Ozone Cues Mitigate Reflected Downwelling Radiance in LWIR Absorption-Based Ranging

Abstract

Passive long-wave infrared (LWIR) absorption-based ranging relies on atmospheric absorption to estimate distances to objects from their emitted thermal radiation. First demonstrated decades ago for objects much hotter than the air and recently extended to scenes with low temperature variations, this ranging has depended on reflected radiance being negligible. Downwelling radiance is especially problematic, sometimes causing large inaccuracies. In two new ranging methods, we use characteristic features from ozone absorption to estimate the contribution of reflected downwelling radiance. The quadspectral method gives a simple closed-form range estimate from four narrowband measurements, two at a water vapor absorption line and two at an ozone absorption line. The hyperspectral method uses a broader spectral range to improve accuracy while also providing estimates of temperature, emissivity profiles, and contributions of downwelling from a collection of zenith angles. Experimental results demonstrate improved ranging accuracy, in one case reducing error from over 100 m when reflected light is not modeled to 6.8 m with the quadspectral method and 1.2 m with the hyperspectral method.

Figures (10)

• Figure 1: Effect of downwelling radiance in absorption-based ranging: (\ref{['fig:intro_RGB']}) RGB photograph of the scene shown for reference but not used in any computations; (\ref{['fig:intro_no_downwelling']}) hyperspectral absorption-based ranging results when neglecting downwelling radiance; (\ref{['fig:intro_with_downwelling']}) hyperspectral absorption-based ranging results when accounting for downwelling radiance (discussed in Section \ref{['sec:Hyperspectral_estimation']}); (\ref{['fig:intro_measurements']}) hyperspectral measurements at reflective panel, grass area, and sky pixels (to improve clarity, the green curve uses a distinct vertical scale provided on the right side). Pixels plotted in (\ref{['fig:intro_measurements']}) are shown with $\times$'s in (\ref{['fig:intro_no_downwelling']}) and (\ref{['fig:intro_with_downwelling']}). The ozone absorption band is shown in gray. In natural scenes, where temperature variations are minimal, reflection from the overhead sky can contribute significantly to the measurements and cause range overestimations depending on the reflectivity of the material. The central innovation of this paper is to use measurements in the ozone absorption band to infer the strengths of downwelling radiance contributions from a set of zenith angles. This helps to separate the reflected downwelling radiance and improve the absorption-based ranging.
• Figure 2: Conceptual figure for radiative transfer model. White and red arrows represent contributions from object emission and air emission to the observed spectrum, respectively. The gray arrow denotes reflected thermal radiation from incident ambient thermal radiation from all angles of the hemisphere, assuming a diffuse reflection model. The ambient thermal radiation is decomposed into downwelling and ground-sourced components.
• Figure 3: Ozone absorption band in LWIR. (\ref{['fig:ozone_feature_1']}) Comparison of ground-level horizontal attenuation and vertical downwelling radiance computed using SpectralCalc SpectralCalc for the U.S. Standard Atmosphere coesa1976standard. (\ref{['fig:ozone_feature_2']}) Comparison of water vapor (0.1 volume mixing ratio) and ozone ($5\times10^{-5}$ volume mixing ratio) attenuation profiles. All spectra are calculated with 40 nm Gaussian ISRF. Most of the absorption features at ground level are due to water vapor and are common to both ground-level attenuation and downwelling radiance. The absorption feature near 9.5 µm is due to ozone and is only observed in downwelling radiance. This is because ozone concentration at ground level is negligible, while the ozone layer at higher altitudes affects the downwelling radiance.
• Figure 4: Downwelling radiances at various zenith angles. (\ref{['fig:Water_ozone_correlation_1']}) Downwelling radiances calculated using SpectralCalcSpectralCalc for 10 zenith angles ranging from $0^\circ$ to $90^\circ$, bottom to top. The ozone absorption band and one water vapor absorption band are highlighted with solid red and black vertical lines respectively. The dashed curves represent the nearby transparent bands to the absorption line with the same color encoding. (\ref{['fig:Water_ozone_correlation_2']}) Correlation between ozone difference (x-axis) and water vapor difference (y-axis), where blue circles represent the 10 zenith angles in (\ref{['fig:Water_ozone_correlation_1']}). Shown water vapor features are at 8.58 µm--8.64 µm and the ozone features are at 9.49 µm--9.57 µm. The resulting correlation coefficient is $s = 0.94$, which is used to compute the estimate $\hat{b}$ of the bias $b$ by scaling the measured radiance difference at the ozone absorption band, as described in \ref{['eq:bias_estimate']}.
• Figure 5: Experimental results for bispectral ranging: (\ref{['fig:Experimental_bispectral_ozone']}) difference of measurements around ozone absorption band; (\ref{['fig:Experimental_bispectral_baseline']}) baseline bispectral method; (\ref{['fig:Experimental_bispectral_ozone_correction']}) quadspectral method; (\ref{['fig:Experimental_bispectral_lidar']}) lidar data approximately registered to hyperspectral LWIR sensor for ground truth; and (\ref{['fig:Experimental_bispectral_comparison']}) comparison of range profiles over the vertical line highlighted in red, with pixels indexed from top to bottom. Histograms of range estimates over $8 \times 8$ patches are shown in (\ref{['fig:bispectral_histogram_checkerboard_1']}) for the front checkerboard target; (\ref{['fig:bispectral_histogram_checkerboard_2']}) for the rear checkerboard target; and (\ref{['fig:bispectral_histogram_tree']}) for the tree; the corresponding locations are indicated in the lidar map. The black pixels in the depth map represent the pixels with invalid estimations or no lidar data. The baseline bispectral method is vulnerable to reflected downwelling radiation resulting in overestimations for reflective objects. Including two more absorption lines around the ozone band and following the quadspectral method gives much more reliable results.