def hartmann(coefficients, r, R):
"""
Generate Hartmann spotdiagram
use circle hartmann plate
coefficients: zernike coefficients
r: distance from the pupil of the wavefront to detect plate
R: radius of mirror under test
"""
coefficients = coefficients.__coefficients__
x_list = []
y_list = []
Ax_list = []
Ay_list = []
s = 40
x = y = __np__.linspace(-R, R, s)
M = []
for i in x:
tmp = []
for j in y:
if i**2 + j**2 < R**2:
x_list.append(i)
y_list.append(j)
W0 = __zernike__.__zernikecartesian__(coefficients, i, j)
Wx = __zernike__.__zernikecartesian__(coefficients, 1.01 * i,
j)
Wy = __zernike__.__zernikecartesian__(coefficients, i,
1.01 * j)
TAx = -(Wx - W0) / (0.01 * i) * r
TAy = -(Wy - W0) / (0.01 * j) * r
Ax_list.append(TAx)
Ay_list.append(TAy)
tmp.append([1, [i, j], [TAx, TAy]])
else:
tmp.append([0, [i, j], [0, 0]])
M.append(tmp)
fig = __plt__.figure(1, figsize=(6, 6))
ax = fig.gca()
ax.set_axis_bgcolor('black')
__plt__.title('Hartmann Spotdiagram', fontsize=18)
__plt__.plot(Ax_list, Ay_list, 'wo')
__plt__.show()
return M, r
def hartmann(coefficients, r, R):
"""
Generate Hartmann spotdiagram
use circle hartmann plate
coefficients: zernike coefficients
r: distance from the pupil of the wavefront to detect plate
R: radius of mirror under test
"""
coefficients = coefficients.__coefficients__
x_list = []
y_list = []
Ax_list = []
Ay_list = []
s = 40
x = y = __np__.linspace(-R, R, s)
M = []
for i in x:
tmp = []
for j in y:
if i**2 + j**2 < R**2:
x_list.append(i)
y_list.append(j)
W0 = __zernike__.__zernikecartesian__(coefficients,i,j)
Wx = __zernike__.__zernikecartesian__(coefficients,1.01*i,j)
Wy = __zernike__.__zernikecartesian__(coefficients,i,1.01*j)
TAx = -(Wx-W0)/(0.01*i)*r
TAy = -(Wy-W0)/(0.01*j)*r
Ax_list.append(TAx)
Ay_list.append(TAy)
tmp.append([1,[i,j],[TAx,TAy]])
else:
tmp.append([0,[i,j],[0,0]])
M.append(tmp)
fig = __plt__.figure(1,figsize=(6, 6))
ax = fig.gca()
ax.set_axis_bgcolor('black')
__plt__.title('Hartmann Spotdiagram',fontsize=18)
__plt__.plot(Ax_list,Ay_list,'wo')
__plt__.show()
return M,r
def twyman_green(coefficients, lambda_1=632, PR=1):
"""
Genertate Twyman_Green Interferogram based on zernike polynomials
=============================================
input
----------------------------------------------
Class zernike polynomials coefficients in wavenumber
see Class:opticspy.zernike.Coefficients
lambda_1: wavelength in nanometer, default = 632nm
PR: pupil radius, default = 1mm
output
----------------------------------------------
Interferogram of aberration
"""
lambda_1 = lambda_1 * (10**-9)
coefficients = coefficients.__coefficients__
r = __np__.linspace(-PR, PR, 400)
x, y = __np__.meshgrid(r, r)
rr = __np__.sqrt(x**2 + y**2)
OPD = __zernike__.__zernikecartesian__(coefficients, x, y) * 2 / PR
ph = 2 * __np__.pi * OPD
I1 = 1
I2 = 1
Ixy = I1 + I2 + 2 * __np__.sqrt(I1 * I2) * __np__.cos(ph)
__tools__.makecircle(Ixy, r, PR)
#======================================================
fig = __plt__.figure(figsize=(9, 6), dpi=80)
__plt__.imshow(-Ixy, extent=[-PR, PR, -PR, PR])
__plt__.set_cmap('Greys')
label = 'Zernike Coefficients:'
m = 1
for i in coefficients:
if i != 0:
label = label + "Z" + str(m) + "=" + str(i) + " "
m = m + 1
__plt__.xlabel(label, fontsize=16)
__plt__.title('Twyman Green Interferogram', fontsize=16)
fig.set_tight_layout(True)
__plt__.show()
def twyman_green(coefficients, lambda_1 = 632, PR = 1):
"""
Genertate Twyman_Green Interferogram based on zernike polynomials
=============================================
input
----------------------------------------------
Class zernike polynomials coefficients in wavenumber
see Class:opticspy.zernike.Coefficients
lambda_1: wavelength in nanometer, default = 632nm
PR: pupil radius, default = 1mm
output
----------------------------------------------
Interferogram of aberration
"""
lambda_1 = lambda_1*(10**-9)
coefficients = coefficients.__coefficients__
r = __np__.linspace(-PR, PR, 400)
x, y = __np__.meshgrid(r,r)
