# Compact Midwave Imaging System: Results from an Airborne Demonstration
## 2 Materials and Methods
### Stereo Technique  
The CMIS stereo-winds are based on stereo-wind methods successfully applied in several multi-angle, multi-platform cases [(4; 8)]. Templates are extracted from the CMIS nadir-looking view on a regular grid. Retrieval sites are generally oversampled with respect to the template size, so with an \(N\times M\) pixel template and 2:1 oversampling, wind retrieval sites would be arranged in a lattice sampled every (\(N/2\)) \(\times\) (\(M/2\)) pixels. Each feature template is searched for in both forward- and aft-looking views using a normalized cross-correlation (NCC) algorithm to find matches. Thus, the algorithm does not require absolute  
Figure 6: Depiction of the aircraft data collection and processing pipeline. radiometric accuracy, but only the relative intensity variations from a feature pattern. The apparent displacement of the feature, or disparity, is interpolated for sub-pixel resolution and tested for significance using the peak NCC value. The fundamental premise of this method is that a translation accurately describes the relationship between the template feature and its match in another view. This premise can be violated when the aircraft experiences turbulence or submits to frequent control inputs during powered flight. To mitigate the adverse impact on feature matching, the imagery is first pre-rectified so that it is uniformly sampled on a plane that is tangent to the WGS-84 ellipsoid at the center of the collect. AT and XT coordinate axes are defined along and across the mean direction of flight. This worked well to improve matching efficiency to yield larger numbers of forward- and aft-nadir matching pairs, but only for cases and holds where the flight trajectory and aircraft attitude were relatively smooth. In other cases, the motion was not sufficiently well compensated in pre-rectification to allow gathering large sets of matches. These types of issues will largely disappear for a space flight. There are individual AT and XT components for each of the two fore-nadir and aft-nadir disparities, for a total of four scalar measurements at each retrieval site, from which to estimate a horizontal wind velocity with AT and XT components and a height above the WGS-84 ellipsoid, for a total of three states. The XT component of disparity can be considered mostly due to XT wind velocity as there are typically several tens of seconds in time between acquisitions of the same feature in the forward- or aft-views (i.e., measurement spacing). Table 4 shows the small difference in measurement spacing, defined here as the time for the aft look vector to intersect the fore look vector at a nominal cloud retrieval height (1000 m) above the ellipsoid, between an aircraft and satellite. Our calculations assumed a linear path for the aircraft and a curved path for the satellite to account for the earth's curvature. The measurement spacing at a given altitude for an aircraft depends on its ground speed, which varies based on the wind velocity at cruise altitude. For our purposes, the speed of a satellite in a circular orbit can be considered as relatively constant. The AT component of disparity can be considered mostly due to a combination of geometric parallax and AT wind velocity. It is not possible to separate the geometric height due to parallax and AT wind without either additional observations or a prior assumption about one of them. This is known as the AT ambiguity. Our retrieval algorithm implements a non-linear least-squares solution to the problem of fitting the best three states (two wind plus height) to the two disparities given the trajectory of the aircraft and the sampling times. A cost to deviate from an _a priori_ wind is added to the cost function to be minimized with weightings so that the cost is negligible to deviate XT but prohibitive to deviate AT. This effectively constrains the AT wind to equal the prior value and leaves the height free to fit the data. The result is correct only if the prior value is correct.