1. Holography and temporal coherence
Coherence lengths required?

2. Two-slit interference

3. Two-slit interference pattern from a plane wave
from narrow slits, incoming light at q = 0 h D d2 d1 Dd
Conditions for 2-slit interference peaks:

4. Find the intensity pattern I(q)
y,q h

5. What is different for a point source off axis by q’?

6. What happens if I have two uncorrelated point sources at different q’1 and q’2?

7. What happens if my source is a star or the sun?
Many two-slit patterns are superposed

8. Contrast (visibility) is less as width of source is increased
So we can use 2-slit fringe visibility to measure the width of a star!

9. New Mexico VLA (radio)
Narrabri , Australia (optical), 640 m

10. Single mirror resolution (it’s diffraction limited)
Two interfering mirrors separated by h have same angular resolution as one mirror of diameter h
Note: modern stellar interferometers use several different interference techniques, but resolution principle is the same.

11. Spatial coherence can be measured by 2 slits
Real light source with many angles at y’, q’
The
factor in front doesn’t affect the visibility
The spatial coherence (2-slit fringe) function
comes from the spatial FT-1 of the source intensity

12. Fringe visibility or contrast

13. Temporal or “longitudinal” coherence length lc or time tc..
Spatial or “transverse” coherence length hc of a beam of light from a star, distant streetlamp.
Hey, we can get the diameter of a star if we know hc!

14. Spatial coherence can be measured by 2 slits
Real light source with many angles at y’, q’
The
factor in front doesn’t affect the visibility
The spatial coherence (2-slit fringe) function
comes from the spatial FT-1 of the source intensity

15. fringe contrast or visibility
To test the spatial coherence we can vary slit spacing h and look at the fringe contrast.

16. Spatial coherence and interference of light
Can we see 2-slit interference from sunlight?
…yes, if we use only a small spot from the beam to illuminate the slits.
…how small? Less than the transverse coherence length

17. To test the spatial coherence we can vary slit spacing h and look at the fringe contrast. When they are mostly washed out, we’re past hc
Or use:

18. I got it mostly wrong, but tried
Sketch visibility V(h) for the sources far from the slits:
A point of light on the axis :
A uniform bar of light perpendicular to the axis
A light source that has brightness like a gaussian fading away from the axis.
A point of light moved off the axis:
I got it mostly right
I got it mostly wrong, but tried

19. Connection with text’s notation
Angular version is much simpler!
The phase factors in front don’t affect what we measure, the fringe visibility, , so we ignore them.