Note: Before you read this article

This how-to expands the earlier article on sphere-based illumination. To make the most of this how-to, it helps to familiarise oneself with the earlier article.

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Just like the sphere-based illumination, the Köhler illumination creates high contrast, uniform illumination. However, the Köhler illumination typically provides significantly higher irradiance than the sphere-based one.

The reason the Köhler illumination is so much more powerful is simple: the sphere-based illumination spreads a given light source’s power uniformly over the entire hemisphere of its exit port, and the Köhler illumination does not. A uniform light distribution over an entire hemisphere makes for convenient optical alignment, but it wastes all the light not hitting the field lens. And the Köhler illumination avoids this waste by first shaping the beam that eventually hits the field lens.

The optical design of a Köhler illumination is admittedly more complex than this of the sphere-based one. This complexity, however, is manageable, and the following how-to runs through the steps needed to convert a sphere-based illumination into a Köhler illumination.

Step 1: Calculate The Required Etendue

Let’s start with the sphere-based illumination designed in an older article, looking like this:

This sphere-based illumination provides light to an object with these parameters:

Parameter	Value
Object Circle Diameter	15 mm
Object NA	0.1
Wavelengths	450 – 650 nm

In other words, the sphere illuminates an area

with a solid angle

amounting to a good approximation of the object-side etendue of

Step 2: Find a suitable Light Source

The next step is to find a light source with an etendue larger or equal to this of the object. Comparing the following two LEDs from Thorlabs and Luminus, one finds that the Thorlabs one will not work for this particular illumination:

	Source 1	Source 2
Manufacturer	Thorlabs	Luminus
Source	LED545L	CBT-90
Area	$\text{22.9 mm}^2$	$\text{9.0 mm}^2$
Solid Angle	$137.3 \cdot 10^{-3} \text{\,sr}$	$1470.0 \cdot 10^{-3} \text{\,sr}$
Etendue	$\text{3.1\,mm}^2\cdot\text{sr}$	$\text{13.2\,mm}^2\cdot\text{sr}$

The Luminus LED, however, will work, since its etendue is larger than that of the object.

Step 3: Replace The Sphere

The next step is to replace the sphere and introduce 2 new groups (Relay Lens and Condenser Lens) to the system, like this:

Apart from the specific element shapes, these 2 new groups are very similar to the field lens, in that they move the system from pupil space to image space (Relay Lens) and from image space to pupil space (Condenser Lens). Their element distance optimisations are similar to the element distance optimisations of the field lens, too.

For the Köhler illumination to work, the following requirements must be met:

1. Relay and Condenser Lens combined must create a spot of light that is smaller than the LED chip; this spot of light must be the rightmost surface and located in air
2. Between Relay and Condenser Lens must be enough space such that an image can form; this image must be located in air

The design shown here satisfies those conditions. This particular design, however, is just one out of many possible designs one could choose.

If these conditions are met, then one can control the system etendue (and thus shape the beam) by placing limiting apertures into the stop positions where pupil and image form, e.g. here:

For clarity, the stops are

• Aperture Stop
  • Between Field and Relay Lens
  • Limits the illuminated NA at the object
• Field Stop
  • Between Relay and Condenser Lens
  • Limits the illuminated area at the object

These limiting apertures ensure that excess light emitted by the LED does not reach the object. Light blocked by the apertures leaves the system and does not contribute to stray light, thus pushing system contrast to its maximum.

Step 4: Improve Uniformity (IF necessary)

The design as such is finished. However, sometimes, small imperfections in the LED reduce the uniformity of the illumination. If the pupil is a bit non-uniform, one can help it by adding a very weak diffuser next to the field stop. Conversely, if the field is a bit non-uniform, one can help that by adding a very weak diffuser next to the aperture stop. Like this:

These diffusers are not always needed. However, it is prudent to plan for them when designing the Köhler illumination.

How much More Powerful is Köhler Then?

With these designs, one can directly compute how much more powerful the Köhler illumination is. The sphere has port diameter of $\text{5.2\,mm}$ (see attached Zemax file) at $2 \pi$ solid angle and thus an etendue of $\text{133.4\,mm}^2\cdot\text{sr}$. Further, its throughput is assumed to be $\text{10\,\%}$ (a typical number for high-performance spheres), thus it compares to the Köhler illumination as follows:

	Sphere-Based Illumination	Köhler Illumination
Etendue
Object Etendue	$\text{5.6\,mm}^2\cdot\text{sr}$	$\text{5.6\,mm}^2\cdot\text{sr}$
Source Etendue	$\text{133.4\,mm}^2\cdot\text{sr}$	$\text{13.2\,mm}^2\cdot\text{sr}$
Used Source Irradiance	$\text{4.2\,\%}$	$\text{42.4\,\%}$
Losses
Internal Transmission*	$\text{-7\,\%}$	$\text{-24\,\%}$
Throughput	$\text{-90\,\%}$	–
Diffuser Losses	–	$\text{-20\,\%}$
TOTAL Used Source Irradiance	$\textbf{0.4\,\%}$	$\textbf{25.8\,\%}$

*see Zemax file

Thus, the Köhler illumination is about 60 times more intense than the sphere-based illumination.

Finished Design

With this, the design is complete and can be downloaded here: