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I'm reading the UAVSAR data format
For definition of two types of file we have:

MLC files (.mlc): calibrated multi-looked cross products, floating point format, three files8 bytes per pixel, three files 4 bytes per pixel, little endian.

Ground projected files (.grd): calibrated complex cross products projected to the ground in simple geographic coordinates (latitude, longitude). There is a fixed number of looks for each pixel. Floating point, little endian, 8 or 4 bytes per pixel.

I know that the schematic form of SLC file is like this:
enter image description here
where I and Q are successively the real and imaginary part of the complex signal for each pixel after sampling and analog to digital conversion but if I take cross product as explained here, how can I imagine MLC or GRD format schematically?
I mean which components in the SLC file are multiplied by each other to form the cross product of each pixel?
What does cross product of the pixel mean in a physical sense?

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If we study UAVSAR data format completely, it is said that:

  • MLC data:

    The MLC is a pure binary file with no header bytes. Three of the files are complex floating point, 8 byte per pixel. These complex products are derived from the average (usually 3 pixels in range, and 12 pixels in azimuth, given precisely by " Number of Range Looks in MLC " and "Number of Azimuth Looks in MLC" in the annotation file) of the product of each SLC pixel and correspond to:

                                          ShhShv*
    
                                          ShhSvv*  
    
                                          ShvSvv*  
    

    Three of the files are real floating point, 4 bytes per pixel. These real powers are derived from the average (usually 3 pixels in range, and 12 pixels in azimuth, given precsely by " Number of Range Looks in MLC " and "Number of Azimuth Looks in MLC" in the annotation file) of the product of each SLC pixel and correspond to:

                                          ShhShh*   
    
                                          ShvShv*   
    
                                          SvvSvv*
    

and

  • GRD data:

    The grd files consists of three real floating point, 4 bytes per pixel, and three complex floating point, 8 bytes per pixel files. The number of lines and samples may be found in the annotation file and are given by grd_mag.set_rows and grd_mag.set_cols respectively. The grd files contain projected multi-looked data for crossproducts HHHH, HVHV, VVVV, HHHV, HVHV, and HVVV:

                                         ShhShv*  
    
                                         ShhSvv*  
    
                                         ShvSvv*  
    
                                         ShhShh*   
    
                                         ShvShv*  
    
                                         SvvSvv*
    

From the four SLC files that enter image description here is stored in each of them and for the monostatic backscattering case enter image description here we can form the scattering matrix as follows:
enter image description here
for each pixel. If we take the Lexicographic matrix basis set as follows:
enter image description here
We can make the 3-D Lexicographic feature vector:
enter image description here
now we can acquire the covariance matrix for each pixel from the ensemble average of the cross product of 3-D Lexicographic feature vector (hear cross product is the same as tensor product or outer product)
enter image description here
which is a hermitian matrix. So we have 6 files, 3 are complex floating point and the off-diagonal terms of the covariance matrix (without the constant coefficient) is stored in them and the other 3 are floating point and the diagonal terms of the covariance matrix is stored in them.
As said ensemble averaging is done by 3 pixels in range, and 12 pixels in azimuth

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