88 INSTRUMENTATION 



substance with refractive index rii is selected for the conjugate area, the 

 use of a material with refractive index /?2 for the complementary area 

 eliminates any contribution of the embedding material to d\. With this 

 choice of coating materials Eq. 2.1 becomes 



(ni - n2)t = d\. (2.2) 



If an absorbing material is also deposited upon or incorporated into 

 either the conjugate or the complementary area, then the amount n^ts 

 must be added to the optical path of that area. Here n^ = refractive 

 index of the absorbing material and /3 = thickness of the absorbing 

 material. If the absorbing substance is applied on the conjugate area 

 of the plate represented by Fig. III. 2 and if the optical path difference 

 between the conjugate and complementary areas remains d\, then 



(rii — )i)li + (n3 — n)ts — (^2 — n)f2 = d\. (2.3) 



If, on the other hand, the absorbing material is applied on the comple- 

 mentary area of such a diffraction plate and if the optical path difference 

 between the conjugate and complementary areas is again c/X, then 



(ni - n)(i - (n-s - n)t-i - (n-. - n)f2 = d\. (2.4) 



As before, it is convenient to choose n = ^2. Equations 2.3 and 2.4 

 become 



{rii - n2)h + (^3 - n2)h = d\; (2.5) 



(ni — W2)/i — (ns — n2)/3 = rfX. (2.6) 



It will be seen (Sections 2.3 and 2.4) that the design specifications for 

 either an achromatic or a color diffraction plate can be satisfied if the 

 refractive indices of the materials constituting the coating on the dif- 

 fraction plate are given functions of the wavelength. If the dispersion 

 is important, then the Ecjs. 2.1-2.6 can be written to include the de- 

 pendence on wavelength explicitly. It may also become advantageous 

 when such specialized dift'raction plates are reriuired to consider only the 

 more general Eq. 2.1 and work with three materials having refractive 

 indices ni(X), n2{\), and n{\). 



Procedures and materials are available which will allow the contribu- 

 tion (^3 — ^2)^3 to be neglected because the re(iuired amount of absorp- 

 tion is obtained when f^ is still very small compared with ^i. For 

 purposes of the discussion it will be sufficient to consider that the 

 optical path difference between the conjugate and complemontaiy areas 

 is given by 



(ni - n2)h = d\ (2.7) 



