Laser NOHD (Nominal Ocular Hazard Distance)
Eye-safety standoff range for a CW laser from output power, beam divergence, and exit aperture — the ANSI Z136.1 range-safety number.
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The engineering
The NOHD is the range along the beam beyond which the irradiance entering an unaided eye falls below the Maximum Permissible Exposure. The card assumes a simple diverging cone: the beam grows linearly at full-angle θ from exit diameter a, and irradiance falls as 1/r². Solve for the range where the beam has spread enough that P over the beam area equals the MPE, and that's your minimum safe standoff — the number that sets laser range fans and exclusion zones.
Two gotchas dominate NOHD mistakes. First, divergence convention: this card wants the full angle; if your data sheet quotes half-angle (common for military designators), double it before entry. Second, the default MPE of 25.5 W/m² is the ANSI Z136.1 visible-CW value for a 0.25 s aversion-response exposure — it does not apply to IR wavelengths (where blinking doesn't protect you) or pulsed lasers, which need per-pulse and average-power MPE checks. Also note this NOHD is for the naked eye: binoculars or scopes collect more beam and stretch the hazard distance (the 'extended' ENOHD), while atmospheric attenuation is ignored, which keeps the answer conservative.
Sanity check: a 5 mW visible pointer with 1 mrad divergence gives an NOHD around 15 m; a 1 W beam at 0.5 mrad is hazardous out to roughly 440 m. If your number seems short for a high-power laser, check that you entered milliwatts, not watts.
Where this math comes from
Laser eye safety is an Army problem before it is a civilian one. Within a few years of Maiman's 1960 ruby laser, ruby rangefinders were on tanks, and the retinal-burn hazard on open ranges forced the question: how far downrange is far enough? David Sliney and colleagues at the U.S. Army Environmental Hygiene Agency (Edgewood/Aberdeen) ran the ocular-damage threshold studies through the 1960s that produced the MPE tables, and the nominal ocular hazard distance emerged as the practical range-safety quantity — a single standoff number a range officer could enforce.
The civilian codification came in 1973 with the first ANSI Z136.1, which carried the MPE tables and the NOHD methodology into general practice; the IEC followed internationally with 60825-1. Sliney and Wolbarsht's 1980 text made the calculation on this card the standard homework of every laser safety officer, and successive Z136.1 revisions have refined the MPE values while leaving the geometry untouched.
- 1960Theodore MaimanFirst working laser (ruby) at Hughes Research Labs — and the first laser eye hazard.
- 1968David Sliney / U.S. Army Environmental Hygiene AgencyRetinal-injury threshold studies establish the MPE basis and the NOHD range-safety concept.
- 1973ANSI Z136 committeeFirst ANSI Z136.1 laser safety standard publishes MPE tables and NOHD methodology.
- 1984IECIEC 60825-1 carries laser classification and hazard-distance practice internationally.
- 2014ANSI Z136 committeeMajor Z136.1 MPE revision aligns limits with updated ICNIRP guidance; the NOHD geometry is unchanged.
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