Renaming and restructuring of code.
This commit is contained in:
parent
33390f8230
commit
623e9dcb7d
@ -1,4 +1,4 @@
|
|||||||
function muchem = ChemicalPotential(psi,Params,Transf,VDk,V)
|
function muchem = calculateChemicalPotential(psi,Params,Transf,VDk,V)
|
||||||
|
|
||||||
%Parameters
|
%Parameters
|
||||||
normfac = Params.Lx*Params.Ly*Params.Lz/numel(psi);
|
normfac = Params.Lx*Params.Ly*Params.Lz/numel(psi);
|
||||||
|
|||||||
@ -1,4 +1,4 @@
|
|||||||
function E = EnergyComponents(psi,Params,Transf,VDk,V)
|
function E = calculateEnergyComponents(psi,Params,Transf,VDk,V)
|
||||||
|
|
||||||
%Parameters
|
%Parameters
|
||||||
|
|
||||||
|
|||||||
@ -1,4 +1,4 @@
|
|||||||
function res = NormalizedResiduals(psi,Params,Transf,VDk,V,muchem)
|
function res = calculateNormalizedResiduals(psi,Params,Transf,VDk,V,muchem)
|
||||||
|
|
||||||
KEop= 0.5*(Transf.KX.^2+Transf.KY.^2+Transf.KZ.^2);
|
KEop= 0.5*(Transf.KX.^2+Transf.KY.^2+Transf.KZ.^2);
|
||||||
|
|
||||||
|
|||||||
@ -1,4 +1,4 @@
|
|||||||
function VDkSemi = NumericalHankelTransform(kr, kz, Rmax, Zmax, Nr)
|
function VDkSemi = calculateNumericalHankelTransform(kr, kz, Rmax, Zmax, Nr)
|
||||||
|
|
||||||
% accuracy inputs for numerical integration
|
% accuracy inputs for numerical integration
|
||||||
if(nargin==4)
|
if(nargin==4)
|
||||||
|
|||||||
@ -1,4 +1,4 @@
|
|||||||
function [m_Order] = OrderParameter(psi,Transf,Params,VDk,V,T,muchem)
|
function [m_Order] = calculateOrderParameter(psi,Transf,Params,VDk,V,T,muchem)
|
||||||
|
|
||||||
NumRealiz = 100;
|
NumRealiz = 100;
|
||||||
|
|
||||||
|
|||||||
@ -1,4 +1,4 @@
|
|||||||
function [PhaseC] = PhaseCoherence(psi,Transf,Params)
|
function [PhaseC] = calculatePhaseCoherence(psi,Transf,Params)
|
||||||
|
|
||||||
norm = sum(sum(sum(abs(psi).^2,1),2),3)*Transf.dx*Transf.dy*Transf.dz;
|
norm = sum(sum(sum(abs(psi).^2,1),2),3)*Transf.dx*Transf.dy*Transf.dz;
|
||||||
psi = psi/sqrt(norm);
|
psi = psi/sqrt(norm);
|
||||||
|
|||||||
@ -1,4 +1,4 @@
|
|||||||
function E = TotalEnergy(psi,Params,Transf,VDk,V)
|
function E = calculateTotalEnergy(psi,Params,Transf,VDk,V)
|
||||||
|
|
||||||
%Parameters
|
%Parameters
|
||||||
|
|
||||||
|
|||||||
@ -1,4 +1,4 @@
|
|||||||
function VDk = VDCutoff(Params, Transf)
|
function VDk = calculateVDCutoff(Params, Transf)
|
||||||
% makes the dipolar interaction matrix, size numel(Params.kr) * numel(Params.kz)
|
% makes the dipolar interaction matrix, size numel(Params.kr) * numel(Params.kz)
|
||||||
% Rmax and Zmax are the interaction cutoffs
|
% Rmax and Zmax are the interaction cutoffs
|
||||||
% VDk needs to be multiplied by Cdd
|
% VDk needs to be multiplied by Cdd
|
||||||
|
|||||||
@ -1,4 +1,4 @@
|
|||||||
function [psi,V,VDk] = Initialize(Params,Transf)
|
function [psi,V,VDk] = initialize(Params,Transf)
|
||||||
|
|
||||||
format long
|
format long
|
||||||
X = Transf.X; Y = Transf.Y; Z = Transf.Z;
|
X = Transf.X; Y = Transf.Y; Z = Transf.Z;
|
||||||
|
|||||||
@ -1,12 +1,11 @@
|
|||||||
%-% Run Simulation %-%
|
%-% Run Simulation %-%
|
||||||
clearvars
|
clearvars
|
||||||
cd(fileparts(matlab.desktop.editor.getActiveFilename));
|
|
||||||
pwd
|
|
||||||
% --- Obtain simulation parameters ---
|
% --- Obtain simulation parameters ---
|
||||||
[Params] = SetupParameters();
|
[Params] = setupParameters();
|
||||||
|
|
||||||
% --- Set up spatial grids and transforms ---
|
% --- Set up spatial grids and transforms ---
|
||||||
[Transf] = SetupSpace(Params);
|
[Transf] = setupSpace(Params);
|
||||||
|
|
||||||
% Plotter.visualizeSpace(Transf)
|
% Plotter.visualizeSpace(Transf)
|
||||||
|
|
||||||
@ -16,7 +15,7 @@ pwd
|
|||||||
|
|
||||||
mkdir(sprintf('./Data'))
|
mkdir(sprintf('./Data'))
|
||||||
|
|
||||||
[psi,V,VDk] = Initialize(Params,Transf);
|
[psi,V,VDk] = initialize(Params,Transf);
|
||||||
|
|
||||||
Observ.EVec = []; Observ.NormVec = []; Observ.PCVec = []; Observ.tVecPlot = []; Observ.mucVec = [];
|
Observ.EVec = []; Observ.NormVec = []; Observ.PCVec = []; Observ.tVecPlot = []; Observ.mucVec = [];
|
||||||
t_idx = 1; %Start at t = 0;
|
t_idx = 1; %Start at t = 0;
|
||||||
|
