如果(Eμ12) = (IER:/2) = 10并令7。=(1-72)/2，则[E1k/) +(K= 2klo{2 + cos[K . (r1 -r2)] + cos[K' . (r1 -72)])(K+k) · (r1 -2)(-) ·(Ti-2)= 2klo /2 + 2cosXcoS22= 4klo(1 + cos[(k + k) ·ro] · cos[(k - k') ·To])
7 如果 �� � = ��! � = �� � = � ��� � + � ���! � 并令�� = (�� − ��)/�，则 = ���� � + ��� � ⋅ �� − �� + ��� �. ⋅ �� − �� = ���� � + ���� (� + �! ) ⋅ �� − �� � ×��� (� − �! ) ⋅ �� − �� � = ���� � + ��� � + �. ⋅ �� ⋅ ��� � − �. ⋅ ��
则 I = 4klo(1 + cos[(K +k) · r] · cos[(K - k) · r])讨论：a）在－k中，大气层的扰动可以抵消（k－k）·ro，调节r，可使p达到元，从而看到干涉p=但cos(k+k)·r项中大气扰动不能抵消b)限制了这种方法的应用（没有达到目的）必须考虑电场强度之间的干涉即以下HBTexperiment8
8 则 � = 4��){1 + cos[ � + �! S �)] S cos[ � − �! S �)]} 讨论： a) 在� − �!中，大气层的扰动可以抵消 � = � − �! S �)，调节�)，可使�达到�，从而看到干涉 b) 但cos � + �! S �)项中大气扰动不能抵消 限制了这种方法的应用（没有达到目的） 必须考虑电场强度之间的干涉 即以下 HBT experiment
1.2Handury-Brown-Twiss interferometer1954到1957年间提出I(ri,t)=K(E(j,t)E*(r,t))r，和r2点间强度干涉with E(,t)=Erek +ExeikiphotonI(,t)=x(E, +Ex-+[ExEr'ei(k-Ki +c.c.]B9
9 1.2 Handury-Brown-Twiss interferometer 1954到1957年间提出 r1和r2点间强度干涉 photon 1 1 1 11 ' 1 ' ( , ) ( , ) *( , ) ( ,) ik r ik r k k Irt Ert E rt with E r t E e E e k × × = = + 1 2 2 1 ' * ( ') ' ( ,) { [ . .]} k k ik k r k k Irt E E E E e cc k - × = + + +
P;(i=1,2)探测器处的光场可以表达为E(ri,t) = Ereiki + Eeik'TiPi(i=1,2)探测器处的光电流为工I(ri,t) = KE*E= [1Er]* + [Er’ + [ErEr,ei(K-R),Ti + c.c. = k[A + B(r)]（光强）进行关联对P,和P2两个探测器上的光电流I(1)I(F2) = k-[A + B(r1)] · [A + B(r2)]= k2[A2 + A · B(r1) + A · B(r2) + B(T1) · B(T2))10
10 ��(� = �, �)探测器处的光场可以表达为 � ��, � = ����� ⋅�� + ��!���!⋅�� ��(� = �, �)探测器处的光电流为 � ��, � = ��∗� = � �� � + ��! � + ����! ∗ �� �-�! ⋅�� + �. �. 对��和��两个探测器上的光电流（光强）进行关联 � �� � �� = �� � + � �� ⋅ � + � �� = �[� + � �� ] = �� �� + � ⋅ � �� + � ⋅ � �� + � �� ⋅ � ��
I(r1)I(T2) = k2[A2 + A . B(r1) + A · B(r2) + B(T1) · B(T2)](A2) = (IErl° + [Er1)")(A · B(T1)) = (IEr’ + [E1°) .[ErE,ei(K-R),T1 + c.c.]e(-R) + (IREEr)e(K-R)(IERI"ERER)+c.c对于来自双星的热态光场，《E）=《E）=0，且(IERl" ERE:) = (IExI"ER) (ER) = 0(IER:"EEx) = (IER"E:) (Ek) = 011
11 �� = �� � + ��! � � � ⋅ � �� = �� � + ��! � ⋅ ����! ∗ �� �-�! ⋅�� + �. �. 对于来自双星的热态光场， �� = ��# = �，且 = �� � ����! ∗ �� �-�! ⋅�� + ��! � ��! ∗ �� �� �-�! ⋅�� +�. � �� � ����! ∗ = �� � �� ⋅ ��! ∗ = � ��! � ��! ∗ �� = ��! � ��! ∗ ⋅ �� = � � �� � �� = �� �� + � ⋅ � �� + � ⋅ � �� + � �� ⋅ � ��