I'd suggest FTK Imager Lite. It's a free tool (but unfortunately not open source) and it's widely used in the computer forensic community for disk imaging. It doesn't require installation.
FTK should be able to make a bit-level copy of the physical disk or specific partitions with no problems. There's a raw (DD) option, but if you use one of the other available (such as E01) you also have compression options, which might save you space on your destination disk (unless your source disk is filled with high entropy content).
There's also FTK Imager, which requires installation but has similar imaging capabilities to the portable version described above. [There's also a command line version, but I think you'd find the GUI easier if you're not familiar with the process.]
Good luck!