Nano-Holographic Interferometry for In-Vivo Observations - Biomedical Optical Phase Microscopy and Nanoscopy - page 349

glass and hence experience changes of direction. The interface between the glass slide and
prism is filled with an index-matching fluid.

At the interface between the prism and the glass slide, from Snell's law the p-beam is:

n g sin φ p
n o

sin φ pg 5 (17.13)

And the s-beam is:

n g sin φ p
n e

sin φ sg 5 (17.14)

Since the two beams enter the glass-saline solution interface with incident angles
corresponding to total reflection, they originate evanescent waves. These evanescent
waves produce propagating waves in the saline solution. Figure 17.6B shows the two
wavefronts corresponding to the ordinary and extraordinary beams. From Eq. (17.12)
it follows that the emerging beams are orthogonal to the direction of the incoming beams'
photons that, according to the preservation of momentum, continue their trajectory
along the incident directions. The electromagnetic field that penetrates the saline medium
generates scattered light in the dielectric medium hence a change of direction of /2

takes place for the emerging wavefronts. It should be noted that these wavefronts are
orthogonally polarized and hence do not interfere. However, they produce interference
fringes whose spacing can be measured experimentally; hence, inferences on wavefronts
can be made. The emerging wavefronts have the same wavelength of the incident beam
and then, assuming that the fringe spacing is determined by the incidence angles, one
can write:

π

8
<
:

pm 5 p pm

exp

sin φ

(17.15)

5 p sm

exp
pm

sin φ

where the values p pm and p sm are the measured pitch values for the observed fringes.

After a long derivation [17] , the following relationships are obtained:

8
<

q

n o 2 n g

sin φ pm 5

n s

q

n e 2 n g

(17.16)

:

sin φ sm 5

n s