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# E - Bibliothèque et Archives Canada

E - Bibliothèque et Archives Canada

## a) 'O' faœ fields: q=oO

a) 'O' faœ fields: q=oO J&P oas(~-9') E:= e E: = -e JLpcos(0+9') from equation 4. i , b) 'n' face fields: Let'sdefine: y=nz-p y'=nx-pp With variables y and y' the 'n' face becorne the 'O' face and vice versa EZ = u(+ (n-1)z)x e J~P=(v-Y') from equation 4.1 we have (sinœ 39 = 4 ÿ. ). H: = U(+(N -~)r)dsin(~ '7 4.1.2 Diffircted field Frorn equations 2.3 and 4.1 - W1)x e J"P -(v -vB) where p> = O' for the 'o'faœ and p = nxf~r the 'n' face

Equation 4.4 can ôe evaluated if is knm. A ptedical way to cornpute it is a~ by using the already existing meaiad and submutine for the SI- dimacoon coefficient. Both are not totelly equivalent and one shoutd be derived from the aer as it will be explained ôeiow. a) Slooe diffraction In chapter 2, formulas for UTD were introduced. As stated in equation 2.3 and 2.4, the diffracted field depends on the incident field at the edge. According to this formula, the diffraded field will be zero if the incident fmld at the edge is zero alsa There are sorne instances where this situation occurs (zero incident field) at the edge itsel only and the incident field is not zero nearby. This situation is dealt with by intmducing a higher order diffraction depmdent not on the magnitude of the incident field but rather on its rate of change (slope). The difftacted field due to dope diffraction is represented by an equation similar to equations 2.3 and 2.4 but the incident fidd term is replaœd by its derivative (rate of change) relatively to the noml and Dsh is replaced by dB,h a@* The majority of existing codes dealing with dimaction coefficients, have al- subroubine for the slope diffraction coenicient. Evaluation of dope difffaction is not in the scope of this work but it will be shown ôelow how to use % to get fi with an easy manipulation. & 3~ b) üerivative of Ds with mmct to 0 iinsteaâ 0' The slope diffraction coefficient formulation can be fwnd easily in the iiterature[2][[23~4].

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