Image:Fresnel integrals.svg

This picture shows the two Fresnel integral functions. I made it working with Octave and Gnuplot, post-processing the output with Sodipodi.

First I created a file called fresnelS.m with the following content:

function y = fresnelS(x)
y = zeros(1,length(x));
F = @(t) sin(t.^2);

for i = 1:length(x)
    y(i) = quad(F,0,x(i));
end

then I created another file called fresnelC.m with the following content:

function y = fresnelC(x)
y = zeros(1,length(x));
F = @(t) cos(t.^2);

for i = 1:length(x)
    y(i) = quad(F,0,x(i));
end

In the same directory where these two files are, I ran the following Octave code:

t = 0:0.01:5;
S = fresnelS(t);
C = fresnelC(t);

F = [t; S; C];
F = F';
save -ascii 'fresnel_integrals.dat' F;

thus creating the file fresnel_integrals.dat. Then, to create the image, I used the following Gnuplot code:

# set the output
set terminal svg
set output "fresnel_integrals.svg"

set title "Fresnel Integrals"

# axis properties
set xrange [0:5]
set yrange [0:1]
set xlabel "x"
set xzeroaxis linetype -1 linewidth 0.5
set yzeroaxis linetype -1 linewidth 0.5
set xtics axis
set ytics axis

plot "fresnel_integrals.dat" using 1:2 title "S(x)" with lines linewidth 2,\
     "fresnel_integrals.dat" using 1:3 title "C(x)" with lines linewidth 2

Finally I opened it with Sodipodi to change the stroke style.

April 2006

Alessio Damato

see below