|||||||
@ -1,4 +1,4 @@
|
|||||||
function [Params] = SetupParameters()
|
function [Params] = setupParameters()
|
||||||
|
|
||||||
%%--%% Parameters %%--%%
|
%%--%% Parameters %%--%%
|
||||||
|
|
||||||
|
|||||||
@ -1,4 +1,4 @@
|
|||||||
function [Transf] = SetupSpace(Params)
|
function [Transf] = setupSpace(Params)
|
||||||
Transf.Xmax = 0.5*Params.Lx;
|
Transf.Xmax = 0.5*Params.Lx;
|
||||||
Transf.Ymax = 0.5*Params.Ly;
|
Transf.Ymax = 0.5*Params.Ly;
|
||||||
Transf.Zmax = 0.5*Params.Lz;
|
Transf.Zmax = 0.5*Params.Lz;
|
||||||
|
|||||||
@ -1,4 +1,4 @@
|
|||||||
function [Transf] = SetupSpaceRadial(Params,morder)
|
function [Transf] = setupSpaceRadial(Params,morder)
|
||||||
Zmax = 0.5*Params.Lz;
|
Zmax = 0.5*Params.Lz;
|
||||||
Rmax = Params.Lr;
|
Rmax = Params.Lr;
|
||||||
Nz = Params.Nz;
|
Nz = Params.Nz;
|
||||||
|
|||||||
@ -1,4 +1,4 @@
|
|||||||
function [psi] = SetupWavefunction()
|
function [psi] = setupWavefunction()
|
||||||
|
|
||||||
ellx = sqrt(Params.hbar/(Params.m*Params.wx))/Params.l0;
|
ellx = sqrt(Params.hbar/(Params.m*Params.wx))/Params.l0;
|
||||||
elly = sqrt(Params.hbar/(Params.m*Params.wy))/Params.l0;
|
elly = sqrt(Params.hbar/(Params.m*Params.wy))/Params.l0;
|
||||||
|
|||||||
@ -1,4 +1,4 @@
|
|||||||
function [psi] = SplitStepFourier(psi,Params,Transf,VDk,V,njob,t_idx,Observ)
|
function [psi] = splitStepFourier(psi,Params,Transf,VDk,V,njob,t_idx,Observ)
|
||||||
|
|
||||||
set(0,'defaulttextInterpreter','latex')
|
set(0,'defaulttextInterpreter','latex')
|
||||||
set(groot, 'defaultAxesTickLabelInterpreter','latex'); set(groot, 'defaultLegendInterpreter','latex');
|
set(groot, 'defaultAxesTickLabelInterpreter','latex'); set(groot, 'defaultLegendInterpreter','latex');
|
||||||
|
|||||||
@ -1,359 +0,0 @@
|
|||||||
# Gaussian Beam Propagation
|
|
||||||
|
|
||||||
## Import files
|
|
||||||
|
|
||||||
|
|
||||||
```python
|
|
||||||
import BeamProp_Script as bs # This is the script that handles the propagation
|
|
||||||
import sympy as sym # For Symbolic examples
|
|
||||||
import numpy as np # Handling of lists and for plotting
|
|
||||||
import matplotlib.pyplot as plt # Plotting
|
|
||||||
```
|
|
||||||
|
|
||||||
### Let's show what BeamProp_Script has
|
|
||||||
|
|
||||||
|
|
||||||
```python
|
|
||||||
help(bs)
|
|
||||||
```
|
|
||||||
|
|
||||||
Help on module BeamProp_Script:
|
|
||||||
|
|
||||||
NAME
|
|
||||||
BeamProp_Script - Created on Wed Feb 19 15:51:54 2020
|
|
||||||
|
|
||||||
DESCRIPTION
|
|
||||||
@author: wrighta
|
|
||||||
|
|
||||||
FUNCTIONS
|
|
||||||
W0(zr, lam)
|
|
||||||
Parameters
|
|
||||||
----------
|
|
||||||
zr : float, integer, symbol
|
|
||||||
Rayleigh range in meters
|
|
||||||
lam : float, integer, symbol
|
|
||||||
Wavelength of light in meters
|
|
||||||
|
|
||||||
Returns
|
|
||||||
-------
|
|
||||||
w0 : float, integer, symbol
|
|
||||||
Beam waist radius in meters
|
|
||||||
|
|
||||||
Zr(wo, lam)
|
|
||||||
Parameters
|
|
||||||
----------
|
|
||||||
wo : float, integer, or symbol
|
|
||||||
Beam waist radius in meters.
|
|
||||||
lam : float, integer, or symbol
|
|
||||||
Wavelength of light in meters.
|
|
||||||
|
|
||||||
Returns
|
|
||||||
-------
|
|
||||||
zr : float, int, symbols
|
|
||||||
Rayleigh range for given beam waist and wavelength.
|
|
||||||
|
|
||||||
lens(f)
|
|
||||||
Parameters
|
|
||||||
----------
|
|
||||||
f : float or integer or sympy symbol in meters
|
|
||||||
Thin lens focal length in meters
|
|
||||||
|
|
||||||
Returns
|
|
||||||
-------
|
|
||||||
mat : 2x2 matrix
|
|
||||||
[
|
|
||||||
[ 1, 0],
|
|
||||||
[-1/f, 1]
|
|
||||||
]
|
|
||||||
|
|
||||||
mult(mat1, *argv)
|
|
||||||
Parameters
|
|
||||||
----------
|
|
||||||
mat1 : 2x2 ABCD matrix
|
|
||||||
Last matrix light interacts with.
|
|
||||||
*argv : 2x2 ABCD matrices
|
|
||||||
From left to right, the matrices should be entered such that the leftmost matrix interacts
|
|
||||||
with light temporally after the rightmost matrix.
|
|
||||||
|
|
||||||
Returns
|
|
||||||
-------
|
|
||||||
Mat : 2x2 matrix
|
|
||||||
The ABCd matrix describing the whole optical system.
