def wolter_for_japanese(cls,p,q,d,q1,theta1,theta2):
############## ellipse ####################################################################################
ae = (p+q1)/2
be = np.sqrt(p*q1)*np.cos(theta1)
f = np.sqrt(ae**2-be**2)
beta = np.arccos((p**2+4*f**2-q1**2)/(4*p*f))
ccc1 = np.array([1. / be ** 2, 1. / be ** 2, 1 / ae ** 2, 0., 0., 0., 0., 0., 0., -1])
y = - p * np.sin(beta)
z = f - p * np.cos(beta)
oe1 = Optical_element.initialize_as_surface_conic_from_coefficients(ccc1)
oe1.set_parameters(p=p, q=q1, theta=theta1)
############## hyperbola ####################################################################################
p1 = q1 - d
ah = (p1 - q)/2
bh = np.sqrt(p1*q)*np.cos(theta2)
z0 = np.sqrt(ae**2-be**2) - np.sqrt(ah**2+bh**2)
print("z0 = %f" %z0)
ccc2 = np.array([-1. / ah ** 2, -1. / ah ** 2, 1 / bh ** 2, 0., 0., 0., 0., 0., 2 * z0 / bh ** 2, z0 ** 2 / bh ** 2 - 1])
oe2 = Optical_element.initialize_as_surface_conic_from_coefficients(ccc2)
oe2.set_parameters(p=p1, q=q, theta=theta2)
return CompoundOpticalElement(oe_list=[oe1, oe2], oe_name="Wolter for japanese")
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 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_montel_parabolic(cls, p, q, theta, bound1, bound2, distance_of_the_screen=None, angle_of_mismatch=0.):
beta = (90. - angle_of_mismatch)*np.pi/180 #### angle beetween the two mirror, if angle_of_mismatch is >0 the two mirror are closer
oe1 = Optical_element.initialize_as_surface_conic_paraboloid_from_focal_distances(p=p, q=q, theta=theta, alpha=0., infinity_location='p', focal=q, cylindrical=1)
oe1.set_bound(bound1)
oe2 = oe1.duplicate()
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, q, 0., 0., "Surface conical mirror")
return CompoundOpticalElement(oe_list=[oe1, oe2, screen], oe_name="Montel parabolic")
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")
print(ccc1)
c1 = ccc1[1]
c2 = ccc1[2]
c4 = ccc1[4]
c8 = ccc1[8]
####### rotation of the oe around y #############################################################################
a = np.cos(beta)
b = np.sin(beta)
ccc2 = np.array([
c2 * b**2, c1, c2 * a**2, -c4 * b, c4 * a, -2 * c2 * a * b, -c8 * b,
0., c8 * a, 0.
])
oe2 = Optical_element.initialize_as_surface_conic_from_coefficients(ccc2)
oe2.p = p
oe2.q = q
oe2.theta = theta
oe2.alpha = 0.
oe2.type = "Surface conical mirror"
# print("\n")
# print(oe1.info())
# print("\n")
# print(oe2.info())
# print("\n")
ccc = np.array([0., 0., 0., 0., 0., 0., 0., 1., 0., -q])
screen = Optical_element.initialize_as_surface_conic_from_coefficients(ccc)
def test_wolter_1_microscope():
p = 0.
beam1 = Beam.initialize_as_person()
beam1.set_flat_divergence_with_different_optical_axis(0.005, 0.005)
beam1.set_point(p, 0., p)
op_ax = Beam (1)
op_ax.set_point(p, 0., p)
beam = op_ax.merge(beam1)
beam.x = beam.x
beam.z = beam.z
#beam.set_divergences_collimated()
beam.plot_xz()
distance_of_focalization = 5.
hyp = Optical_element.initialize_my_hyperboloid(p=distance_of_focalization, q=0., theta=0., alpha=0., wolter=1.1, z0=0., distance_of_focalization=distance_of_focalization)
ah = distance_of_focalization/np.sqrt(2)
q = 20.
z0 = 0.5*(q - np.sqrt(2)*ah)
c = z0 + np.sqrt(2)*ah
#b = c + 0.1
#a=np.sqrt(b**2-c**2)
b = c*1.5
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])
ellips = Optical_element.initialize_as_surface_conic_from_coefficients(ccc)
hyp.effect_of_optical_element(beam)
beam.plot_yx(0)
plt.title("footprint %s" % (hyp.type))
ellips.p = 0.
ellips.theta = 90*np.pi/180
ellips.effect_of_optical_element(beam)
beam.plot_yx(0)
plt.title("footprint %s" % (ellips.type))
t = -beam.y/beam.vy
beam.x = beam.x + beam.vx * t
beam.y = beam.y + beam.vy * t
beam.z = beam.z + beam.vz * t
beam.plot_yx(0)
beam.plot_xz()
print("a of ellips is: %f" %(a))
print("b of ellips is: %f" %(b))
print("c of ellips is: %f" %(c))
print(np.mean(beam.z))
beam.histogram()
plt.show()