Posts Made By: Brian Tung

Roland Christen wrote:
From a paper on MTF I read last year (cannot find it right now)I believe that the correct curves would show that the obstructed scope begins at a lower value at the lowest frequency at the left, and continues to a higher frquency level at the right hand part of the chart.

Surely not the paper you read, but there is an article in Sky and Telescope that gets at some of the same issues that you discuss. Note that in Rickey's article, the MTF curve very definitely is normalized to 100 percent at zero spatial frequency; it is not scaled downward to account for the lower light throughput. That is precisely the motivation for the "system characteristic function"--a singularly uninformative name, incidentally, but I admit I don't have a better one of the top of my head.

Anyway, for those who are interested, the article is "Secrets of Telescope Resolution," by Daniel Rickey, in the June* 2006 issue of Sky and Telescope.

*I corrected this; it used to say January 2006, but it's really the June 2006 issue.

I posted a classified on Astromart for one of these, but I was wondering if anyone listening to this forum might know of any other good way to get one. I do have a screw-on cap that I got through mail-order, but it's too thin and is difficult to get on and off.

Rick Olson said:

I have what I think is a stupid question, but I cannot find any publication that addresses it. Historically, I have always been interested in planets and DSO's. Recently, I have developed an interest in double stars. I have been actively seeking them out for observation. Now I am wondering why there are so many double stars. Why can't triple stars or quadruple stars, etc. exist? am I not looking in the right place? What laws of physics apply that keep multiple stars from attracting and orbiting eachother relative to double stars? :S

As Michael Connelley point out, non-hierarchical multiples don't seem to exist. I think it's pretty unlikely that they don't form, so the question is really, why aren't they stable?

Here's one stab at a reason. Consider the triples that are hierarchical. There are a couple of kinds (not necessarily mutually exclusive). One is where the AB separation is much less than the AC separation, so that we can take AB first as a pair, and then treat that pair as a single entity in the (AB)C pair.

The other kind is where A is much larger than both B and C, so that even if they are comparable distances, B and C don't affect one another and we can treat the AB pair independently of the AC pair. It wouldn't be much different from the Sun and any two of the planets.

In both cases, the bodies can be taken two at a time, which Newton long ago showed results in the elliptical orbits that Kepler characterized in his three laws. In the first case, A and B orbit each other in a pair of ellipses, and the center of mass of A and B orbits with C in another pair of ellipses. In the second case, B and C both orbit A in two distinct ellipses.

You may have heard of the so-called three-body problem, which remains unsolved more than 300 years after Newton's Principia Mathematica. What this means is that we don't know the full set of equilibrium orbits that three mutually attracting bodies can take, although we do know some of them, corresponding to cases where the stars *cannot* be taken one at a time. When I say "orbits," incidentally, these orbits may be very odd-looking indeed, with loops and swirls, not at all like the staid ellipses we are used to when considering only two mutually attracting bodies.

My guess is that these weird orbits are an indication that these three-body solutions, although in equilibrium, are not really stable. They probably exhibit some kind of positive feedback, so that once the stars begin deviating from their orbits, there is no mechanism that brings them "back on track," so to speak; rather, they tend to deviate even further, at an ever increasing pace, until one of the stars is ejected and the system can now be treated as a stable binary.

We might imagine, for instance, that as a deviation from equilibrium begins, two of the stars get closer to each other at closest approach than they had before. Each time, the close approach accelerates them more than at previous approach, which in turn brings the next close approach even closer, until finally, they approach so closely that the speed of the smaller one exceeds the escape velocity of the larger one, ejecting the smaller one clean out of the system.

This would be an example of positive feedback in operation. It may be that there is no three-body solution that exhibits negative feedback, which would serve to bring the orbits back on track if they began deviating, but I don't know if that's been proven.

It's a very interesting question!

