# How does Laser Surface Authentication work?

As a mathematical graduate student I have some trouble to fully understand Laser Surface Authentication technology.

According to Wikipedia:

LSA analyses the naturally occurring random structure of a surface and from this, generates a signature or code unique to that surface. This code can then be used to authenticate and identify the item in the same way as a fingerprint. The technology can be used for paper, cardboard, plastics, metals and ceramics, and has found many applications across a diverse number of markets.

Some things unclear to me:

1. "The odds of two pieces of paper having indistinguishable fingerprints are less than 10-72. For smoother surfaces such as matte-finished plastic cards, the probability increases, but only to 10-20."

How do we define 'smoothness' of surfaces? How can we describe the relation between surface smoothness and and the odds of 2 surfaces having indistinguishable fingerprints?

2. On page 12 of a powerpoint (http://www.wcoomd.org/fr/events/event-history/2005/biometrics/~/media/66D04022D64F4837897113A3647DACA5.ashx) there is a graph with fraction of bits matching as a function of 'positional shift'. What is positional shift? Has this something to do with the surface smoothness?

3. In Impact of surface roughness on laser surface authentication signatures under linear and rotational displacements (http://www.ncbi.nlm.nih.gov/pubmed/19838264) the authors define fractional intensity of the ac-coupled signal (second paragraph of page 2).

"The fractional intensity of each scan is calculated by dividing the standard deviation of the intensity values by thein mean".

Why do they we need those? Can anybody explain the main points in normal understandable clear language (I have some math background)

(If anybody has better tags for this, please improve)