def __psfcaculator__(self,lambda_1=632*10**(-9),z=0.1): """ height: Exit pupil height width: Exit pupil width z: Distance from exit pupil to image plane """ a = self.__a__ b = __sqrt__(1-a**2) l1 = 100; x1 = __np__.linspace(-a, a, l1) y1 = __np__.linspace(-b, b, l1) [X,Y] = __np__.meshgrid(x1,y1) Z = __zernikecartesian__(self.__coefficients__,a,X,Y) d = 400 # background A = __np__.zeros([d,d]) A[d//2-l1//2+1:d//2+l1//2+1,d//2-l1//2+1:d//2+l1//2+1] = Z # fig = __plt__.figure() # __plt__.imshow(A) # __plt__.colorbar() # __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 PSF = __fftshift__(__fft2__(__fftshift__(abbe)))**2 PSF = PSF/PSF.max() return PSF
def __seidelcartesian__(coefficient,x,y): W = coefficient h = 1 u = __arctan2__(y,x) r = __sqrt__(x**2+y**2) W = __seidelpolar__(coefficient,r,u) return W
def __seidelcartesian__(coefficient, x, y):
W = coefficient
h = 1
u = __arctan2__(y, x)
r = __sqrt__(x**2 + y**2)
W = __seidelpolar__(coefficient, r, u)
return W
def __psfcaculator__(self, lambda_1=632 * 10**(-9), z=0.1):
"""
height: Exit pupil height
width: Exit pupil width
z: Distance from exit pupil to image plane
"""
a = self.__a__
b = __sqrt__(1 - a**2)
l1 = 100
x1 = __np__.linspace(-a, a, l1)
y1 = __np__.linspace(-b, b, l1)
[X, Y] = __np__.meshgrid(x1, y1)
Z = __zernikecartesian__(self.__coefficients__, a, X, Y)
d = 400 # background
A = __np__.zeros([d, d])
A[d // 2 - l1 // 2 + 1:d // 2 + l1 // 2 + 1,
d // 2 - l1 // 2 + 1:d // 2 + l1 // 2 + 1] = Z
# fig = __plt__.figure()
# __plt__.imshow(A)
# __plt__.colorbar()
# __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
PSF = __fftshift__(__fft2__(__fftshift__(abbe)))**2
PSF = PSF / PSF.max()
return PSF
def asphereline(self):
R, k, a2, a3, a4, a5, a6, a7, a8, a9, a10 = self.__coefficients__
r = __np__.linspace(-R, R, 100)
C = 1 / R
Z = C*r**2*(1+__sqrt__(1-(1+k)*r**2*C**2)) + a2*r**4 + a3*r**6 + a4*r**8 + \
+ a5*r**10 + a6*r**12 + a7*r**14 + a8*r**16 + a9*r**18 + a10*r**20
Z = -Z
fig = __plt__.figure(figsize=(12, 8), dpi=80)
__plt__.plot(r, Z)
__plt__.axis('equal')
__plt__.show()
def asphereline(self):
R,k,a2,a3,a4,a5,a6,a7,a8,a9,a10 = self.__coefficients__
r = __np__.linspace(-R,R,100)
C = 1/R
Z = C*r**2*(1+__sqrt__(1-(1+k)*r**2*C**2)) + a2*r**4 + a3*r**6 + a4*r**8 + \
+ a5*r**10 + a6*r**12 + a7*r**14 + a8*r**16 + a9*r**18 + a10*r**20
Z = -Z
fig = __plt__.figure(figsize=(12, 8), dpi=80)
__plt__.plot(r,Z)
__plt__.axis('equal')
__plt__.show()
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 zernikemap(self):
a = self.__a__
b = __sqrt__(1-a**2)
