Gamma-corrected to IRE

[chris319]

I have the following code for gamma correcting a reflectance value. For example, if the reflectance is 18% (0.18) and the gamma is 0.45, this gives me a value of 40.9. The 40.9 value agrees with everything I've read.

=(1.099*0.18^0.45-0.099)*100


The question is, what is the math to convert this to IRE units? I am expecting to see a value of 43.4 according to everything I've read.

If I change the reflectance to 90% as found on a typical test chart:

=(1.099*0.9^0.45-0.099)*100

I get a value of 94.9. I believe this is correct. After conversion to IRE units it should be 100.

What is the correct way to convert these gamma-corrected numbers based on reflectance to IRE units?

Thank you.

[raffriff42]

To translate from your 0-to-100 scale to IRE (assuming 7.5 IRE setup), you would use
(100-7.5)/100 * x + 7.5

to do the reverse,
100/(100-7.5) * (x - 7.5)

[chris319]

To translate from your 0-to-100 scale to IRE (assuming 7.5 IRE setup), you would use
(100-7.5)/100 * x + 7.5

to do the reverse,
100/(100-7.5) * (x - 7.5)

If there's no setup then:

(100 - 0)/100 * ( x + 0)

or

1 * x

This puts Y' at 90 IRE for 90% reflectance. It should be 100 IRE or 235 digital.

This may help: https://docs.google.com/spreadsheets/d/1wGZd5_OEPSE08CC_RpP5X_hTxOgapWw7pihrKeFOWls/edit#gid=0

I realize the IRE value for 18% reflectance is only off by a little (43.1 vs 43.4), but it seems more like simple rounding error and makes me wonder if I'm doing the calculation correctly.

[jagabo]

7.5 IRE setup is only applicable to analog video. Digital video has IRE 0 at Y=16, IRE 100 at Y=235.

[chris319]

7.5 IRE setup is only applicable to analog video. Digital video has IRE 0 at Y=16, IRE 100 at Y=235.

I know that. 7.5 setup doesn't even enter the discussion. See my response above.

[raffriff42]

(delete)

[raffriff42]

the formulas used in that spreadsheet:

Corrected reflectance =IF(B4>=0.018,1.099*B4^B$25-0.099,B4*B$25)
or
(Reflectance>=0.018)
? 1.099 * Reflectance^Gamma - 0.099
: Reflectance * Gamma

IRE Units =((100*$C4))*(1/$C$4)
or
100 * CorrectedReflectance * 1 / (CorrectedReflectance @ 90%)

[chris319]

the formulas used in that spreadsheet:

Corrected reflectance =IF(B4>=0.018,1.099*B4^B$25-0.099,B4*B$25)
or
(Reflectance>=0.018)
? 1.099 * Reflectance^Gamma - 0.099
: Reflectance * Gamma

IRE Units =((100*$C4))*(1/$C$4)
or
100 * CorrectedReflectance * 1 / (CorrectedReflectance @ 90%)

What is your point?

[raffriff42]

Your question in post #1 was:
What is the correct way to convert these gamma-corrected numbers based on reflectance to IRE units?
I tried to answer it, based on your assumed 90% reflectance = 100 IRE.

[chris319]

Isn't that what I already have in cell D4?

https://docs.google.com/spreadsheets/d/1wGZd5_OEPSE08CC_RpP5X_hTxOgapWw7pihrKeFOWls/edit#gid=0

Does cell D12 look right? If it is right, why does every reference I've read say the value should be 43.4 IRE for an 18% gray card instead of 43.1? It seems like more than just rounding error.

[raffriff42]

OK the problem was using 90% reflectance as "white" without normalizing it so that "white" == full scale == 1.00. Make that adjustment and the result comes out as expected: 18% reflectance => 43.4 IRE.


[Attachment 45658 - Click to enlarge]

EDIT fixed an error in the spreadsheet...

[chris319]

Sure enough, that fixed it! Thank you very, very much for your help!

https://docs.google.com/spreadsheets/d/1wGZd5_OEPSE08CC_RpP5X_hTxOgapWw7pihrKeFOWls/edit#gid=0