Effects of Atmospheric Path on Airborne Multispectral Sensors

Experimental data were acquired for a study of the effects of variable atmospheric path on the spectral signals obtained by remote sensors in the optical region of the spectrum. Multichannel optical-mechanical scanners which provide calibrated apparent spectral radiance data were flown over agricultural test sites, and passes were made at several different altitudes between 2000 and 10,000 ft. The quantitative results compare favorably with qualitative theoretical predictions. Optical-mechanical scanners and aerial photographic systems are compared to show the relative importance of potentially detrimental atmospheric path effects with regard to the operation of these systems in remote sensing. Introduction Investigators in the field of remote sensing have long been concerned with the effects of altitude on the data acquired. This has been especially true since high-altitude aircraft and satellite platforms became available. Historically. the initial (and so far the greatest) emphasis has been on understanding the manner in which increasing atmospheric path lengths affect the spatial ground resolution attainable with long-focal-length highresolution camera systems. Even with the advent of optical scanning systems, the emphasis was still on resolution, because classical photointerpretat ion techniques are based on the common denominator in all such imagery, geometric shape. Concern with the effects of altitude on the apparent intensity of the radiat ion emanat ing from the target has usually been restricted to the question of whether or not enough contrast would be present to allow interpretation of geometric "clues.'" It has become increasingly apparent in recent years, however, that op t imum utilization of remote sensing systems requires use of the information contained in the intensity and spectral character of the radiation sensed. In fact, for many applications, knowledge of the spectral distribution of radiat ion intensity for the object viewed can facilitate identifications or discriminations which would be impossible to make if only the geometric shape were considered. In view of this, it has become increasingly important to understand the effects of variable atmospheric path (resulting from variation in altitude and atmospheric conditions) on spectral intensity distributions. This paper presents the results of an exploratory investigation of the effects of altitude on multispectral data. The investigation was limited to effects relating to the spectral intensity problem, as the effects of altitude on spatial resolution have been well documented elsewhere (e.g.. Middleton, 1958). Theoretical Considerations ALTITUDE EQUATION The effect of sensor altitude on the apparent radiance of a target at the ear th 's surface which fills the sensor's instantaneous field of view can be ascribed to two simultaneous processes. The matter in the atmospheric path between the target viewed and the sensor (i) at tenuates by absorpt ion or scattering the radiation emanat ing (by reflection or self emission) from the target, and (ii) scatters and emits unwanted radiation into the field of view so that it appears to come from the target. These effects can be shown in equation form as follows: if Lff is the actual radiance of the target t in a small spectral bandwidth centered at wavelength ,~, then the apparent radiance L~,h sensed vertically from altitude h is given by Lt --rP r , ± I P a.n-a,h.~a T~a.a, (1) where ~'~.h is the path transmission coefficient which indicates the degree to which the actual target radiance is attenuated, and L~.h is the extraneous radiation emitted or scattered by the atmosphere into the beam and collected by the sensor. The path transmission coefficient and path radiance are functions of A, h, and the atmospheric conditions. I t is of interest to consider the implications o f ( l ) in order to visualize, at least qualitatively, how such an altitude-radiance relationship affects the remote sensor data. In particular, it is of interest to know not only how the apparent radiance of a given target is modified, but also how the radiance difference between two (or more) targets is affected. In order to observe the effect of altitude on a given target's apparent radiance, the relation in ( I) may be differentiated relative to altitude, producing. 0() ()0() 0() g L, ' -~ L' ~-~ rh p + g L,p , (2) where the common subscript ,~ has been deleted for clarity. Now a-~hz'/ah has a negative value since the overall transmission of the path decreases as the path length increases. On the other hand, aL,~,/ah has a positive value because (except for some unusual circumstances) the amount of radiation scattered or emitted by the atmosphere into the sensor's field of view increases as the amount of matter (atmospheric path) between the sensor and target increases. Consequently, the direction of the net change with altitude of the apparent target radiance will depend on the relative magnitudes of arP/c3h and aLT,/ah and ou the magnitude of the actual target radiance. For instance, it can be seen that, if the actual target radiance L t were quite small, then the positive term ~Lv/ah (2) could well dominate, so that the apparent target radiance Lff would increase with altitude. Conversely, if the actual target radiance were quite large, then the negative term a~-n/ah could well dominate, thus producing a decrease in apparent radiance with altitude. The radiance difference between two targets, a and b, of actual radiance L, and L ~, respectively, is given by zlL" .~ = L a -L b. (3) The effect of altitude on this difference can be seen by using (1) to obtain the apparent spectral radiance difference: AL~'b=Lh"--Lh,= ('rhPLa+LhP)--('rh~Lb+L,~) or, substi tuting (3), AL~ 'b = -rhP AL a,~, (4) XThe work reported herein was supported by the National Aeronautics and Space Administration under Grant NsG 715/23-05-071. Remote Sensing of Environment 1 (1970). 