The diffractive and surface scattering properties of a parent object are inherited by the Boolean object too. For example, open the file {zemaxroot}/samples/non-sequential/boolean/diffractive scattering Boolean object.zmx.

In this case, the parent objects are a Diffraction Grating object, and an Extruded object based on the LETTERC.UDA sample file:

These obejcts are set to "Do Not Draw This Object" in the file, and so they will not appear in the layouts unless you change this setting. The Boolean object is formed by taking the intersection of these objects, A AND B:

Now the diffractive object has a parabolic surface shape, and the following surface properties on Face 1:

So, this face is set to be reflective, with 40% probability of a ray being scattered by a Lambertian scattering function. No coating is defined, and so ZEMAX assumes the face has the reflectivity of bare Aluminum. It is also set to diffract 40% of the unscattered light into order -1, 40% into order +1, and 20% into the zero order. All these properties are inherited by the Boolean object:

Rays are reflected, diffracted and scattered by the Boolean object. Rays that land outside the aperture defined by the extruded object are transmitted normally, and you can see the C-shaped shadow cast by the Boolean object clearly. Looking at the focal region of the Boolean mirror we see:

The zeroth order rays come to a geometrically perfect focus at the focal point of the parabola (although diffraction due to the aperture of the mirror prevents the spot size from being infinitesimally small: see the article on Point Spread Functions for more information). The + and -1 order rays show coma due to the phase added by the diffraction grating.