1. Diffraction through a circular hole
Diffraction of single l

3. 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

4. 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!

5. Diffraction limitations on imaging
Every star gives the same shape on the screen

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

8. Diffraction orders

9. Spectrometer
Put slits at f from mirrors. Grating in center

10. Diffraction orders may overlap

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

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

13. Modern methods
Blazed gratings put more light into a nonzero order

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

18. 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).

19. The phasor diagram approximates this integral

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

21. Fresnel zones on a wavefront

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

23. 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

24. 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

25. 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

26. 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

27. Poisson’s spot in shadow of ball bearing
Suppose a ball blocks zones 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!

28. 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.

29. 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