A non-invasive, in-situ calibration method for Total Internal Reflection Microscopy (TIRM) based on optical tweezing is presented which greatly expands the capabilities of this technique. We show that by making only simple modifications to the basic
TIRM sensing setup and procedure, a probe particles absolute position relative to a dielectric interface may be known with better than 10 nm precision out to a distance greater than 1 $mu$m from the surface. This represents an approximate 10x improvement in error and 3x improvement in measurement range over conventional TIRM methods. The techniques advantage is in the direct measurement of the probe particles scattering intensity vs. height profile in-situ, rather than relying on calculations or inexact system analogs for calibration. To demonstrate the improved versatility of the TIRM method in terms of tunability, precision, and range, we show our results for the hindered near-wall diffusion coefficient for a spherical dielectric particle.
We introduce a probabilistic approach to the problem of counting dwarf satellites around host galaxies in databases with limited redshift information. This technique is used to investigate the occurrence of satellites with luminosities similar to the
Magellanic Clouds around hosts with properties similar to the Milky Way in the object catalog of the Sloan Digital Sky Survey. Our analysis uses data from SDSS Data Release 7, selecting candidate Milky-Way-like hosts from the spectroscopic catalog and candidate analogs of the Magellanic Clouds from the photometric catalog. Our principal result is the probability for a Milky-Way-like galaxy to host N_{sat} close satellites with luminosities similar to the Magellanic Clouds. We find that 81 percent of galaxies like the Milky Way are have no such satellites within a radius of 150 kpc, 11 percent have one, and only 3.5 percent of hosts have two. The probabilities are robust to changes in host and satellite selection criteria, background-estimation technique, and survey depth. These results demonstrate that the Milky Way has significantly more satellites than a typical galaxy of its luminosity; this fact is useful for understanding the larger cosmological context of our home galaxy.
