This is the distance from the source at which the intensity or the energy per surface unit becomes lower than the Maximum Permissible Exposure (M.P.E.) on the cornea and on the skin. The laser beam can thus be considered as dangerous if the operator is closer from the source than the N.O.H.D.
Like the M.P.E., this distance depends on several parameters :
the beam characteristics : output power, diameter and divergence
the M.P.E. value on the cornea
eventually, the optical system inserted in the beam trajectory
For example, this distance can be extremely long for class 3B and 4 laser sources (see exercises). It is thus necessary to stop the beam at the end of the optical system.
When looking at the beam with an optical system, one has to consider the possible higher intensity entering the eye, and thus to expand the evaluated N.O.H.D. (called afterwards expanded N.O.H.D.)
As long as the beam propagates freely, this distance can be evaluated according to the following expression :
In this formula, N.O.H.D is the Nominal Ocular Hazard Distance (in meter), P0 the power of the source (in Watts) or eventually the total energy carried by one pulse (in Joules), M.P.E the Maximum Permissible Exposure (in W/rad or J/m²) , w the waist of the Gaussian beam (m), and the divergence of the beam.
When using an optical system to look at the beam, one has to take into account the beam focusing induced by the system. Defining f the focal length f of the optical system and the half-aperture angle of the beam, the expression turns to :
Inside this area, the intensity or the energy per surface unit is higher than the M.P.E. on the cornea. The size of this area is defined by the N.O.H.D. However, it is very difficult to define this area as it depends on the environment (dusty or not,...) and on the objects than can be on the beam trajectory – in other words, one has to take into account the specular reflections.