In this article we will demonstrate how to set up a scanning mirror such that a mirror scans +5° about its nominal position of 90°. The file starting point.zmx is in the zip archive you can download from the last page of this article. It shows a simple focussing lens, with a dummy surface (drawn in red) where the scanning mirror is to be located:

The lens was set up as follows:

• 5 mm thickness of N-BK7
• an f/5 solve defines the radius of the rear curve
• The front radius and back focal distance are optimized for best RMS spot size.

We now want to make surface 2 a mirror, such that the lens is rotated through 90 degrees with respect to surface 1. Click on Tools > Coordinates > Add Fold Mirror, and enter:

By using this tool, ZEMAX has:

• Make the selected surface a MIRROR
• Reversed the signs of the thicknesses of all surfaces after the mirror, because light now propagates in the opposite direction
• Added a coordinate break with an x-tilt of -45 degrees prior to the mirror
• Added a coordinate break with an x-tilt of -45 degrees after the mirror 

Remember that coordinate break surfaces have no power and do not bend rays: they just define a new coordinate system in terms of a decentration and tilt with respect to the previous surface. This is very useful, as it allows us to separate the coordinate geometry from the optical properties of the surfaces.

Now, to make the mirror a scanning mirror, we need to tilt it. Let's say we want to tilt it by ±5° about the nominal 45° position. It will be incorrect to simply change the tilt about x angles of the coordinate break surfaces to say -50 degrees: this will shift the location of the lens and image plane as well:

As can be seen, changing the fold mirror angle just gives us a -100° fold: this is not the same as a 90° degree fold with a scan angle of ±5°.Set the tilt about x back to -45° before continuing.

To make the mirror a scan mirror, we must tilt it using the Tilt/Decenter Elements tool. This is found under Tools > Coordinates > Tilt/Decenter Elements. The mirror is surface number 3, so enter:

Note that this tool has inserted two more coordinate break surfaces, so that the mirror is now tilted by 5° around its nominal 45° position. The scan angle can be set to any value by setting the value of the Tilt About X of surface 3: the pickup solves automatically inserted by the two tools means that the total tilt seen between surfaces 1 and 7 must always be -90°.

So the correct way to set up a scanning mirror is to use two sets of Coordinate Break surfaces. The first, or outer set, is most easily added by Tools > Add Fold Mirror to implement the geoemtry of the nominal position. The second, inner set, is implemented using Tools > Miscellaneous > Tilt/Decenter Elements to define the perturbation about this point.