# Density

In traditional film processing and printing, the concept of density is central to the objective measurement of the relationship between exposure and negative, and between negative and print. The science of this relationship is called sensitometry. “The Zone System is a practical expression of sensitometry”, wrote Ansel Adams in The Negative (p.84).

If density is important to the traditional Zone System, we should first understand what density is, and then consider whether or not we should continue with this concept or introduce an alternative. As I have mentioned earlier in this set of pages on the Zone System, when light strikes a surface like that of a print or negative, the light may be reflected back, transmitted through, or absorbed. The total of the reflected, transmitted, and absorbed light energy must equal what strikes the surface. In the case of a print, the maximum amount of light that can be reflected is a property of the paper. The more ink (or silver, traditionally) that is laid down on the paper, the greater its density, the more light is absorbed, the less light is reflected. In the case of a negative, the maximum amount of light that can be transmitted is a property of the film base. The more silver that is deposited on the film base, the greater its density, the more light is absorbed, the less light is transmitted.

So, we have this relationship between the density of material (ink, silver, etc) on the print or the negative, and the reflection or transmission of light. We begin with an exposure of the negative, that maps Value V in terms of the light power from an 18% diffuse surface, to a density on the developed negative. This exposure involves the intensity of the light for a duration of time, in other words, an energy (energy = power x time). We map the light energy of the exposure to some density on the developed negative. Similarly, in the making of the traditional print, we pass light of a fixed intensity through the negative onto the print paper. Again, the intensity of light that passes through the negative and strikes the print surface for the duration of the exposure produces the final density of silver on the paper. Once more, the physics of the process is a relationship between the energy of light delivered to the print surface and the final density.

If you follow the entire chain through the traditional process, we have the energy of the exposure produce a density on the negative, then the density of the negative induces a certain amount of energy onto the print that yields a final density. Finally, when we view the print, the density of the print allows for a certain amount of energy to fall on our retinas. The chain goes Energy -> Density -> Energy -> Density -> Energy as we move from Scene -> Negative Creation -> Negative -> Print Creation -> Print -> Print Viewing.

What is this thing called density? Mathematically, density is a function of either the transmission of light, in the case of the negative, or the reflection of light, in the case of the print. If transmission is $T$ or if reflection is $R$, expressed as a ratio to the incident light, then density, $D$ is $D = -log_{10}(T)$

for a negative, or, in the case of the print $D = -log_{10}(R)$

We have encountered this idea of diffuse reflection from a surface before though: it is identical to $Y/Y_n$. Hence, this is all equivalent to $D = -log_{10}(Y/Y_n)$

Expressing this the other way around, $Y/Y_n = 10^{-D}$

Previously, I showed the equations that relate human visual perception to diffuse reflection through L*. These relationships for diffuse reflection; that is, $Y/Y_n$ and density, $D$, now allow us to tie L-Values and D-Values together. For example, if Value V in a print is $Y/Y_n = 0.184$, then the corresponding density is $D = 0.745$ and we hardly have to think about it to remember that this is $L=50$.

Modern inkjet printers can achieve maximum densities, $D_{max}$ values of around 2.2 to 2.4. A little figuring tells us that this corresponds to $Y/Y_n$ values of 0.0063 or 0.0040, respectively. Below is the mathematical relation between L-Value and density:

You can see that the relationship is not quite linear. It is also a strictly theoretical relationship. Let me be clear on this point. This curve does not imply, for example, that if I created an LAB image file in Photoshop with squares filled with particular L-Values, and I then printed that file, that the ink densities on the paper could be read off this curve. That might be a highly desirable situation; but it would depend on the printer, the paper, the ICC profile, and so on. But it does mean that I can just as easily think about the density of a pixel in an image file as easily as I can think about its L-Value or its neutral RGB-Value.

In a previous page in this topic on a modern Zone System, I gave a graph showing the relationship between Zone Exposures for my D700 and L-Values. Here is that same relationship expressed in terms of densities:

