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NPSmethods_Single.py
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# %%
# -*- coding: utf-8 -*-
"""
Created on Wed Aug 7 09:35:43 2019
@author: Wenjun Zhang
"""
##############################################################################
# import packages
import os
import numpy as np
from numpy import log as ln
from scipy.optimize import curve_fit
from scipy.interpolate import InterpolatedUnivariateSpline
import matplotlib.pyplot as plt
import matplotlib.cm as cm
from mpl_toolkits.axes_grid1 import make_axes_locatable
from matplotlib.ticker import MultipleLocator
##############################################################################
# Functions for reading in data
def readInImages(imgDir, numOfImgsInEachRun, parameter, \
trapRegion=(slice(0, 65535), slice(0, 65535)), \
noiseRegion=(slice(0, 65535), slice(0, 65535))):
"""
Read in images, and calculate optical depth (OD).
It selects two regions, one with atoms, one without atoms. The latter is
served as an estimation of noise and to be subtracted in Fourier space.
----------
parameters
imgDir: string, the directory where the images of atoms are stored.
numOfImgsInEachRun: int, the number of images you want to include.
trapRegion: slice, mark the position of the atoms.
[(xmin, xmax), (ymin, ymax)] (pixel)
noiseRegion: slice, mark the position chosen to serve as an estimation
of noise. [(xmin, xmax), (ymin, ymax)] (pixel)
-------
returns
atomODs: list, each element of which is a numpy.ndarray, the matrix
for optical depth of the region with atoms.
atomODAvg: numpy.ndarray, the average of all images in `atomODs`.
noiseODs: list, each element of which is a numpy.ndarray, the matrix
for optical depth of the region without atoms.
noiseODAvg: numpy.ndarray, the average of all images in `noiseODs`.
imgIndexMin, imgIndexMax: string, the minimum and maximum index of the
images included
"""
# get filenames and the minimum and maximum index of the images
imgFileNames = []
for _, _, files in os.walk(imgDir):
# select file name
for file in files:
# check the extension of files
if file.startswith("rawimg_"):
# print whole path of files
imgFileNames.append(imgDir + "\\" + file)
# paraFile = open(imgDir + "\\parameters.txt", "r")
# lines = paraFile.readlines()
# #for line in lines[-numOfImgsInEachRun:]:
# for line in lines[1:]:
# if line.split()[0] == "img#":
# raise ValueError(\
# "Total number of images is less than required: {}<{}".format(\
# len(lines)-1, numOfImgsInEachRun))
# if float(line.split()[1]) == parameter:
# imgFileNames.append(imgDir + "\\rawimg_" + line.split()[0])
# #imgIndexMin = lines[-numOfImgsInEachRun].split()[0]
# imgIndexMin = lines[1].split()[0]
# imgIndexMax = lines[-1].split()[0] # these are strings
imgIndexMin = 0
imgIndexMax = 1
# paraFile.close()
# read in images
atomODs = []
noiseODs = []
for filename in imgFileNames:
dim = np.fromfile(filename, '>u2')[0:4]
print(dim)
img_temp = np.fromfile(filename, '>u2')[4:]
print(np.shape(img_temp))
img_temp = np.fromfile(filename, '>u2')[4:].reshape((dim[1], dim[3]))
atomImg_WithAtom_temp = \
img_temp[:dim[1]//2, :].astype(int)[trapRegion[::-1]]
atomImg_WithoutAtom_temp = \
img_temp[dim[1]//2:, :].astype(int)[trapRegion[::-1]]
noiseImg_WithAtom_temp = \
img_temp[:dim[1]//2, :].astype(int)[noiseRegion[::-1]]
noiseImg_WithoutAtom_temp = \
img_temp[dim[1]//2:, :].astype(int)[noiseRegion[::-1]]
#
atomODs.append(-ln(atomImg_WithAtom_temp/atomImg_WithoutAtom_temp))
noiseODs.append(-ln(noiseImg_WithAtom_temp/noiseImg_WithoutAtom_temp))
atomODAvg = sum(atomODs) / len(atomODs)
atomODAvg = np.nan_to_num(atomODAvg)
noiseODAvg = sum(noiseODs) / len(noiseODs)
return atomODs, atomODAvg, noiseODs, noiseODAvg, imgIndexMin, imgIndexMax
##############################################################################
# Functions for data process
def OD2AtomNum(OD, imgSysData=None):
"""
Calculate surface density from optical density.
"""
if imgSysData["ODtoAtom"] == 'beer':
px = imgSysData["CCDPixelSize"] / imgSysData["magnification"]
AtomNum = OD * 2*np.pi / (3*imgSysData["wavelen"]**2) * px**2
else:
AtomNum = OD * imgSysData["ODtoAtom"]
return AtomNum
def __calcNPS(ODs, ODAvg, norm=False, imgSysData=None):
"""
Calculate the noise power spectrum (NPS), from a set of images and their
average. Note that `ODs` is considered as an ensemble, which means each
image of `ODs` should be taken under identical conditions, and `ODAvg`
is considered as the ensemble average.
ODs: list, each element of which is a numpy.ndarray, the matrix of each
image.
ODAvg: numpy.ndarray, the ensemble average of `ODs`.
norm: bool. If true, use the atom number to normalize the noise power
spectrum. If false, use OD to calculate. In the latter case, the
absolute value of the noise power spectrum is meaningless.
noisePowSpecs: list, each element of which is the noise power spectrums of
an image in `ODs`.
