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Gaussian Quadrature

Zemax has used Gaussian Quadrature when computing RMS Spot Size and RMS Wavefront Error for optimization since its inception. It is a clever technique that uses the inherent polynomial nature of wavefront aberrations so you can use very few rays to compute the spot size or WFE to high precision. In Zemax, Gaussian Quadrature can now be used to solve annular pupil design problems and build better chromatic lens designs.

At the last IODC conference, Brian Baumann and Hong Xiao of Lawrence Livermore Laboratories showed how to extend this method to the selection of wavelengths within a desired range, and to pupils with annular obscurations, such as obscured telescopes. This has now been built into Zemax, so you can access this new capability very easily. Let's look at what this means when optimizing a lens.

Here we have a standard double Gauss lens file, optimized as we would normally do it with a default RMS spot size merit function, normal edge and thickness controls, a distortion constraint and a minimum back focal distance constraint. Nothing unusual here. It was optimized it to give good performance over the F,d,C visible range at all field points. Let's look at how the wavelength range is defined:

The file has three wavelengths, all of equal weight. It gives this performance over wavelength:

Let's look at the new Gaussian Quadrature part of this dialog. This is available in all versions of Zemax, from SE up. The GQ algorithm needs to use an even number of wavelengths:

Note that the maximum and minimum wavelengths stay the same, but Zemax has chosen new intermediate
wavelengths, and new weights for each wavelength. We just need to rebuild the merit function and re-optimize to get
better performance:

And note how the merit function drops and performance improves. We have not added any new variables: we've just come up with a better solution to the same problem. If you're involved with any kind of chromatic lens design, this new feature in Zemax will help you to build better designs with hardly any extra effort!

In addition, there is a new 'Obscuration' control in the default merit function tool

That allows you use use Gaussian Quadrature in systems with obscured pupils.

These new capabilities in all editions of Zemax are fantastic news for anyone doing lens design of chromatic systems, and for people designing systems with obscured pupils. These really do let you get better lens designs, faster.