# Can you use Fourier transformations (or other) to read multiple superimposed barcodes?

If you printed bar codes on tracing paper/acetate etc. and then positioned several in front of one another, could you extract the individual codes from the aggregate overlaid image? I feel intuitively like there would be a limit on this, as given enough bar codes, the aggregate image would be plain black. It would be good to understand if this is possible in any circumstances and if so, what are the mathematical limits.

It looks as though I wouldn't be able to tell the difference between black on white and white on black. However, if all the items are at slightly different positions, unlike the picture, i.e. different x,y positions and different angles, then can I distinguish each one, from a single "Scan"?

Thanks.

• My guess is that this can't be done, because superimposed codes are not orthogonal. As far as I know, bar codes were not designed to have this property. – MBaz Nov 29 '15 at 18:35
• This would only work if you separate the codes quite well in frequency or angle. – Jazzmaniac Nov 29 '15 at 18:48
• @Jazzmaniac If they were separated by differing angles, mathematically, how would I filter out individual codes? – George Edwards Nov 29 '15 at 22:51
• @GeorgeEdwards, if you have angular separation, the Radon transform will give you the different bar codes. – Jazzmaniac Nov 30 '15 at 12:09