The aero-optical effects (
) in the near-wall regime are expressed in terms of phase distortions of
electromagnetic waves:
 | (11–1) |
where 
is the fluctuating index of refraction at the ray grid points, as calculated
using the Gladstone-Dale relation coefficient (
):
 | (11–2) |
The phase of the optical wavefront that propagates in the y`-direction
for a distance 
can be represented by the optical path length (
):
 | (11–3) |
The wavefront phase distortions are represented by the relative phase difference or optical
path difference (
). The instantaneous and are composed of mean and fluctuating terms:
 | (11–4) |
 | (11–5) |
where 
is the steady-lensing component of defined as
 | (11–6) |
and 
is the fluctuations of , that is, the with the steady-lensing component removed, defined as
 | (11–7) |
Note that in the previous equations, the angle brackets (
) indicate spatial averaging.
can be described as being composed of low order and high order components
(referred to as 
and 
, respectively):
 | (11–8) |
is the sum of the jitter components, that is, the unsteady spatially-constant
term (referred to as the "piston" and represented by 
) and the unsteady spatially-linear terms (referred to as the "tilt" and "tip",
and represented by 
and 
, respectively) from the wavefront distortions:
 | (11–9) |
Note that the piston, tilt, and tip components are calculated using the least-square method by minimizing the following function:
 | (11–10) |
