This will be the third of a series about how to optimize telescope designs using the OSLO software program. This is a free download available from Sinclair Optics at: http://www.sinopt.com
Please email me with questions or comments at: jsfejes@swva.net
Let's start with an apochromatic triplet lens. Apochromatic generally
means that a lens has exceptional color correction, much better than a
regular achromatic lens.
Here is Peter Smith's apochromatic triplet objective design. This is a very good design, which you can use to compare with your designs. This is an oiled design, which uses a few drops of oil between the glass surfaces. These glass surfaces need to have closely matching radii for this to work right.
Notice how I set this lens up, I did not enter two surfaces for the first lens, then two more for the second and third lenses. I used the first surface of the second lens for the second surface of the first lens.
There are a couple of things I want to draw your attention to. The first one is the Chromatic Focal Shift. Notice how the curve is shaped like a backwards "S" instead of the "c" shape of a normal achromatic lens. It is possible to keep the chromatic focal shift smaller like this when you use three different kinds of glass. Remember that the chromatic focal shift shows where the different wavelengths come to a focus. In this example the 0.400 wavelength (violet) comes to a focus about 2mm behind the best focus. This is very good, especially compared with a normal achromatic refractor's color correction which is about 10mm. So the improvement here is about 5 times better color correction for the violet compared with a normal refractor lens.
This color correction is the key to why apochromatic lenses can have such good images. Selecting the right glass types is very important. There are many combinations which can give good results. But most of them will require very steep curves to get such good color correction. Steep curves will require thicker pieces of expensive glass. And it also means that the tolerances are very tight for the steep curves.
The other thing to notice is the Longitudinal Spherical Aberration graph.
Notice that the scale is small compared with a normal achromatic design.
And he has the blue and red lines well balanced, and on opposite sides
of the green line. The green line is at the zero LSA vertical line.
Having the blue line on the left of center means that in this design the
violet light will have less longitudinal spherical aberration. The
violet line will be on the right side, farther away than the red line.
But still this is very good compared to a normal achromatic design.
There are two ways to get excellent color correction with lenses. The first way is to have a very long focal ratio, like f/40 for a 6" diameter lens, or f/25 for a 4" diameter lens. This makes a long tube and is not very practical.
The second way to get exceptional color correction is to use special glass. This allows excellent color correction with reasonable focal ratios. This special glass is expensive, starting about seven times the cost of BK7 glass. A 6 inch disk of BK7 glass may cost $125 in the year 2002. So, apochromatic glass can give excellent color correction, but it will cost a lot more money.
SPECIAL GLASS TYPES
There are two catagories of special glass types.
The first catagory is the most expensive, it is Fluorite and the Fluorocrown glasses. These are ED glass, which means Extra low Dispersion. A 6 inch disk of Fluorocrown glass (like Schott's FK51) costs about $2500 in the year 2002. Fluorite is even more expensive than FK51. These are often used in a doublet design combined with a more common glass type. This combination can give the best color correction at the shortest focal lengths.
The other catagory of special glass uses a glass type like Schott's KzFSN4. A 6 inch disk of KzFSN4 costs about $840 in the year 2002. KzFSN4 is combined with two different glass types to make a triplet lens design. The other two glass types must be carefully chosen to match the Kz type glass. Peter Smith's design used Ohara's BPM51 glass for the center lens, which is very similar to Schott's KzFSN4.
To make a good triplet design you will need to select the right three glass types. I will give you a list of glass types in three catagories. This should help you get started selecting glass. This is just a starting point because there are many other glass types which can be used. You will want to look at the relative partial dispersion in blue light, and in violet light to select your glass types. See Rutten and van Venrooij's book Telescope Optics for more detail.
Catagory 1
BAFN10 - is the most available, BAF52,
BAF51, BAF3 are harder to find
Catagory 2
KzFSN4 - is the most available, KzFS1 works
better but is hard to find
Catagory 3
BK7, K5, SK4, SK16, BAK1, - all of these are good
So, you want to pick one glass from each of these catagories. For example, BAFN10 and KzFSN4 and BK7. This would make a good combination - if you can find a good optimization. You could put either the BAFN10 or the BK7 as the first lens element.
