1. INTRODUCTION

The ability to measure beam transmittance over a horizontal extended path of a few kilometers in the atmosphere is important for several applications, including visibility studies and testing of instruments such as lasers. The most common systems for measuring optical extinction in the atmosphere are either transmissometers, which utilize a transmitter and a receiver at opposite ends of the path, or point scatter meters (PSMs), which measure the scattering in a small parcel of air at a single location. Lidars can also provide measurements of backscatter, but do not normally acquire the total beam transmittance over a path of sight. Both transmissometers and lidars make use of a beam of light projected into the surround, and thus may be problematic in urban environments or for covert applications.

Transmissometers are well able to measure the transmittance and thus the effective extinction coefficient over extended paths in situations where it is practical to mount a transmitter at one end of the path and a receiver at the other end of the path. However, in situations, such as on ships, this may not be practical if there is not a platform at the other end of the path of sight. Similarly, the use of a transmissometer may not be practical for monitoring the surround in many directions. PSMs (and related systems such as nephelometers and visibility meters) only measure the scattering coefficient in a small volume, and thus may not accurately represent the transmission losses for extended paths.

The goal of this research was to determine whether it is feasible to develop a reasonably accurate method to determine the beam transmittance over an extended path using a single-ended system consisting of a radiometrically calibrated digital imager. Our goal was to be able to measure transmittance in a variety of directions, such as in multiple directions surrounding a ship or urban location, without use of an active beam such as used in a lidar or transmissometer. Additional goals were to develop a system that is robust and relatively low cost, and to test the feasibility of using the concepts in either visible wavelengths or short-wave IR (SWIR) wavelengths near 1.6 μm. During this research, we designed, built, and fielded two systems we designated as extinction imagers (EIs), and evaluated both with respect to both transmissometers and PSM systems.

The theory of radiative transfer and extinction in the atmosphere has been developed over many years and documented in many texts. Some of the early developers include Koschmeider [1] and Duntley et al. [2]. The theory as it applies to EIs will be discussed in the Theory section. Many researchers have been involved in measurements of extinction coefficients and other related atmospheric parameters over the years. For example, early work by Duntley (e.g., [3]) included extensive measurements of scattering coefficients in several wavelengths in the visible and near-infrared (NIR) using airborne systems.

The new EI concept uses either dark targets, or dark features in the surround to determine the effective extinction coefficient for the extended path. Early developments of some of the concepts used in the EI systems include Hood in 1964 [4]. In the 1980s, radiometers were used with black targets by Malm [5,6] for determining extinction over extended paths. Janeiro has recently developed systems using two black targets [7]. Like these approaches, the EI systems use one or more dark targets, but they need not be black targets, and thus dark features of the surround such as the ocean surface can be utilized. Some of the advantages of the new methods over these previous methods will be discussed at the end of the Theory section.

In the late 1980s, we developed an imager for determination of extinction over extended paths [8,9] in urban environments. This instrument was designated the horizon scanning imager (HSI). It used an off-the-shelf lens and a digital imager mounted on a rotary table in an environmental housing and acquired images of the surround. It used dark “targets of opportunity” such as open doors or dark buildings for its targets. This is the first example of using the EI concept with digital imagers that we are aware of. Using an imaging sensor as opposed to a radiometer meant that multiple dark targets could be used and the horizon could also be measured. Although the digital imagers available to us at the time were somewhat primitive, the results of this early research were a major step forward and also yielded experience in understanding the types of uncertainties inherent in the method. In this article, we document the new research, in which we have used more modern digital imagers, extended the capability to include the SWIR as well as use of the instrument in the open ocean, and done considerably more testing and evaluation of the capabilities.

2. THEORY

Our goal with EI systems is to determine the beam transmittance and effective extinction coefficient over a horizontal path through the atmosphere. The equations are derived from the basic properties of atmospheric radiative transfer [2,3].

