overlap correction on the BG signal

[HolgerPollyNet]

1. Why does the code apply overlap correction on the BG signal?
   https://github.com/PollyNET/Pollynet_Processing_Chain/blob/b4f0cb38613f1059cf0e9cb2b60211e62e59bdb4/lib/qc/pollyOLCor.m#L108C19-L108C24
   The laser does not affect the BG signal, so there is no need to apply overlap correction on the BG signal.

[HolgerPollyNet]

@ZPYin : The intention of overlap correction on the BG signal is to propagate the uncertainty of overlap correction to the background signal. The overlap correction will lead to additional error to the BG signal. In order to account for this additional error, I make BG signal at overlap correction zone larger, thinking about (BG / overlap factor). It's NOT rigorous.
But if the BG is inherited from the constant BG signal, this error message will be lost in the subsequent calculations (i.e., Klett-Fernald retrieval).

When we developed the PollyNET processing chain at the beginning, overlap correction was not one of our priorities. So we didn't consider it thoroughly.

[HolgerPollyNet]

Hey @ZPYin ,

I did not really get your comments. When you apply overlap correction to the background, the wrong error is propagated forward....and the signal in the overlap region becomes wrong. Can you explain in more detail?