ADDENDUM: TECHNICAL UNDERPINNINGS

This addendum provides some technical underpinnings for the notion of ETTR. Since exposure is obviously central to this concept, it is important that it be specifically defined. I use the term exposure here as defined in Exposure vs. Brightening to mean the amount of light falling per unit area on a sensor: it is determined by the scene luminance, the f-ratio, and the shutter speed. This definition does not include ISO. Whether you agree with this usage or not is unimportant; it is important, however, to accept it momentarily for a proper understanding of this material. I also hope and trust that by the end you will realize, if you don't already, why it is indeed important to distinguish between exposure (light) and brightening (including ISO).

I begin with some background about the concept of signal-to-noise, which is the underlying motive for ETTR. I then examine how maximal signal-to-noise is achieved when shooting, aided by distinguishing between sensor saturation and maximal raw-data values. Simplifications will be made and liberties taken when it is possible to ignore details, subtleties, and nuances that merely cloud basic understanding.

Light, Signal, Shot Noise, and Signal-to-Noise (s/n)

The original information from which a photograph is made comes from the light from the scene that is conveyed to and recorded on the camera's sensor. The light coming from each point in the scene, even when it appears as a steady illumination, is really varying. The variations are imperceptibly fast, but they are there. This is because a ray of light as it impinges on the sensor is effectively arriving as a series of independent packets of energy called photons, and the density of photons over time, even from a seemingly steady light source, is not a steady stream but rather haphazard bursts of rapidly varying numbers and timings.

These variations are called shot noise, and the greater the amount of light, the greater this noise. But – and this is the important fact – while the noise increases as the amount of light increases, it does so less than proportionately. The noise varies as the square root of the amount of light. Thus, if the amount of light increases four-fold, the noise that attends it increases only two-fold. If the light increases 9-fold, the noise increases only 3-fold, etc.

The amount of light is commonly referred to as signal and its variations as noise. Using this terminology, we see that the signal increases faster than its accompanying noise, and hence, as the amount of light increases, the ratio of signal-to-noise gets larger, which is good for photography: the more light we can capture, the greater will be the desirable signal relative to its noise, and, hence, the better the quality of the capture.*

When you press the shutter button, light from the scene is allowed to enter the camera and strike the sensor. The density (per unit area) of this light striking the sensor is determined by the f-ratio and the shutter speed. The signal and the accompanying (shot) noise that characterize this light are inherent in the light itself – they arrive together as a unit – and have nothing to do with the camera or the electronics or software that subsequently transform the fundamental exposure information into the raw-data file from which images will ultimately be made, either in-camera or in a raw processor. Thus, to obtain an exposure that maximizes the s/n of the capture, we must let the greatest allowable amount of light strike the sensor; that is, if shooting conditions allow it, we must expose so that the sensor is driven just up to its saturation point, and this is the goal of ETTR.

The light conveyed to the sensor (photons) and recorded on the sensor (electrical charges) are not the same. Only a fraction of the photons striking the sensor are actually converted to electrons and recorded as charges. This fraction, which varies among different camera types, is called the sensor's quantum efficiency (QE). Most modern dSLRs and mirrorless cameras have QEs in the range of 30-60%. The numbers of and variations in the electrons creating the recorded electrical charges effectively follow those of the incident photons in the proportion of the QE, so the signal-to-noise of the recorded charges essentially mirrors that of the incoming light. ETTR, then, exposes to maximize this recorded s/n.

Sensor Saturation vs. Maximal Raw-Data Values (DNs or ADUs)

ETTR attempts to use the information from the camera's exposure indicators (histograms and/or blinkies) to set an exposure that just saturates the sensor, thereby maximizing s/n and supporting the best potential IQ. Ideally we would like to use raw-data histograms for this purpose but, unfortunately, the camera's histograms and blinkies are based on JPEGs formed from the raw data and not the raw data themselves. In what follows, then, I assume one has established camera settings (see Best Camera Settings for ETTR on page 1) that allow the camera's histograms and/or blinkies to be effective indicators of when the underlying raw data have reached their maximal values. It now becomes important to distinguish between sensor saturation and maximal raw-data values and understand the relation between them.

