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If I open a raw file in ACR or Lightroom and move the exposure slider, why does the shape of the histogram change?

If all I'm doing is changing the exposure, I would expect the shape itself to remain the same whilst moving right or left depending on whether I was increasing or decreasing the exposure respectively (other than becoming clipped at the edges.

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Proper exposure would be simply a multiplication in linear space, so the shape would have to change as values get redistributed. What you are thinking of would happen if they did an addition to all the pixels. That would also change the exposure but would not correspond in any way closely to what happens in case you had changed the exposure in-camera.

In practice, Lightroom seems to have its own secret recipe for changing exposures and other params. It probably performs multiplication on the luminance channel of mid-tone values while compressing shadow areas and highlights to maintain a smooth distribution of tonalities. There are plenty of mysterious things that happen when looking at the Lightroom histogram and some of them still puzzle me too!

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Someone at Adobe says:

It is the same as photographic exposure, but like Lee Jay says, in Lr 4 Beta with PV 2012 the response is more similar to film.
Photographic exposure simply means that an increase in 1 stop means doubling the amount of light (photons) and decrease in 1 stop means halving the amount of light. This is still very much the case. The only exception to that is how highlights are handled. In digital, if you clip the highlights, they're gone. In other words, they hard-clip: there's no highlight shoulder, just a (approximately) linear increase in light till you hit the saturation point of the sensor. With film, the highlights roll off much more smoothly -- so, as you increase the exposure time, your highlights will get brighter, but gradually. Photographers still call this exposure (and have done so for many years, long before digital exposure), even though the response is different than digital. Exposure in PV 2012 is more similar to the latter case. (Photographers who deliberately want clipped highlights for a edgier, harsher "look" can use the Whites slider, or the Point Curve.)

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