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Wild Card 005 “Is There Any Other Way to Get Apo-Performance on an Achro-Budget?”

Posted by Rick Shaffer   07/18/2004 12:00AM

Wild Card 005 “Is There Any Other Way to Get Apo-Performance on an Achro-Budget?”
Wild Card 005 “Apos Are Purely Wonderful! Is There Any Other Way to Get Apo-Performance on an Achro-Budget?”

In the 45+ years I’ve been doing amateur astronomy, the three most important advances in telescopes have been the Dobsonian mount, the Schmidt-Cassegrain telescope, and the apochromatic refractor. (Now, before you get all “het up” about your favorite being left off the list, remember that I’m just talking about advances in telescopes, not in eyepieces, filters, or in imaging equipment.)

Of the three advances, the most expensive has been the apochromatic refractor. In any but the smaller sizes, you have to have a pretty good-sized wheelbarrow to haul the money to “the refractor store” if you want to own a large apo.

Are they worth it? I think so, and, if I had the funds, I’d certainly own one. The reasons are many, but the first thing to consider is that an apo brings all the wavelengths we can see so close to the same focus that we see an almost perfectly color-free image. The figure will illustrate what I mean.

The two telescopes I’m using to demonstrate the difference in performance between an achromatic refractor and an apo aren’t real. Rather, they’re “cyber-matic” refractors. I designed the achro in a few minutes using an optical-design program called SODA, an old DOS-based program from the 80s. I also used SODA to create the apo, but I didn’t design it. Rather, I scaled an existing design to the same diameter and focal length as the achro. (That existing design is an excellent 8” f/15 John Gregory doublet.)

As you can see, the focal length of both lenses varies with the wavelength of light passing through it. However, the focal length of the achro varies by about 1.65-mm, while the same telescope made as an apo varies by only 0.15-mm. So, the color correction of the apo is about ten-times better than the achro.

If we looked through the achro telescope, we’d see a slight blue haze around bright objects when we focused this telescope for the yellow-green around 550-nm wavelength. That’s because the blue and red ends of the spectrum wouldn’t be in focus. Since our eyes aren’t as sensitive to red as they are to blue, we don’t see the red enough to bother with.

The apo would make it really hard for us to see blue haze at all. It’s an essentially perfect optical system.

You’ve likely notice that I made both these refractors rather long. The reasons are as follows:

1. I don’t know the specifications of the various refractor telescopes available today, and I don’t want to know them. And, of course, their makers are very happy to keep their proprietary designs secret. My purpose here is NOT to compare any existing refractors, but to give you an idea of the differences between the two types.

2. I also wanted to point out that, at this relatively long focal length, the achromatic refractor is actually quite good, although you will see the blue haze I mentioned earlier.

I’ve either owned or had access to achromatic refractors of 2.4”, 3”, 4”, 5.5”, and 6”. The 6” was an f/8, and I also briefly had access to an f/15. All provided great images, but in the larger sizes, I had to learn to ignore the blue haze, especially with the 6” f/8.

I’ve looked through a large number of quality apo refractors, and I’ve tested a couple extensively. Besides the obvious advantage of having about 90% less color than an achromat, an apo can achieve that superior color correction at a much shorter focal length. So, instead of having to lug a 6” f/18 refractor around, the owner of an apo might only have to haul a 6” f/7.5. Half the tube length might mean radically less than half the hernia!

An apochromat of 6”f7.5 will have more chromatic aberration than the f/18 apo I scaled for the graph above. But it will still have considerably less color than the f/18 achromat. It’s only disadvantage is price. Apochromatic objectives are made with relatively expensive optical glasses, and they’re often triplets rather than doublets, especially in the larger sizes, so there’s another lens to make on top of the cost of the glass.

Pilots have a saying:

“There are old pilots, and there are bold pilots. But there are no old, bold pilots.”

I think there’s a parallel saying we amateur astronomers could adopt:

“There are cheap apos, and there are good apos. But there are no good, cheap apos.”

Another consideration about apochromatic refractors is that if a designer is going to all the trouble to have enough elements or use expensive enough glass to make an apo, it’s not particularly hard to correct them over a wide field of view. So, an apo can be used from very low to very high power, and give very sharp images over a wide field. Because of the presence of the secondary mirror, Newtonian and Cassegrain reflectors have a lower limit on power.

A final consideration is that refractors in general provide as high contrast a view as can be obtained, because they have no central obstruction. Many folks will have nothing but a refractor for planetary observation on that score alone.

So, if you have some extra cash laying around, an apochromatic refractor would leave little to be desired.


If you have your heart set on a large apochromatic refractor, please don’t let me stop you. They’re purely wonderful telescopes, and if you invite me over for a look, I’ll be there with bells on. But there are alternatives. I’ll present a couple this week, and some more next week.

From the curve above, you can see that an achromatic refractor of long focal length can yield quite good images, albeit not as good as an apo. The big objection to such a telescope is its great size. There are several ways to at least partially get around that:

1. You can obtain a long focal-length achromat and mount it in a tube that breaks in half or folds in half. This makes it a bit easier to handle a long tube or to even lash it to the roof of your Volvo. But it doesn’t do anything about the need for a large mount, unless you have the telescope mounted on the roof of your Volvo permanently.

