© 2006 by Nicole Boenig-McGrade, all rights reserved

Appendix

 

Technical Fundamentals

Numbering sequences, logarithms and some photo-mathematics

Photography is an art form. When people think about art, they think about self-expression, creativity and aesthetics, but not necessarily about craft and hard work. However, as Brett Weston so knowingly stated: “Photography is 90% sheer, brutal drudgery. The other 10% is inspiration.” The brutal drudgery is the craft of photography; the knowledge of equipment and materials allows creativity to flow unhampered.

This book is about the craft of photography. It takes a balanced scientific approach, supported by many practical applications and examples. This combination, we hope, avoids misconception about conclusions and dispels unsubstantiated myths, of which there are many. This chapter refreshes the fundamental mathematical and optical concepts to explore the characteristics of film and paper.

Arithmetic and Geometric Sequences

There are two types of numbering sequences common in camera and photographic work, arithmetic and geometric. The simplest number sequence is found on the exposure counter, where each number varies by one increment from its adjacent values (fig.1). This is called an arithmetic sequence, in this case, with an increment of 1. Sometimes, arithmetic sequences are called linear sequences, because they form a straight line when plotted on a graph.

Geometric sequences are also common in photography. The familiar lens-aperture, shutter-speed and film-sensitivity dials on a camera are examples of geometric sequences. Lens-aperture values (fig.2) form a geometric sequence with a factor equal to the square root of 2, approximated to 1.41. Each number is 1.41x more or less than its adjacent value, and it takes two steps to double or half the previous value. One might ask why the lens-aperture sequence has a factor of 1.41, when we know that each aperture setting doubles or halves the exposure. The aperture value is the focal length of the lens, divided by the diameter of the opening. The area of the opening, and hence the exposure, is proportional to the diameter squared. The area of each increasing aperture is, therefore, 1.41 squared or twice the size of the previous aperture value.

Shutter-speed markings (fig.3) are another example of a geometric sequence, because each number indicates half the exposure time of the previous setting. Some of the engraved markings are approximated to make the shutter-speed numbers easier to deal with. The film-sensitivity, or film-speed, values also form a geometric sequence with a factor of the cube root of 2, or approximately 1.26. In this sequence, it takes three steps to double or half the previous value.

Lens Aperture, Shutter Speed and Film Sensitivity in Stops

Although the original definition for ‘f/stop’ referred to the lens aperture itself, the term ‘stop’ is commonly used to imply any doubling or halving of exposure. For instance, ‘reduce the exposure by 2 stops’ can mean either ‘close the aperture by two f/stops’ or ‘set a shutter speed to 4x as fast’. Alternatively, one may choose to keep both exposure settings as is and reduce the film-speed by ‘2 stops’.

The term ‘stop’ is most useful when describing film and print exposures. However, when examining the material response to exposure, in order to evaluate film or print characteristics, it is more practical to work with reflection and transmission values, described in logarithmic density units.

Logarithms

The elements controlling exposure all increase in geometric sequences. Therefore, the absolute values of exposure increase very quickly, leaving us with low and high values of equivalent importance, but making low values hard to decipher. For this reason, we use logarithmic scales extensively in our graphs, in particular when describing the results from paper and film tests. These results often show print or negative density on the vertical axis of a graph and exposure along the horizontal, both plotted in logarithmic units.

fig.1       The exposure counter is an example of an arithmetic numbering sequence.

fig.2       The common progression of lens-aperture values, or f/stops, is an example of a geometric numbering sequence using a factor of 1.41.

fig.3       The settings for shutter speed and film sensitivity (shown in the small dial window) are other examples of geometric numbering sequences.

fig.4       Rounded-off values for film speed, aperture and exposure times are incremented in stops, so when one is increased and another is decreased by the same factor, the total exposure remains constant.

It is not practical to use linear axes on these graphs, as it would make low-value interpretation difficult and limit their usefulness. For instance, the small horizontal difference between two closely spaced points (a&b) of low x-value may create the same vertical response as two other points (c&d) of higher x-value (fig.5). By comparison, the low-value information is easier to comprehend and quantify, when x-values are plotted in logarithmic units (fig.6).