We define transmittance $T_r(r)$ as the fraction of incident radiance $L$ that passes through a medium or through a path of sight (such as in the atmosphere) of length $r$. Extinction coefficient ${\propto }_r(r)$ is defined over an incremental path at location $r$ by Eq. (1),

If the extinction coefficient is uniform along the path, this reduces to Eq. (3),

In the atmosphere, when viewing a target at range $r$, the radiance of the target is diminished by the transmittance $T_r$. We also have a gain term, the path radiance, given by Eq. (4),

We also define the inherent radiance of a target $L_0$ as the radiance of the target as measured from range 0, and the apparent radiance of a target $L_r$ as the radiance of the target from range $r$. These terms are related by the following equation:

A similar equation defines inherent contrast, using the inherent radiance of both background and target,

Combining Eqs. (5)–(7), we derive the following equation:

In Eq. (8), note that the background ratio term is the ratio of the horizon sky as measured from the target position to the horizon sky as measured from the sensor position. Under most conditions, this ratio is 1. This follows from atmospheric theory because under nearly all conditions, the horizon sky will be at equilibrium, i.e., will equal the equilibrium radiance [2,10]. Under most conditions, if one measures the horizon sky from the location of the target and from the location of the sensor, the radiances will be the same.

A situation in which these background radiances might not be identical is if very bright or dark clouds are very close to the target. In that case, the error in the ratio should be small, and the resulting error in transmittance will be the ratio of these background radiances. We developed algorithms that would minimize the impacts of errors in the ratio, and flag extreme cases. In analysis of the data we acquired, we found no flagged conditions. From analysis of several cases with both clouds and gaps in the clouds on the horizon, we determined that the clouds did not affect the resulting extinction determination during our test periods. Thus, we make the approximation shown in Eq. (9),

It is also convenient, as an aid in analysis of the imagery, to derive a visibility term. Equation (8) is applicable to human vision in the photopic wave band near 555 nm. If an observer observes an object against the horizon sky, then Eq. (11) is also valid. If the human views a totally black object, the $C_0$ term becomes $-1$. Visibility can be defined as the range at which the apparent contrast of a large black object with respect to the horizon sky is at the human contrast threshold. A value of $-0.05$ is often used as an approximation of the human contrast threshold for these viewing conditions. Substituting $V$ for $r$ and $-.05$ for $C_r$ in Eq. (11) yields a definition of visibility given in Eq. (12)

This equation is usually expressed in terms of the scattering coefficient $s$; however, in the photopic wave band the absorption coefficient is usually near zero relative to the scattering coefficient, and for our purposes it is more convenient to use the absorption coefficient, strictly as an aid in evaluation of the imagery. (Note that the use of a contrast threshold of $-0.02$ yields a definition for visual range.) A human is rarely in a position to view a totally black object against the horizon sky, and in practice the human contrast threshold is not a constant. However, for evaluation of the imagery, this derived visibility term is useful because it is easier to visualize than extinction coefficient magnitude. In addition to using the above definition for our near-photopic wavelength data, we also found it useful to derive a pseudo-visibility $V^{\prime }(\lambda )$ from ${\propto }_r(\lambda )$ at our other test wavelengths by applying Eq. (12) to ${\propto }_r(\lambda )$, strictly for aid in visual assessment of the imagery. We will designate this term “spectral visibility.” The visual appearance of the images should correspond with the spectral visibility for the wavelength band in which the image was acquired.

Although systems using either a single black target and the horizon sky or two black targets have been known and used by many others in the past, as discussed in the introduction, we have made several advances that have made this technique far more effective than in the past, in our opinion. By the use of the equations developed in this section, we do not have to assume that the inherent contrast of a dark target is $-1.00$. We can determine the inherent contrast and use this input value in the algorithms. This significantly improves the accuracy of the method, and enables the use of nonideal targets of opportunity in the scene. The use of an imager also means that the horizon and the target need not be immediately adjacent, since nonadjacent regions of interest (ROIs) can be extracted from the imagery.

The new algorithms include use of radiometric calibrations [11] that significantly improve the accuracy over what might otherwise be obtained. The linearity calibrations, which measure signal as a function of flux level, are especially important with the SWIR imager that used complementary metal-oxide-semiconductor chip (CMOS) technology as opposed to the charge-coupled device (CCD) technology used with the visible sensors. Characterizing this response has been a key step in enabling us to extend the technique into the SWIR wavelengths.

