def initialize_as_kirkpatrick_baez_parabolic(cls, p, q, separation, theta, bound1=None, bound2=None, infinity_location='p'):
p1 = p - 0.5 * separation
q1 = p - p1
q2 = q - 0.5 * separation
p2 = q - q2
f1p = p1
f1q = p + q - p1
f2q = q2
f2p = p + q - q2
oe1 = Optical_element.initialize_as_surface_conic_paraboloid_from_focal_distances(p= f1p, q= f1q, theta= theta, alpha=0., cylindrical=1, infinity_location=infinity_location)
#oe1.bound = bound1
oe1.set_bound(bound1)
oe1.p = p1
oe1.q = q1
oe2 = Optical_element.initialize_as_surface_conic_paraboloid_from_focal_distances(p= f2p, q= f2q, theta= theta, alpha=90.*np.pi/180, cylindrical=1, infinity_location=infinity_location)
#oe2.bound = bound2
oe2.set_bound(bound2)
oe2.p = p2
oe2.q = q2
print(oe1.ccc_object.get_coefficients())
print(oe2.ccc_object.get_coefficients())
return CompoundOpticalElement(oe_list=[oe1,oe2],oe_name="Kirkpatrick Baez")
def initialize_as_montel_parabolic(cls,
p,
q,
theta_z,
theta_x=None,
bound1=None,
bound2=None,
distance_of_the_screen=None,
angle_of_mismatch=0.,
infinity_location='q'):
beta = np.pi / 2 + angle_of_mismatch #### angle beetween the two mirror, if angle_of_mismatch is <0 the two mirror are closer
if theta_x == None:
theta_x = theta_z
oe1 = Optical_element.initialize_as_surface_conic_paraboloid_from_focal_distances(
p=p,
q=q,
theta=theta_z,
alpha=0. * np.pi / 180,
infinity_location=infinity_location,
cylindrical=1.)
oe2 = Optical_element.initialize_as_surface_conic_paraboloid_from_focal_distances(
p=p,
q=q,
theta=theta_x,
alpha=0. * np.pi / 180,
infinity_location=infinity_location,
cylindrical=1.)
oe1.set_bound(bound1)
oe2.rotation_surface_conic(beta, 'y')
oe2.set_bound(bound2)
if distance_of_the_screen == None:
distance_of_the_screen = q
ccc = np.array(
[0., 0., 0., 0., 0., 0., 0., 1., 0., -distance_of_the_screen])
screen = Optical_element.initialize_as_surface_conic_from_coefficients(
ccc)
screen.set_parameters(p, distance_of_the_screen, 0., 0.,
"Surface conical mirror")
return CompoundOpticalElement(oe_list=[oe1, oe2, screen],
oe_name="Montel parabolic")
def initialiaze_as_wolter_1(cls,p1,q1,z0):
theta1 = 0.
alpha1 = 0.
print(q1)
print(2*z0)
print("dof=%f" %(2*z0-q1))
oe1 = Optical_element.initialize_as_surface_conic_paraboloid_from_focal_distances(p1, 0., theta1, alpha1, "p", 2*z0-q1)
oe2 = Optical_element.initialize_my_hyperboloid(p=0., q=q1, theta=90 * np.pi / 180, alpha=0, wolter=1, z0=z0,distance_of_focalization=2*z0-q1)
return CompoundOpticalElement(oe_list=[oe1,oe2],oe_name="Wolter 1")
def initialiaze_as_wolter_2(cls,p1,q1,z0):
#q1 = - q1
focal = q1+2*z0
print("focal=%f" %(focal))
theta1 = 0.
alpha1 = 0.
