Before turning to experimental data, it is useful to compare the two theories to see how their predictions for the shapes of the scattering peaks differ. Figure 2 compares the MCT and PT curves for the same values of the parameters that are typical of those that fit some of our experimental data (vide infra). Both theories predict substantial increases in the diffuse or tail scattering between the peaks, but the PT peaks broaden and disappear much more rapidly while the MCT peaks retain a sharper top.
The more interesting way to compare the two theories is shown in Fig. 3 which shows the same first three MCT peaks in Fig. 2. However, the parameters for the PT peaks have now been chosen to provide the best fits to the MCT curves. The fits are performed simultaneously for all three peaks shown in both figures, with, of course, the same sample parameters for PT for each peak. It should be emphasized that, when we start with peaks calculated from PT and fit them with MCT peaks, the same differences are observed, so the comparison is not biased toward either theory. Figure 3 emphasizes that the central parts of the MCT peaks remain sharp and the tails increase substantially with increasing order h. For PT, in contrast, the central peaks broaden much more and the tails grow much more slowly with increasing h. Therefore, PT predicts larger values of the intensity near half-maximum intensity and smaller values of the scattering near maximum intensity as well as in the tails.
It is important to consider how the aforementioned differences affect
the determination of the form factors in Eq. 4.
The total integrated area under the peaks in Fig. 3
is different for MCT and for PT and the ratio 
of the MCT area to the PT area gives the ratio of the square of the form
factors F(h). For the first order we set R(1) = 1 because our X-ray measurements
do not give absolute intensities. Then, from the fit in Fig. 3
we obtain R(2) = 1.10 and R(3) = 1.38. This shows that PT fits to the data
progressively underestimate higher order form factors used for obtaining
electron density profiles if the sample obeys the dynamics of MCT; this
is primarily due to the loss of the intensity in the long power law tails
of the Caillé theory. Similarly, MCT fits to data overestimate higher order
form factors if PT were correct. Therefore, determining the appropriate
theory of disorder and fluctuations affects the determination of average
bilayer structure through electron density profiles. Deciding which is
the appropriate theory, in turn, requires high precision experimental data
to resolve the peak shapes.