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interferometer_diff_3d.py
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interferometer_diff_3d.py
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import numpy as np
import matplotlib.pyplot as plt
from numpy import cos, pi, abs
import matplotlib
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
from matplotlib.animation import FuncAnimation
from matplotlib.ticker import LinearLocator, FormatStrFormatter
from functools import partial
outdir="/home/zoltan/publications/interferometer/trunk/pictures/"
do_plot_3d = False
do_plot_rhos = False
if False:
matplotlib.use('pgf')
pgf_with_custom_preamble = {
"pgf.texsystem": "pdflatex",
"font.family": "serif", # use serif/main font for text elements
"text.usetex": True, # use inline math for ticks
"pgf.rcfonts": False, # don't setup fonts from rc parameters
"figure.figsize": (3.3914487339144874*1.1, 2.0960305886619515*0.8*1.1),
"axes.labelsize": 8,
"axes.grid": True,
"font.size": 7,
"legend.fontsize": 8,
"legend.handlelength": 2,
"legend.handletextpad": 0.4,
"legend.columnspacing": 1,
# 'legend.title_fonstize':7,
"xtick.labelsize": 8,
"ytick.labelsize": 8,
"xtick.direction":"in",
"ytick.direction":"in",
"xtick.major.size":1.5,
"ytick.major.size":1.5,
"xtick.minor.size":0.25,
"ytick.minor.size":0.25,
"grid.alpha": 0.6,
"lines.markersize": 4,
# "lines.markeredgecolor": None,
"savefig.pad_inches":0,
"savefig.bbox":"tight",
"savefig.dpi":300,
"pgf.preamble": r"\usepackage[detect-all,locale=US]{siunitx}\usepackage{amsmath}\usepackage[utf8x]{inputenc}\usepackage[T1]{fontenc}"
}
matplotlib.rcParams.update(pgf_with_custom_preamble)
matplotlib.rcParams['axes.unicode_minus'] = False
l_tl=0.384
l_tl = 405/2158
l_tl=0.5
# guided wavelength: 2158um @61GHz
# Z0 = 58.50 - j*1.94
# epsilon: 5.20
# L`=4.439e-7
# R`=11717.64
# C`=1.2989e-10
# G`=0.1208
l_ym = []
l_xm = []
l_l = np.linspace(0.01, 0.5, 50)
x = np.linspace(0, 0.5, 50)
# for l in l_l:
# y = abs(cos(x*2*pi)) + abs(cos(2*pi*(l-x)))
# ymin = y.min()
# xmin = x[np.where( y == y.min())]
# l_ym.append(ymin)
# l_xm.append(xmin)
# # plt.plot(x,y, label="%.2f"%l)
# plt.plot(l_l,l_ym)
# plt.xlabel("Line length [$l/\lambda$]")
# plt.ylabel("Worst case sum")
# # print(np.amin(y))
# # print(np.min(y))
# plt.grid()
# plt.legend()
# plt.show()
# plt.close()
###############################################
def pd_sum(n, x, l, r, rho):
""" Sum of the peak detector outputs
Note: Since x is swept, no phsae shift constant is necessary to be included
Paramters:
----------
x: array
location of the first tap point in electrical length;
l: float
the total length of the measurment medium in electrical length
n: integer
number of the equidistant tap points
r: float in [0,1]
the ratio of the amplitudes
rho: float in [0,2*pi)
the phase difference between the waves
"""
s = 0
t = l / (n-1)
for i in range(n):
s += abs(cos( 2*pi*(i*t -x) )) - r*abs(cos(2*pi*(i*t -x)-rho))
return s
def pd_sum1(n, x, l, r, rho):
s = 0
t = l / (n-1)
for i in range(n):
s += abs(cos( 2*pi*(i*t -x) ))
return s
def pd_sum2(n, x, l, r, rho):
s = 0
t = l / (n-1)
for i in range(n):
s += r*abs(cos(2*pi*(i*t -x)-rho))
return s
def sum_minmax(n, x, l):
""" Worst case of the standing wave for 'n' detectors.
