here is an example of how a profile picture that its privacy is set to friends only maybe and thats mean you can click it to see it up close.. all you have to do is right click and open the image in a new tab or copy the image location (it might be different for your browser, but it should be something to indicate the same thing) and you get address like that :-
**the previous link has been changed to link back to no real image**
as we can see, the first part of the link up until the square size s160x160 is for the server or the domain where facebook keep the pp.. we are really interested in the last part. in this case its ” 540357_540713522608785_490429185_n.jpg “
the next step would be going to a picture from your gallery, click it and then right-click and copy image location or open in a new tab as we did with the pp and we should have a link that looks like this :-
https://fbcdn-sphotos-a-a.akamaihd.net/hphotos-ak-frc1/68750_11151103425656347_1344072401_n.jpg
all you we need to do here is replacing the last part of the link with the last part of the previous link. make sure to notice the -ak-ash3 and the -ak-frc1 part in the link and you should replace it with the right one from the pp link so it be something like this :-
https://fbcdn-sphotos-a-a.akamaihd.net/hphotos-ak-ash3/540357_540713522608785_490429185_n.jpg
and thats it. you should have the full sized image and the full imaged if its cropped.
the solution for the cropped photos is to crop them outside facebook and then upload them directly to the profile picture section.
I have sent this issue to Facebook a while ago and said that I will talk about this publicly in one month. I think everyone should know of this issue for better privacy.