Related
Find the error as a function of n, where the error is defined as the difference between two the voltage from the Fourier series (vF (t)) and the value from the ideal function (v(t)), normalized to the maximum magnitude (Vm ):
I am given this prompt where Vm = 1 V. Below this line is the code which I have written.
I am trying to write a function to solve this question: Plot the error versus time for n=3,n=5,n=10, and n=50. (10points). What does it look like I am doing incorrectly?
clc;
close all;
clear all;
% define the signal parameters
Vm = 1;
T = 1;
w0 = 2*pi/T;
% define the symbolic variables
syms n t;
% define the signal
v1 = Vm*sin(4*pi*t/T);
v2 = 2*Vm*sin(4*pi*t/T);
% evaluate the fourier series integral
an1 = 2/T*int(v1*cos(n*w0*t),0,T/2) + 2/T*int(v2*cos(n*w0*t),T/2,T);
bn1 = 2/T*int(v1*sin(n*w0*t),0,T/2) + 2/T*int(v2*sin(n*w0*t),T/2,T);
a0 = 1/T*int(v1,0,T/2) + 1/T*int(v2,T/2,T);
% obtain C by substituting n in c[n]
nmax = 100;
n = 1:nmax;
a = subs(an1);
b = subs(bn1);
% define the time vector
ts = 1e-2; % ts is sampling the
t = 0:ts:3*T-ts;
% directly plot the signal x(t)
t1 = 0:ts:T-ts;
v1 = Vm*sin(4*pi*t1/T).*(t1<=T/2);
v2 = 2*Vm*sin(4*pi*t1/T).*(t1>T/2).*(t1<T);
v = v1+v2;
x = repmat(v,1,3);
% Now fourier series reconstruction
N = [3];
for p = 1:length(N)
for i = 1:length(t)
for k = N(p)
x(k,i) = a(k)*cos(k*w0*t(i)) + b(k)*sin(k*w0*t(i));
end
% y(k,i) = a0+sum(x(:,i)); % Add DC term
end
end
z = a0 + sum(x);
figure(1);
plot(t,z);
%Percent error
function [per_error] = percent_error(measured, actual)
per_error = abs(( (measured - actual) ./ 1) * 100);
end
The purpose of the forum is helping with specific technical questions, not doing your homework.
I am interested in modifying the code below to find the parameters I_1, I_2, I_3 and I_4, to be used in another code. Every time I run the code, it throws up
In an assignment A(:) = B, the number of elements in A and B must be the same
on this line " mult(mult == 0) = B;".
I have spent eternity figuring out what the problem could be. Here is the code:
%%% Some Parameters %%
delta = 0.6; % Blanked subframe ratio
B = [0 0.2 0.4 0.6 0.8 1]; %Power splitting factor
k = 2.3; %Macro BS density
f = k*5; %Small cell density
j = 300; %users density
P_m = 46; %Macro BS transmission power
P_s = 23; %SC transmit power
Zm = -15;
Zs = -15;
iter = 30; %Iteration run
h = 500; %Simulation area
hu = 0.8*h; %users simulation area
Vm = round(k*h); %Macro BS average no in h
Vs = round(f*h); %SC average no in h
Vu = round(j*hu); %%users average no in hu
Pm = 10^(P_m/10)/1000*10^(Zm/10);
Ps = 10^(P_s/10)/1000*10^(Zs/10);
for i = iter;
%% XY coodinates for Macrocell, small cells and users.
