Holography and temporal coherence

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Presentation transcript:

Holography and temporal coherence Coherence lengths required?

Two-slit interference

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:

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

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

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

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

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!

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

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.

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

Fringe visibility or contrast

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!

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

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

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

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:

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

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.