rr = __np__.sqrt(x**2 + y**2)
OPD = __zernike__.__zernikecartesian__(coefficients,x,y)*2/PR
ph = 2 * __np__.pi * OPD
I1 = 1
I2 = 1
Ixy = I1 + I2 + 2 * __np__.sqrt(I1*I2) * __np__.cos(ph)
__tools__.makecircle(Ixy, r, PR)
#======================================================
fig = __plt__.figure(figsize=(9, 6), dpi=80)
__plt__.imshow(-Ixy, extent=[-PR,PR,-PR,PR])
__plt__.set_cmap('Greys')
label = 'Zernike Coefficients:'
m = 1
for i in coefficients:
if i!=0:
label = label + "Z" + str(m) + "=" + str(i) +" "
m = m + 1
__plt__.xlabel(label,fontsize=16)
__plt__.title('Twyman Green Interferogram',fontsize=16)
fig.set_tight_layout(True)
__plt__.show()
def twyman_green(coefficients, lambda_1=632, PR=1):
"""
Genertate Twyman_Green Interferogram based on zernike polynomials
=============================================
input
----------------------------------------------
Class zernike polynomials coefficients in wavenumber
see Class:opticspy.zernike.Coefficients
lambda_1: wavelength in nanometer, default = 632nm
PR: pupil radius, default = 1mm
output
----------------------------------------------
Interferogram of aberration
"""
lambda_1 = lambda_1 * (10**-9)
coefficients = coefficients.__coefficients__
r = __np__.linspace(-PR, PR, 400)
x, y = __np__.meshgrid(r, r)
rr = __np__.sqrt(x**2 + y**2)
OPD = __zernike__.__zernikecartesian__(coefficients, x, y) * 2 / PR
ph = 2 * __np__.pi * OPD
I1 = 1
I2 = 1
Ixy = I1 + I2 + 2 * __np__.sqrt(I1 * I2) * __np__.cos(ph)
__tools__.makecircle(Ixy, r, PR)
#======================================================
fig = __plt__.figure(figsize=(11, 9), dpi=60)
__plt__.imshow(-Ixy, extent=[-PR, PR, -PR, PR])
ax = fig.gca()
ax.set_aspect('equal', 'datalim')
__plt__.set_cmap('Greys')
__plt__.title('Twyman Green Interferogram', fontsize=18)
__plt__.colorbar()
fig.set_tight_layout(True)
return fig
################################################################
def twyman_green(coefficients, lambda_1 = 632, PR = 1):
"""
Genertate Twyman_Green Interferogram based on zernike polynomials
=============================================
input
----------------------------------------------
Class zernike polynomials coefficients in wavenumber
see Class:opticspy.zernike.Coefficients
lambda_1: wavelength in nanometer, default = 632nm
PR: pupil radius, default = 1mm
output
----------------------------------------------
Interferogram of aberration
"""
lambda_1 = lambda_1*(10**-9)
coefficients = coefficients.__coefficients__
r = __np__.linspace(-PR, PR, 400)
x, y = __np__.meshgrid(r,r)
rr = __np__.sqrt(x**2 + y**2)
OPD = __zernike__.__zernikecartesian__(coefficients,x,y)*2/PR
ph = 2 * __np__.pi * OPD
I1 = 1
I2 = 1
Ixy = I1 + I2 + 2 * __np__.sqrt(I1*I2) * __np__.cos(ph)
__tools__.makecircle(Ixy, r, PR)
#======================================================
fig = __plt__.figure(figsize=(11, 9), dpi=60)
__plt__.imshow(-Ixy, extent=[-PR,PR,-PR,PR])
ax = fig.gca()
ax.set_aspect('equal', 'datalim')
__plt__.set_cmap('Greys')
__plt__.title('Twyman Green Interferogram',fontsize=18)
__plt__.colorbar()
fig.set_tight_layout(True)
return fig
################################################################
def phase_shift(coefficients,
lambda_1=632,
PR=1,
type='4-step',
noise=0,
sample=200):
"""
Genertate phase_shift Interferogram from interferometer
based on zernike polynomials and twyman_green interferometer
===========================================================
input
----------------------------------------------
Class zernike polynomials coefficients in wavenumber
see Class:opticspy.zernike.Coefficients
lambda_1: wavelength in nanometer, default = 632nm
PR: pupil radius, default = 1(also use this value for aperture matrix generate)
type: PSI algorithm default:'4-step'
boundary: if have a aperture
noise: from 0 to 1, default 0
sample: sample points
output
----------------------------------------------
Interferogram of aberration
"""
lambda_1 = lambda_1 * (10**-9)
coefficients = coefficients.__coefficients__