Brian Tung

Mike Sloane said:

I've been using my 2x Barlow on a Celestron NexStar 5, and have been pretty pleased with the results. I have been inserting the barlow between the diagonal and the eyepieces, since that was the obvious way of connecting things up. Sure enough, things look about 100% bigger than with the eyepiece alone.

I've read in a couple of places that you can increase the effective magnification using a barlow, if you connect it before the diagonal (between the scope and the diagonal). I've read that you can get about 150% more magnification in this configuration, so that a 2x barlow suddenly produces images like a 3x barlow used in the "Obvious" configuration.

Is this true? I'm having trouble seeing how changing the position of the barlow would change the overall magnification.

Can someone explain how this works?

Thanks

I once wrote this in response to the same question:

The easiest way to understand how a Barlow works, I have found, is to consider just the on-axis rays--that is, those rays travelling parallel to the tube. Off-axis rays just confuse the matter at first blush. I will use a refractor to discuss it, but the same principle applies to a reflector or compound scope.

You have, perhaps, seen those cutaway diagrams of a refractor showing a shaft of light shining onto the objective lens. After passing through the objective, that shaft becomes a cone, which narrows to a point--the focal point of the objective. The cone then widens on the other side, where it is captured by the eyepiece and becomes a shaft again--the exit pupil of the scope/eyepiece. This is an approximation, of course, but a useful one. (This just to forestall any protests from the optical designer segment.) It is maybe important to note that the exit pupil is not in general the same as the width of the eyepiece; it is usually quite a bit smaller.

Let's play with some sample numbers. Suppose our scope has an aperture of 100 mm (about 4 inches). If the scope has a focal ratio of f/10, then the focal length is 1000 mm, and the light cone has a length 10 times longer than its width. If the eyepiece has a focal length of 10 mm, the magnification is 1000 mm / 10 mm, or 100x. The exit pupil is then just 100 mm / 100x, or 1 mm. In order to reach focus, the eyepiece must be placed 10 mm in back of the focal point. The distance between eyepiece and objective must therefore be 1000 mm + 10 mm, or 1010 mm.

However, suppose we put a Barlow between the objective and the eyepiece. When we reach focus, the Barlow is actually between the objective and its focal point--it is just a little less than 1000 mm from the objective. It captures the light cone just before it converges to a point. Since a Barlow consists essentially of a negative lens, its effect is to make that cone converge even slower--instead of a ratio of 10-to-1, it might make it a 20-to-1 cone, or a 25-to-1 cone, or a 30-to-1 cone. The exact change depends on how close the Barlow is to the original focal point.

Because the Barlow has stretched the light cone, the focal point is no longer 1000 mm away from the objective. It will be some greater distance away--exactly how far depends on the characteristics of the Barlow. If you've heard of Shorty Barlows, you know that design has a part to play in this. However far it is back, though, the eyepiece MUST STILL BE 10 mm away from the new focal point. And because the light cone is more stretched out, the eyepiece "thinks" it is seeing an f/20 or f/25 or f/30 scope, instead of an f/10 one. Thus, the power amplification is 2x or 2.5x or 3x.

But what makes it 2x or 2.5x or 3x? Is it just the strength of the lens? And how do variable power Barlows work?

Remember that the exact stretching of the light cone depends on how close the Barlow is to the original focal point. The closer it is, the less "time" the Barlow has to change the light cone, and the less stretched out the cone is. In fact, if you put it right at the focal point, the light cone is unchanged and comes out the way it did before you put the Barlow in.

The further in front it is, in contrast, the more stretched out the light cone is. In fact, if you move it far enough in front of the original focal point, the rays coming out of the Barlow will actually diverge and never come to a focus at all.

If you put the Barlow very close to the original focal point, then the new focal point isn't changed very much and is still very close to the Barlow. Since the eyepiece has to be 10 mm behind the focal point in any case, the distance between the Barlow and the eyepiece is relatively short and the power amplification low.

