# Light beam reduction

1. Sep 13, 2006

### GeorgeSol

I've been wondering if it is possible for a large aperture lens, or mirror, to receive parallel rays of light, converge them, then diverge them into a smaller beam of parallel rays as they exited the optical device?

If so, directing this greater flux density into a telescope matching the beam's diameter should increase the apparent surface brightness of an extended celestial object, a non-point source (e.g. star). This would improve imaging exposure times and allow for the design of a telescope which one could see celestial objects in color - a colorscope.

Improving surface brightness of extended objects is supposedly a violation of the 2nd law, but I don't see it.

Any ideas?

2. Sep 14, 2006

### Kurdt

Staff Emeritus
Well a device that takes parrallel rays and condenses them into a smaller parallel beam is a telescope. Are you attempting to stack telescopes in an attempt to get a better image?

3. Sep 14, 2006

### GeorgeSol

Normal telescopes, as far as I know, do not produce parallel rays. They focus light which allows an object to appear magnified, or enlarged on a sensor.

However, if a pre-scope could be added that would create parallel rays, I would expect objects would appear brighter, but would have less magnification.

The optical equations which deal with these indicate you can not achieve it. Consider the following....

Exit Pupil = Aperture/ Magnification

The exit pupil is the diameter of the cone of light exiting the telescope. The eye has an "entrance pupil" of between 5mm to 7mm, depending on age, etc., in darkened conditions (2mm to 3mm for daytime). Therefore, scopes and binoculars, are designed to get most of the light into the eye by limiting the exit pupil.

My hope is that the above equation is a design equation and not one physics has cast in stone.

If parallel rays exit the scope, they would offer no magnification. A magnification of one, per the equation, would mean the exit pupil diameter would equal the aperture of the scope. A 12 inch aperture telescope with parallel ray output would produce an exit pupil of 12 inches. Nothing would be gained, if this equation is mandated by physics.

It just seems to me that some optical arrangement would easily allow an output of parallel rays of less diameter.

I don't see the Zeroth law preventing it as their is no gain in "temperature" over the objects, only increased flux density. I also don't see how the 2nd law would prevent it.

The 2nd law would be an issue if the claim was to increase surface brightness at little to no loss in magnification. There are only so many photons to play with, afterall. :)

Astronomers say it can't be done and will site the 2nd law but fail to explain why, at least so far.

4. Sep 14, 2006

### Kurdt

Staff Emeritus
The eye piece magnifies a telescope image. The telescope itself produces a parallel beam. In effect what you are suggesting is just the same as making a single telescope with a mirror or lens the size of the of your pre-scope.

Last edited: Sep 14, 2006
5. Sep 14, 2006

### Kurdt

Staff Emeritus
For example look at the ray diagram of a refracting telescope near the bottom of the page on the following web page.

http://www.antonine-education.co.uk/Physics_A2/Options/Module_5A/Topic_1/topic_1_lenses_and__refracting_t.htm [Broken]

I hope this makes things clearer.

Last edited by a moderator: May 2, 2017
6. Sep 14, 2006

### GeorgeSol

Yes, you're right. What was I thinking? Apparently, without the eyepiece, they aren't parallel, but what's a telescope without an eyepiece.

However, increasing the aperture would, according to the equation, increase the exit pupil. Surprisingly, this will not increase the apparent surface brightness of celestial objects. An 8 meter telescope does not improve the surface brightness as would be seen by the naked eye, but does magnifiy it signicantly.

Yet, using the pre-scope idea for illustration only, greater flux density would seem to occur, and should cause an object's surface brightness to increase. Is this likely? What am I missing?

7. Sep 14, 2006

### Kurdt

Staff Emeritus
I haven't worked with telescopes in a while so apologies for that eyepiece stuff but you got what I was getting at so thats alright. Really your idea about the pre-scope gathering more light and making things brighter is exactly how telescopes work now. The reason we can see some stars with telescopes and binoculars that we can't see with the naked eye is because they have gathered light over a larger area and concentrated it into something that we can see. If you want to observe fainter objects you generally make a larger objective lens or mirror to cover a wider area. You pre-scope idea would work but its not practical because you have twice the amount of optics and as I hope you know optics is an expensive business. Unfortunately the idea is unnecessary.

8. Sep 14, 2006

### GeorgeSol

I should point out I haven't worked with their design at all. I have thought about buying optical design software to try different ideas, but I have a lot on my plate already.