Taking advantage of the abilities of imagers, the new algorithms include logic to automatically find the apparent location of the target in the image even if the apparent location has changed due to refraction and/or turbulence. Also, the use of ROIs within the image enabled development of new algorithm features to detect and handle nonideal conditions such as whitecaps on the ocean and clouds on the horizon. These advances have enabled us to extend the technique to work in multiple wavelengths, including SWIR wavelengths. They have also enabled the use of the ocean as a dark target in essentially any direction, enabling monitoring of nearly the full surround from a ship.

3. INITIAL EXPERIMENTS FOR A VISIBLE SYSTEM USING A BLACK TARGET

For our initial research, we tested the use of a calibrated imager viewing a black box at a range of approximately 7.2 km [10,12,13]. The sensor was a 16-bit low-noise Photometrics $512\times 512$ digital camera, with a filter changer built by our team, and a commercial zoom lens [Fig. 1(a)]. This sensor (except for the lens) had been retired from another research effort developing whole sky imagers [14]. It acquired data in wavelengths near 450, 550, 650, and 800 nm. The target was a hollow $2.4\mathrm{m}\times 2.4\mathrm{m}\times 3.7\mathrm{m}$ deep black box, using paint that had been verified to be black in all the sensor wave bands [Fig. 1(b)]. The system is designated the multispectral extinction imager (MSI) (previously multispectral scattering imager, but this was a misnomer since it actually measures extinction). The path of sight was from Point Loma in San Diego, across the entrance to San Diego Bay and the Zuniga Shoals to the Silver Strand. Transmissometers, a nephelometer (similar to a PSM), and other instruments were fielded by colleagues from several research groups [12].

 

Fig. 1. MSI sensor and target as used in initial research.

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A typical image acquired with a near-photopic filter (near 550 nm) on a day with light haze is shown in Fig. 2. The target is the small black spot just above the bright sand in the image. In spite of its small size, a new algorithm feature enabled the software to find the target, as noted later in this section. An ROI was selected by the algorithm inside the target location. A larger ROI just above the hills was chosen to represent the horizon sky. Having to use this elevated horizon ROI caused a small bias at both ends of the sensitivity range [10], but it was adequate for our purposes. In this example, the MSI algorithm indicated a visibility of 46 km. Our colleagues with offices on the west side of Point Loma indicated that they could clearly see the Coronados Islands at 40 km range at the time of the image acquisition. As expected, the MSI images in the other wave bands have the appearance of more haze or less haze as a result of the variation in extinction as a function of wavelength λ [10], with the blue images appearing the haziest and the NIR images appearing least hazy.

 

Fig. 2. MSI imagery under light haze.

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We developed data acquisition software to enable continuous automated acquisition of the raw imagery in all filters, as well as processing software to process the archived data. One of the early steps in the processing is the application of the results of the radiometric calibrations acquired in our calibration facility [11]. These calibrations include dark calibrations, linearity calibrations, and uniformity calibrations. Absolute radiances are not required by the algorithm, because the algorithm equations only use the radiance ratios, as can be seen in Eqs. (6) and (11).

For this setup, the target occupied roughly $5\text{pixels}\times 5\text{pixels}$ within each image. Refraction and/or turbulence caused the location of the target in the image to vary somewhat, so an adaptive algorithm searched for a dark region near the expected location in order to detect the target. To adaptively locate the target in each image, the software searched for the darkest $3\times 3$ region within $\pm 10$ pixels of the anticipated position. The percent standard deviation (STD) within the $3\times 3$ region was checked. If it was not less than an input threshold, that meant the target was not found, and the data point was flagged as invalid. A number of other new quality checks were applied to the data extracted from the target and horizon ROIs. For example, STD thresholds for the horizon ROI detected cases when the horizon radiance was not quite at equilibrium. All data in both the target and horizon ROIs were verified to be on-scale (i.e., not off-scale bright or below a dark threshold). Following these steps, the apparent contrast of the target with respect to the horizon was derived [Eq. (6)], as well as the beam transmittance, path attenuation coefficient, and visibility or spectral visibility in each wavelength [Eqs. (10)–(12)].