NPS: numpy.ndarray, the average of noisePowSpecs, which is taken as
ensemble average
"""
noisePowSpecs = []
for k in range(len(ODs)):
if len(ODs) > 1:
noise = ODs[k] - ODAvg
else:
noise = ODs[k]
if norm:
noise = OD2AtomNum(noise, imgSysData)
noiseFFT = np.fft.fftshift(np.fft.fft2(np.fft.fftshift(noise)))
noisePowSpec = np.abs(noiseFFT)**2
# noisePowSpec = noisePowSpec / ODs[k].sum()
noisePowSpecs.append(noisePowSpec)
NPS = sum(noisePowSpecs) / len(noisePowSpecs)
#NPS = NPS / ODAvg
return NPS, noisePowSpecs
def calcNPS(imgDir, numOfImgsInEachRun, parameter, trapRegion, noiseRegion, \
norm=False, imgSysData=None):
"""
This is a combination of `ReadInImages` and `calcNPS__`.
Calculate the experimental imaging response function.
----------
parameters
same as `ReadInImages`
-------
returns
M2k_Exp: numpy.ndarray, the calculated imaging response function
aalready subtracted by pure noise result).
M2k_Exp_atom: numpy.ndarray, the imaging response function calculated
from images of atoms (suffered from shot noise).
M2k_Exp_noise: numpy.ndarray, the imaging response function calculated
from images of pure noise (only shot noise affects)
imgIndexMin, imgIndexMax, atomODs, noiseODs, atomODAvg, noiseODAvg:
same as `readInImages`
"""
atomODs, atomODAvg, noiseODs, noiseODAvg, imgIndexMin, imgIndexMax = \
readInImages(imgDir, numOfImgsInEachRun, parameter, trapRegion, noiseRegion)
M2k_Exp_atom, _ = __calcNPS(atomODs, atomODAvg, norm=norm, imgSysData=imgSysData)
M2k_Exp_noise, _ = __calcNPS(noiseODs, noiseODAvg, norm=norm, imgSysData=imgSysData)
M2k_Exp_atom = M2k_Exp_atom / atomODAvg.sum()
M2k_Exp_noise = M2k_Exp_noise / atomODAvg.sum()
M2k_Exp_atom[M2k_Exp_atom.shape[0]//2, M2k_Exp_atom.shape[1]//2] = 0
M2k_Exp = M2k_Exp_atom #- M2k_Exp_noise
_, _, K_x, K_y = getFreq(imgSysData["CCDPixelSize"], imgSysData["magnification"], M2k_Exp.shape)
d = imgSysData["wavelen"] / (2*np.pi*imgSysData["NA"])
M2k_Fit_fake = M2kFuncAnal(K_x, K_y, d, 1.5, 1, .5, -1.6, 0, -1)
bkg = np.mean(M2k_Exp[M2k_Fit_fake==0])
M2k_Exp -= bkg
M2k_Exp[M2k_Exp < 0] = 0
M2k_Exp[M2k_Fit_fake == 0] = 0
return M2k_Exp, M2k_Exp_atom, M2k_Exp_noise, imgIndexMin, imgIndexMax, \
atomODAvg, noiseODAvg
##############################################################################
# Functions for physics and fitting
def pupilFunc(R_p, Theta_p, tau, S0, alpha, phi, beta):
"""
Given the polar coordinates, aberration parameters,
calculate the exit pupil function.
----------
parameters
R_p: radial coordinate
Theta_p: azimuthal coordinate
tau: describe the radial transmission decaying of the pupil.
$T(r) = T_0 \\exp\\left( -r^2 / tau^2 \\right)$
S0: spherical aberration, $S_0 r^4$
alpha, phi: astigmatism,
$\\alpha r^2 \\cos\\left(2\\theta - 2\\phi\\right)$
beta: defocus, $\\beta r^2$
------
return
Exit pupil function
"""
U = np.exp(-(R_p/tau)**4) * np.array(R_p <= 1, dtype=float)
Phase = S0 * (R_p**4) + \
alpha * (R_p**2) * np.cos(2*Theta_p - 2*phi) + \
beta * (R_p**2)
return U * np.exp(1j*Phase)
def M2kFuncAnal(K_X, K_Y, d, tau, S0, alpha, phi, beta, delta_s):
"""
Given the spatial frequency, aberration parameters and the phase
introduced by the atom scattering process,
calculate the imaging response function
----------
parameters
K_X, K_Y: spacial frequencies
d: the ratio for converting the spacial frequencies into
coordinates at exit pupil plane
tau: describe the radial transmission decaying of the pupil.
$T(r) = T_0 \\exp\\left( -r^2 / tau^2 \\right)$
S0: spherical aberration, $S_0 r^4$
alpha, phi: astigmatism,
$\\alpha r^2 \\cos\\left(2\\theta - 2\\phi\\right)$
beta: defocus, $\\beta r^2$
delta_s: the phase introduced by the atom scattering process
------
return
Exit pupil function
"""
R_p, Theta_p = np.abs(K_X + 1j*K_Y) * d, np.angle(K_X + 1j*K_Y)
p1 = pupilFunc(R_p, Theta_p + np.pi, tau, S0, alpha, phi, beta)
p2 = np.conj(pupilFunc(R_p, Theta_p, tau, S0, alpha, phi, beta)) * \
np.exp(-2*1j*delta_s)
PSF = (p1 + p2) / (2 * np.cos(delta_s))
M2k = np.abs(PSF)**2
return M2k
def getFreq(CCDPixelSize, magnification, M2k_mat_shape):
"""
Calculate the corresponding spacial frequency $k$.
