"The proper exposure"

You've answered your own question 😀

I would describe a photo as a representation of a scene. To say a photo replicates a scene suggests a physical recreation; a process more akin to 3D printing than photography.

Interesting.

I've been using the phrase, optimal exposure, as meaning the maximum exposure within my needs for depth of field and rendering of movement that does not blow out important highlights.

Optimal, is an adjective often understood as meaning the best or most advantageous. Proper, is an adjective often understood as meaning suitable or acceptable.

Some use proper as synonymous for correct or right. In that context, if a person believes there is only one correct or right answer, proper could be viewed as synonymous with optimal. Personally, I use the term in the former context: his conduct was not perfect but it was proper.

In many people's usage - including mine - proper is not synonymous with optimal.

Truth be told, I sometimes strive to achieve a proper exposure. In other words, I'm not always seeking the best exposure. It's not always a priority to maximize exposure within my creative goals for a photo. I often seek an acceptable exposure within the constraints of my creative objectives.

The difference may be as little as 1/3 to 2/3 stop of light, but it's measurable and, in the opinion of at least some, of enough significance to merit a distinction between an optimal and proper exposure.

I would slightly modify the above-quoted definition to read: a proper exposure is one that produces acceptable noise, depth of field and motion blur without blowing out important highlights.

In other words it's an exposure that puts enough light on the sensor that noise visibility in the photo will be acceptable, that doesn't put so much light on the sensor that important highlight details are irrecoverlable, and that meets my needs for depth of field and rendering of movement.

It's subjective - perhaps, more a characterization than a definition - but I have difficulty separating the photographer's personal aesthetic and goals from the pursuit of an acceptable or optimal exposure.

If I could reference the Blackjack analogy that I used in my Lenrentals post, I don't generally try for 21 when I'm picking the exposure. 18 or 19 is fine with me.

What makes the exposure acceptable? What makes the exposure pleasing?

While the standards of one photograher are often at least a bit different from the standards of another, it's often the case that a group of people share many of the same standards in common.

This can be illustrated by a shared respect for traffic laws. I'm not talking about strict adherence to those laws but the common practice in many communities of drivers being observant enough that avoidable accidents are kept to a minimum.

In the same vein, the photographic community may not universally agree on a precise list of standards that determine a "proper exposure," but people share enough in common that a productive discussion of those qualities can be had.

No clipping in significant highlights.
Acceptable shadow noise
Acceptable DOF
Acceptable motion blur.

No clipping in significant highlights.
Pleasing shadow noise
Pleasing DOF
Pleasing motion blur.

In my opinion, DOF and motion blur are not associated with exposure, but with aperture and shutter speed respectively.

I would consider 1/100s at f/8 and 1/200s at f/5.6 as the same exposure. Presumably you would consider them to be different exposures?

Being within the latitude from the hottest possible.

True, but aperture and shutter speed both affect exposure. I consider 1/100s at f/8 and 1/200s at f/5.6 to give the same exposure assuming the same scene and lighting.

DOF and motion blur constraints are the main reasons we sometimes have difficulty getting enough light on the sensor, in situations where we don't control the lighting level.

Yep. Don't try for 21.

Yes, yet another meaning of 'exposure'!

Indeed, but today it is less commonly used by photographers than the corrupted meanings. Colloquial meanings are often not the 'proper' scientific meanings.

lets change replicate to "closest representation" of the scene. is = "proper exposure."

No such thing as "closest representation" without an acceptable metric of closeness.

when photographing museum peices, what word/words do you discribe your process/ final images ?

in the 70s Pentax used the word "exposition" because other variables (light , film speed) were used to set the cameras exposure.