Optimizing a design

[dibyendumajumdar]

I am working on an optimizer - its restricted to optimizing an existing design only. I wanted to get a view on what analysis results to target for following:

• coma
• spherical aberration
• astigmatism

I assume one target is the third order Siedel aberrations?
I also wonder if the ray and opd aberrations can be a meaningful target?

[mjhoptics]

This came up recently in a different issue. See this comment for using a ray fan as the optimizer target. The classes in the raytr.analyses package for ray grids and wavefront could be used to supply the aberration targets. For the types of lenses you've been looking at, 3rd order aberrations are inadequate as a sole measure of performance.
Mike

[dibyendumajumdar]

Hi Mike

Thank you for the reference - I had looked at that already.

I wanted to give more idea of what I am trying to do. Sorry this is a longish post.

I am interested in reconstructing past optical designs - especially 35mm photo lenses. In most cases this involves taking prescription data from patents, applying modern glass types and then re-optimizing the design.

In some cases I am also trying to rebuild the design where no patent data is available: by measuring the curvatures from published documents, assigning glass types, and then attempting to optimize the design. Usually to do this, I need some information regarding the original design beyond just the diagrams, because diagrams are often not accurate.

Here are two examples of my attempts:

• Noct Nikkor 58mm f1.2. For this one I used published paraxial information to assign glass types before attempting to optimize. Best try so far
• Leica Noctilux 50mm f1.0. For this fortunately there were publications that identified the glass types used. Best try so far

There are some other folks doing something like this. The notable example is this one:

• Zeiss Otus 55mm f1.4

So far I have not used ray-optics for my attempts. This is due to following reasons:

• I am not as comfortable with Python.
• I need some features that are not available by default:
  • Getting all the data from analysis without any plotting / GUI. (I have now figured out ways to do this)
  • Modifying the analysis in some cases - for instance using hexapolar circular patterns for ray tracing to produce spot diagrams.

Currently I am using an implementation based on GNU Optical - but this is limited to ray tracing and generating spot diagrams. I am also calculating paraxial data constrain the design.

I face some challenges when trying to optimize designs:

• The optimization needs to be constrained somehow otherwise it changes the design too much so that the lens no longer has the original focal length or back focus distance etc. I use paraxial parameters as constraints. I use weights to influence the minimization.
• It seems insufficient to just optimize spot sizes; the MTF output seems not fully correlated. Unfortunately I have no easy way to check MTFs at the moment - I use a version of Zemax (student edition) to check the MTF curves after creating a design.
• The older designs aimed for specific aberration balance. This is hard to achieve as we do not know the data associated with those choices. But in some cases such as the Noct Nikkor - we know it was optimized to reduce coma at the expense of astigmatism. It is hard to do this type of optimization.
• It seems hard to optimize the aspheric coefficients because they need to be of a particular scale. The approach I used most successfully so far is to use scaling before applying numeric shifts and reverse it to original scale.
• I am also finding that the default Minpack lmder is not giving me results I hoped. I am using a version of least squares implementation developed by Michael Lampton - this seems to work better.

Recently I have been thinking about using aberration data to improve optimization. However because my current implementation is in Java and I have difficulty working with Python - I created a Java port of ray-optics. The aim of this was to help me use ray-optics in the optimization and analysis. Ray-optics is also better in how it handles ray tracing for wide angles - because my current GNU Optical based solution does not apply vignetting and so skewed rays are not efficiently targeted.

I am making some progress with using my Java port of ray-optics in my optimization framework. It is not fully working yet, especially for aspherics scaling.

I think in your example you have chosen to minimize the fan ray aberrations as much as possible. I believe that this is not possible in the lens designs I am looking at - because they have the problem that optimizing for spherical aberration increases coma etc. So a balance is needed. I am trying to figure out what balance to aim for if I wanted to for example focus on coma correction, and how to specify this. The thought I have is to aim for a specific aberration curve shape.

[mjhoptics]

Well, yes, optimization is complicated. I developed the smart equation solver in CODE V with Tom Harris. One of the key points was how inequality constraints were handled, especially when a constrained item was at a boundary, but wanted to move interior to the boundary later in the process, e.g. varying a glass within the boundaries of the glass map. There are entire books written on constrained optimization.
Using Ray-based merit functions are the best way to balance aberrations. CODE V uses weighting to control the aberration balance. You can weigh fields and wavelengths separately and there is an aperture weight that controls the relative emphasis of the inner vs outer rays in the pupil.
The sensitivity of the different variable parameters, as you note with aspheric coefficients, can vary significantly. Finite differences are usually used to calculate first derivatives and having good estimates of the derivative increments needed for this calculation are needed for the optimizer to converge.
If you want to optimize these patent lenses, you really need a pretty sophisticated optimizer.