Yes, but that is for stars which do not increase in size (ie magnification). Larger aperture will, of course, gather more light but for "extened objects", e.g. nebula, this light is spread out due to the magnification. Albeit, your eye will be able to see extended objects appear as if they were somewhat brighter due to physiological reasons, which I don't really understand much. But the light flux per unit area of an extended object, with the aid of a telescope, on your retina, or on a sensor, will be less than the flux per unit area on your unaided retina. The rule is...you can not increase this flux density. But, I ask....why not?

If we can establish a double telescope, or other impractical contraption :), will increase surface brightness, then the optical experts can take it from there. If not, I'll do it myself. First, I have to know if it can be done using any gedankenexperiment. :)

9. Sep 15, 2006

### Kurdt

Staff Emeritus
I don't see any reasaon why your setup should not work if you want to make it.

10. Sep 15, 2006

### GeorgeSol

Odd, you're suppose to!

It's suppose to be a violation of the 2nd law, or some radiation law. How's your thermo? Mine is rusty, but what little I recall, I just don't see why it would be a problem either. I tried bautforum.com but the answer was not resolved there either.

I had a little correspondence with a professional in optical accessories. He revealed that a telecompressor can improve surface brightness by as much as 44x, but, apparently, only when the exit pupil is so large it requires this much reconcentration. He indicated that we can not increase surface brightness beyond that of the naked eye, but offered no infomration why this was his view.

"Why not" is still the question?

One weak explanation as to why it is not done, assuming it could be, is due to the purpose of the scope for the amount of money invested -magnification is too important to sacrifice for surface brightness. Most astronomy is not visual, thus longer exposure times will indirectly raise the surface brightness of any object. However, recently, more very fast exposure times with subequent image stacking provides superior resolution. One amateur, using a small telescope (10 or 12 inch I think), recently imaged Jupiter and its moons that showed surface features on Ganymede!

If this is the case, it is time to rethink using today's lower cost large apertures to improve surface brightness and reduce exposure times. [Also, there is still that desire I have to see objects in full color. ]

Do you know where else I could go for help?

Last edited: Sep 15, 2006
11. Sep 15, 2006

### Kurdt

Staff Emeritus
Well I'll have a proper look into it if you wish and see if I can find any explaination. Like I say I'm more into general relativity and quantum mechanics at the minute so I might have to re-educate myself on a few things since its been a while since I've dealt with them. If you can find out what specific 2nd law you're alluding to aswell that would help. if I remember correctly the second law of thermodynamics relates to heat engines or something so I doubt its a thermo law. Most likely a black body radiation one. As for other sources, I frankly have no idea. You could try contacting some professionals more into optics or if they have an optics forum somewhere they might know better than me. Where to find an optics forum? I do not know.

I'm fairly busy but you have grabbed my interest so when I get any spare seconds I'll do some research. Good luck though if you head off anywhere else.

12. Sep 15, 2006

### GeorgeSol

Great if you can, or direct me somewhere.

Hmmmm...the photoelectric effect has popped into my head a time or two about this topic. We can't increase the energy but there is no reason why we can't concentrate the volume. I see no qm issue with this idea, but, admittedly, I know very little of qm.

It applies to all energy exchange. My favorite definition is...."heat won't flow from a cooler to a hotter, you can try if you like, but you far better notter".

The claim against surface brightening appears to stem around this idea that light can't be concentrated more than it is (perhaps in the focal plane only).

Yes, there are some but they're pretty inactive.

Thanks.

Perhaps another physicist is in the house, also. [hint]

13. Sep 15, 2006

### cesiumfrog

This has to do with Liouville's theorem, conservation of phase space volume; I'm not sure whether it relates to entropy. I'll try to post something intuitive regarding surface brightness later, or you could google some astronomy info.

14. Sep 15, 2006

### Labguy

Some of the posts above are at least 20% correct and the rest are ridiculous. Looking for any laws of thermodynamics to figure a "pre-telescope" is a dead end.

Your first quoted line above is correct, but "The exit pupil is the diameter of the cone of light exiting the telescope" is totally incorrect. In any telescope, the diameter (aperture) of the light entering the scope (or any optical instrument) is the entrance pupil, not exit pupil. The objective (lens or mirror) does not produce parallel rays, it forms a "virtual image" at the focal plane where it takes a device of some type to form an image. For visual, this would be an eyepiece as Kurdt mentioned somewhere above. It is the eyepiece that makes the large amount of focused (conical) light turn back into a parallel smaller bundle of light, the exit pupil. Then, your eye takes in the parallel light from a large beam (entrance pupil) that has been converted to a small beam (exit pupil). The smaller the exit pupil (different eyepieces) the greater the magnification.

Brightness and image size,of extended objects, depend on just focal length and magnification. More magnification = less surface brightness.

