Retinal Image Size
Apparent source of a laser beam: retinal image diameter and angular subtense α with the eye accommodating from 100 mm to infinity, for any waist size and beam quality M².
Educational only — not compliance-grade
These pages implement the published exposure limits for the cases each one states, but they are educational tools: no laser safety officer has signed them off.
- Do not use these results alone for PPE selection, NHZ / NOHD approval, controlled-area sign-off, enclosure/interlock approval, or formal classification.
- Always verify against ANSI Z136.1, IEC 60825-1, your local procedures, and the responsible laser safety officer / CLSO.
Apparent source subtense α
2.83 mrad
Extended source: C_E = 1.89 for exposures of 0.25 s or more
Retinal image diameter, 1/e²
68.0 µm
63 % (1/e) diameter 48.1 µm
Beam at the eye, 1/e²
20.0 mm
Overfills a 7 mm pupil
Wavefront curvature radius at the eye
10.0 cm
Accommodation used
10.0 D of 10
The eye brings the image to focus
Beam quality M²
77.8
The chart shows α against the distance from the waist (log scales), with α_min = 1.5 mrad and α_max = 100 mrad (for t ≥ 0.25 s) dashed. Nearer than 100 mm the eye can't focus and the blurred image grows.
The apparent source is the object the eye images to the smallest retinal spot within its accommodation range, 100 mm to infinity (IEC 60825-1:2014). For a beam that is its waist: seen from r, the beam has the 1/e² radius (d₀/2)√(1 + (r/zR)²) and a wavefront of radius r(1 + (zR/r)²), zR = d₀/θ. The eye (a 17 mm air-equivalent lens) adds up to 10 dioptres to cancel that curvature and images the waist; α is the 63 % image diameter over 17 mm, which far from the waist is d₀/(√2 r). A beam wider than the pupil is diffraction limited by the 7 mm pupil; a waist nearer than 100 mm stays out of focus.
A TEM₀₀ (M² = 1) beam seen from r ≥ 100 mm has α ≤ √(λ/(πr)) (the largest when zR = r): at 100 mm 1.42 mrad at 633 nm, so a point source in the visible, and at most 1.84 mrad at 1064 nm. Beams of poor quality (fibre-coupled diodes, multimode fibres, stacks) or a waist inside 100 mm give larger sources, which raises the retinal thermal limit by CE = α/αmin (up to αmax). Not modelled: aberrations of the eye (below 1.5 mrad they don't matter), a beam converging to a waist behind the eye.
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
Embedded-Gaussian beam (M²) from its waist; 17 mm air-equivalent eye accommodating 0–10 D; 7 mm pupil diffraction; α from the 63 % image diameter. Not modelled: aberrations of the eye, beams converging behind it.
- IEC 60825-1:2014, Safety of laser products – Part 1. Definitions of the apparent source and the angular subtense (63 % energy diameter); accommodation from 100 mm to infinity.
- ICNIRP (2013). Guidelines on limits of exposure to laser radiation of wavelengths between 180 nm and 1,000 µm. Health Phys. 105(3), 271–295. Table 2 (α_min, α_max, C_E). doi:10.1097/HP.0b013e3182983fd4
- ISO 11146-1:2021, Lasers and laser-related equipment – Test methods for laser beam widths, divergence angles and beam propagation ratios (M²).