Cone Half Angle Effects on Bandpass Filters

Key takeaway As CHA increases, the chief ray stays at the nominal passband while marginal rays hit the filter at larger angles and shift toward shorter wavelengths. Their combined output becomes bluer and broader.

A bandpass filter sees every ray at a different angle. Open the cone and watch the marginal rays tune bluer. Then see those ray-by-ray passbands combine into a shifted, broader output.

02 · Follow the rays

Cone angle at the filter

Each ray reaches the filter at a different angle. Its output color marks the angle shifted center wavelength. The downstream collimator is outside this view; ray angles are to scale.

±3.0° cone
Diverging rays passing through a bandpass filter before collimation A small three degree cone reaches the bandpass filter before the downstream collimator. The rays remain close to the chief ray and their passband centers are almost equal. optical axis / filter normal bandpass filter source
Broadband cone Angle shifted rays Filter normal
Combined peak 549.9 nm after angular averaging
Blue shift 0.1 nm from nominal center
Output FWHM 10.0 nm nominal: 10 nm
Peak transmission 95.0% angular average

03 · Read the result

Transmitted spectrum

Move across the graph for exact transmission values.

0° nominal Cone average Marginal-ray peak
1

Every angle has its own passband

For a multilayer interference filter, oblique rays tune to shorter wavelength. The chief ray stays nominal; the marginal ray shifts most.

λ(θ) = λ₀ √[1 − sin²θ / n²eff]
2

Small CHA keeps rays together

A slow, narrow cone contains only small incidence angles. Its ray-by-ray spectra nearly overlap, so the combined passband stays close to nominal.

3

Large CHA mixes more blue shifts

A fast, wide cone includes many oblique rays. Averaging their offset spectra moves the peak blue, broadens the band, and can reduce peak transmission.