光学OPTICS教学课件：11 Coherence Theory

1、Chapter 11 Basics of Coherence Theory (2 hours,Visibility Mutual coherence function Coherent vs. incoherent interference,Waves that combine in phase add up to relatively high irradiance,Waves that combine 180 out of phase cancel out and yield zero irradiance,Waves that combine with many different ra

2、ndom phases nearly cancel out and yield very low irradiance,Constructive interference(coherent,Destructive interference(coherent,Incoherent addition,Interfering many waves: in phase, out of phase, or with random phase,If we plot the complex amplitudes,The relative phases are the key,Recall that the

3、irradiance of the sum of two waves is,If we write the amplitudes in terms of their intensities, Ii, and absolute phases, qi,Re,Im,q1 q2,I,0,The intensity can be anywhere between,depending on the value of q1 q2,and,Adding many fields with random phases,Itotal = I1 + I2 + + In,I1, I2, In are the irrad

4、iances of the various beamlets. Theyre all positive real numbers and they add,If there are many fields, each with a random phase, qi,Ei Ej* are cross terms, which have the phase factors: expi(qi-qj). When the qs are random, they cancel out,All the relative phases,The intensities simply add! Two 20W

5、light bulbs yield 40W,I1+I2+IN,Light bulbs,Light from a light bulb is very complicated,Light from a light bulb is incoherent,Itotal = I1 + I2 + + In,When many light waves add with random phases, we say the light is incoherent, and the light wave total irradiance is just the sum of the individual irr

6、adiances,Other characteristics of incoherent light: 1. Its relatively weak. 2. Its omni-directional. 3. Its irradiance is proportional to the number of emitters,Coherent vs. Incoherent Light,Itotal = I1 + I2 + + In,Etotal = E1 + E2 + + En,Coherent light: 1. Its strong. 2. Its uni-directional. 3. Tot

7、al irradiance N2 or 0. 4. Total irradiance is the mag-square of the sum of individual fields,Incoherent light: 1. Its relatively weak. 2. Its omni-directional. 3. Total irradiance N. 4. Total irradiance is the sum of individual irradiances,Temporal coherence in Youngs double slit experiment,Temporal

8、 coherence in thin film interference,p,Maximum thickness of thin film to observe interference,Temporal coherence in Michelson interferometer,Temporal Coherence Fringe Visibility,Spatial Coherence,Width of light source is b, incoherent and uniform. The total interference field is incoherent superposi

9、tion of each point source of the light source,R,Fringe Visibility,Variation of fringe visibility with source width,Visibility of a Circular Source,Visibility curve of a circular source is proportional to a first-order Bessel function,Same functional form as that of a circular aperture diffraction pa

10、ttern,Consequence of van Cittert-Zernike theorem,Visibility variation with the width of light source,Visibility variation with the separation of apertures,Effect of light source bandwidth on fringe visibility,Youngs double split experiment demonstrate both spatial and temporal coherence effect,Mutua

11、l Coherence Function,Assumed the wave field is stationary, so its statistical nature does not alter with time. We can shift the time origin in the time average,Self coherence function,Complex degree of coherence,General interference law for partially coherent light,Degree of coherence,Relationship b

12、etween Visibility and Degree of Coherence,The modulus of the complex degree of coherence is identical to the visibility of the fringes for equal incident irradiance,Measurements of the visibility and fringe position yield both the amplitude and phase of the complex degree of coherence,The off-axis s

13、hift in the location of the central fringe is a measure of a12(t,Temporal Coherence,If the primary source S shrinks down to a point source on the central axis having a finite frequency bandwidth, temporal coherence effects will predominate. The optical disturbances at S1 and S2 will be identical,Com

14、plex degree of temporal coherence,For a strictly monochromatic plane wave of infinite coherence length,For a quasi-monochromatic wave where t is greater than the coherence time, Df will be random, varying between 0 and 2p such that the integral averages to zero, corresponding to complete incoherence

15、,The Fourier transform of the self-coherence function, , is the power spectrum, which describes the spectral energy distribution of the light,Spatial Coherence,If we go back to Youngs experiment with a very narrow-bandwidth extended source, spatial coherence effects will predominate,The optical dist

16、urbances at S1 and S2 will differ, and the fringe pattern will depend on,Complex degree of spatial coherence of the two points at the same instant in time,例题：从地球上看太阳的视角10-2rad，光波长区取太阳光谱的最大值的波长，550nm，问太阳在地球的相干间隔,解,此方法可以测量星体对地球的孔径角：测量出干涉条纹消失时的d，就计算出了光源的孔径角,Problem: Normally the aperture angle of a sta

17、r is very small, for example Orion Betelgeuse, its 2 10-7rad, only when d = 3.07m Youngs interference fringes start to dissappear. Since d is so large, the resulting interference fringes is too dense for human eyes and observation instruments to resolve, so the detection of visibility changes is no

18、longer possible. How to solve the contradicting requirements between angle resolution and fringe spacing resolution,Michelson Stellar Interferometer,Michelson Stellar Interferometer,No extra optical path length is added from (S1, S2) to (S1, S2), so the coherence level at (S1, S2) is the same as tha

19、t of (S1, S2,remote star,B,A,O1,O2,B1,B2,M1,M4,S2,S1,d,remote star,Twenty-foot Michelson interferometer for measuring star diameters, attached to the upper end of the skeleton tube of the 100-inch Hooker telescope,Betelgeuse (a Orionis) was the first star whose angular diameter was measured by Michelson with this device. One c