LabViewDDM/Protocols/Micro-rheology.md

@@ -5,15 +5,18 @@
 2. Convert the DICF into an MSD
    1. Get good estimates for A(q) and B(q) using the following options
 	  * fit data with suitable model
-	  * Estimate from g(q,tau_min) and g(q, tau_max)
+	  * Estimate from $g(q,\tau_{min})$ and $g(q, \tau_{max})$
 		
    2. Estimate mean squared displacement as  
-MSD(tau; q) = -4/q^2 ln(1 - (g(q,tau)-B(q))/A(q)).  
-**Note:** This assumes motion in 2D (for 3D the 4 needs to be replaced by 6)
-      1. This can be displayed in my software by selecting 'Representation'-> 'MSD' in the 'Display & Fit' tab
-	  2. Rather than plotting it for all tau it uses 'MSDcutoff' to suppress values too close to the noise level: if correlation has dropped by more than 'MSDcutoff' (default 85%) it is not plotted and when saving a NaN values is saved.
-      3. MSD(tau; q)  can be saved by using 'Save as displayed' button
-   3. In principle this MSD should be independent of the q used to calculate it, but in practice they differ (if nothing else in the timescales/displacements they can reliably access...).
+
+   $$MSD(\tau; q) = -\frac{4}{q^2} \ln(1 - (g(q,\tau)-B(q))/A(q)).$$
+  
+   **Note:** This assumes motion in 2D (for 3D the 4 needs to be replaced by 6)
+
+   1. This can be displayed in my software by selecting 'Representation'-> 'MSD' in the 'Display & Fit' tab
+   2. Rather than plotting it for all $\tau$ it uses 'MSDcutoff' to suppress values too close to the noise level: if correlation has dropped by more than 'MSDcutoff' (default 85%) it is not plotted and when saving a NaN values is saved.
+   3. MSD$(\tau; q)$  can be saved by using 'Save as displayed' button
+   4. In principle this MSD should be independent of the q used to calculate it, but in practice they differ (if nothing else in the timescales/displacements they can reliably access...).
 
 3. Extract G* from MSD
    1. The 'Microrheology' tab is sometimes hidden: if so, go to 'Select Movies' -> Advanced settings' -> 'Misc' and activate the 'Show u-rheo Tab?' button