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Additional resources for Optical Image Formation and Processing
18) shows that 2 I = I0 cos (nvC0/X). The distribution of light along Fz is the same as that given by the interference of two coherent point sources separated by a distance ζ0. Consequently, the diffraction by the slits modulates the interference pattern. Along the axis Fz the intensity distribution is represented by the curve of Fig. 15. 8, it will be necessary to consider not two slits, but two very small identical apertures. 19) The interference phenomena are modulated by the diffraction pattern of a square.
3). 3 gives the intensity distribution 2 | F ( C ) | in the plane of the grating. [F(C)] = [sinc^j (f) ® *™(^Ίγ) (46) which one may write: [z>(f)-*-^] (f) <«, e /Rect(f) Fig. 3 50 4 Diffraction Gratings and since convolution is distributive with respect t o addition, o n e has further: ( nvL\ ". (πνζ'\ smc δ(ν — nv0) (x) sine . 8) In the case of a grating, L > ζ0 and consequently the function unc(nvL/X\ as a practical matter, extends only over an interval which is very small compared to v0 = λ/ζ0.
16 explain. In the first place, at the center F, Δ„ = 0 for all the apertures, 2 the amplitude is equal to Ν and the intensity to N 9 if we s e t / (0, 0) = 1. Thus one observes at the center a small and very bright spot. F a r from the axis, the phase difference KAn take on various values between 0 and In. At another point, even one which is very close, all the phase differences change. Even if all the changes are small, they may produce at the end of the calculation significant variations in the amplitude and consequently in the intensity.