Paramters:
----------
x: array
location of the first tap point in electrical length;
l: float
the total length of the measurment medium in electrical length
n: integer
number of the equidistant tap points
r: float in [0,1]
the ratio of the amplitudes
rho: float in [0,2*pi)
the phase difference between the waves
"""
a_min = np.full(len(x),999)
i_r = 0.5
if True:
# for i_r in np.linspace(0, 0.7, 10, endpoint=False):
i_rho=0.0
# for i_rho in np.linspace(0, 2*pi, 10, endpoint=False):
if True:
i = pd_sum(n=n,x=x,l=l,r=i_r, rho=i_rho)
print(f"l={l:.3} n={n} r={i_r:.2} rho={i_rho:.3} min(sum)={i.min():.3}")
a_min = np.minimum(i.min(),a_min)
print("--------------------")
print(a_min)
return a_min
def my_formatter(x, pos):
if x.is_integer():
# return f"{x:.0}"
return str(int(x))
else:
return f"{x:.1}"
###############################################
if do_plot_3d:
fig, ax = plt.subplots()
ax = fig.gca(projection='3d')
n = 4
X, Y = np.meshgrid(range(100),range(100), indexing='ij')
z = np.zeros(X.shape)
for r in X[:,0]:
for rho in Y[0,:]:
z[r,rho] = pd_sum(x=x, n=n, l=l_tl, r=r/8, rho=rho/4/2/pi).min()
l_x = x[:]
m = np.full(X.shape,999)
for x in l_x:
p = pd_sum(x=x, n=n, l=l_tl, r=X/len(X), rho=Y*2*pi/len(Y))
m = np.minimum(m,p)
# surf = ax.plot_surface(X,Y,z, cmap=cm.coolwarm)
surf = ax.plot_surface(X/len(X),Y*2*pi/len(Y),m, cmap=cm.coolwarm)
ax.set_xlabel(r"$r$", labelpad=2)
ax.set_ylabel(r"$\rho$", labelpad=2)
fig.colorbar(surf, shrink=0.75, aspect=5)
plt.show()
# ==> Conclusion: rho barely changes the results
if do_plot_rhos:
n_plots = 8
n_columns = 4
fig, ax = plt.subplots(int(n_plots/n_columns), n_columns, figsize=(16,8))
n=4
cnt=0
r=0.3
rho=np.linspace(0,2*pi,100)
l_y2 = []
l_n = np.linspace(0.05,0.4,8,endpoint=True)
for l in l_n:
l_y = []
for i in rho:
l_y.append(pd_sum(n=n,x=x,l=l,r=r,rho=i).min())
l_y2.append(l_y)
for i in range(n_plots):
row = int(i / n_columns)
col = i % n_columns
ax[row,col].plot(rho,l_y2[i],label=f"n={l_n[i]:.3}")
ax[row,col].set_title(f"l={l_n[i]:.3}")
for i in range(n_columns):
ax[1,i].set_xlabel(r"$\rho$", labelpad=2)
for i in range(int(n_plots/n_columns)):
ax[i,0].set_ylabel(r"$\min \left \{ \Delta V_{\Sigma}(x) \right \}$", labelpad=2)
# ax[0,0].plot(rho,l_y2[0],label=f"n={l_n[0]:.3}")
# ax[0,0].set_title(f"l={l_n[0]:.3}")
# ax[0,1].plot(rho,l_y2[1],label=f"n={l_n[1]:.3}")
# ax[0,1].set_title(f"l={l_n[1]:.3}")
# ax[1,0].plot(rho,l_y2[2],label=f"n={l_n[2]:.3}")
# ax[1,0].set_title(f"l={l_n[2]:.3}")
# ax[1,1].plot(rho,l_y2[3],label=f"n={l_n[3]:.3}")
# ax[1,1].set_title(f"l={l_n[3]:.3}")
fig.suptitle(f"r={r:.1}, n={n}")
plt.tight_layout()
# fig.savefig(outdir + f"sw_amp_diff_r{r:.1}_n{n}")
plt.show()
####################################
# Plot the two part of the difference separately
# X axis: the electrical length of the tl
# assume r=0.1, plot multiple rho values, n=4
# fig, ax = plt.subplots(int(n_plots/n_columns), n_columns, figsize=(16,8))
# fig, ax = plt.subplots()
# n = 4
# r = 0.1
# x = np.linspace(0, 0.5, 50)
# ax.plot(x, pd_sum1(n=n, x=x, r=r, rho=0, l=l_tl), linestyle="--")
# for rho in np.linspace(0,pi,7):
# ax.plot(x, abs(pd_sum(n=n, x=x, r=r, rho=rho, l=l_tl)), linestyle="-")
# ax.plot(x, pd_sum2(n=n, x=x, r=r, rho=rho, l=l_tl), linestyle=":")
# plt.show()
l_tl = 0.5
r=0.0
rho=0.0
for r in np.arange(0,0.61,0.1):
for rho in np.arange(0,pi+0.01,pi/20):
for l_tl in np.arange(0.05,0.51,0.05):
N=10
fig, ax = plt.subplots()
ax.set_xlim(0,0.5)
ax.set_ylim(0,N)
ax.set_xlabel("position of the SW maximum to the transmission line")
ax.set_ylabel("SW & $V_{\Sigma}$ normalized to SW amplitude")
fig.suptitle(f"T-line length: {l_tl}; r: {r:.0f} $\\rho$: {rho:.0f}")
ax.grid(which='both')
x=np.linspace(0, 0.5, 50)