Peter Smith used a different glass type from Catagory 1. He used BAF4. This is a common glass type which works very well. The problem with BAF4 is that the dispersion value is a lower number than KzFSN4. This means that OSLO will try to use the BAF4 as the negative element. The negative lens needs to be the KzFSN4 to make an apochromatic design. So, while Peter Smith shows that BAF4 can work well, OSLO will not optimize such a combination easilly.
There are other Kz type glasses available too, but I won't go into detail
on them now.
OPTIMIZING AN APOCHROMATIC DESIGN
Let's see if we can optimize an apochromatic triplet design. This will be a 4" f/12 design. Please enter the following data, then set it up to optimize. Then save the file for reference and in case you need to start over again.
Here is the first optimization results. The images are pretty good. There is some longitudinal spherical aberration. A conic constant of 0.02 on surface 1 will minimize it.
So, why don't I enter -0.02 conic constant on surface 1, then optimize it again. Below are the results. I have removed the conic on surface 1, so it is back to a sphere now. And this time OSLO has optimized the design so that after I removed the conic constant of -0.02 there is very little spherical aberration.
This is a pretty good design. I will save it. This design is very close to the first optimization we did above. The inner curves differ between these two designs by only a couple of millimeters.
In fact you might be interested to see what happens if you change R3 by a millimeter or two, then refocus and evaluate the design. Does the design give better images when R3 is 234mm or 235mm? It looks like it, but what is the Strehl ratio? The polychromatic Strehl ratio is a better way to evaluate a design like a good apochromatic design once you get images this good.
Anyhow it is an interesting exercise to see how a small difference in the radius of curvature affects the images. This will help you understand the tolerances for the lens radii. The two inner curves R2 and R3 have the tightest tolerances. The tolerance for R1 is a bit looser, and R4 can vary a lot by comparison.
Now we might be able to do a bit better if we set R1 at a different value. So, if you want you can enter a new value for R1, say 740mm. Then go through the optimization again. Save the new design, and evaluate it. Is it better, or worse? If it is worse then I would try setting R1 to 780mm and optimizing from this starting point.
HOW TO SCALE A DESIGN TO A DIFFERENT SIZE
An optical design can be scaled to a different size. Right click on one of the gray SRF (surface) boxes. Move your mouse cursor down to the Scale Lens, then click on either option. I have highlighted Scale Lens By Constant, click this and you will see a small window (below).
Enter the factor to scale by here. 0.75 will give 3/4 the size, click OK. This will scale the diameter and the focal length.
If you click on Scale To New Focal Length, then you need to enter the focal length you want. If you enter 1500, then 1500mm will be the effective focal length of the design. Click OK.
A LESS EXPENSIVE TRIPLET DESIGN
Can a good design be made with less expensive glass types? Yes, but you will need to learn which glass types you want to try. Here is an example I came up with using Schott's KzFN2. This glass should cost only half as much as KzFSN4, but it is not as easy to find. And KzFN2 has less dispersion, so it will need steeper curves than KzFSN4 for a similar design.
KzFN2 has a refractive index of 1.52944, and a dispersion of 51.63. I have designed a 4" f/15 design with has good color correction compared with a normal doublet refractor design. But you will notice that the chromatic focal shift is the "C" shape. I have not found a way to get the "S" shape by OSLO's optimizing three wavelengths to a common focus with this glass combination.
You will see that this design has a 2mm air space between the first lens and the second lens. The second and third lenses are oiled together. This design gives good color correction. You should analyze this design if you care about this kind of lens.
Here are the three catagories of glass for a KzFN2 triplet:
Catagory 1
BALF5, BALF4, SSK51, BAK4, SK10, SK2
Catagory 2
KzFN2
Catagory 3
BK7, SK16, K5, SK4, BAK1
You will notice that Catagory 3 is the same as the first list for KzFSN4, but Catagory 1 is different.
BALF4 should be the easiest to find in catagory 1, while BALF5 might give a little better correction. SSK51 might also be a good glass to try.
Any lens with a dispersion over 55 may give good results for catagory
3. I have listed some of the best possibilities above.
I hope this has been a helpful exploration of apochromatic designs. There are several other Kz type glasses available which can give good results also. I will leave it to you if you want to explore these.
Steve Fejes jsfejes@swva.net