Mujeres de origen extranjero

As wake vortices form and then descend, there is no a priori way to tell where in the field of view they exist. They could form below the captured scene or be carried away by crosswinds and not be captured at all. With no way to determine where in the scene the vortices are located, a search methodology was developed which exploits the fact that vortices tend to entrain exhaust gases, such as CO2, CO, NOx, and H2O [15]. The spectra of these gases, if they exist in the datacubes,

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are in mixed pixels that may show spectral influences from all scene elements, including the gas of interest, the background, and the intervening atmosphere. Because these gases are in the exhaust, if they can be detected immediately upon exiting the aircraft engine, it could be possible to follow the gases through the next datacubes in the sequence of measurements as they either become entrained in a vortex or disperse into the atmosphere.

Gas detection algorithms investigated in this program included the Spectral Angle Mapper (SAM) and the Clutter Matched Filter (CMF) [25]; the Matched (MF) and Adaptive Matched Filter (AMF), and the Adaptive Coherence/Cosine Estimator (ACE) [26], [27]. All of the algorithms depend on finding a correlation or covariance in the data. The SAM algorithm finds the correlation between the target gas spectrum and every pixel in the datacube; a SAM result near 1 strongly indicates that a gas is present. All other algorithms depend on the covariance of the data, e.g. how much each pixel varies spectrally with the others. They are variants of the Generalized Likelihood Ratio Test [26] [27]. The Matched Filter, the Adaptive Matched Filter, and the Adaptive Coherence/Cosine Estimator were chosen as the most appropriate for the entrained gasses.

These gas detection algorithms depend on a priori knowledge of the gas spectrum under search, i.e. the target gas spectrum. Under a controlled gas release, gas constituents, abundances, temperatures, and concentrations are known. However, in the data sets under investigation, these characteristics must be estimated. To model the target gas spectrum effectively, the background and the atmosphere must also be considered. Therefore, the online tool Spectral Calc [28], which accesses the HITRAN database, was utilized to model the target gas. Many methods of modeling the target gas were investigated, including:

1. Creating the gas spectrum with the Spectral Calc atmospheric path radiance tool, then downsampling this spectrum to match the resolution needed. This spectrum then becomes the target gas.

2. Creating the gas spectrum with the Spectral Calc gas cell radiance tool, then downsampling this spectrum to match the resolution needed. This spectrum then becomes the target gas.

3. Creating the gas spectrum with the Spectral Calc gas cell radiance tool, smoothing it with a Lorentzian or Gaussian function with a width equal to the resolution needed, then downsampling this spectrum to match the resolution needed. This spectrum then becomes the target gas.

4. Creating the gas spectrum with the Spectral Calc gas cell radiance tool, using Spectral Calc’s built in Gaussian smoother to smooth it, then downsampling this spectrum to match the resolution needed. This spectrum becomes then becomes the target gas.

5. Creating the gas spectrum in the same manner as 2 through 4, only the final spectrum is added to an average of the background from the actual datacube. Each horizontal strip of sky is averaged independently.

The gases searched for were H₂O, CO₂, NO₂, and HNO₃. As the largest component of the exhaust, water vapor at 425 K was chosen as the first target. The temperature was based on a derivation of aircraft exhaust temperature following the method described by Mattingly [29].

The best results were obtained when the gas cell spectrum was smoothed with the Spectral Calc Gaussian smoother, and the result added to the background averages. This process is thus

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described in more detail here. The gas cell radiance spectrum was downloaded from Spectral Calc after having been smoothed with the Gaussian and the resulting spectrum was interpolated to match the resolution needed for each datacube that was collected. This result was combined with the measured data in the following manner. First, the datacube following the passage of the aircraft was divided into horizontal strips of sky and the radiance of each strip was averaged.

These averages were done for each piece of sky independently, because the radiance of the sky is expected to change with elevation angle. This method of averaging the radiance for horizontal strips of sky is similar to the Directional Mean Filter [30], with the exception that we limited the direction of our background average to the horizontal. The resulting radiances give a measure of the background atmospheric conditions as a function of elevation angle at the time of measurement. Next, the gas cell data was added to each resulting radiance average; the gas cell data was added because in this case, the hot engine exhaust was expected to act as an emitter against the cold sky. This method gives the semi-empirically modeled target gas spectrum for each elevation angle.

A median filter was used on these images to eliminate noise. The result of the median filter was an image where every pixel takes the value of the median value of the 3 x 3 block of pixels around it in the original image. This filtering serves to eliminate pixels that score positively but have no positive scoring pixels around them, and are more likely false detections.

Originally, the CMF and the SAM algorithms were going to be run on the data from the September field test at ATL. These data were selected because the Hyper-Cam was allowed to run continuously for every flight instead of being started and stopped before and after each aircraft landing. However, this entire data set was collected at 16 cm^-1 resolution. Also, only the data collected at zero zenith angle had valid calibration files; the sets angled to catch the cross-section of any falling vortices had blackbody files that were somehow corrupted. Therefore, the July dataset was analyzed more extensively. The July dataset had seven flights collected at 4 cm^-1 resolution. The drawback with this set is that the Hyper-Cam did not run continuously, so the recording of vortex formation may have been cut off by the end of the measurement.