"""
pixelSize = CCDPixelSize / magnification # pixel size in object plane, in micron
px_x = 1.0 * pixelSize # micron
px_y = 1.0 * pixelSize # micron
sampleNum_x = M2k_mat_shape[1]
sampleNum_y = M2k_mat_shape[0]
k_x = np.fft.fftshift(np.fft.fftfreq(sampleNum_x, px_x)) * 2*np.pi
k_y = np.fft.fftshift(np.fft.fftfreq(sampleNum_y, px_y)) * 2*np.pi
K_x, K_y = np.meshgrid(k_x, k_y)
return k_x, k_y, K_x, K_y
def fitM2k(M2k_Exp, imgSysData, paras_guess=None, paras_bounds=None):
"""
Fit the imaging response function using the model provided in
Chen-Lung Hung et al. 2011 New J. Phys. 13 075019
"""
k_x, k_y, K_x, K_y = getFreq(imgSysData["CCDPixelSize"], imgSysData["magnification"], M2k_Exp.shape)
d = imgSysData["wavelen"] / (2*np.pi*imgSysData["NA"])
def fitFunc(M, *args):
k_x, k_y = M
A, tau, S0, alpha, phi, beta, delta_s = args
return A * M2kFuncAnal(k_x, k_y, d, tau, S0, alpha, phi, beta, delta_s)
if paras_guess == None:
# A , tau, S0, alpha, phi, beta, delta_s
paras_guess = [
[.23, 1.22, .0, 1.24, -1.94, 0.12, 0], \
[.15, 1.22, .0, 1.43, -1.9, .36, 0], \
[.25, 1.22, .0, 2.04, -1.9, -1.76, 0], \
[.15, 1.22, .0, 1.76, -1.9, -0.32, 0], \
[.15, 1.22, .0, 1.54, -1.9, -0.14, -0], \
]
elif paras_guess == 'focus':
paras_guess = [1 , 0.8, 0, 1, -1.9, 0, 0]
elif paras_guess == 'defocus':
paras_guess = [1 , 0.8, -10 -0.5, -2.3, 17, 3.3]
if paras_bounds == None:
# A, tau, S0, alpha, phi, beta, delta_s
paras_bounds = ([ .1, 1.00, .0, 1.00,-1.94, -2., -2],
[ .5, 2.00, .01, 2.46,-1.83, 4., 2])
M2k_Exp_cut = np.clip(M2k_Exp, 0, M2k_Exp.max())
# cut the negative values, which are meaningless
xdata = np.vstack((K_x.ravel(), K_y.ravel()))
# prepare the independent variables, i.e., the coordinates
xdata = np.delete(xdata, (K_x.shape[0]//2)*K_x.shape[1]+K_x.shape[1]//2, axis=1)
ydata = np.delete(M2k_Exp_cut.ravel(), (K_x.shape[0]//2)*K_x.shape[1]+K_x.shape[1]//2, axis=0)
# leave out the center bright point
rms_min = np.inf
for pg in paras_guess:
popt_temp, pcov = curve_fit(fitFunc, xdata, ydata, \
p0=pg, max_nfev=500000, bounds=paras_bounds)
A_fit, tau_fit, S0_fit, alpha_fit, phi_fit, beta_fit, delta_s_fit = popt_temp
M2k_Fit_temp = A_fit * M2kFuncAnal(K_x, K_y, d, tau_fit, \
S0_fit, alpha_fit, phi_fit, beta_fit, delta_s_fit)
rms = np.sqrt( np.mean( (M2k_Fit_temp - M2k_Exp_cut)**2 ) )
if rms < rms_min:
rms_min = rms
popt = popt_temp
M2k_Fit = M2k_Fit_temp
elif rms == rms_min:
print("Warning from 'FitM2k': "
" Similar optimal rms error for several sets of initial parameters!")
return M2k_Fit, rms_min, popt, pcov, k_x, k_y, K_x, K_y, d
##############################################################################
# Further data processing
def azmAvgSq(X, Y, Z):
"""
Do the azimuthal average for a square matrix given in Cartesian
coordinates. The origin is considered to be at the center.
----------
parameters
X: numpy.ndarray, x-coordinate.
Y: numpy.ndarray, y-coordinate.
Z; numpy.ndarray, value at (x, y). X, Y and Z should have same shapes.
------
return
sorted_r: numpy.ndarray, radial coordinate, sorted from small to large.
sorted_v: numpy.ndarray, averaged value at r
"""
if X.shape != Y.shape or X.shape != Z.shape:
raise ValueError('X, Y and Z have different shapes!')
if X.shape[0] != X.shape[1]:
raise ValueError("X isn't a square! Consider to use `azmAvgNonSq`")
ind_max = X.shape[0] - 1
R = np.sqrt(X**2 + Y**2)
r_list = []
v_list = []
cind = ind_max // 2
for ii in range(cind + 1):
for jj in range(ii + 1):
r_list.append(R[ii, jj])
v_temp = [Z[ii, jj], Z[jj, ii], \
Z[ind_max - ii, jj], Z[ind_max - jj, ii], \
Z[ii, ind_max - jj], Z[jj, ind_max - ii], \
Z[ind_max - ii, ind_max - jj], \
Z[ind_max - jj, ind_max - ii] ]
v_list.append(np.mean(v_temp))
r_list = np.array(r_list)
v_list = np.array(v_list)
sorted_indices = np.argsort(r_list)
sorted_r = r_list[sorted_indices]
sorted_v = v_list[sorted_indices]
if len(sorted_r.tolist()) != len(set(sorted_r.tolist())):
print("Warning from `azmAvgSq`: there're duplicate elements in output!")
return sorted_r, sorted_v
def azmAvgNonSq(X, Y, Z):
"""
Do the azimuthal average for a non-square matrix given in Cartesian
coordinates. The origin is considered to be at the center.