If, on the other hand, you put the Barlow further in front of the focal point, then the new focal point is quite a bit further back from where it would have been, and it now can be quite a distance away from the Barlow lens. In consequence, the eyepiece has to be far away from the Barlow also. The light cone is considerably stretched out, and the power amplification is high.

You can think of power amplification as depending essentially on the spacing between the Barlow and the eyepiece. It makes sense to do so because the usual way to use a Barlow is to put the eyepiece into the Barlow, and then put the whole combination into the telescope and try to focus it as if the combination were just one big eyepiece. If the distance between the Barlow and the eyepiece is 100 mm, then the new focal point has to be 100 mm - 10 mm or 90 mm in back of the Barlow, and you have to rack focus in and out until the Barlow lens is placed in the right position to reach that focus.

That's why a 2x Barlow can work as a 3x Barlow by putting it between the objective and the diagonal. In essence all you are doing is putting more space between the Barlow and the eyepiece.

Variable power Barlows work by allowing the user to adjust the distance between the Barlow lens and the eyepiece. Far-out spacings allow the Barlow to stretch out the light cone a lot and increase power. Close-in spacings require the Barlow the stretch the cone only a little bit and reduce power. The problem is that most Barlows are optimized for a relatively narrow power range. Thus it may work sufficiently well at 2x but be poor at 3x.

Many zoom eyepieces, in turn, are essentially variable power Barlows mated to an eyepiece all in one casing. When you turn the knurled ring, you are sliding the Barlow up and down the eyepiece shaft. The difference between this and the variable power Barlow is that since you will only be using one "eyepiece" with the Barlow, the designer can perform some optimization to make sure that the zoom works at least tolerably well at all powers. Of course, it is always possible that no such optimization will be done, and that is part of why zooms have such a poor reputation among many veteran observers (though that is beginning to change).

Larry Seguin said:

So how do you measure wavefront error at the EYEPIECE, anyway? Example: If your primary AND your secondary both have the same measurement (say, 1/15 wavefront leaving the surface of the mirror) then do you have a 1/15th wavefront optical system at the eyepiece? Or do you add the measurements together for (1/15th+1/15th=1/7.5th wave) at the eyepiece? A lot of talk is heard about "diffraction limited" optics, but is that at the primary or at the eyepiece? And what is considered an "acceptable" minimum for wavefront error AT THE EYEPIECE? Any help with these questions would be very greatly appreciated, thanks in advance!
Larry Seguin
Taos, New Mexico

Ideally, the rating should measure system wavefront error--that is, wavefront error at the eyepiece. You would not ordinarily expect the surface error of the primary and that of the secondary to be related in any way. (Exception: Any situation where the secondary is shaped or selected to match the primary, as in many commercial SCTs.) So giving just the primary's surface error would not be sufficient.

The wavefront errors represented by the primaries and secondaries (and other optical elements) also do not add in the way that you're probably used to. In this connection, we'll use RMS wavefront error; it is not very useful to use P-V errors. If one element contributes 1/40-wave RMS, and another contributes 1/30-wave RMS, the result is not 1/40 + 1/30 = 7/120 (which is about 1/17). Rather, since they're RMS, you add them by first squaring each, then adding the squares, then taking the square root of the result.

In this case, that gives you 1/1600 + 1/900 = 1/576, and then taking the square root yields 1/24. One caveat: This only works well for errors that cover the whole surface of the mirror, and are uncorrelated with one another. For example, in some sense, light has to deal with the surface error of a primary mirror twice, once upon incidence, and a second time upon reflection. If its surface error is 1/40-wave RMS, however, it does not add as 1/1600 + 1/1600 = 1/800, with the square root yielding about 1/28. No--the errors are perfectly correlated (because they're exactly the same), so in this case, they add the way you're used to: as 1/40 + 1/40 = 1/20. In short, a primary mirror's contribution to system wavefront error is double its surface error.

