206 RADIATION BIOLOGY 



used at one time. Wood showed that, by making the sides of the groove 

 of a reflection grating smooth and by controlling the angla of one side 

 so that each ruling behaved as an elementary line mirror, it was possible 

 to obtain a grating with most of the energy in one order and on one side 

 of the central image. This type of grating he called an "echelette" 

 (Babcock, 1944; Stamm and Whalen, 1946), and it is used in nearly all 

 modern gratings. The high eflficiency obtains for only a certain range of 

 wave lengths or blaze where the angle of the groove, or blaze angle, is 

 such as to cause specular reflection. Since the groove angle determines 

 the wave length of the blaze, or the most intense portion of the spectrum, 

 it is important to specify the region where maximum efficiency is desired 

 when ordering a blazed grating. For example, one commercial grating 

 of 10 X 10 cm with 600 lines per millimeter and in a Littrow mounting has 

 the following efficiencies for different wave lengths in the first order on 

 one side: 254 m^, 62 per cent; 265 m,i, 72 per cent; 313 mn, 48 p* cent; 

 and 546 m^, 18 per cent. It is evident that this grating is most useful in 

 the ultraviolet. 



The groove angle a required to produce the maximum intensity at the 

 blaze wave length can be calculated from simple geometrical analysis, 

 considering the bottom of each groove or fine as an elementary mirror 

 inchned at the angle a to the grating surface (Babcock, 1944). The 

 incident ray and diffracted ray of the blaze wave length must make equal 

 angles with a normal to the bottom of the groove for specular reflection 

 and maximum energy transfer. The following relations then hold : 



mX = d(sin i ± sin d), 



which is Eq. (3-20), and 



a = a ± d)/2. (3-23) 



The upper signs apply when the incident and diffracted rays are on the 

 same side of the grating normal, and the lower signs when they are on 

 opposite sides. From these two formulas the value of the groove angle 

 necessary for any value of A and i or 9 can be calculated. It will be 

 noted that the values of i and 6 as determined by the optical arrangement 

 or mounting have only a small effect on the value of a. 



In order to cover the ultraviolet and visible at high efficiency with 

 echelette gratings, several gratings must be available with the same 

 grating spacing d but different groove angles a. The grating previously 

 mentioned as having the blaze at 265 m^ was designed for a Littrow 

 mounting in which t = 6 and the incident and diffracted rays were on 

 the same side of the normal. For this condition a = 4° 33', as predicted 

 by Eq. (3-23). Maximum eflftciency at 400 m/x for the same arrangement 

 requires a groove angle of 6° 54', and for 600 m/x an angle of 10° 22'. 

 However, if an incandescent source is used, the groove angle should be 



