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

Transcribed Image Text:

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