Holography and temporal coherence Coherence lengths required?

Why a long, dispersed pulse will have the same I(  ) as the original short one.

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

Temporal or “longitudinal” coherence length l c or time t c.. Spatial or “transverse” coherence length h c of a beam of light from a star, distant streetlamp. Hey, we can get the diameter of a star if we know h c !

Derive h If we move a distance h across the beam, how much does the path change for the light from a point at maximum  ? Find distance h where it shifts by . That’s approx h c d W Path lengths from all points change, and they all change differently. That’s why we lose coherence for big  L1L1 L2L2

Two-slit interference pattern (Phys 123) from very narrow slits, incoming light at  = 0 Conditions for 2-slit interference peaks: h D d2d2 d1d1 dd

Spatial coh. can be measured by 2 slit diffraction Single source at y’  0 (at small  ’), far away so parallel phase difference of two beams arriving at y (or  ?

Spatial coh. can be measured by 2 slit diffraction Real light source with many angles at y’,  ’. Each spot emits with its own phase, so we add intensity patterns from each.

Effect of finite slit width In measuring spatial coherence, we measure the visibility of the double slit fringes (closest one)

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

Fringe visibility or contrast

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 h c Or use:

Sketch visibility V(h) for the sources far from the slits: 1. A point of light on the axis : 2. A uniform bar of light perpendicular to the axis 3. A light source that has brightness like a gaussian fading away from the axis. 4. A point of light moved off the axis: a)I got it mostly right b)I got it mostly wrong, but tried

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

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

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

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