342 GENERIC TYPES OF RADAR SYSTEMS AND TECHNIQUES 



optical elements themselves, for example an imperfectly transparent dome 

 heated in flight, contribute significant and undesirable radiation. The 

 usable signal results from the difference between radiation collected from 

 the target and all other sources. This "contrast" signal is proportional to: 



m 



V.^AE K^-7; 



^z?o-' 



SxTxd,. (6-55) 



where F^ = signal output (volts) from the detector 



A = area (cm^) of main collector mirror 



a = field of view of radiometer (radians) = width of square detector 

 divided by the focal length of collector mirror 



E = efficiency (%) of windows, filters, mirrors, etc. in the optical 

 system (dimensionless). This is here assumed to be independ- 

 ent of the wavelength 



JxT = spectral distribution of target radiation (watts micron"^ 

 steradian"^) 



JxB = spectral distribution of background and other unwanted 

 radiation (watts cm~^ steradian"^ micron"^) 



6'x = spectral response (volts /watt) of detector 



Tx = spectral transmission (%) of the atmosphere between the 

 target and detector (dimensionless) 



Xi,X2 = wavelength limits (microns) of system sensitivity defined by 

 the optical filter or sensitivity limits of the detector. 



R = target range (cm). 



The detector will have a noise output F„ which will be a function of the 

 type of detector, the bandwidth A/ of the amplification system, and the 

 radiation environment of the detector. Specifying the minimum signal-to- 

 noise ratio Fs jVn required for reliable detection of a target, the system noise 

 defines the minimum required V^. Since 7xr, 7\b, and T^ are beyond our 

 control and E is always optimized anyhow, the remaining parameters are 

 chosen to give the required Vs at the desired target range. Actually Xi and 

 X2 are generally determined by consideration of Jxr, 7\b, and T^. Fig. 6-35 

 shows J-^T, J\B, and T^ plotted as a function of wavelength for a specific 

 application: the detection of a 600° K blackbody viewed against a back- 

 ground of clouds or heavy haze through 10 miles of moderately clear sea 

 level air. It is plain that the best choice of wavelength limits are Xi and 

 X2 = 3.3 and 4.1 microns, respectively. The properties of available de- 

 tectors — sensitivity, time constant, ruggedness, reliability, etc. — may, of 