r = __np__.linspace(-PR, PR, sample)
x, y = __np__.meshgrid(r, r)
rr = __np__.sqrt(x**2 + y**2)
OPD = __zernike__.__zernikecartesian__(coefficients, x, y) * 2 / PR
Ia = 1
Ib = 1
ph = 2 * __np__.pi * OPD
if type == "4-step":
__tools__.makecircle_boundary(OPD, r, PR, 0)
im = __plt__.imshow(OPD, extent=[-PR, PR, -PR, PR], cmap=__cm__.RdYlGn)
__plt__.colorbar()
__plt__.title('Surface figure', fontsize=16)
__plt__.show()
I1 = Ia + Ib + 2 * __np__.sqrt(Ia * Ib) * __np__.cos(ph)
I2 = Ia + Ib + 2 * __np__.sqrt(
Ia * Ib) * __np__.cos(ph + 90.0 / 180 * __np__.pi)
I3 = Ia + Ib + 2 * __np__.sqrt(
Ia * Ib) * __np__.cos(ph + 180.0 / 180 * __np__.pi)
I4 = Ia + Ib + 2 * __np__.sqrt(
Ia * Ib) * __np__.cos(ph + 270.0 / 180 * __np__.pi)
if noise != 0:
# add noise / default noise 0
I1 = I1 + I1 * noise * __np__.random.randn(sample, sample)
I2 = I2 + I2 * noise * __np__.random.randn(sample, sample)
I3 = I3 + I3 * noise * __np__.random.randn(sample, sample)
I4 = I4 + I4 * noise * __np__.random.randn(sample, sample)
__tools__.makecircle_boundary(I1, r, PR, 0)
__tools__.makecircle_boundary(I2, r, PR, 0)
__tools__.makecircle_boundary(I3, r, PR, 0)
__tools__.makecircle_boundary(I4, r, PR, 0)
I = [I1, I2, I3, I4]
__tools__.phase_shift_figure(I, PR, type="4-step")
M = __np__.ones([sample, sample]) #map matrix, which is boundary
__tools__.makecircle_boundary(M, r, PR, 0)
# fig = __plt__.figure(figsize=(8, 6), dpi=80)
# im = __plt__.pcolormesh(M,cmap=__cm__.RdYlGn)
# __plt__.title('Phase value map',fontsize=16)
# __plt__.colorbar()
# __plt__.show()
return [I, PR, M, sample]
else:
print("No this type of PSI")
def phase_shift(coefficients, lambda_1 = 632, PR = 1, type = '4-step', noise = 0, sample = 200):
"""
Genertate phase_shift Interferogram from interferometer
based on zernike polynomials and twyman_green interferometer
===========================================================
input
----------------------------------------------
Class zernike polynomials coefficients in wavenumber
see Class:opticspy.zernike.Coefficients
lambda_1: wavelength in nanometer, default = 632nm
PR: pupil radius, default = 1(also use this value for aperture matrix generate)
type: PSI algorithm default:'4-step'
boundary: if have a aperture
noise: from 0 to 1, default 0
sample: sample points
output
----------------------------------------------
Interferogram of aberration
"""
lambda_1 = lambda_1*(10**-9)
coefficients = coefficients.__coefficients__
r = __np__.linspace(-PR, PR, sample)
x, y = __np__.meshgrid(r,r)
rr = __np__.sqrt(x**2 + y**2)
OPD = __zernike__.__zernikecartesian__(coefficients,x,y)*2/PR
Ia = 1
Ib = 1
ph = 2 * __np__.pi * OPD
if type == "4-step":
__tools__.makecircle_boundary(OPD, r, PR, 0)
im = __plt__.imshow(OPD,extent=[-PR,PR,-PR,PR],cmap=__cm__.RdYlGn)
__plt__.colorbar()
__plt__.title('Surface figure',fontsize=16)
__plt__.show()
I1 = Ia + Ib + 2 * __np__.sqrt(Ia*Ib) * __np__.cos(ph)
I2 = Ia + Ib + 2 * __np__.sqrt(Ia*Ib) * __np__.cos(ph+90.0/180*__np__.pi)
I3 = Ia + Ib + 2 * __np__.sqrt(Ia*Ib) * __np__.cos(ph+180.0/180*__np__.pi)
I4 = Ia + Ib + 2 * __np__.sqrt(Ia*Ib) * __np__.cos(ph+270.0/180*__np__.pi)
if noise != 0:
# add noise / default noise 0
I1 = I1 + I1*noise*__np__.random.randn(sample,sample)
I2 = I2 + I2*noise*__np__.random.randn(sample,sample)
I3 = I3 + I3*noise*__np__.random.randn(sample,sample)
I4 = I4 + I4*noise*__np__.random.randn(sample,sample)
__tools__.makecircle_boundary(I1, r, PR, 0)
__tools__.makecircle_boundary(I2, r, PR, 0)
__tools__.makecircle_boundary(I3, r, PR, 0)
__tools__.makecircle_boundary(I4, r, PR, 0)
I = [I1,I2,I3,I4]
__tools__.phase_shift_figure(I,PR,type = "4-step")
M = __np__.ones([sample,sample]) #map matrix, which is boundary
__tools__.makecircle_boundary(M, r, PR, 0)
# fig = __plt__.figure(figsize=(8, 6), dpi=80)
# im = __plt__.pcolormesh(M,cmap=__cm__.RdYlGn)
# __plt__.title('Phase value map',fontsize=16)
# __plt__.colorbar()
# __plt__.show()
return [I,PR,M,sample]
else:
print("No this type of PSI")