Prior to deployment, we had measured the inherent contrast in each wavelength by placing the target and sensor together in an outside environment and measuring the target and horizon intermittently throughout the day (and thus at a variety of sun angles). The resulting inherent contrast was found to have a value of $-0.99$, with a temporal variation of $\pm 0.005$ and an additional spectral variation of $\pm 0.005$ and all values falling between $-0.979$ and $-0.994$. With the inherent contrast determined, the new algorithm determined the beam transmittance, path extinction, and visibility using the equations in the Theory section.

Our initial analysis consisted of evaluating the appearance of the imagery in comparison with the derived visibility in the photopic wave band. Although this can be only a qualitative comparison, the results were excellent [10], with images that appeared hazier, corresponding with higher calculated extinction values.

More quantitative comparisons with the data provided by our colleagues from the visible transmissometer (operating at 550 nm) and nephelometer (operating in a pseudo-photopic bandpass near 555 nm) were more limited. Our colleagues who operated the transmissometer and nephelometer provided data listings to us for two test periods (August 2005 and November–December 2006) that we could use for initial analysis; however, the transmissometer data were not yet fully calibrated at that time. They also later calibrated the data from the November–December 2006 period, and provided us with the resulting comparison plots, but not the actual data tables. The August 2005 transmissometer data were never calibrated, to the best of our knowledge. The primary reason for this limited data acquisition was that the transmissometer required constant realignment due to the long range, and thus could not be run autonomously. Also, our colleagues indicated that the performance of the open-cell nephelometer degraded after about 1 month of exposure to the maritime atmosphere [12].

A comparison between the MSI and the calibrated transmissometer path extinction coefficients is shown in Figs. 3 and 4. Figure 3 shows the path extinction coefficients for the period from 28 November–11 December 2006, and Fig. 4 shows a time series plot for the first week of this period.

 

Fig. 3. MSI versus transmissometer path extinction coefficients for 28 November–11 December 2006.

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Fig. 4. Time series comparing MSI and transmissometer extinction coefficients for 28 November–5 December 2006.

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As shown in both of these figures, the relationship between these two measures of extinction is generally quite good, although there is more variance in the correlation than would be ideal. Unfortunately, we do not have access to the data listings for the calibrated data shown in Fig. 3, so we cannot derive the $R^2$ correlation constants for the calibrated data. However, the correlation constants for the uncalibrated transmissometer data are available for both test periods. Although we recognize that there will be some error in these estimated correlations, the plot in Fig. 3 is quite similar to the plot of uncalibrated data (not shown) that we originally worked with. Thus, we find it reasonable to present the correlation coefficient $R^2$ between the uncalibrated transmittance extinctions and the MSI extinctions.

The correlation between the uncalibrated transmittance extinctions and the MSI extinctions during the November–December 2006 period (i.e., data similar to those shown in Fig. 3) was 0.87. The comparison between the MSI extinction coefficients and the uncalibrated extinction coefficients from the August 2005 period were much better, with a value of 0.92. The comparison between the uncalibrated data for two “gold standards” (i.e., the nephelometer and the transmissometer) for the August 2005 period was 0.73.

Further analysis of additional test periods by our colleagues revealed that the relationship between the final calibrated transmissometer extinction coefficients and nephelometer scattering coefficients was generally quite poor, but improved significantly if sorted as a function of wind speed, thus indicating that much of the difference is due to the difference between the aerosols along the path and the aerosols at the shore [12].

We believe that the differences between the August MSI transmissometer correlation and the November–December MSI transmissometer correlation are related to the differences in the atmospheric conditions between the two periods. Analysis of scintillometer data by our colleagues revealed that there was significantly more turbulence along the path during the November–December period, as indicated by elevated levels of measured refractive index structure constant $C_n^2$ [12]. This could affect the transmissometer, which does not have an adaptive algorithm to detect the source in real time. It could also affect the MSI, which is using a rather small target with a fairly low spatial-resolution camera. Acquiring and averaging several measurements each minute might have helped alleviate these issues.

