PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

the beam and remains visible up to very high interference orders [1]. However, here the phase
varies significantly with θ as
2 2
I0 c a a B B
2 Nb N b Dd 1 cot {1 2cot }/ 2 ,
(85)
introducing dispersion due to a horizontal sample misalignment δθ. The nondispersivity condition
therefore requires the sample to be aligned with arcsec precision (cf. Fig.52 and 0-I and II-0
curves in Fig.53 (bottom)). Only at the exact nondispersive setting (viz., θ= θ B , to within arcsec),
can Ф I be increased to arbitrarily large values by increasing D without losing interference contrast.
At even a slight misalignment δθ, the -dependence of the first order term in δθ of the Ф I-0
variation (85) is large enough to make the phase dispersive (Fig.52), thereby limiting b c precision.
Ioffe et al. [127] obviated the need for this precise sample alignment by measuring the phase shift
between interferograms recorded with the sample placed alternately in subbeams I and II (Fig.50).
For a symmetric LLL IFM, this method requires that the sample be parallel translated from path I
to path II. Upon translation, the horizontal misset angle δθ changes sign. The phase shift then
equals ( ) ( ( )) ( ) ( ) . This eliminates the large first order variation of the
phase (cf. Eq.(85) and 0-I and II-0 curves in Fig.53 (bottom) for 0 ) with δθ. The sample
alignment thus requires only arcminute precision to locate the minimum in the magnitude of I-II
(cf. I-II curves in Fig.53), occurring at the intersection of 0-I and II-0 curves. For small
deviations in the incidence angles, the nondispersive phase shift
2 Nbc Naba Dd 2
2
2
{1 2cot
B } ,
III
cos
(86)
then determines the coherent scattering length
96