Two datacubes from the July dataset showed potential detection of exhaust plumes in the sense that the high-scoring pixels from the algorithm tests were located in an area of the image consistent with being part of an exhaust plume. One of the datasets was recorded at 4 cm^-1 resolution, and results from its analysis are shown here. Water vapor was searched for in the cube following the passage of the aircraft and in all other succeeding cubes until that run ended. The visible image and a radiance image of the aircraft itself are displayed in Figure 50.

Figure 50. The visible image of the aircraft that passed through the FOV (left), and the radiance image of the same aircraft (right).

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The three algorithms that were run on the cube following the passage of the aircraft (cube 1452) were the MF, AMF, and ACE. Water vapor was the target spectrum. The radiance image of the entire datacube is shown in Figure 51, and the results of the algorithms are shown in Figure 52 through Figure 54.

Figure 51. Average radiance of entire datacube 1452.

Figure 52. The MF results on datacube 1452.

Figure 53. The AMF results on datacube 1452.

Figure 54. The ACE results on datacube 1452.

The target in all three runs is water vapor, and two trails in the air behind the aircraft are definitely detected; however, whether or not the algorithms are detecting water or anomalies is debatable. Nevertheless, there are two distinct trails, on the right side of all three images above that are not present in the radiance image of Figure 51.

All the algorithms depend on some kind of comparison of the target spectrum with the

“demeaned data.” This demeaned data is the spectrum of each pixel with the background

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subtracted out. The average background is computed for every row of sky, since the sky radiance changes greatly with increasing viewing angle. Once the vapor trails were located, the algorithms were re-run, but when computing the average background for the demeaned data, only columns 1 – 90 (left side) were used so that we ensured no plume was present in our background average.

The results of these tests are shown in Figure 55 through Figure 57.

Figure 55. The MF results on datacube 1452, using only columns 1 – 90 as background in the calculation.

Figure 56. The AMF results on datacube 1452, using only columns 1 – 90 as background in the calculation.

Figure 57. The ACE results on datacube 1452, using only columns 1 – 90 as background in the calculation.

Comparison of Figure 52 through Figure 54 to Figure 55 through Figure 57 shows improvement in the performance of all detectors when the plume-free background is used as an average.

However, one still cannot say definitively whether water vapor is being detected. Therefore, we compared the spectrum of a pixel that scored high for all three algorithms to a pixel that was definitely only background. While there were differences in the observed spectra, they were at locations that could not be correlated with the water vapor spectrum.

The evolution of the water vapor trails can be studied by analyzing successive datacubes. The results shown in Figure 58 though Figure 63 are for water vapor, searched for with an AMF, to which a median filter has been applied.

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Figure 58. The radiance image of the datacube following the passage of the aircraft.

Figure 59. The adaptive matched filter results 1 second after the passage of the aircraft.

Figure 60. The adaptive matched filter results 5 seconds after the passage of the aircraft.

Figure 61. The adaptive matched filter results 10 seconds after the passage of the aircraft.

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Figure 62. The adaptive matched filter results 15 seconds after the passage of the aircraft.

Figure 63. The adaptive matched filter results 20 seconds after the passage of the aircraft.

Figure 58 though Figure 63 demonstrate that the water vapor trails dissipate quickly, probably because the air behind the aircraft is very turbulent. However, the vapor can still be detected for a few seconds on the right side of the image, where the trails once were. We also analyzed a datacube before the aircraft entered the field of view, and the right side of that image scores higher as well. It may be that, due to the high volume of air traffic at ATL (there was a landing approximately every two minutes), the background has enhanced water vapor due to the exhaust from a nearly constant stream of incoming aircraft, making detection more difficult.

Questions arose as to whether the detection algorithms were acting as gas detectors or anomaly detectors. Therefore, a more in-depth look at the algorithms themselves was undertaken. Tests were run in which random targets were used instead of the actual gases, in an attempt to see whether or not the plumes could be detected. These random targets were modeled as vectors of zeros with ones inserted at random wavenumbers. In the instance of the MF, the random target was found in the area of the plume, which would lead one to believe that it is detecting an anomaly and not necessarily the gas itself. Something is being detected in the aircraft exhaust, but whether or not this can be identified as a specific gas is not clear. Thus, a methodology was developed to see if, once detected, the anomaly could be identified in a second step by comparison of its spectrum to that of a background pixel.

Gas detection algorithms run on ATL data using a plume-free background as an average showed improvement in performance; however, water vapor could still not be identified. In order to attempt to identify water vapor in the plume, the pixels in a 6-pixel high by 4-pixel wide region of plume that scored highly for all detection algorithms were averaged and labeled as plume. Then, the same 6-pixel high strip of sky was taken from a datacube that was recorded two frames before the airplane entered the field of view. These pixels, once averaged, were labeled as background.

The plume and background plots are shown in Figure 64.

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Figure 64. The radiance of the averaged plume pixels, plotted with the radiance of the averaged background pixels.

No obvious differences between the two spectra can be seen in Figure 64; therefore, to see if any differences do exist and where, the background was subtracted from the plume and the residuals plotted in Figure 65.

Figure 65. The difference of the plume and background.

The differences seen in Figure 65 are small and are not correlated with spectral features of the water vapor spectrum. It has not been possible to identify particular gases by the methods described here.