The sensor saturates when it has received and converted enough photons to allow its pixels (or some of them) to reach their full capacity. They can take no more. The raw data, which are measured in DNs (Digital Numbers) or, equivalently, ADUs (Analog Digital Units), reach their maximal value when their ADU bit-depth has been filled. They can go no higher.

As an example, let us suppose a camera like the D2X with a sensor whose pixels can "hold" a charge up to 20141 electrons – and no more. The sensor's saturation point, then, is 20141 electrons, and this represents its greatest possible response to light. Further suppose that the camera has a bit-depth of 12 and, as a result, has a maximal ADU value of 2^12 = 4096. At the camera's base ISO, say 100, a saturated pixel with 20141 electrons gets transformed by the camera's electronics and software into the maximal raw ADU value of 4096. This is the only ISO for which sensor saturation is translated into a maximal raw-data value.** As the camera's ISO is increased above the base level, the sensor's pixels need to acquire fewer electrons (receive less light) to result in the maximal ADU value of 4096. At ISO 200, for example, the D2X requires only 11182 electrons to produce a maximal ADU of 4096, and the higher the ISO, the fewer the electrons that are needed to produce this maximal raw ADU. At any ISO above the base ISO, then, the raw data will max out before the sensor is fully saturated, that is, before the sensor receives the greatest amount of light it can accommodate, and, therefore, before you have achieved ETTR. If, then, we want the maximal raw-data values to indicate sensor saturation and ETTR, we must shoot at base ISO. This is a fundamental concept in understanding ETTR.

The preceding deals with maximal raw-data values, which we cannot observe in-camera. Rather, as noted above, we attempt to find camera settings that allow the camera's histogram and/or blinkies to tell us a reasonably accurate story about the underlying raw data and their reaching their maximal value – and I assume this is the case. What we have learned from the preceding paragraph, then, is that, if we want the emerging blinkies or a full histogram to indicate a full sensor, we must shoot at base ISO. ETTR is not just about filling the histogram all the way to the right, it is doing so under conditions that allow that full histogram or emerging blilnkies also to indicate a sensor that is just saturated. And that means we want the blinkies to emerge or the histogram to be all the way to the right at base ISO. At any higher ISO, the blinkies would emerge and the histogram would reach its right-hand edge before the sensor is saturated – before ETTR is achieved.

By way of a quick summary: if we wish ETTR to mean exposing to get the best possible signal-to-noise, and thus the best potential IQ, then it must mean exposing to fill the sensor just to saturation, and that means having saturation correctly assessed either by the onset of blinkies or by a histogram that just touches its right-hand edge, and that means doing all this at base ISO. ETTR works, then, because, when done correctly, it results in a capture with maximized signal-to-noise.

An Historical Wrap-Up

Those who have done some previous reading on ETTR may find the preceding story to be missing some principal ingredients and some main characters. The history of the technical underpinnings for ETTR is of interest in part because some of the initial justifications for ETTR, some that remain current today, involve notions that have subsequently been found to be misconceived. A beautifully detailed technical treatment of the these issues, along with full demonstrations, can be found in a remarkable document by Emil J. Martinec. While this not a completely easy read, its thrust is reasonably accessible, even by those without strong technical backgrounds, and it is one of the very best expositions of the issues surrounding ETTR available.

The initial justification for ETTR was based on the idea that the sensor responds linearly to light and the raw data reflect this linearity. With linear data, each EV of exposure takes up half the loaf. So the brightest EV of data occupies the top half of all raw data values (ADUs), the next brightest EV grabs the top half of what's left, etc. Under-exposing by 1 EV, then, means that half of the possible raw-data values, and what would appear to be their potential detail and gradations, are going to waste. It was to prevent this seemingly undesirable situation that proponents of ETTR suggested adjusting camera settings to fill the top values by pushing the histogram fully to the right.