lines = [ax.plot([],[],label='det No.{i}')[0] for i in range(N+2)]
lines2 = lines[:]
for line in lines2:
plt.setp(line, linestyle=":", alpha=0.7)
lines.append(ax.plot([],[], 'k-', label="sum", alpha=0.7)[0])
hlines = [ax.plot([min(x),max(x)],[0,0], linestyle=":", color='black',alpha=0.7)[0] for _ in range(2)]
my_text = ax.text(.35, 7.5, '')
dV_text = ax.text(.35, 7.0, '')
patches = lines + [my_text]
def init():
for line in lines:
line.set_data([],[])
my_text.set_text('')
return patches
def animate(n):
m = n+2
s = np.zeros(x.shape)
for i in range(m):
yp = abs(cos( 2*pi*(l_tl/(m-1)*i -x) ))
ym = r*abs(cos( 2*pi*(l_tl/(m-1)*i -x)-rho))
y = abs(yp - ym)
lines[i].set_data(x,y)
lines[i].set_label("det No. {i}")
# ax.plot(x,y,label=f"{n}")
s+=y
for i in range(m,N+2):
lines[i].set_data([],[])
lines[N+2].set_data(x,s)
hlines[0].set_data([min(x),max(x)],[min(s),min(s)])
hlines[1].set_data([min(x),max(x)],[max(s),max(s)])
my_text.set_text(f"N={m}")
dV_text.set_text("$\Delta V_{\Sigma}=%.2f$" % ( max(s)-min(s))) #, 200*(max(s)-min(s))/(max(s)+min(s)) ) )
ani = FuncAnimation(fig, animate, interval=500, frames=N-2)
#, blit=True)
# # Set up formatting for the movie files
# Writer = matplotlib.animation.writers['ffmpeg']
# writer = Writer(fps=15, metadata=dict(artist='Me'), bitrate=1800)
# ani.save("/home/zoltan/publications/interferometer/trunk/pictures/det_sum_vs_Ndet_Xinput_phase_r0_rho0.mp4", writer=writer)
ani.save(f"/home/zoltan/publications/interferometer/trunk/pictures/det_sum_vs_Ndet_Xinput_phase_lenTL{l_tl*100:.0f}_r{r:.0f}_rho{rho/pi*180:.0f}.gif", writer=matplotlib.animation.ImageMagickFileWriter())
plt.close(fig)
# plt.show()
#ax.grid(True,which='minor', alpha=0.1, axis='both')
#ax.grid(True,which='major', alpha=0.7, axis='both')
#ax.set_xlabel(r"Electrical length of the transmission line ($l$)", labelpad=2)
#ax.set_ylabel(r"$\min \left ( V_{\Sigma}(x, \rho, x_0) \right )$", labelpad=2)
#ax.tick_params(axis='both', which='major', pad=2)
#ax.set_xlim(0,0.5)
#ax.set_ylim(bottom=0,top=6)
#ax.yaxis.set_minor_locator(matplotlib.ticker.MultipleLocator(0.25))
#ax.xaxis.set_minor_locator(matplotlib.ticker.MultipleLocator(0.01))
## markers
#m = ['o','s','^','v','x']
#me = 50
#for i in range(2,7):
# # smallest value for the sum of the peak detector outputs, for different line lengths (l_l)
# # it is swept for different starting phases and the smallest value is selected
# ymin = np.array([sum_minmax(i,x,l)[0] for l in l_l])
# ax.plot(l_l, ymin, label=i, marker=m[i-2], markevery=(int(me*(i-1)/3), me))
## The two ranges are separated to plot the with the same color
#ax.set_prop_cycle(None)
#for i in range(2,7):
# ymax = np.array([sum_minmax(i,x,l)[1] for l in l_l])
# # ax.plot(l_l, ymax, marker=m[i-2], markevery=(int(me*(i-1)/3), me), linestyle="--")
# ax.plot(l_l, ymax, markevery=(int(me*(i-1)/3), me), linestyle=":")
#legend_style = {"frameon":False, "handletextpad":0.4, "borderaxespad":0, "ncol":5, "loc":'lower center', "mode":"expand", "handlelength":1}
#ax.legend(bbox_to_anchor=(0.1, 1.0, 0.9, 0.04), **legend_style)
#ax.annotate("$N$:", xy=(0.01,1.05), xycoords="axes fraction")
#ax.xaxis.set_major_formatter(matplotlib.ticker.FuncFormatter(my_formatter))
#for ext in ("png", "pgf"):
# fig.savefig(outdir + "interferometer_calc." + ext)
################################################
#if False:
# n = 4
# a=0
# color = ["#7fc97f","#beaed4","#fdc086","#ffff99","#386cb0","#f0027f","#bf5b17"]
# for l_tl in np.linspace(0.25,0.5,21):
# for i in range(n):
# plt.plot(x, abs(cos(2*pi*(i*l_tl/(n-1) - x))))
# plt.plot(x, pd_sum(n,x,l_tl), label=l_tl)
# plt.xlabel("SW peak location")
# plt.ylabel("")
# plt.grid()
# plt.savefig(f"./interfero_n4_tl{l_tl:.2}sum.png")