How to Derive the Equation for Radial Dependence of Light in a Galaxy Image?

[Gantar]

Homework Statement

Explain how to derive the equation

Relevant Equations

I=[N*4*h*c*f^2]/[λ*π*η*t*S*D^2]

So we have a project and we are required to write how to derive the given equation yet we can't find any explenation, only the equation itself.
The equation is basically what we are supposed to use to get radial dependence of light for a given picture of a galaxy when we have values in photons per pixle and want to get W/m^2*steradian

N is the numbr of photons per pixle, h is Plancks constant, c is the speed of light, f is the focal length of the telescope, λ is the wavelength of visible light, η is the quantuum efficiency of the camera, t is time of exposure, S the surface of a pixle, D is diameter of the telescopes mirror.

 

[haruspex]

Homework Statement:: Explain how to derive the equation
Relevant Equations:: I=[N*4*h*c*f^2]/[λ*π*η*t*S*D^2]

So we have a project and we are required to write how to derive the given equation yet we can't find any explenation, only the equation itself.
The equation is basically what we are supposed to use to get radial dependence of light for a given picture of a galaxy when we have values in photons per pixle and want to get W/m^2*steradian

N is the numbr of photons per pixle, h is Plancks constant, c is the speed of light, f is the focal length of the telescope, λ is the wavelength of visible light, η is the quantuum efficiency of the camera, t is time of exposure, S the surface of a pixle, D is diameter of the telescopes mirror.

You have not defined I. (What does "radial dependence" mean?)
Much of the way the variables combine is reasonably obvious. E.g. can you at least group hc/λ into something you can give a name to? What else?

 

[Gantar]

You have not defined I. (What does "radial dependence" mean?)
Much of the way the variables combine is reasonably obvious. E.g. can you at least group hc/λ into something you can give a name to? What else?

Im guessing its called irradiance in english (sorry i lack a bit of english knowledge) basically we need to make a profile of irradiance for a galaxy, but i think that's not as important at the moment. I am more looking for getting grayscale to irradiance.
Okay so hc/λ I am guessing is energy of a photon, so therefore we need to divide it by time to get power, so that's where the wats come from. N is just so we have power of all photons combined and we divide by S to get power per m^2 right?
Then I am a bit confussed by the η , don't really see a connection to anything there.
Also the f^2 and D^2 they mostlikely have something to do with steradian?

Also thank you for responding and helping, i really appreciate it:)

 

[haruspex]

Okay so hc/λ I am guessing is energy of a photon, so therefore we need to divide it by time to get power, so that's where the wats come from. N is just so we have power of all photons combined and we divide by S to get power per m^2 right?

Yes, that all looks right. And that would be W/m² as recorded by the camera.

Then I am a bit confussed by the η

To work back to the W/m² actually striking the receptor one would divide by the efficiency.

Also the f^2 and D^2 they mostlikely have something to do with steradian?

Indeed. The terms you have left are $\frac 4\pi(\frac fD)^2$. Can you relate f/D to anything?