Refractive-turbulence profiles measured by one-dimensional spatial filtering of scintillations

Measurements of atmospheric turbulence with airborne beacons by using a differential scintillation method

By using the differential scintillation method suggested and described in this work, vibrations of unmanned aircraft vehicle platforms can be eliminated. Therefore, airborne beacons have great potential applications in turbulence measurements along an arbitrary atmospheric path. The experiment with a constant beacon shows that the retrieved results of the differential scintillation method have good consistency with the scintillation index inversion method. Additionally, a similar verification was carried out between a simulative airborne beacon and a constant beacon; the differential scintillation method indicated more consistent results than the scintillation index inversion method, and its retrieved results of different beacons were in good agreement with a correlation coefficient close to 1, reaching 0.994. In verification experiments over a slant path, the retrieved results of the differential scintillation method showed good statistical properties when an airborne beacon was measured under various weather conditions. The results indicated that the new, to the best of our knowledge, proposed differential scintillation method is a reliable and feasible technique for eliminating stability issues in the measurements of airborne beacons.

Useful relations for the analysis of stellar scintillation at the entrance pupil of a telescope

The development of new techniques for characterizing atmospheric optical turbulence (OT) has become an active topic of research again in recent years. In order to facilitate these studies, we reconsidered known theoretical results and obtained some new practically useful conclusions. We introduce a dimensionless Fresnel filter, which allows us to approximate a polychromatic weighting function (WF) by a monochromatic one with a typical precision of several percent. A so-called dimensionless WF can be easily scaled for a receiving aperture of any size. For the case of a circular aperture and monochromatic radiation, an analytical expression for the WF was found. The WFs for a square aperture and for a circular aperture match with relative difference less than 0.01 if the circular aperture diameter is 1.15 times larger than the square aperture side. A linear digital filter can be applied to the scintillation signal from an image detector. As an example of digital filtering, we considered the power law filter ∝f^5/3 with the WF being constant in a wide range of altitudes. We discuss the main limitations of this approach for measuring OT integral: finite pixel size, aliasing, and finite image detector size.

Influence of the source spectrum on the optical measurements of turbulence

It is considered how the source spectrum influences the measurement accuracy of optical wave arrival angles, as well as the estimation of the path-averaged structure parameter of the refractive index fluctuations. Two reasons that can cause the wavelength dependence of the variance of fluctuations of wave arrival angles are analyzed. The first one is connected with the fact that phases depend on a wavelength in the approximation of smooth perturbations. The second reason is associated with the wavelength dependence of the refractive index and, consequently, its fluctuations. Strict equations are obtained to take into account the influence of the source spectrum on the measurement accuracy of the variance of arrival angle fluctuations and, indirectly, on the estimation accuracy of the path-averaged refractive index structure parameter. It can be stated that for most radiation sources (even nonmonochromatic) the influence of the source spectral composition can be neglected.

First retrieval of vertical profiles of turbulence characteristics and horizontal wind velocity from solar transmission measurements at 212 and 405 GHz

We report on the investigation and successful application of vertical profiling of the structure parameter C2m and of the outer scale L0 of absorption fluctuations and of the horizontal wind velocity (vector) during daytime by the analysis of solar transmission measurements. The method is relatively simple and straightforward so that the presented (or a similar) technique could be used in the routine remote sensing of daytime C2m, L0, and wind profiles. It requires multiple beams pointing in different directions at the Sun. The retrieved profiles are consistent with the current knowledge of atmospheric physics. Simultaneous in situ wind velocity measurements agree with the retrieved wind velocity in the lowest 100 m above ground within the measurement uncertainties of less than +/-2 m/s. The derived values of C2m at 200 m above ground are in good agreement (within a factor of 1.5) with the findings of an earlier investigation at the same test site. Finally, it is shown that irradiance fluctuations of millimeter and submillimeter waves are dominantly affected by humidity fluctuations, even at a dry and elevated site.