Xm = sqrt(h)*(rand(Vm,1)-0.5);
Ym = sqrt(h)*(rand(Vm,1)-0.5);
Xs = sqrt(h)*(rand(Vs,1)-0.5);
Ys = sqrt(h)*(rand(Vs,1)-0.5);
Xu = sqrt(hu)*(rand(Vu,1)-0.5);
Yu = sqrt(hu)*(rand(Vu,1)-0.5);
%Total coordinates for MBS and small cells
Total_Coord = [Xs Ys ones(size(Xs)) Xm Ym 2*ones(size(Xm))];
%Distance between BSs and users
[Xsm_mat, Xu_mat] = meshgrid(Total_Coord(:,1),Xu);
[Ysm_mat, Yu_mat] = meshgrid(Total_Coord(:,2),Yu);
Distance = sqrt((Xsm_mat-Xu_mat).^2 + (Ysm_mat-Yu_mat).^2);
%% To determine serving BS for each user
[D_m,idx_m] = min(Distance(:,(length(Xs)+1):end),[],2);
idx_m = idx_m + length(Xs);
[D_s,idx_s] = min(Distance(:,1:length(Xs)),[],2);
%% Power received by users from each BS
Psm_mat = [Ps*ones(length(Xu),length(Xs))
Pm*ones(length(Xu),length(Xm))]; % Transmit power of MBS and small cells
Pr_n = Psm_mat.*exprnd(1,size(Psm_mat))./(Distance*1e3).^4;
mult = binornd(1,delta,1,length(Xm)); % Full transmission power of each
interfering MBS for delta
mult(mult == 0) = B; % Reduced transmission power for (1-delta)
Pr = Pr_n.*[ones(length(Xu),length(Xs)) repmat(mult,length(Xu),1)];%
Interference from each BS
%% Power received by each user from serving BSs
Prm = Pr(sub2ind(size(Pr),(1:length(idx_m))',idx_m));
Prs = Pr(sub2ind(size(Pr),(1:length(idx_s))',idx_s));
P_m_n = Pr_n(sub2ind(size(Pr_n),(1:length(idx_m))',idx_m));
%% Total interference for each UE
I_T = sum(Pr,2) - Prm - Prs;
I_1 = P_m_n./(Prs + I_T);
I_2 = Prs./(P_m_n + I_T);
I_3 = B*I_1;
I_4 = Prs./(B*P_m_n + I_T);
end
The error appeared on this line "mult(mult == 0) = B;".
I know it to be assignment problem which requires equality in both the left and right dimensions. Suggestions for correction will be appreciated.
Your vector mult has length Vm (number of macro BS?). Assigning to mult(mult==0) will assign to a subset of this vector (those that have a value equal to zero). What you are assigning is your variable B which you define as B = [0 0.2 0.4 0.6 0.8 1], i.e., it is a length-6 vector. The assignment fails unless mult has exactly 6 zeros.
I highly doubt that this is what you want. It looks like you are trying to assign the same value ("Reduced transmission power"). Then your B should be scalar though.
Since we have no idea what you are trying to do (and your code is not exactly an MCVE), we can only guess.
I have a Matlab code that simulates frisbee flight dynamics. I would like to add a wind variable. I did it, but after seeing the plots I think my wind is reducing the speed of the disc. I mean it should change the speed of the disc but via lift and drag force, now it looks like wind speed variable direcly changes disc speed variable. What I want is to affect only the lift and drag forces with wind, but I can't make it work. Here is my current code that is not working. This is an external M-file which is used by the ode45 function in the main script:
[t,x]=ode45(#discfltEOM,tspan,x0,options,CoefUsed);
function xdot=discfltEOM(t,x,CoefUsed)
% Equations of Motion for the frisbee
% The inertial frame, xyz = forward, right and down
global m g Ia Id A d rho
global CLo CLa CDo CDa CMo CMa CRr
global CL_data CD_data CM_data CRr_rad CRr_AdvR CRr_data
global CMq CRp CNr
% x = [ x y z vx vy vz f th fd thd gd gamma Wx Wy]
% 1 2 3 4 5 6 7 8 9 10 11 12 13 14
%% give states normal names
vx = x(4);
vy = x(5);
vz = x(6);
f = x(7);
th = x(8);
st = sin(th);
ct = cos(th);
sf = sin(f);
cf = cos(f);
fd = x(9);
thd= x(10);
gd = x(11);
Wx = x(13);
Wy = x(14);
%% Define transformation matrix
%% [c]=[T_c_N] * [N]
T_c_N=[ct st*sf -st*cf; 0 cf sf; st -ct*sf ct*cf];
%% [d]=[T_d_N] * [N]
%T_d_N(1,:)=[cg*ct sg*cf+sf*st*cg sf*sg-st*cf*cg];
%T_d_N(2,:)=[ -sg*ct cf*cg-sf*sg*st sf*cg+sg*st*cf];
%T_d_N(3,:)=[ st -sf*ct cf*ct]
[evec,eval]=eig(T_c_N);
eigM1=diag(eval);
m1=norm(eigM1(1));
m2=norm(eigM1(2));
m3=norm(eigM1(3));
c1=T_c_N(1,:); % c1 expressed in N frame
c2=T_c_N(2,:); % c2 expressed in N frame
c3=T_c_N(3,:); % c3 expressed in N frame
%% calculate aerodynamic forces and moments
%% every vector is expressed in the N frame
vel = [vx vy vz]; %expressed in N
vmag = norm(vel);
Vwiatr = [Wx Wy 0];
Vw = norm(Vwiatr);
vc3=dot(vel,c3); % velocity (scalar) in the c3 direction
vp= [vel-vc3*c3]; % subtract the c3 velocity component to get the velocity vector
% projected onto the plane of the disc, expressed in N
alpha = atan(vc3/norm(vp));
Adp = A*rho*(vmag-Vw)*(vmag-Vw)/2;
uvel = vel/vmag; % unit vector in vel direction, expressed in N
uvp = vp/norm(vp); % unit vector in the projected velocity direction, expressed in N
ulat = cross(c3,uvp); % unit vec perp to v and d3 that points to right, right?
