Optical turbulence research contributes to improved laser communications, adaptive optics, and long-range imaging systems. This paper presents experimental measurements of scintillation and focal spot displacement to obtain optical turbulence information along a near-horizontal 2.33 km free-space laser propagation path. Calculated values for the refractive index structure constant (C 2 n) and Fried parameter (r 0) are compared to scintillometer-based measurements for several cases in winter and spring. Optical measurements were investigated using two different laser sources for the first and second parts of the experiment. Scintillation index estimates from recorded signal intensities were corrected to account for aperture averaging. As a result, we found that an earlier calculation algorithm based on analysis of log-amplitude intensity variance was the best estimator of optical turbulence parameters over the propagation path considered.
© 2008 Optical Society of America
Optical turbulence is an important microphysical effect that acts on the propagation of light waves to distort optical propagation paths and intensity. Along the propagation path of a free-space laser communication system, optical turbulence can produce significant intensity fluctuations and variations in the direction the transmitting beam propagates [1–5]. These circumstances typically lead to signal fading at the receiving aperture, which can result in data loss and increased transmission bit errors, i.e., when detection hardware does not receive adequate optical power. In turn, these effects can severely impact the performance of Army free-space laser optics communication systems . Therefore, optical turbulence research can contribute greatly to improving laser communications, adaptive optics, and long-range imaging systems.
As discussed previously [7–12], the U.S. Army Research Laboratory (ARL), Atmospheric Laser Optics Testbed (A_LOT) is a unique experimental facility to examine optical turbulence and its effects on laser optical signal propagation over its complex, non-uniform landscape. Within the A_LOT, a near horizontal, 2.33 km optical path extends from the top of a tall water tower to the Intelligent Optics Laboratory (IOL) rooftop at ARL (Fig. 1). The A_LOT optical path traverses an open sand lot, a fairly continuous forest stand, several local roads, and various building arrays. Complex microphysical influences may (at times) affect the A_LOT measured data and research applications. Some microclimate influences may be due to irregular wind flow patterns around the IOL (High Bay building) and the water tower. Other effects may be due to varying wind shears, temperature gradients, and moisture changes across the top of nearby (and underlying) building and forest canopies. To this end, computer simulation models may provide some meaningful results even though all the pertinent landscape or canopy characterization data along the optical path may not yet be known or available . At the same time, detailed data analysis from new laser-optics experiments may help us to better understand the physics relationships between refractive index structure, scintillation, beam wander, and microclimate fluctuations. Also, exploring methods to obtain atmospheric parameters from optical measurements at the ARL A_LOT can provide a basis for obtaining these kinds of data over alternate propagation paths in diverse microclimate environments. In this paper, we present further experimental research to obtain useful optical turbulence information along the A_LOT propagation path from simultaneous measurements of laser signal intensity and focal spot displacement. Our approach and equation set are outlined in Section 2, followed by a description of the experiment in Section 3 and our data analysis in Section 4. Section 5 contains a summary and conclusions.
The normalized variance of free-space laser signals or scintillation index (σ 2 I) can be determined experimentally as,
where I is the measured signal intensity and 〈 〉 is the temporal mean. However, aperture averaging can significantly reduce the measured variances if the aperture radius of the receiving optics (D/2) is larger than the spatial scales of the optical scintillations of interest, i.e., when , where L is the propagation path length, k=2π/λ is the wave number and λ is wavelength. For weak turbulence conditions (Rytov variance, σ 2 1≤0.3), Andrews et al.  suggest that the normalized variance for a circular aperture [σ 2 I(D)] can be corrected for aperture averaging as,
where σ 2 I(0) is the normalized variance for a point aperture, and A is the aperture averaging factor, e.g., for spherical waves
In addition, it is widely accepted that for weak turbulence conditions,
where σ 2 1 is the Rytov variance and C 2 n is the refractive index structure constant. Here, C 2 n represents a quantitative measure of the intensity of optical turbulence. Thus, Eq. (4) suggests that C 2 n can be derived directly from optical measurements of laser signal intensity. However, to what extent can the above equations be applied when turbulence conditions are stronger, e.g., if scintillation is measured within the transition region from weak to strong turbulence, i.e., 0.3<σ 2 1≤1.0, or higher? This question will be examined in Section 4 (Data analysis).
Alternately, C 2 n can be estimated as a function of the log-amplitude variance (σ 2 χ) of the measured laser signal as shown in a recent paper . This model is based on an earlier expression derived by Wang et al. , i.e.,
where C=4.48Dr/Dt, Dt is the transmitting aperture diameter and Dr is the receiving aperture diameter. Here, application of Eq. (5) requires that the light source be partially incoherent and uniformly illuminated across the transmitting aperture. Hence, it may be useful to re-examine calculated values for C 2 n from Eq. (5) for different turbulence conditions in comparison to those calculated from Eq. (4).
