Cone Half Angle vs AOI in Fluorescence Imaging

In bio-imaging and fluorescence microscopy systems, it is common to see angular specifications reported only as an AOI (Angle of Incidence) range. However, AOI and Cone Half Angle (CHA) describe fundamentally different optical effects and should always be stated as separate parameters.

Confusing these two can lead to:

• Unexpected spectral shifts
• Reduced filter transmission
• Distorted bandpass shape
• Performance loss in narrowband fluorescence filters

This article explains what Cone Half Angle and AOI are, how they differ, and why both are critical in bio-fluorescent imaging systems.

What Is Cone Half Angle (CHA)?

Cone Half Angle (CHA) describes the angular spread of a beam and indicates how strongly the beam is converging or diverging.

It is defined as:

The angle between the central (chief) ray AOI and the most oblique marginal ray within the beam.

Key interpretations:

• CHA = 0° → perfectly collimated light
• Larger CHA → increasingly convergent or divergent beams
• CHA is a property of the beam geometry, not a single ray

In practical terms, CHA represents an ensemble of angles of incidence, not just one.

Examples of Cone Half Angle in Bio-Imaging Optics

Typical cases include:

• (a) Optical filter at 0° AOI with uncollimated illumination
• (b) Dichroic filter at 45° AOI with finite cone angle
• (c) High-reflectivity mirror at 45° AOI with converging beam

In all cases, AOI defines the orientation, while CHA defines the angular spread of rays striking the optic.

Relationship Between Cone Half Angle, NA, and F-Number

Cone Half Angle can also be expressed using Numerical Aperture (NA) or F-number (F#), both commonly used in microscopy.

Using Abbe’s Sine Condition:

Where:

• θₕ = Cone Half Angle
• n = refractive index of incident medium (≈1 for air)
• F# = f-number

Thus:

• High-NA objectives → large CHA
• Low-F# systems → large CHA

What Is Angle of Incidence (AOI)?

Angle of Incidence (AOI) refers to the angle between a single ray (usually the chief ray) and the surface normal of an optical component.

Key points:

• AOI is a single-ray parameter

• Often specified for:

  • Dichroic mirrors (e.g. 45° AOI)

  • Long-pass / short-pass filters

• AOI strongly affects:

  • Polarization behavior

  • Spectral shift magnitude

Optical Filter Effects: AOI vs Cone Half Angle

Spectral Shift Behavior

Both increasing AOI and increasing CHA cause a blue shift in interference filter spectra.
However:

CHA represents many AOIs simultaneously, so:

• The spectral shift is averaged
• Filter edges become less steep
• Passbands lose their “square” shape

The graph below shows the effect of differing cone half angle values on optical filter transmission spectra. Theory data for a narrowband filter is shown at 0° AOI with average polarization.

Why Cone Half Angle Matters in Fluorescence Imaging

For bandpass filters:

• Large CHA produces a cone-shaped passband
• Transmission drops near band edges
• Center wavelength becomes less well-defined

For narrowband and ultra-narrowband filters, even small CHA values can:

• Reduce peak transmission
• Broaden passband
• Increase spectral leakage

These effects are especially critical in:

• Multi-color fluorescence imaging
• Ratiometric imaging
• High-signal-to-noise biological assays