%% first calc moments in uvp (roll), ulat(pitch) directions, then express in n1,n2,n3
omegaD_N_inC = [fd*ct thd fd*st+gd]; % expressed in c1,c2,c3
omegaD_N_inN = T_c_N'*omegaD_N_inC'; % expressed in n1,n2,n3
omegavp = dot(omegaD_N_inN,uvp);
omegalat = dot(omegaD_N_inN,ulat);
omegaspin = dot(omegaD_N_inN,c3); % omegaspin = p1=fd*st+gd
AdvR= d*omegaspin/2/vmag ; % advanced ration
if CoefUsed==1 % using short flights coefficients
CL = CLo + CLa*alpha;
alphaeq = -CLo/CLa; % this is angle of attack at zero lift
CD = CDo + CDa*(alpha-alphaeq)*(alpha-alphaeq);
CM=CMo + CMa*alpha;
%CRr= CRr*d*omegaspinv/2./vmagv';
%CRr= CRr*sqrt(d/g)*omegaspinv; % this line produces NaN, so leave it in Mvp equation
%Mvp = Adp*d* (CRr*d*omegaspin/2/vmag + CRp*omegavp)*uvp; % expressed in N
Mvp = Adp*d*(sqrt(d/g)*CRr*omegaspin + CRp*omegavp)*uvp; % expressed in N
end % if CoefUsed==1 % using short flights coefficients
if CoefUsed==2 % using potts coefficients
%% interpolation of Potts and Crowther (2002) data
CL = interp1(CL_data(:,1), CL_data(:,2), alpha,'spline');
CD = interp1(CD_data(:,1), CD_data(:,2), alpha,'spline');
CM = interp1(CM_data(:,1), CM_data(:,2), alpha,'spline');
CRr = interp2(CRr_rad,CRr_AdvR,CRr_data,alpha,AdvR,'spline');
Mvp = Adp*d* (CRr* + CRp*omegavp)*uvp; % Roll moment, expressed in N
end % if CoefUsed==2 % using potts coefficients
lift = CL*Adp;
drag = CD*Adp;
ulift = -cross(uvel,ulat); % ulift always has - d3 component
udrag = -uvel;
Faero = lift*ulift + drag*udrag; % aero force in N
FgN = [ 0 0 m*g]'; % gravity force in N
F = Faero' + FgN;
Mlat = Adp*d*(CM + CMq*omegalat)*ulat; % Pitch moment expressed in N
Mspin = [0 0 +CNr*(omegaspin)]; % Spin Down moment expressed in C
M = T_c_N*Mvp' + T_c_N*Mlat' + Mspin'; % Total moment expressed in C
% set moments equal to zero if wanted...
