Pushing the dynamic range envelope and E.T.T.R.
At this point I'm not going to get into a necesarily lengthy discussion as to which image is the "best" or most correct. I'll only say the discussion needs to look at how the eye and brain work when looking at an actual scene, the difference between this and the way a camera captures the scene and the difference between the way the eye/brain looks at an actual scene and they way they look at a photograph.
E.T.T.R. Jim Kasson is the guru of this technique and id anyone wants more info, search him out.
The principles of ETTR remain valid. It is worth knowing about. How useful the technique is today is another matter. Cameras and sensors have moved on. ETTR is probably more relevant to users of older model dslrs. The extended dynamic range of newer sensors has decreased the general usefulness of ETTR. Mirrorless cameras have somewhat changed things as well because you have a live histogram to work with in the viewfinder before taking the shot. If you really want to work with the ETTR approach you need an understanding of the difference between histogram readings for RAW and jpeg. Camera histograms are only giving jpeg readings.
Here's a recent article on ETTR, the gains it can give and whether or not it is worthwhile.
photographylife.com/exposing-to-the-right-explained
and here are a couple of discussions including one from Jim K's site
www.kasson.com/bleeding_edge/?s=ettr
www.dpreview.com/forums/thread/4700397?page=2#forum-post-66889036
As the subject here is about pushing the dynamic range in general, it should be pointed out that there are other approaches as well. Sony and Nikon (and maybe others) have an optional mode that was originally used under licence from a British company (Irix, I think it was). In Sony it is called Dynamic Range Optimizer. It can extend DRO with one exposure but has plusses and minuses. Some early reviews claimed it simply mapped the image and boosted the shadows. It does more than this as it adjusts the exposure for the highlights as well. If you have it on your camera, for a lot of shooting it covers the bases.
Sony and Nikon cameras have Dynamic Range Optimizer (Nikon uses another name) built in which can be another and faster way into similar results.
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