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.type = type self.angle = 0 self.delta = delta self.ref = False # FIXME: move this to UI or System 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]])) else: return None M = np.matmul(R(-self.angle - self.delta), \ np.matmul(self.M, R(self.angle + self.delta))) return np.dot(M, state) class System: def __init__(self): self.elements = list() self.ignore = list() def recalculate(system): system.states = [None] * len(system.elements) system.ellipses = list() state = None for i, pol in enumerate(system.elements): if i >= len(system.ignore) or not system.ignore[i]: state = pol.mul(state) system.states[i] = state system.ellipses.append(Ellipse(state))