|
|
||||||
|
|
||||||
plot(func, var, rang=array([0. , 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1 ,
|
|
||||||
0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.2 , 0.21,
|
|
||||||
0.22, 0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.3 , 0.31, 0.32,
|
|
||||||
0.33, 0.34, 0.35, 0.36, 0.37, 0.38, 0.39, 0.4 , 0.41, 0.42, 0.43,
|
|
||||||
0.44, 0.45, 0.46, 0.47, 0.48, 0.49, 0.5 , 0.51, 0.52, 0.53, 0.54,
|
|
||||||
0.55, 0.56, 0.57, 0.58, 0.59, 0.6 , 0.61, 0.62, 0.63, 0.64, 0.65,
|
|
||||||
0.66, 0.67, 0.68, 0.69, 0.7 , 0.71, 0.72, 0.73, 0.74, 0.75, 0.76,
|
|
||||||
0.77, 0.78, 0.79, 0.8 , 0.81, 0.82, 0.83, 0.84, 0.85, 0.86, 0.87,
|
|
||||||
0.88, 0.89, 0.9 , 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98,
|
|
||||||
0.99, 1. , 1.01, 1.02, 1.03, 1.04, 1.05, 1.06, 1.07, 1.08, 1.09,
|
|
||||||
1.1 , 1.11, 1.12, 1.13, 1.14, 1.15, 1.16, 1.17, 1.18, 1.19, 1.2 ,
|
|
||||||
1.21, 1.22, 1.23, 1.24, 1.25, 1.26, 1.27, 1.28, 1.29, 1.3 , 1.31,
|
|
||||||
1.32, 1.33, 1.34, 1.35, 1.36, 1.37, 1.38, 1.39, 1.4 , 1.41, 1.42,
|
|
||||||
1.43, 1.44, 1.45, 1.46, 1.47, 1.48, 1.49, 1.5 , 1.51, 1.52, 1.53,
|
|
||||||
1.54, 1.55, 1.56, 1.57, 1.58, 1.59, 1.6 , 1.61, 1.62, 1.63, 1.64,
|
|
||||||
1.65, 1.66, 1.67, 1.68, 1.69, 1.7 , 1.71, 1.72, 1.73, 1.74, 1.75,
|
|
||||||
1.76, 1.77, 1.78, 1.79, 1.8 , 1.81, 1.82, 1.83, 1.84, 1.85, 1.86,
|
|
||||||
1.87, 1.88, 1.89, 1.9 , 1.91, 1.92, 1.93, 1.94, 1.95, 1.96, 1.97,
|
|
||||||
1.98, 1.99, 2. , 2.01, 2.02, 2.03, 2.04, 2.05, 2.06, 2.07, 2.08,
|
|
||||||
2.09, 2.1 , 2.11, 2.12, 2.13, 2.14, 2.15, 2.16, 2.17, 2.18, 2.19,
|
|
||||||
2.2 , 2.21, 2.22, 2.23, 2.24, 2.25, 2.26, 2.27, 2.28, 2.29, 2.3 ,
|
|
||||||
2.31, 2.32, 2.33, 2.34, 2.35, 2.36, 2.37, 2.38, 2.39, 2.4 , 2.41,
|
|
||||||
2.42, 2.43, 2.44, 2.45, 2.46, 2.47, 2.48, 2.49, 2.5 , 2.51, 2.52,
|
|
||||||
2.53, 2.54, 2.55, 2.56, 2.57, 2.58, 2.59, 2.6 , 2.61, 2.62, 2.63,
|
|
||||||
2.64, 2.65, 2.66, 2.67, 2.68, 2.69, 2.7 , 2.71, 2.72, 2.73, 2.74,
|
|
||||||
2.75, 2.76, 2.77, 2.78, 2.79, 2.8 , 2.81, 2.82, 2.83, 2.84, 2.85,
|
|
||||||
2.86, 2.87, 2.88, 2.89, 2.9 , 2.91, 2.92, 2.93, 2.94, 2.95, 2.96,
|
|
||||||
2.97, 2.98, 2.99]))
|
|
||||||
Parameters
|
|
||||||
----------
|
|
||||||
func : Sympy function of one variable
|
|
||||||
Sympy function defining the beam width after the last optical element.
|
|
||||||
var : sympy variable
|
|
||||||
Variable in func that will be plotted.
|
|
||||||
rang : numpy array
|
|
||||||
Array of the values along the optical axis to be plotted
|
|
||||||
|
|
||||||
Returns
|
|
||||||
-------
|
|
||||||
plot : matplotlib graph
|
|
||||||
Graph of the beam width of var
|
|
||||||
|
|
||||||
prop(d)
|
|
||||||
Parameters
|
|
||||||
----------
|
|
||||||
d : float or integer or sympy symbol
|
|
||||||
Distance light is propagating along the z-axis.
|
|
||||||
|
|
||||||
Returns
|
|
||||||
-------
|
|
||||||
mat: 2x2 matrix
|
|
||||||
[
|
|
||||||
[1, d],
|
|
||||||
[0, 1]
|
|
||||||
]
|
|
||||||
|
|
||||||
q1_func(z, w0, lam, mat)
|
|
||||||
Parameters
|
|
||||||
----------
|
|
||||||
z : float, int, symbol
|
|
||||||
Position of the beam waist in meters.
|
|
||||||
w0 : float, int, symbol
|
|
||||||
Radial waist size in meters (of the embedded Gaussian, i.e. W0/M).
|
|
||||||
lam : float, int, symbol
|
|
||||||
Wavelength of light in meters.
|
|
||||||
mat : float, int, symbol
|
|
||||||
The ABCD 2x2 matrix describing the optical system.
|
|
||||||
|
|
||||||
Returns
|
|
||||||
-------
|
|
||||||
z: float, int, symbol
|
|
||||||
Position of the beam waist after the optical system
|
|
||||||
zr: float, int, symbol
|
|
||||||
Rayleigh range of the beam after the optical system
|
|
||||||
|
|
||||||
q1_inv_func(z, w0, lam, mat)
|
|
||||||
Parameters
|
|
||||||
----------
|
|
||||||
z : float, int, symbol
|
|
||||||
Position of the beam waist in meters.
|
|
||||||
w0 : float, int, symbol
|
|
||||||
Radial waist size in meters (of the embedded Gaussian, i.e. W0/M).
|
|
||||||
lam : float, int, symbol
|
|
||||||
Wavelength of light in meters.
|
|
||||||
mat : float, int, symbol
|
|
||||||
The ABCD 2x2 matrix describing the optical system.
|
|
||||||
|
|
||||||
Returns
|
|
||||||
-------
|
|
||||||
R : float, int, symbol
|
|
||||||
Radius of curvature of the wavefront in meters.