x1 = __np__.linspace(-a, a, 100)
y1 = __np__.linspace(-b, b, 100)
[X,Y] = __np__.meshgrid(x1,y1)
Z = __zernikecartesian__(self.__coefficients__,a,X,Y)
fig = __plt__.figure(figsize=(12, 8), dpi=80)
ax = fig.gca()
im = __plt__.pcolormesh(X, Y, Z, cmap=__cm__.RdYlGn)
__plt__.colorbar()
ax.set_aspect('equal', 'datalim')
__plt__.show()
return 0
def zernikemap(self):
a = self.__a__
b = __sqrt__(1 - a**2)
x1 = __np__.linspace(-a, a, 100)
y1 = __np__.linspace(-b, b, 100)
[X, Y] = __np__.meshgrid(x1, y1)
Z = __zernikecartesian__(self.__coefficients__, a, X, Y)
fig = __plt__.figure(figsize=(12, 8), dpi=80)
ax = fig.gca()
im = __plt__.pcolormesh(X, Y, Z, cmap=__cm__.RdYlGn)
__plt__.colorbar()
ax.set_aspect('equal', 'datalim')
__plt__.show()
return 0
def aspherematrix(self): l = 100 R = self.__coefficients__[0] x1 = __np__.linspace(-R, R, l) [X,Y] = __np__.meshgrid(x1,x1) r = __sqrt__(X**2+Y**2) Z = __aspherepolar__(self.__coefficients__,r) for i in range(l): for j in range(l): if x1[i]**2+x1[j]**2 > R**2: Z[i][j] = 0 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) __plt__.show() return Z
def aspherematrix(self): l = 100 R = self.__coefficients__[0] x1 = __np__.linspace(-R, R, l) [X,Y] = __np__.meshgrid(x1,x1) r = __sqrt__(X**2+Y**2) Z = __aspherepolar__(self.__coefficients__,r) for i in range(l): for j in range(l): if x1[i]**2+x1[j]**2 > R**2: Z[i][j] = 0 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) __plt__.show() return Z
def zernikesurface(self):
"""
------------------------------------------------
zernikesurface(self, label_1 = True):
Return a 3D Zernike Polynomials surface figure
label_1: default show label
------------------------------------------------
"""
a = self.__a__
b = __sqrt__(1 - a**2)
x1 = __np__.linspace(-a, a, 50)
y1 = __np__.linspace(-b, b, 50)
[X, Y] = __np__.meshgrid(x1, y1)
Z = __zernikecartesian__(self.__coefficients__, a, X, Y)
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)
ax.auto_scale_xyz([-1, 1], [-1, 1], [Z.max(), Z.min()])
# ax.set_xlim(-a, a)
# ax.set_ylim(-b, b)
# 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)
# p2v = round(__tools__.peak2valley(Z),5)
# rms1 = round(__tools__.rms(Z),5)
__plt__.show()
def zernikesurface(self):
"""
------------------------------------------------
zernikesurface(self, label_1 = True):
Return a 3D Zernike Polynomials surface figure
label_1: default show label
------------------------------------------------
"""
a = self.__a__
b = __sqrt__(1-a**2)
x1 = __np__.linspace(-a, a, 50)
y1 = __np__.linspace(-b, b, 50)
[X,Y] = __np__.meshgrid(x1,y1)
