I donβt think you can get the exact same image using the checksum that you uploaded to your servers. I would think that Facebook changes them to certain formats so that the photo is consistent throughout the site.
However, they could keep a copy of the original photo that was uploaded. But as regards accessing it through the API or in some other way, I think it is best to look at the source in accordance with the Facebook documentation on the Photo Object :
The original image of the photo - currently it can have a maximum width or height of 720 pixels, increasing to 960 pixels from March 1, 2012.
You can get it through the API:
/<photo id>/?fields=source
Sorry this is not an exact answer, but I hope this helps.
Jayncoke
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