Understanding view-/formfactor for radiation with a specific example There is radiation coming from a point source (black body).
How much of the total emitted energy (from the point source) hits a spherical surface given by $\phi = 0 - \pi $ and $\theta = 0 - \pi/2 $?
What are the correct names for the angles $\phi$ and $\theta$, and what do these angles actually tell you, is it what the radiation from the point source actually hits (from the perspective of the point source)?

I know about the following equation, but what do you use as the limits for the integrals, the angles given above? :

 A: The equation that you have is right, but actually a little more complicated than you need for this problem. A point source is infinitely small and you don't need to integrate over it . This problem can be handled without working through integrals formally.
Consider a full sphere around the point (rather than the partial surface that you've got).  In that case, all of the radiation leaving the point hits the sphere ($F=1$). Also, since the point emits equally in all directions, the is flux uniform on the surface. Therefore the fraction of the radiation that reaches a section of the sphere is equal to the fraction of the total area of the sphere that the section makes up.
Using $ 0 \leq \phi \leq \pi$, divides the sphere in half. Then $ 0 \leq \theta \leq \pi/2$ divides the remaining hemisphere in two.  So the section has an area $1/4$ of the total area and will receive $1/4$ of the emitted radiation. That's equivalent to saying $F_{1\rightarrow2}=1/4$.
To clarify the notation that you asked about $\phi$ and $\theta$ just spherical coordinates, used here to conveniently define the surface. You see them called the azimuthal and polar angles, respectively, in many cases.  There are other names and notations used as well.
The integral, you're integrating over two surfaces. In practice, the area integral will usually be broken into two integrals over single dimensions that describe the surface (as was done with $\phi$ and $\theta$.  
The two $\theta_i$ values describe the relative orientation of the surfaces at a given location. Any two differential areas in the integral, you can be connected with a line. The $\theta$s are the angle between the normal direction of each surface and the line connecting them. So, $\theta_1=0$ would mean that the first surface is exactly facing the second.