Z = __zernikecartesian__(self.__coefficients__,a,X,Y)
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)
ax.auto_scale_xyz([-1, 1], [-1, 1], [Z.max(), Z.min()])
# ax.set_xlim(-a, a)
# ax.set_ylim(-b, b)
# 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)
# p2v = round(__tools__.peak2valley(Z),5)
# rms1 = round(__tools__.rms(Z),5)
__plt__.show()
def Z12(self,r,u): return __sqrt__(10)*(4*r**2-3)*r**2*__cos__(2*u)
def Z11(self,r,u): return __sqrt__(5)*(1-6*r**2+6*r**4)
def Z10(self,r,u): return __sqrt__(8)*r**3*__cos__(3*u)
def Z9(self,r,u): return __sqrt__(8)*r**3*__sin__(3*u)
def Z8(self,r,u): return __sqrt__(8)*(3*r**2-2)*r*__cos__(u)
def __zernikecartesian__(coefficient,a,x,y): """ ------------------------------------------------ __zernikecartesian__(coefficient,a,x,y): Return combined aberration Orthonormal Rectangle Aperture Polynomials Caculation for Rectangle aperture in Cartesian coordinates coefficient: Zernike Polynomials Coefficient from input a: 1/2 aperture width in a circle(See reference) x: x in Cartesian coordinates y: y in Cartesian coordinates ------------------------------------------------ """ mu = __sqrt__(9-36*a**2+103*a**4-134*a**6+67*a**6+67*a**8) v = __sqrt__(49-196*a**2+330*a**4-268*a**6+134*a**8) tau = 1/(128*v*a**4*(1-a**2)**2) eta = 9-45*a**2+139*a**4-237*a**6+210*a**8-67*a**10 r = x**2+y**2 R = [0]+coefficient R1 = R[1] * 1 R2 = R[2] * __sqrt__(3)/a*x R3 = R[3] * __sqrt__(3/(1-a**2))*y R4 = R[4] * __sqrt__(5)/2/__sqrt__(1-2*a**2+2*a**4)*(3*r**2-1) R5 = R[5] * 3/a/__sqrt__(1-a**2)*x*y R6 = R[6] * __sqrt__(5)/4/a**2/(1-a**2)/__sqrt__(1-2*a**2+2*a**4)*\ (3*(1-a**2)**2*x**2-3*a**4*y**2-a*82*(1-3*a**2+2*a**4)) R7 = R[7] * __sqrt__(21)/2/__sqrt__(27-81*a**2+116*a**4-62*a**6)*\ (15*r**2-9+4*a**2)*y R8 = R[8] * __sqrt__(21)/2/a/__sqrt__(35-70*a**2+62*a**4)*\ (15*r**2-5-4*a**2)*x R9 = R[9] * (__sqrt__(5)*__sqrt__((27-54*a**2+62*a**4)/(1-a**2))/\ (2*a**2*(27-81*a**2+116*a**4-62*a**6)))*(27*(1-a**2)**2*x**2-\ 35*a**4*y**2-a**2*(9-39*a**2+30*a**4))*y r1 = 35-70*a**2+62*a**4 R10 = R[10] * (__sqrt__(5)/(2*a**3*(1-a**2)*__sqrt__(r1)))*(35*(1-a**2)**2*x**2-\ 27*a**4*y**2-a**2*(21-51*a**2+30*a**4))*x R11 = R[11] * 1/8/mu*(315*r**4+30*(7+2*a**2)*x**2-30*(9-2*a**2)*y**2+27+16*a**2-16*a**4) R12 = R[12] * (3*mu/(8*a**2*v*eta))*(35*(1-a**2)**2*(18-36*a**2+67*a**4)*x**4+\ 630*(1-2*a**2)*(1-2*a**2+2*a**4)*x**2*y**2-35*a**4*(49-98*a**2+67*a**4)*y**4-\ 30*(1-a**2)*(7-10*a**2-12*a**4+75*a**6-67*a**8)*x**2-\ 30*a**2*(7-77*a**2+189*a**4-193*a**6+67*a**8)*y**2+\ a**2*(1-a**2)*(1-2*a**2)*(70-233*a**2+233*a**4)) R13 = R[13] * __sqrt__(21)/(2*a*__sqrt__(1-3*a**2+4*a**4-2*a**6))*(5*r**2-3)*x*y R14 = R[14] * 16*tau*(735*(1-a**2)**4*x**4-540*a**4*(1-a**2)**2*x**2*y**2+735*a**8*y**4-\ 90*a**2*(1-a**2)**3*(7-9*a**2)*x**2+90*a**6*(1-a**2)*(2-9*a**2)*y**2+\ +3*a**4*(1-a**2)**2*(21-62*a**2+62*a**4)) R15 = R[15] * __sqrt__(21)/(2*a**3*(1-a**2)*__sqrt__(1-3*a**2+4*a**4-2*a**6))*\ (5*(1-a**2)**2*x**2-5*a**4*y**2-a**2*(3-9*a**2+6*a**4))*x*y RW = R1 + R2 + R3+ R4+ R5+ R6+ R7+ R8+ R9+ \ R10+ R11+ R12+ R13+ R14+ R15 return RW
def Z15(self,r,u): return __sqrt__(10)*r**4*__sin__(4*u)
def Z26(self,r,u): return __sqrt__(14)*(6*r**2-5)*r**4*__cos__(4*u)
def Z24(self,r,u): return __sqrt__(14)*(15*r**4-20*r**2+6)*r**2*__cos__(2*u)
def Z21(self,r,u): return __sqrt__(12)*r**5*__sin__(5*u)
def Z19(self,r,u): return __sqrt__(12)*(5*r**2-4)*r**3*__sin__(3*u)
def Z17(self,r,u): return __sqrt__(12)*(10*r**4-12*r**2+3)*r*__sin__(u)
def __zernikepolar__(coefficient,a,r,u): """ ------------------------------------------------ __zernikepolar__(coefficient,r,u): Return combined aberration Orthonormal Rectangle Aperture Polynomials Caculation in polar coordinates coefficient: Orthonormal Rectangle Aperture Polynomials Coefficient from input r: rho in polar coordinates u: theta in polar coordinates ------------------------------------------------ """ mu = __sqrt__(9-36*a**2+103*a**4-134*a**6+67*a**6+67*a**8) v = __sqrt__(49-196*a**2+330*a**4-268*a**6+134*a**8) tau = 1/(128*v*a**4*(1-a**2)**2) eta = 9-45*a**2+139*a**4-237*a**6+210*a**8-67*a**10 R = [0]+coefficient R1 = R[1] * 1 R2 = R[2] * __sqrt__(3)/a*r*__cos__(u) R3 = R[3] * __sqrt__(3/(1-a**2))*r*__sin__(u) R4 = R[4] * __sqrt__(5)/2/__sqrt__(1-2*a**2+2*a**4)*(3*r**2-1) R5 = R[5] * 3/2/a/__sqrt__(1-a**2)*r**2*__sin__(2*u) R6 = R[6] * __sqrt__(5)/2/a**2/(1-a**2)/__sqrt__(1-2*a**2+2*a**4)*\ (3*(1-2*a**2+2*a**4)*r**2*__cos__(2*u)+3*(1-2*a**2)*r**2-\ 2*a**2*(1-a**2)*(1-2*a**2)) R7 = R[7] * __sqrt__(21)/2/__sqrt__(27-81*a**2+116*a**4-62*a**6)*\ (15*r**2-9+4*a**2)*r*__sin__(u) R8 = R[8] * __sqrt__(21)/2/a/__sqrt__(35-70*a**2+62*a**4)*\ (15*r**2-5-4*a**2)*r*__cos__(u) R9 = R[9] * (__sqrt__(5)*__sqrt__((27-54*a**2+62*a**4)/(1-a**2))/\ (8*a**2*(27-81*a**2+116*a**4-62*a**6)))*((27-54*a**2+62*a**4)*\ r*__sin__(3*u)-3*(4*a**2*(3-13*a**2+10*a**4)-(9-18*a**2-26*a**4))\ *r*__sin__(u)) r1 = 35-70*a**2+62*a**4 R10 = R[10] * (__sqrt__(5)/(8*a**3*(1-a**2)*__sqrt__(r1)))*((r1)*r**3*__cos__(3*u)-\ 3*(4*a**2*(7-17*a**2+10*a**4)-(r1)*r**2)*r*__cos__(u)) R11 = R[11] * 1/8/mu*(315*r**4+30*(1-2*a**2)*r**2*__cos__(2*u)-240*r**2+27+16*a*2-16*a**4) R12 = R[12] * (3*mu/(8*a**2*v*eta))*(315*(1-2*a**2)*(1-2*a**2+2*a**4)*r**4+\ 5*(7*mu**2*r**2-21+72*a**2-225*a**4+306*a**6-152*a**8)*r**2*__cos__(2*u)-\ 15*(1-2*a**2)*(7+4*a**2-71*a**4+134*a**6-67*a**8)*r**2+\ a**2*(1-a**2)*(1-2*a**2)*(70-233*a**2+233*a**4)) R13 = R[13] * __sqrt__(21)/(4*a*__sqrt__(1-3*a**2+4*a**4-2*a**6))*(5*r**2-3)*r**2*__sin__(2*u) R14 = R[14] * 6*tau*(5*v**2*r**4*__cos__(4*u)-20*(1-2*a**2)*(6*a**2*(7-16*a**2+18*a**4-9*a**6)-\ 49*(1-2*a**2+2*a**4)*r**2)*r**2*__cos__(u)+8*a**4*(1-a**2)**2*(21-62*a**2+62*a**4)-\ 120*a**2*(7-30*a**2+46*a**4-23*a**6)*r**2+\ 15*(49-196*a**2+282*a**4-172*a**6+86*a**8)*r**4) R15 = R[15] * (__sqrt__(21)/(8*a**3*__sqrt__((1-a**2)**3))/__sqrt__(1-2*a**2+2*a**4))*\ (-(1-2*a**2)*(6*a**2-6*a**4-5*r**2)*r**2*__sin__(2*u)+\ (5/2)*(1-2*a**2+2**a**4)*r**4*__sin__(4*u)) RW = R1 + R2 + R3+ R4+ R5+ R6+ R7+ R8+ R9+ \ R10+ R11+ R12+ R13+ R14+ R15 return RW
def Z13(self,r,u): return __sqrt__(10)*(4*r**2-3)*r**2*__sin__(2*u)
def Z14(self,r,u): return __sqrt__(10)*r**4*__cos__(4*u)
def Z28(self,r,u): return __sqrt__(14)*r**6*__cos__(6*u)
def Z16(self,r,u): return __sqrt__(12)*(10*r**4-12*r**2+3)*r*__cos__(u)
def __aspherepolar__(coefficient,r): R,k,a2,a3,a4,a5,a6,a7,a8,a9,a10 = coefficient C = 1/R Z = C*r**2*(1+__sqrt__(1-(1+k)*r**2*C**2)) + a2*r**4 + a3*r**6 + a4*r**8 + \ + a5*r**10 + a6*r**12 + a7*r**14 + a8*r**16 + a9*r**18 + a10*r**20 return -Z
def Z18(self,r,u): return __sqrt__(12)*(5*r**2-4)*r**3*__cos__(3*u)
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 numpy.fft import fftshift as __fftshift__ from numpy.fft import ifftshift as __ifftshift__ from numpy.fft import fft2 as __fft2__ 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 = 20*X 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 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() def exp_func(a): if a == 0: return 0
def Z20(self,r,u): return __sqrt__(12)*r**5*__cos__(5*u)
def zernike2seidel(self):
'''
Ap is the piston aberration,coefficients Ai represent the
peak value of the corresponding Seidel aberration term,
'''
a = [0]+self.__coefficients__
#Piston
Ap = a[1]-__sqrt__(3)*a[4]+__sqrt__(5)*a[11]
#tilt
At = 2*__sqrt__((a[2]-__sqrt__(8)*a[8])**2+(a[3]-__sqrt__(8)*a[7])**2)
Bt = __arctan2__(a[3]-__sqrt__(8)*a[7],a[2]-__sqrt__(8)*a[8])*180/__np__.pi
#Astigmatism
Aa = 2*__sqrt__(6*(a[5]**2+a[6]**2))
Ba = 0.5*__arctan2__(a[5],a[6])*180/__np__.pi
#defocus
Ad = 2*(__sqrt__(3)*a[4]-3*__sqrt__(5)*a[11]-Aa)
#Coma
Ac = 6*__sqrt__(2*(a[7]**2+a[8]**2))
Bc = __arctan2__(a[7],a[8])*180/__np__.pi
#Spherical