Clearly, more studies with coaligned EI systems and transmissometers would be useful. However, we feel it is fair to conclude from this data set that the MSI appears to compare quite well with the transmissometer data in this data set. In comparison with the transmissometer, the MSI has the advantage that, unlike the transmissometer, it can self-align with the target and thus be run autonomously without an attendant. In addition, it has the flexibility to provide results in several wavelengths and provided good results in four wave bands [10]. Our colleagues found that the nephelometer provided much less accurate assessments of the extended path than the transmissometer, in part due to the variance between conditions for the extended path and conditions on the shore [12]. On this basis, we also conclude that the MSI provided a much better assessment of the extended path than a PSM could, at least for this experimental setup.

4. EXTENSION TO SWIR AND OCEAN TARGET

The next major step in our research had two primary goals. One goal was to determine whether it would be possible to use the ocean surface as a dark target for wavelengths around 650 nm (red) and beyond, so that the EI approach could be truly single-ended for the ocean environment. (Our early work with the HSI had already demonstrated the use of “targets of opportunity” in the urban environment for a fully single-ended system on land [9].) The second primary goal of this phase of the research was to determine whether it would be possible to use a SWIR imager to determine extinction results in the SWIR.

In order to test the possibility of using the ocean surface as a target, we mounted the MSI on a rotary table in an environmental housing so that it could be fielded on the west side of Point Loma. In addition, we designed, built, and fielded a Short-wave IR Extinction Imager system (SRI) operating near 1.6 μm, and set up a new experimental site on the west side of Point Loma. In order to use the ocean surface as a target, it would be necessary to characterize the inherent contrast of the ocean surface with respect to the horizon sky with sufficient accuracy, particularly with varying solar positions. We limited the research to wavelengths of 650 nm and beyond, where the upwelling radiance from the ocean is very low. To determine whether it is feasible to measure extinction in the SWIR with the EI methods, it was necessary to characterize the calibration performance of the SWIR imager, and determine whether system characteristics such as noise and stability were sufficient to provide accurate results.

The SRI used a 12-bit Alpha-NIR camera with peak responsivity near 1.6 μm, and a $320\times 256$ resolution. A commercial zoom lens was used. No filters were used in the SRI. Although the use of no filter results in some uncertainties, detailed analysis revealed that the derived path extinction coefficients provide a reasonably accurate assessment of the extinction at 1.6 μm [10]. The SRI sensor package is shown in Fig. 5.

 

Fig. 5. SRI mounted on rotary table (placed on top of environmental housing for picture).

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The instruments were set up on the west side of Point Loma with a full 180° view of the ocean. They were placed on a platform at 20–21 m above the ocean surface. Colleagues from the Naval Post Graduate School in Monterey and MIT Lincoln Labs fielded supporting instrumentation, including a weather station, buoy, ceilometer, PSM, and transmissometers. The setup (minus the ceilometer) is shown in Fig. 6. The transmissometers were mounted looking north over a 0.72 km path along the coast, because we needed a place to mount both the transmitters and the receivers. The MSI and SRI acquired data looking over the ocean from azimuth angles 0°–180° relative to true north. Typically target ROIs at ranges of about 4–8 km were used. The range to these ROIs was determined with calculations involving the number of pixels below the horizon, the angular calibration of the images, and the height of the platform.

 

Fig. 6. Experimental site with EI systems and supporting instrumentation.

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The data acquisition software was quite similar to that developed in the first stage of the research, with the addition of automatic scanning of the horizon at 30° azimuthal increments. The processing software was set up to evaluate several different input target ROIs. Sample calibrated MSI and SRI images looking south, with some typical selected ROIs, are shown in Figs. 7 and 8. The islands in the scene are at approximately 40 km range. As illustrated in Fig. 7, the target ROIs were set up to avoid the kelp beds (seen between the two target ROIs), where abnormally high amounts of reflected skylight affected the data.

 

Fig. 7. Typical MSI Image at 650 nm showing typical ROIs, 4 March 2008; uncalibrated image.

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Fig. 8. Typical SWIR image with scattered clouds, 18 February 2010; calibrated image.