From an earlier post a long time ago:
and:
All of this has been hashed before,so do a search and find the old thread.

15. Sep 15, 2006

### GeorgeSol

That would be most appreciated.

Try to look past the grammar and address the issue. At least 40% is correct.

The pre-telescope idea is an illustratitive tool to emphasize improvement to flux density. Improving the flux density onto the retina, or sensor, without change in magnification should improve surface brightness. Is this not correct?

The bold emphasis may help see your error. However, I did not mean to say the exiting light was conical, but I thought it would pass inspection.

I had not seen the term entrance pupil applied to the light entering a telescope. Is this a common use?

Good point. However, a telecompressor will reduce the exit pupil without increasing the magnfication. So, optics have power over this rule. It is this kind of thing that I am trying to learn; which rules can be broken, and which can't?

Yes, of course, since we only have a fixed amount of flux. Yet, what if we, somehow, could increase the flux for any given exit pupil? This would increase the surface brightness. But, how this can be done is my quest.

Your quote from another thread covers a lot of nice information concisely, yet none of it directly helps this issue of surface brightness, however. I tried searching but have failed. Is there a thread which shows searching terms?

Last edited: Sep 15, 2006
16. Sep 15, 2006

### Labguy

Try to look past the grammar and address the issue. At least 40% is correct.

Ok, I'll concede that.

The pre-telescope idea is an illustratitive tool to emphasize improvement to flux density. Improving the flux density onto the retina, or sensor, without change in magnification should improve surface brightness. Is this not correct?

Yes, but all you need to do for that is increase the aperture of the telescope and use an eyepiece that will keep the same magnification as in the original, smaller scope. BUT, that will also increase the exit pupil which can soon become too large to enter the eye, as described in one of my "brightness examples" in my last post. It will also change the size of the "virtual image" falling on any type sensor where it would likely become larger than the sensor 's detection area.

The bold emphasis may help see your error. However, I did not mean to say the exiting light was conical, but I thought it would pass inspection.

Yes, the entrance pupil is the light entering the scope, the exit pupil is the beam diameter leaving the scope/eyepiece combination. My answer was correct, but your post said: "The exit pupil is the diameter of the cone of light exiting the telescope" which is not correct. It (exit pupil) is not a cone.

I had not seen the term entrance pupil applied to the light entering a telescope. Is this a common use?

Yes it is. Exit pupil can be figured by (1) the entrance pupil/magnification OR by turning the math around where it equals (2) (Eyepiece focal length / telescope f-ratio)

Good point. However, a telecompressor will reduce the exit pupil without increasing the magnfication. So, optics have power over this rule. It is this kind of thing that I am trying to learn; which rules can be broken, and which can't?

A telecompressor will shorten the effective focal length (EFL) of a scope and a teleconverter (Barlow lens) will lengthen the EFL. Either one of these will change both the image scale AND the power of any given eyepiece.

Yes, of course, since we only have a fixed amount of flux. Yet, what if we, somehow, could increase the flux for any given exit pupil? This would increase the surface brightness. But, how this can be done is my quest.

As above, no way to do it except increase the aperture. It will increase image scale and/or magnification, but the "flux" will remain a constant total

Your quote from another thread covers a lot of nice information concisely, yet none of it directly helps this issue of surface brightness, however. I tried searching but have failed. Is there a thread which shows searching terms?

The brightest you will ever see "surface brightness" is with your unaided eye. Period. BUT, the image scale is so small that you can't resolve any detail in any object with a small angular distension. A telescope will get you more magnification to see detail, but every increase in power will result in less surface brightness. That has and will always be the trade-off between brightness and power. That was also explained in one of the "telescope brightness" items I posted before. Think about it, an object like the Crab Nebula only emits a finite number of photons. If you increase the image scale (with a telescope) you spread the same number of photons over a larger apparent area, so the surface brightness will be decreased.

Last edited: Sep 15, 2006
17. Sep 16, 2006

### cesiumfrog

What is surface brightness? A measure of the power (energy per unit observation time) received from some source, per unit area of instrument aperture, per unit (solid-) angle of the source. (Note that the power received from a source can be determined by that source's total luminosity together with what fraction of the source's sky that is subtended by the receiver aperture's area.)