|
|
||||||
w : float, int, symbol
|
|
||||||
Radius of the beam in meters.
|
|
||||||
|
|
||||||
ray(y, theta)
|
|
||||||
Parameters
|
|
||||||
----------
|
|
||||||
y : float or integer or sympy symbol in meters
|
|
||||||
The vertical height of a ray.
|
|
||||||
theta : float or integer in radians
|
|
||||||
The angle of divergence of the ray.
|
|
||||||
|
|
||||||
Returns
|
|
||||||
-------
|
|
||||||
mat : 2x1 matrix
|
|
||||||
[
|
|
||||||
[y],
|
|
||||||
[teta]
|
|
||||||
]
|
|
||||||
|
|
||||||
DATA
|
|
||||||
oo = oo
|
|
||||||
|
|
||||||
FILE
|
|
||||||
c:\users\wrighta\documents\beamprop\beamprop_script.py
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
## Let's first see how we define a beam and how we can visualize it propagating.
|
|
||||||
|
|
||||||
### A Gaussian beam can be defined by it's (radial) waist, $w_0$, it's Rayleigh range, $z_R = \frac{\pi * w_0^2}{\lambda}$, and the location of its waist, $z_0$.
|
|
||||||
|
|
||||||
|
|
||||||
```python
|
|
||||||
w0 = 1E-3 # 1mm beam waist
|
|
||||||
lam = 355E-9 # wavelength of 355 nm (UV)
|
|
||||||
zR = bs.Zr(w0, lam) # Rayleigh range in m
|
|
||||||
z0 = 0 # location of waist in m
|
|
||||||
```
|
|
||||||
|
|
||||||
### We now want to define our "optical system" using matrices. For this first example, we will just use a free space propagation matrix, and let the beam propagate a distance $d$ which we will define using a symbol.
|
|
||||||
|
|
||||||
|
|
||||||
```python
|
|
||||||
d = sym.symbols('d')
|
|
||||||
M = bs.prop(d)
|
|
||||||
```
|
|
||||||
|
|
||||||
### We now use the bs script to do all the ABCD and q-parameter math, and return the waist and radius of curvature functions
|
|
||||||
|
|
||||||
|
|
||||||
```python
|
|
||||||
R, w = bs.q1_inv_func(0, w0, lam, M)
|
|
||||||
```
|
|
||||||
|
|
||||||
|
|
||||||
```python
|
|
||||||
print('w = {}'.format(w))
|
|
||||||
```
|
|
||||||
|
|
||||||
w = 0.001*(0.0127690021685256*d**2 + 1)**0.5
|
|
||||||
|
|
||||||
|
|
||||||
### And as simple as that, we have a function for our waist. Let's plot it and see what it looks like
|
|
||||||
|
|
||||||
|
|
||||||
```python
|
|
||||||
bs.plot(w, d, rang = np.arange(0,10))
|
|
||||||
```
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
### Let's show what happens when a beam travels through a lens. We use the "mult" function to multiply multiple ABCD matrices together.
|
|
||||||
|
|
||||||
|
|
||||||
```python
|
|
||||||
w0 = 1E-3 # 1mm beam waist
|
|
||||||
lam = 355E-9 # wavelength of 355 nm (UV)
|
|
||||||
zR = bs.Zr(w0, lam) # Rayleigh range in m
|
|
||||||
z0 = 0 # location of waist in m
|
|
||||||
|
|
||||||
d = sym.symbols('d')
|
|
||||||
M = bs.mult(bs.prop(d), bs.lens(.5), bs.prop(1))
|
|
||||||
|
|
||||||
R, w = bs.q1_inv_func(0, w0, lam, M)
|
|
||||||
|
|
||||||
bs.plot(w, d, rang = np.arange(0,1,.01))
|
|
||||||
```
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
### Lets look at how to expand and collimate a beam with a two lens system
|
|
||||||
|
|
||||||
|
|
||||||
```python
|
|
||||||
w0 = 1E-3 # 1mm beam waist
|
|
||||||
lam = 355E-9 # wavelength of 355 nm (UV)
|
|
||||||
zR = bs.Zr(w0, lam) # Rayleigh range in m
|
|
||||||
z0 = 0 # location of waist in m
|
|
||||||
|
|
||||||
d1, d2, d3, f1, f2 = sym.symbols('d1 d2 d3 f1 f2')
|
|
||||||
|
|
||||||
M = bs.mult(bs.prop(d3),bs.lens(f2),bs.prop(d2), bs.lens(f1), bs.prop(d1))
|
|
||||||
|
|
||||||
R, w = bs.q1_inv_func(0, w0, lam, M)
|
|
||||||
```
|
|
||||||
|
|
||||||
### For example, lets say the beam travels 1 m before hitting the first lens, and we want the beam to be 5x w0 after coming out of the second lens. We substitute d1 for 1 meter, since the beam propagates 1 meter, and we substitute d3 for 0, since we only care about the beam size right at the second lens. This gives us a relation between f1 and d2 (the separation between the lenses).
|
|
||||||
|
|
||||||
|
|
||||||
```python
|
|
||||||
w = w.subs(d1,1).subs(d3,0)
|
|
||||||
f1_eq = sym.solve(w - 5*w0, f1)[0]
|
|
||||||
print('f = {}'.format(f1_eq))
|
|
||||||
```
|
|
||||||
|
|
||||||
f = 1.0084642216545e+15*d2*(1.12051580183833e+27*d2 - 4.41556446152598e+29*sqrt(1 - 0.000504320418227052*d2**2) + 8.88733242867719e+28)/(1.13000009595246e+42*d2**2 + 2.26000019190491e+42*d2 - 2.12276362486616e+45)
|
|
||||||
|
|
||||||
|
|
||||||
#### Suppose we wanted the distance between the lenses to be 1 meter, we could find what f1 we need.
|
|
||||||
|
|
||||||
|
|
||||||
```python
|
|
||||||
print('f1 = {:.2f} m, for a lens separation of 1 meter'.format(f1_eq.subs(d2, 1)))
|
|
||||||
```
|
|
||||||
|
|
||||||
f1 = 0.17 m, for a lens separation of 1 meter
|
|
||||||
|
|
||||||
|
|
||||||
### Now we need to collimate the beam. Lets still assume the beam propagates 1 m, and f1 = .17 m.
|
|
||||||
|
|
||||||
There are a couple different ways to think about collimation. One is that the beam size doesn't change over a long distance. The other is that the radius of curvature is infinite (i.e. a plane wave). Lets us the latter interpretation. Thus, we want to find the focal length f2 that makes R infinite, or that makes 1/R =0.