----------
parameters
X: numpy.ndarray, x-coordinate.
Y: numpy.ndarray, y-coordinate.
Z; numpy.ndarray, value at (x, y). X, Y and Z should have same shapes.
------
return
sorted_r: numpy.ndarray, radial coordinate, sorted from small to large.
sorted_v: numpy.ndarray, averaged value at r
"""
if X.shape != Y.shape or X.shape != Z.shape:
raise ValueError('X, Y and Z have different shapes!')
if X.shape[0] == X.shape[1]:
raise ValueError('X is a square matrix! Consider use `azmAvgSq`.')
row_ind_max = X.shape[0] - 1
col_ind_max = X.shape[1] - 1
R = np.sqrt(X**2 + Y**2)
r_list = []
v_list = []
row_cind = row_ind_max // 2
col_cind = col_ind_max // 2
for ii in range(row_cind + 1):
for jj in range(col_cind + 1):
r_list.append(R[ii, jj])
v_temp = [Z[ii, jj], Z[row_ind_max - ii, jj], \
Z[ii, col_ind_max - jj], \
Z[row_ind_max - ii, col_ind_max - jj]]
v_list.append(np.mean(v_temp))
r_list = np.array(r_list)
v_list = np.array(v_list)
sorted_indices = np.argsort(r_list)
sorted_r = r_list[sorted_indices]
sorted_v = v_list[sorted_indices]
if len(sorted_r.tolist()) != len(set(sorted_r.tolist())):
print("Warning from `azmAvgNonSq`: there're duplicate elements in output!")
return sorted_r, sorted_v
def azmAvg_0(X, Y, Z):
"""
Do the azimuthal average for any matrix given in Cartesian coordinates.
The origin is considered to be at the center.
----------
parameters
X: numpy.ndarray, x-coordinate.
Y: numpy.ndarray, y-coordinate.
Z; numpy.ndarray, value at (x, y). X, Y and Z should have same shapes.
------
return
sorted_r: numpy.ndarray, radial coordinate, sorted from small to large.
sorted_v: numpy.ndarray, averaged value at r
"""
if X.shape != Y.shape or X.shape != Z.shape:
raise ValueError('X, Y and Z have different shapes!')
if X.shape[0] == X.shape[1]:
return azmAvgSq(X, Y, Z)
else:
return azmAvgNonSq(X, Y, Z)
def azmAvg(X, Y, Z):
"""
Do the azimuthal average for a matrix given in Cartesian coordinates.
----------
parameters
X: numpy.ndarray, x-coordinate.
Y: numpy.ndarray, y-coordinate.
Z; numpy.ndarray, value at (x, y). X, Y and Z should have same shapes.
------
return
sorted_r: numpy.ndarray, radial coordinate, sorted from small to large.
sorted_v: numpy.ndarray, averaged value at r
"""
if X.shape != Y.shape or X.shape != Z.shape:
raise ValueError('X, Y and Z have different shapes!')
row_ind_max = X.shape[0] - 1
col_ind_max = X.shape[1] - 1
R = np.sqrt(X**2 + Y**2)
row_cind = row_ind_max // 2
col_cind = col_ind_max // 2
res_dict = {}
for ii in range(row_cind + 1):
for jj in range(col_cind + 1):
res_dict[R[ii, jj]] = []
for ii in range(row_cind + 1):
for jj in range(col_cind + 1):
v_temp = [Z[ii, jj], Z[row_ind_max - ii, jj], \
Z[ii, col_ind_max - jj], Z[row_ind_max - ii, col_ind_max - jj]]
res_dict[R[ii, jj]].append(np.mean(v_temp))
for ii in range(row_cind + 1):
for jj in range(col_cind + 1):
res_dict[R[ii, jj]] = np.mean(res_dict[R[ii, jj]])
r_list = []
v_list = []
for r in res_dict:
r_list.append(r)
v_list.append(res_dict[r])
r_list = np.array(r_list)
v_list = np.array(v_list)
sorted_indices = np.argsort(r_list)
sorted_r = r_list[sorted_indices]
sorted_v = v_list[sorted_indices]
if len(sorted_r.tolist()) != len(set(sorted_r.tolist())):
print("Warning: there're duplicate elements in output!")
return sorted_r, sorted_v
def calcSk(NPS, M2k, imgSysData, if_plot=False):
"""
Given the normalized density fluctuation power spectrum, calculate the
static structure factor and do the azimuthal average.
"""
M2k[M2k==0] = np.inf
S = NPS / M2k
_1, _2, K_x, K_y = getFreq(imgSysData["CCDPixelSize"], imgSysData["magnification"], S.shape)
k, S_azmAvg = azmAvg(K_x, K_y, S)
# extrapolation = InterpolatedUnivariateSpline(k[k.shape[0]//4:3*k.shape[0]//4], S_azmAvg[k.shape[0]//4:3*k.shape[0]//4], k=2)
# S_k0 = extrapolation(0)
return K_x, K_y, S, k, S_azmAvg
##############################################################################
# Functions for making plots
# all the functions for making plots return a figure handle and an axes
# handle for further manipulations of the plot
def fplot_Intensity(imgDir, num):
"""
Show raw data of intensity.
imgDir: string, the directory where the images with atoms are stored.
num: int, you want to show the num-th image.
"""
paraFile = open(imgDir + "\\parameters.txt", "r")
line = paraFile.readlines()[num]
filename = imgDir + "\\rawimg_" + line.split()[0]
dim = np.fromfile(filename, '>u2')[0:4]
img = np.fromfile(filename, '>u2')[4:].reshape((dim[1], dim[3]))
fig_intens = plt.figure()
ax_intens = fig_intens.add_subplot(111)
pc = ax_intens.pcolor(img, cmap=cm.jet)
ax_intens.set_aspect(1)
ax_intens.set_title("Raw data (intensity)")
plt.colorbar(pc)
return fig_intens, ax_intens
def showExampleImg(imgDir, numOfImgsInEachRun, parameter, \
trapRegion=(slice(0, 65535), slice(0, 65535)), \
noiseRegion=(slice(0, 65535), slice(0, 65535)), \
vRange=[0, 0.5]):
atomODs, atomODAvg, noiseODs, noiseODAvg, imgIndexMin, imgIndexMax = readInImages(imgDir, numOfImgsInEachRun, parameter)
fig_atom = plt.figure()
ax_atom = fig_atom.add_subplot(111)
pc = ax_atom.pcolor(atomODAvg, cmap=cm.jet, vmin=vRange[0], vmax=vRange[1])
ax_atom.set_aspect(1)
ax_atom.set_title("Example of OD")
plt.colorbar(pc)
xmin = range(atomODAvg.shape[1])[trapRegion[0]][0]
xmax = range(atomODAvg.shape[1])[trapRegion[0]][-1]
ymin = range(atomODAvg.shape[0])[trapRegion[1]][0]
ymax = range(atomODAvg.shape[0])[trapRegion[1]][-1]
xroute = [xmin, xmin, xmax, xmax, xmin]
yroute = [ymin, ymax, ymax, ymin, ymin]
ax_atom.plot(xroute, yroute, '-r', linewidth=2)
xmin = range(atomODAvg.shape[1])[noiseRegion[0]][0]
xmax = range(atomODAvg.shape[1])[noiseRegion[0]][-1]
ymin = range(atomODAvg.shape[0])[noiseRegion[1]][0]
ymax = range(atomODAvg.shape[0])[noiseRegion[1]][-1]
xroute = [xmin, xmin, xmax, xmax, xmin]
yroute = [ymin, ymax, ymax, ymin, ymin]
ax_atom.plot(xroute, yroute, '-m', linewidth=2)
plt.show()
return fig_atom, ax_atom
def fplot_OD(atomOD, if_Save=False, saveDir=None, X=None, Y=None, axes=None, cMap=cm.jet, vRange=None):
"""
Plot the averaged image (OD) of the 2D thermal atmoic gas
"""
if axes == None:
fig_atom = plt.figure(figsize=(6, 4.5))
ax_atom = fig_atom.add_subplot(111)
else:
ax_atom = axes
if X == None or Y == None:
if vRange == None:
pc_atom = ax_atom.pcolor(atomOD, cmap=cMap)
else:
pc_atom = ax_atom.pcolor(atomOD, cmap=cMap, \
vmin=max(vRange[0], atomOD.min()), \
vmax=min(vRange[1], atomOD.max()))
ax_atom.set_xlabel('$x$ (px)')
ax_atom.set_ylabel('$y$ (px)')
else:
if vRange == None:
pc_atom = ax_atom.pcolor(X, Y, atomOD, cmap=cMap)
else:
pc_atom = ax_atom.pcolor(X, Y, atomOD, cmap=cMap, \
vmin=max(vRange[0], atomOD.min()), \
vmax=min(vRange[1], atomOD.max()))
ax_atom.set_xlabel('$x$ ($\\mu$m)')
ax_atom.set_ylabel('$y$ ($\\mu$m)')
plt.colorbar(pc_atom, extend='both')
ax_atom.set_aspect(1)
ax_atom.set_title("2D thermal gas (OD)")
if if_Save:
plt.savefig(saveDir + "\\2Dgas.png", dpi='figure')
return fig_atom, ax_atom
def fplot_NPS_Exp(K_x, K_y, M2k_Exp, if_Save=False, saveDir=None, axes=None, cMap=cm.jet, vRange=None):
"""
Plot noise power spectrum (only experimental result)
"""
if axes == None:
fig_NPS_Exp = plt.figure(figsize=(6, 4.5))
ax_NPS_Exp = fig_NPS_Exp.add_subplot(111)
else:
ax_NPS_Exp = axes
if vRange == None:
pc_NPS_Exp = ax_NPS_Exp.pcolor(K_x, K_y, M2k_Exp, cmap=cMap)
else:
pc_NPS_Exp = ax_NPS_Exp.pcolor(K_x, K_y, M2k_Exp, cmap=cMap, vmin=vRange[0], vmax=vRange[1])
plt.colorbar(pc_NPS_Exp)
ax_NPS_Exp.set_aspect(1)
ax_NPS_Exp.set_title("Noise Power Spectrum (Exp.)")
