最近做大物实验，萌生了将迈克尔逊干涉仪等倾干涉有关实验利用Python进行仿真的想法。主要利用tkinter库构建UI，matplotlib/numpy库进行计算和绘图，FigureCanvasTkAgg, NavigationToolbar2Tk用于把利用matplotlib库生成的图片绘制到tkinter画布上：
from tkinter import * from matplotlib.figure import Figure import matplotlib.pyplot as plt import matplotlib as mpl from matplotlib.backends.backend_tkagg import FigureCanvasTkAgg, NavigationToolbar2Tk import numpy as np import math
基本设置：
plt.ion() # Open the interactive mode.
mpl.use('TkAgg') # Tkinter & matplotlib linker.
# Control
window = Tk()
fig = Figure()
image = fig.add_subplot()
label = [Label(), Label(), Label(), Label()]
scale = [[Scale(), Scale()],
[Scale(), Scale()],
[Scale()],
[Scale(), Scale()]]
# Data
distance = 0
distance_accuracy = IntVar()
delta_distance = 0
focal = 200
focal_part_1 = DoubleVar()
angle_part_2 = DoubleVar()
wavelength_1 = 0
wavelength_1_part_1 = DoubleVar()
wavelength_1_part_2 = DoubleVar()
wavelength_2 = 0
wavelength_2_part_1 = DoubleVar()
wavelength_2_part_2 = DoubleVar()
VALUE_RANGE = 20
ACCURACY = 500 首先构建交互界面，在下面的函数中对基本参数做了设置。
def WindowCreate():
window.title("迈克尔逊干涉仪实验仿真")
window.geometry("1500x750")
window.resizable(False, False) 对界面进行初始化，label和distance_accuracy是定义在函数外的全局变量。用scale调整光的波长和透镜焦距，距离由于需要连续调整，故使用鼠标滚轮控制，变化量由用户通过scale控件决定。
def WindowInitialize():
global label
global distance_accuracy
window.bind('<MouseWheel>', DistanceRefresh)
window.bind('<ButtonRelease>', WavelengthAndFocalRefresh)
# Scales control wavelength 1.
scale[0][0] = Scale(window, length=1000, orient=HORIZONTAL, activebackground='red', from_=0, to=999,
digits=3, resolution=1, label='波长1(整数部分)', variable=wavelength_1_part_1)
scale[0][0].place(x=0, y=0)
scale[0][1] = Scale(window, length=200, orient=HORIZONTAL, activebackground='red', from_=0, to=0.99,
digits=2, resolution=0.01, label='波长1(小数部分)', variable=wavelength_1_part_2)
scale[0][1].place(x=1100, y=0)
# Scales control wavelength 2.
scale[1][0] = Scale(window, length=1000, orient=HORIZONTAL, activebackground='red', from_=0, to=999,
digits=3, resolution=1, label='波长2(整数部分)', variable=wavelength_2_part_1)
scale[1][0].place(x=0, y=80)
scale[1][1] = Scale(window, length=200, orient=HORIZONTAL, activebackground='red', from_=0, to=0.99,
digits=2, resolution=0.01, label='波长2(小数部分)', variable=wavelength_2_part_2)
scale[1][1].place(x=1100, y=80)
# Scale controls accuracy of distance.
scale[2][0] = Scale(window, length=200, orient=HORIZONTAL, activebackground='red', from_=1, to=5,
digits=1, resolution=1, label='距离(滚轮控制精度)', variable=distance_accuracy)
scale[2][0].place(x=0, y=160)
# Scales control angle.
scale[3][0] = Scale(window, length=400, orient=HORIZONTAL, activebackground='red', from_=1, to=200,
digits=3, resolution=1, label='焦距(整数部分)/mm', variable=focal_part_1)
scale[3][0].place(x=0, y=240)
scale[3][0].set(100)
scale[3][1] = Scale(window, length=200, orient=HORIZONTAL, activebackground='red', from_=0, to=0.9,
digits=1, resolution=0.1, label='焦距(小数部分)/mm', variable=angle_part_2)
scale[3][1].place(x=0, y=320)