As = 6*__sqrt__(5)*a[11]
A = [Ap,At,Bt,Ad,Aa,Ba,Ac,Bc,As]
seidellist=["Piston",
"Tilt",
"Defocus",
"Astigmatism",
"Coma",
"Spherical"]
Atable = [[Ap,0.0],[At,Bt],[Ad,0.0],[Aa,Ba],[Ac,Bc],[As,0.0]]
print" Magnitude Angle (Degrees)"
print"-------------------------------------------"
for i in range(len(seidellist)):
print "| {0:>13s} | {1:>8s} | {2:>8s} |".\
format(seidellist[i],str(round(Atable[i][0],3)),str(round(Atable[i][1],3)))
print"-------------------------------------------"
SeidelCoefficient = __seidel2__.Coefficient(Atable)
return SeidelCoefficient
def Z22(self,r,u): return __sqrt__(7)*(20*r**6-30*r**4+12*r**2-1)
def __zernikepolar__(coefficient,r,u): """ ------------------------------------------------ __zernikepolar__(coefficient,r,u): Return combined aberration Zernike Polynomials Caculation in polar coordinates coefficient: Zernike Polynomials Coefficient from input r: rho in polar coordinates u: theta in polar coordinates ------------------------------------------------ """ Z = [0]+coefficient Z1 = Z[1] * 1*(__cos__(u)**2+__sin__(u)**2) Z2 = Z[2] * 2*r*__cos__(u) Z3 = Z[3] * 2*r*__sin__(u) Z4 = Z[4] * __sqrt__(3)*(2*r**2-1) Z5 = Z[5] * __sqrt__(6)*r**2*__sin__(2*u) Z6 = Z[6] * __sqrt__(6)*r**2*__cos__(2*u) Z7 = Z[7] * __sqrt__(8)*(3*r**2-2)*r*__sin__(u) Z8 = Z[8] * __sqrt__(8)*(3*r**2-2)*r*__cos__(u) Z9 = Z[9] * __sqrt__(8)*r**3*__sin__(3*u) Z10 = Z[10] * __sqrt__(8)*r**3*__cos__(3*u) Z11 = Z[11] * __sqrt__(5)*(1-6*r**2+6*r**4) Z12 = Z[12] * __sqrt__(10)*(4*r**2-3)*r**2*__cos__(2*u) Z13 = Z[13] * __sqrt__(10)*(4*r**2-3)*r**2*__sin__(2*u) Z14 = Z[14] * __sqrt__(10)*r**4*__cos__(4*u) Z15 = Z[15] * __sqrt__(10)*r**4*__sin__(4*u) Z16 = Z[16] * __sqrt__(12)*(10*r**4-12*r**2+3)*r*__cos__(u) Z17 = Z[17] * __sqrt__(12)*(10*r**4-12*r**2+3)*r*__sin__(u) Z18 = Z[18] * __sqrt__(12)*(5*r**2-4)*r**3*__cos__(3*u) Z19 = Z[19] * __sqrt__(12)*(5*r**2-4)*r**3*__sin__(3*u) Z20 = Z[20] * __sqrt__(12)*r**5*__cos__(5*u) Z21 = Z[21] * __sqrt__(12)*r**5*__sin__(5*u) Z22 = Z[22] * __sqrt__(7)*(20*r**6-30*r**4+12*r**2-1) Z23 = Z[23] * __sqrt__(14)*(15*r**4-20*r**2+6)*r**2*__sin__(2*u) Z24 = Z[24] * __sqrt__(14)*(15*r**4-20*r**2+6)*r**2*__cos__(2*u) Z25 = Z[25] * __sqrt__(14)*(6*r**2-5)*r**4*__sin__(4*u) Z26 = Z[26] * __sqrt__(14)*(6*r**2-5)*r**4*__cos__(4*u) Z27 = Z[27] * __sqrt__(14)*r**6*__sin__(6*u) Z28 = Z[28] * __sqrt__(14)*r**6*__cos__(6*u) Z29 = Z[29] * 4*(35*r**6-60*r**4+30*r**2-4)*r*__sin__(u) Z30 = Z[30] * 4*(35*r**6-60*r**4+30*r**2-4)*r*__cos__(u) Z31 = Z[31] * 4*(21*r**4-30*r**2+10)*r**3*__sin__(3*u) Z32 = Z[32] * 4*(21*r**4-30*r**2+10)*r**3*__cos__(3*u) Z33 = Z[33] * 4*(7*r**2-6)*r**5*__sin__(5*u) Z34 = Z[34] * 4*(7*r**2-6)*r**5*__cos__(5*u) Z35 = Z[35] * 4*r**7*__sin__(7*u) Z36 = Z[36] * 4*r**7*__cos__(7*u) Z37 = Z[37] * 3*(70*r**8-140*r**6+90*r**4-20*r**2+1) Z = 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 Z