The effects of optical turbulence also can result in random displacement of a received image in the focal plane of an imaging system, i.e., focal spot displacement  If one assumes that focal spot displacement (σF) is only caused by fluctuations in wavefront angle of arrival, then σF can be expressed as,
where F is the focal length (m) of the collecting lens of the receiver and 〈α 2〉 is the mean (horizontal component) angle of arrival variance. For spherical waves, 〈α 2〉 can be expressed as,
Hence, Eq. (7) may be similarly useful to estimate values for C 2 n via optical measurements of focal spot displacement. Note that estimates of C 2 n based on the mean (vertical component) angle of arrival variance 〈β 2〉 can be determined as,
Finally, the Fried parameter (r 0), a length scale of refractive-index fluctuations, can be calculated from estimates of C 2 n, as shown in Ref. , i.e.,
where typically r 0~2.5 cm for wavelength, λ=808 nm in strong optical turbulence conditions (C 2 n=2×10-14) at the ARL A_LOT.
3. Experimental setup
The wave propagation geometry for this experiment is shown in Fig. 2. A beam-splitter was mounted within a cube with an appropriate laser filter to send equal amounts of received laser light to a high-speed photo-detector and a position sensing detector (Fig. 3). A video camera (to the left of the beam splitter) was focused toward the center of the photo-detector to optimize focal spot alignment and received signal strength. The beam-splitter cube was positioned behind a Schmidt-Cassegrain compound telescope (receiving aperture diameter, Dr=127 mm; focal length, fl=1347 mm). The optical detectors were connected to a data acquisition module to record high frequency (f>100 Hz), aperture averaged signal intensity and focal spot displacement. The laser transceiver (aperture diameter Dt=60 mm) was located on top of the 73 m water tower, while the receiving optics were located at 12 m (above ground level) within a climate controlled equipment shed located on the IOL rooftop. For the first part of the experiment the source for the optical transmitter at the water tower was an 80 mW single-mode laser diode (wavelength, λ=1064 nm) located at ground level and coupled to a 100 m long multimode fiber. For the second part of the experiment the laser source was a 100 mW (λ=808 nm) laser diode coupled directly to the 100 m multimode fiber. It was assumed that when either laser source propagated within the long multi-mode fiber, the exiting light could be considered a collimated, partially coherent beacon due to modal dispersion and fiber vibrations9, although initially the 808 nm laser was a more incoherent source. As a result, a cursory visual analysis of scintillation intensity patterns showed slightly more uniform illumination across the pupil plane of the receiving optics from the 808 nm beacon. The effects from such differences in laser signal intensity recorded during the first and second parts of the experiment will be discussed in the next section (Data analysis). Note, to capture simple scintillation intensity pattern images, a second video camera, which included an appropriate laser filter, was mounted behind an objective lens (fl=50 mm) focused at the pupil plane of the second telescope (to the left in Fig. 3). The second telescope was identical to the first, and together with apparatus mentioned above, was mounted on top of a large vibration isolation platform to increase stability.
In addition, a boundary layer scintillometer  measured continuous, path-averaged values for C 2 n along the A_LOT line-of-sight. The scintillometer transmitter is mounted on top of the water tower and the receiver is located in front of the equipment shed on the IOL rooftop. Also, a single 3-axis sonic anemometer  is mounted on a 2 m tripod on the IOL rooftop. The anemometer provided additional characterization of microclimate conditions, e.g., mean (one-minute averaged) wind velocity and temperature data.
4. Data analysis
The data set is comprised of 35 cases collected during winter and 28 cases collected during spring. A general data section criterion was for fair weather conditions, i.e., no rain or snow. Signal intensity and linear position data were recorded for individual two-minute periods during daytime hours only. Scintillometer retrieved C 2 n data (in units m-2/3) represent two-minute averages recorded along the 2.33 km A_LOT propagation path. The observed Fried parameter and Rytov variance data are based on the measured scintillometer data.
Figure 4 presents optical turbulence calculations based on signal intensity data analysis during winter and spring. Here, calculation of C 2 n based on an expression for the Rytov variance (Eq. (4)) is compared to calculation of C 2 n as a function of the log-amplitude variance of the measured laser signal (Eq. (5)). In the first case, the calculation incorporates values for the measured scintillation index corrected for aperture averaging. In the latter case, receiver and transmitter aperture diameter information are included in the calculation. Much of the data analyzed agree within a factor of two (or better), although the reason for the offset in the scintillation index based estimates shown in Fig. 4b is not yet clear. Nevertheless, the results in the spring, to include the estimates of C 2 n based on Eq. (5), appear to have fewer extreme outliers than those calculated in winter (Fig. 4(a)). Perhaps, the signal variance statistics for the winter cases were (at times) affected by optical jitter of the transmitting beacon due to high wind velocities. Optical jitter would artificially increase scintillation variance statistics beyond that which represents atmospheric effects. While wind velocity data are not available at the water tower, some justification for suspecting optical jitter is provided by IOL rooftop recorded winds, in particular, those data associated with the largest discrepancies (see Fig. 5). However, wind velocity analysis for the entire winter data set was inconclusive.
