A very common task in optical metrology is to illuminate an object, often a reticle (e.g. Thorlabs R1DS3N) like this:

For the metrology to be effective, the illumination has to be perfectly uniform at maximum possible contrast. Such an illumination is almost always a telecentric illumination at some given numerical aperture, meaning that the chief rays of each cone of light illuminating a given part of the object are perfectly parallel to each other, like this:

A rather easy and cost-effective way to achieve such an illumination is to use a (homemade) integrating sphere and off-the-shelf optics in a very simple arrangement like this:

This not yet optimised setup is perhaps one of the fastest possible ways to get such an illumination, since nearly all parts, including the mechanics, are off the shelf. It consists of 3 major components:

• The Object (usually a reticle or an aperture of some sort)
• The Field Lens (often a pair of achromatic doublets)
• The Integrating Sphere (often homemade, even 3D printed ones can work)

For this particular example the following system parameters apply:

Parameter	Value
Object Circle Diameter	15 mm
Object NA	0.1
Wavelengths	450 – 650 nm
Field Lens Doublet Focal Length	50 mm
Integrating Sphere Diameter	30 mm

Each application has slightly different parameters, but the principles that are about to follow hold generally. Those parameters chosen here are just for illustration and do not reflect any particular use case.

The goal is now to optimise the setup such that the illumination is uniform and telecentric. And by varying the distances between the object, field lens, and sphere, one can achieve this goal.

Step 1: Optimise The Field Lens

The first step is to minimise the distance between the two doublets making up the field lens; the closer the doublets, the better. However, they may not touch and it thus makes sense to keep them separated with retainers rings at the closest possible distance.

Staying with the Thorlabs example, their retainer rings (SM1RR) are 2 mm thick at 22.9 mm clear aperture, and thus 3 of them put between the doublets separates them by 1.944 mm.

In Zemax, this is expressed with an edge thickness solve like this:

Step 2: Optimise Telecentricity

The next step is to make the illumination telecentric, that is to say to make the chief rays at the reticle parallel to each other. In this system, this chief ray angle is entirely controlled by the distance between the field lens and the integrating sphere, e.g.:

Thus by changing this distance, the illumination becomes telecentric. In Zemax, one can easily force telecentricity by firing a ray at maximum field but minimum pupil and bringing the angle at the 2nd reticle surface to 0. It looks like this:

Step 3: Optimise Uniformity

The last step is to optimise uniformity. The illumination at the object is uniform, when the pencil of rays associated with each point of the reticle is perfectly defocused at the surface of the integrating sphere. And this defocus, e.g., the degree of collimation, can be controlled by changing the distance between the object and the field lens, e.g.:

In Zemax, an easy way to check this degree of collimation is to monitor “Incident Angle vs. Image Height” and change the object-field lens distance until chief and marginal ray at 0 image height have identical values, like this:

Finished Design

With these small optimisations, the design is complete and looks like this:

You can check out the finished design directly in Zemax using this file: