In the world of traditional silver photography, characteristic curves (also known as D-Log E or H&D curves) serve as the transform between actual scenes and the images we create of those scenes. They make it possible to meter an item in a scene and know the shade of gray it will lead to in a finished print. By using the elaborate calculations of four- quadrant tone-reproduction diagrams, that gray shade can be forecast in density units with a precision of two decimal points. Even a general knowledge of curve shapes and how they are influenced by development allows prediction of which of ten tonal ranges or Zones an object will appear in. Successful photography in no way requires an understanding of these curves, but they certainly make it easier to manage tonal relationships in moving from scene to negative to print.
Sadly these curves did not make the transition to digital. In fact the “D” of D-Log E (density) doesn’t even exist in the digital world of on-screen images. But happily there is a digital counterpart, a camera characteristic curve that provides photographers with similar information. Instead of density we have image brightness values (BV), readily measured on a scale of 0 to 255, with no need to own transmission or ref lection densitometers. And it is easy enough to relate these BVs to an exposure axis to appreciate how the camera translates between scene brightness and image brightness. Each of the many thousands of film and paper curves that have been published is unique to the product and processing it represents. Likewise, a digital camera characteristic curve is specific to a particular model of camera and the settings employed in its operation. In this article we will work through the procedures for creating and analyzing these curves for a pair of cameras. Both are basic fixed-lens units operating in JPEG mode. Our intent is not to share the characterization of these particular cameras but rather to illustrate the process that can be applied to anything from a camera phone to DSLR, from JPEG to Raw.
Building the curve
Position a neutral card in the sun or bright shade so it is evenly illuminated and free from any specular reflections. Set your digital camera to the appropriate white balance, ISO 100, ƒ/8, and get close enough to fill the frame with the card. Take a series pictures ranging from perhaps 1/2000 second to one second in one-stop increments. The goal is to assemble a series of frames like those of Figure 1, running from full black to full white.
Open one of the files in Photoshop and eyedropper its tone to establish its BV on a scale of 0 to 255. Better yet for this experiment, open the file and note the number opposite Mean in the expanded view of its histogram. This value averages all the pixels in the frame rather than a five-by-five sample like the eyedropper tool and there is no need to average RGB values if the image is not perfectly neutral. We have made note of these BV values for one of our sample cameras immediately beneath each frame in Figure 1.
Relating these values of image brightness to those of scene brightness requires a Log E scale. The simplest scale is one of Relative Log E: Arbitrarily assign a value of zero to Log E for the blackest patch in Figure 1’s upper left corner. Log E for the second patch then is 0.3 (log of 2) because the exposure increased by a factor of two (one stop) between successive patches. Similarly, the Log E of the third patch is 0.6; that of the fourth patch is 0.9, and so on. These values are plotted one against the other in Figure 2, our first version of a characteristic curve for our camera. Even this very basic curve permits us to quantify one of the camera’s most important features, the scene brightness range it is capable of displaying (also termed “dynamic range” in the digital world).
Assessing the contrast
In the interest of linking our process back to traditional photography, consider how this assessment is made in the silver world: Two tones in a finished silver print are paramount. One occurs at 0.04 above the paper’s minimum density. It is just off-white, a diffuse highlight typically regarded as a scene element of 80% reflectivity
(Reflectance, R, = 0.8). This might correspond to a white shirt in full sun. The other tone is very dark, devoid of texture and just discernibly lighter than the paper’s maximum density (Dmax). Specifically, this occurs at 90% of the paper’s Dmax. Identify the film negative densities that led to these points in the print and locate them on the film’s D-Log E curve. The horizontal separation between them defines scene brightness range: The range of exposures captured between almost black and almost white. It is generally accepted that for average scenes, photographed with a lens of low to moderate flare, this separation is always very close to 1.95 Log E units, or 6.5 stops. (1.95/0.30 = 6.5). Similarly, a “flat” scene is regarded as having about 5 stops separation and a contrasty scene 8 stops. We will use these values of 5, 6.5, and 8 stops as guideposts in evaluating digital cameras.
So how do we identify the two critical tones, almost black and almost white, in a digital image? Open a new file in Photoshop with Background Contents set to White (BV = 255). Now add a few rectangles of very slighter darker tones and judge for yourself which one you would consider appropriate to the proverbial white shirt in full sun, a diffuse highlight. The choice will depend on how your monitor is set up, but you will probably select a value somewhere in the range of 245 to 250. We will use 248 for our example. Close that file and open a new one f illed with pure black (BV = 0). Add a few rectangles of progressively lighter tones and judge what you deem to be just discernibly lighter than the pure black surround. Again the choice will depend on your monitor and its ambient lighting. We choose a value of 15 for this exercise.
In Figure 3, we have added a pair of vertical lines to our camera’s characteristic curve, one at BV = 15, the other at BV = 248. Note the Relative Log E values where these intersect the x-axis: 1.53 and 3.22 respectively. The difference between these is 1.69 Relative Log E units. One stop being 0.3 of these units, the difference can also be expressed as 1.69/0.3 = 5.6 stops. This figure represents the range of scene brightnesses that our camera will accommodate between not quite maximum black and a diffuse highlight. Contrast this with the 6.5 stops ascribed to average scenes.
Digital cameras have a reputation for being “contrasty” or “like shooting transparency film,” and this one is no exception: Unable to see more than 5.6 stops of tonal range, near white to near black, it fails to image (in useful fashion) almost a stop of the average scene’s 6.5-stop range. Since it is imperative that highlights look right (the white shirt cannot be either empty white or dirty gray), the missing stop is relegated to the shadow end of the scale. When adjusted for good highlights, the image will lack shadow detail we would have expected it to have in the silver world. It is like what would happen if film were underexposed one stop and printed on a higher paper grade to provide a full density scale.
This result, of course encouraged us to play with the camera’s adjustable contrast feature. It has 11 settings ranging from Low through Normal to High. Figure 4 adds to our normal curve the BV-Log E curves, determined in exactly the same fashion as above, for the lowest and highest of the 11 settings. Conclusion? The camera’s contrast button does indeed change contrast, but not by very much. Measuring the scene brightness range each curve traverses in going from BV 15 to 248 yields these numbers: 5.2 stops at the highest contrast setting, 5.9 stops at the lowest, (and 5.6 at “normal”). Contrast this with our expectations of 5, 8, and 6.5 respectively. (It is a mystery why the manufacturer included nine additional settings between these lowest and highest values.)
Before leaving Figure 4, it is instructive to consider the tactics this camera manufacturer employed to achieve even this limited contrast range. Note the three curves all pivot around a point at the shadow end of the scale, with a BV of about 15. They are effectively matched for shadow speed. When we changed the contrast setting from low to high, the appearance of the shadows changed little. But at the same time, the middle grays and especially the highlights became appreciably brighter. As noted earlier, the highlights have to look right, with diffuse highlights being rendered just off- white, and this means that if the camera’s contrast setting is changed, the exposure settings need to be changed also to preserve proper highlight tonality. It would have been helpful if the three curves pivoted around a BV of 248 instead. In the world of film, the adage was: expose for the shadows and print for the highlights. On the digital side, the adage is: expose for the highlights and let the shadows go where they will, employing contrast controls to adjust their position— but only slightly with this camera.
A second camera
Figure 5 examines a similar set of three contrast curves for a second digital camera. We do this for two reasons. The first is to illustrate that different manufacturers approach this issue differently.
The second reason is to persuade the reader that constructing such curves for one’s cameras is worthwhile for understanding how they work and how best to use them.
This manufacturer chose to have the contrast curves pivot around middle gray rather than a shadow point, but they are virtually matched in the highlights as well, meaning there is no need to adjust exposure when changing contrast settings with this camera. Going through the exercise of determining scene brightness range for these curves leads to values of: 5.2 stops (Low), 7.8 stops (High), and 6.6 stops (Normal). These are much closer than the first camera to the traditional values of 5, 8, and 6.5 stops. There is a huge compromise however. The only signif icant differences among the three curves are in the region between shadows and middle gray. Changing the camera’s contrast setting does not alter the appearance of lighter grays and highlights. Only the shadows compress or expand. With the f irst camera all the tones except the very darkest moved as contrast was altered. Technically (numerically), this second camera sports a more decent contrast range, but functionally, only the dark tones of an image are affected by contrast adjustments.
The approach to adjusting contrast with the two cameras is different, one requiring exposure adjustments, the other not. And the pictorial consequences are different, one camera providing tonal variations primarily in lighter tones, the other exclusively in darker tones. Actually though, the two cameras have a remarkable amount in common. Figure 6 plots the curves for both cameras, both set to normal contrast, on the same graph. We can do this because the two sets of measurements were made in the same light, same aperture, same ISO, same series of shutter speeds. Above a BV of about 80—a moderately dark tone—the curves superimpose: The cameras deliver images that are indistinguishable throughout a range from darker middle grays to the brightest highlights. They do treat shadows differently and we have pondered whether this is due to: (1) manufacturer’s design, (2) more flare with the second camera (it has a much longer zoom with more glass), (3) some form of digital reciprocity effect related to the long exposure times at this end of the scale, or (4) some combination of these.
In any event, the identical fashion in which they treat so much of the tonal range is striking.
Improving the curves
Lastly, we want to make an important improvement to our digital characteristic curves. The axis we have to this point called “Relative Log E” is a construct based on our arbitrary choice of 0 to represent the blackest patch of Figure 1. The graphs would be more meaningful if we could replace that axis with one that was actually related to the original scenes. We can do this by replacing relative values of Log E with absolute values of Log R, where R represents the reflectance of scene elements. All the new Log R values will be offset from the old Relative Log E values by a constant amount. So what is the constant? Consider again the diffuse highlight.
We earlier noted that diffuse highlights typically reflect 80% of the available light. This corresponds to R = 0.80, or Log R = –0.10. We also specified that such a highlight should image with a BV of 248, meaning that in our new curve we want BV = 248 to occur at Log R = –0.10. Currently, in Figure 6, this BV occurs at a Relative Log E of 3.22. Subtract 3.32 from 3.22 and the result is -0.10, the correct Log R value. So we will subtract the constant 3.32 from all the relative values of Figure 6 and relabel the entire axis Log R.
We have done this in Figure 7, which repeats the previous graph but with a much more meaningful x-axis. This chart quantifies the relation between how bright something appears (its reflectivity) in a scene and how bright it appears (its BV) on screen if properly exposed and displayed (i.e., the highlights look right).
As an example of how this improved camera characteristic curve can be used, consider a column we published in PT May/June 2008. Our goal was to understand how the average reflectance of real scenes compared to that of an 18% gray card. Such a card has an R value of 0.18. The log of 0.18 is –0.74, and inspection of Figure 7 shows this to correlate with a BV of 142. A world that is, on average, 18% reflective would give rise to digital images that have an average BV of 142. (Keep in mind this number represents with certainty only the specific cameras we are discussing here.) We mentioned earlier that Photoshop’s Expanded Histogram reports the average BV for an image, so we tabulated it for each of 150 outdoor scenes, and averaged the averages to arrive at a Grand Average BV of all the pixels in all the images—which turned out not to be 142. It was only 114. Referring again to Figure 7, it is apparent that BV 114 lines up with Log R = –0.89, meaning R = 10^(–.89) = 0.13: The world as captured in these 150 images is only 13% reflective, not 18%. (The difference, 13% versus 18%, and its implications and significance to gray-card design, is discussed in more depth in that previous column.)
So is the construction of digital characteristic curves a worthwhile exercise? We think it is. We come away from it with a better understanding of two cameras’ intrinsic differences, and an intuitive appreciation for pictorial circumstances wherein one or the other would have an advantage. It is the same kind of awareness we had in the pre-digital era when we would select one film or paper over another based on how their curves would direct print tonalities. Your camera will be different than the ones we used here: DSLRs with their larger pixels have an intrinsic advantage in the scene brightness range (dynamic range) they can image correctly. Camera firmware overlays unique tonal curves on JPEG images that restrict their brightness range compared to what the same camera can record as a Raw file. Different lenses of differing flare characteristics give rise to different curves. We have learned from other curve constructs that the ISO settings of one of these cameras is not as consistently spaced as its menu indicates. All in all, the time investment in creating a characteristic curve for a camera is small compared to the understanding to be gained from it. And the perspective of scene-to-image tone translation such a curve provides brings us back to the comfort range we have long enjoyed with the D-Log E curves of traditional photography.