|
|
||||||
|
|
||||||
|
|
||||||
```python
|
|
||||||
R_coll = R.subs(d1,1).subs(d2,1).subs(f1,.17).subs(d3,0)
|
|
||||||
f2_coll = sym.solve(1/R_coll,f2)[0]
|
|
||||||
print('f2 = {:.2f}, for a collimated beam, 5x the original waist, after propagating 1m to the first lens of f1 = .17m, and propagating another 1m to the second lens'.format(f2_coll))
|
|
||||||
```
|
|
||||||
|
|
||||||
f2 = 0.83, for a collimated beam, 5x the original waist, after propagating 1m to the first lens of f1 = .17m, and propagating another 1m to the second lens
|
|
||||||
|
|
||||||
|
|
||||||
### Lets plot the beam profile after the second lens, and see if it is collimated.
|
|
||||||
|
|
||||||
|
|
||||||
```python
|
|
||||||
M = bs.mult(bs.prop(d3),bs.lens(.83),bs.prop(1), bs.lens(.17), bs.prop(1))
|
|
||||||
|
|
||||||
R, w = bs.q1_inv_func(0, w0, lam, M)
|
|
||||||
|
|
||||||
bs.plot(w,d3)
|
|
||||||
```
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
### Looks very collimated. Lets check the beam size (to make sure its 5* w0) and check the collimation
|
|
||||||
|
|
||||||
|
|
||||||
```python
|
|
||||||
expansion_factor = w.subs(d3,0)/ w0
|
|
||||||
print('beam is w = {:.2f} x w0'.format(expansion_factor))
|
|
||||||
```
|
|
||||||
|
|
||||||
beam is w = 4.90 x w0
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
```python
|
|
||||||
beam_size_change = (w.subs(d3,10) - w.subs(d3,0)) / w.subs(d3,0) * 100
|
|
||||||
print('Over 10 m after second lens, beam changes by {:.0f}%'.format(beam_size_change))
|
|
||||||
```
|
|
||||||
|
|
||||||
Over 10 m after second lens, beam changes by 1%
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
```python
|
|
||||||
|
|
||||||
```
|
|
||||||
@ -1,86 +0,0 @@
|
|||||||
function [result,avgpic]=doNoiseCorrelation(imgs,mask)
|
|
||||||
%imgs:cell arrays of the Nim images to treat together. each element of
|
|
||||||
%imgs should have the same size:(sy,sy)
|
|
||||||
|
|
||||||
Nim=numel(imgs);
|
|
||||||
|
|
||||||
%% initialize sizes
|
|
||||||
enlarge=1;%use so that it works well whatever the images sizes are (even/odd)
|
|
||||||
ROIsizey = size(imgs{1},1)-1;
|
|
||||||
if enlarge; maxsizey = ROIsizey*2; else maxsizey = ROIsizey+1; end%*2;
|
|
||||||
sy = ROIsizey+1;
|
|
||||||
ROIsizex = size(imgs{1},2)-1;
|
|
||||||
if enlarge; maxsizex = ROIsizex*2; else maxsizex = ROIsizex+1; end%*2
|
|
||||||
sx = ROIsizex+1;
|
|
||||||
|
|
||||||
xcors=(-ROIsizex/2:ROIsizex/2);%center=0
|
|
||||||
ycors=(-ROIsizey/2:ROIsizey/2);%center=0
|
|
||||||
avgpic = zeros(maxsizey,maxsizex);
|
|
||||||
avgpicFFT = zeros(maxsizey,maxsizex);
|
|
||||||
|
|
||||||
counter = 0;% not really need if all images of the table are used as then always equal to indim but can come useful is selection is done
|
|
||||||
m0=0.01;%for plot
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
for indim=1:Nim
|
|
||||||
|
|
||||||
disp(['>>>>>>>>>>>>>>>>>>>>>> Image ' num2str(indim) '/' num2str(numel(Nim)) ' <<<<<<<<<<<<<<<<<<<<<'])
|
|
||||||
counter=counter+1;
|
|
||||||
|
|
||||||
%% resized data for the NoiseCorrelations.
|
|
||||||
if nargin==1;ROI1=imgs{indim};else ROI1=imgs{indim}.*mask;end
|
|
||||||
text1='raw images';
|
|
||||||
|
|
||||||
|
|
||||||
pixToCalc = zeros(maxsizey,maxsizex);
|
|
||||||
pixToCalc(1:sy,1:sx) = ROI1;
|
|
||||||
pixToCalc = pixToCalc/sum(sum(pixToCalc));
|
|
||||||
|
|
||||||
%Calculate correlation function
|
|
||||||
picAuxFFT = ifftshift(ifft2((abs(fft2(pixToCalc)).^2)));
|
|
||||||
|
|
||||||
%for means
|
|
||||||
avgpic = avgpic+pixToCalc;
|
|
||||||
avgpicFFT = avgpicFFT+picAuxFFT;
|
|
||||||
|
|
||||||
%temporary means:
|
|
||||||
avgpictemp = avgpic/counter;
|
|
||||||
figure(1); clf;
|
|
||||||
subplot(2,2,1);imagesc(avgpictemp); colorbar;hold all
|
|
||||||
|
|
||||||
avgpicFFTtemp = avgpicFFT/counter;
|
|
||||||
subplot(2,2,2);imagesc(abs(avgpicFFTtemp)); colorbar;hold all
|
|
||||||
|
|
||||||
avgpictemp = ifftshift(ifft2((abs(fft2(avgpictemp)).^2)));
|
|
||||||
subplot(2,2,3);imagesc(abs(avgpictemp)); colorbar;hold all
|
|
||||||
|
|
||||||
|
|
||||||
%temporary results:
|
|
||||||
result = (avgpicFFTtemp./avgpictemp-1);
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
if enlarge result=result(ROIsizey/2+1:ROIsizey*3/2+1,ROIsizex/2+1:ROIsizex*3/2+1); end%/result(ROIsizey+1,ROIsizex+1);
|
|
||||||
subplot(2,2,4);imagesc(real(result),[-1 1]); colorbar;hold all
|
|
||||||
plot(ROIsizey/2+1,ROIsizex/2+1,'w+')
|
|
||||||
|
|
||||||
normr=result(ROIsizey/2+1,ROIsizex/2+1);
|
|
||||||
disp(['Normalization:' num2str(normr)])
|
|
||||||
|
|
||||||
%temporary plot
|
|
||||||
disp(['plot ' num2str(indim) '...'])
