def trace_ideal_lens(self,beam1):
beam=beam1.duplicate()
t = self.p / beam.vy
beam.x = beam.x + beam.vx * t
beam.y = beam.y + beam.vy * t
beam.z = beam.z + beam.vz * t
gamma = np.arctan( beam.x/self.fx)
alpha = np.arctan( -beam.z/self.fz)
velocity = Vector(beam.vx, beam.vy, beam.vz)
velocity.rotation(gamma, "z")
velocity.rotation(alpha, "x")
[beam.vx, beam.vy, beam.vz] = [velocity.x, velocity.y, velocity.z]
#self.q=0
t = self.q / beam.vy
beam.x = beam.x + beam.vx * t
beam.y = beam.y + beam.vy * t
beam.z = beam.z + beam.vz * t
beam.y *= 0.
return beam
def translation_to_the_optical_element(self, beam):
vector_point=Vector(0,self.p,0)
vector_point.rotation(self.alpha,"y")
vector_point.rotation(-(np.pi/2-self.theta),"x")
beam.x=beam.x-vector_point.x
beam.y=beam.y-vector_point.y
beam.z=beam.z-vector_point.z
def test_rotation_1(self):
print(">> test_rotation_1")
theta=0*np.pi/180
v = Vector(0,1,0)
v.rotation(-(90*np.pi/180-theta),"x")
print(v.info())
assert_almost_equal ( v.x , 0.0 , 15)
assert_almost_equal ( v.y , 0.0 , 15)
assert_almost_equal ( v.z , -1.0 , 15)
def test_rotation_3(self):
print(">> test_rotation_3")
alpha=90*np.pi/180
v = Vector(0,1,0)
v.rotation(alpha,"y")
print(v.info())
assert_almost_equal ( v.x , 0.0 , 15)
assert_almost_equal ( v.y , 1.0 , 15)
assert_almost_equal ( v.z , 0.0 , 15)
def test_rotation_2(self):
print(">> test_rotation_2")
theta=45*np.pi/180
v = Vector(0,1,0)
v.rotation(-(90*np.pi/180-theta),"x")
print(v.info())
assert_almost_equal ( v.x , 0.0 , 15)
assert_almost_equal ( v.y , 1/np.sqrt(2) , 15)
assert_almost_equal ( v.z , -1/np.sqrt(2) , 15)
def lens_output_direction(self,beam):
gamma = np.arctan( beam.x/self.fx)
alpha = np.arctan( -beam.y/self.fz)
velocity = Vector(beam.vx, beam.vy, beam.vz)
velocity.rotation(gamma, "y")
velocity.rotation(alpha, "x")
[beam.vx, beam.vy, beam.vz] = [velocity.x, velocity.y, velocity.z]
def rotation(self, beam, angle, axis):
velocity = Vector(beam.vx, beam.vy, beam.vz)
position = Vector(beam.x, beam.y, beam.z)
velocity.rotation(angle, axis)
position.rotation(angle, axis)
beam.x = position.x
beam.y = position.y
beam.z = position.z
beam.vx = velocity.x
beam.vy = velocity.y
beam.vz = velocity.z
def tras_rot2(beam, p, theta):
theta_grazing = np.pi / 2 - theta
y = Vector(0., 1., 0.)
y.rotation(-theta_grazing, 'x')
x = Vector(1., 0., 0.)
xp = x.vector_product(y)
vrot = y.rodrigues_formula(xp, -theta_grazing)
vrot.normalization()
position = Vector(beam.x, beam.y, beam.z)
velocity = Vector(beam.vx, beam.vy, beam.vz)
position.rotation(-theta_grazing, 'x')
velocity.rotation(-theta_grazing, 'x')
#position = position.rodrigues_formula(xp, -theta_grazing)
#velocity = velocity.rodrigues_formula(xp, -theta_grazing)
velocity.normalization()
beam.vx = velocity.x
beam.vy = velocity.y
beam.vz = velocity.z
vector_point = Vector(0, p, 0)
vector_point.rotation(-theta_grazing, "x")
print(vector_point.info())
#vector_point = vector_point.rodrigues_formula(xp, -theta_grazing)
vector_point.normalization()
beam.x = position.x - vector_point.x * p
beam.y = position.y - vector_point.y * p
beam.z = position.z - vector_point.z * p
def test_rotation_10_array(self):
print(">> test_rotation_10_array")
theta = 45*np.pi/180
alpha = 90*np.pi/180
x=np.zeros(10)
y=np.ones(10)
z=np.zeros(10)
v=Vector(x,y,z)
v.rotation(alpha,"y")
v.rotation(-(90*np.pi/180 - theta), "x")
print (v.info())
assert_almost_equal(v.x,np.zeros(10))
assert_almost_equal(v.y,1/np.sqrt(2) *np.ones(10))
assert_almost_equal(v.z,-1/np.sqrt(2)*np.ones(10))
def rotation_to_the_optical_element(self, beam):
