Some Ramblings on Exposure, the Zone System,
18% Gray Card
There are lots of good books and articles on exposure, and they'll do a far better job of educating you in the basics than I can. There are also some better researched and better written papers at a more advanced level than this one. See in particularhttp://largeformatphotography.info/articles/conrad-meter-cal.pdf (no relation to me). Still, there are a few ideas here that are phrased or viewed differently, and may be of use.
Brighter-Darker, More Exposure-Less Exposure?
Measuring subject brightness, setting the exposure, and how that affects the resulting negative, can be confusing. For the moment, let's assume ideal meter and film characteristics, and we'll define the scene reflectivity until we're ready to talk about real world situations.
We approach a scene having objects of varying brightness, or luminescence. All together, those objects reflect an average of 18% of the light that hits them. We set our meter to a film speed of 125 and take a reading. The result is 1/125 second at f/16, or any equivalent combination. You may recognize the "sunny 16" rule, and can assume it was a nice sunny day and all is right with the world. These relationships have served as a rough approximation for many decades. We'll accept them as true, just for a moment.
We now approach a new scene, with the same illumination as above, but with an average reflectivity of 72%. It's a snow scene. We take a meter reading and get 1/500 second at f/16, two stops more light, two stops less exposure. The resulting negative is underexposed. Darker objects that were correctly exposed in the first situation are just as dark in the snow scene, but have now received two stops less exposure.
The classic way to understand this problem is to consider three subjects. The first is a chess board consisting of equal numbers of black and white squares. The second is a similar board, black with one white square in the middle. The third is white, with one black square in the middle. You'll get a different meter reading from each board, yet it should be obvious that the correct exposure is the same for all of them. Unfortunately, none of the readings are the correct exposure! The two "one square" boards are wildly biased towards black or white, and the normal board has a reflectivity of somewhat under 50%, not what the typical meter has been adjusted to see as "average".
With that understanding, we can now think about what reflectivity might be chosen as "average".
The Real World
The most important metering method is the reflected reading from the average scene, often center weighted. That's what we've been discussing above. It's the most important because it covers the vast majority of exposures made today. The advanced amateur or pro who takes a more sophisticated view of exposure is a small percentage of the market. Thus, in-camera meters have to yield a high percentage of correct exposures when aimed directly at the subject, and that fact creates a defacto calibration standard for in-camera meters. Because hand held meters are often used in a similar fashion, and because it would be rather confusing to have different standards, hand held meters are calibrated similarly.
Calibrating Light Meters
You'll often hear talk of light meters being calibrated to 12%, 18%, or some other figure. In reality, light meters are calibrated using standard light sources. The ANSI standard includes a fudge factor, called the k factor, to fine tune the readings from any given meter.
Calibration sources are specified in exposure value (EV) numbers. The EV system is film speed dependent, so ISO 100 is almost always specified when the system is used for specific light levels. As an example, the source could be set to EV13. A properly adjusted light meter set to ISO 100 and pointed at the source would read EV13 (1/125 @ f/8, or any equivalent combination).
The k factor is a multiplier that makes the calibration source brighter or dimmer than the EV level set. It's buried in some formulas, so may not be a direct multiplier. This gets a bit confusing, so follow closely. k factors are generally positive, making the source brighter. With a k factor applied, the light meter would be adjusted to read EV13, even though the source was a bit brighter. The sensitivity of the meter would have to be reduced slightly to accomplish this. Thus, when the meter was pointed at a true EV13 source, it would read low. The resulting longer shutter speed or larger aperture would increase the exposure on the film. The proper use of the k factor allows a high percentage of correct exposures to be made using in-camera meters with typical subjects. It also compensates for differences in lens transmission, flare, and any peculiarities of individual cameras. Note that some calibration source manufacturers specifically recommend not applying any k factor when calibrating hand held meters.
Studies have shown that prints require good shadow detail to be considered excellent. That work was done long ago by Kodak & RIT, and is widely accepted as correct. Film speed is based on shadow exposure, as it's measured in the toe of the D log E (H&D) curve. Because this area of the curve is relatively insensitive to changes in development, and because it's the shadow area, it's the logical place to reference critical exposure measurements. This is completely at odds with the philosophy used above.
We have to accept the fact that an average mid gray measurement alone, while useful, does not give sufficient information to guarantee accurate exposure in all cases. That's an inherent limitation of average, incident, and gray card readings that no amount of calibration or good technique can overcome. The photographer has to rely on judgement and experience to recognize scenes where those methods will fail, and make adjustments or use a different method.
The 18% gray card is used as a substitute subject from which to make meter readings. That seems reasonable, as it's of known reflectivity and may be placed in a more convenient position, as long as it's illuminated by the same light source as the subject. There are however, many pitfalls for the unwary. The actual reflectivity of the card may vary, depending on manufacturer, age, storage, color, and the angle of the card in relation to both the light source and meter. Standards for light meter calibration vary. Finally, the card may be a flawless 18% gray, and the user's technique perfect, but that's no guarantee that a particular scene will be best rendered at the indicated exposure.
