Köhler Illumination Calculator

Köhler illumination settings: field of view FN/M for the field diaphragm, condenser aperture against the objective's back aperture, and the resolution λ/(NA_obj + NA_c).

Model: Textbook approximation

Objective magnification (×)Objective NATube lens focal length (mm)Condenser NA (aperture diaphragm setting)Condenser focal length (mm)Eyepiece field number (mm)Wavelength (nm)

Results

Field of view FN/M (field diaphragm to open to)500 µm

Objective focal length f_TL/M5.00 mm

Objective back aperture 2·f_obj·NA9.50 mm

Condenser iris image in it9.00 mm (95 %)

Condenser iris diameter 2·f_c·NA_c21.6 mm

Usual condenser NA, 0.7–0.8 × NA_obj0.66–0.76

Abbe period limit λ/(NA_obj + NA_c)297.3 nm

Rayleigh rule of thumb 1.22λ/(NA_obj + NA_c)362.7 nm

Above the usual 0.7–0.8: close to full resolution, but low contrast and more glare.

Resolution vs condenser aperture

Model

Field of view = FN / M_obj; pupil diameters 2·f·NA (Abbe sine condition)

d = λ / (NA_obj + NA_c), or 1.22λ / (NA_obj + NA_c) as a two-point rule of thumb, NA_c ≤ NA_obj

Köhler illumination images the lamp into the condenser aperture diaphragm, which is in turn imaged into the objective's back focal plane, and images the field diaphragm onto the specimen. Open the field diaphragm just past the field of view; the aperture diaphragm sets the condenser NA, usually 0.7–0.8 of the objective's, a trade between resolution and contrast. Condenser light beyond the objective NA misses the objective unless the specimen scatters it, as in darkfield, so in brightfield it adds glare and no resolution. A closed condenser (NA_c → 0) gives coherent illumination and the Abbe limit λ/NA_obj. The 1.22 form is the Rayleigh criterion only at NA_c = NA_obj (0.61λ/NA, incoherent); with coherent light two-point resolution depends on their relative phase.

Model and references

Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers

First-order Köhler layout with aberration-free optics. Pupil diameters follow the Abbe sine condition (2·f·NA). The resolution uses min(NA_c, NA_obj): Abbe's grating period, and 1.22× it as a rule of thumb that is Rayleigh's only at NA_c = NA_obj.

Nikon MicroscopyU. Microscope Resolution: Concepts, Factors and Calculation. r = 1.22λ/(NA_obj + NA_cond). microscopyu.com
Nikon MicroscopyU. Field of View. Field of view = field number / objective magnification. microscopyu.com
Evident (Olympus). Microscope maintenance: Köhler illumination, upright microscope (2020). Condenser aperture set to about 0.7–0.8 of the objective NA. adobeassets.evidentscientific.com

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