|
|
||||||
%plot correlation function
|
|
||||||
figure(100);clf
|
|
||||||
subplot(1,2,1); imagesc(ROI1);title(['Im' num2str(indim)])
|
|
||||||
subplot(1,2,2); imagesc(xcors,ycors,real(result),[-m0/2,m0]);hold all; plot(0,0,'w+');colorbar;
|
|
||||||
nametitle = [text1 '- Nb averages: ',num2str(counter) ', norm: ' num2str(normr)];
|
|
||||||
title(nametitle);
|
|
||||||
|
|
||||||
drawnow;
|
|
||||||
|
|
||||||
end
|
|
||||||
avgpic=avgpic(1:sy,1:sx);
|
|
||||||
end
|
|
||||||
|
|
||||||
|
|
||||||
@ -1,69 +0,0 @@
|
|||||||
function [optrefimages] = fringeremoval(absimages, refimages, bgmask)
|
|
||||||
% FRINGEREMOVAL - Fringe removal and noise reduction from absorption images.
|
|
||||||
% Creates an optimal reference image for each absorption image in a set as
|
|
||||||
% a linear combination of reference images, with coefficients chosen to
|
|
||||||
% minimize the least-squares residuals between each absorption image and
|
|
||||||
% the optimal reference image. The coefficients are obtained by solving a
|
|
||||||
% linear set of equations using matrix inverse by LU decomposition.
|
|
||||||
%
|
|
||||||
% Application of the algorithm is described in C. F. Ockeloen et al, Improved
|
|
||||||
% detection of small atom numbers through image processing, arXiv:1007.2136 (2010).
|
|
||||||
%
|
|
||||||
% Syntax:
|
|
||||||
% [optrefimages] = fringeremoval(absimages,refimages,bgmask);
|
|
||||||
%
|
|
||||||
% Required inputs:
|
|
||||||
% absimages - Absorption image data,
|
|
||||||
% typically 16 bit grayscale images
|
|
||||||
% refimages - Raw reference image data
|
|
||||||
% absimages and refimages are both cell arrays containing
|
|
||||||
% 2D array data. The number of refimages can differ from the
|
|
||||||
% number of absimages.
|
|
||||||
%
|
|
||||||
% Optional inputs:
|
|
||||||
% bgmask - Array specifying background region used,
|
|
||||||
% 1=background, 0=data. Defaults to all ones.
|
|
||||||
% Outputs:
|
|
||||||
% optrefimages - Cell array of optimal reference images,
|
|
||||||
% equal in size to absimages.
|
|
||||||
%
|
|
||||||
|
|
||||||
% Dependencies: none
|
|
||||||
%
|
|
||||||
% Authors: Shannon Whitlock, Caspar Ockeloen
|
|
||||||
% Reference: C. F. Ockeloen, A. F. Tauschinsky, R. J. C. Spreeuw, and
|
|
||||||
% S. Whitlock, Improved detection of small atom numbers through
|
|
||||||
% image processing, arXiv:1007.2136
|
|
||||||
% Email:
|
|
||||||
% May 2009; Last revision: 11 August 2010
|
|
||||||
|
|
||||||
% Process inputs
|
|
||||||
|
|
||||||
% Set variables, and flatten absorption and reference images
|
|
||||||
nimgs = size(absimages,3);
|
|
||||||
nimgsR = size(refimages,3);
|
|
||||||
xdim = size(absimages(:,:,1),2);
|
|
||||||
ydim = size(absimages(:,:,1),1);
|
|
||||||
|
|
||||||
R = single(reshape(refimages,xdim*ydim,nimgsR));
|
|
||||||
A = single(reshape(absimages,xdim*ydim,nimgs));
|
|
||||||
optrefimages=zeros(size(absimages)); % preallocate
|
|
||||||
|
|
||||||
if not(exist('bgmask','var')); bgmask=ones(ydim,xdim); end
|
|
||||||
k = find(bgmask(:)==1); % Index k specifying background region
|
|
||||||
|
|
||||||
% Ensure there are no duplicate reference images
|
|
||||||
%R=unique(R','rows')'; % comment this line if you run out of memory
|
|
||||||
|
|
||||||
% Decompose B = R*R' using singular value or LU decomposition
|
|
||||||
[L,U,p] = lu(R(k,:)'*R(k,:),'vector'); % LU decomposition
|
|
||||||
|
|
||||||
for j=1:nimgs
|
|
||||||
b=R(k,:)'*A(k,j);
|
|
||||||
% Obtain coefficients c which minimise least-square residuals
|
|
||||||
lower.LT = true; upper.UT = true;
|
|
||||||
c = linsolve(U,linsolve(L,b(p,:),lower),upper);
|
|
||||||
|
|
||||||
% Compute optimised reference image
|
|
||||||
optrefimages(:,:,j)=reshape(R*c,[ydim xdim]);
|
|
||||||
end
|
|
||||||
@ -1,179 +0,0 @@
|
|||||||
% Demo to threshold an image to find regions (blobs).
|
|
||||||
% Then let user point to a blob that you want to eliminate.
|
|
||||||
|
|
||||||
clc; % Clear the command window.
|
|
||||||
close all; % Close all figures (except those of imtool.)
|
|
||||||
imtool close all; % Close all imtool figures if you have the Image Processing Toolbox.
|
|
||||||
clearvars; % Erase all existing variables.
|
|
||||||
workspace; % Make sure the workspace panel is showing.
|
|
||||||
format long g;
|
|
||||||
format compact;
|
|
||||||
fontSize = 20;
|
|
||||||
|
|
||||||
% Check that user has the Image Processing Toolbox installed.
