View Full Version : Surface Brightening II

2006-Sep-21, 04:11 AM
There may be a graphical approach to understanding why an extended objects surface brightness can never be increased optically. Lens designs and arrangements just can’t do it.

[Since this is a fresh approach, two actually, to surface brightening, the prior surface brightening thread (http://www.bautforum.com/showthread.php?t=46471) was not bumped.]

Of course, thermodynamics also has something to say about it, as Ken valiantly tried to convey its merits in the previous thread. Thanks to a physics forum helper, there is an interesting web page illustrating the problem in trying to improve the surface brightness of an object. It uses Liouville’s theorem.

The term used there is phase space (http://www.av8n.com/physics/phase-space-thin-lens.htm). [That just sounds cool to me.]

Another approach I offer for your review... I have hope that it will demonstrate graphically why surface brightening is limited to the level the naked eye observes.

Imagine using a telescope to look at a small region of the sun (see crude heliochromological depiction below. Hmm, the yellow is unlikely, though. We’ll use a white region to avoid color comments :) ).

We will only consider parallel rays for simplicity. These rays, those vertical lines in the illus., travel into this simplified refractor and exit as parallel rays into the eye. Lets skip over the discussion that might be raised due to the apparent concentration of rays into the eye and go to the next illustration. [It is a concentration but it represents a larger area of the sun, restricting any improvement in surface brightness.]

http://img181.imageshack.us/img181/2381/surfbright1dc1.th.jpg (http://img181.imageshack.us/my.php?image=surfbright1dc1.jpg)

Now look at the next illustration. In order to increase the apparent surface brightness of an extended object, more light emitted from the same emitting spot must be captured and routed to the same spot on the eye (retina). This would be necessary if we want to boost the brightness. The ray, R4, is one of those rays our eye does not receive, normally. If we can combine it with the R3 ray, or photon if your prefer, in order to see brightnening at that spot.

The problem is that the R4 is entering the eyepiece lens (the little concave one) at a different angle than the R3 ray. Snel’s (it should be one "l", right?) Law shows that if you change the incident angle, you change the exit angle, too. Therefore, there is no way to allow the eye to capture photons emitted from the same point to be recombined in any consistent manner. Even if you structure it to align two rays, the others can not be similarly aligned.

http://img221.imageshack.us/img221/2750/surfbright2kv4.th.jpg (http://img221.imageshack.us/my.php?image=surfbright2kv4.jpg)

Am I close, yet?

[Added: I may have trouble getting on line for a few days]