def curvature_optimisation_test(curv0):
curv1 = nk.set_right_curv(curv0, focal_length, separation, n1)
lensb = oe.BiconvexLens(z0, curv0, curv1, n0, n1, separation)
rays = []
for rad, t in nk.rtuniform(n, m, rmax):
x, y = rad * np.cos(t), rad * np.sin(t)
ray = tr.Ray(r=[x, y, 0], k=[0, 0, 1], wavelength=wvlength)
lensb.propagate(ray)
output.propagate(ray)
rays.append(ray)
rms_radius = np.log(nk.rms_radius(rays))
return rms_radius
def curvature_optimisation(curvs):
curvs = np.array(curvs, dtype=float)
curv_left, curv_right = curvs[0], curvs[1]
lensb = oe.BiconvexLens(z0, curv_left, curv_right, n0, n1,
separation)
rays = []
for rad, t in nk.rtuniform(n, m, rmax):
x, y = rad * np.cos(t), rad * np.sin(t)
ray = tr.Ray(r=[x, y, 0], k=[0, 0, 1], wavelength=wvlength)
lensb.propagate(ray)
output.propagate(ray)
rays.append(ray)
rms_radius = np.log(nk.rms_radius(rays))
return rms_radius
def focal_length_analysis(fxi=20., fxf=120., fxs=1.):
wvlength, z0, n0, separation = 588., 100., 1., 5.
n1 = nk.disperse(wvlength)
n, m, rmax = 5, 6, 5.
curvl, curvr, diff, rms = [], [], [], []
x0try, maxfuntry = 0.005, 1000
xvalues = np.arange(fxi, fxf, fxs)
for focal_length in xvalues:
paraxial_focus = nk.paraxial_focus(separation, z0, focal_length)
output = oe.OutputPlane(paraxial_focus)
def curvature_optimisation_test(curv0):
curv1 = nk.set_right_curv(curv0, focal_length, separation, n1)
lensb = oe.BiconvexLens(z0, curv0, curv1, n0, n1, separation)
rays = []
for rad, t in nk.rtuniform(n, m, rmax):
x, y = rad * np.cos(t), rad * np.sin(t)
ray = tr.Ray(r=[x, y, 0], k=[0, 0, 1], wavelength=wvlength)
lensb.propagate(ray)
output.propagate(ray)
rays.append(ray)
rms_radius = np.log(nk.rms_radius(rays))
return rms_radius
curv0 = spo.fmin_tnc(func = curvature_optimisation_test,
x0 = x0try, approx_grad = True,
maxfun = maxfuntry)[0][0]
curv1 = nk.set_right_curv(curv0, focal_length, separation, n1)
initial_guess = [curv0, curv1]
def curvature_optimisation(curvs):
curvs = np.array(curvs, dtype=float)
curv_left, curv_right = curvs[0], curvs[1]
lensb = oe.BiconvexLens(z0, curv_left, curv_right, n0, n1,
separation)
rays = []
for rad, t in nk.rtuniform(n, m, rmax):
x, y = rad * np.cos(t), rad * np.sin(t)
ray = tr.Ray(r=[x, y, 0], k=[0, 0, 1], wavelength=wvlength)
lensb.propagate(ray)
output.propagate(ray)
rays.append(ray)
rms_radius = np.log(nk.rms_radius(rays))
return rms_radius
optimal_curv = spo.fmin_tnc(func = curvature_optimisation,
x0 = initial_guess, approx_grad = True, maxfun = maxfuntry)[0]
curvl.append(optimal_curv[0])
curvr.append(optimal_curv[1])
lensb = oe.BiconvexLens(z0, optimal_curv[0], optimal_curv[1],
n0, n1, separation)
rays = []
for rad, t in nk.rtuniform(n, m, rmax):
x, y = rad * np.cos(t), rad * np.sin(t)
ray = tr.Ray(r=[x, y, 0], k=[0, 0, 1], wavelength=wvlength)
lensb.propagate(ray)
output.propagate(ray)
rays.append(ray)
diff_scale = nk.diffraction_scale_biconvex(paraxial_focus, lensb,
wvlength, rmax)
rms_radius = nk.rms_radius(rays)
diff.append(diff_scale)
rms.append(rms_radius)
plt.close("all")
f, (ax1, ax2) = plt.subplots(2, sharex=True)
diff, rms = np.log(np.array(diff)), np.log(np.array(rms))
ax1.plot(xvalues, curvl, color = 'c', label='Left surface curvature')
ax1.plot(xvalues, curvr, color = 'b', label='Right surface curvature')
ax1.plot(xvalues, [0]*len(xvalues), 'm--')
ax1.legend(loc='best')
ax2.plot(xvalues, diff, color = 'g', label='Diffraction scale')
ax2.plot(xvalues, rms, color = 'r', label='RMS radius')
ax2.set_xlabel('focal length ('r'mm'')', fontsize=14)
ax2.legend(loc='best')
f.subplots_adjust(hspace=0)
