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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. According to (http://www.scientificamerican.com/article/papers-natural-fingerprin/)

    "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)

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You are asking three questions, but they are closely related.

  1. The smoothness is defined as the scale on which the surface features change - both "how far do you have to move left or right for the height to change", and "how much does the height change". This can be computed with the autocorrelation of the height: if height changes quickly, the height between two points that are some distance apart will have little correlation, while a smooth (slowly varying) surface will show a lot of correlation. This relates directly to the answer to your second question:
  2. When you measure the same piece of paper in the same place, you will see the same "signature". But if you measure in a slightly different place, the signature will change. How far you have to move before it becomes significantly different is a function of the smoothness - since really you are probing the cross correlation between two surface roughness functions, and if it is in fact the same surface, then if the two surfaces are aligned to the same point they will give you the same signature and a very good correlation (the intensity from the speckle image will follow the same pattern).
  3. The Seem et al paper you cite normalizes the intensity data. This is necessary because you remove variability due to the illumination source etc. This operation will basically allow you to classify each point on the surface as either "above average", "average" or "below average". Since "below average" might still have a significant intensity associated with it, if you just did the correlation of the intensities (without normalizing) your entire correlation plot would have a huge offset. The problem with that is that variation in reflectivity caused by something other than microscopic features might start to affect your results. By scaling the data first, you can find "bright spot/dark spot" classifications and remove all lower frequency effects (including DC offsets) in the signal that would make processing difficult.

I tried to keep this at the level of a non technical description - but if this is not clear, please ask questions.

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