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# How to Specify Intermediate Field Points

This article explains what the optimum values for the intermediate fields should be relative to the maximum field.

Name-Hyong Kim
04/03/2007

Field as discrete sample point

The field specified in the field data window represents discrete sampling points on the two dimensional object surface. The default merit function will minimize the root mean squared (RMS) of the criteria (spot size, wavefront, MTF etc.) across all fields. Normally, the defined field points will include at least the on-axis and the maximum field points. Because the performance in-between the on-axis and max field can change, we often need to specify intermediate field points. Since we are sampling 2D object surface, and not 1D object line, it make sense to specify the intermediate sample points such that equal areas (not equal distances) on the object surface are sampled. The intermediate field point, if 3 fields are specified, will not be at the half point between the on-axis and the max field when sampling equal areas (see picture below). Note that the sample system below is rotationally symmetric and we only need to sample the field along one radial arm. From simple geometry, the field values when dividing into n rings of equal areas are: where "n" is number of field points and HFOV (Half Field of View) is the radial max field.

If n = 3 then the intermediate field point is 1/root(2) times the max field as shown below. The number of intermediate field points need not be large for most systems since the performance don't often change too quickly as function of field. A sensible approach is to define only one or two intermediate fields, optimize and then evaluate the performance as function of continuous fields (using analysis such as RMS vs. Field)  to determine if addition fields are needed.