Implementation of fast-Fourier-transform-based simulations of extra-large atmospheric phase and scintillation screens

Fast-Fourier-transform-based simulations of single-layer atmospheric von Kármán phase screens and Kolmogorov scintillation screens up to hundreds of meters in size were implemented and tested for applications with percent range accuracy. The tests included the expected and the observed structure and pupil variance functions; for the phase, the tests also included the Fried turbulence parameter r0 measured by the seeing and by a simulated differential image motion monitor. The standard compensations used to correct the undersampling at low spatial frequencies were improved, and those needed for the high spatial frequencies were determined analytically. The limiting ratios of the screen sampling step to r0 and of the screen size to the pupil aperture were estimated by means of the simulated data. Sample results are shown that demonstrate the performances of the simulations for single-layer Kolmogorov and von Kármán phase screens up to 200 m in size and for Kolmogorov scintillation screens for pupils up to 50 m of aperture.

Polychromatic scintillation

A formula to compute the index of stellar scintillation detected with a finite spectral bandpass and with arbitrary aperture is derived in the limit of weak perturbations. It also applies to differential scintillation (relative fluctuations of light intensity in a pair of apertures), where the effect of finite bandpass turns out to be significant. The new formula is used for measurements of free-atmosphere seeing and low-resolution turbulence profiles with concentric-ring apertures.

Measurement of seeing and the atmospheric time constant by differential scintillations

A simple differential analysis of stellar scintillations measured simultaneously with two apertures opens the possibility to estimate seeing. Moreover, some information on the vertical turbulence distribution can be obtained. A general expression for the differential scintillation index for apertures of arbitrary shape and for finite exposure time is derived, and its applications are studied. Correction for exposure time bias by use of the ratio of scintillation indices with and without time binning is studied. A bandpass-filtered scintillation in a small aperture (computed as the differential-exposure index) provides a reasonably good estimate of the atmospheric time constant for adaptive optics.

Myopic Deconvolution of Adaptive Optics Images by use of Object and Point-Spread Function Power Spectra: Comment

It is suggested here that the lack of total image correction that is typical in adaptive optics (AO) imaging can be attributed in part to blur derived from small-angle scatter of light by aerosols, known also as the adjacency effect, especially as it is a well-established fact that such atmospheric blur is dominant in satellite imagery and the shape of the modulation transfer function after AO correction is strikingly similar to the unique shape of the aerosol modulation transfer function. Further investigation of AO systems to confirm this would aid in and improve image restoration.

Remote sensing of wind velocity and strength of refractive turbulence using a two-spatial-filter receiver

Wind velocity across an optical path and refractive turbulence strength can be measured by observing a light source through the atmosphere with a receiver that contains two spatial filters. The frequency of the detected signal gives the transverse velocity of the turbulent structure, whereas signal intensity is proportional to refractive turbulence strength. The size of turbulent eddies that produce signals is determined by the optical setup. The position along the detector's field of view at which the measurement is made depends on the separation of the filters, and profiles can be made by varying the separation and using a telescope. The system requires longer integration times than one which uses a spatial filter at each end of the optical path, but it has the advantage of being able to use a natural source such as the Sun or a planet. An analysis of the system is presented along with numerical simulations and results from a short-range (several meters) laboratory experiment. The analysis assumes a single layer of refractive turbulence. Scales of the refractive turbulence in the inertial subrange from 5 to 20 cm will be of primary interest for this method.

Instrument comparison: corrected stellar scintillometer versus isoplanometer

The scintillation pattern from a single star can be utilized to provide information on the refractive turbulence along the line of sight. Instruments that provide refractive turbulence parameters are the isoplanometer and the stellar scintillometer. Attention is drawn to the fact that the National Oceanic and Atmospheric Administration theoretical treatment and implementation of the stellar scintillometer is incomplete. The theory is corrected for spectral effects and finite aperture. A comparison is made of simultaneously obtained isoplanometer values and stellar scintillometer-derived values for isoplanatic angle. The measurements are obtained from an electro-optical/meteorological experiment conducted at Pennsylvania State University in April and May 1986. An atmospheric drop-off model is used to extrapolate the scintillometer measurements beyond the heights probed. Agreement between the two instruments is significantly improved after the appropriate corrections are applied to the scintillometer data. These data were obtained during widely varying meteorological conditions that provided the opportunity for comparisons over a wide range of isoplanatic angles (3 to 14 µrad). Over the 5 days that data were obtained, relative percent departures of mean isoplanatic angles derived from the corrected stellar scintillometer are within 10% of the mean isoplanometer isoplanatic angle values. The uncorrected departures range from 16% to 24%.

