Koehler Illumination Calculator

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.

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: **-- **

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

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

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

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

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

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

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

d_{1} |
Source to Lens 1 Distance |

d_{2} |
Lens 1 to Lens 2 Distance |

d_{3} |
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 |