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import re, sys, traceback
import numpy as np
import scipy.optimize
from PyQt5.QtWidgets import *
from PyQt5.QtGui import *
from PyQt5.QtCore import *
from ui import *
def R(theta):
return np.array([[np.cos(theta), np.sin(theta)],
[-np.sin(theta), np.cos(theta)]])
class Ellipse:
def __init__(self, state):
# FIXME: a less brute-force way of doing this
if state is None:
self.alpha = np.nan
self.theta = np.nan
self.e = np.nan
self.a = np.nan
self.b = np.nan
return
def x(theta):
return np.real(np.exp(1j * theta) * state)
def r(theta):
return np.linalg.norm(x(theta))
def angle(x):
a = np.arctan2(x[1], x[0])
if a < 0:
a += 2 * np.pi
if a > np.pi:
a -= np.pi
return a
opt = scipy.optimize.minimize_scalar(r, bounds=[0, np.pi], \
method="bounded")
self.b = r(opt.x)
opt = scipy.optimize.minimize_scalar(lambda x: -r(x), \
bounds=[0, np.pi], method="bounded")
self.a = r(opt.x)
self.alpha = angle(x(opt.x))
self.e = self.b / self.a
self.theta = np.arctan(self.e)
if self.alpha > angle(x(opt.x + 0.001)):
self.theta *= -1
class Polarizer:
def __init__(self, type, delta=0):
self.name = "New element" # FIXME
self.type = type
self.angle = 0
self.delta = delta
self.ref = False
self.t1 = 1
self.t2 = 0
self.enable = True
self.set_type(type)
def set_type(self, type):
if type == "linear":
self.M = np.array([[1, 0], [0, 0]])
elif type == "quarterwave":
self.M = np.exp(-1j / 4 * np.pi) * \
np.array([[1, 0], [0, 1j]])
else:
raise ValueError("bad Polarizer type: %s" % type)
self.type = type
def mul(self, state):
# unpolarized light
if state is None:
if self.type == "linear":
return np.dot(R(-self.angle - self.delta), \
np.array([[1], [0]])) * np.sqrt(self.t1)
else:
return None
if type == "linear":
A = np.sqrt(np.array([[self.t1, 0], [0, self.t2]]))
else:
A = np.sqrt(np.array([[self.t1, 0], [0, self.t1]]))
M = np.matmul(R(-self.angle - self.delta), \
np.matmul(np.matmul(self.M, A), R(self.angle + self.delta)))
return np.dot(M, state)
class System:
def __init__(self):
self.elements = list()
def recalculate(system):
system.states = [None] * len(system.elements)
system.ellipses = list()
state = None
for i, pol in enumerate(system.elements):
if pol.enable:
state = pol.mul(state)
system.states[i] = state
system.ellipses.append(Ellipse(state))
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