def test_save(self):
rho_j = np.array([
0, 0.11111111111111, 0.22222222222222, 0.33333333333333,
0.44444444444444, 0.55555555555556, 0.66666666666667,
0.77777777777778, 0.88888888888889, 1
])
theta_i = np.array([
0, 0.69813170079773, 1.3962634015955, 2.0943951023932,
2.7925268031909, 3.4906585039887, 4.1887902047864, 4.8869219055841,
5.5850536063819, 6.2831853071796
])
enz1 = CPsf(8)
f_sp = np.linspace(-3, 3, 9)
enz1.make_cart_grid(x_sp=np.linspace(-1, 1, 10),
y_sp=np.linspace(-2, 2, 11),
f_sp=np.linspace(-3, 3, 12))
enz1.czern.make_pol_grid(rho_j, theta_i)
# create tmp path
tmpfile = NamedTemporaryFile()
tmppath = tmpfile.name
tmpfile.close()
enz1.save(tmppath)
enz2 = CPsf.load(tmppath)
for i in range(f_sp.size):
beta = normal(size=enz1.czern.nk) + 1j * normal(size=enz1.czern.nk)
self.assertTrue(
norm(
enz1.eval_grid_f(beta, i).ravel() -
enz2.eval_grid_f(beta, i).ravel()) < self.max_enorm)
self.assertTrue(norm(enz1.Ugrid.ravel() - enz2.Ugrid.ravel()) == 0)
self.assertTrue(norm(enz1.Vnm.ravel() - enz2.Vnm.ravel()) == 0)
self.assertTrue(norm(enz1.Cnm.ravel() - enz2.Cnm.ravel()) == 0)
self.assertTrue(norm(enz1.czern.coefnorm - enz2.czern.coefnorm) == 0)
self.assertTrue(norm(enz1.czern.ntab - enz2.czern.ntab) == 0)
self.assertTrue(norm(enz1.czern.mtab - enz2.czern.mtab) == 0)
self.assertTrue(enz1.czern.n == enz2.czern.n)
self.assertTrue(enz1.czern.nk == enz2.czern.nk)
self.assertTrue(enz1.czern.normalise == enz2.czern.normalise)
self.assertTrue(norm(enz1.czern.rhoitab - enz2.czern.rhoitab) == 0)
self.assertTrue(norm(enz1.czern.rhotab - enz2.czern.rhotab) == 0)
self.assertTrue(enz1.czern.numpy_dtype == enz2.czern.numpy_dtype)
self.assertTrue(norm(enz1.czern.ZZ - enz2.czern.ZZ) == 0)
os.unlink(tmppath)
def __init__(
self,
wavelength=632.8e-9, # wavelength in [m]
aperture_radius=0.002, # aperture radius in [m]
focal_length=500e-3, # focal length in [m]
pixel_size=7.4e-6, # pixel size in [m]
image_width=75, # [pixels], odd to get the origin as well
image_height=151, # [pixels]
fspace=np.linspace( # defocus planes specified by an array of
-3.0, 2.0, 6), # defocus parameters
n_beta=4 # max radial order for the Zernikes
):
# compute the diffraction unit (lambda/NA)
fu = enz.get_field_unit(
wavelength=wavelength,
aperture_radius=aperture_radius,
exit_pupil_sphere_radius=focal_length)
def make_space(w, p, fu):
if w % 2 == 0:
return np.linspace(-(w/2 - 0.5), w/2 - 0.5, w)*p/fu
else:
return np.linspace(-(w - 1)/2, (w - 1)/2, w)*p/fu
# image side space
xspace = make_space(image_width, pixel_size, fu)
yspace = make_space(image_height, pixel_size, fu)
# consider complex-valued Zernike polynomials up to the radial order
# n_beta to approximate the PSF, see Eq. (1) and Eq. (2) in [A2015]
cpsf = CPsf(n_beta)
# make a cartesian grid to evaluate the PSF
t1 = time()
cpsf.make_cart_grid(x_sp=xspace, y_sp=yspace, f_sp=fspace)
t2 = time()
print('make_cart_grid {:.6f} sec'.format(t2 - t1))
self.xspace = xspace
self.yspace = yspace
self.fspace = fspace
self.cpsf = cpsf
self.image_size = (image_height, image_width)
def test_eval_U_grid1(self):
log = logging.getLogger('TestCPsf.test_eval_U_grid1')
enz = CPsf(8)
r_sp = float(abs(normal(size=1, ))[0])
ph_sp = float(normal(size=1, )[0])
f_sp = float(normal(size=1, )[0])
enz.make_pol_grid([r_sp], [ph_sp], [f_sp])
beta = normal(size=enz.czern.nk) + 1j * normal(size=enz.czern.nk)
a = enz.eval_grid(beta, 0, 0, 0)
b = enz.U(beta, r_sp, ph_sp, f_sp)
log.debug('r = {:e}, ph = {:e}, f = {:e}'.format(r_sp, ph_sp, f_sp))
log.debug('a {:s} {}'.format(str(type(a)), a))
log.debug('b {:s} {}'.format(str(type(b)), b))
log.debug('{}'.format(abs(a - b)))
self.assertTrue(abs(a - b) < self.max_enorm)
def test_eval_U_grid2(self):
log = logging.getLogger('TestCPsf.test_eval_U_grid2')
