The presence of clouds of ice particles in the uplink and downlink path of an illumination beam can severely impede the performance of an active imaging system. Depending on the optical depth of the cloud, i.e., its density and depth, the beam can be completely scattered and extinguished, or the beam can pass through the cloud with some fraction attenuated, scattered, and depolarized. In particular, subvisual cirrus clouds, i.e., high, thin cirrus clouds that cannot be observed from the ground, can affect the properties and alignment of both uplink and downlink beams. This paper discusses the potential for active imaging in the presence of cirrus clouds. We document field data results from an active imaging experiment conducted several years ago, which the authors believe to show the effects of cirrus clouds on an active imaging system. To verify these conclusions, we include the results of a simulation of the interaction of a coherent illumination scheme with a cirrus cloud.
©1997 Optical Society of America
In the past decade, the US Air Force Research Laboratory, Phillips Site has been simulating, modeling and conducting experiments in unconventional imaging. This research has involved the detection of nonimaged speckle return from a space-borne object in the presence of either solar illumination or coherent illumination from a ground-based laser. The latter illumination scheme is known as active imaging and one such technique that has been tested in the field is called sheared beam imaging, or SBI.
In 1990 and 1991, AFRL/DEBS conducted the Retro-Assisted Imaging Laser Experiment (RAILE).1 This experiment was designed to test the concept of sheared beam imaging using a cooperative target, on which had been mounted four corner cube reflectors. The experiment did not take into account diffuse reflection from the target and the corner cube point sources generated fringe patterns, not typical speckle patterns, at the receiver. Nevertheless, RAILE did serve as a proof-of-concept experiment for SBI. The experiment operated on Maui, whenever weather permitted, and operations frequently were conducted when various cloud formations were present, including cirrus. The authors used raw speckle data from the field experiment, not processed images, to illustrate what they suspect to be some effects of cirrus clouds on the coherent return signal.
In section 2, we briefly describe sheared beam imaging and the effect of target depth on the detected signal since the authors believe this effect would be mimicked by a cirrus cloud bank. In section 3, we describe the RAILE experiment and, in particular, the synthetic aperture used to detect the speckle return. We discuss raw field data in section 4, and in section 5, we suggest a possible explanation for the phenomena observed in this data, which the authors suspect could be the result of beam reflection from a bank of cirrus clouds. A computer simulation of the interaction of the coherent illumination beams in an SBI configuration with a cirrus cloud model is discussed in section 6. Finally, we present our conclusions in section 7.
2. Sheared beam imaging
In sheared beam imaging a moving space object is illuminated with three sheared, pulsed, and modulated laser beams. [2,3,4] The target reflects the resultant interferometric pattern, which propagates to the receiver on the ground. The receiver consists of a telescope whose entrance pupil is conjugate to the detector array. A schematic diagram of this imaging technique is illustrated in Fig. 1 below.
The receiver incorporates an array of light buckets, which detects the difference in phase between the x-sheared beam and the reference, the y-sheared beam and the reference, and between the x-sheared and y-sheared beams. Detection of phase differences eliminates common-path aberrations in the downlink propagation. It does not eliminate errors in the downlink propagation due to scintillation and non common-path aberrations. Errors in the uplink propagation create shear errors at the target and therefore remain at the detected signal. For greater detail on the sheared beam imaging technique, the reader is urged to consult the references.
Apart from the uplink atmospheric effects, which would include scattering and depolarization effects, as well as the shear errors induced by the presence of clouds, a number of other physical phenomena impact the laser speckle pattern detected at the receiver. These phenomena include, but are not limited to, photon noise, speckle noise, the effects of finite detectors, the pupil geometry, target motion and size, camera integration time, and laser pulse nonuniformities. In particular, variations in the laser frequency will seriously impact the return signal at the detector, as we explain next.
In previous work,  we derived the governing equations for sheared beam imaging, assuming a two-dimensional target, in the presence of a number of physical effects, such as finite detectors, target motion, finite camera integration time, and laser nonuniformities. Subsequent work  illustrated the effect on SBI demodulation with these governing equations, modified for a 3D target, in the presence of a linear variation in the laser frequency, called chirp. This latter effect significantly complicates the imaging process. Since the laser frequency now varies with time, different depths on the target will reflect different laser frequencies as a result of finite travel time of the light from the front of the target to the rear. One frequency reflected from one portion of the target will “look like” a different frequency reflected from a different target depth. As a result, the energy at the receiver contains a spread of frequencies around each of the three modulation frequencies.
The SBI imaging algorithm assumes that phase differences in x only, in y only, and on the xy diagonal are separately encoded on each of the modulation peaks. Obviously, if a spread of frequencies around each of the peaks causes aliasing between the modulation frequencies, phase difference information will likewise be aliased among the three directions, generating significant errors in the imaging process.
