One thing PDR is missing is that up-collimators have been shipping on high end laser pointers for a long time. The two milli-Radians he uses in his example are a low end toy at this time. Its easily possible to achieve 0.1 mR with a few external optics.
Laser pointer companies like to cater to their mainly teenager and 20-something customers, and those customers are often into "burning", ie seeing what they can burn with a focused beam, Power, which equates to the teenage desire for more horsepower in muscle cars, and Distance. Distance is becoming more and more popular, which is a problem.
When we do Laser in Airspace Calculations, we look not just at the Nominal Ocular Hazard Distance, but the Sensitive Zone Exposure Distance and the Critical Zone Exposure Distance. CZED and SZED are more about what pilots need to worry.
This is not just about laser shows accessing airspace legally, there are Lidar Systems, and Laser Guide Stars for astronomy, and Laser Wind Profilers. The cloud height sensor at most airports is a pulsed infrared laser of very low power. There are also laser based glideslope systems for a variety of applications, including some that are directly visible to the pilots eye (Those are intrinsically safe, btw)
So lets start with NOHD. NOHD is a statistical likelihood that there will be large, observable damage to the retina for a visible laser. Not all retinal burns readily show up in basic ophthalmic testing. It usually takes a retinal profiler to detect small damage, and those machines do not grow on trees. The famed Amsler grid referenced earlier pretty much only shows large scale or very severe laser injury to the eye.
For the record, it is often possible to discolor the proteins in the back of the retina and do damage that heals, as well as permanent damage.
So each case must be evaluated on a case by case basis.
A quick approximation for NOHD in feet for a continuous wave laser is
NOHD = (32.8/theta ) times the Square Root of (( 1.27 * average power)/0.00254)) Where theta is the 1/e divergence of the laser.
1/e Divergence is basically the 10% and 90% points in the power distribution curve across the beam in the laser. This curve is most often a Gaussian distribution, although cheap laser pointers often have horrible beam profiles, most of the high power green pointers are starting to ship with much better beam quality.
So lets move away from the damage threshold, which is a probability of damage occurring, not a absolute guarantee that there will be damage if you observe a beam that is over the NOHD. After all these beams are moving, and greatly disturbed by atmospheric turbulence.
Next Post, CZED and SZED.
Steve