Reading Quiz What does the “Rayleigh criterion” tell us? The angular separation resolvable by an imaging system The angle of diffraction around atmospheric droplets The number of orders produced by a diffraction grating

Reading Quiz A lens placed after a diffraction aperture causes the Fraunhofer pattern to be produced: before the focal length at the focal length after the focal length (but at a finite distance) at infinity

Diffraction through a circular hole Diffraction of single l

Imaging diffraction with a lens/mirror A lens puts the far-field diffraction on a screen at f from the lens, but must be measured from the lens. So the far-field can be observed easily even if the far-field d>a2/l 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, usually due to diffraction. (Aberrations might also contribute to “point spread function).

Diffraction limitations on imaging Rayleigh limit: One peak over the other star’s first zero

Let’s see why the center changes bright-dark-bright in Fresnel diffraction of apertures. .

Understand diffraction from phases arriving from aperture We consider here 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). Or it can change only a little (Fraunhoffer regime)

The phasor diagram approximates this integral as I open the aperture steadily

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

Phasor addition from Fresnel zones on aperture For illustration, we color aperture areas white and black between these p boundaries. Aperture colored by alternating zones

Calculation of Fresnel zones boundaries This is the aperture colored by alternating zones

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

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

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, the screen angular pattern doesn’t change with d Can 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.

For off-center points on screen, Fresnel zones on aperture are displaced …harder to “integrate” mentally. When white and black areas are equal, light at P’ is _____ a) dimmest b) brightest P’

Fresnel zone plates as “lenses” f is the distance used to calculate the zones. Will change with l Spatial resolution of image is ,width of narrowest zone

Fresnel zone plates as “lenses” Thinnest zone included: Dr=25 nm. Used to image cell structures with soft xrays

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 that interfere with zone 1 How high to raise an antenna from the ground? If the ground reflects zone 2, you may do better lowering the antenna