enz = CPsf(8)
L, K, P = 50, 70, 3
A = L * K * P
r_sp = np.linspace(.01, 2, L)
ph_sp = [2 * math.pi * i / L for i in range(K)]
f_sp = [normal(size=1, ) for i in range(P)]
t1 = time()
enz.make_pol_grid(r_sp, ph_sp, f_sp)
t2 = time()
log.debug('make_pol_grid {:.6f}'.format(t2 - t1))
self.assertTrue(enz.Ugrid.size == A * enz.czern.nk)
beta = normal(size=enz.czern.nk) + 1j * normal(size=enz.czern.nk)
T1 = np.zeros((L, K, P), order='F', dtype=np.complex)
self.assertTrue(r_sp.size == L)
self.assertTrue(len(ph_sp) == K)
self.assertTrue(len(f_sp) == P)
self.assertTrue(T1.size == L * K * P)
log.debug(r_sp.size)
t1 = time()
for i, r in enumerate(r_sp):
for j, ph in enumerate(ph_sp):
for k, f in enumerate(f_sp):
T1[i, j, k] = enz.U(beta, r, ph, f)
t2 = time()
log.debug('scalar {:.6f}'.format(t2 - t1))
t1 = time()
T2 = np.dot(enz.Ugrid, beta)
t2 = time()
log.debug('vect {:.6f}'.format(t2 - t1))
log.debug(enz.Ugrid.flags)
self.assertTrue(norm(T1.ravel() - T2.ravel()) < self.max_enorm)
def make(self, wavelength, aperture_radius, focal_length, pixel_size,
image_width, image_height, n_alpha, n_beta, fit_L, fit_K,
focus_positions):
self.wavelength = wavelength
self.aperture_radius = aperture_radius
self.focal_length = focal_length
self.image_width = image_width
self.image_height = image_height
self.pixel_size = pixel_size
self.n_alpha, self.n_beta = n_alpha, n_beta
self.fit_L, self.fit_K = fit_L, fit_K
self.focus_positions = np.array(focus_positions)
fu = enz.get_field_unit(wavelength, aperture_radius, focal_length)
def make_space(w, p, fu):
if w % 2 == 0:
return np.linspace(-(w / 2 - 0.5), w / 2 - 0.5, w) * p / fu
else:
return np.linspace(-(w - 1) / 2, (w - 1) / 2, w) * p / fu
# image side space
xspace = make_space(image_width, pixel_size, fu)
yspace = make_space(image_height, pixel_size, fu)
self.xspace, self.yspace = xspace, yspace
# phase
self.phase_grid = RZern(n_alpha)
self.phase_fit = FitZern(self.phase_grid, self.fit_L, self.fit_K)
print('phase: n_alpha = {}, N_alpha = {}'.format(
self.n_alpha, self.phase_grid.nk))
# complex psf
self.cpsf = CPsf(n_beta)
self.gpf_fit = FitZern(self.cpsf.czern, self.fit_L, self.fit_K)
print('cpsf: n_beta = {}, N_beta = {}, N_f = {}'.format(
n_beta, self.cpsf.czern.nk, self.focus_positions.size))
# make phase polar grid
t1 = time.time()
self.phase_grid.make_pol_grid(self.phase_fit.rho_j,
self.phase_fit.theta_i)
t2 = time.time()
print('make phase pol grid {:.6f}'.format(t2 - t1))
# make gpf polar grid (Zernike approximation)
t1 = time.time()
self.cpsf.czern.make_pol_grid(self.phase_fit.rho_j,
self.phase_fit.theta_i)
t2 = time.time()
print('make gpf pol grid {:.6f}'.format(t2 - t1))
# make cpsf cart grid
t1 = time.time()
self.cpsf.make_cart_grid(x_sp=xspace,
y_sp=yspace,
f_sp=focus_positions)
t2 = time.time()
print('make cpsf cart grid {:.6f}'.format(t2 - t1))
if __name__ == '__main__':
NA = 0.50 # numerical aperture
diam = 0.25 # diameter [um]
wavelength = 0.200 # lambda [um]
eps = 0.00001 # offset to avoid division by zero
radius = diam / 2
ap = 2 * pi * (NA / wavelength) * radius
d = 1 / 8 * ap**2 + 1 / 384 * ap**4 + 1 / 10240 * ap**6 # optimal d. Why!?
scale_z = wavelength / (2 * pi) * 1 / (1 - sqrt(1 - NA**2))
rspace = (np.arange(0, 0.5, 0.05) + eps) * NA / wavelength
fspace = np.arange(-2, 2, 0.05) / scale_z + 1j * d
cpsf = CPsf(0) # aberration free, only n = m = 0
t1 = time()
field1 = cpsf.V(n=0, m=0, r=rspace, f=fspace)
t2 = time()
print('field1 {:.6f} sec'.format(t2 - t1))
field1 = np.squeeze(field1)
I1 = np.square(np.abs(field1))
I1 *= (1 / I1.max())
ff, rr = np.meshgrid(np.real(fspace), rspace)
levels = np.sort(
np.concatenate((np.array([0.025, 0.05]), np.arange(0, 1, 0.1))))
c = p.contour(ff, rr, I1, levels)
p.clabel(c, inline=1)