I have two Kodak gray cards and an accurate reflection densitometer. My cards measure 19.95% and 16.98%. Not perfect, but close enough. The first card is from the Kodak Color Darkroom Data Guide and has explicit instructions: Hold the card in front of the subject pointing halfway between the camera and the light source. Give 1/2 stop more exposure than is indicated by the card. The second card is from the Black & White Darkroom Data Guide and simply says that a reading from the card should give close to the correct exposure. Hmmm.
I should note that many of the differences under discussion here are small. There is a general engineering principle that requires one to explain all discrepancies, even small ones. Only by doing this can one say with confidence that a system is correctly thought out and that no surprises lurk behind murky data.
Let's assume the more detailed instructions are correct. Tilting the card should prevent reflections if the surface isn't completely matte. It should also lower the reflectivity, but with a broad source the effect is small and hard to quantify. 1/2 stop more exposure would result if the card reflected 70.8% of it's previous value. (darker card causes meter to indicate the need for more exposure) Thus, the implication is that a reading from a 12.7% gray card gives the correct exposure for some average scene.
Ansel Adams states in The Negative that an increase in exposure of about 1/3 stop is needed for about 85% of simple on-axis readings made with an uncompensated meter, i.e., no k-factor. Applying this to our 18% gray card gives 14.3%. Further, he states that an incident reading and a gray card reading should both agree, though he doesn't recommend incident metering since it doesn't apply to the Zone System.
Here is a point that I believe has been confused in many writings on this topic. The above does not mean that the reflectivity of an average scene is 14%. Consider a snow scene. You have to give it more exposure than indicated, lest the white snow record as gray. A scene consisting of very dark low reflectivity objects will require less exposure than indicated, lest the dark objects record as gray. The meter gives an exposure reading to record objects as 18% gray, depending on it's calibration. The implication is that the average scene has a reflectivity higher than 18%, and the meter indicates less exposure than is necessary. My opinion is that the average scene has about 22.7% reflectivity. This isn't surprising, since many scenes contain an appreciable amount of bright sky area.
Some Zone System Connections
Many photographers have found that the Zone System provides exceptional insight into tone reproduction, so it may be useful to review some basic Zone System concepts.
Zone I is not quite black and should expose the film to a density level of base+fog+0.1, the lowest usable density per Adams. Zone I is, by definition, four stops below Zone V in the original scene. The old adage "expose for the shadows and develop for the highlights" sums up the situation. As we all know from practical experience, sufficient shadow detail has to be recorded during the original exposure, as no later manipulation can extract information from clear film!
From those ideas we can establish meter calibration for the Zone System, either by adjustment or by changing the film speed setting (We'll assume the meter was correctly designed and reads different light levels correctly, i.e., it has linear response). The meter should yield an exposure that renders any target as Zone V (18% gray). Thus, any uniform surface should record on film as a density of 0.1 when exposed four stops below the meter reading from that surface. A series of tests at various film speeds should be run to find the optimum setting. That's the usual first step to calibrating your equipment using Zone System methods.
The next step is to establish the correct normal development time so Zone VIII and higher are at the correct density and print on normal paper. Once those tests are complete, Zone V will have established itself as some arbitrary print density, for better or worse. N+ and N- development times are also established to alter contrast.
Note that many scenes have greater range than photo paper. The nature of the photographic process compresses shadows and highlight, but mid tones are usually reproduced with a slope of close to one. That's how the typical scene gets mapped into a 100:1 range. There is, however, no guarantee that an 18% reflectance in the original scene can or should reproduce as 18% in the finished print. Regardless, the Zone System allows one to expose for the amount of shadow detail desired, and control the highlights if development is altered.
Now, some opinion, worth what you've paid for it. Manufacturers rated E.I. numbers generally produce acceptable results. Zone System film speed tests usually suggest that a lower E.I. be used, often less than half (1 full stop). The Zone System places a high priority on shadow detail and tonal separation. That's a good thing, but may give low effective film speeds. The speed numbers resulting from Zone System tests may not be suitable for simple average readings because the metering assumptions are now different. If you calibrate for the Zone System, you need to use the Zone System!
More opinion. In a typical sunny scene, the brightest objects will be specular reflections (the sun off a chrome bumper) and plain white (a piece of white paper at 90% reflectivity). The specular reflection will easily go to Dmax and need not be considered. The white reflector will have a definite and repeatable luminosity because sunlight is fairly constant. The darkest directly illuminated objects will also have predictable luminosity, as most so-called black objects have a reflectivity of about 1%. That's a ratio of 90:1, not too difficult to deal with and near the limit of black & white printing paper. These are just rough estimates. The problem is objects in shadow. They can be far darker than a simple directly illuminated object and the value will be completely unknown unless measured. An open barn door might reveal a luminosity 13 stops below the sunlit white paint outside, or 8000:1. A range far beyond what film with normal processing can accommodate. Obviously the detail inside the barn will have to be allowed to go completely black if the rest of the scene is to be correctly rendered.
