Diffraction through a circular hole Diffraction of single

Imaging diffraction with a lens/mirror A lens images the far-field on a screen at f from the lens, but must be measured from ______ So the far-field can be observed easily even if the far-field d is too far away to be convenient

Imaging diffraction with a lens/mirror The lens/mirror may be placed anywhere at/after the aperture. In fact the lens/mirror diameter itself could be the aperture!

Diffraction limitations on imaging Every star gives the same shape on the screen, due to diffraction. (Aberrations might also contribute to “point spread function). D

Diffraction limitations on imaging Rayleigh limit:Peaks are over the other star’s first zero

Understand diffraction from phases arriving from aperture We consider now only the center of the screen I(0,0,d) How does the phase of the light from general x’ differ from that coming from x’=0? For small enough d (large enough a), it can differ by  to many  (Fresnel regime).

The phasor diagram approximates this integral

Fresnel zones Light from the first “zone” in the aperture all tends to make the screen brighter at (0,0,d)

Calculation of Fresnel zones boundaries

Phasor addition from Fresnel zones on aperture In our minds, we color aperture areas white and black when we cross these  boundaries.

Fresnel zones for a slit d,a are such that the above aperture is 9 zones wide: Bright at center Aperture zones Resultant diffraction Intensity on screen

Fresnel zones for circular apertures circular aperture zones have almost identical areas Resultant diffraction Intensity on screen d,a are such that the above aperture is filled with 9 zones: Bright at center

If we move the screen back, there are ________ circular zones in the same aperture a) more b) fewer Eventually, if d grows or a shrinks, we get less than one zone in the aperture. This is the Fraunhofer regime After that, nothing much changes for bigger d or smaller a. Show this occurs when d > a 2 /

Draw the phasor on the spiral that shows the E-field with no obstacle there (  zones open..represents the incoming light). A.I got it mostly right B.I got it mostly wrong but I tried

Poisson’s spot in shadow of ball bearing Suppose a ball blocks zones 1-3. Show the beginning and ending points on the phasor diagram of the light that reaches center spot on the screen Estimate I at center of screen in terms of the incident I o. A.I got it mostly right B.I got it mostly wrong but I tried Center is always bright, and is about as bright as the incoming light!

Suppose you make a zone plate that lets only zones 2, 5 and 8 through. Find the strength of I at center of screen in terms of I o that hits the plates. Zone plates used to focus ultrasonic waves

No aperture: The zones here have to do with the phase of reflections from other objects that interfere with zone 1 How high to raise an antenna from the ground? Fresnel zones are widely used in antenna-receiver tech If the ground reflects zone 2, you may do better lowering the antenna L L+ /2 L+