In our last post we started the optimization process in Zemax on a wide angle lens. In this post we will continue the optimization process on the lens, showing how the lens can be improved further and increase the as-manufactured performance.
Our first step is to add additional operands to the merit function to help make the lens more manufacturable. First, we want to control the glass index to be less than 1.85. This will help to decrease the material cost because many high index materials are more expensive. Controlling the index also helps avoid potential problems that high-index glasses sometimes exhibit. To control the index we use the MXIN operand and set the target to 1.85 with a weight of 1.
We also want to control the ray angles at each surface interface to be as small as possible. This will help reduce the sensitivity of the lens to manufacturing tolerances. To do this we use the MXRE and MXRI operands (maximum ray angle of exitance and maximum ray angle of incidence, respectively). We set the surfaces to include all surfaces 2-21. Then specify the normalized field and pupil coordinates to target the marginal rays of the maximum field. We then set the maximum angle to 50 degrees and set the weights to 1.
Finally, we would like to control the contribution of spherical aberration of each surface. If the surface spherical contribution is controlled in a lens it will make the lens less sensitive to misalignment. This is because the lateral shear of spherical wavefronts creates coma, which will significantly reduce MTF. For more information see our post on Surface Spherical Contribution.
To control the spherical aberration contribution we use the SPHA operand to target surfaces with a large spherical contribution. The target depends on the F/# of the lens as described in the surface spherical contribution post linked above.
Below is a Seidel Diagram, showing the different aberrations induced by each surface in the lens. We can use this diagram to identify which surfaces need to be targeted by the SPHA operands.
When controlling the spherical contribution it is often best to start reducing incrementally for each surface. This allows the Zemax to “spread out” the spherical aberration across other elements in the system.
After adding these operands to the merit function we do a local optimization, then a Hammer optimization and we get the results below:
The spot radius on axis is 1.3um and 6um at the corner. This is fairly good, but we also notice that the curvature on surface 16 is almost hemispheric.
We can control this with a few operands in the merit function:
We use the CVVA and DMVA operands to get the surface curvature (1/radius) and diameter, respectively. Then we use the PROD operand to take the product of the merit function lines 20 and 21 (surface 16 curvature and diameter). We then force this value to be less than 1.9 so that the surface cannot be a hemisphere (if D/R = 2 you get a hemisphere).
We also want to disable the clear aperture SD margin under the Surface 16 properties and add a 0.4mm chip zone to the surface. This allows the lens to meet the D/R < 1.9 requirement a bit easier and since the surface is buried (middle surface of the doublet) we do not need as much margin at the edge.
We also notice that surface 12 is not manufacturable with traditional grinding methods so we place a pickup solve on the surface to pickup the semi-diameter from surface 11.
With these manufacturability targets we do another local and hammer optimizations and get the following results:
The lens is looking close to where it was before the manufacturability operands were added. The RMS spot size on axis is 1.23um and 4.9um at the corner.
At this point we notice that element 3 is a very weak lens element. Maybe this element can be removed and get similar performance?
Below is the performance after removing element 3 and re-optimizing:
This 10-element design performs better than the 11-element design! We now have an RMS spot radius of 1.12um on axis and 4.25um at the corner. The MTF has also reached the design specification of 20% at 145 lp/mm. The next steps on this design will be to make sure it is manufacturable which will lead into tolerance sensitivity analysis.
Completed Zemax File:
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