Diffraction through a circular hole Diffraction of single l

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 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

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

Diffraction orders

Spectrometer Put slits at f from mirrors. Grating in center

Diffraction orders may overlap

Diffraction orders may overlap Have to use short-pass or long-pass filters to “clean out” overlapping parts.

Gratings cut by an “engine” Typical grating for visible to UV light: 1000-2000 grooves/mm, 10 cm wide105 lines.

Modern methods Blazed gratings put more light into a nonzero order

Resolving power of a grating How much must l change so peak moves by half its width?

Understand 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 p to many p (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)

Fresnel zones on a wavefront

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

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

Fresnel zones for circular apertures Resultant diffraction Intensity on screen circular aperture zones have almost identical areas 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 > a2/ l

Draw the phasor on the spiral that shows the E-field with no obstacle there ( zones open..represents the incoming light). I got it mostly right 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 Io. I got it mostly right I got it mostly wrong but I tried Center is always bright, and is about as bright as the incoming light!

Zone plates used to focus ultrasonic waves 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 Io that hits the plates.

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