Detailed analysis of MSE spectra

Now we make use of the expansions
cos(A) = cos(A 1 cos(ω 1 t)) = J 0 (A 1 ) − 2J 2 (A 1 ) cos(2ω 1 t)
cos(B) = cos(A 2 cos(ω 2 t)) = J 0 (A 2 ) − 2J 2 (A 2 ) cos(2ω 2 t))
sin(A) = sin(A 1 cos(ω 1 t)) = 2J 1 (A 1 ) cos(ω 1 t)
sin(B) = sin(A 2 cos(ω 2 t)) = 2J 1 (A 2 ) cos(ω 2 t)) (23)
We can now evaluate the intensities at the frequencies: ω 1 , 2ω 1 , ω 2 , and 2ω 2 :
I ω1 = I 0 sin(δ) √ r m J 1 (A 1 )
√ sin(2γ)
2
I ω2 = − I 0 sin(δ) √ r m J 0 (A 1 )J 1 (A 2 )
√
2
I 2ω1 = (I b + I 0 )J 2 (A 1 )(1 − r m )
2 √ 2
sin(2γ)
− I 0J 2 (A 1 )(1 + r m )
2 √ 2
cos(2γ)
I 2ω2 = − I 0J 2 (A 2 ) √ r m cos(δ)
√
2
sin(2γ). (24)
The expressions for I ω1 , I 2ω1 , and I 2ω2 agree with those of Hawkes (Hawkes didn’t publish
the result for I ω2 .) So we come to the same conclusion as before, namely
I ω2
= − J 0(A 1 )J 1 (A 2 )
I ω1 J 1 (A 1 )
(25)
Conclusions
40