A useful concept in understanding exposure is that the fixed reference point for film is the shadow area, but illumination attenuates down almost forever from some relatively fixed highlight luminosity. The Zone System is the tool that allows one to match the moving target of shadow luminosity to the fixed film sensitivity, and the moving target of highlight luminosity to the also moving target of film development (if you use N+ and N- to alter gamma). Yikes- read that a couple times till it makes sense!
Miscellaneous Gray Card Thoughts
The step tablets we've purchased from Kodak are in fact aimed at the graphic arts market. The color patches are specifically designed for identifying separation negatives and most pictorial photographers don't have much use for the registration marks that are included in the package.
The graphic arts industry is more technically grounded than most pictorial photographers and the use of transmissive and reflective step tablets is de rigour. The only important single point measurement commonly made is evaluation of the "50% dot". That's the halftone pattern where the dot coverage is 50%. It ideally occurs for a subject reflection density of .65 (22.4% per DuPont, once a supplier of halftone screens). Sometimes the base density of the subject is added, so the figure might approach .74 (18%), but the gray card is basically the wrong value. Further, it gives too little information to the cameraperson, which is why step tablets are more commonly used. I don't believe the 18% gray card is or has ever been an important tool in the graphic arts industry. That's not to say it isn't used on occasion, but the graphic arts industry wasn't the driving force in it's creation. The Kodak 18% Neutral Test Card is suggested in their materials for amateur photographers, and for non-halftone copying, and that appears to be it's main purpose.
Is 18% really the geometric mean between black and white? It should be straightforward math, but there are complications. The eye is very good at creating a white reference, regardless of the actual luminescence level. There are also many degrees of black, not easily distinguished by eye, but differing greatly in measured luminescence. Now the question becomes "the geometric mean between what two numbers?" Note that the geometric mean is found by taking the Nth root of the product of N numbers. It should be obvious that if one of the numbers is zero, the geometric mean becomes zero, thus we can't start with perfect black. Here are some examples using various reflectivities:
.001% to 89% (GM=0.3%) the range between a black cat in a coal bin and bright photo paper
1% to 89% (GM=9.4%) a real grayscale made on good glossy photo paper
3.64% to 89% (GM=18%) black adjusted to give the answer we're looking for- not very black!
These numbers are all for a reflective target like a ten step gray scale. But wait- the normal subject isn't a gray scale with a range of about 100:1. If it were, we wouldn't need the Zone System to understand contrast and map it into the limited range of film and paper. We'd just make a shadow reading and be confident that the scene would map within the range of the print.
When Adams worked out the Zone System he decided that there should be eleven Zones, spaced one stop apart. He also declared that Zone V was 18%. Since the zones are 1 stop apart, that makes Zone 0 .5625%. Interestingly, Zone X ends up at 576%. That makes sense since the luminescence range of a scene is often far greater than a simple reflective target lit by a single source. Now, let's see if Mr. Adams' system is internally consistent:
Finally, an unambiguous answer appears! Unfortunately, it will work with any number. If Adams had declared Zone V to be 37%, the formula would dutifully return 37%. All we've proven is that Zone V is the exact geometric mean of an eleven zone system with one stop spacing between zones. Works for a five zone system too. Not terribly enlightening.
There's another approach. Since Zone V is defined as four stops up from Zone 1, we can start with a reflection density of 1.94 (1.1%), go down 1.2 (four stops), and get .74 (18%). That sounds much better, since 1.94 is a very respectable black, though not quite the maximum black for most good photo papers. It fits the definition of Zone 1. This method doesn't work going from paper base up, as .05 plus 1.2 is 1.25, or 5.62%. You'd have to start with a base density of minus .46 (luminous paper?) to be four stops below 18%. See the Zone System and scene range above. The four stop Zone I to Zone V difference may be the best numerical justification of 18% that we'll find.
Conclusion (a.k.a. more opinion!)
When the Zone System was invented, the four stop difference between Zone V and Zone I was derived from actual practice. Note that the system would work with any meter calibration, as long as it was in terms of a particular Zone, and as long as both shadow and highlight readings were taken. A mid gray calibration makes sense for two reasons. First, a meter calibrated for other than a mid gray would be useless in the hands of a tyro. Second, early selenium meters weren't terribly accurate or sensitive, so calibration at a mid gray level (where it was most used) made the most sense.
The average photographer with reasonably well calibrated equipment should get acceptable results much of the time using nothing more than average reflected meter readings. The use of a gray card or incident meter will help when subjects are far from normal. There should be a significant improvement if he or she also establishes a personal film speed, and attempts to meter both shadows and highlights, and place them within appropriate Zones, even if the development adjustments of the Zone System have to be abandoned due to multiple subjects on a single roll of film.
4/14/01 to 7/7/01
The Negative, 1981, Ansel Adams
Photographic Sensitometry, 1969, Todd & Zakia
The Contact Screen Story, (no date), E.I. DuPont Corp.
Practical Densitometry (pamphlet E-59), 1972, Eastman Kodak Co.
Various step tablet products, Eastman Kodak Co.