PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

cos
bc
4NDd1 1 2cot
2
III
2
2
B
Nab
N
a
.
(87)
Here δγ denotes the vertical misalignment of the sample. The phase Φ I-II is a quadratic function of
δθ as well as δγ, (vide Eq.(86)). The exact nondispersive sample alignment hence yields the
minimum phase magnitude. Ioffe et al. thus measured parabolic variations Φ I-II individually in each
path I and II by changing δθ and δγ by a few degrees in the vicinity of θ B incidence and located the
corresponding minimum in the phase magnitude to arrive at δθ = δγ=0 settings. With this method,
Ioffe et al., [127] achieved b c /b c of 5.1x10 -5 , whose source-wise constituents are listed in the first
column of Table 3.
However, it must be noted here that phase vide Eqs.(82 and 86) and hence b c (Eq.(87)) formulas
used hitherto, are approximate. The exact phase formula that accounts for refraction corrections at
the ambient-sample interfaces for the sample placed in path I is given by Eq.(81) and for path II,
. Thus, the difference of exactly non-dispersive phases for the sample placed in path I and
II
I
II alternatively with its surfaces aligned parallel to the IFM Bragg planes, equals
1 Nb N b 1
c a a
III 4D .
2
4d 2d
(88)
This phase is rigorously nondispersive not only in vacuum but also in air. Eq.(88) yields the
coherent scattering length
2
III III Nab a
bc
2
.
4NDd 16ND
N
(89)
Therefore the correction to the inferred b c due to the refraction effects
b
b
c
c
Nbcd
2
. (90)
98