1. We first correct the images under the assumption that the Landscape is uniform. We obtain a surface reflectance under uniform absorption which is noted $$\rho_{s,unif}$$.
2. We compute the neighbourhood reflectance ($$\rho_{s,adj}$$) using a convolution filter with a 2km radius, that computes the average neighborhood reflectance weighted by the distance to the target. To be fully rigorous, this filter should depend on the optical thickness and on the viewing and sun angle (The less aerosols, the larger radius), but as we did not work on an accurate model, we used a constant radius.
3. We correct for the contribution of paths 3 and 4 using :

$$\rho_{s}=\frac{\rho_{s,unif}.T^{\uparrow}.\frac{1-\rho_{s,unif}.s}{1-\rho_{s,adj}.s}-\rho_{s,adj}. T_{dif}^{\uparrow}}{T_{dir}^{\uparrow}}$$

• where $$T^{\uparrow}=T_{dif}^{\uparrow}+T_{dir}^{\uparrow}$$ is the total upward transmission, sum of diffuse and direct upward transmissions, and s is the atmosphere spheric albedo. These quantities depend on the wavelength, on the aerosol model and on the AOT. They are computed using Look up Tables based on radiative transfer calculations.

As this processing uses convolution with a large radius, it takes quite a large part of the atmospheric processing time.

##### Result Exemples

The images below show 3 stages of the atmospheric processing, for 2 Formosat-2 images obtained over Montreal (Canada) with a 2 days interval. The first image was acquired on a hazy day (aerosol optical thickness (AOT) of 0.47 according to MACCS estimate); and the second one on a clear day (AOT=0.1).

• The first line corresponds to the Top Of Atmosphere images, without atmospheric correction. The left image is obviously blurred compared to the right image.
• The second line corresponds to the atmospheric correction under uniform landscape assumption (as in step 1). The left image is still obviously blurred compared to the right image.
• the third line show the same images after adjacency effect correction. In that case, the left image is not blurred any more, it is even maybe a little over corrected as it seems somewhat sharper that the right image.

TOA Images (On the left, the hazy image)

Surface reflectance under uniform landscape assumption (on the left, the hazy image)

Surface reflectance after adjacency effect correction (on the left, the hazy image) The pixel wise comparison of reflectances is also a way to show the enhancement due to the adjacency effect correction. The plot below compares the images of both dates corrected under the uniform landscape assumption (on the left), and after adjacency effect correction (on the right). You may observe that the dots are closer the the black diagonal on the right. On the hazy image (May 27th), the high reflectances are a little too low, while the low reflectances are a little too high, which is the symptom of a loss of contrast.

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