Further, some (but not all) interpretations of this justification seem to suggest that anything that pushes the data upwards into those top values would work to achieve ETTR. Thus, one could increase the actual exposure by increasing the scene luminance (if possible), or by opening the aperture further (lower f-ratio, if possible), or by increasing exposure-time (longer shutter speed, if possible) – or one could perhaps (mistakenly) even bump the histogram rightwards by means that do not affect the actual exposure at all, but rather just raise the ADU numbers that characterize the exposure, namely by increasing ISO.

Well, it turns out that all of this seemingly plausible reasoning is spurious. Martinec's paper demonstrates that as long as the noise component in the raw data exceeds the increments in ADU values used to record the raw data (the so-called quantization step of the data), a condition that is always the case with raw-data values – particularly at the higher brightness levels that are dominated by shot noise and are of such importance to ETTR – a goodly proportion of those inviting values in the top half are rendered informationally superflous, so much so that there are no real detail or gradation gains to be had from their use. And, moreover, any attempt to exploit those top values simply by increasing ISO fails completely because that action merely transforms the existing exposure information and provides no new and useful information at all.

So, while the initial motivation for ETTR falls short of the mark, we have seen that there is nevertheless a fully valid justification for ETTR provided by signal-to-noise. What makes ETTR effective, then, is not added data detail and gradations, but rather the fact that the larger the actual exposure, the higher the signal-to-noise, and the higher the signal-to-noise, the better the resulting IQ (presuming, of course, the data are properly processed). And therefore the best potential IQ comes from capturing the scene on the sensor with the largest possible amount of light, the highest actual exposure the sensor can accommodate, i.e., ETTR.

At the risk of being unduly repetitive, allow me nevertheless to repeat: all this excludes any role for ISO in achieving ETTR. And we can now see why. ISO, after all, has no effect on the amount of light captured on the sensor and, hence, can play no role in maximizing this capture. ISO merely transforms the exposure information by electronic and/or computational means. It is by increasing actual exposure that one increases s/n, not by increasing ISO.

It should, however, be noted that, when shooting conditions preclude ETTR, increasing ISO can reduce read noise for some cameras in ways that can be beneficial at low-light levels. Read noise is another source of noise, completely independent from shot noise, created by the camera's electronics and software during the conversion of the sensor's electrical charges into the final raw data. I ignore read noise here because, when shooting ETTR at base ISO, its consideration is an unnecessary complication that does not substantially alter the practice of ETTR, and, at the higher lightness levels associated with ETTR, it is dominated by the shot noise. Read noise can, however, be of significance in the shadow values, and so, when ETTR is not possible, efforts to reduce it can sometimes be of value, particularly with ISO-variant cameras. See the section What if ETTR is not Possible? on page 1 of this article and Endnote 5 on page 2 of Exposure vs. Brightening for more details on this issue.

Notes

* Symbolically, if we refer to the amount of light as the signal s, then the attendant shot noise n is Sqrt(s), and hence the signal-to-noise ratio (s/n) is s/Sqrt(s) = Sqrt(s). As s increases, then, s/n = Sqrt(s) increases. The greater the amount of light, the better the signal-to-noise. All this arises because light's photons are found to follow a Poisson process, which rather generally describes the numbers and arrival times of a series of independent events in a given time interval. One of the characteristics of the distribution of a Poisson process is that its standard deviation is the square-root of its mean. So, the signal of such a process is its mean value, s, and the noise is its standard deviation, n = Sqrt(s).

** It is also worth repeating here the substance of a footnote on page 1 of the article. A stop or two of ISO may be beneficial for certain cameras, like the Canon 5D and 6D series, that have banding issues at base ISO. Clearly if a camera's IQ is problematic at base ISO, higher values may profitably be employed. Further, some cameras, like the Nikon D300 or Olympus E-M1, have extended low ISOs that are not suitable to be used as base ISO. Other cameras, such as the Nikon D810 and the Sony A7Rii, employ a sensor technology (DR-Pix) that effectively has two base ISOs. As with any shooting technique, proper ETTR requires one to know one's equipment.