def Z25(self,r,u): return __sqrt__(14)*(6*r**2-5)*r**4*__sin__(4*u)
def __zernikecartesian__(coefficient,x,y): """ ------------------------------------------------ __zernikecartesian__(coefficient,x,y): Return combined aberration Zernike Polynomials Caculation in Cartesian coordinates coefficient: Zernike Polynomials Coefficient from input x: x in Cartesian coordinates y: y in Cartesian coordinates ------------------------------------------------ """ Z = [0]+coefficient r = __sqrt__(x**2 + y**2) Z1 = Z[1] * 1 Z2 = Z[2] * 2*x Z3 = Z[3] * 2*y Z4 = Z[4] * __sqrt__(3)*(2*r**2-1) Z5 = Z[5] * 2*__sqrt__(6)*x*y Z6 = Z[6] * __sqrt__(6)*(x**2-y**2) Z7 = Z[7] * __sqrt__(8)*y*(3*r**2-2) Z8 = Z[8] * __sqrt__(8)*x*(3*r**2-2) Z9 = Z[9] * __sqrt__(8)*y*(3*x**2-y**2) Z10 = Z[10] * __sqrt__(8)*x*(x**2-3*y**2) Z11 = Z[11] * __sqrt__(5)*(6*r**4-6*r**2+1) Z12 = Z[12] * __sqrt__(10)*(x**2-y**2)*(4*r**2-3) Z13 = Z[13] * 2*__sqrt__(10)*x*y*(4*r**2-3) Z14 = Z[14] * __sqrt__(10)*(r**4-8*x**2*y**2) Z15 = Z[15] * 4*__sqrt__(10)*x*y*(x**2-y**2) Z16 = Z[16] * __sqrt__(12)*x*(10*r**4-12*r**2+3) Z17 = Z[17] * __sqrt__(12)*y*(10*r**4-12*r**2+3) Z18 = Z[18] * __sqrt__(12)*x*(x**2-3*y**2)*(5*r**2-4) Z19 = Z[19] * __sqrt__(12)*y*(3*x**2-y**2)*(5*r**2-4) Z20 = Z[20] * __sqrt__(12)*x*(16*x**4-20*x**2*r**2+5*r**4) Z21 = Z[21] * __sqrt__(12)*y*(16*y**4-20*y**2*r**2+5*r**4) Z22 = Z[22] * __sqrt__(7)*(20*r**6-30*r**4+12*r**2-1) Z23 = Z[23] * 2*__sqrt__(14)*x*y*(15*r**4-20*r**2+6) Z24 = Z[24] * __sqrt__(14)*(x**2-y**2)*(15*r**4-20*r**2+6) Z25 = Z[25] * 4*__sqrt__(14)*x*y*(x**2-y**2)*(6*r**2-5) Z26 = Z[26] * __sqrt__(14)*(8*x**4-8*x**2*r**2+r**4)*(6*r**2-5) Z27 = Z[27] * __sqrt__(14)*x*y*(32*x**4-32*x**2*r**2+6*r**4) Z28 = Z[28] * __sqrt__(14)*(32*x**6-48*x**4*r**2+18*x**2*r**4-r**6) Z29 = Z[29] * 4*y*(35*r**6-60*r**4+30*r**2+10) Z30 = Z[30] * 4*x*(35*r**6-60*r**4+30*r**2+10) Z31 = Z[31] * 4*y*(3*x**2-y**2)*(21*r**4-30*r**2+10) Z32 = Z[32] * 4*x*(x**2-3*y**2)*(21*r**4-30*r**2+10) Z33 = Z[33] * 4*(7*r**2-6)*(4*x**2*y*(x**2-y**2)+y*(r**4-8*x**2*y**2)) Z34 = Z[34] * (4*(7*r**2-6)*(x*(r**4-8*x**2*y**2)-4*x*y**2*(x**2-y**2))) Z35 = Z[35] * (8*x**2*y*(3*r**4-16*x**2*y**2)+4*y*(x**2-y**2)*(r**4-16*x**2*y**2)) Z36 = Z[36] * (4*x*(x**2-y**2)*(r**4-16*x**2*y**2)-8*x*y**2*(3*r**4-16*x**2*y**2)) Z37 = Z[37] * 3*(70*r**8-140*r**6+90*r**4-20*r**2+1) ZW = 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 ZW