% M=[0 0 0];
% calculate the derivatives of the states
xdot = vel';
xdot(4) = (F(1)/m); %accx
xdot(5) = (F(2)/m); %accy
xdot(6) = (F(3)/m); %accz
xdot(7) = fd;
xdot(8) = thd;
xdot(9) = (M(1) + Id*thd*fd*st - Ia*thd*(fd*st+gd) + Id*thd*fd*st)/Id/ct;
xdot(10) = (M(2) + Ia*fd*ct*(fd*st +gd) - Id*fd*fd*ct*st)/Id;
fdd=xdot(9);
xdot(11) = (M(3) - Ia*(fdd*st + thd*fd*ct))/Ia;
xdot(12) = x(11);
xdot(13) = Wx;
xdot(14) = Wy;
xdott=xdot';
% calculate angular momentum
H = [Id 0 0 ; 0 Id 0; 0 0 Ia]*omegaD_N_inC';
format long;
magH = norm(H);
format short;
state=x';
Wx and Wy are wind vectors. I'm trying to affect the Adp variable because it is direcly connected with lift and drag. I made Wx = 1 [m/s] and the effect is immense, but should be very little. I'm terrible with Matlab so I'm sure I making some kind of stupid mistake from not understanding well how it all works.
A filter g is called separable if it can be expressed as the multiplication of two vectors grow and gcol . Employing one dimensional filters decreases the two dimensional filter's computational complexity from O(M^2 N^2) to O(2M N^2) where M and N are the width (and height) of the filter mask and the image respectively.
In this stackoverflow link, I wrote the equation of a Gabor filter in the spatial domain, then I wrote a matlab code which serves to create 64 gabor features.
According to the definition of separable filters, the Gabor filters are parallel to the image axes - theta = k*pi/2 where k=0,1,2,etc.. So if theta=pi/2 ==> the equation in this stackoverflow link can be rewritten as:
The equation above is extracted from this article.
Note: theta can be extented to be equal k*pi/4. By comparing to the equation in this stackoverflow link, we can consider that f= 1 / lambda.
By changing my previous code in this stackoverflow link, I wrote a matlab code to make the Gabor filters separable by using the equation above, but I am sure that my code below is not correct especially when I initialized the gbp and glp equations. That is why I need your help. I will appreciate your help very much.
Let's show now my code:
function [fSiz,filters1,filters2,c1OL,numSimpleFilters] = init_gabor(rot, RF_siz)
image=imread('xxx.jpg');
image_gray=rgb2gray(image);
image_gray=imresize(image_gray, [100 100]);
image_double=double(image_gray);
rot = [0 45 90 135]; % we have four orientations
RF_siz = [7:2:37]; %we get 16 scales (7x7 to 37x37 in steps of two pixels)
minFS = 7; % the minimum receptive field
maxFS = 37; % the maximum receptive field
sigma = 0.0036*RF_siz.^2 + 0.35*RF_siz + 0.18; %define the equation of effective width
lambda = sigma/0.8; % it the equation of wavelength (lambda)
G = 0.3; % spatial aspect ratio: 0.23 < gamma < 0.92
numFilterSizes = length(RF_siz); % we get 16
numSimpleFilters = length(rot); % we get 4
numFilters = numFilterSizes*numSimpleFilters; % we get 16x4 = 64 filters
fSiz = zeros(numFilters,1); % It is a vector of size numFilters where each cell contains the size of the filter (7,7,7,7,9,9,9,9,11,11,11,11,......,37,37,37,37)
filters1 = zeros(max(RF_siz),numFilters);
filters2 = zeros(numFilters,max(RF_siz));
for k = 1:numFilterSizes
for r = 1:numSimpleFilters
theta = rot(r)*pi/180;
filtSize = RF_siz(k);
center = ceil(filtSize/2);
filtSizeL = center-1;
filtSizeR = filtSize-filtSizeL-1;
sigmaq = sigma(k)^2;
for x = -filtSizeL:filtSizeR
fx = exp(-(x^2)/(2*sigmaq))*cos(2*pi*x/lambda(k));
f1(x+center,1) = fx;
end
for y = -filtSizeL:filtSizeR
gy = exp(-(y^2)/(2*sigmaq));
f2(1,y+center) = gy;
end
f1 = f1 - mean(mean(f1));
f1 = f1 ./ sqrt(sum(sum(f1.^2)));
f2 = f2 - mean(mean(f2));
f2 = f2 ./ sqrt(sum(sum(f2.^2)));
p = numSimpleFilters*(k-1) + r;
filters1(1:filtSize,p)=f1;
filters2(p,1:filtSize)=f2;
convv1=imfilter(image_double, filters1(1:filtSize,p),'conv');
convv2=imfilter(double(convv1), filters2(p,1:filtSize),'conv');
figure
imagesc(convv2);
colormap(gray);
end
end
I think the code is correct provided your previous version of Gabor filter code is correct too. The only thing is that if theta = k * pi/4;, your formula here should be separated to:
fx = exp(-(x^2)/(2*sigmaq))*cos(2*pi*x/lambda(k));
gy = exp(-(G^2 * y^2)/(2*sigmaq));
To be consistent, you may use
f1(1,x+center) = fx;
f2(y+center,1) = gy;
or keep f1 and f2 as it is but transpose your filters1 and filters2 thereafter.