# Label shows the distance.
label[0] = Label(window, text="{:.2f}".format(wavelength_1) + 'nm', font=("", 20))
label[0].place(x=1350, y=30)
label[1] = Label(window, text="{:.2f}".format(wavelength_2) + 'nm', font=("", 20))
label[1].place(x=1350, y=110)
label[2] = Label(window, text="{:.5f}".format(distance) + 'mm', font=("", 20))
label[2].place(x=250, y=190)
label[3] = Label(window, text="{:.1f}".format(focal) + 'mm', font=("", 20))
label[3].place(x=250, y=350)
fig_frame = Frame(window, width=500, height=500)
fig_frame.place(x=500, y=200)
canvas = FigureCanvasTkAgg(fig, fig_frame)
canvas.get_tk_widget().pack(side=TOP, fill=BOTH, expand=YES)
toolbar = NavigationToolbar2Tk(canvas, fig_frame, pack_toolbar=False)
toolbar.update()
toolbar.pack(side=RIGHT) 每次鼠标按键释放和滚轮滚动都会调用函数刷新图片，最后一行image.cla()不加上（用于删除上次图片数据）会造成严重卡顿，当时在这卡了好久才考虑到这个问题：
def WavelengthAndFocalRefresh(event):
# Check the change of wavelength and focal length.
global label
global wavelength_1
global wavelength_2
global focal
wavelength_1 = wavelength_1_part_1.get() + wavelength_1_part_2.get()
wavelength_2 = wavelength_2_part_1.get() + wavelength_2_part_2.get()
focal = focal_part_1.get() + angle_part_2.get()
label[0].config(text="{:.2f}".format(wavelength_1) + 'nm')
label[1].config(text="{:.2f}".format(wavelength_2) + 'nm')
label[3].config(text="{:.1f}".format(focal) + 'mm')
if 1000 <= event.x <= 1500 and 250 <= event.y <= 750:
# In the area of the interference image.
pass
ImageRefresh()
def DistanceRefresh(event):
# Check the change of distance.
global distance
global delta_distance
delta_distance = 10 ** (-1 * distance_accuracy.get())
if event.delta > 0:
distance += delta_distance
else:
distance -= delta_distance
if distance < 0:
distance = 0
distance = float('%.5f' % distance)
label[2].config(text="{:.5f}".format(distance) + 'mm')
ImageRefresh()
def ImageRefresh():
wavelength_A = wavelength_1 * 10 ** -6
wavelength_B = wavelength_2 * 10 ** -6
if wavelength_A != 0:
x_A, y_A = np.meshgrid(np.linspace(-VALUE_RANGE, VALUE_RANGE, ACCURACY),
np.linspace(-VALUE_RANGE, VALUE_RANGE, ACCURACY))
r_A = np.sqrt(x_A ** 2 + y_A ** 2)
A = np.cos(math.pi * (2 * distance * np.cos(np.arcsin(np.sin(np.arctan(r_A / focal))))) / wavelength_A) ** 2
else:
A = 0
if wavelength_B != 0:
x_B, y_B = np.meshgrid(np.linspace(-VALUE_RANGE, VALUE_RANGE, ACCURACY),
np.linspace(-VALUE_RANGE, VALUE_RANGE, ACCURACY))
r_B = np.sqrt(x_B ** 2 + y_B ** 2)
B = np.cos(math.pi * (2 * distance * np.cos(np.arcsin(np.sin(np.arctan(r_B / focal))))) / wavelength_B) ** 2
else:
B = 0
if wavelength_A != 0 or wavelength_B != 0:
image.imshow(A/2.0+B/2.0)
fig.canvas.draw()
image.cla() 最后调用函数就可以正常运行啦！
WindowCreate() WindowInitialize() window.mainloop()
贴一张结果图（钠黄光双谱线，视见度下降）：