  This paper compares the performance of two different high-precision,
photometric measurement techniques for bright (<11 magnitude) stars using the
small telescope systems that today's amateur astronomers typically use. One
technique is based on recent work using a beam-shaping diffuser method
(Stefansson et al., (2017).) The other is based on the widely used "defocusing"
method. We also developed and used a statistical photometric performance model
to better understand the error components of the measurements to identify and
quantify any difference in performance between the two methods. AstroImageJ
(Collins et al. (2017)) was used for the exoplanet image analysis to provide
the measured values and exoplanet models described in this study. Both methods
were used at the Mark Slade Remote Observatory (MSRO) to conduct in-transit
exoplanet observations of exoplanets HAT-P-30b/WASP-51b, HAT-P-16b, and a
partial of WASP-93b. Observations of exoplanets KELT-1b and K2-100b and other
stars were also performed at the MSRO to further understand and characterize
the performance of the diffuser method under various sky conditions. In
addition, both in-transit and out-of-transit observations of exoplanets
HAT-P-23b, HAT-P-33b, and HAT-P-34b were performed at the Conti Private
Observatory. We found that for observing bright stars, the diffuser method
outperformed the defocus method when using small telescopes with poor tracking.
We also found the diffuser method noticeably reduced the scintillation noise
compared with the defocus method and provided high-precision results in
typical, average sky conditions through all lunar phases. For small telescopes
using excellent auto-guiding techniques and effective calibration procedures,
we found the defocus method was equal to or in some cases better than the
diffuser method when observing with good-to-excellent sky conditions.
