With the No Child Left Behind Act of 2001, a stronger emphasis has been placed on state testing and accountability at the state and local levels. The news media continues to report testing irregularities as professional and community pressures are levied on educators to increase test scores. Test scores have been tied to community affluence, real estate values, encouraging job growth, and state and federal monies. The purpose of this case study is to foster discussion concerning testing regulations and procedures. A beginning second year teacher trying to make extra money opts to teach summer school. The state mandated standardized End-of-Grade test was administered for the third time at the end of the summer school session for all students in attendance. The young teacher finds a used red test book after the testing sessions are over and keeps it. In the subsequent school year, he tutors students with the test booklet he found at the summer school site and uses the questions as warm-ups for the entire class. It is not his intention to circumvent testing procedures and policies.

Scintillation is one of the most common statistics in the literature of mathematical modeling of laser propagation through random media; One approach to estimating scintillation is through the Rytov approximation, which is limited to weak atmospheric turbulence with the standard Kolmogorov spectrum. Recently, a modification to the Rytov approximation was developed. Through a filter function approach, the new results for scintillation are valid for moderate to strong fluctuations along a horizontal path. To date, expressions governing scintillation for plane, spherical, and Gaussian beam waves has been developed for horizontal propagation paths. For the special cases of plane and spherical waves, expressions have been developed for slant paths. In this paper, an expression governing scintillation of a Gaussian beam along an uplink slant path valid in all regimes of turbulence is presented.

The Rytov perturbation method can be used to derive analytic expressions governing statistical quantities of an optical wave propagating through the Earth's atmosphere. It is generally accepted that the validity of these expressions is restricted to the weak fluctuation regime, and that the wave structure function for plane and spherical waves obtained via the Rytov method is valid in all fluctuation regimes, for sufficiently small separation distances. Data from experimental results for the wave structure function as a junction of the fluctuation strength for a fixed value of the separation distance indicate that the Rytov method does not accurately model the behaviour of the wave structure function in moderate to strong fluctuation regimes. This is similar to what is observed for the scintillation index. Recently, however, it was shown that the integral definition of the scintillation index obtained via the Rytov perturbation yields analytic expressions that are valid in all fluctuation regimes when a filter function is applied to the atmospheric spectrum. The underlying physical theory is that as the wave propagates, intermediate refractive index scale sizes fail to refract or diffract the beam. Hence, these scale sizes do not contribute to the scintillation index. In this paper, we investigate the results of applying this concept to the wave structure function. Specifically, we apply a filter function to the atmospheric spectrum and develop analytic expressions for the wave structure function for plane, spherical and Gaussian beam waves using the Rytov perturbation method. It is shown that in weak fluctuations these expressions yield similar results to standard expressions obtained where no filter function is applied. However, in moderate to strong fluctuations, these new expressions predict a decrease in the value of the wave structure function as compared to the standard expressions, following the trend of the experimental data presented by Gurvich.

Recently, new theory governing laser beam scintillation was developed for all regimes of optical turbulence. This theory is based on the Rytov approximation but modified with a filter function that eliminates intermediate scale sizes that do not contribute to the refractive and diffractive effects of propagation. This modification extends the validity of the Rytov approximation into moderate to strong regimes as evidenced by the agreement with simulations and experimental data. In this paper we apply this theory to the phase covariance and new expressions governing phase fluctuations are presented. The phase structure function is then compared with previous experimental data.

Recently, a heuristic model for scintillation in moderate to strong turbulence was developed. It is based on the idea of filter functions that eliminate scale sizes that lose their ability to affect a laser beam as it propagates. This approach allows the validity of the Rytov approximation to be extended into moderate to strong turbulence. In this paper, we investigate applying this theory to second order statistics.