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How to Specify Fields for Non-Rotationally Symmetric Systems

This article explains how to assign appropriate weight for the on-axis field when specifying fields for non-rotationally symmetric systems.  


Name-Hyong Kim
Frequently Asked Questions

Weighting on fields

For most non-rotationally symmetric systems, both the plus and minus fields need to be specified in the field data window. When optimizing, we normally want to minimize the RMS of all criteria across the fields. In the included example with only X symmetry, the field data window has plus and minus Y fields specified, as one would expect. Since both the plus and minus Y fields include the on-axis fields, but we specify the on-axis field only once in the fields data window, we need to assign a weighting of 2 to the on-axis field. In other words, we want the RMS of criterias belonging to +Y (0,0 and 0,5 ) and -Y (0,0 and 0,-5) fields.  As will be demonstrated, the default merit function will account for the specified field weights.

Load the attached file.

3d layout

In the Field Data window note the weight of 2 for the on-axis field.


Now, build a RMS spot radius centroid default merit function with no boundary constraints.

merit fct

To verify that the merit function value is indeed the RMS of RMS spot sizes across the fields accounting for field weights, let's calculate manually using the values reported in the spot diagram. 

The pupil sampling method used in the default merit function is Gaussian Quadrature. To ensure that the pupil sampling is uniform and sufficient for the spot diagram, the ray density in the spot diagram settings is set to 20.

spot diagram

The RMS of all RMS spot sizes is:

Root((2*64.596^2+169.420^2+50.187^2)/4) = 99.457um or 0.099457mm

The reported merit function value is:

merit fct 2

For a system with no X or Y symmetry, the on axis field weight needs to be 4 for the reason mentioned previously.

When tolerancing using one of the built-in fields option, Y-Symmetric or XY-Symmetric, Zemax OpticStudio automatically adds +/- Y or +/- XY fields , for tolerancing purposes, with appropriate weights for the on axis field (2 for Y-Symmetric and 4 for XY-Symmetric).