# Boost :

Subject: [boost] [units] - learning to use
From: Janek Kozicki (janek_listy_at_[hidden])
Date: 2011-11-24 09:25:00

Hi, I wrote a short function that integrates Huyghens spherical wave
for diffraction. (This is a single slit experiment btw).

I have some questions, marked with (*)

double integral(
const quantity<length> x // x - position where light intensity is calculated
, const quantity<length> R // R - distance from slit to screen
, const quantity<length> D // D - slit width
, const quantity<length> lambda // lambda - wavelength
, double steps // steps - number of integration steps // (*)
)
{
complex<double> i(0,1);
complex<double> a(0);
static const double pi = 3.14159265358979323846; // (**)
quantity<wavenumber,complex<double> > k=2*pi/lambda;
quantity<length> d=-0.5*D; // d - position on the slit
quantity<length> dd=D/steps; // dd - width of integral step
// integrate from -d to d: exp(i*k*r)/r
for( ; d<= 0.5*D ; d+=dd )
{
quantity<length> r=sqrt(pow<2>(R)+pow<2>(x-d));
a += (dd*exp(i*k*r)/r).value(); // (***)
}
return pow<2>(abs(a));
}

(*)
it should be `int steps` but if I write it this way I get a compilation error here:
quantity<length> dd=D/steps; // dd - width of integral step
That looks like a conversion problem.

(**)
why do I need to define pi ? I expected to find it somewhere, but I couldn't.

(***)
it seems strange that I need to take .value() here. The result is
dimensionless, why can't it directly convert to complex<double> ?
There is a risk that .value() would be expressed in millimeters or
angstroms or whatever (maybe depending on dd), and then .value()
would return a wrongly scaled number?

Another question, why this works:

quantity<length> wavelength ( 632.8 *nano*meters);

and this does not?

quantity<length> wavelength = 632.8 *nano*meters;

Of course I know about extra copying, and waste of CPU resources on
execution, when compiler isn't able to optimize this away (and
usually it is able to do that). But why the heck this simple
assignment can't work?

PS: I am attaching a short test version of this program, it's in
polish, but I hope you don't mind.

```--