Exposure to the right results in different TRC than normal exposure

Question

Exposure to the right is advocated by most experts to improve tonality and dynamic range. On the Luminous Landscape a photographer noted that ETTR all the way to the right followed by negative exposure correction in ACR produces a different image than is produced by normal exposure, and that he preferred the latter image.
Luminous Landscape Thread
Most responders to this post postulated that, since ACR is operating on linear data, underexposure by 1 EV followed by a 1 EV boost in ACR would produce the same results.
I had some exposures of a Stouffer step wedge. The first was exposed so that step 1 has a pixel value of 250 when converted with ACR at default settings into aRGB. This is exposed to the right as far as possible. A second exposure placed the same step at 221, and this step was brought back to 250 in ACR, which required an exposure compensation of +1.05 EV.
If you compare the resultant images in Photoshop using the difference blending mode, the differences too dark to make out on the screen, but can be detected with the eye dropper. In this image, normal exposure to the right is on top, and the difference between normal exposure and underexposure followed by a boost of 1 EV in ACR is shown on the bottom.
The different resulting tone response curves are better shown by Imatest plots of the two images. As is evident the TRCs are different, contrary to my expectation. Comments are invited.

Answer 1

The ETTR Myth
ETTR is short for expose to the right. Some folks have promoted it as a replacement for traditional exposure metering. The premise is that you can validate camera metering by simply reading the histogram in the cameras preview window.
Unfortunately, it is based on some basic misunderstandings about digital photographic technology. The first misunderstanding is the premise that each bit level in a digitally encoded image represents an exposure stop. The second misunderstanding is the premise that all digital cameras capture light in a perfectly linear fashion. The third misunderstanding is the premise that the histogram represents the raw image data captured by the camera. I will briefly address each of these.
Any correlation between exposure stops and digital bit levels can only be accidental at best. The total exposure range in a scene or an image is correctly known as the dynamic range. The dynamic range of digital cameras is wider than most folks assumes and usually equal to or better than film or paper. It can be defined in terms of tone density, decibels, or exposure stops. It is a function of the optics and sensor electronics in the camera. The few cases where an accurate range is provided by the vendors, it varies from 8 to 12 f/stops.
The image data is converted from analog measurements by the analog/digital (A/D) circuits early in the capture. This can wind up as an 8-bit, 12-bit, 14-bit, or even 16-bit digital value depending on the camera and its user settings. It is simply a number that has been digitized. Any correlation between bits and exposure levels is pure speculation, end of subject.
Second, the digital capture of light is not strictly linear. It is true that the silicon sensor itself will capture light in a very linear fashion. But this ignores reciprocity at the toe and heel of the extremes, the quantum efficiency of the substrate, and most importantly it ignores the optical filters in front of the sensor. If the color filter array were linear it would be impossible to reconstruct colors. And these are not the only optical filters in your camera. Then, the A/D circuits have gain controls based on the current ISO setting. And some A/D circuits perform some pre-processing based on the illuminant color temperature (white balance) and limited noise reduction based on the ISO setting. The point is that there are many steps in the pipeline that can introduce non-linearity.
Finally, the image in the preview window has been color rendered and re-sampled down to a small size. This is the data shown in the histogram. The camera can capture all colors in the spectrum, but the rendered image is limited to the gamut of an RGB color space. So, in addition to exposure clipping the histogram will include gamut clipping. This is also true for the blinking highlight and shadow tools. This might imply an exposure problem when none exists. There is no practical way to map all the data in a raw image into a histogram that you could use effectively in the preview window.
If you capture an image of a gray scale chart that fits within the dynamic range of the camera, at the right exposure, you can create a linear graph of the raw data. But if you underexpose or overexpose this same image, the graph will not be linear and it is unlikely that software will be able to restore true linearity. End of subject.
If you typically shoot JPG format, the histogram will accurately represent the image data. But clipping can still be from either gamut or exposure limits. If you typically shoot RAW format, the cameras histogram is only an approximation of what the final rendered image might look like. There is a significant amount of latitude provided by the RAW image editor. This is probably why you are shooting RAW in the first place.
So, in closing, I am not saying that histograms are bad. They are part of a wonderful toolkit of digital image processing tools. I am saying ETTR is not a replacement for exposure metering. If you understand what the tone and color range of the scene is, you can evaluate the histogram much better. And if you master traditional photographic metering, you will capture it more accurately more often.
I hope this clears up my previous statements on this subject. And I hope it explains why I think ETTR and linear capture are based more on technical theology than on technical fact.
Cheers, Rags :-)