2. You can fold the refractor back on itself with a flat. This gets the eyepiece up near the objective. With the addition of a diagonal, you’d have telescope no less portable than a small to medium-sized Newtonian, and the eyepiece would be more easily accessible. There are some things to think about, though:

a. The two flats must be of very high quality. Otherwise, you’re System Strehl Ratio will plummet. (See “Wild Card 003.1 for a discussion of the System Strehl Ratio.)

b. The two flats should also receive high-efficiency coatings, because you don’t want to squander so much as a photon that you don’t have to. This factors into the System Strehl Ration, as well.

I’m surprised that there aren’t more folded refractors on Dobsonian mountings. An 8” f/16.66 refractor would be only about 72” long if folded in half, and that’s allowing for a rather long dew shield built into the tube. The 6” f/18 I used for the graph above would only be about 60” long when folded. AND, if you made it so that the tube would break at the midpoint, it would be only 30” long. (When folded up, it would be a bit chubby, though!)

(The reason I chose the unusual f/ratio for the 8” example above is that the late John C. Brandt made several of those. I also note that John Gregory designed a two-element apo that was 8” f/15. It runs through my optical design program cleaner than any other large refractor design I can find. However, it uses FK-52 glass for the flint element, which makes cost a bit high.)

On the refractor side, there’s one more option: the medial telescope. This is a radical hybrid of refractor and reflector. The great 19th Century lunar observer Philip Fauth made all his wonderful drawings of the Moon using such a telescope. The most popular of this type is known as the Schupmann, which uses a single element lens as its objective, but has a fairly complex optical system internally to obtain apochromatic performance over a fairly narrow field. The largest one I’ve ever seen is the 6” that Gerry Logan exhibited at RTMC several years ago. It was just plain exquisite, but, then, ALL of Gerry’s many creations are deserving of that adjective.

The largest operating Schupmann medial refractor in the World, a 13” is mounted in the MacGregor Observatory at Stellafane in Springfield, VT. It was designed and built by a group of dedicated members of the ATMs of Boston, including AstroMart member Scott Milligan. If you want to read about this, just google on “Schuppman Stellafane”.

That’s all on this subject for now. NEXT WEEK: Unobstructed reflector telescopes.


In last week’s column, I posed the following problem as part of the discussion of “Chaos & Critical Thinking”:

“Here’s a little problem for you: We know that the average pressure at sea level here on Earth is 14.7-lbs-per-square-inch. If we assume that the Earth is a perfect sphere, how much does the Earth’s atmosphere weigh? (BTW, this is a problem I couldn’t solve in my senior year Physical Chemistry class in college. May you see the obvious that I missed!) Answer next week.”

There was a lively discussion of the problem in one of the forums. And several folks got answers that are correct, although looking it up isn’t exactly sporting! Here’s how the problem is solved, including my rationale for the solution:

For there to be a pressure at sea level of 14.7-lbs-per-square-inch, that means that every square inch of the surface of the Earth must have that weight of air stacked up above it. The barometric pressure does affect this. An area where the pressure is low must have fewer molecules of air stacked up above it than an area of high pressure. But, on the average, every square inch of the surface has 14.7-lbs of air stacked up above it.

So, the problem comes down to finding the area of the surface of the Earth in square inches, and multiplying by 14.7 to get the weight of the atmosphere. The Earth has a radius of approx. 3963.324 statute miles. If we multiply that figure by 5280 to get feet, and by 12 to get inches, we have:

R(earth) = 3963.324*5280*12 = 251,116,230 inches.

So that I won’t get complaints, here it is in scientific notation: 2.51116230E+08 inches.

The area of a sphere is 4*PI*R^2. So, let’s plug that number into the equation to get the area of the Earth:

A(earth) = 4*3.1415926*(2.51116230E+08)^2 = 7.924273006E+17 square inches.

So, all we have to do is multiply by 14.7-lbs=per-square inch. That gives us:

W(atmosphere) = 14.7*7.924273006E+17 = 1.164868132E+19-lbs.

We can divide by 2000 to get tons. The answer is still a large number: 5.82E+15 tons. No wonder the innards of 6E+09-odd folks here on Earth stay in place!

Why didn’t I keep on with all those lovely digits? The reason is that we might convince ourselves that we can find the area of the perfectly-spherical Earth to the level of accuracy I was using, but we only know the first three significant figures of the pressure, so figuring our answer to any greater degree of accuracy wouldn’t do us any good.

If you want to think of this another way, even if you could indicate or display that you’re driving down the road at 74.99338075-mph, could you actually measure the diameter of your tires to that accuracy? As you drove down the road, would your tires stay the same diameter for any length of time? Or, is 75-mph a better way to put it?

Finally, when I ran into this problem in senior year Physical Chemistry in college, the above explanation was far from obvious to me. I tried to figure the number of air molecules in the first 1000-feet, and then the next, and so on, right up the altitude where the satellites orbit. Talk about overkill!

RICK SHAFFER is an astronomer, telescope designer, writer, and teacher who lives and works in Sedona, AZ. He’s done time for overkilling several different problems over the years….