In the spring (Fig. 4(b)), the C 2 n values calculated from Eq. (5) agree remarkably well with the measured scintillometer data. Of course, the scintillometer (with an incoherent LED light source) uses a similar algorithm  to derive its values for C 2 n. Nevertheless, we suggest that the main differences between the winter and spring cases shown in Fig. 4 were due to the change in laser source. In contrast, the estimates of C 2 n based on Eq. (4) agree only within a factor of about two or three for both weak and strong turbulence conditions. This later result follows from the comparison of observed Rytov variance versus measured scintillation index (Fig. 6). Interestingly, Fig. 6a shows fairly close agreement between these two parameters under strong (σ 2 1>1) turbulence conditions (contrary to widely held theoretical limitations ).
Alternately, Fig. 7 presents optical turbulence (C 2 n) calculations based on focal spot displacement data analysis for winter and spring. In the winter (Fig. 7a), agreement between calculated C 2 n and the scintillometer is less than optimal (a factor of 10 or more) for both weak and strong turbulence conditions. Also, in Fig. 7a, the values for C 2 n calculated from the vertical component of the angle of arrival variance 〈β 2〉 provided slightly better agreement to the scintillometer data than those calculated from the horizontal component 〈α 2〉. In the spring (Fig. 7b), the opposite effect is shown. More noticeably, however, the modeled estimates of C 2 n (overall) were improved slightly, particularly in strong turbulence conditions. Others investigating this approach [19, 20] have reported similar results. Nevertheless, we are fairly confident that our data and C 2 n estimates were affected by the use of different laser sources (as discussed earlier) as well as other possible influences from platform or rooftop vibrations and/or noise in the position detector signal, particularly in weak turbulence conditions. Also, our angle of arrival measurements may have been sensitive to intermittent turbulence sources located close to the receiving optics, e.g., from air vents and heating ducts on adjacent buildings. In contrast, the scintillometer data are (by design) centrally weighted along the propagation path, and thus remain mostly unaffected by disturbances close to the receiver or transmitter. Therefore, assuming uniform turbulence conditions may be deficient or in error for the A_LOT landscape [13, 21].
Finally, Fig. 8 presents modeled versus measured Fried parameter (r 0) calculations based on four different estimates C 2 n for the data set collected during winter and spring, i.e., based on scintillation index (σ 2 I), log-amplitude variance(σ 2 χ), horizontal component of angle of arrival variance 〈α 2〉 and vertical component of angle of arrival variance 〈β2〉. Rather close agreement (better than a factor of two) is shown for r 0 values calculated from signal intensity variance analysis for weak and strong turbulence conditions. In contrast, r 0 values calculated from angle of arrival variance analysis agreed poorly with the observed data, especially in winter. In the end, however, the use of Eq. (5), which is based on log-amplitude intensity variance analysis, provided the best estimates of optical turbulence parameters over the A_LOT propagation path.
5. Summary and conclusions
An experiment was conducted to obtain optical turbulence information along the 2.33 km A_LOT propagation path from measurements of scintillation and focal spot displacement. Calculated values for the refractive index structure constant and Fried parameter were compared to scintillometer-based measurements for several cases in winter and spring. Optical measurements provided slightly better estimates for C 2 n and r 0 during the second part of the experiment in comparison to the first part. This result was due (in part) to several factors, to include the laser source, magnitude and direction of the winds, platform vibrations, detector signal noise, and intermittent turbulence in the vicinity of the receiving optics. Nevertheless, we found that an earlier calculation algorithm based on analysis of log-amplitude intensity variance was the best estimator of optical turbulence parameters across the A_LOT propagation path. In future works, we will integrate more analysis of optical measurements into the A_LOT system.
The author gratefully acknowledges the anonymous reviewers for providing helpful comments with regard to the manuscript and its content. In addition, the author extends thanks to Thomas Weyrauch (University of Maryland) and Ronald Meyers (ARL) for providing helpful and instructive comments with regard to the experimental setup and data acquisition. The author would also like to thank Mikhail Vorontsov (ARL) for scientific guidance and Gary Carhart (ARL) for technical support with regard to A_LOT hardware and software.
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