One of the most frequently used tools in OpticStudio is the Spot Diagram. It reports RMS spot radius for different fields at different wavelengths. Very often after checking RMS spot radius using Spot Diagram, user needs to report spot radius in Merit Function Editor (MFE) to run optimization and minimize spot size for better image quality. OpticStudio provides four optimization operands for RMS spot radius, RSCE, RSCH, RERE, RSRH. When it comes to these four operands, we often see user ask two questions.

First, what is the difference among the four operands? There are two main differences. One is the reference point. Using Centroid or using Chief ray intercept as the reference will make a difference in the computed RMS spot radius. The other is the pupil sampling method, Gaussian Quadrature (GQ) vs Rectangular Array (RA). The GQ algorithm is in general superior, but the one drawback is that the algorithm assumes the pupil is a circle, or more generally, an ellipse. For non-elliptical pupils, GQ does not work accurately.  For example, if there are surface apertures in the optical system that vignette enough rays to alter the effective shape of the pupil significantly, GQ should not be used. The RA algorithm traces a grid of rays through the pupil. The advantage to the RA algorithm is the ability to accurately account for the effects of vignetting in the merit function. This is useful in systems such as obscured telescopes and camera lenses which intentionally clip troublesome rays. The RSCE and RSCH operands use GQ algorithm, whereas RSRE and RSRH operands use RA algorithm. And the last letter E or H indicates whether the spot is referenced to Centroid or Chief ray. You can find this explained in the help file at The Optimize Tab (sequential ui mode) > Automatic Optimization Group > Merit Function Editor (automatic optimization group) > Optimization Operands (Alphabetically).

The second common question is why these 4 operands report different RMS spot radius than the radius I see in Spot Diagram for the same field and wavelength? This difference usually comes from three settings in the Spot Diagram: the Ray Density, Ray Pattern, and Refer To. For a system that has vignetting or non-circular pupil, Rectangular Array algorithm is the preferred pupil sampling method. In this case we should use RSRE or RSRH operand. Since these operands use rectangular grid of rays, in Spot Diagram we may also choose Square as the Ray Pattern. If you still see a difference between the MFE operand spot radius and the Spot Diagram, you could also ramp up the Ray Density to its maximum value of 200. The more rays traced, the greater the accuracy of the RMS Spot Radius, although the computation time also increases. Last is the Refer To option. If you want to match operand value with Spot Diagram, they should have the same reference, both refer to Centroid or both to Chief Ray. As shown in this example below, the RSRE operand and the left Spot Diagram, (Square ray pattern, 200 ray density, and centroid as reference), match very well.