ratio of singly-scattered intensity per particle from the concentrated sample to that from the dilute sample: $S(q)=(\left<I^S\right>/\phi)/(\left<I_{dil}\right>/\phi_{dil})$. This was calculated by taking into account multiple scattering and attenuation of light through the sample: $$\label{eq:Sq}
S(q) = \frac{\phi_{dil}}{\phi}\frac{\sqrt{T_{B,dil} T_{G,dil}}}{\sqrt{T_B T_G}}
\frac{\sqrt{\left<I_B\right> \left<I_G\right>\beta^2\beta_{MS}^2}}
{\sqrt{\left<I_{B,dil}\right>
\left<I_{G,dil}\right>\beta^2}}\;,$$ where $T$ is the transmission coefficient of the sample, and subscripts $B,G$ are for blue and green light respectively.

Dynamic light scattering aims to measure the dynamic structure factor (DSF), $f(q,\tau)$. This can be extracted from normalizing the ICF using Eq. \[eq:g2\]: $$\label{eq:DSF}
f(q,\tau) = \sqrt{\frac{{g^{(2)}}(q,\tau)-1}{{g^{(2)}}(q,0)-1}}\;.$$ However, since most of our samples were either non-ergodic or had very slow relaxation times, the time-averaged ICF only measured fluctuations in a small subspace of the whole configuration space. Explicit ensemble averaging was therefore required, and was performed by two methods. For short times ($10^{-7}\;\mbox{s} < \tau <
20\; \mbox{s}$), brute-force ensemble averaging was done. Several hundred (typically between 500-865) of time-averaged ICF’s, ${g^{(2)}}_t(q,\tau)$, and associated scattered intensities, $I_{Bt}$ and $I_{Gt}$, were measured, each for a duration of 40-60 s. Between each measurement, the sample was rotated by a small angle to a different position so that each time-averaged ICF sampled a different Fourier component. The ensemble-averaged ICF was then 