Folded Bench Geometry — Working Distance and Lens Travel

Folded imaging benches use mirrors or prisms to fit a long optical path into a compact mechanical envelope. This example uses a two-arm inspection layout to distinguish path length, optical conjugates, working distance, and available mechanical travel.

The figures describe one example geometry. Their dimensions and calculated curves are specific to that layout and are not general component limits.

Unfold the path first

Example unfolded chain showing optical segments, lens position, and mechanical gap labels

Follow the chief ray through every interface and record the physical length, medium, and fold direction of each segment. A prescription’s station coordinate may differ from a distance measured between mechanical faces.

Keep these quantities separate:

  • Physical path length along the traced ray.

  • Optical path length \(\sum_i n_i d_i\).

  • Paraxial propagation distance in the chosen ray convention.

  • Straight-line clearance between mechanical bodies.

Working distance needs a reference

State whether working distance is measured from a lens vertex, front housing face, or another datum. Principal-plane object distance is an optical quantity and generally differs from this mechanical distance.

Example folded bench with prisms, lens assembly, and physical clearance dimensions

A zero nominal gap in an unfolded prescription does not prove that two physical bodies touch. Inspect the transformed body positions and the nearest relevant faces.

Lens travel and field of view

For a fixed sensor width \(w_s\) and object field width \(w_o\), the magnification magnitude is

\[|m|=\frac{w_s}{w_o}.\]

For a thin equivalent lens in air, with positive real conjugate distances,

\[s=f\left(1+\frac{1}{|m|}\right), \qquad s'=f(1+|m|).\]

Use these relations as a first-order check. A real multi-element assembly also requires principal-plane positions, clearances, and a focus condition.

Example first-order lens travel and object field relationship

If two air gaps are labelled A5 and C1, moving a fixed lens group between fixed surrounding components increases one gap while decreasing the other. Their available sum sets a travel budget only after lens length, mount envelopes, collision clearances, and stage limits have been included.

Review checklist

  1. Specify the object field, sensor size, spectrum, and focus criterion.

  2. Trace the nominal path and verify each fold.

  3. Compare principal-plane conjugates with measured mechanical datums.

  4. Check the complete lens and stage envelopes over the required travel.

  5. Evaluate vignetting at every field and travel extreme.

  6. Trace unwanted cross-arm and ghost paths.

  7. Compare ray-count statistics with power-weighted stray-light quantities.

See Machine-Vision Camera and Lens EOL Qualification for the bench acceptance workflow and Folded Coaxial Illumination — Projection Physics and the MV-150 for folded illumination.