The effect of a small amount of linear chirp on SBI demodulation for two different targets is shown in Fig. 2. In this plot, the modulation frequencies are 0.4, 0.8, and 1.2 MHz. The pulse width was 50 μsec to achieve a frequency resolution of 20 kHz.
The two different targets used in this simulation were a bar target, called BIG, which extended 32 × 32 pixels in a 64 × 64 array and a rendering of the DMSP satellite, of approximately the same size. Both targets were modeled as one meter deep. In both cases, a small amount of linear chirp, 5 mHz/μsec, typical of one high-power chemical laser proposed for an SBI experiment, was added to the model of the laser pulse. The saw tooth pattern at the base of each modulation peak is due to the aliasing effect of the chirp. Without chirp, there are no sidelobes; only sharp peaks appear at each of the three frequencies. Finally, the demodulation shown here is the Fourier transform of a series of temporal data points. Each data point in time is the result of summing the entire 2D detected speckle pattern to obtain a single intensity value. This demodulation occurs very early in the SBI imaging retrieval algorithm. Consequently, demodulation data for very different targets will appear to be very similar.
Sidelobes, much like those shown in Fig. 2, appear in the demodulation data of the RAILE field experiment. The sidelobes are prominent on nights when there was significant cirrus coverage. In contrast, we did not find evidence of the sidelobes in data acquired on clear nights. If the illumination laser has a time-varying laser frequency and reflects from an object with depth, such as a cloud, sidelobes like those due to chirp will appear in SBI demodulation data. Another possible explanation for the presence of the sidelobes originates in the synthetic aperture detection scheme used in the RAILE experiment, which will be discussed in the next section.
The RAILE experiment was performed to demonstrate high-resolution imaging of a space-borne object from the ground using an active imaging technique called sheared beam imaging. The receiver on the ground consisted of a linear array of 20 photo multiplier tubes (PMTs) or light buckets in an inverse synthetic aperture receiving scheme, to achieve a larger effective aperture. Image reconstruction was performed in post-detection software.
The transmitter consisted of a single 20W argon laser split into three beams, which were individually modulated and separated spatially. The beams were propagated in parallel to the target where they overlapped, due to diffraction. The overlap and the beam modulation create a time-varying interference pattern, a portion of which was reflected by the four corner cubes mounted on the satellite, back to the ground. The intensity pattern on the ground swept across the detector bar, which sampled the signal in individual detector channels. Software algorithms demodulated the raw signal and produced an estimate of the Fourier modulus and phase differences of the pattern received at the detectors. The phase differences were integrated, yielding the field phase estimate. The modulus and phase estimates, which comprise a complex pupil plane distribution, were Fourier transformed and the squared magnitude of the result was the final image.
The four corner cube reflectors on the satellite target acted as point sources in the SBI system and therefore generated fringe patterns, not a typical speckle pattern, on the ground. The fringe patterns would sweep across the detector bar in the synthetic aperture direction at roughly twice the satellite velocity. Appropriate sampling of the detector signal generated the synthetic aperture. Fig. 3 illustrates typical fringe patterns for three different satellite velocities shown against a rectangle, representing the detector bar, and an arrow that represents the direction of the fringe motion. The effect of these moving fringes on the demodulation data will be discussed in section 5.
The RAILE argon laser used an intra-cavity etalon to tune the wavelength from 514.4 nm to 488 nm. In addition, the etalon provided mode stability for the laser, significantly reducing variations in the laser frequency. According to an engineering report on the laser/etalon combination, however, some instability, called mode jitter, of approximately 10 GHz/sec remained. This instability, reflected from a target with a depth of a few hundred meters like a cloud, would be enough to create the sidelobes seen in the data, which we will discuss in the next section.
4. Field data
Working from the RAILE engagement summary, the authors searched for extant demodulation data from days with different weather profiles. That is, the authors sought to compare data from clear nights with data from nights with cloud cover. There were three days of data that fulfilled this requirement. These days were 15 Jan. 1991, 16 Jan. 1991, and 15 March 1991, whose Julian days are 91015, 91016, and 91074, respectively. Day 91016 was clear, 91074 had 7/8 of the sky covered by cirrus, and day 91015 had 2/8 coverage by strato cumulus.
Fig. 4 shows a typical sample of the demodulation data from day 91016, which was clear. The designation “910161 20_38.ASC” on the graph represents the file name for this data set. The data has been plotted as power versus normalized frequency. The modulation frequencies 1, 2, and 3 were 46.3 kHz, 92.6 kHz, and 138.7 kHz, respectively. The four different plotted curves are for four different “bursts” of data, a nomenclature associated with the data acquisition. Note the absence of sidelobes around the well-defined modulation peaks. Day 91016 was an excellent night for viewing and a great quantity of data was amassed. None of the demodulation data showed sidelobes. Further, note the displayed power level. A maximum level of 15 seemed standard for this set of data.
