A point source of monochromatic light (500 nm) is 50 cm from an aperture plane. The detect...

A point source of monochromatic light (500 nm) is 50 cm from an aperture plane. The detection point is located 50 cm on the other side of the aperture plane.

a. The transmitting portion of the aperture plane is an annular ring of inner radius 0.500 mm and outer radius 0.935 mm. What is the irradiance at the detector relative to the irradiance there for an unobstructed wavefront? The results of problem 1 will be helpful.

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b. Answer the same question if the outer radius is 1.00 mm.

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c. How many half-period zones are included in the annular ring in each case?

Problem 1

The zone plate radii given by Eq. (13-20) were derived for the case of plane waves incident on the aperture. If instead the incident waves are spherical, from an axial point source at distance p from the aperture, show that the necessary modification yields

where q is the distance from aperture to the axial point of detection and L is defined by 1/L = 1/p + 1/q.

Figure 1.