How Does Light Intensity Vary with Distance from an Incoherent Extended Source?

[reasonableman]

I'm currently trying to look into the optics of extended sources. Google doesn't seem too helpful.

Anyway, I have just been thinking about it and thought that surely one of the easiest problems would be the intensity at a screen at a particular distance from an incoherent, spatial extended source.

To me it looks pretty much like an electrostatics problem, common as an undergraduate.

I'm envisioning a line of infinitesimal sources, which will each contribute some light to a point. Which assuming a Lambertian emitter will be the intensity of that infinitesimal point but taking into account the 1/r^2 drop off and the cosine of the angle of the point.

I then integrate over the whole source. However when I put this into maxima (can't do it manually) I get some horrendously long expressions.

Am I doing something wrong with my model and can anyone suggest an introductory text for extended sources?

 

[Andy Resnick]

It is covered in many optics courses, but disguised. In fact, what you are asking is the far-field diffraction pattern for an aperture, when the field aperture is not a (coherent) plane wave but an incoherent field, and the aperture is shaped like your source. Try that approach and see what happens.

 

[astrokreng]

I would suggest approaching this problem using the principles of geometrical optics. This involves considering light as rays and using laws of reflection and refraction to determine the behavior of light from an extended source.

One way to simplify the problem is to consider the extended source as a collection of point sources, as you have mentioned. However, instead of using an integration approach, you can use the concept of radiance, which is the amount of light per unit area per unit solid angle emitted from a surface. This can be calculated for each point source and then summed up to get the total radiance of the extended source. From there, you can use the inverse square law and the cosine law to determine the intensity at a particular point on the screen.

An introductory text that covers extended sources and geometrical optics in detail is "Introduction to Modern Optics" by Grant R. Fowles. It covers topics such as radiometry, photometry, and the behavior of light from extended sources. I would also recommend consulting with a professor or colleague who is familiar with optics to discuss your approach and any possible errors.