With Fig. 13.36 in mind, show that the transverse magnification of the system is given by -Æ’_i/Æ’_tand draw the appropriate ray diagram. Draw a ray up through the center of the first lens at an angle θ with the axis. From the point where that ray intersects Σ_t, draw a ray downward that passes through the center of the second lens at an angle Φ. Prove that Φ/θ = Æ’_t/Æ’_i. Using the notion of spatial frequency, from Eq. (11.64), show that Κ_Oat the object plane is related to Κ_Iat the image plane by 

Κ_I = Κ_O(f_t/f_i)

What does this mean with respect to the size of the image when Æ’_i > Æ’_t? What can then be said about the spatial periods of the input data as compared with the image output?

 Fig. 13.36

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