Now for the Liouville theorem: volume in phase space stays constant. Imagine the light beam from a torch: Close to the torch the beam has a narrow cross-sectional area and, at each point there, there are photons travelling in a wide range of directions. Much further from the torch the beam has a far wider cross-sectional area but the rays there are almost parallel (there is a proportionally narrow range of photon momenta at any such point). Even if you try (say, using some lenses) to reduce part of the beam onto a smaller area, the photons that reach any given point in this smal area are again moving in a wide range of directions.

$$B_{Surface} = \frac P {\Omega\ A_{aperture}} = \frac{L \frac \Theta {4\pi}}{\Omega\ A_{{ap.}}} = \frac{L ({\frac{A_{ap.}}{A_{total}}})}{\Omega\ A_{ap.}} = \frac{L_{source}}{(\Omega\ A_{total})_{Liouville}} = \frac{L_{source}}{({(2\pi)(4 \pi R_{source}^2)})}$$
$$\Omega$$ is subtended by source, at observer. (Also describes range of photon momentum there.)
$$\Theta$$ subtended by aperture, at source.

Geodesics in GRT are just one application of Liouville's theorem. The above equation is missing various factors of redshift (since time, energy and area become subjective) but should illustrate the idea that surface brightness is a constant of the source.

The relation to entropy http://www.av8n.com/physics/phase-space-thin-lens.htm" [Broken]has to do with how small an area you can focus light onto.. and hence, whether you can use sunlight to heat something above the temperature of the sun.

Last edited by a moderator: May 2, 2017
18. Sep 16, 2006

### Labguy

Which is a clearer way of stating exactly what I was trying to explain in my post above. The link also says:
Which IS exactly as I explained above but with different wording. Thanks for the link.

19. Sep 17, 2006

### GeorgeSol

I only marginally grasp the equation, but I think it may show that the suface brightness can not change regardless of whether you move closer or further. If so, it can be shown in a lucid explanation. If you double the distance between you and the object, the amount of from the object will be reduced as the inverse square of the distance traveled. But, the apparent size of the object will also be reduced by the inverse square. Therefore, they will cancel and the same surface brightness will be seen.

However, on second thought, the theorem seems to deal more with the light angle. I learned that if a magnfiying glass was placed in front of an infinitely wide isotropic light source, it would not be able to burn a leaf any faster than without a magnifying glass. [I recently bet an ice cream that a magnifying glass at the sun would burn a leaf faster than without using a magnifying glass. Surprisingly, it will.] Since only the parallel rays into the glass would be concentrated onto the leaf, the other rays will be concentrated elsewhere due to their angle. Moving the glass further from the source will increase the number of parallel rays but fewer photons will arrive. Is this a better explanation of the theorem?

Now take two observers who have adjacent telescopes, if their optics are perfect, and light had no obstructions from an extended object, they will each see the object at the same surface brightness (per unit area). The total flux will be twice that of just one observer. If we could take the flux from one and add it to the other, we would double the surface brightness seen. This, hopefully, is a little different than usuall.

I thought I had a handle on the inability to increase surface brightness by using the zeroth law. Using a magnifying glass to concentrate light onto something, say a leaf, we can realize that the spot can not be hotter or brighter than the source because if it could, then we could reverse the light and produce a hotter source; which, of course, is impossible.

However, once again, if we augment the light from one area onto another, we may be able to produce a brighter image. We would be taken energy, i.e. photons, from one area and routing them onto another.

This works easy enough for mass. My rain gauge has a large opening at the top to increase the normal accumulation of drops in order to amplilfy the volume received. Here, we can see the flux density is increased by the funnel action at the top. We could use numerous examples, of course. The temperature of the water, ignoring the P.E. difference, is not higher, so the 2nd law is fine. Only an increase in flux has been demonstrated. Yet, we can not do it with photons and maintain an image, for some reason.

Ooohh, there she be, apparently. Thanks, that has to be it. [Let me babble a little and see if anything sticks.]

Yet, consider this gedankenexperiment... Let's take mirrors and surround one hemisphere of the sun. All the mirrors will concentrate their reflected light onto one small spot on the surface. Will this not increase the surface temperature at that spot? Albeit, even if we cut a hole in the middle of the mirrors to allow observation of a solar area, unfortunately, I see no way to redirect the light into the path seen by a telescope. As for ideas, I suppose the rain gage holds more water, so to speak.

So, in my limited mind, it still makes sense that if we could combine the light of two scopes of equal aperture, then we could double the brightness. Yet, I can't see how. One would think larger aperture would work, as per the rain gauge model. I still don't grasp why not.

Perhaps, if I understood the dX/dt aspect of phase space, I would see why light is so different to restrict flux concentration.

If we increase photon flux onto an object, will it increase temperature? Maybe this is a good approach.

Last edited by a moderator: May 2, 2017
20. Sep 18, 2006

### cesiumfrog

No it will not. If it did, that spot would heat the rest of the sun further, ad perpetuum. Try sketching the ray diagram.

As for babble, expressing your ideas succinctly promotes sharper thought!