Whats the Duel Lens About
If you take the Fourier transform of converging Zonal Lens with focal length z,

you see that you get something that looks much like a diverging lens with a focal length fc2/z. If we were to write the same transformation in the format that is used internally by the program and using the fact that canonical focal length for the rasterized lens system is defined as the transformation used in the program is the one below.

Actually it only resembles this when z/fc is close to one. Since instead of an integral we are doing a sum from -N/2 to +N/2-1 which produces profound changes in the result. If z/fc was larger than one we find that the result was convolved with a sync before being rasterized which produces the square diffraction shadow you so often see. In the case where z/fc is much less than one then there are serious under-sampling effects which very much depend upon wether z/fc and N are relatively prime.

So since there are times when we want this expression, so it is built into both the "Zonal Lens" window and icon. When you need it, it is there.

What do you need it for?
When you need to do a series of fast calculations of propagation, You would do a series of "Fast Fresnel" transforms. These consist of (1) an inverse Fourier (fast) transform (2) the Duel lens appropriate for the wave length, pitch, and step (distance traveled) (3) a Fourier transform. If you think about it it is pretty clear that you can chain these steps with little loss in precision. (Don't try to chain with the direct propagation option since at every step you will be simulating the act of placing that step on a grid of finite sized pixels.)

If you are calculating on a very fine grid, with a pixel pitch on the order of a wave length of light you should use the non-paraxial form of the duel lens. You will notice that when using this duel lens in the fast Fresnel calculations that features in your propagated image which are finer than a wave length rapidly fade away. (as they should)

Below you see the amplitude and phase of an extreme non-paraxial lens made with a pixel pitch which is one fifth of a wave length and a step of two fifths of a wave length. Notice that the amplitude drops off exponentially past a radius of NΔ/λ (in pixel coordinates) and the phase goes to zero at that same radius.


amplitude of non-paraxial duel lens

phase of non-paraxial duel lens