Modelling LED illumination for the poor people.

Hi, There!

I want to experiment with some calculations to estimate the intensity
distribution of an LED backlight. Maybe you can help me to get an
intensity distribution over x.

The Idea:

There is a surface along x (---) where I want to know the intensity
distribution.

In a distance h there is a second surface (___) with assembled LEDs
{x1, x2, x3, ...} with a certain intensity distribution Irel(phi)
and a certain gap g on the left side (x<0).

For simplicity I reduced this problem to 1-dimension to get started.

             d                 0
---------a-----x--------------+-------------------------> x
          |    /
         h|   /r
          |phi
          | /
__x0_____x1_____x2_____x3_____x4________________________
          g

The intensity distribuion according to the LED's datasheet is
approximately:

Irel(phi):=0.6*cos(phi)+0.4 (quite spheric)
with phi:=atan(d/h)

In a certain distance r of the LED, the illumination intensity
is approx.:

Ix(r):=1/r^2
with r:=sqrt(h^2+d^2)

I modelled d:=x-a to be able to move over several positions...
And when I put all this together I end up with:

h:15;
a:20;
f(x):=(0.6*cos(atan((x-a)/h))+0.4)*1/((x-a)^2+h^2);
plot2d(f,[x,-100,100]);

for one LED... looks basically okay.

But how can I get the superimposition of all LEDs with that
gap g (i.e. g:6)?
I think about summing up all f(x,a).
Unfortunately, my maxima syntax knowledge is at beginner's level.
Can you please help me to get the integral light of all LEDs depending
on h and g?

Thank you very much,

Clemens