|
|
||||||
hasIPT = license('test', 'image_toolbox');
|
|
||||||
if ~hasIPT
|
|
||||||
% User does not have the toolbox installed.
|
|
||||||
message = sprintf('Sorry, but you do not seem to have the Image Processing Toolbox.\nDo you want to try to continue anyway?');
|
|
||||||
reply = questdlg(message, 'Toolbox missing', 'Yes', 'No', 'Yes');
|
|
||||||
if strcmpi(reply, 'No')
|
|
||||||
% User said No, so exit.
|
|
||||||
return;
|
|
||||||
end
|
|
||||||
end
|
|
||||||
baseFileName = 'coins.png'; % Default
|
|
||||||
|
|
||||||
% % Read in a standard MATLAB gray scale demo image.
|
|
||||||
% folder = fullfile(matlabroot, '\toolbox\images\imdemos');
|
|
||||||
% button = menu('Use which demo image?', 'CameraMan', 'Moon', 'Eight', 'Coins', 'Pout');
|
|
||||||
% if button == 1
|
|
||||||
% baseFileName = 'cameraman.tif';
|
|
||||||
% elseif button == 2
|
|
||||||
% baseFileName = 'moon.tif';
|
|
||||||
% elseif button == 3
|
|
||||||
% baseFileName = 'coins.png';
|
|
||||||
% else
|
|
||||||
% baseFileName = 'pout.tif';
|
|
||||||
% end
|
|
||||||
|
|
||||||
% Read in a standard MATLAB gray scale demo image.
|
|
||||||
folder = fullfile(matlabroot, '\toolbox\images\imdemos');
|
|
||||||
% Get the full filename, with path prepended.
|
|
||||||
fullFileName = fullfile(folder, baseFileName);
|
|
||||||
% Check if file exists.
|
|
||||||
if ~exist(fullFileName, 'file')
|
|
||||||
% File doesn't exist -- didn't find it there. Check the search path for it.
|
|
||||||
fullFileName = baseFileName; % No path this time.
|
|
||||||
if ~exist(fullFileName, 'file')
|
|
||||||
% Still didn't find it. Alert user.
|
|
||||||
errorMessage = sprintf('Error: %s does not exist in the search path folders.', fullFileName);
|
|
||||||
uiwait(warndlg(errorMessage));
|
|
||||||
return;
|
|
||||||
end
|
|
||||||
end
|
|
||||||
grayImage = imread(fullFileName);
|
|
||||||
% Get the dimensions of the image.
|
|
||||||
% numberOfColorBands should be = 1.
|
|
||||||
[rows, columns, numberOfColorBands] = size(grayImage);
|
|
||||||
if numberOfColorBands > 1
|
|
||||||
% It's not really gray scale like we expected - it's color.
|
|
||||||
% Convert it to gray scale by taking only the green channel.
|
|
||||||
grayImage = grayImage(:, :, 2); % Take green channel.
|
|
||||||
end
|
|
||||||
% Display the original gray scale image.
|
|
||||||
subplot(2, 3, 1);
|
|
||||||
imshow(grayImage, []);
|
|
||||||
title('Original Grayscale Image', 'FontSize', fontSize);
|
|
||||||
% Enlarge figure to full screen.
|
|
||||||
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0 0 1 1]);
|
|
||||||
% Give a name to the title bar.
|
|
||||||
set(gcf, 'Name', 'Demo by ImageAnalyst', 'NumberTitle', 'Off')
|
|
||||||
|
|
||||||
% Let's compute and display the histogram.
|
|
||||||
[pixelCount, grayLevels] = imhist(grayImage);
|
|
||||||
subplot(2, 3, 2);
|
|
||||||
bar(grayLevels, pixelCount);
|
|
||||||
grid on;
|
|
||||||
title('Histogram of original image', 'FontSize', fontSize);
|
|
||||||
xlim([0 grayLevels(end)]); % Scale x axis manually.
|
|
||||||
|
|
||||||
% Threshold the image.
|
|
||||||
binaryImage = grayImage > 100;
|
|
||||||
% Clean up a bit
|
|
||||||
binaryImage = bwareaopen(binaryImage, 500);
|
|
||||||
binaryImage = imfill(binaryImage, 'holes');
|
|
||||||
% Display the binary image.
|
|
||||||
subplot(2, 3, 3);
|
|
||||||
imshow(binaryImage, []);
|
|
||||||
title('Binary Image', 'FontSize', fontSize);
|
|
||||||
|
|
||||||
doAnother = true;
|
|
||||||
while doAnother
|
|
||||||
% Find pixels
|
|
||||||
[labeledImage, numberOfBlobs] = bwlabel(binaryImage);
|
|
||||||
measurements = regionprops(labeledImage, 'PixelIdxList', 'Centroid')
|
|
||||||
allCentroids = [measurements.Centroid];
|
|
||||||
centroidX = allCentroids(1:2:end);
|
|
||||||
centroidY = allCentroids(2:2:end);
|
|
||||||
% Plot the centroids over the blobs
|
|
||||||
hold on;
|
|
||||||
plot(centroidX, centroidY, 'bo', 'MarkerSize', 10);
|
|
||||||
axis on;
|
|
||||||
% Put text labels on them.
|
|
||||||
for k = 1 : numberOfBlobs
|
|
||||||
text(centroidX(k), centroidY(k)+10, num2str(k), 'Color', 'b', 'FontWeight', 'bold');
|
|
||||||
end
|
|
||||||
promptMessage = sprintf('On the binary image in the upper right,\nClick the region to remove,\nor Cancel to abort processing?');
|
|
||||||
titleBarCaption = 'Continue?';
|
|
||||||
subplot(2, 3, 3);
|
|
||||||
button = questdlg(promptMessage, titleBarCaption, 'Continue', 'Cancel', 'Continue');
|
|
||||||
if strcmpi(button, 'Cancel')
|
|
||||||
break;
|
|
||||||
end
|
|
||||||
[x,y] = ginput(1)
|
|
||||||
% Plot where they clicked.
|
|
||||||
plot(x, y, 'r+', 'MarkerSize', 20, 'LineWidth', 3);
|
|
||||||
|
|
||||||
% Find which centroid this (x,y) is closest to
|
|
||||||
% First find out the distance from where user clicked to every other centroid.
