Neshyba. 



square law rather than the inverse fourth power law. 



The power density at range of a target in an absorbing and 

 scattering medium, for the model lidar, is given by 



P.D. = PtGte-^^ 



target — LJ (5) 



4ttR^ 



where P.^ = transmitted power, 1 megawatt peak 



Gt = transmitter gain factor, 10° for the 6" telescope 

 o( = attenuation coefficient, 5 x 10" at 470(4,, and 

 R = range to target in cms. 



Let r be the diffuse reflectance of the target, here taken as 

 10%. The target area within the^ield of view is given by 



4 

 where cjj = the beamwidth in milliradians 



The total power reflected by the target is then 



P ,, =(P. D.\ X Area^ xr. (7) 



refl ^ 'Target Target ^ ' 



Taking into account that this power is reflected into a solid angle of 

 2iT steradians, and accounting for the total attenuation encountered 

 during signal return, the power density at the receiver is then 



P.G e 



■2c(R 



2r,2 



— Rcvr 7 — ^ ' 



^ 4R'^ 4 2tt 



Considering now the numerical values from the specifications, the 



power density at the receiver aperture is computed and plotted as 



curve (a) in Fig. 2 as a function of target range. 



Minimum Detectable Signal at Receiver Aperture 



Consider now that the energy intercepted by the receiving 

 aperture above is focused so as to illuminate the total active photo- 

 cathode surface of the 6199 receiver tube, i. e. , 7. 75 cm'^. From 

 equation (4) the minimum detectable signal at the photocathode sur- 

 face is 9. 4 X 10" ■^ microwatts /cm^. For the receiver with 5" tele- 

 scopic aperture, the minimum detectable signal level at the a.perture 

 can now be found by 



,,^„ ,,^^ Area of Cathode 



M. D. S. ^ , = M. D. S.^ ^^ ^ X— 9) 



Aperture Cathode Area of Aperture 



= 5. 78 xlO-^^microwatts/cm^ 



For an allowable signal- to- noise ratio of one, the maxiinum 

 useful mapping range for this value of minimum detectable signal is 

 shown as point n on curve (a). Fig. 2. This is about 250 meters, 



433 