Remote probing of a distant turbulent layer using various spatial filtering methods

A theoretical analysis of short-exposure, spatial power spectra of defocused images viewed through a thin scattering layer is given. Information about the position of the layer can be recovered from these spectra by using a class of quasi-one-dimensional incoherent sources and a spatial filter on the aperture plane. The same approach can be used to obtain refractive turbulent profiles with high spatial resolution in an extended medium.

Sensing refractive-turbulence profiles (C(n)(2)) using wave front phase measurements from multiple reference sources

A new technique for sensing refractive-turbulence profiles is described. The technique is based on performing a spatial correlation of the measured wave front phase from two reference sources. This technique is unique in that the correlation properties of the wave front phase are used instead of the more common approach of using optical scintillations. The geometry between the reference sources and the two wave front sensor apertures is arranged such that the two optical paths cross at some point in front of the sensor plane. The wave front phase for each reference source is reconstructed from the measured wave front sensor data. A spatial correlation of the two reconstructed phase maps is performed. From this correlation we are able to extract a measure of the structure constant of the refractive-index fluctuations C(n)(2). The resolution of the technique depends on the angle between the optical paths, the spatial frequency response of the wave front sensors, as well as the size of the wave front sensorapertures. For sensing the vertical profile of C(n)(2), we can obtain resolution of the order of 100 m by using sources separated by 1.15 degrees .

Refractive turbulence profiling using an orbiting light source

The possibility of obtaining vertical profiles of refractive turbulence C(2)(n)using an orbiting monochromatic light source is examined. The method employs spatial and temporal filtering of the observed scintillation pattern arising from density fluctuations in the atmosphere to measure C(2)(n). The impact of atmospheric motion on the method is discussed along with ways to mitigate its effect. Single and array receiver configurations are examined and the multiple response problem inherent in array configurations is corrected by tuning the individual array elements to the array response. The method is expected to be significantly better than the existing stellar scintillometer method.

Refractive turbulence profiling using stellar scintillation and radar wind profiles

The fluctuations of spatially filtered starlight contain information about refractive turbulence strength (C(2)(n)) at the spatial filter wavenumber. If the turbulence at different heights in the atmosphere is moving at different speeds, the contribution to the fluctuations from those heights will occur at different frequencies. Therefore, the C(2)(n) profile can be inferred from the power spectrum of the fluctuations and the wind velocity profile. Vertical resolution is expected to be in the range of several hundred meters to about a kilometer. Turbulence strength measurements to better than 50% should be easily obtainable.

Effects of C(2)(n) on a vertically pointing diffraction-limited lidar

Examples of different C(2)(n) profiles lead to substantially different profiles of lidar image radius in a study of the calculated performance of a diffraction-limited lidar system. The differences in image radii indicate the usefulness of a ground-based lidar for measurement of C(2)(n) profiles used to predict optical propagation phenomena. We conclude that the overall strength of the C(2)(n) profile and its general altitude dependence can be determined from inspection of the image radius profile. Approximate calculations of available and required SNRs show that a lidar with a telescope aperture of 0.5 m and a few pulses of ~1-J total transmitted energy will provide useful image radius data to an altitude of 20 km under daytime conditions. The weighting function for sensitivity of the fractional increase in image radius to changes of C(2)(n) on a logarithmic altitude scale is approximately constant with height.

Structure function C(2)(n) profiling by two-color stellar scintillation with atmospheric dispersion

Two-color single-star scintillation cross-correlation functions are estimated involving the use of two wavelength filters centered on 409 and 800 nm. From these estimations and using the atmospheric dispersion theory already proposed by Hudgin, turbulent layer heights are measured. Then, vertical C(2)(n)Deltah profiles are obtained every 2 min 45 sec using the slowly decreasing elevation of Sirius. The coherence with another method proves its interest. Furthermore, when the zenith angle of the observed star exceeds ~70 degrees , turbulence heights smaller than 800 m (otherwise unattainable with stellar scintillation measurements) can be detected with a vertical resolution of 300 m.