position = Vector(beam.x,beam.y,beam.z)
velocity = Vector(beam.vx,beam.vy,beam.vz)
position.rotation(self.alpha,"y")
position.rotation(-(np.pi/2-self.theta),"x")
velocity.rotation(self.alpha,"y")
velocity.rotation(-(np.pi/2-self.theta),"x")
[beam.x,beam.y,beam.z] = [position.x,position.y,position.z]
[beam.vx,beam.vy,beam.vz] = [velocity.x,velocity.y,velocity.z]
def tras_rot(beam, p):
velocity = Vector(beam.vx, beam.vy, beam.vz)
velocity.rotation(-gamma, 'z')
velocity.rotation(-alpha, 'x')
velocity.normalization()
beam.vx = velocity.x
beam.vy = velocity.y
beam.vz = velocity.z
position = Vector(beam.x, beam.y, beam.z)
position.rotation(-gamma, 'z')
position.rotation(-alpha, 'x')
beam.x = position.x
beam.y = position.y
beam.z = position.z
beam.x -= beam.vx[0] * p
beam.y -= beam.vy[0] * p
beam.z -= beam.vz[0] * p
def rotation_to_the_screen(self,beam):
position = Vector(beam.x,beam.y,beam.z)
velocity = Vector(beam.vx,beam.vy,beam.vz)
if self.type == "Ideal lens":
position.rotation((np.pi/2-self.theta),"x")
velocity.rotation((np.pi/2-self.theta),"x")
else:
position.rotation(-(np.pi/2-self.theta),"x")
velocity.rotation(-(np.pi/2-self.theta),"x")
[beam.x,beam.y,beam.z] = [position.x,position.y,position.z]
[beam.vx,beam.vy,beam.vz] = [velocity.x,velocity.y,velocity.z]
def out(beam, q):
print("\nOut")
velocity = Vector(beam.vx, beam.vy, beam.vz)
velocity.rotation(-alpha, 'x')
print(velocity.x[0], velocity.y[0], velocity.z[0])
velocity.rotation(-gamma, 'z')
print(velocity.x[0], velocity.y[0], velocity.z[0])
beam.vx = velocity.x
beam.vy = velocity.y
beam.vz = velocity.z
position = Vector(beam.x, beam.y, beam.z)
position.rotation(-alpha, 'x')
position.rotation(-gamma, 'z')
beam.x = position.x
beam.y = position.y
beam.z = position.z
beam.retrace(q)
y = Vector(0., 1., 0.)
y.z = -np.tan(theta_grazing) / np.sqrt(1 + np.tan(theta_grazing)**2)
y.x = +np.tan(theta_grazing) / np.sqrt(1 + np.tan(theta_grazing)**2)
y.y = np.sqrt(1 - y.x**2 - y.z**2)
y.x = y.x
y.y = y.y
y.z = y.z
print(y.x, y.y, y.z)
print(
np.arctan(y.x / np.sqrt(y.y**2 + y.z**2)) * 180 / np.pi - 90.,
90. + np.arctan(y.z / np.sqrt(y.y**2 + y.x**2)) * 180 / np.pi)
alpha = -np.arctan(y.z / y.y)
y.rotation(alpha, 'x')
gamma = np.arctan(y.x / y.y)
y.rotation(gamma, 'z')
print(y.x, y.y, y.z)
y = Vector(0., 1., 0.)
y.rotation(-gamma, 'z')
y.rotation(-alpha, 'x')
print(y.x, y.y, y.z)
print("End Vector")
#y = Vector(0., 1., 0.)
#y.z = - np.tan(theta_grazing) / np.sqrt(2 + (np.tan(theta_grazing))**2)
#y.x = np.tan(theta_grazing) / np.sqrt(2 + (np.tan(theta_grazing))**2)
#y.y = 1 / np.sqrt(2 + np.tan(theta_grazing)**2)
z = f - p * np.cos(beta)
v = Vector(0., y, z - f)
v.normalization()
v0 = Vector(0., 0., -1.)
v0.normalization()
alpha = np.arccos(v.dot(v0))
t = (-v.x * beam.x - v.y * beam.y -
v.z * beam.z) / (v.x * beam.vx + v.y * beam.vy + v.z * beam.vz)
beam.x += beam.vx * t
beam.y += beam.vy * t
beam.z += beam.vz * t
velocity = Vector(beam.vx, beam.vz, -beam.vy)
velocity.rotation(-alpha, 'x')
beam.vx = velocity.x
beam.vy = velocity.y
beam.vz = velocity.z
wolter_japanese.oe[0].set_parameters(p=0., q=0., theta=90 * np.pi / 180)
########################################################################################################################
wolter_japanese.oe[0].intersection_with_optical_element(beam)
wolter_japanese.oe[0].output_direction_from_optical_element(beam)
wolter_japanese.oe[1].intersection_with_optical_element(beam)
wolter_japanese.oe[1].output_direction_from_optical_element(beam)
ccc = wolter_japanese.oe[1].ccc_object.get_coefficients()