Telecentric Lens Design

Magnification change Δm/m = −Δz/(s_EP + Δz) of an ordinary lens against a telecentric lens with a residual chief-ray slope, and the depth of field λ/NA² + e/(m·NA).

Model: Textbook approximation

Magnification |m|Object-side NAWavelength (nm)Acceptable blur at the sensor (µm)Object field height h (mm)Ordinary lens: entrance pupil distance (mm)Object displacement Δz, + away (mm)Telecentric lens: residual slope at h (°)

Results

Ordinary: chief ray at h, atan(h/s_EP)1.432°

Ordinary: Δm/m = −Δz/(s_EP + Δz)-0.249 %

Ordinary: edge image shift-6.23 µm

Telecentric: equivalent pupil h/tan θ_t2865 mm

Telecentric: Δm/m-0.0175 %

Telecentric: edge image shift-0.44 µm

Depth of field, wave λ/NA²0.880 mm

Depth of field, geometric e/(m·NA)0.800 mm

Depth of field, total1.680 mm

With the sensor fixed, an image point lands where its chief ray does, so a lens whose entrance pupil sits s_EP from the object changes magnification as the object moves. Telecentricity puts the pupil at infinity; a residual slope θ_t at the field edge acts like a distant pupil. A negative slope is hypercentric.

Magnification change vs object displacement

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

Paraxial chief ray with the sensor fixed: the blur centroid follows the chief ray. A residual telecentric slope is treated as a distant entrance pupil. The depth of field is Inoué's sum of a wave and a geometric term in air.

Greivenkamp J. E. (2004). Field Guide to Geometrical Optics. SPIE Press. Telecentricity: the entrance pupil at infinity keeps the chief ray parallel to the axis, so magnification does not change with focus. doi:10.1117/3.547461
Inoué S., Spring K. R. (1997). Microscope Image Formation. In: Video Microscopy, 2nd ed., ch. 2, pp. 13–117. Plenum. Total depth of field d = λ₀n/NA² + n·e/(M·NA). doi:10.1007/978-1-4615-5859-0_2

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