Localized measurements of refractive turbulence using spatial filtering of scintillations

Remote measurements of refractive turbulence strength with high spatial resolution are demonstrated. The technique uses spatial and temporal filtering of scintillation from a spatially filtered incoherent optical source. Spatial resolution as fine as 4.5 m was observed at the center of a 110-m propagation path. An analytic approximation to the theory agrees very well with the data. This theory predicts the spatial resolution of a system of this type to be in the vicinity of the path length divided by the total number of cycles in the transmitter and receiver spatial filters.

Wind and C(2)(N) profiling by single-star scintillation analysis

The spatiotemporal cross-correlation function of single-star scintillation is estimated. From this estimation and using a priori knowledge of the theoretical shape of the correlation peaks, a method for simultaneously measuring horizontal velocity, altitude, and integrated C(2)(N) value for each atmospheric turbulent layer between 2 and 20 km is described. Taylor's hypothesis is tested for one particular layer and the lifetime of certain turbulent eddies is estimated. Results are in good agreement with two other methods.

Refractive turbulence profiling using synthetic aperture spatial filtering of scintillation

High spatial resolution vertical profiles of refractive turbulence C(2)(n) can be obtained using a translating airborne light source. From spatially filtered observations of the optical scintillation pattern on the ground, caused by atmospheric density fluctuations, it is possible to infer both vertical profiles of C(2)(n) and the shape of the refractive turbulence spectrum. Profiles of key parameters such as the turbulence microscale are thereby accessible from ground-based measurements. The required signal-to-noise ratio and resultant spatial and spectral resolutions are determined.

Radar and optical measurements of C2n

Comparison is made of C(2)(n) profile measurements obtained with a stellar scintillometer and uhf 440-MHz radar. The scintillometer C(2)(n) was obtained at altitude positions between 5 and 18 km, each with a broad height resolution. The radar C(2)(n) was obtained at 400-m intervals with 550-m height resolution. The radar C(2)(n) measurements, when smoothed with the scintillometer weighting function, are in good agreement with the scintillometer C(2)(n) measurements.

Turbulence of the upper atmosphere and isoplanatism

We report the results of 1,049 measurements of the vertical profile of optical turbulence as recorded by a scintillometer above a site at White Sands Missile Range. The distributional law for these measurements is shown to be approximately log normal and examples of monthly to hourly variations in profile structure are presented. An estimate is formed for the isoplanatic angle for wave propagation through each profile by calculating its five-third moment. The ensemble of these calculations is found to be log normally distributed with a mean of 7.2 microrad at a wavelength of 0.5 microm. A strong temporal correction is observed between the size of the isoplanatic angle and the intensity of scintillations. We develop a theory based upon aperture averaging to account for this phenomenon and propose the use of scintillometry to make direct measurements of isoplanatism.

Finite aperture optical scintillometer for profiling wind and C(2)(n)

A new optical technique is described for measuring the path profiles of crosswind and of a refractive-index structure parameter C(2)(n) along a line-of-sight path. Different sizes of transmitters and receivers are used to control the path-weighting function so that it will peak at different path locations. Various linear combinations of these measurements yield the path profile of crosswind and C(2)(n). A prototype instrument has been built and tested. Experimental results show good agreement with the theoretical predictions.

Spectral characteristics of image quality for imaging horizontally through the atmosphere

Spectral effects of visible and near ir imaging for horizontal paths through the atmosphere are considered. For high glare and long range imaging situations, image resolution and quality in the near ir are significantly improved over that in the visible spectrum in clear weather, primarily as a result of less atmospheric scattering of radiation at longer wavelengths.

Relative contribution of upper and lower atmosphere to integrated refractive-index profiles

We measure the wavefront coherence and the irradiance fluctuations of stellar sources to obtain integrated refractive-turbulence profiles of two regions of the atmosphere. Comparison of experimental data during our measurement program shows an equal contribution of upper and lower layers to the limitation of the optical seeing. We also note the great variability of turbulence located above 3 km up to the stratosphere, from night to night. When simultaneously operated, these two methods are suitable for astronomical site testing.