• Please use real names.

    Greetings to all who have registered to OPF and those guests taking a look around. Please use real names. Registrations with fictitious names will not be processed. REAL NAMES ONLY will be processed

    Firstname Lastname

    Register

    We are a courteous and supportive community. No need to hide behind an alia. If you have a genuine need for privacy/secrecy then let me know!
  • Welcome to the new site. Here's a thread about the update where you can post your feedback, ask questions or spot those nasty bugs!

A little something on "exposure"

Doug Kerr

Well-known member
Our discussions here about many important topics (like "exposing to the right") are often hampered by the fact that there are two quite different, but equally legitimate, meanings of the term "exposure". I thought I would talk a little about this and make some proposals as to how we can avoid confusion.

In my own technical articles, I often take the extreme measure of using two coined terms, "exposure1" and "exposure2", to avoid ambiguity. I'm not proposing that as our general solution, but I will use it here for a little while just so I can make clear what two things I am talking about. The brief definitions of these two terms are as follows:

Exposure1 - the measure of joint effect of exposure time (shutter speed) and relative aperture (f/number).

Exposure2 - the measure of the physical phenomenon to which film, or a digital sensor, responds, formally called "photometric exposure". It is the product of the illuminance on the medium and the time it persists (the exposure time). Note that illuminance is the amount of luminous flux (the "stuff of light") falling on each unit of the surface of the medium.

Now let me expand.

"Exposure1" (in its basic mathematical form) does not have a standard scientific symbol (nor even an unambiguous name - it is often called just "exposure").

But there is a standard symbol we can easily use to mention this quantity, and that is "Ev" (so long as we don't get sucked into the "other use of Ev" to describe scene luminance). Ev, numerically, is a logarithmic expression of exposure1. If we cut the shutter speed in half, or decrease the aperture (increase the f/number) by "one stop", Ev increases by one unit.

I suggest that when we are speaking of exposure1 in the narrative sense we just use "Ev" ("If we keep the same Ev, then we can . . .")

Note that if we allow into our writing the unfortunate convention is which Ev is also used to express scene luminance, it will mess this up. So don't do that. There is a perfectly good factor, in the same vein as Ev (logarithmic) for scene luminance: Bv. More about that in another note.

"Exposure2" (photometric exposure) today has the scientific symbol H. It formerly had the symbol E, as in the traditional description of the curve of negative film response, the "D log E" curve. But E has another use in photometric science (it represents illuminance) and so as these things got sorted out by the boffins, H was adopted for photometric exposure.

I suggest that when we are speaking of photometric exposure, we call it "photometric exposure" or (once we get rolling), just "H", as in: "Then, the brightest spot on the scene will receive, on the sensor, an H that is almost the largest H the sensor can distinguish".

I'll generally be following these practices in my correspondence in these forums.
 

KrisCarnmarker

New member
Thanks again Doug. Do you have any reference/tutorial on "photometric exposure"? I've seen it in use, and I think I understand, but I'd like to know a bit more.
 

Doug Kerr

Well-known member
Hi, Kris,

Thanks again Doug. Do you have any reference/tutorial on "photometric exposure"? I've seen it in use, and I think I understand, but I'd like to know a bit more.

I'll see what I can dig up.

In the meantime, here is a little more on the topic.

Photometric exposure (and that term isn't universally used) is more generally spoken of as the "illuminance-time product".

Illuminance is the amount of luminance flux per unit of area landing on a surface. The SI ("metric") unit is the lux, which is actually a special name for the lumen per square meter. The lumen is the unit of luminous flux. You can think of luminous flux as broadly analogous to power in an electrical setting. It is "the stuff of light".

Just as the product of power and time in an electrical setting is energy, the product of luminous flux and time is what is called "photometric energy". Photometric exposure turns out to be photometric energy per unit area. Its unit is the lux-second.

Early workers in the field of photography determined that the effect of light on a sensitized surface was approximately based on the amount of the arriving photometric exposure.

I say approximately because of the phenomenon of "reciprocity failure". this says that the impact of 10 lux of illuminance for 2 seconds would not necessarily be exactly the same as the impact of 20 lux of illuminance for 1 second (both representing the same photometric exposure, 20 lux-seconds. But, over a reasonable range of exposure times, the relationship we would expect is very nearly followed.

The two researchers Hurter and Driffield published early papers on the response of photosensitive materials. The often presented their result on a graph that plotted the density (the measure of how opaque the film, after development, became in response to the impact of light) versus the logarithm of the photometric exposure. The measure of density is already logarithmic, and the use of a logarithmic scale for photometric exposure made the relationship turn out to be nearly a straight line for many types of photographic materials over a good portion of their range.

The (logarithmic) measure of sensitivity is designated "D", and the researchers used "E" for photometric exposure. Thus the curve was (and still is) widely spoken of as the "D log E" curve.

But it is also often called the "H &D curve", referencing the researchers who first brought it to attention.

A problem with "E" for photometric exposure in the broader scientific realm is that it also was the symbol for energy, and, even worse, at a certain point, E was adopted for the quantity illuminance. (A nice mnemonic is to think of "EE-lum-i-nance.)

So a new symbol was needed for photometric exposure. Many people, hearing the response curve called the "H &D" curve, thought that the curve must plot D versus H. Not so of course, but when the boffins needed a symbol for photometric exposure to replace "E", they played a wonderful joke and called it "H". That is the scientific symbol used today.

At the focal plane (that is, on the film or digital sensor), in a part of the image that corresponds to a certain small region in the scene, the illuminance is:

-directly proportional to the luminance (brightness) of that scene region

-inversely proportional to the square of the f/number (assuming focus is at a substantial distance)

-directly proportional to the lens transmission (a factor that is 1 if the lens doesn't "absorb" any light; this isn't a big deal, but I mention it for completeness - I'll leave it out from here on)


The exposure time is, of course, just the shutter speed. Thus, for that same part of the image, the photometric exposure, H, is:

-directly proportional to the luminance (brightness) of that scene region

-inversely proportional to the square of the f/number (assuming focus is at a substantial distance)

-directly proportional to shutter speed


It is this relationship that underlies the development of "metering/exposure strategies" and "exposure equations" that pursue them.

Now, the ISO speed of the sensor (that is, the real ISO speed, determined under the ISO standard) tells us the value of H that, for the camera (operating, of course, in a particular "ISO speed mode") produces the maximum digital output (RGB255/255/255 for an object of the reference white chromaticity). This is called Hsat ("saturation H").

One metering/exposure strategy for digital cameras seeks to have the average value of H on the sensor be a certain fraction of Hsat. (How and why we might choose that is beyond the scope of this note.)

An automatic exposure system, which works from the average measured luminance of the scene, with the ISO speed of the system also provided to it, can fulfill that strategy by practicing a "metering equation" that flows from all the matters I discussed above.

Aren't you glad you asked?

Best regards,

Doug
 
Top