Everything else looks good to me.
EDIT
My answer above works for theta = k * pi/4;, with other angles, based on your paper,
x = i*cos(theta) - j*sin(theta);
y = i*sin(theta) + j*cos(theta);
fx = exp(-(x^2)/(2*sigmaq))*exp(sqrt(-1)*x*cos(theta));
gy = exp(-(G^2 * y^2)/(2*sigmaq))*exp(sqrt(-1)*y*sin(theta));
The final code will be:
function [fSiz,filters1,filters2,c1OL,numSimpleFilters] = init_gabor(rot, RF_siz)
image=imread('xxx.jpg');
image_gray=rgb2gray(image);
image_gray=imresize(image_gray, [100 100]);
image_double=double(image_gray);
rot = [0 45 90 135];
RF_siz = [7:2:37];
minFS = 7;
maxFS = 37;
sigma = 0.0036*RF_siz.^2 + 0.35*RF_siz + 0.18;
lambda = sigma/0.8;
G = 0.3;
numFilterSizes = length(RF_siz);
numSimpleFilters = length(rot);
numFilters = numFilterSizes*numSimpleFilters;
fSiz = zeros(numFilters,1);
filters1 = zeros(max(RF_siz),numFilters);
filters2 = zeros(numFilters,max(RF_siz));
for k = 1:numFilterSizes
for r = 1:numSimpleFilters
theta = rot(r)*pi/180;
filtSize = RF_siz(k);
center = ceil(filtSize/2);
filtSizeL = center-1;
filtSizeR = filtSize-filtSizeL-1;
sigmaq = sigma(k)^2;
for x = -filtSizeL:filtSizeR
fx = exp(-(x^2)/(2*sigmaq))*exp(sqrt(-1)*x*cos(theta));
f1(1, x+center) = fx;
end
for y = -filtSizeL:filtSizeR
gy=exp(-(y^2)/(2*sigmaq))*exp(sqrt(-1)*y*sin(theta));
f2(y+center,1) = gy;
end
f1 = f1 - mean(mean(f1));
f1 = f1 ./ sqrt(sum(sum(f1.^2)));
f2 = f2 - mean(mean(f2));
f2 = f2 ./ sqrt(sum(sum(f2.^2)));
p = numSimpleFilters*(k-1) + r;
filters1(1:filtSize,p)=f1;
filters2(p,1:filtSize)=f2;
convv1=imfilter(image_double, filters1(1:filtSize,p),'conv');
convv2=imfilter(double(convv1), filters2(p,1:filtSize),'conv');
figure
imagesc(imag(convv2));
colormap(gray);
end
end
I'm trying to produce some computer generated holograms by using MATLAB. I used equally spaced mesh grid to initialize the spatial grid, and I got the following image
This pattern is sort of what I need except the center region. The fringe should be sharp but blurred. I think it might be the problem of the mesh grid. I tried generate a grid in polar coordinates and the map it into Cartesian coordinates by using MATLAB's pol2cart function. Unfortunately, it doesn't work as well. One may suggest that using fine grids. It doesn't work too. I think if I can generate a spiral mesh grid, perhaps the problem is solvable. In addition, the number of the spiral arms could, in general, be arbitrary, could anyone give me a hint on this?