|
|
||||||
xDistances = (centroidX - x);
|
|
||||||
yDistances = (centroidY - y);
|
|
||||||
distances = sqrt(xDistances .^ 2 + yDistances .^ 2);
|
|
||||||
% Find the closest one.
|
|
||||||
[minDistance, indexOfClosest] = min(distances)
|
|
||||||
% Plot an X over the closest blob.
|
|
||||||
plot(centroidX(indexOfClosest), centroidY(indexOfClosest), 'rx', 'MarkerSize', 40, 'LineWidth', 3);
|
|
||||||
% Draw a line between them.
|
|
||||||
line([x, centroidX(indexOfClosest)], [y, centroidY(indexOfClosest)], 'Color', 'r', 'LineWidth', 2);
|
|
||||||
|
|
||||||
% Now remove this index.
|
|
||||||
keeperIndexes = 1 : numberOfBlobs; % All of them
|
|
||||||
keeperIndexes(indexOfClosest) = []; % Remove this particular blob from the list of blobs.
|
|
||||||
% Remove it from the labeled image.
|
|
||||||
newLabeledImage = ismember(labeledImage, keeperIndexes);
|
|
||||||
% Get new indexes in consequtive order since one if now missing.
|
|
||||||
newBinaryImage = newLabeledImage > 0; % All except selected blob.
|
|
||||||
% Display the binary image.
|
|
||||||
subplot(2, 3, 4);
|
|
||||||
imshow(newBinaryImage, []);
|
|
||||||
title('New Binary Image', 'FontSize', fontSize);
|
|
||||||
% Now make measurements all over again with the indicated blob removed (optional).
|
|
||||||
[labeledImage, numberOfBlobs] = bwlabel(binaryImage);
|
|
||||||
measurements = regionprops(labeledImage, 'Area');
|
|
||||||
|
|
||||||
% Mask the image to make selected blob 0
|
|
||||||
% Get the selected blob alone
|
|
||||||
selectedBlob = binaryImage & ~newBinaryImage;
|
|
||||||
maskedImage1 = grayImage; % Initialize.
|
|
||||||
maskedImage1(selectedBlob) = 0;
|
|
||||||
% Display the masked image.
|
|
||||||
subplot(2, 3, 5);
|
|
||||||
imshow(maskedImage1, []);
|
|
||||||
title('Masked Image', 'FontSize', fontSize);
|
|
||||||
|
|
||||||
% Fill the image with surrounding background.
|
|
||||||
% First enlarge blob
|
|
||||||
selectedBlob = imdilate(selectedBlob, ones(7));
|
|
||||||
% Now do the fill from the boundary.
|
|
||||||
maskedImage2 = roifill(grayImage, selectedBlob);
|
|
||||||
% Display the masked image.
|
|
||||||
subplot(2, 3, 6);
|
|
||||||
imshow(maskedImage2, []);
|
|
||||||
title('Filled Image', 'FontSize', fontSize);
|
|
||||||
|
|
||||||
% If we've deleted the last blob, exit.
|
|
||||||
if numberOfBlobs <= 1
|
|
||||||
% Bail out if there are no more blobs.
|
|
||||||
break;
|
|
||||||
end
|
|
||||||
|
|
||||||
cumulativeRemoval = true;
|
|
||||||
if cumulativeRemoval
|
|
||||||
% If you want the removal to be cumulative, set grayImage to be maskedImage2 or maskedImage1.
|
|
||||||
% Otherwise comment out the line below to start from the original gray image every time.
|
|
||||||
grayImage = maskedImage2;
|
|
||||||
binaryImage = newBinaryImage;
|
|
||||||
end
|
|
||||||
end
|
|
||||||
|
|
||||||
|
|
||||||
@ -42,7 +42,7 @@ for k = 1 : length(files)
|
|||||||
end
|
end
|
||||||
%% Fringe removal
|
%% Fringe removal
|
||||||
|
|
||||||
optrefimages = fringeremoval(absimages, refimages);
|
optrefimages = removefringesInImage(absimages, refimages);
|
||||||
absimages_fringe_removed = absimages(:, :, :) - optrefimages(:, :, :);
|
absimages_fringe_removed = absimages(:, :, :) - optrefimages(:, :, :);
|
||||||
|
|
||||||
nimgs = size(absimages_fringe_removed,3);
|
nimgs = size(absimages_fringe_removed,3);
|
||||||
@ -397,8 +397,8 @@ function [RadialResponseFunc] = RadialImagingResponseFunction(C, k, kmax)
|
|||||||
RadialResponseFunc = C(6)*1/2*A.*RadialResponseFunc;
|
RadialResponseFunc = C(6)*1/2*A.*RadialResponseFunc;
|
||||||
end
|
end
|
||||||
|
|
||||||
function [optrefimages] = fringeremoval(absimages, refimages, bgmask)
|
function [optrefimages] = removefringesInImage(absimages, refimages, bgmask)
|
||||||
% FRINGEREMOVAL - Fringe removal and noise reduction from absorption images.
|
% removefringesInImage - Fringe removal and noise reduction from absorption images.
|
||||||
% Creates an optimal reference image for each absorption image in a set as
|
% Creates an optimal reference image for each absorption image in a set as
|
||||||
% a linear combination of reference images, with coefficients chosen to
|
% a linear combination of reference images, with coefficients chosen to
|
||||||
% minimize the least-squares residuals between each absorption image and
|
% minimize the least-squares residuals between each absorption image and
|
||||||
@ -409,7 +409,7 @@ function [optrefimages] = fringeremoval(absimages, refimages, bgmask)
|
|||||||
% detection of small atom numbers through image processing, arXiv:1007.2136 (2010).
|
% detection of small atom numbers through image processing, arXiv:1007.2136 (2010).
|
||||||
%
|
%
|
||||||
% Syntax:
|
% Syntax:
|
||||||
% [optrefimages] = fringeremoval(absimages,refimages,bgmask);
|
% [optrefimages] = removefringesInImage(absimages,refimages,bgmask);
|
||||||
%
|
%
|
||||||
% Required inputs:
|
% Required inputs:
|
||||||
% absimages - Absorption image data,
|
% absimages - Absorption image data,
|
||||||
Loading…
Reference in New Issue
Block a user