Application and Optimisation of the Spatial Phase Shifting ...

196 Appendix A: Counting events
and with S equal to the area unit we then have
( )
ρ = ∫ ∫ ∫ ∫ p 0, 0, A , A , A , A ∂( A , A ) / ∂( x, y)
dA dA dA dA
disl r, x i, x r, y i, y r i r, x i, x r, y i,
y
Ar , x Ai , x Ar , y Ai , x
;
(A.6)
with p(A r , A i , A r,x , A i,x , A r,y , A i,y ) given by (2.1), the integration is not trivial; it has been shown in [Ber78,
Eq. 43] that the integral is best evaluated in polar co-ordinates, i.e. after conversion to I and ϕ, similar to
(2.4). Fortunately, this needed be done only once and for all, since the "threshold" intensity is fixed to
zero in this case.