1. Young’s double slit experiment & Spatial coherence of light
Ivana Hamarová

2. Monochromatic plane wave propagating along axis z
Electrical field
Phase j
amplitude l l
j = 2p

3. Monochromatic plane wave
Electrical field
Phase j
amplitude l l
j = 2p
crests
troughs

4. wavefronts
Plane wave
Spherical wave

5. Young’s double slit experiment
Path difference
Phase difference x z
Constructive
interference +
Destructive
interference +

6. Young’s double slit experimentz
D >> a, a >> l
Dj.. phase difference
d… path difference
a….distance between slits
D…distance between slits and
observation plane
Period of
interference pattern

7. Effect of slit width on the interference pattern
light block

8. Monochromatic plane wave
Electrical field
Phase j
amplitude l l
j = 2p

9. Monochromatic plane wave
Electric field
amplitude
Phase j E
j = 0 …t1, E(z0,t1)
j = p/2 …t2, E(z0,t2)
j= p …t3, E(z0,t3) z0 z

10. Phase at two points x1, x2 x j1 = 0 …t1 j 1= p/2 …t2 x1 j 1= p …t3z
phase difference between two points j 2 - j 1 = Dj = 0, 0, 0
is constant in time = spatially coherent light

11. Phase at two points x1, x2
Disturbance
(x)
(x,t) x x1 z x2

12. Phase at two points x1, x2 t1 t2 Disturbance (x,t1) x x1 z x2
phase difference between two points j 2 - j 1 = Dj ≠ konst
is not constant in time =spatially incoherent light

13. Complex degree of spatial coherence g(Δx)
..describes spatial coherence of light
..a measure of the degree of spatial coherence
..function of distance Dx=x2-x1

14. Spatial coherence of lightΔx x1 x2 1 2

15. Complex degree of spatial coherence g(Δx)
for all points of interest
=> Fully spatially coherent light
for x1 ≠ x2
=> Fully spatially incoherent light

16. Complex degree of spatial coherence g(Δx)
For experimental setup (far field) y h
rectangular aperture x x2
Disturbance z Δx x1 R
h.. aperture width
R...distance between rectangular aperture and the points x1 and x2
coherence distance
First minimum of function g (x1,x2)

17. Effect of the aperture width on the spatial coherenceac
coherence distance ac
increases as aperture width h decreases ac

18. Effect of the aperture width on the spatial coherenceac a h h
a..distance between S1 and S2
a = ac => g(a) =0
a < ac => g(a) = 0.55

19. Visibility of interference fringes (intensity modulation)=ac a
|g(Δx)|
I(x)
a << ac
visibility = 1 x
I(x)
a < ac
partial visibility x
I(x)
a=ac
visibility = 0 x

20. Thank you for your attention