An error in an objective lens's surface is much less damaging. It depends on the index of refraction of the glass: the wavefront error contribution is roughly the surface error times the excess of the index of refraction over one. For instance, if the surface error is 1/30 and the index of refraction is 1.6, then the wavefront error contribution is 1/30 times 0.6, or 1/50. On the other hand, each lens has two surfaces, not one. If both surfaces yield 1/50-wave RMS of wavefront error, then they add as 1/2500 + 1/2500 = 1/1250, square root yielding about 1/35. (Also, with a lens, you must worry some about inhomogeneities, which are much less of a concern with mirrors.)

In spite of all this addition, we do generally concern ourselves more with the optical quality of the primary (whether it's a lens or a mirror) because it's so large, and it's rather more difficult to get a 1/50-wave RMS surface on a 10-inch mirror, say, than it is to get it on a 2-inch diagonal. It's also easier to replace a diagonal with a better one than it is to replace the primary mirror with an equivalently better one. It's the element that represents the telescope to many of us: we might replace the tube, the focuser, even the mount, and still retain some of the telescope's identity, but many of us (myself included) would feel that something vital had changed if we swapped out the primary.

As I understand it, it used to be that some unscrupulous manufacturers would give primary surface errors where system wavefront errors were expected, making their telescopes look better than they were. Fortunately, that practice has essentially vanished.

Brian Tung

Michael Baca said:
So anyway this is getting really long. My question is are refractors or reflectors better for astromonmy? I understand the the views are "crisper" on refractors but have the ghost image (sorry can't remember what those colors seen on the edge are) then reflectors, but what other then that and the different types of mirror/lenses is the difference?

As others have noted, this is often a contentious issue. In practice, it's a non-starter; optical performance is determined chiefly by aperture, and only secondarily by optical quality and design.

That being said, differences exist. The following are just my opinion, but of course I think my opinion is right. They are also not absolute--just because I say a design is better for something doesn't mean that the other designs can't do it also. Just not as well, I think.

Refractors and SCTs for astrophotography. Reflectors and apochromatic refractors for solar system work. SCTs and Dobsonian-mounted reflectors for portability. SCTs and reflectors for deep sky. Refractors and SCTs for ease of maintenance.

Now, before you all get started, let me say that I am already factoring in that large-aperture refractors tend to get bulky, or color-ridden, or expensive. You can't avoid all three. Aside from that, I've got reasons for saying what I do, but I don't want to make this a long essay...

jack bitters said:
I could use some help I have a scope that I rescued from the scrap pile it is a Mead 114 Reflector and is in good cond but when I look at an object I see three Images, like at the moon one is in the middle and one on boths sides kinda lighter !! What can I do to correct this problem
Any Help would be great!!

That's a bizarre problem, seeing as you experience it with all the eyepieces. Still, if you can get your hands on someone else's eyepieces, which are known to work well with some telescope or another, try them out to confirm that it's the telescope, and not the eyepieces.

It just doesn't sound like a collimation issue, since all collimation does is align the telescope's optical axis with that of the eyepiece; it can't create a triple image all on its own. The only thing I can think of is that either the primary or the secondary, or both, is not a first-surface mirror like it ought to be, and you're getting ghost images off the front of the mirror. That seems unlikely, too, given that it's a Meade. Still, if that's the case, you're better off ditching the telescope and buying a new one.

One last possibility: Is your Meade a longish tube (around 3 to 4 feet long), or is it stubbier than that?

Philip Canard said:
I bought Rutten and van Venrooji's book, Telescope Optics. What grabbed my attention was a chart on page 219 and another on page 221 that shows that contrast is higher in obstructed scopes vs. refractors at the highest magnifications possible with diffraction limited optics. It varies a bit according to central obstruction, but on average at the top 30% of magnification the obstructed scope wins. This seems to be confirmed in comparisons between my perfectly collimated Stellarvue 80mm refractor and LOMO 102mm Maksutov-Newtonian. It has been said you need about 20% to 25% more aperure in an obstructed design to get the same resolution as in a refractor, but in my case the LOMO very clearly outperforms the Stellarvue. The LOMO is without question the superior lunar and planetary scope, due to the increased contrast at high mags that I typically use with both scopes. Of course, for deep sky work at low mags, the situation could reverse according to the charts, but I'm not really seeing much to that effect. The light gathering ability is about equal in both scopes, since the central obstruction does cut down on light throughput a bit in the Mak-Newt. The mirror in the LOMO doesn't cover a 23mm Axiom or 30mm Ultima as well as the Stellarvue does and vignetting is apparent. That's the most obvious difference at low mags.