def Z27(self,r,u): return __sqrt__(14)*r**6*__sin__(6*u)
def Z6(self,r,u): return __sqrt__(6)*r**2*__cos__(2*u)
def __zernikepolar__(coefficient,r,u): """ ------------------------------------------------ __zernikepolar__(coefficient,r,u): Return combined aberration Zernike Polynomials Caculation in polar coordinates coefficient: Zernike Polynomials Coefficient from input r: rho in polar coordinates u: theta in polar coordinates ------------------------------------------------ """ Z = [0]+coefficient Z1 = Z[1] * 1*(__cos__(u)**2+__sin__(u)**2) Z2 = Z[2] * 2*r*__cos__(u) Z3 = Z[3] * 2*r*__sin__(u) Z4 = Z[4] * __sqrt__(3)*(2*r**2-1) Z5 = Z[5] * __sqrt__(6)*r**2*__sin__(2*u) Z6 = Z[6] * __sqrt__(6)*r**2*__cos__(2*u) Z7 = Z[7] * __sqrt__(8)*(3*r**2-2)*r*__sin__(u) Z8 = Z[8] * __sqrt__(8)*(3*r**2-2)*r*__cos__(u) Z9 = Z[9] * __sqrt__(8)*r**3*__sin__(3*u) Z10 = Z[10] * __sqrt__(8)*r**3*__cos__(3*u) Z11 = Z[11] * __sqrt__(5)*(1-6*r**2+6*r**4) Z12 = Z[12] * __sqrt__(10)*(4*r**2-3)*r**2*__cos__(2*u) Z13 = Z[13] * __sqrt__(10)*(4*r**2-3)*r**2*__sin__(2*u) Z14 = Z[14] * __sqrt__(10)*r**4*__cos__(4*u) Z15 = Z[15] * __sqrt__(10)*r**4*__sin__(4*u) Z16 = Z[16] * __sqrt__(12)*(10*r**4-12*r**2+3)*r*__cos__(u) Z17 = Z[17] * __sqrt__(12)*(10*r**4-12*r**2+3)*r*__sin__(u) Z18 = Z[18] * __sqrt__(12)*(5*r**2-4)*r**3*__cos__(3*u) Z19 = Z[19] * __sqrt__(12)*(5*r**2-4)*r**3*__sin__(3*u) Z20 = Z[20] * __sqrt__(12)*r**5*__cos__(5*u) Z21 = Z[21] * __sqrt__(12)*r**5*__sin__(5*u) Z22 = Z[22] * __sqrt__(7)*(20*r**6-30*r**4+12*r**2-1) Z23 = Z[23] * __sqrt__(14)*(15*r**4-20*r**2+6)*r**2*__sin__(2*u) Z24 = Z[24] * __sqrt__(14)*(15*r**4-20*r**2+6)*r**2*__cos__(2*u) Z25 = Z[25] * __sqrt__(14)*(6*r**2-5)*r**4*__sin__(4*u) Z26 = Z[26] * __sqrt__(14)*(6*r**2-5)*r**4*__cos__(4*u) Z27 = Z[27] * __sqrt__(14)*r**6*__sin__(6*u) Z28 = Z[28] * __sqrt__(14)*r**6*__cos__(6*u) Z29 = Z[29] * 4*(35*r**6-60*r**4+30*r**2-4)*r*__sin__(u) Z30 = Z[30] * 4*(35*r**6-60*r**4+30*r**2-4)*r*__cos__(u) Z31 = Z[31] * 4*(21*r**4-30*r**2+10)*r**3*__sin__(3*u) Z32 = Z[32] * 4*(21*r**4-30*r**2+10)*r**3*__cos__(3*u) Z33 = Z[33] * 4*(7*r**2-6)*r**5*__sin__(5*u) Z34 = Z[34] * 4*(7*r**2-6)*r**5*__cos__(5*u) Z35 = Z[35] * 4*r**7*__sin__(7*u) Z36 = Z[36] * 4*r**7*__cos__(7*u) Z37 = Z[37] * 3*(70*r**8-140*r**6+90*r**4-20*r**2+1) Z = 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 Z
def Z7(self,r,u): return __sqrt__(8)*(3*r**2-2)*r*__sin__(u)