MATLAB: I tried to call a function but it failed

functionmatlab function

When i tried to return a value from the function (rate) to main file it failed and it shows undefined variable R_tow.

%main file
clc
clear all
close all
T=1;
tow_min=0;
tow_max=T;
tow=0.5
while (tow_max-tow_min)>0.02
    tow_bar=(tow_max+tow_min)/2;
    if crn(tow_bar)==crn(tow_min)
        tow_min=tow_bar;
    else
        tow_max=tow_bar;
    end
end
tow0=tow_bar;
disp("tow0="+tow0);
rate(tow0);
("R_tow="+R_tow);
plot(R_tow,tow0);

 function R_tow=rate(tow)
PH0=0.1
Pa=10;
Q=20;
y=0.1;
N=3;
yi=[1,3,5];
Pdbar=0.2;
Pi=[3,4,2];
alpha=sqrt((2*y)+1)*qfuncinv(Pdbar);
beta=0
    for i =2:N
    x=1+((Pi(i)*yi(i))/((1+sum(Pi(i)*yi(3:N)))));
    beta=beta+log2(x);
    end
fs=100000;
z=1+sum(Pi(2:N).*yi(2:N));
S=(Pa*yi(1))/z;
x1=(1-(qfunc(alpha+(sqrt(tow*fs)*y))))
y1=log2(1+(((tow*Pa/1-tow)-sum(Pi(2:N)))*yi(1))/z)
R_tow=PH0*(1-tow)*x1*y1+beta;
%disp(R_tow)
 end

Best Answer

It is fundamental to the idea of functions in all programming languages that the variable names inside the function are internal to the function, that assigning to a variable inside the function does not affect the calling environment unless special arrangements are made.

Your assigning to the R_tow variable that belongs to the function rate() does not affect any variable outside of rate().

In order to get what you want, at the place you have

rate(tow0);

You need instead

R_tow = rate(tow0);

This R_tow is not the same variable as the one inside of rate(). Assignment of results is positional not according to name.

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MATLAB: Error: Too many output arguments

Hi, this is because you function crn is not returning anything. If you want to return dR_tow then use the code below.

function dR_tow = crn(tow)
    Q =20;
    Pi=[0.3,0.4,0.2,0.5,0.4];
    Pa=10;
    %tow=0.5
    Pdbar=15;
    Y=4;
    fs=10000;
    yi=[1,3,5,2,3];
    y1=[1,2,5,8,7];
    y2=10;
    yj=[2,3,4,5,2];
    N=5;
    z=sum(Pi(2:N).*yi(2:N));
    S=(Pa*y2)/(1+z);
    alpha=sqrt((2*Y)+1)*Q^-1*Pdbar;
    a=sum(Pi(2:N).*y1(2:N));
    yj=yj(3:N);
    yj=[yj 0];
    b=sum(Pi(2:N).*yj);
    bet=sum(log2((1+(sum(Pi(2:N).*yi(2:N))/(1+b)))))-(a/(1+a));
    A = ((1-(Q*(alpha+(sqrt(tow*fs)*Y))))+((1-tow)*((Y*sqrt(fs))/(2*sqrt(2*3.14)))*tow^(-0.5)*exp(-(alpha+(sqrt(tow*fs)*Y))^2)/2));
    B = (log2(1+((tow*S)/(1-tow)))+((1-tow)*(1-(Q*(alpha+(sqrt(tow*fs)*Y))))*(S/(((bet+1)*(1-tow))+(S*tow))*(1-tow))));
    dR_tow=((A*B*10^(-7))/3);
end

Hope this helps!

MATLAB: Spherical aberration and Chromatic aberration

The following code lets you simulate the PSF associated with spherical aberration (as well as diffraction). You need to specify the PSF sampling pitch, the wavelength, the aperture diameter, the system focal length, the amount of spherical aberration, and the PSF array size.

The idea is to calculate a wavefront with spherical aberration and then use the Fourier transform to calculate the PSF. You need to be careful with sampling, hence the assert() statement.

You can easily include other aberrations as well, if desired. Simply modify how the wavefront is calculated.

You can check that this code is working by setting RMS_SA to zero (i.e., simulate a diffraction-limited system, in which case the PSF is an Airy disk). Then the first null of the PSF should have a radius of 1.22*lambda*focal_length/aperture_diameter.

You'll have to do some work to simulate a spectrally broad system. In that case you could simulate a number of monochromatic PSFs and then sum them together. You would need to know how the spherical aberration varies as a function of wavelength (variation as the reciprocal of wavelength would be a good estimate - i.e., longer wavelengths have less aberration) as well as the spectral output of the source, the spectral transmittance of the optical system, and the spectral responsivity of the detector. The product of these spectral terms would be used as the weights in a weighted average to calculate the broadband PSF from the monochromatic PSFs.

Once you get the PSF you can convolve this with your scene to simulate imaging performance. imfilter() may work, but I like convnfft ( http://www.mathworks.com/matlabcentral/fileexchange/24504-fft-based-convolution) from the File Exchange. You could use conv2() as well.

Good luck,

Eric

%%Define parameters
clear all;close all;
psf_sampling = 0.5e-6;%focal plane sampling in meters
lambda = 0.6328e-6;%wavelength in meters
N = 256;
aperture_diameter = 0.0254;%meters; 1 inch
focal_length = 5*aperture_diameter;%meters
RMS_SA = 0.25;%RMS spherical aberration content in waves
%%Calculate pupil plane sampling
delta_fx = 1/(psf_sampling*N);
x_pupil = (-fix(N/2):fix((N-1)/2)) * delta_fx * lambda * focal_length;
[X_pupil,Y_pupil] = meshgrid(x_pupil);
R_pupil = sqrt(X_pupil.^2 + Y_pupil.^2);
R_norm = R_pupil/(aperture_diameter/2);%Pupil normalized to aperture diameter
assert(max(R_norm(:))>=sqrt(2),'Sampling is not sufficient to reconstruct the entire wavefront.');
%%Create wavefront
W = RMS_SA * sqrt(5) * (6*R_norm.^4 - 6*R_norm.^2 + 1);%Spherical Aberration wavefront
W(R_norm>1) = 0;
E = exp(1i*2*pi*W);%Complex amplitude
E(R_norm>1) = 0;%Impose aperture size
figure;imagesc(angle(E)/(2*pi));colorbar;title('Wavefront Phase (waves)');
%%Create point-spread function
psf = abs(fftshift(fft2(ifftshift(E)))).^2;
psf = psf/sum(psf(:));%Normalize to unity energy
x_psf = (-fix(N/2):fix((N-1)/2)) * psf_sampling;
figure;imagesc(x_psf*1e6,x_psf*1e6,psf);
title(sprintf('PSF with %.4f waves RMS of Spherical Aberration', RMS_SA));
xlabel(sprintf('Position (\\mum)'));
ylabel(sprintf('Position (\\mum)'));

Best Answer

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