I've attached the code (My final projects are not exactly the same, but it has a similar problem).
clc; clear all; close all;
%% initialization
tic
lambda = 1.55e-6;
k0 = 2*pi/lambda;
c0 = 3e8;
eta0 = 377;
scale = 0.25e-6;
NELEMENTS = 1600;
GoldenRatio = (1+sqrt(5))/2;
g = 2*pi*(1-1/GoldenRatio);
pntsrc = zeros(NELEMENTS, 3);
phisrc = zeros(NELEMENTS, 1);
for idxe = 1:NELEMENTS
pntsrc(idxe, :) = scale*sqrt(idxe)*[cos(idxe*g), sin(idxe*g), 0];
phisrc(idxe) = angle(-sin(idxe*g)+1i*cos(idxe*g));
end
phisrc = 3*phisrc/2; % 3 arms (topological charge ell=3)
%% post processing
sigma = 1;
polfilter = [0, 0, 1i*sigma; 0, 0, -1; -1i*sigma, 1, 0]; % cp filter
xboundl = -100e-6; xboundu = 100e-6;
yboundl = -100e-6; yboundu = 100e-6;
xf = linspace(xboundl, xboundu, 100);
yf = linspace(yboundl, yboundu, 100);
zf = -400e-6;
[pntobsx, pntobsy] = meshgrid(xf, yf);
% how to generate a right mesh grid such that we can generate a decent result?
pntobs = [pntobsx(:), pntobsy(:), zf*ones(size(pntobsx(:)))];
% arbitrary mesh may result in "wrong" results
NPNTOBS = size(pntobs, 1);
nxp = length(xf);
nyp = length(yf);
%% observation
Eobs = zeros(NPNTOBS, 3);
matlabpool open local 12
parfor nobs = 1:NPNTOBS
rp = pntobs(nobs, :);
Erad = [0; 0; 0];
for idx = 1:NELEMENTS
rs = pntsrc(idx, :);
p = exp(sigma*1i*2*phisrc(idx))*[1 -sigma*1i 0]/2; % simplified here
u = rp - rs;
r = sqrt(u(1)^2+u(2)^2+u(3)^2); %norm(u);
u = u/r; % unit vector
ut = [u(2)*p(3)-u(3)*p(2),...
u(3)*p(1)-u(1)*p(3), ...
u(1)*p(2)-u(2)*p(1)]; % cross product: u cross p
Erad = Erad + ... % u cross p cross u, do not use the built-in func
c0*k0^2/4/pi*exp(1i*k0*r)/r*eta0*...
[ut(2)*u(3)-ut(3)*u(2);...
ut(3)*u(1)-ut(1)*u(3); ...
ut(1)*u(2)-ut(2)*u(1)];
end
Eobs(nobs, :) = Erad; % filter neglected here
end
matlabpool close
Eobs = Eobs/max(max(sum(abs(Eobs), 2))); % normailized
%% source, gaussian beam
E0 = 1;
w0 = 80e-6;
theta = 0; % may be titled
RotateX = [1, 0, 0; ...
0, cosd(theta), -sind(theta); ...
0, sind(theta), cosd(theta)];
Esrc = zeros(NPNTOBS, 3);
for nobs = 1:NPNTOBS
rp = RotateX*[pntobs(nobs, 1:2).'; 0];
z = rp(3);
r = sqrt(sum(abs(rp(1:2)).^2));
zR = pi*w0^2/lambda;
wz = w0*sqrt(1+z^2/zR^2);
Rz = z^2+zR^2;
zetaz = atan(z/zR);
gaussian = E0*w0/wz*exp(-r^2/wz^2-1i*k0*z-1i*k0*0*r^2/Rz/2+1i*zetaz);% ...
Esrc(nobs, :) = (polfilter*gaussian*[1; -1i; 0]).'/sqrt(2)/2;
end
Esrc = [Esrc(:, 2), Esrc(:, 3), Esrc(:, 1)];
Esrc = Esrc/max(max(sum(abs(Esrc), 2))); % normailized
toc
%% visualization
fringe = Eobs + Esrc; % I'll have a different formula in my code
normEsrc = reshape(sum(abs(Esrc).^2, 2), [nyp nxp]);
normEobs = reshape(sum(abs(Eobs).^2, 2), [nyp nxp]);
normFringe = reshape(sum(abs(fringe).^2, 2), [nyp nxp]);
close all;
xf0 = linspace(xboundl, xboundu, 500);
yf0 = linspace(yboundl, yboundu, 500);
[xfi, yfi] = meshgrid(xf0, yf0);
data = interp2(xf, yf, normFringe, xfi, yfi);
figure; surf(xfi, yfi, data,'edgecolor','none');
% tri = delaunay(xfi, yfi); trisurf(tri, xfi, yfi, data, 'edgecolor','none');
xlim([xboundl, xboundu])
ylim([yboundl, yboundu])
% colorbar
view(0,90)
colormap(hot)
axis equal
axis off
title('fringe thereo. ', ...
