF = __zernikepolar__(C,r,u)
for i in range(l):
for j in range(l):
if x2[i]**2+y2[j]**2>1:
ZF[i][j]=0
a = sum(sum(Z*ZF))*2*2/l/l/__np__.pi
fitlist.append(round(a,3))
l1 = len(fitlist)
fitlist = fitlist+[0]*(37-l1)
Z_new = Z - __zernikepolar__(fitlist,r,u)
for i in range(l):
for j in range(l):
if x2[i]**2+y2[j]**2>1:
Z_new[i][j]=0
#plot bar chart of zernike
if barchart == True:
fitlist1 = fitlist[0:n]
index = __np__.arange(n)
fig = __plt__.figure(figsize=(9, 6), dpi=80)
xticklist = []
width = 0.6
for i in index:
xticklist.append('Z'+str(i+1))
barfigure = __plt__.bar(index, fitlist1, width,color = '#2E9AFE',edgecolor = '#2E9AFE')
__plt__.xticks( index+width/2, xticklist )
__plt__.xlabel('Zernike Polynomials',fontsize=18)
__plt__.ylabel('Coefficient',fontsize=18)
__plt__.title('Fitting Zernike Polynomials Coefficient',fontsize=18)
__plt__.show()
else:
pass
if remain3D == True:
fig = __plt__.figure(figsize=(12, 8), dpi=80)
ax = fig.gca(projection='3d')
surf = ax.plot_surface(X2, Y2, Z_new, rstride=1, cstride=1, cmap=__cm__.RdYlGn,
linewidth=0, antialiased=False, alpha = 0.6)
v = max(abs(Z.max()),abs(Z.min()))
ax.set_zlim(-v, v)
ax.zaxis.set_major_locator(__LinearLocator__(10))
ax.zaxis.set_major_formatter(__FormatStrFormatter__('%.02f'))
cset = ax.contourf(X2, Y2, Z_new, zdir='z', offset=-v, cmap=__cm__.RdYlGn)
fig.colorbar(surf, shrink=1, aspect=30)
__plt__.title('Remaining Aberration',fontsize=18)
p2v = round(__tools__.peak2valley(Z_new),5)
rms1 = round(__tools__.rms(Z_new),5)
label_new = "P-V: "+str(p2v)+"\n"+"RMS: "+str(rms1)
ax.text2D(0.02, 0.1,label_new, transform=ax.transAxes)
__plt__.show()
else:
pass
if remain2D == True:
fig = __plt__.figure(figsize=(9, 6), dpi=80)
ax = fig.gca()
im = __plt__.pcolormesh(X2, Y2, Z_new, cmap=__cm__.RdYlGn)
__plt__.colorbar()
__plt__.title('Remaining Aberration',fontsize=18)
ax.set_aspect('equal', 'datalim')
__plt__.show()
else:
pass
if interferogram == True:
zernike_coefficient = Coefficient(fitlist)
__interferometer__.twyman_green(zernike_coefficient)
else:
pass
if removepiston == True:
fitlist[0] = 0
else:
pass
C = Coefficient(fitlist) #output zernike Coefficient class
__tools__.zernikeprint(fitlist)
return fitlist,C
def fitting(Z,n,remain3D=False,remain2D=False,barchart=False,interferogram=False,removepiston=True):
"""
------------------------------------------------
fitting(Z,n)
Fitting an aberration to several orthonormal Zernike
polynomials.
Return: n-th Zernike coefficients for a fitting surface aberration
Zernike coefficients barchart
Remaining aberration
Fiting surface plot
Input:
Z: A surface or aberration matrix measure from inteferometer
or something else.
n: How many order of Zernike Polynomials you want to fit
reamin(default==Flase): show the surface after remove fitting
aberrations.
removepiston: if remove piston, default = True
------------------------------------------------
"""
fitlist = []
l = len(Z)
x2 = __np__.linspace(-1, 1, l)
y2 = __np__.linspace(-1, 1, l)
[X2,Y2] = __np__.meshgrid(x2,y2)
r = __np__.sqrt(X2**2 + Y2**2)
u = __np__.arctan2(Y2, X2)
for i in range(n):
C = [0]*i+[1]+[0]*(37-i-1)
ZF = __interferometer__.__zernikepolar__(C,r,u)
for i in range(l):
for j in range(l):
if x2[i]**2+y2[j]**2>1:
ZF[i][j]=0
a = sum(sum(Z*ZF))*2*2/l/l/__np__.pi
fitlist.append(round(a,3))
l1 = len(fitlist)
fitlist = fitlist+[0]*(37-l1)
Z_new = Z - __interferometer__.__zernikepolar__(fitlist,r,u)
for i in range(l):
for j in range(l):
if x2[i]**2+y2[j]**2>1:
Z_new[i][j]=0
#plot bar chart of zernike
if barchart == True:
fitlist1 = fitlist[0:n]
index = __np__.arange(n)
fig = __plt__.figure(figsize=(9, 6), dpi=80)
xticklist = []
width = 0.6
for i in index:
xticklist.append('Z'+str(i+1))
barfigure = __plt__.bar(index, fitlist1, width,color = '#2E9AFE',edgecolor = '#2E9AFE')
__plt__.xticks( index+width/2, xticklist )
__plt__.xlabel('Zernike Polynomials',fontsize=18)
__plt__.ylabel('Coefficient',fontsize=18)
__plt__.title('Fitting Zernike Polynomials Coefficient',fontsize=18)
__plt__.show()
else:
pass
if remain3D == True:
fig = __plt__.figure(figsize=(12, 8), dpi=80)
ax = fig.gca(projection='3d')
surf = ax.plot_surface(X2, Y2, Z_new, rstride=1, cstride=1, cmap=__cm__.RdYlGn,
linewidth=0, antialiased=False, alpha = 0.6)
v = max(abs(Z.max()),abs(Z.min()))
ax.set_zlim(-v, v)
ax.zaxis.set_major_locator(__LinearLocator__(10))
ax.zaxis.set_major_formatter(__FormatStrFormatter__('%.02f'))
cset = ax.contourf(X2, Y2, Z_new, zdir='z', offset=-v, cmap=__cm__.RdYlGn)
fig.colorbar(surf, shrink=1, aspect=30)
__plt__.title('Remaining Aberration',fontsize=18)
p2v = round(__tools__.peak2valley(Z_new),5)
rms1 = round(__tools__.rms(Z_new),5)
label_new = "P-V: "+str(p2v)+"\n"+"RMS: "+str(rms1)
ax.text2D(0.02, 0.1,label_new, transform=ax.transAxes)
__plt__.show()
else:
pass
if remain2D == True:
fig = __plt__.figure(figsize=(9, 6), dpi=80)
ax = fig.gca()
im = __plt__.pcolormesh(X2, Y2, Z_new, cmap=__cm__.RdYlGn)
__plt__.colorbar()
__plt__.title('Remaining Aberration',fontsize=18)
ax.set_aspect('equal', 'datalim')
__plt__.show()
else:
pass
if interferogram == True:
zernike_coefficient = Coefficient(fitlist)
__interferometer__.twyman_green(zernike_coefficient)
else:
pass
if removepiston == True:
fitlist[0] = 0
else:
pass
C = Coefficient(fitlist) #output zernike Coefficient class
__tools__.zernikeprint(fitlist)
return fitlist,C
def lens_param_to_psf():
import numpy as __np__
from numpy import sqrt as __sqrt__
from numpy import cos as __cos__
from numpy import sin as __sin__
import matplotlib.pyplot as __plt__
from matplotlib import cm as __cm__
from matplotlib.ticker import LinearLocator as __LinearLocator__
from matplotlib.ticker import FormatStrFormatter as __FormatStrFormatter__
from mpl_toolkits.mplot3d import Axes3D
from numpy.fft import fftshift as __fftshift__
from numpy.fft import ifftshift as __ifftshift__
from numpy.fft import fft2 as __fft2__
def __apershow__(obj):
obj = -abs(obj)
__plt__.imshow(obj)
__plt__.set_cmap('Greys')
__plt__.show()
l1 = 100
# Generate test surface matrix from a detector
x = __np__.linspace(-1, 1, l1)
y = __np__.linspace(-1, 1, l1)
[X, Y] = __np__.meshgrid(x, y)
r = __sqrt__(X**2 + Y**2)
Z = __sqrt__(14) * (8 * X**4 - 8 * X**2 * r**2 + r**4) * (6 * r**2 - 5)
for i in range(len(Z)):
for j in range(len(Z)):
if x[i]**2 + y[j]**2 > 1:
Z[i][j] = 0
fig = __plt__.figure(1)
ax = fig.gca(projection='3d')
surf = ax.plot_surface(X,
Y,
Z,
rstride=1,
cstride=1,
cmap=__cm__.RdYlGn,
linewidth=0,
antialiased=False,
alpha=0.6)
v = max(abs(Z.max()), abs(Z.min()))
ax.set_zlim(-v * 5, v * 5)
cset = ax.contourf(X, Y, Z, zdir='z', offset=-v * 5, cmap=__cm__.RdYlGn)
ax.zaxis.set_major_locator(__LinearLocator__(10))
ax.zaxis.set_major_formatter(__FormatStrFormatter__('%.02f'))
fig.colorbar(surf, shrink=1, aspect=30)
__plt__.show()
d = 800
A = __np__.zeros([d, d])
A[d // 2 - 49:d // 2 + 51, d // 2 - 49:d // 2 + 51] = Z
__plt__.imshow(A)
__plt__.show()
abbe = __np__.exp(1j * 2 * __np__.pi * A)
for i in range(len(abbe)):
for j in range(len(abbe)):
if abbe[i][j] == 1:
abbe[i][j] = 0
fig = __plt__.figure(2)
AP = abs(__fftshift__(__fft2__(__fftshift__(abbe))))**2
AP = AP / AP.max()
__plt__.imshow(AP)
__plt__.show()
Z = __sqrt__(14)*(8*X**4-8*X**2*r**2+r**4)*(6*r**2-5)
for i in range(len(Z)):
for j in range(len(Z)):
if x[i]**2+y[j]**2>1:
Z[i][j]=0
fig = __plt__.figure(1)
ax = fig.gca(projection='3d')
surf = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=__cm__.RdYlGn,
linewidth=0, antialiased=False, alpha = 0.6)
v = max(abs(Z.max()),abs(Z.min()))
ax.set_zlim(-v*5, v*5)
cset = ax.contourf(X, Y, Z, zdir='z', offset=-v*5, cmap=__cm__.RdYlGn)
ax.zaxis.set_major_locator(__LinearLocator__(10))
ax.zaxis.set_major_formatter(__FormatStrFormatter__('%.02f'))
fig.colorbar(surf, shrink=1, aspect=30)
__plt__.show()
d = 400
A = __np__.zeros([d,d])
A[d/2-49:d/2+51,d/2-49:d/2+51] = Z
__plt__.imshow(A)
__plt__.show()
abbe = __np__.exp(1j*2*__np__.pi*A)
for i in range(len(abbe)):
for j in range(len(abbe)):
if abbe[i][j]==1:
abbe[i][j]=0
fig = __plt__.figure(2)