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As anticipated, the radiometric calibration results for the SWIR camera, which uses a CMOS sensor, were quite nonlinear, meaning that the relationship between input flux and dark-corrected signal was not linear. The SWIR camera also showed significant spatial nonuniformities due to the readout process [10,11]. Near the low end of the scale, at a dark-corrected signal of 100 (on a scale of 0–4095), the nonlinearity was about 50%. That is, if we had not corrected for nonlinearity, the errors in the relative radiances for this signal would have been about 1.5. Calibration tests of noise and stability (particularly repeatability of the linearities) verified that the calibration characteristics were quite stable and thus could be adequately corrected for [10,11].

Nearly all of the analysis used the data acquired in the red passband near 650 nm and SWIR near 1.6 μm. In order to deal with the ocean environment, several new algorithm features were developed. For example, instead of using the average within the target and horizon ROIs, the software was updated to use those values that fell between 5% and 35% in the histogram of the relative radiances within each ROI. This effectively removed whitecaps, birds, and so on, yet introduced no significant bias, because the pixels that were not outliers were typically quite consistent. Also, when looking up-sun near the same azimuth angle as the sun, there was sometimes a glitter pattern caused by reflections of the sun on the waves. Algorithm features were developed that provided special handing for this case. This algorithm feature used both the azimuth angle relative to the solar position and the STD within the ROI to detect glitter, and then it flagged extreme cases or used modified logic in less extreme cases to provide good results.

Because we could not measure the inherent contrast of the ocean surface with respect to the horizon directly, we used data from very clear days (i.e., when we could clearly see the features on the islands) to calculate an estimated inherent contrast. This inherent contrast calculation used the measured apparent contrast and an estimated value of path extinction coefficient based in part on the Rayleigh extinction coefficient in the appropriate wavelength. These estimated values were checked by applying them to imagery taken under a variety of conditions. We found this inherent contrast to be independent of the azimuth angle relative to the sun. Even though the horizon radiance increased near the solar azimuth angle, the ocean surface also increased in a similar manner, and the derived inherent contrast showed no azimuthal dependence.

The resulting inherent contrast values were approximately $-0.85$ near 650 nm and $-0.73$ near 1.6 μm. That is, the ocean surface was not quite as dark as a black box, but was sufficiently dark in these wavelengths to provide a reasonable target. In sensitivity studies, we evaluated the impact of estimating an inherent contrast of $-0.85\pm .05$. The resulting uncertainty in extinction was less than 4% for spectral visibilities $V^{\prime }$ of 18 km or less, and greater than 15% for spectral visibilities of 30 km or more. We felt that this level of uncertainty was acceptable, since the PSM system truncated at spectral visibilities of 20 km or more, and since we would expect the actual uncertainty in inherent contrast to be somewhat less than given above.

A detailed evaluation of the path extinction coefficients derived from the measured data showed that under most conditions the results looked very reasonable. For example, Fig. 9 shows a case in which the path extinction changed dramatically within less than 2 h, but comparison with the imagery shows this change to be valid. The spectral visibility $V^{\prime }$ corresponding with the determined extinction coefficients from the MSI and scattering coefficients from the PSM are superimposed on the image. Analysis of data at a variety of azimuthal angles, for varying solar angles and weather conditions, supported the thesis that the EI results were reasonable, except in cases of gloss, which will be discussed below.

 

Fig. 9. MSI images at 650 nm, 21 February 2010, 1700 GMT and 1820 GMT, illustrating very dynamic situation.

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For a more qualitative analysis, we compared the MSI and SRI path extinction coefficients with the PSM scattering coefficients and the transmissometer path extinction coefficients. We would not expect any of these comparisons to be exact. The PSM measures a very small atmospheric volume on the shore, and it measures the scattering coefficient (as opposed to the extinction coefficient) at 875 nm. This wavelength avoids regions close to atmospheric absorption peaks, and the scattering coefficient should be quite close to the extinction coefficient. The transmissometers were measuring the path extinction coefficients, but only for a short path along the shore. They were operating at 550 and 1060 nm. Modeling studies [10] illustrated the approximate magnitude of anticipated inconsistencies caused by wavelength differences from 550 to 875 nm should be about 50% or less. Similarly, anticipated inconsistencies between the SWIR instruments due to wavelength differences should be about 50% or less. In addition, we would anticipate differences due to the PSM only measuring one location on the shore, and the transmissometers looking north along a 0.72 km path on the shore. Thus, neither the PSM nor the transmissometers were at exactly the same wavelengths, nor could they replicate the extended path of the EI systems. While this is a weakness in the analysis, it is precisely the strength of the EI concept that these extended lines of sight can be measured with EI systems.

