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On 34 nights between December 1980 and May 1986, 171 monochromatic gravity waves were observed in the mesospheric Na layer at Urbana, Illinois, using a lidar system. The characteristics of the waves are compared with radar measurements of gravity wave activity and theoretical models of wave saturation and dissipation phenomena. The measured vertical wavelengths (λz) range from 2 km to 17 km, the observed periods (Tob) range from 25 min to 800 min and the horizontal wavelengths (λx) range from 20 km to almost 3000 km. The most apparent seasonal characteristic of the waves is the absence in summer of periods greater than 200 min and horizontal wavelengths greater than 400 km. The wave kinetic energy distributions are approximately proportional to kz−3, kx−15/14 and ƒ−5/3. Because the average amplitude growth length for the data is only 19 km and linear saturation theory predicts a kz−2 dependence for the kinetic energy distribution of saturated waves, the observed waves are not strongly damped and appear to be influenced more by dissipation rather than by saturation effects. Both λz and λx show a strong tendency to increase with Tob. The measured power law relationships are approximately λz ∝ Tob5/9 and λx ∝ Tob14/9. The wave induced mean flow acceleration ranges from 0 to −200 m s−1 day−1 and the average value is −27.2 m s−1 day−1. The effective viscosity limiting wave amplitudes ranges from 0 to 140 m² s−1 and the average value is 37 m² s−1.

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Sodium lidar measurements obtained between December 1980 and May 1986 at Urbana, Illinois, are compared with other reported lidar measurements and with recently developed models of the layer. Sodium abundance at Urbana reaches a maximum value in November, December and January which is approximately 4.5 times larger than the June minimum value of 2.15 x 109 cm -2. Also in November and December, the layer centroid height is about 1.5 km lower than the yearly average value of 92 km. There is no significant seasonal variation of the rms layer width whi•ch• has an average value of approximately 4.25 km. The peak-to-peak variations of the centroid height and rms width of the average nocturnal layer are 1 km and 600 m, respectively. The semidiurnal tide is primarily responsible for a 36% peak-to-peak abundance variation in the average nocturnal layer which is compatible with a 20 cm s-x amplitude for the vertical wind velocity. The vertical phase velocity of the density perturbations is approximately 1 m s-x which implies a 45 km vertical wavelength for the semidiurnal tide. Because of gravity waves and tides the structure of the nocturnal layer changes substantially throughout the night. Variations of over 200% in abundance, 2 km in centroid height, and 1 km in rms width have been observed within the time span of a few hours. 109-10 •ø m -3. Before lidar systems became available, sodium measurements were largely restricted to studying resonantly scattered sunlight. Groundbased observations of this type were able to define seasonal variations in column abundance [Blamont and Donahue, 1961; Gadsden and Purdy, 1970], but the sharp layer boundaries were not revealed until rocketborne dayglow measurements were made [Hunten and Wallace, 1967]. Lidar observations of the vertical structure of the layer were first made in England [Bowman et al., 1969]. Since then similar measurements have been reported from a variety of locations including France [Me•lie and Blamont, 1977], Brazil [Simonich et al., 1979], Japan [Aru•la et al., 1974], Illinois [Richter et al., 1981], California [Hake et al., 1972] and at the high latitudes of Franz Joseph Land, USSR [Juramy et al., 1981] and Andoya, Norway [Fricke and yon Zahn, 1985]. During the past few years numerous chemical and dynamical processes have been proposed in an attempt to explain the general characteristics of the seasonal, diurnal and geographical variations of the layer structure. Sodium chloride from the oceans and volcanic eruptions have been discussed as possible sodium sources. However, meteoric ablation is generally regarded as the dominant source of all the alkali metal layers including sodium [Clemesha et al., 1978; Richter and Sechrist, 1979a, b; Je•lou et al., 1985a, b]. Much of the intrinsic character of the layer is apparently governed by a complex chemistry involving many reactions among numerous neutral and ionic species [e.g., Sze et al., 1982; Kirchhoff, 1983; Jegou, 1985a]. The dominant loss mechanisms are believed to include the conversion of neutral sodium to t...

Accurate simulation of scalar optical diffraction requires consideration of the sampling requirement for the phase chirp function that appears in the Fresnel diffraction expression. We describe three sampling regimes for FFT-based propagation approaches: ideally sampled, oversampled, and undersampled. Ideal sampling, where the chirp and its FFT both have values that match analytic chirp expressions, usually provides the most accurate results but can be difficult to realize in practical simulations. Under- or oversampling leads to a reduction in the available source plane support size, the available source bandwidth, or the available observation support size, depending on the approach and simulation scenario. We discuss three Fresnel propagation approaches: the impulse response/transfer function (angular spectrum) method, the single FFT (direct) method, and the two-step method. With illustrations and simulation examples we show the form of the sampled chirp functions and their discrete transforms, common relationships between the three methods under ideal sampling conditions, and define conditions and consequences to be considered when using nonideal sampling. The analysis is extended to describe the sampling limitations for the more exact Rayleigh-Sommerfeld diffraction solution.

A passive-polarization-based imaging system records the polarization state of light reflected by objects that are illuminated with an unpolarized and generally uncontrolled source. Such systems can be useful in many remote sensing applications including target detection, object segmentation, and material classification. We present a method to jointly estimate the complex index of refraction and the reflection angle (reflected zenith angle) of a target from multiple measurements collected by a passive polarimeter. An expression for the degree of polarization is derived from the microfacet polarimetric bidirectional reflectance model for the case of scattering in the plane of incidence. Using this expression, we develop a nonlinear least-squares estimation algorithm for extracting an apparent index of refraction and the reflection angle from a set of polarization measurements collected from multiple source positions. Computer simulation results show that the estimation accuracy generally improves with an increasing number of source position measurements. Laboratory results indicate that the proposed method is effective for recovering the reflection angle and that the estimated index of refraction provides a feature vector that is robust to the reflection angle.

A technique is presented to produce any desired partially coherent Schell-model source using a single phase-only liquid-crystal spatial light modulator (SLM). Existing methods use SLMs in combination with amplitude filters to manipulate the phase and amplitude of an initially coherent source. The technique presented here controls both the phase and amplitude using a single SLM, thereby making the amplitude filters unnecessary. This simplifies the optical setup and significantly increases the utility and flexibility of the resulting system. The analytical development of the technique is presented and discussed. To validate the proposed approach, experimental results of three partially coherent Schell-model sources are presented and analyzed. A brief discussion of possible applications is provided in closing.

An approach is described for creating random complex screens to be used in computer simulations of arbitrary Schell-model beams with a prescribed far-field intensity distribution. Simulation examples including beam profiles with reflection symmetry and rotational symmetry, flat-top, and pyramidal shapes are presented to verify the proposed approach. A more general scenario with a nonsymmetric far-field beam shape is illustrated to demonstrate the evolution in the free-space propagation from the source plane to the far zone.