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fa ,l ,o pipe; Class 4, if more than 0.5 W is emitted from the laser system as an unenclosed beam; or Class 3b, if after passing through beam-forming optics the total optical power in the beam werc greater than 5 mW but less than 0.5 W(see3.3). Etample 15: Find the appropriate beam diameter to be used for calculations in this standard if a laser beam diameter is specified as being 3 mm in diameter as measured at l/e'-of-peak-inadiance points. The beam is further specified to be single-mode and Gaussian. Since the beam is Gaussian, use may be made of the relation that the beam diameter measured at the l/e2 points is greater by a factor of {T= l.4l than the diameaer measured at the l/e points. Henc€: 0.3 cm a=- = tr-l I cm \12 This exercise was purely academic, since the calculation of diameters below 7 mm is not necessary to determine laser classification. The value a could, however, have been used for the laser range equalion Eq 87 (see 84.l ). Emmple 16: Classify a 0.6328 pm visible laser (He- Ne) used as a remote-control switch. The laser is electronically pulsed with a I mW peak-power output, a pulse duration of 0.1 s (hence an energy of l0{ J per pulse) and a beam diameter of I cm. The recycle time of the laser is 5 s (maximum prf = 0.2 Hz). Since the device is pulse.d with an exposure duration of 0.1 s, the applicable MPE for intrabeam viewing from Table 5 or Fig. 4 is 3.2 x l0-3 W.cm-? or 3.2 x lt' ! . cm-z. Using Eq 86, the emergent beam radiant exposure per pulse is l.27xl0{J.cm-2, which is less than half the MPE, indicating the laser is Class I if repeated exposure is not considered possible. In the absence of biologic dara and MPEs for exposures repeated at prfs less than I Hz, the exposures should be considered linearly additive. Following this rule, at least two exposures are possible considering all three aspects in a hazard evaluation (see 3.1); the prudent approach would be to apply a caution label to the device with the words "Do Nor Stare Continuously Into Laser Beam". APPENDIX 84. Formulas and Examples Useful in Evaluation of Various Laser Applicftions* 84.l Correction for Atmospherlc Attenuation. Beam irradiance, f, or radiant exposure, f/, for a nondiverging beam at range r which is attenuated by the atmosphere is given by E_E ^itr or H = Hoe-[' (Eq 87) NOTE: The anenuation coeffcic[I. l-1. varies from l0{ per centimeter in thick fog to l0-' in air of very good visibilily. The Rayleigh scattering coeflicienr at 0.6943 pm is 4.llx l0 xcm-r, and l.8x l0-7cm-r at 0.500 um, The eflect of acrosols in cvcn thc clcanest atmosphcrcs uliuitlly raises p at 0.6943 pm to at least l0-7 cm r. 84.2 The Laser Range Equation, Average irradiance at range r (for a direct circular beam) is the total power in the beam at ,' divided by the area of the beam at ,'; likewise, the radiant exposure in a nonturbulent medium is the total energy in the beam at r divided by its total area. ' @e lt' | .2'1 Q e-r (Eq 88) ' z=----f--|T= la+r-Ol nl " I L - _ t n"-lt | | j1 /'la-l.r r H = --Y--------,-t'- = :::29:- " l la+rbl' ? | L - J (a+rQ>' (Eq 89) NOTE l: These formulas are accurate only for small 0 values: the accur,rcy is belter than l% tbr angles less than 0.l7rad (10') and better than 5% tbr angl€s less than 0.37 rad (21'). NOTE 2: For a Gaussian beam the mdximum iffadiance at the beam axis is calculatcd using Eq 88, if a and S are defined at the l/e points of maximum irradiance. * Adrpted ironr C.'l 1l .'J ltu:ar.l! kt Hutlth ft1'n Lu:ttr Rudiution, U.S. Depanment of the Afmy Technical Bulletin I'B-MED-524 {1985). S€€ Applndix C, References for Control
APPENDIX NOTE 3: For rectangular or elliptical beams see 84.7. Example I7'. Find the radiant exposure at I km (105 cm) from a O.lJ Q switched ruby laser (pulse length = 20 ns) which has a beam div€rgence of I mrad (lfr rad) and an emergent beam diameter of 0.7 cm. Using !t = l0-7 cm-r to provide a worst case estimate, " 'J = , ,rrn , ,,_fl0 ' )rtd ) jj:j-:::j=- (0.7 + 1t05;116-111: _ (1.27) (0.1) (0.ee) (0.7 + 100)2 = 1.25 x l0-5 J . cm-2 84.2.1 Norninal Ocular Hazrrd Distance (NOHD). If the atmospheric attenuation coefficient is neglected, a worst case estimate of the NOHD (rMoflD) for Example l7 can be calculated from: 1 rNoHD = 6 o [,_ I =# h/+*P -.'J ( 5.M km 84,2.2 Range Nomogram, Fig, 86. The range nomogram in Fig. 86 (which includes the attenuation coefficient) can also be used to determine rNoHD. For the values given in Example 17, draw a line between l00mJ and l.0mrad. This line intercepts the "lntegrated Radiant lntensity" scale at approximately 0.13 MJ ' s.'. A line is then drawn from the above point to 0.5 lrJ.cm-z on the "Radiant Exposure" scale, intercepting the "Range" scale at 4.9 km for a clear day and 4 km for a hazy day. 84,3 Bearn Diameter. The minimum beam diameter. for a small 0 at range r, is given by F4 84: Dt=a +Qr Example 18: Find the diameter of a laser beam at l km where the emergent beam diameter is lOcm and the beam divergence is 0.1 mrad. 66 Dr = l0 cm + (l0r rad) (105 cm) P1 E= tD cosO" or H= and = l0+ l0=20cm 84,4 Diffuse Refl ections. The reflected irradiance or radiant exposure for a dif. fuse reflector (for rl :> D.) is given by --;4- pr O cos0" --;i- {@=,,.,". '(rr)(10-") (Eqs Bl0 Example 19: Find the maximum rcflected mdiad exposure at a point along the beam axis of a 0.1 I laser, lOm from a diffuse matte of reflectance 0.6 . (cos 0l = 1). H_ (0.1J)(9.6), = 1.9t x tga J.cm-2 (3.14) (10' cm)' Example 20: Find the minimum safe viewing distane for looking at a diffuse target having a rcflectivity P;, = 0.9 from a laboratory Ar laser with O = 2W and d = 2 mm (assume a l0 s exposure duration). (fhis is also the border of the NHZ, see Fig. B4). The emergent beam irradiance is 6^3.7 W.cm-2 which ir greater than the 6,8 W 'cm-' maximum permissible irradiance incident on a 100 percent diffusely reflecting surface for a lOs exposure duration (s€e TableBl). It is therefore concluded that 4vflz must be greater than Dllohin and intmbeam MPEs apply. Hence, the l0 s MPE is I x l0-3 w'cm-2 (Table 5 or Fig. 4) and the expression for rpsT can be found by reananging Eq Bl0. Hence (Eq BI0a) Figure 86 may also be used to determine this distance graphically.
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o SECTION 10. Revision of American
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SECTION Figures Fig. Bl Fig. 92 Fig
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American National Standard for the
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accessible radiation. Radiation to
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lhe eye and skin are detailed in Se
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(See Appendix C for references.) If
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3.3.4 Ctass 4 Lasers and Laser Syst
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APPENDIX simple heat flow models aP
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o APPENDIX Goldman, L., Rockwell, R
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Table l0 Control Measures for the F
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