At least the book exposes the myth that obstructed optics are always lower contrast than unobstructed optics. It is entirely magnification related and also related to percentage of central obstruction with the most obstructed designs getting the best contrast at the highest possible magnifications allowed by a particular aperture. Sort of like wild camshafts in high performance engines. That tends to make the obstructed scopes the true "Ferraris" of the scope world. More limited in scope of usefullness, but unsurpassed in that narrow band of performance they favor.

This seems compelling, but I would caution you to interpret the graph carefully. First of all, resolution is shown (in units of lp/mm) along a linear scale. In practice, this is misleading, because detail size tends to distribute itself according to some kind of power law. As a result, there aren't just as many details between, let's say, 120 and 180 lp/mm as there are between 60 and 120 lp/mm; there are more in the latter range. Most of the visible interesting detail on Jupiter falls in there, for instance.

Secondly, even though the MTF is higher for the obstructed scope than for the unobstructed one in the highest frequency range, both functions are very low in an absolute sense. Visually, it's a nonstarter, partly because of seeing, partly because at those highest resolutions, your eye is going to need all the help it can get. You can increase the magnification in order to increase the sampling rate for your eye, but then your brain has a harder time finding the gradient. (These sorts of considerations, incidentally, are what lead to that 50x per inch rule of thumb, stuff like that.) Just keep in mind that neither scope is a good performer on low-contrast, high-frequency details, in an absolute sense; they work better on high-contrast objects like double stars.

Thirdly, as Roland points out, the transmission of the obstructed scope is lower, and this may make features of equal contrast (but lower brightness) more difficult to see, anyway.

In short, this doesn't really mean as much as it seems like it does.

Joel Munoz said:
I'm planning to build a fast newtonian as a grab n go scope. Maybe 5" f/5 or 6" f/5 from Meridian: http://www.meridiantelescopes.com/primary.htm. This will be for low power viewing. What performance can I expect from these mirrors?

That depends on what they mean by 1/3-wave mirror. If they mean that its surface is accurate to 1/3-wave, that's pretty bad indeed, since the error in the image will be double the error in the surface--i.e., 2/3-wave.

If they mean that the "wavefront error"--the error created in the image as a result of imperfections in the mirror--is 1/3-wave (meaning the mirror's surface is accurate to 1/6-wave), that's merely a mediocre mirror.

In any event, I would forego any place that says 1/3-wave is pretty good. It may once have been, but these days, you should be able to find a promise of 1/4-wave, and have a reasonable chance of getting it, too.

Michael Baca said:
I was thinking about buying a 3X barlow and perhaps stacking it with the 2x for better views of Venus and what not. But I'm not quite sure it will help all that much. I do want to get some more powerful EP's also. But I'll see what this weekend brings.

Good stuff! I would pass on the 3x Barlow. About the only thing of interest to see on Venus is its phases. There are a couple of other things: near its inferior conjunction (when it lies between us and the Sun), its crescent can occasionally be seen to wrap entirely around the disc of the planet. Also, if your eyes are exceptionally sensitive to the far violet, there's some minimal cloud deck detail you can see. However, most people have essentially no sensitivity at that wavelength.

I would work on Jupiter. It and Mars are my favorite planets, showing a wealth of detail under the right conditions. Between the two, Jupiter is larger and easier to observe for a beginner. I usually want at least 200x to observe it.