oe1 = Optical_element.initialize_as_surface_conic_paraboloid_from_focal_distances(p1,0.,theta1,alpha1,"p", focal)
oe2 = Optical_element.initialize_my_hyperboloid(p=0. ,q=-(focal-2*z0), theta=90*np.pi/180, alpha=0, wolter=2, z0=z0, distance_of_focalization=focal)
return CompoundOpticalElement(oe_list=[oe1,oe2],oe_name="Wolter 2")
def initialiaze_as_wolter_1_with_two_parameters(cls, p1, R, theta):
cp1 = -2 * R / np.tan(theta)
cp2 = 2 * R * np.tan(theta)
cp = max(cp1, cp2)
f = cp / 4
print("focal=%f" % (f))
oe1 = Optical_element.initialize_as_surface_conic_paraboloid_from_focal_distances(
p=p1, q=f, theta=0., alpha=0., infinity_location="p")
s1 = R / np.tan(2 * theta)
s2 = R / np.tan(4 * theta)
c = (s1 - s2) / 2
z0 = f + c
b1 = np.sqrt(0.5 * c**2 + 0.5 * R**2 + 0.5 * R**4 / cp**2 -
R**2 * z0 / cp + 0.5 * z0**2 - 0.5 / cp**2 * np.sqrt(
(-c**2 * cp**2 - cp**2 * R**2 - R**4 +
2 * cp * R**2 * z0 - cp**2 * z0**2)**2 - 4 * cp**2 *
(c**2 * R**4 - 2 * c**2 * cp * R**2 * z0 +
c**2 * cp**2 * z0**2)))
b2 = np.sqrt(0.5 * c**2 + 0.5 * R**2 + 0.5 * R**4 / cp**2 -
R**2 * z0 / cp + 0.5 * z0**2 + 0.5 / cp**2 * np.sqrt(
(-c**2 * cp**2 - cp**2 * R**2 - R**4 +
2 * cp * R**2 * z0 - cp**2 * z0**2)**2 - 4 * cp**2 *
(c**2 * R**4 - 2 * c**2 * cp * R**2 * z0 +
c**2 * cp**2 * z0**2)))
b = min(b1, b2)
a = np.sqrt(c**2 - b**2)
ccc = np.array([
-1 / a**2, -1 / a**2, 1 / b**2, 0., 0., 0., 0., 0., -2 * z0 / b**2,
z0**2 / b**2 - 1
])
oe2 = Optical_element.initialize_as_surface_conic_from_coefficients(
ccc)
oe2.set_parameters(p=0.,
q=z0 + c,
theta=90 * np.pi / 180,
alpha=0.,
type="My hyperbolic mirror")
#oe2.type = "My hyperbolic mirror"
#oe2.p = 0.
#oe2.q = z0 + c
#oe2.theta = 90 * np.pi / 180
#oe2.alpha = 0.
return CompoundOpticalElement(oe_list=[oe1, oe2], oe_name="Wolter 1")
def initialize_as_wolter_3(cls, p, q, distance_between_the_foci):
f=-q
oe1 = Optical_element.initialize_as_surface_conic_paraboloid_from_focal_distances(p=p, q=f, theta=0., alpha=0., infinity_location="p")
#c = z0+np.abs(f)
c = distance_between_the_foci/2
z0 = np.abs(c)-np.abs(f)
b = c+100
a = np.sqrt((b**2-c**2))
ccc = np.array([1/a**2, 1/a**2, 1/b**2, 0., 0., 0., 0., 0., -2*z0/b**2, z0**2/b**2-1])
oe2 = Optical_element.initialize_as_surface_conic_from_coefficients(ccc)
oe2.set_parameters(p=0., q=z0+z0+np.abs(q), theta=90*np.pi/180)
return CompoundOpticalElement(oe_list=[oe1,oe2],oe_name="Wolter 3")
def test_paraboloid_mirror(self):
print(">>>>>>>>>>>>>>> test_paraboloid_mirror")
#beam1=Beam(5000)
#beam1.set_point(0,0,0)
#beam1.set_flat_divergence(5e-3,5e-2)
shadow_beam = run_shadow_source()
beam1=Beam()
beam1.initialize_from_arrays(
shadow_beam.getshonecol(1),
shadow_beam.getshonecol(2),
shadow_beam.getshonecol(3),
shadow_beam.getshonecol(4),
shadow_beam.getshonecol(5),
shadow_beam.getshonecol(6),
shadow_beam.getshonecol(10),
)
p=10.
q=20.
theta=72*np.pi/180
alpha=0*np.pi/180
spherical_mirror=Optical_element.initialize_as_surface_conic_paraboloid_from_focal_distances(p,q,theta,alpha)
beam1=spherical_mirror.trace_optical_element(beam1)
if do_plot:
beam1.plot_xz()
beam1.plot_xpzp()
plt.title("Paraboloid mirror with p=10, q=20, theta=72")
print(spherical_mirror.ccc_object.get_coefficients())
plt.show()
shadow_beam = run_shadow_parabolic_mirror(shadow_beam)
assert_almost_equal(beam1.x, shadow_beam.getshonecol(1), 7)
assert_almost_equal(beam1.y, shadow_beam.getshonecol(2), 7)
assert_almost_equal(beam1.z, shadow_beam.getshonecol(3), 7)
def initialiaze_as_wolter_12(cls, p1, q1, focal_parabola, Rmin):
focal = focal_parabola
d = q1 - focal_parabola
z0 = focal_parabola + d / 2
print("focal=%f" % (focal))
theta1 = 0.
alpha1 = 0.
