Koehler Illumination Calculator

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Source Diameter (mm):

Lens 1 Diameter (mm):

Lens 1 Focal Length (mm):

Lens 2 Diameter (mm):

Lens 2 Focal Length (mm):

Source to Lens 1 Distance (mm): --

Lens 1 to Lens 2 Distance (mm): --

Lens 2 to Spot Diameter Distance (mm): --

System Length (mm): --

Spot Diameter (mm): --

Input Numerical Aperture, NA: --

Output Numerical Aperture, NA: --

$$ d_1 = \text{FL}_1 \left[ \frac{D_{\text{Source}} + D_{L_2}}{D_{L_2}} \right] $$

$$ d_2 = \frac{d_1 \, \text{FL}_1}{d_1 - \text{FL}_1} $$

$$ d_3 = \frac{d_2 \, \text{FL}_2}{d_2 - \text{FL}_2} $$

$$ \text{System Length} = d_1 + d_2 + d_3 $$

$$ D_{\text{Spot}} = \frac{D_{L_1} \, \text{FL}_2}{d_2 - \text{FL}_2} $$

$$ \text{NA}_{\text{Input}} = \sin{\left[ \tan^{-1}{\left( \frac{D_{L_1}}{2 d_1} \right)} \right]} $$

$$ \text{NA}_{\text{Output}} = \sin{\left[ \tan^{-1}{\left( \frac{D_{L_2}}{2 d_3} \right)} \right]} $$

d₁	Source to Lens 1 Distance
d₂	Lens 1 to Lens 2 Distance
d₃	Lens 2 to Spot Distance
D_L1	Diameter of Lens 1
D_L2	Diameter of Lens 2
F_L1	Focal Length of Lens 1

F_L2	Focal Length of Lens 2
D_source	Source Diameter
D_spot	Spot Diameter
NA_input	Input Numerical Aperture
NA_output	Output Numerical Aperture

Description

Mathematically determine how to configure a source and two lenses into a Koehler Illumination setup. Calculator uses the paraxial lens approximation and enables an initial lens selection. Once lenses are selected, EO recommends modeling one's Koehler Illumination setup in optical design software such as Zemax, CodeV, or FRED to analyze and revise as needed. Please note that performance will vary based on source and lens selections.

Resources

Application Note

Understanding Microscopes and Objectives

Related Product Category: Optical Lenses

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