203-21 5 203 Copyright © 1970 by American Elsevier Publishing Company, Inc. where it has been assumed that a and b are close enough together that changes in atmospheric path length or composition can be neglected. Equation (4) indicates that the apparent radiance difference between two targets will be affected only by atmospheric transmission changes as altitude increases and will be independent of the level of path radiance since the latter quantity is a constant addition and cancels in the differencing. As stated previously, the integrated path transmission will decrease with increasing altitude. Consequently, (4) indicates that the apparent radiance difference between two targets will also decrease with increasing altitude. ATMOSPHERIC MODELS The expected direction of the variation of apparent target radiance with altitude can be related to the manner of interaction of the radiation and the atmosphere. As stated previously, the atmosphere alters the radiation from the target by either scattering or absorption. The qualitative effects when one of these mechanisms is predominant can be predicted. SCATTERING ATMOSPHERE Suppose that the predominant manner of atmospheric interaction is scattering. The variation of apparent target radiance with altitude will depend on the magnitude of the actual target radiance relative to some average radiance of the surroundings. The surroundings include the atmosphere, clouds, the sun, and any other object from which radiation can reach the matter in the path between the target and the sensor. Three simplified conditions can hold: 1. If the actual target radiance (per unit solid angle) is less than the average radiance of the surroundings (per unit solid angle), then the apparent target radiance must increase with altitude because the radiance from the surroundings available for scattering into the beam is greater than the target radiance available for attenuation. This is the common condition for imagery at wavelengths of less than 3 v.m, where most natural targets reflect much less than 100% of the environmental radiation. This situation can also exist for thermal infrared wavelengths if the apparent temperature of the target is less than the average apparent temperature of the surroundings in the particular spectral band. 2. If the actual target radiance is greater than the average radiance of the surroundings, the apparent target radiance will necessarily decrease with increasing altitude since there is not enough extraneous radiation available for scattering into the beam to make up for the actual target radiance scattered out of the beam. Such a situation usually exists only when the target is actively emitting radiation. For thermal wavelengths this situation is common, requiring only that the target have a higher apparent temperature than the average of the surroundings. For wavelengths at which solar radiation dominates (< 3 ~m), such a situation usually obtains only when a target actively emits light under low solar illumination conditions (e.g., city lights at night), or possibly when direct solar radiation is specularly reflected by a high-reflectance target. 3. If the actual target radiance is equal to the average radiance of the surroundings, the situation is equivalent to the target being part of an integrating sphere, or "holraum." No variation in apparent radiance with altitude is to be expected since the actual target radiance attenuated by scattering is made up for exactly by the extraneous radiance scattered into the beam. Remote Sensing of Environment I (1970), 203-21 5 ABSORBING ATMOSPHERE For an atmosphere which interacts with the target radiation only by absorption, the variation of apparent target radiance with altitude becomes much more straightforward than for the scattering atmosphere. For radiation at wavelengths less than about 3 ~m the only effect of the path is to attenuate and thus decrease the apparent target radiance with altitude since, for realistic atmospheric temperatures, the self-emission of the path at wavelengths below 3 ~m is negligible. The relationship between the target radiance and the average radiance of the surroundings is of no consequence in this case. For infrared wavelengths greater than 3 ~m, however, the atmospheric path can emit significant radiation, and in fact there is an equivalence between the absorptance and emittance of a given path. As a consequence, the relative effect of the path depends only on the relative temperature of the path and of the target. Assuming, for simplicity, a blackbody target and uniform path temperature, if L n n ( T ~) is the actual radiance of a blackbody at temperature T ~, then Eq. (1), defining apparent radiance, can be rewritten L , t = r h v L t + L h p = ( I ah v) L nn ( T t) + c d ' L nn ( T v) = L ' n ( T O + ~ h P E L t ' ~ ( T p ) L m t ( T t ) ] (5) since, from Kirchhoff's law, ~ v = ~ , . Thus the apparent target radiance will be greater than, equal to, or less than the actual target radiance, depending on whether the atmospheric path temperature T, is greater than, equal to, or less than the target temperature T t. The degree of absorption affects only the magnitude and not the direction of this change. REAL ATMOSPHERE A real atmosphere will affect target radiation by simultaneous scattering and absorption. A comparison of the qualitative aspects of each indicates that, depending on conditions, scattering and absorption can either reinforce or counteract each other in altering the apparent target radiance. It is possible, however, to make some general statements about the relative importance of the two. In the near-ultraviolet and blue portions of the spectrum, for instance, it is observed that scattering is usually predominant. This is due to the high degree of molecular (Rayleigh) scattering, which varies inversely as the fourth power of the wavelength. Conversely, at infrared wavelengths, absorption is often predominant because of the presence of numerous water vapor and carbon dioxide absorption bands. At intermediate wavelengths the relative importance of scattering and absorption can be expected to be dependent on the specific atmospheric conditions. Experimental Results The data chosen for analysis were acquired during the summer of 1966 at the Agronomy Farm of Purdue University near Lafayette, Indiana. On 26 July 1966, multichannel imagery was acquired in consecutive passes at altitudes of 6000, 4000, and 2000 ft. On 15 September 1966, multichannel imagery was acquired at five altitudes ranging from 10,000 to 2000 ft. In both cases the altitudes were flown in descending order to minimize the time lapse between the first and last passes. The data analyzed were acquired by a 12-channel scanner which senses in 12 contiguous narrow bands over the wavelength range from 0.4 to 1.0 ~m. Table I shows the spectral range for each of the 12 channels. These data w e r e calibrated at the time of acquisition, so that subsequent processing in the laboratory produced apparent spectral radiance distributions for the targets of Robert Horvath, John G. Braithwaite. and Fabian C. Polcyn