This is a very film-like curve. The most significant differences are in terms of the maximum and minimum densities, which are much broader than what could be delivered in a traditional negative. (I suppose another difference between this and any characteristic curve for a negative is that it is reversed; that is, density goes down as exposure goes up here. If I’d flipped the images in the sequence over with a Cmd-I in Photoshop, the mapping to densities from Zones would have been like a negative’s characteristic curve, aka its HD curve.) A film negative’s curve goes the other way around. The span of $D_{max}$ to $D_{min}$ is a measure of the contrast of the process. In traditional film, “normal” development might achieve a negative with a $D_{max}$ of around 1.8 or so and a $D_{min}$ could be about 0.05 for a net contrast of 1.75. The D700 is showing a contrast of nearly 3, much superior to a negative with normal development. But the range of possible $D_{max}$ values depended significantly on the development process. In Appendix 2 of The Negative, Adams shows values between 1.75 and 3.1 for Kodak Tri-X film for N-1 to N+2 development with Zone XII exposures. (Yes, Zone XII). It was also possible to use “intensifiers” such as selenium to increase negative density. Adams shows this for Kodak Plus-X film, for which $D_{max}$ can be boosted from 2.1 to 2.65 at Zone XII exposure. Adams also discusses Kodak Technical Pan film, which he shows can vary anywhere from a $D_{max}$ of 1.45 at Zone XII exposure to 3.6 at Zone VIII, depending on the development process used. This was a film that was extremely sensitive to the choice of development procedure.

The full contrast of the NEF is not capable of being printed. Consider the following range of Epson papers:

 Paper Brightness Contrast Hot Press Bright 96% 2.18 Hot Press Natural 90% 2.15 Exhibition Fiber 95% 2.18 Cold Press Bright 96% 2.18 Cold Press Natural 90% 2.15 Velvet Fine Art 94% 2.17 Ultra Premium Luster 97% 2.19

I set this table up with a working assumption of a $D_{max}$ of 2.2. You may note that the overall contrast available depends less on the paper brightness, even between 90% and 97%, than it does on $D_{max}$. The variations in this table are all in the second decimal place. Going from a $D_{max}$ of 2.2 to 2.4 is a more profound impact on the available contrast. That is, a paper that absorbs more ink may yield higher contrast than one that is brighter by a few percent.

Actual $D_{max}$ for these papers will depend on the printer, its calibration, the ink set, the print driver, and so on. You may now appreciate why many print makers prefer papers that claim high $D_{max}$ values. Well, many make claims like “extremely high $D_{max}$” or “the highest $D_{max}$“, but it’s hard to find specifications that will quote a number. You can find web sites that list papers and their characteristics. Imatest quotes that generally, matte papers will give $D_{max}$ values around 1.7, while gloss and luster papers will achieve 2.0 or so. Epson printers with Epson premium luster paper can achieve 2.3 according to them. In calibrating my printers to various papers, (using a Data Color Spyder3Print system) I have measured Dmax values of this order on Hahnemühle Baryta Papers, Epson Exhibition Fiber and Epson Premium Luster. This is likely to be a reason behind the rise in their use over the past decade or so. I have lately purchased a box of Ilford Galerie Gold Mono Silk paper, designed specifically for B&W printing, but I am yet to test it out.

So the bottom line on inkjet paper and $D_{max}$ is that mileage will vary. As well, there is no consumer protection agency or testing magazine that will do your work for you in this regard. Plug “Dmax” into to Google and see what happens. Not much of value.

This struggle with the limited contrast range of the print process is nothing new. In discussing his print of Dogwood Blossoms, Yosemite National Park, In The Negative (p. 78), Adams wrote “Lighting was from the open sky only. The “flowers” are a waxy white and it is difficult to hold subtle values. They were placed on Zone VI1/2, and N+1 development was given the negative. The dark background rock and leaves fell on Zones II and III, with some of the rock and foliage approaching Zone V. As we will discuss in Book 3, this negative is printed in somewhat lower values for reproduction than for visual appreciation to hold subtle values in the whites.” In other words, to capture as much texture in the flowers as possible, he exposed them a couple of stops down from where they would have otherwise been if he’d done a normal exposure. Then he expanded them up only 1 Zone in development leaving them about 1 stop too low on the print, again, in order to retain textural quality in their whites on the print. However, by printing large fields of textural black at Zone II and a border near Zone I, a sense of deep contrast remains in the final image. You can see what I am talking about here.

This raises a big question, doesn’t it? If Adams is struggling with the range of contrast available in the prints of his day, and we can assume that his Zone V is our Zone V; namely, 18% diffuse from the print surface, where was his Zone II? Where was his Zone VII? In fact, where were any of his Zones, in terms of density, on his prints relative to what we are doing now.

It’s not like the man hid this information. His volume, The Print, is full of his data (see Appendix 2 there). In effect, the traditional dark room printing process added another stage of image contrast and compression that is missing in our current print-curve-linearization-mad world. It is worth further consideration of what happened in the dark room. Stay tuned…  