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How To Optimize for Worst-Case Performance
- By Mark Nicholson
- Published 10 May 2008
- Optimization
- Unrated
Introduction
In most cases, we want to optimize for best performance over some average of the field of view or wavelength range of a system. In some cases, its useful to optimize only the worse-case scenario.
For example, the default merit function tool will create a merit function which minimizes spot size, wavefront error, angular radius etc as an RMS average over the defined field of view. But what if your specification states that the MTF should never be worse than say 50% at 30 cycles/mm at any point in the field of view?
Here's an example. The file you can download from the last page of this article is a derivative of the double Gauss sample file that is distributed in the samples folder with ZEMAX. It's an f/3 photographic objective, optimized across the visible wavelength range and across a 28 degree field of view. The default RMS wavefront error merit function was used, with reasonable boundary conditions of glass and air thicknesses.
The MTF looks fine:
But, our customer requires the MTF at 30 cycles/mm to be greater than 50% everywhere in the field. Open Analysis...MTF...FFT MTF versus Field, and set it to showe the response at 30 cycles/mm:
The horizontal line at 50% MTF was drawn in by hand using Window...Annotate...Line, and it shows that we are outside of our customer's specification. How do we put this 'minimum MTF across the field' requirement into the merit function?
For example, the default merit function tool will create a merit function which minimizes spot size, wavefront error, angular radius etc as an RMS average over the defined field of view. But what if your specification states that the MTF should never be worse than say 50% at 30 cycles/mm at any point in the field of view?
Here's an example. The file you can download from the last page of this article is a derivative of the double Gauss sample file that is distributed in the samples folder with ZEMAX. It's an f/3 photographic objective, optimized across the visible wavelength range and across a 28 degree field of view. The default RMS wavefront error merit function was used, with reasonable boundary conditions of glass and air thicknesses.
The MTF looks fine:
But, our customer requires the MTF at 30 cycles/mm to be greater than 50% everywhere in the field. Open Analysis...MTF...FFT MTF versus Field, and set it to showe the response at 30 cycles/mm:
The horizontal line at 50% MTF was drawn in by hand using Window...Annotate...Line, and it shows that we are outside of our customer's specification. How do we put this 'minimum MTF across the field' requirement into the merit function?