'fontsize', 18)
I didn't read your code because it is too long to do such a simple thing. I wrote mine and here is the result:
the code is
%spiral.m
function val = spiral(x,y)
r = sqrt( x*x + y*y);
a = atan2(y,x)*2+r;
x = r*cos(a);
y = r*sin(a);
val = exp(-x*x*y*y);
val = 1/(1+exp(-1000*(val)));
endfunction
%show.m
n=300;
l = 7;
A = zeros(n);
for i=1:n
for j=1:n
A(i,j) = spiral( 2*(i/n-0.5)*l,2*(j/n-0.5)*l);
end
end
imshow(A) %don't know if imshow is in matlab. I used octave.
the key for the sharpnes is line
val = 1/(1+exp(-1000*(val)));
It is logistic function. The number 1000 defines how sharp your image will be. So lower it for more blurry image or higher it for sharper.
I hope this answers your question ;)
Edit: It is real fun to play with. Here is another spiral:
function val = spiral(x,y)
s= 0.5;
r = sqrt( x*x + y*y);
a = atan2(y,x)*2+r*r*r;
x = r*cos(a);
y = r*sin(a);
val = 0;
if (abs(x)<s )
val = s-abs(x);
endif
if(abs(y)<s)
val =max(s-abs(y),val);
endif
%val = 1/(1+exp(-1*(val)));
endfunction
Edit2: Fun, fun, fun! Here the arms do not get thinner.
function val = spiral(x,y)
s= 0.1;
r = sqrt( x*x + y*y);
a = atan2(y,x)*2+r*r; % h
x = r*cos(a);
y = r*sin(a);
val = 0;
s = s*exp(r);
if (abs(x)<s )
val = s-abs(x);
endif
if(abs(y)<s)
val =max(s-abs(y),val);
endif
val = val/s;
val = 1/(1+exp(-10*(val)));
endfunction
Damn your question I really need to study for my exam, arghhh!
Edit3:
I vectorised the code and it runs much faster.
%spiral.m
function val = spiral(x,y)
s= 2;
r = sqrt( x.*x + y.*y);
a = atan2(y,x)*8+exp(r);
x = r.*cos(a);
y = r.*sin(a);
val = 0;
s = s.*exp(-0.1*r);
val = r;
val = (abs(x)<s ).*(s-abs(x));
val = val./s;
% val = 1./(1.+exp(-1*(val)));
endfunction
%show.m
n=1000;
l = 3;
A = zeros(n);
[X,Y] = meshgrid(-l:2*l/n:l);
A = spiral(X,Y);
imshow(A)
Sorry, can't post figures. But this might help. I wrote it for experiments with amplitude spatial modulators...
R=70; % radius of curvature of fresnel lens (in pixel units)
A=0; % oblique incidence by linear grating (1=oblique 0=collinear)
B=1; % expanding by fresnel lens (1=yes 0=no)
L=7; % topological charge
Lambda=30; % linear grating fringe spacing (in pixels)
aspect=1/2; % fraction of fringe period that is white/clear
xsize=1024; % resolution (xres x yres number data pts calculated)
ysize=768; %
% define the X and Y ranges (defined to skip zero)
xvec = linspace(-xsize/2, xsize/2, xsize); % list of x values
yvec = linspace(-ysize/2, ysize/2, ysize); % list of y values
% define the meshes - matrices linear in one dimension
[xmesh, ymesh] = meshgrid(xvec, yvec);
% calculate the individual phase components
vortexPh = atan2(ymesh,xmesh); % the vortex phase
linPh = -2*pi*ymesh; % a phase of linear grating
radialPh = (xmesh.^2+ymesh.^2); % a phase of defocus
% combine the phases with appropriate scales (phases are additive)
% the 'pi' at the end causes inversion of the pattern
Ph = L*vortexPh + A*linPh/Lambda + B*radialPh/R^2;
% transmittance function (the real part of exp(I*Ph))
T = cos(Ph);
% the binary version
binT = T > cos(pi*aspect);
% plot the pattern
% imagesc(binT)
imagesc(T)
colormap(gray)