Hi Bill,
This commutative relation between Linear scaling and Gamma is a very interesting aspect as I find. Thanks for the testing. As we know, it can be disturbed – measurably and visibly: a.) by a non-regular gamma such as with sRGB, and b.) application of an S-curve in-between, such as used to render from 'native' Raw to a pleasing tonality.
Both limitations a.) and b.) can be seen as given with an already processed image file. For ex-post correction of white balance, it is certainly not wrong to change to a linear space. Anyway, it can easily be that any one-point procedure via linear scaling of the highlights is not enough.
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Peter,
To evaluate the extent of the effect of tone curves beyond a straight gamma 2.2 encoding, I looked at some old work I did with Stouffer stepwedges and Imatest with the Nikon D200. The linear raw file as converted by DCRaw is shown; it is linear except for the shadows where I think there is some flare light.
The Nikon Capture defaults are those with normal contrast set in the camera and are very similar to in camera JPEGs. The ACR with default settings applies an S-curve and rolls off the shadows rather markedly, somewhat greater than Nikon Capture. The default ACR curve with black set to 0 shows the S curve to better advantage. ACR with linear settings (brightness = 0, contrast = 0, black = 0, tone curve = linear) is also shown. It is linear, but the gamma is about 1/2.01.
The conversions were sRGB in Photoshop except for the Nikon Capture conversion. I don't know if these programs use a linear curve for the shadows or not. I remember vaguely that Photoshop may use a simplified curve without a linear segment.
For white balancing, it might be possible to apply a curve to undo the above renderings, but obviously clipped data can not be restored. Otherwise, the white balance would not be optimal--I would image that it would vary between shadows and highlights. Overall, Guillermo's method shows a marked improvement, but he now recognizes that it is not essential to convert to a gamma 1.0 rendering.
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Bill