ax_NPS_Exp.set_xlabel('$k_x$ ($\\mu$m$^{-1}$)')
ax_NPS_Exp.set_ylabel('$k_y$ ($\\mu$m$^{-1}$)')
if if_Save:
plt.savefig(saveDir + "\\NoisePowerSpec_Exp.png", dpi='figure')
return fig_NPS_Exp, ax_NPS_Exp
def fplot_NPS_ExpAndFit(K_x, K_y, M2k_Exp, M2k_Fit=None, if_Save=False, saveDir=None, fig=None, cMap=cm.jet, \
vRange_Exp=None, vRange_Fit=None):
"""
Plot noise power spectrum (experimental result and fit result)
"""
if fig == None:
fig_NPS = plt.figure('NPS', figsize=(12, 5))
else:
fig_NPS = fig
if vRange_Exp == None:
vMin_Exp = 0
vMax_Exp = M2k_Fit.max()
if vRange_Fit == None:
vMin_Fit = 0
vMax_Fit = M2k_Fit.max()
ax_NPS_Exp = fig_NPS.add_subplot(121)
pc_NPS_Exp = ax_NPS_Exp.pcolor(K_x, K_y, M2k_Exp, cmap=cMap, vmin=vMin_Exp, vmax=vMax_Exp)
divider = make_axes_locatable(ax_NPS_Exp)
cax = divider.append_axes("right", size="5%", pad=0.1)
plt.colorbar(pc_NPS_Exp, cax=cax, extend='both')
ax_NPS_Exp.set_aspect(1)
ax_NPS_Exp.set_title("Noise Power Spectrum (Exp.)")
ax_NPS_Exp.set_xlabel('$k_x$ ($\\mu$m$^{-1}$)')
ax_NPS_Exp.set_ylabel('$k_y$ ($\\mu$m$^{-1}$)')
ax_NPS_Fit = fig_NPS.add_subplot(122)
pc_NPS_Fit = ax_NPS_Fit.pcolor(K_x, K_y, M2k_Fit, cmap=cMap, vmin=vMin_Fit, vmax=vMax_Fit)
divider = make_axes_locatable(ax_NPS_Fit)
cax = divider.append_axes("right", size="5%", pad=0.1)
plt.colorbar(pc_NPS_Fit, cax=cax, extend='both')
ax_NPS_Fit.set_aspect(1)
ax_NPS_Fit.set_title("Noise Power Spectrum (Fit)")
ax_NPS_Fit.set_xlabel('$k_x$ ($\\mu$m$^{-1}$)')
ax_NPS_Fit.set_ylabel('$k_y$ ($\\mu$m$^{-1}$)')
if if_Save:
plt.savefig(saveDir + "\\NoisePowerSpec_ExpAndFit.png", dpi='figure')
return fig_NPS, ax_NPS_Exp, ax_NPS_Fit
def fplot_NPS_LineCut(k_x, k_y, M2k_Exp, M2k_Fit, if_Save=False, saveDir=None):
"""
Plot noise power spectrum - line cut
"""
ll = M2k_Exp.shape[0]
k_r = np.linspace(-4, 4, ll)
t_scan = [0, np.pi/4, np.pi/2, 3*np.pi/4]
linetype = [['.-b', '-b'], ['.-k', '-k'], ['.-r', '-r'], ['.-m', '-m']]
title = ['0', 'pi/4', 'pi/2', '3*pi/4']
fig_NPS_LineCut = plt.figure('NPS_LineCut', figsize=(12, 9))
for k in range(len(t_scan)):
t = t_scan[k]
kx, ky = k_r * np.cos(t), k_r * np.sin(t)
ix= np.array(k_x.shape[0]*(kx-k_x.min()) / (k_x.max()-k_x.min()), dtype=int)
iy= np.array(k_y.shape[0]*(ky-k_y.min()) / (k_y.max()-k_y.min()), dtype=int)
M2k_r_exp = M2k_Exp[iy, ix]
M2k_r_fit = M2k_Fit[iy, ix]
axNPS_LineCut = fig_NPS_LineCut.add_subplot(2, 2, k+1)
axNPS_LineCut.plot(k_r, M2k_r_exp, linetype[k][0], linewidth=0.5, label=title[k]+'-Exp.')
axNPS_LineCut.plot(k_r, M2k_r_fit, linetype[k][1], linewidth=2, label=title[k]+'-Fit')
axNPS_LineCut.legend()
axNPS_LineCut.set_xlabel('$k$ ($\\mu$m$^{-1}$)')
axNPS_LineCut.set_ylabel('Noise Power Spectrum (a.u.)')