Figure 10 shows a typical comparison among the five systems from 19–26 February 2010, with the MSI and SRI looking south. The green curve shows the PSM results, which the manufacturer truncates at 20 km spectral visibility or scattering coefficient values of $0.15{\mathrm{km}}^{-1}$. When the PSM data are on-scale, they generally compare well with the EI data. The major exception is 25 February, or Day 56, when the MSI and SRI yielded path extinction coefficients below $0.1{\mathrm{km}}^{-1}$ ($V^{\prime }$ greater than 30 km) for much of the day, while the PSM yielded scattering coefficients of about $0.5{\mathrm{km}}^{-1}$($V^{\prime }$ about 6 km) throughout the same period. Evaluation of the hourly images during this period showed that the extended path of sight was quite clear throughout the period. A sample image from this period is shown in Fig. 11(a). The islands at 40 km range are quite clear, indicating that the spectral visibility was greater than 30 km, as measured by the MSI. The fact that the transmissometer extinction coefficients for the short path on shore were consistent with the PSM onshore scattering coefficients during this period may indicate that there was an onshore heavy haze, and yet the imagery supports the fact that the EI extinctions were much more accurate for the extended path.

 

Fig. 10. Extinction and scattering coefficients, 19–26 February 2010.

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Fig. 11. Two sample images for evaluation of instrument comparisons. (a) MSI, 25 February 2010, 1900 GMT; (b) SRI, 14 February 2010 2300 GMT.

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In the 16-day February data set we evaluated (of which Fig. 10 shows half), we found that the EI and PSM results matched well on 11 of the 16 days. Cases in which they did not agree were carefully evaluated, in conjunction with the actual imagery. We determined that in these cases, the PSM was reporting much more haze than the EI systems, and yet the islands at 40 km range were visible in the imagery, as in Fig. 11(a). Another example in which the PSM and EI systems differed significantly is shown in Fig. 11(b), using the SRI image (the MSI image was similar). In this example, the PSM scattering coefficient was $1.12{\mathrm{km}}^{-1}$ ($V^{\prime }$ about 2.7 km), and the SRI path extinction coefficient was $0.168{\mathrm{km}}^{-1}$ ($V^{\prime }$ about 18 km). The islands at 40 km range are reasonably visible, supporting the SRI value for the extended path.

The transmissometer data in Fig. 10 sometimes match the PSM scattering coefficients reasonably well, and sometimes do not, as might be expected due to the differences in their configurations. As with the PSM, careful analysis of the transmissometer data in comparison with the EI data yielded the conclusion that the EI measurements provided a more accurate assessment of the extended path over the ocean. Extensive analysis of additional data and imagery showed that under most conditions, the EI extinction results appear to be valid and appear to provide a better assessment of the extended path than the other systems, which could not duplicate the desired path of sight.

The exception was when the ocean surface had high gloss, as mentioned earlier. The gloss condition is the situation in which the ocean surface or patches of the ocean surface become highly reflective due to a temporary and localized absence of capillary waves. This typically occurred at near-zero wind speeds measured on the shore and the buoy, but this correlation with the wind speed at the ends of the path was not strong enough to use in the algorithm. Visual assessment of the ocean surface using polarizers suggests that this situation might be dealt with by taking two images with two linear polarizers at 90° relative orientations. We believe that acquiring such images and using them to distinguish gloss from high haze amounts would be effective. This is an area that would require further research.

We also carefully evaluated cases with clouds on the horizon. As noted in the Theory section, if the apparent radiance of the clouds is the same when measured at the sensor location as measured at the target location, then there should be no resulting error in the extinctions. In a 22-day data set we analyzed for this purpose, we found only two cases in which the horizon clouds within the horizon ROI appeared to not be at equilibrium. In both cases the special horizon algorithm features handled the calculations properly, and the resulting extinctions were not impaired.