In contrast, Fig. 5 plots a typical set of demodulation data for day 91074, a day with 7/8 cirrus coverage. On this plot, the modulation frequencies 1, 2, 3 were 23.08 kHz, 46.3 kHz, and 69.4 kHz, respectively. In this data, the sidelobes are prominent and were present in every frame. Finally, note the maximum return power level of 200. This power level was significantly greater than the return on the clear night. We will discuss the significance of this power level in the next section.
The data for day 91015, not shown here due to space limitations, occasionally showed the same sidelobes as seen in the 91074 data. This day had 2/8 coverage of strato cumulus and the presence of subvisual cirrus was a strong possibility, based on balloon- launched weather data from that day. A large quantity of data was collected on day 91015, some of which showed sidelobes and some of which did not. Finally, the return power for day 91015 was approximately 25 for all data.
The phenomenon of subvisual cirrus is quite distinct from cirrus. Subvisual cirrus is generally defined as any ice cloud whose optical depth or thickness is less than 0.1. Platt  gives the boundary for hazy, but visible, cirrus as τ=0.06. This formation can rarely be seen by ground observers, although LIDAR and airborne observers have noted its presence. Very little radiometric information exists for subvisual cirrus, although recent active imaging experiments at the Phillips Laboratory suggest its effect on the coherent return from a satellite target. The authors theorize that the occasional appearance of sidelobes in the data for 91015 could be consistent with the illumination beam passing in and out of portions of the sky containing subvisual cirrus.
In the next section, we will discuss the effect the synthetic aperture would have on the demodulation, as well as an alternative explanation for the different return power levels.
5. Synthetic aperture effects
The intensity pattern due to the return signal from the retros sweeping across the detector bar represents more than the modulation frequencies of the illuminating laser. The signal is further modulated by the spatial frequencies of the fringes formed by different pairs of the four corner cubes.
Each corner cube acts as a point source and each pair of point sources produces a set of fringes at the detector. The spatial frequency of these fringes depends upon the satellite orientation and the engagement geometry and it varies with time, due to the satellite velocity. These spatial frequencies are converted into temporal frequencies as the moving fringes are detected and read out by the detector bar and associated electronics. These temporal fringe frequencies for each of the six combinations of retros were computed as a function of time for each engagement, where time is zero for point of closest approach (PCA).
The authors simulated the SBI demodulation for each of the three engagements, 91015, 91016, and 91074, using the computed temporal fringe frequencies. Plots of this demodulation simulation are shown in Figures 6–8 for normalized amplitude versus actual frequency in kHz.
The amplitude of each of the frequencies was unknown, so all fringe frequency amplitudes were set to one and different combinations of frequencies were tried in an attempt to replicate the field data. In general, a combination consisting of the three highest frequencies plus one of the lower frequencies would generate sidelobes to the modulation peaks similar to those found in the data. Using all of the frequencies never replicated the actual data. The mixture of frequencies chosen represents the pairs of retros having the largest spatial separation on the satellite.
Although the simulation produced sidelobes similar to those seen in the data, differences remain. The most significant difference is seen in the 91016 engagement. Simulating the synthetic aperture effects clearly showed the presence of sidelobes, although they never appear in the field data.
The other anomaly yet unexplained by the mission specifics is the very large power return on day 91074, with cirrus, compared to the significantly smaller return on the clear day 91016 and the partly cloudy day 91015. The authors suspect that this power could be a function of laser light reflected from the cirrus, which, at an altitude of approximately 10 km, would have been much closer to the receiver than the satellite, which was at a range of 433 km. More recent active imaging experiments at the Phillips Laboratory have included sensors located near the receiver telescope to measure laser return backscattered from cirrus clouds. The backscattered light invariably saturates the detector. RAILE Mission planners believe the different power returns were due to different gain settings on the PMTs. With varying PMT gain, the power output from the detectors would vary widely due to the inherent nonlinear response of photo multiplier tubes. Unfortunately, no information on these gain settings could be found in the extant data, or in engineering files. This result must remain a mystery until further experimentation.
In the next section, we present and discuss the results from a computer simulation of the interaction of the coherent illumination with a cirrus cloud.
6. Computer simulation
The computer simulation used to produce Figures 9 and 10 consisted of two major components. The first component synthesized a three-dimensional model of a cirrus cloud. The program created a distribution in three-dimensional space of hexagonal ice crystals in the shape of columns (tall hexagons) and plates (flattened hexagons). Three-dimensional space was divided into 1 cm3 volume elements. In every horizontal plane, the occurrence of a crystal and its orientation in any volume element was randomly distributed according to uniform probability density functions. The distribution of the crystals by shape and by size varied with altitude. That is, particles at the higher elevations were smaller (typically about 300 μm in longest dimension) and more numerous than particles at the lowest elevations which approached 1,000 μm in longest dimension. This altitude variation was modeled on particle size data collected by the High Altitude Reconnaissance Platform (HARP) for the Space-Based Infrared Systems (SBIRs) program .