axNPS_LineCut.set_ylim([0, 1.5*M2k_Fit.max()])
#axNPS_LineCut.set_ylim([0, 1])
if if_Save:
plt.savefig(saveDir + "\\NoisePowerSpec_LineCut.png", dpi='figure')
return fig_NPS_LineCut
def fplot_pupil(tau_fit, S0_fit, alpha_fit, phi_fit, beta_fit, if_Save=False, saveDir=None):
"""
Plot the pupil
"""
r_p_pupilplt = np.linspace(0, 1, 200)
theta_p_pupilplt = np.linspace(-np.pi, np.pi, 300)
R_p_pupilplt, Theta_p_pupilplt = np.meshgrid(r_p_pupilplt, theta_p_pupilplt)
pupilplt = pupilFunc(R_p_pupilplt, Theta_p_pupilplt, tau_fit, S0_fit, alpha_fit, phi_fit, beta_fit)
X_pupilplt = R_p_pupilplt * np.cos(Theta_p_pupilplt)
Y_pupilplt = R_p_pupilplt * np.sin(Theta_p_pupilplt)
fig_pupil = plt.figure('pupil', figsize=(12, 6))
ax_pupil = fig_pupil.add_subplot(121)
pc_pupil = ax_pupil.pcolor(X_pupilplt, Y_pupilplt, np.angle(pupilplt), cmap=cm.twilight_shifted, vmin=-np.pi, vmax=np.pi)
ax_pupil.set_aspect(1)
ax_pupil.set_title('Phase of exit pupil (radian)')
ax_pupil.axis('off')
divider = make_axes_locatable(ax_pupil)
cax = divider.append_axes("right", size="5%", pad=0.2)
plt.colorbar(pc_pupil, cax=cax)
ax_pupil_2 = fig_pupil.add_subplot(122)
pc_pupil_2 = ax_pupil_2.pcolor(X_pupilplt, Y_pupilplt, np.angle(pupilplt), cmap=cm.RdYlGn)
ax_pupil_2.set_aspect(1)
ax_pupil_2.set_title('Phase of exit pupil (radian)')
ax_pupil_2.axis('off')
divider = make_axes_locatable(ax_pupil_2)
cax = divider.append_axes("right", size="5%", pad=0.2)
plt.colorbar(pc_pupil_2, cax=cax)
if if_Save:
plt.savefig(saveDir + "\\Pupil.png", dpi='figure')
return fig_pupil, ax_pupil, ax_pupil_2
def fplot_PSF(tau_fit, S0_fit, alpha_fit, phi_fit, beta_fit, delta_s_fit, d, if_Save=False, saveDir=None):
"""
Plot the PSF as defined in Chen-Lung Hung et al 2011 New J. Phys. 13 075019
"""
rg_PSF = 8
px_PSF = 0.05
px_Pupil = 1 / (2*rg_PSF)
rg_Pupil = 1 / (2*px_PSF)
sampleNum = np.int(2*rg_Pupil / px_Pupil)
x = np.linspace(-rg_Pupil, rg_Pupil, sampleNum)
Xi, Eta = np.meshgrid(x, x)
R_p_PSFplt, Theta_p_PSFplt = np.abs(Xi + 1j*Eta), np.angle(Xi + 1j*Eta)
Pupil = pupilFunc(R_p_PSFplt, Theta_p_PSFplt, tau_fit, S0_fit, alpha_fit, phi_fit, beta_fit)
U = np.fft.fftshift(np.fft.fft2(np.fft.fftshift(Pupil)))
PSF = np.real(np.exp(1j*delta_s_fit) * U)
fx = np.fft.fftshift(np.fft.fftfreq(x.shape[0], px_Pupil))
X, Y = np.meshgrid(fx*d*2*np.pi, fx*d*2*np.pi)
fig_PSF = plt.figure('PSF', figsize=(6, 4.5))
ax_PSF = fig_PSF.add_subplot(111)
MM = np.max([np.abs(PSF.max()), np.abs(PSF.min())])
pc_PSF = ax_PSF.pcolor(X, Y, PSF, cmap=cm.bwr, vmin=-MM, vmax=MM)
ax_PSF.set_aspect(1)
ax_PSF.set_xlim([-10, 10])
ax_PSF.set_ylim([-10, 10])
ax_PSF.set_title('Point spread function')
ax_PSF.set_xlabel('$x$ in object plane ($\\mu$m)')
ax_PSF.set_ylabel('$y$ in object plane ($\\mu$m)')
plt.colorbar(pc_PSF)
if if_Save:
plt.savefig(saveDir + "\\PSF.png", dpi='figure')
return fig_PSF, ax_PSF
def fplot_PSF_LineCut(tau_fit, S0_fit, alpha_fit, phi_fit, beta_fit, delta_s_fit, d, if_Save=False, saveDir=None):
"""
Plot the linecut of PSF as defined in Chen-Lung Hung et al 2011 New J. Phys. 13 075019
"""
rg_PSF = 8
px_PSF = 0.05
px_Pupil = 1 / (2*rg_PSF)
rg_Pupil = 1 / (2*px_PSF)
sampleNum = np.int(2*rg_Pupil / px_Pupil)
x = np.linspace(-rg_Pupil, rg_Pupil, sampleNum)
Xi, Eta = np.meshgrid(x, x)
R_p_PSFplt, Theta_p_PSFplt = np.abs(Xi + 1j*Eta), np.angle(Xi + 1j*Eta)
Pupil = pupilFunc(R_p_PSFplt, Theta_p_PSFplt, tau_fit, S0_fit, alpha_fit, phi_fit, beta_fit)
cind = x.shape[0]//2
U = np.fft.fftshift(np.fft.fft2(np.fft.fftshift(Pupil)))
PSF = np.real(np.exp(1j*delta_s_fit) * U)
fx = np.fft.fftshift(np.fft.fftfreq(x.shape[0], px_Pupil))
X, Y = np.meshgrid(fx*d*2*np.pi, fx*d*2*np.pi)
Pupil2 = np.array(R_p_PSFplt<=1, dtype=float)
U2 = np.fft.fftshift(np.fft.fft2(np.fft.fftshift(Pupil2)))
PSF2 = np.real(np.exp(1j*delta_s_fit) * U2)
PSF = PSF / PSF[cind, cind]
PSF2 = PSF2 / PSF2[cind, cind]
fig_PSF_LineCut = plt.figure('PSF_LineCut', figsize=(6, 4.5))
ax_PSF_LineCut = fig_PSF_LineCut.add_subplot(111)
ax_PSF_LineCut.plot(X[cind, :], PSF[cind, :], '-k', label='Fit')
ax_PSF_LineCut.set_title('Point spread function')
ax_PSF_LineCut.plot(X[cind, :], PSF2[cind, :], '--k', label='Ideal')
ax_PSF_LineCut.xaxis.set_major_locator(MultipleLocator(1))
ax_PSF_LineCut.xaxis.set_minor_locator(MultipleLocator(0.2))
ax_PSF_LineCut.set_xlabel('$x$ in object plane ($\\mu$m)')
ax_PSF_LineCut.set_ylabel('Point spread function (a.u.)')
