This is the second How To Optimize telescope designs using the OSLO software program.  This is a free download from Sinclair Optics at: http://www.sinopt.com

Please email me, Steve Fejes with questions or comments at:  jsfejes@swva.net

I will start with an air spaced refractor objective.  I have previously showed how to enter data, analyze a design, and how to optimize.  Please see those pages if you are not familiar with this information because I am not going to spend much time explaining it again here.

OSLO should do a good job optimizing the color correction and wavefront errors.  OSLO might not find the best solution, but it should be pretty good.  My first goal here is to find a design which gives good correction of off axis coma.

The first and last surfaces in our design will control the focal length, and the coma.  I am going to optimize a few designs to find which one gives good correction of coma.  The air space and the two inner lens surfaces will control the color correction and the spherical aberration.

Make the following design by entering this information into the surface data window, radius 4 is 49000 which OSLO records as 4.9e+4.  Set the radius of surfaces 2, 3, and 4 as variables.

I have the IMS thickness set at a value a little less than the desired focal length.  I am not allowing this to vary, so OSLO will hold the focal length to this value.  This is how to tell OSLO where the light should come to a focus.

Now - optimize this design.  The outline below is a reminder about how to optimize, then focus.

First: Generate Error Functions, select:

   Generate Error Functions
      GENII Ray Aberrations
         OK - to accept default values

Second: Iterate

      OK - to accept default values

Now focus the optimized design:

      Minimum Spot Size (monochromatic)

Look at the spot diagram.  The image below is how OSLO optimized this design for me.

Congratulations, you have just optimized an achromatic refractor lens.  I would save this file for reference, I might call it 6inF12air1a, and put it in a folder labeled Bak1F2.  This way I would know what this design is just by looking at its name and folder.

I have shown the off axis spot diagram enlarged.  This shows that coma is not well corrected with this design.  The colored images should be concentric around the Airy disk.  This image has a lot of light spread out below the Airy disk.

Let's try to improve this off axis image, enter a new value for R1 (the radius of surface 1), we will try a longer radius.  Enter 1400 in the surface 1 radius box, you can leave R2, R3 and R4 the same.  OSLO will change them when you optimize.  Now optimize the design and see what happens.

Below is the result, which shows the off axis image still has coma, but it is the opposite from the above design.  This image has too much light above the center.  So, we have narrowed down the range for R1, it is between 900mm and 1400mm.

I would now save this file as 6inF12air1b.

Enter 1100 in the surface 1 radius box, then optimize.  My optimization is shown below.  Now we have found the value for R1 which minimizes coma in the off axis images.  This value of 1100mm is not perfect, but it's close to the optimum value.  I would save this file as 6inF12air1c.  This should be a good performer.

You can continue this process of trying different values for R1 until you are satisfied with the images.   I might try 1150 for my next trial, which I will not show.

There are other things to evaluate now, I would be most interested in the wavefront error, and color correction.  OSLO tends to do a good job with both of these, if there are enough variables.  The above design is fairly well corrected overall for a 6" f/12 achromatic refractor.

What else could be allowed to vary in order to find a better solution?

The lens thickness could vary a small amount, this is probably not worth while.
The air space between the lenses could vary, normally the best images are obtained with a very small air gap.
The glass types could be different, The following are common and inexpensive - crown glasses BK7 or K5 or BAK1 ; flint glasses F2 or SF2 or SF10 .
R1 could be different, we have covered this briefly.
The field angle could be different, maybe wider for a 2" diameter eyepiece.
The wavelengths could be different, this setup is the default.  But the "e" line at 0.546 is also good for visual use.

Now we will try a different approach.  What would happen if we set R1 as a variable, so all four surfaces could vary?

Below is the result, R1 is now a concave surface.  The images are worse than before.  I tried the same thing with the IMS set to -600mm and got similar results as the surface data below, so having a different IMS radius will not help.

I don't know why OSLO found this solution.  Overall this design looks worse to me than the starting design, but there are a few slight improvements in some areas.  I believe that OSLO was trying to reduce those aberrations the best it could.  I think this is a case where OSLO has different priorities than I have.

So, normally I set R1 as fixed, and allow the other three radii to vary.  This will keep R1 from becoming concave.  Another option is to set R4 to a fixed radius and allow R1 to be a variable.  This will limit R1 also.

What if we wanted to make R1 = R2.  Set the R2 radius as a minus curve pickup with the pickup source surface as 1.  Now optimize.  The results I got at first had a large wavefront error.  So I kept trying different values for R4, which is my non-variable surface.  I started with R4 = -5579mm.  My next try was with R4 = -5000mm, this was worse.  I tried R4 = -3000mm, this was much worse.

So, I tried R4 = 0, this was a little better, but still not good.  Next I tried a concave surface for R4, R4 = 5000mm.  This gave good results as far as the wavefront error is concerned.  I watch the Longitudinal Spherical Aberration graph.  The green line is the LSA for the primary wavelength.  I adjusted R4 until the green line was about vertical.  This should minimize the wavefront error.

The design below has pretty good images, but off axis they are worse than previously when we allowed R1 and R2 to be different from each other.  So, I conclude that this glass combination does not work as well with R1 = R2.

Next I tried making R3 = R2.  I set R3 as a curve pickup, with the pickup source as surface 2.  I was not able to get a good result with this setup.  I could not reduce the longitudinal spherical aberration enough with spherical surfaces.  An aspherical surface should be able to reduce this wavefront error.  It is best to avoid aspherical designs in general because spherical surfaces should be easier to make and test.  But on the other hand there are times when a slightly aspherical surface can give good images and should be fairly easy to make.

Here is an example I found optimizing with R2 = R3.  I needed to aspherize one surface to correct for spherical aberration.  I chose R3 because it is concave and can be tested directly if needed.  The following design has a conic constant of 0.02 for R3.  This is a very slight correction, but it makes a difference in the images.

I found the conic constant by entering different values for the conic constant, then refocusing and evaluating.  I watched the green line on the Longitudinal Spherical Aberration graph, I was trying to get it on the zero line in the center of the graph.  I came up with 0.02 which resulted in a good wavefront accuracy.  There is some off axis coma though.  So probably the first good design we found which had 4 different curves would give the best images.

Here is a trick I have used sometimes when I am having trouble getting a good correction for spherical aberration.  Let's say that we have a design where we need a conic constant of -0.5 to correct the spherical aberration.  We can enter a conic constant of +0.5 for that surface, then optimize.  After optimizing we can change that +0.5 cc to a sphere with cc = 0.  Then refocus and evaluate.  Sometimes this can eliminate the need for an aspherical surface by forcing OSLO to compensate for an opposite aspherical surface.  Figuring out how strong to make the conic constant is a trial and error process for me.  I should be able to show this on my next How To Guide when I optimize an apochromatic triplet.


Here are the items which can be set as a variable.  Click on Optimize, then Variables.

Click twice on the box under Type and you will see the following options.  You can choose one of these.  You can also add more surfaces and item to vary if you want.

You can also enter values for the minimum and maximum allowable range.  OSLO sets a high penalty for exceeding your limits, so it tries hard to keep within your limits.

This lesson shows how I would optimize an achromatic lens.

Steve             jsfejes@swva.net