We report on new results of simultaneous measurements of sodium layer column density and the absolute return flux from laser guide stars created by a monochromatic approximately 1 W CW laser, tuned to the peak of the sodium D2 hyperfine structure. The return was measured at the MMT while the sodium abundance was measured at the CFA 60 inch telescope, about 1 km away, with the Advanced Fiber Optic Echelle spectrograph. The laser frequency stability, which can greatly affect the return flux, was monitored at the same time in order to improve the measurement accuracy. After the correction for laser frequency jitter and atmospheric transmission, the absolute flux return above the atmosphere for circularly polarized light is 1.2 X 106 photons s-1 m-2 per watt launched above the atmosphere, per unit column density, which we taken as our measured mean over the year of N(Na) equals 3.7 X 109 cm-2 at Tucson. The solidification of a final well-determined relationship between the sodium laser guide star brightness and sodium layer column density is pivotal in the design of the next generation laser guide star adaptive optics systems. We also report the measurements and analysis of the relationship between the projected beam waist of the sodium laser and the resultant spot size on the sodium layer under typical atmospheric conditions. Since wavefront measured error is proportional to spot size, and also to 1/(root) power, minimum spot size is crucial for lowest laser power requirement. By projecting the laser through diffraction limited optics of 0.5 m diameter, roughly 3 r0, we have achieved the smallest artificial beacon yet recorded, about 0.8 arcsec.