ax_PSF_LineCut.legend()
ax_PSF_LineCut.grid(True)
ax_PSF_LineCut.set_xlim([-10, 10])
if if_Save:
plt.savefig(saveDir + "\\PSF_LineCut.png", dpi='figure')
return fig_PSF_LineCut, ax_PSF_LineCut
def fplot_PSF_abs2(tau_fit, S0_fit, alpha_fit, phi_fit, beta_fit, delta_s_fit, d, if_Save=False, saveDir=None):
"""
Plot the PSF as traditionally defined
"""
rg_PSF = 8
px_PSF = 0.05
px_Pupil = 1 / (2*rg_PSF)
rg_Pupil = 1 / (2*px_PSF)
sampleNum = np.int(2*rg_Pupil / px_Pupil)
x = np.linspace(-rg_Pupil, rg_Pupil, sampleNum)
Xi, Eta = np.meshgrid(x, x)
R_p_PSFplt, Theta_p_PSFplt = np.abs(Xi + 1j*Eta), np.angle(Xi + 1j*Eta)
Pupil = pupilFunc(R_p_PSFplt, Theta_p_PSFplt, tau_fit, S0_fit, alpha_fit, phi_fit, beta_fit)
cind = x.shape[0]//2
U = np.fft.fftshift(np.fft.fft2(np.fft.fftshift(Pupil)))
PSF = np.abs(np.exp(1j*delta_s_fit) * U)**2
fx = np.fft.fftshift(np.fft.fftfreq(x.shape[0], px_Pupil))
X, Y = np.meshgrid(fx*d*2*np.pi, fx*d*2*np.pi)
fig_PSF_abs2 = plt.figure('PSF_abs2', figsize=(6, 4.5))
ax_PSF_abs2 = fig_PSF_abs2.add_subplot(111)
MM = np.max([np.abs(PSF.max()), np.abs(PSF.min())])
pc = ax_PSF_abs2.pcolor(X, Y, PSF, cmap=cm.bwr, vmin=-MM, vmax=MM)
ax_PSF_abs2.set_aspect(1)
ax_PSF_abs2.set_xlim([-10, 10])
ax_PSF_abs2.set_ylim([-10, 10])
ax_PSF_abs2.set_title('Point spread function (classical def.)')
ax_PSF_abs2.set_xlabel('$x$ in object plane ($\\mu$m)')
ax_PSF_abs2.set_ylabel('$y$ in object plane ($\\mu$m)')
plt.colorbar(pc)
if if_Save:
plt.savefig(saveDir + "\\PSF_abs2.png", dpi='figure')
return fig_PSF_abs2, ax_PSF_abs2
# plot the PSF_abs2 - line cut
def lin_interp(x, y, i, half):
return x[i] + (x[i+1] - x[i]) * ((half - y[i]) / (y[i+1] - y[i]))
def uPercent_max_x(x, y):
h = max(y)/100.0
signs = np.sign(np.add(y, -h))
zero_crossings = (signs[0:-2] != signs[1:-1])
zero_crossings_i = np.where(zero_crossings)[0]
return [lin_interp(x, y, zero_crossings_i[0], h),
lin_interp(x, y, zero_crossings_i[1], h)], h
def calcResolution(PSF_abs2_linecut, x):
# find the two crossing points
hmx, h = uPercent_max_x(x, PSF_abs2_linecut)
res = (hmx[1] - hmx[0]) / 2
return res, hmx[1], hmx[0], h
def fplot_PSF_abs2_LineCut(tau_fit, S0_fit, alpha_fit, phi_fit, beta_fit, delta_s_fit, d, if_Save=False, saveDir=None):
"""
Plot the linecut of PSF as traditionally defined. Estimate the resolution.
"""
rg_PSF = 8
px_PSF = 0.05
px_Pupil = 1 / (2*rg_PSF)
rg_Pupil = 1 / (2*px_PSF)
sampleNum = np.int(2*rg_Pupil / px_Pupil)
x = np.linspace(-rg_Pupil, rg_Pupil, sampleNum)
Xi, Eta = np.meshgrid(x, x)
R_p_PSFplt, Theta_p_PSFplt = np.abs(Xi + 1j*Eta), np.angle(Xi + 1j*Eta)
Pupil = pupilFunc(R_p_PSFplt, Theta_p_PSFplt, tau_fit, S0_fit, alpha_fit, phi_fit, beta_fit)
cind = x.shape[0]//2
U = np.fft.fftshift(np.fft.fft2(np.fft.fftshift(Pupil)))
PSF = np.abs(np.exp(1j*delta_s_fit) * U)**2
fx = np.fft.fftshift(np.fft.fftfreq(x.shape[0], px_Pupil))
X, Y = np.meshgrid(fx*d*2*np.pi, fx*d*2*np.pi)
Pupil2 = np.array(R_p_PSFplt<=1, dtype=float)
U2 = np.fft.fftshift(np.fft.fft2(np.fft.fftshift(Pupil2)))
PSF2 = np.abs(np.exp(1j*delta_s_fit) * U2)**2