oe1 = Optical_element.initialize_as_surface_conic_paraboloid_from_focal_distances(
p1, 0., theta1, alpha1, "p", focal)
ccc = oe1.ccc_object.get_coefficients()
cp = -ccc[8]
print("R=%f, d=%f, cp=%f, z0=%f" % (Rmin, d, cp, z0))
#b1 = np.sqrt(0.125*d**2+Rmin+2*Rmin**4/cp**2-2*Rmin**2*z0/cp+0.5*z0**2-0.125/cp**2*np.sqrt((-cp**2*d**2-8*cp**2*Rmin-16*Rmin**4+16*cp*Rmin**2*z0-4*cp*z0**2)**2-16*cp**2*(4*d**2*Rmin**4-4*cp*d**2*Rmin**2*z0+cp**2*d**2*z0**2)))
#b2 = np.sqrt(0.125*d**2+Rmin+2*Rmin**4/cp**2-2*Rmin**2*z0/cp+0.5*z0**2+0.125/cp**2*np.sqrt((-cp**2*d**2-8*cp**2*Rmin-16*Rmin**4+16*cp*Rmin**2*z0-4*cp*z0**2)**2-16*cp**2*(4*d**2*Rmin**4-4*cp*d**2*Rmin**2*z0+cp**2*d**2*z0**2)))
p1 = -cp**2 * d**2 - 8 * cp**2 * Rmin - 16 * Rmin**4 + 16 * cp * Rmin**2 * z0 - 4 * cp**2 * z0**2
p1 = p1**2
p2 = 16 * cp**2 * (4 * d**2 * Rmin**4 - 4 * cp * d**2 * Rmin**2 * z0 +
cp**2 * d**2 * z0**2)
sp = 0.125 / cp**2 * np.sqrt(p1 - p2)
sp0 = 0.125 * d**2 + Rmin + 2 * Rmin**4 / cp**2 - 2 * Rmin**2 * z0 / cp + 0.5 * z0**2
b = np.sqrt(sp0 - sp)
a = np.sqrt(d**2 / 4 - b**2)
print("a=%f, b=%f" % (a, b))
#oe2 = Optical_element.initialize_my_hyperboloid(p=0. ,q=-(focal-2*z0), theta=90*np.pi/180, alpha=0, wolter=1.1, z0=z0, distance_of_focalization=focal)
cc = np.array([
-1 / a**2, -1 / a**2, 1 / b**2, 0., 0., 0., 0., 0., -2 * z0 / b**2,
(z0 / b)**2 - 1
])
oe2 = Optical_element.initialize_as_surface_conic_from_coefficients(cc)
oe2.type = "My hyperbolic mirror"
oe2.set_parameters(p=0., q=q1, theta=90. * np.pi / 180, alpha=0.)
return CompoundOpticalElement(oe_list=[oe1, oe2], oe_name="Wolter 1.2")
beam_2_04 = comp_oe2_04.trace_compound(beam_2_04)
beam_2_14 = comp_oe2_14.trace_compound(beam_2_14)
beam_2_04.plot_xz()
plt.title('Final plot of a KirkPatrickBaez system with parameter = 0.4')
beam_2_14.plot_xz()
plt.title('Final plot of a KirkPatrickBaez system with parameter = 1.471')
plt.show()
if main == "__paraboloid__":
beam = beam()
oe1 = Optical_element.initialize_as_surface_conic_paraboloid_from_focal_distances(
p=0.3, q=0.4, theta=theta, infinity_location='q')
beam = oe1.trace_optical_element(beam)
beam_2_04 = beam.duplicate()
beam_2_14 = beam.duplicate()
oe2_04 = Optical_element.initialize_as_surface_conic_paraboloid_from_focal_distances(
p=0.3, q=0.4, theta=theta, infinity_location='p')
oe2_14 = Optical_element.initialize_as_surface_conic_paraboloid_from_focal_distances(
p=0.3, q=1.471, theta=theta, infinity_location='p')
beam_2_04 = oe2_04.trace_optical_element(beam_2_04)
beam_2_14 = oe2_14.trace_optical_element(beam_2_14)
beam_2_04.plot_xz()
zmax = 0.01
zmin = 0.0
bound = BoundaryRectangle(xmax=xmax,
xmin=xmin,
ymax=ymax,
ymin=ymin,
zmax=zmax,
zmin=zmin)
montel = CompoundOpticalElement.initialize_as_montel_parabolic(
p=0.351,
q=1.,
theta=theta,
bound1=bound,
bound2=bound,
infinity_location='p')
par = Optical_element.initialize_as_surface_conic_paraboloid_from_focal_distances(
0.351, 1., theta, 0.0, 'p', None, 1)
#velocity = Vector(beam.vx, beam.vy, beam.vz)
#velocity.rotation(-gamma, 'z')
#velocity.rotation(-alpha, 'x')
#beam.vx = velocity.x
#beam.vy = velocity.y
#beam.vz = velocity.z
#
#
#print(beam.vx, beam.vy, beam.vz)
#
#
#position = Vector(beam.x, beam.y, beam.z)
#position.rotation(-gamma, 'z')
#position.rotation(-alpha, 'x')