1. Module 2 : Linearity AGENDA TVI Vision, Kari Siren Linearity in general Theory, what does non-linearity mean when measuring “true” colour How to measure, compute and characterize linearity error Demanding case: Linearity in colour grading

2. TVI Vision TVI Vision cameras 3 CCD line scan cameras, colour separation by beam splitter 3 x 1024, 3 x 2048 or 3 x 4096 pixels speed 5 kiloLines/sec to 35 kiloLines/sec Up to 12 bit output per channel

3. Linearity Relative out put of ideal camera and camera with Peak Linearity Error 3.5% Output [DN] increases directly proportional to increase of light (photons) without depending the light level. Non-linearity is in fact small variation of overall system gain K [DN/e -1 ] Some times it is necessary to operate with offset to avoid clipping the signal against zero, just take care in calculation….

4. Theory of measuring colour Colour is independent of brightness Colour is proportion of R to G to B Brightness level should not effect the colour Why not measure always in same brightness level?  illumination may vary, lamps getting old  target may vary  shadows  dirty factory without people 24/7 you need margin  with the same line you have to measure bright and dark targets 1% error in linearity is some how visible

5. Theory of measuring colour X axes is the brightness Y presents out put of 8 bit camera with 3.5% Peak Linearity Error, same linearity error on each channel Color is proportion of R to G to B Right values are R=246 G=143 and B=90 when full brightness

6. Theory of measuring colour Proportion of R to G vary from 1.8 to 1.3 Proportion of R to B vary from 3.0 to 1.8 Worst effect at level 25% of brightness In this example linearity error start from zero in darkness, many case there is a drastic change near darkness

7. Theory of measuring colour To visualize the color error Measured R, G an B values are multiplied with inverse of brightness level Left you see color in darkness and right in brightness And with double linearity error it looks like that…..

8. The standard How to measure, compute and characterize linearity error

9. The standard

10. “The linearity error of the illumination setup must be at least a factor of 2 smaller than the linearity error that shall be characterized by this set up.” To characterize 12 bit camera linearity you must be able to know intensity level with accuracy 13 bit - this is not easy

11. Demanding case: Grading mink fur color 3 x 12 bit camera “white” fur, levels about 3900 DN “black” fur level can be about 15-25 DN over offset black/dark brown fur are divided in 16 different groups difference between groups can be 2-3 DN difference between groups 0.5 ‰, not %