Depth of Field Calculator for Machine Vision Lenses
Calculate the total depth of field (DoF) for machine vision lenses — the range of object distances that produce an acceptably sharp image on the sensor.
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Formulas
Circle of Confusion:
c = pixel_size × multiplier (µm → mm)
Hyperfocal Distance:
H = f² / (N × c)
Near Depth of Field Limit:
Dnear = u·f·(u − f) / [f² + N·c·(u − f)]
Far Depth of Field Limit:
Dfar = u·f·(u − f) / [f² − N·c·(u − f)]
(= ∞ when denominator ≤ 0, i.e., u ≥ H)
Total Depth of Field:
DoF = Dfar − Dnear
Magnification:
m = f / (u − f) (thin lens)
Depth of Focus (image side):
δ = 2·N·c·(1 + m)
Assumptions & References
- Thin lens model is assumed; real lenses may deviate due to aberrations and principal plane separation.
- The Circle of Confusion (CoC) is set as a multiple of the pixel size — a common machine vision convention. A multiplier of 2 means blur up to 2 pixels is acceptable.
- All distances are in millimetres; pixel size input is in micrometres.
- The hyperfocal distance formula H = f²/(N·c) assumes f ≪ H (paraxial approximation).
- When the object distance equals or exceeds the hyperfocal distance, the far limit of DoF extends to infinity.
- Depth of focus (image-side) is the tolerance on sensor position for acceptable sharpness.
- References: Hecht, Optics (5th ed.); Edmund Optics Machine Vision Learning Centre; Ray, Applied Photographic Optics.