Imagine that you have a cosine grating (i.e., a transparency whose amplitude transmission profile is cosinusoidal varying between 0 and 1) with a spatial period of 0.01 mm. The grating is illuminated by quasimonochromatic plane waves of λ = 500 nm, and the setup is the same as that of Fig. 13.36, where the focal lengths of the transform and imaging lenses are 2.0 m and 1.0 m, respectively.

a) Discuss the resulting pattern and design a filter that will pass only the first-order terms. Describe it in detail.

b) What will the image look like on Σ_i with that filter in place?

c) How might you pass only the DC term, and what would the image look like then?

Fig. 13.36

Plane wave Object plane Transform plane Image plane (a) (b) (d)