In order to assess the anticipated accuracy of the EI systems, several sensitivity studies were performed. For example, uncertainties due to signal noise are a function of the magnitude of the extinction and hence, spectral visibility. For a target at 4.75 km and an inherent contrast of $-0.9$, these uncertainties were about 1% for $V^{\prime }$ greater than about 3 km. For $V^{\prime }$ below 3 km (very hazy or foggy), the uncertainty becomes quite large when using a target at 4.75 km, but this uncertainty is easily avoided by choosing an ocean target at a shorter target range. These calculations assume that a reasonable quality sensor, such as a 12-bit sensor, is used, and that calibrations are performed as needed. The largest uncertainty we determined was the uncertainty in extinction as a function of uncertainty in inherent contrast, as noted earlier. While these uncertainties are quite small, more extensive sensitivity studies would be useful, as well as more studies of the inherent contrast determination.

We should also note that in Fig. 10, the PSM and transmissometer data are continuous, whereas the EI data are only for daytime. The equations derived in the Theory section are equally valid at night. During our research, we tested the possibility of using the ocean surface as a target at night; however, we found that the ocean surface was not well behaved at night, and speculated that this might be due to phosphorescence from algal blooms. This phosphorescence could potentially be filtered out, but clearly more work would be required to develop and test night capability with a variety of dark targets.

To extend the capability to urban and other environments, it would be necessary to determine inherent contrast values for each target of opportunity (as was done with the HSI system) using techniques similar to those used with the ocean targets.

We also developed software to extend the results to slant paths, i.e., paths looking somewhat upward at nonzero elevation angles [10]. This slant path algorithm was based in large part on an extensive library of vertical profiles of extinction coefficients in four wavelengths, for altitudes between 0 and about 6 km, measured and modeled by our research group (e.g., [3,15]). The slant path algorithm logic also uses ceilometer data if available.

5. CONCLUSIONS

In this research, we have developed new methods of applying the atmospheric equations of transfer, in order to test the feasibility of using a calibrated imager to determine the beam transmittance, and hence, the effective path extinction coefficient, for an extended path of sight. Our primary goals were to evaluate whether reasonably accurate path extinction coefficients could be determined using dark targets such as the ocean surface, and to evaluate whether the techniques could be extended into the SWIR wavelengths with relatively simple and robust hardware.

We have designed, built, and fielded new EIs using off-the-shelf digital cameras capable of acquiring images in the visible and NIR or SWIR wave bands. Using imagers in place of radiometers, which were used historically, we have introduced the use of radiometric calibrations to enable application of this technique to multiple visible and NIR wavelengths as well as SWIR wavelengths near 1.6 μm. Our advancements in the theory have enabled using dark targets in the surround that are not fully black, including the ocean surface or other targets in the surrounding environment. Our use of imagers has also enabled us to develop many sophisticated algorithm features, including the ability to compensate for atmospheric conditions such as changes in refractive index, and conditions such as obstructions in the regions of interest. In comparisons with transmissometers and PSMs, we believe we have demonstrated that the EI systems provide a much more accurate assessment of extended paths of sight requiring a single-ended setup. When both ends of the path are accessible, the EI systems appear to provide comparable results with a transmissometer, and also lend themselves much more readily to autonomous operation due to the adaptive target detection feature.

As a result, the EI concepts enable use of an imager to determine the transmittance over extended paths surrounding a location. The system does not use any active sources such as lasers, which makes it more practical than existing systems for many applications. The hardware is relatively inexpensive and robust. Also, the EI systems are readily adapted to different wavelengths in the visible and SWIR. The new capabilities of being single-ended and able to scan the horizon in multiple directions are significant advantages for many applications. At this point the capability is not commercially available, and the setup requires tests to determine the inherent contrast prior to automated processing. However, once the inherent contrast is known, the system can be run fully automatically over extended periods, providing an assessment for paths of sight that are difficult to characterize using other known methods. We feel that these developments have been a major step forward, and the results are quite reasonable for multiple purposes.