# Correct Exposure and Gamma Correction

1. Apr 23, 2009

### daved2424

This is a problem I have been struggling with for the past couple of weeks and it is just making my head hurt now. I am no mathematician but get the basics. I wasn't sure whether to post here or the Physics forum so please forgive me if I have posted in error.

At work we have a camera http://dsclabs.com/images/CDMs/SW16(CDM12) - 6.1.jpg".

The whitest chip on the chart has a reflectance of 89.1%. The camera is exposed so that this chip meets 'peak white' so when gamma is applied no change to its value takes place. However the remaining 10 chips will change after gamma. Their original reflectances are
1: 89.2%, 2: 74.1%, 3: 58.3%, 4: 46.0%, 5: 37.0%, 6: 26.0%, 7: 18.2%, 8: 11.7%, 9: 8.0%, 10: 4.5%, 11: 2.2%. After these have been normalised to 100% and gamma has been applied they become: 1: 100%, 2: 92.0%, 3: 82.6%, 4: 74.2%, 5: 67.3%, 6: 57.4%, 7: 48.9%, 8: 40.1%, 9: 34.2%, 10: 26.1%, 11: 18.9%; which are linear.

However I want to expose the chart to simulate 60% reflectance of light and want to work out which chip is the nearest value to simulate this. Of course, I can't just look at the values above and take the third chip because this will be skewed for a gamma corrected figure assuming the chart is being used correctly.

I hope that makes sense, and I really hope someone can help me. I am pretty sure the answer is the second chip from just trial and error, but I want the maths to back it up. Many thanks for any help given in advance.

Last edited by a moderator: Apr 24, 2017