I'm reading a text on ray tracing. There is this section about radiometric quantities where radiance is defined as
$L = \frac{d^2\Phi}{dA cos\Theta d\omega}$
$\Phi$ is the radiant flux
$\Theta$ is the solid angle (sr) subtended by the observation or measurement
$\omega$ is the incidence angle measured from the surface normal
This is just one of many equations using $d$ and $d^2$. I'm pretty sure that $d$ has something to do with differential equations. I already read some texts on differential equations but I still don't understand the meaning of $d$ and $d^2$ in this context.
Can someone explain this to me or point me to some reference/resource/book whatever?
Especially the $d^2$ puzzles me.
Best Answer
This is fundamental notation in differential calculus. I suggested you pick up a book on the subject and read up; you won't regret it, as its very useful knowledge whatever you do!
In your specific cases, the expression is in fact a second-order partial derivative. The
ds should be written in the curly style - this may be a fault of wherever you saw the expression from.Here are some of the basics of notation, to get you started.
$\frac{dy}{dx}$ = the derivative (rate of change) of $y$ with respect to $x$. (1st order derivative)
$\frac{d^2y}{dx^2}$ = the derivative (rate of change) of $dy/dx$ with respect to $x$. (2nd order derivative, also called curvature)
Note: a common elementary mistake is to treat differentials as fractions. They are indirectly related, but do not treat them the same.