Problem with matlab fit

While this might not solely be a matlab problem, I guess I could still ask it here:

I measured a grayscale chart with spectrophotometer and with a scanner. I have two data sets (already in Matlab). One of the data sets is the Y value of the scanner (combination of R, G and B) and the Y value the spectrophotometer gives. I want to make an OECF curve so I use the fitting tool:

this looks allright. Now my supervisor told me that I can show the Density on the X-axis instead of the reflectance. but still use the same fit!!

Density = -log10(reflectance/100).

That will look like this:

How can the same fit as used in the first picture still work for the graph with the Density instead othe reflectance, the graphs form is completely different! Matlab also gives a completely different fit.

The fit:

19.9+10.28*X^0686

should work for both graphs (according to my supervisor), by changing something with the X in the formula. This is for a program that I'm writing that analyses test charts for scanners.

Kind regards,

Thomas Koelen

Answer 1

[Torsten]

Density = -log10(reflectance/100), thus

Reflectance = 100*10^(-Density).

Inserting into your fit equation gives

Scanner Luminance = 19.9+10.28*(100*10^(-Density))^0.686

Scanner Luminance = 19.9+242.1*10^(-0.686*Density)

Thus the fit can used for both graphical representations.

Best wishes

Torsten.

[Thomas Koelen]

Thanks Torsten!

Great help as always.