Once the cloud had been built, the program traced a number of rays through the crystal distribution. Ray direction, position, optical length, and ‘amplitude’ were continuously tracked and updated. Only backscattered rays, that is, rays that exited the cloud from the bottom were recorded. The ray ‘amplitude’ was a real number, which allowed a fractional splitting of the ray at an air/ice interface, and provided a check on multiple bounces.
The second major component of the simulation was the model of sheared beam illumination, followed by demodulation on the ground. Illumination consisted of three collimated ‘beams’ of rays in a 30×30 grid. One beam entered the cloud vertically; the remaining two beams were tilted from this reference by 10 microradians about the orthogonal axes. Output ray fans for each of the beams were used to reconstruct output wavefronts, which were then multiplied by a phase term representing the appropriate modulation frequency. A total wavefront, comprising the sum of the three was created, complex conjugate multiplied and propagated to the ground. The resultant two-dimensional array was summed to produce a single intensity value for one instant in time. The process was then repeated for 200 individual time sequences. Each time increment was 2.5 μsec for a total simulated pulse width of 500 μsec. The sheared beam modulation frequencies were set to 40 kHz, 80 kHz, and 120 kHz. Finally, the intensity versus time array was Fourier transformed and the resulting normalized demodulated signal plotted with a frequency resolution of 2 kHz. These parameters were chosen to provide as great a resolution in frequency as possible, not to simulate the RAILE experiment exactly.
A key element in producing sidelobes in the demodulated data is the presence of an instability in the illuminating laser. According to the report of a systems test of the argon laser/etalon combination, some residual frequency jitter was present in the laser. The authors assumed a nonlinear variation for this jitter, based on a normal random distribution, whose mean and standard deviation were scaled from values documented in the engineering report. This variation, called beta, was multiplied by the ray length and treated as an additional phase variation on the wavefront.
Figures 9 and 10 illustrate some of the simulation results. Figure 9 shows the result of reflecting three modulated beams off a cirrus cloud, with no laser instability. No sidelobes occur. Figure 10 illustrates the same ray trace results but with a random variation in the laser frequency. With this variation, some sidelobe structure can be seen, although it differs markedly from the RAILE field data results. The authors attribute much of this difference to the difficulty in emulating the laser behavior, since the structure would originate from the phase term created by the laser frequency variation and different “depths” in the cloud. That is, different rays propagate to various altitudes before ultimately being backscattered and these unequal altitudes can mimic the behavior of different depths on a target. Finally, the most striking similarity between the simulated results and the RAILE field data is the suppression of the third modulation frequency. This suppression was always observed in the field data as well as the simulation.
The data presented in this paper raise many more questions than they answer. The results of the simulation are far from conclusive proof that the sidelobes seen in the demodulated RAILE field data were produced by reflections from multiple target depths. Too many of the parameters of a very complex system could not be specified or determined.
For example, the exact frequency variation in the laser is largely unknown. The engineering report suggests that this variation could be modeled as a skewed normal distribution, but only a normal distribution was used. Furthermore, the rate of the variation was unknown. The authors updated the variation every fourth time increment, assuming that the frequency variation was no more frequent than every 10 μsec.
Certain aspects of the RAILE field data suggest that the experiment demonstrated the inadvertent active imaging of cirrus clouds. The RAILE mission planners did not expect to image clouds and did not include the range gating common in more recent LIDAR experiments to differentiate laser return from lower elevations from that returned from higher elevations. Elements such as the abnormally high power return on the night of cirrus cover and the complete absence of sidelobes on the clear night could not be completely explained by the extant data. More compelling yet are the sidelobes seen in the demodulated signal from the simulation of an SBI illumination of a cirrus cloud shown in Figure 10. This admittedly noisy structure suggests that a here-to-fore unrealized deterministic component may exist in the coherent light backscattered from a cirrus cloud. Such a component could possibly be used to great advantage for remote detection and imaging in the presence of cirrus clouds. A deterministic component in light backscattered from a cloud would presumably be similar to light forward scattered through the cloud from a target. In this case, the backscattered illumination, which could be separated from the forward scattered light via range gating, would be used to deconvolve the return from the satellite and thereby image it.
This work was performed entirely under USAF contract number F29601-93-C-0211. The authors gratefully acknowledge the many helpful discussions with Tom Caudill and Dave Voelz of the USAF Phillips Laboratory, John Belsher of tOSC, and Keith Bush of Logicon/RDA. The University of Hawaii Satellite Oceanography Laboratory graciously provided assistance with weather data for this research.
References and links
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7. T. Caudill, Private communication.