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Dear Zemax Community!

I am doing some learning and practice in Optical Lens Design using YNU raytracing. It is quite fascinating to put paraxial functions in the spreadsheet and work out how ray bends (chromatic and aberrations) at each surface defined during propagation. Big shout out to Kats at “Lens Design - A Pencil of Rays” for spending lots of his time to put all the materials together. 

I have an issue about the comparison of the results obtained from YNU raytrace with the ZEMAX Merit function. The curvature of each lens surface is quite close between YNU and ZEMAX, however the ZEMAX results is still not as good as parameters extracted from YNU. I think the root cause is with the define and setup of the merit function. 😵 I tried a long time last night with all different settings and parameters.


The telescope objective consists of a crown and flint lenses (see Fig.1), the key parameters are listed below:

  • Focal length is designed to be 100mm
  • F/# of 5, means D is 20mm
  • Crown is N-BK7 and flint is SF10
  • Crown has a thickness of 8mm, flint is 3mm. The air gap is 5mm
  • Used wavelength F, d, and c in ZEMAX and YNU Rayrace calculation
Figure 1. Separated telescope lens.​​​​​

Please see the Table.1 below, the last two columns are the final results from YNU and ZEMAX optimzations. They are quite close, however, I tried all sorts of things but could not get the R4 of ZEMAX to bend more. The motivation is through lens bending, to improve the spherical aberration (SA), Coma (CM) and Chromatics. All depends on the lens power. Here other 3rd order aberrations are not considered to be optimized. 

In Table. 3, the last column shows the target values for SA, CM and Chromatic, 0.03, 0.01, and 0.0015. You can see that the YNU iteration 3 (the 4th column) achieved the target, but the ZEMAX’s SA doesnt... 

 

  YNU Raytrace  
Curvature initial 1 2 3 ZEMAX
R1 50 50 44.25 44.7 45.33
R2 -53.173 -53.173 -61 -60.16 -62.535
R3 -60 -53.0012 -46.3656 -46.336 -47.533
R4 -791.35 -285.92 -169.27 -168.876 -161.003

Table.1 Four surface curvatures for the crown and flint lens. Iteration 1 to 3 are obtained from YNU whereas the fourth column is from ZEMAX.

Iterations initial 1 2 3 ZEMAX Target
Spherical Aberration 6.497663 4.535099 -0.15034 0.010082 -0.10144 0.03
Coma -0.60336 -0.54679 0.126841 0.071973 0.090979 0.1
Astigmatism 1.250316 1.28068 1.376386 1.372256 1.346841 -
Petzval Sum 0.673154 0.674524 0.66874 0.669346 0.671332 -
Field Curvature 1.923471 1.955204 2.045125 2.041602 2.018173 -
Distortion -0.09593 -0.07951 -0.08492 -0.08318 -0.07309 -
Longitutional Chromatic 0.001178 0.00112 0.001204 0.001158 0.001779 0.0015
Transverse Chromatic -0.00255 -0.00246 -0.00251 -0.0025 -0.00235 -

Table. 2 Third order aberration calculated in YNU. Due to the lens geometry, here we only focus on Spherical Aberration (0.03), Coma (0.1), and Longitudinal Chromatic (0.0015).

 

Figure.2 ZEMAX optimized results. The Lens Data corresponds to the Table. 2 curvatures in the last column.

 
Figure. 3 YNU optimized results. The Lens Data corresponds to the Table. 2 curvatures in the 4th column.

The merit functions that I used for ZEMAX in Figure.2 shows here. I think the problem is here, but I could not figure out. In the end, I have attached the zmx file in case. If you guys can give me some suggestions to improve the merit functions?

 

Hi Yadong,

The quality of a design is defined by the size of the merit function used to optimize it. I can see in your example the merit function you use, and the OPD map of the system, but I cannot see how to establish that the YNU is ‘better’. Better in what regard?

One small comment on your merit function: you have three EFFL statements targeting the EFFL to be 100 at all three wavelengths. You cannot achieve this with just two glasses, and it’s usual to optimize only for a single wavelength and then to let the residual aberration fall as it will when being balanced against all the others.

  • Mark

Oh wait, I think I see what you mean. If you enter the values from the YNU caculation (only the last one seems different) then

 

Note the values of the EFFL and their contribution to the MF. Approx 18%of the merit function comes from the effl operands. Reoptimize and you’ll get a lower value of the merit function

some of the improvement comes from the EFFL statements and the rest from the OPD improvements.

  • Mark

Hi Yadong,

The quality of a design is defined by the size of the merit function used to optimize it. I can see in your example the merit function you use, and the OPD map of the system, but I cannot see how to establish that the YNU is ‘better’. Better in what regard?

One small comment on your merit function: you have three EFFL statements targeting the EFFL to be 100 at all three wavelengths. You cannot achieve this with just two glasses, and it’s usual to optimize only for a single wavelength and then to let the residual aberration fall as it will when being balanced against all the others.

  • Mark

Thanks Mark for your suggestion. I will definitely note down this. I did not realize that the select three waves (c,d and f) here Zemax cannot handle to find a optimal. Now I understand why in Scott’s (from OpticsRealm) tutorial that he normally chose the d line for optimization. 
Yes, I understand that there is a physical limit with the cemented doublet. To improve the 3rd order aberrations, I guess Cooke triplets needs to be used here.


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