The logarithm, or log, of a number is equal to the number of times by which the base value, most commonly ‘10’, is multiplied by itself to produce that number. In mathematical terms, 10^(log(x)) = x. The numbers 10, 100 and 1000 have logs of 1, 2 and 3, respectively. Other numbers are more obscure, but easily found using a log table or scientific calculator.

For each stop up or down, the exposure doubles or halves, respectively, which is why it is important to remember two essential logs, log(2) = 0.3 and log(1/2) = -0.3. For each additional stop of exposure, the log exposure increases by 0.3. Therefore, a logarithmic exposure axis, marked in stops, will have markings at 0.3, 0.6, 0.9, 1.2 and so on.

fig.5       In this example, sample curve data is charted using a linear scale for the vertical and horizontal axis. The first few hundred units of the horizontal axis contain most of the data, making a detailed interpretation in this area difficult and potentially inaccurate.

fig.6       fig.6 In this graph, the same sample data as in fig.5 is charted, but this time, a logarithmic scale is used for the horizontal axis. The graph emphasizes the first hundred units of the horizontal axis, allowing for a more detailed and accurate interpretation in this area.

If we take two numbers and add their logs together, the result is the same as multiplying the two numbers and taking their log. Similarly, if we wish to divide two numbers, a simple subtraction of their respective logarithms performs the division. For example, log(100/10) = log(100) - log(10).

For geometric sequences, working in logarithms makes the mathematics simpler. We know that three 1/3 stop increases in exposure equal 1 stop. Consequently, for each 1/3 stop increase in exposure, the log exposure increases by log(2)/3 or 0.1. This fact is the premise behind the once popular slide rule, which uses two sliding log scales to multiply or divide numbers by simply adding or subtracting distances along the scales. Logarithms are also used with photographic filters. A 3-stop neutral density filter may have any one of three exposure-compensation markings, as in +3, 8x or 0.9 marked on the rim, which are in stops, exposure ratio and transmission density, respectively.

Logarithms are commonly used to graphically display many photographic parameters. They are applied to exposure, light intensity, time or the optical density of a negative or print. For example, each doubling of exposure occupies an even 0.3 log unit along the horizontal axis of a graph, thereby converting a geometric number sequence into an arithmetic sequence.

Densities

Throughout this book, the terms reflection and transmission density are used to describe the appearance of prints and negatives. We can quantify how light or dark a certain area of the print is, by measuring the fraction of incident light reflected from its surface. Since the print surface never reflects or absorbs all of the light it receives, the reflectance value is always between 0 and 1. Reflection density is defined as the log of the reciprocal of reflection:

Consider several examples. If the reflected light intensity equals the incident light intensity then the reflection density is log(1/1) = 0. The Kodak Gray Card has an 18% reflectance, which means for every 1 unit of light that falls upon its surface, 0.18 units are reflected. Its reflection density is, therefore, calculated as log(1/0.18) = 0.74. The above equation can also be solved for the actual reflection from a measured reflection density value (see equations in fig.7). For example, if the paper’s white base (Dmin) has a density value of 0.05, then this paper reflects up to 89% of the incident light it receives (1/10^0.05 = 0.89), and if its maximum density (Dmax) measures 2.15, then it absorbs up to 99.3% (1/10^2.15 = 0.007) of the received light.

Since the print is the final stage of the photographic process, the appearance of the print is usually described in absolute terms of the ‘absolute reflection density’ or simply ‘reflection density’. Therefore, two entirely different papers, with different base whites, will measure and look the same. In practice, a known reflection reference is placed under the densitometer and the display calibrated to the reference value. Densitometers that only have a zero reset button cannot measure absolute print densities and are limited to measure reflection densities relative to paper white. Densities measured with such a densitometer should be clearly labeled as ‘relative reflection density’.

With a photographic negative, we are interested in the amount of light that passes through the film. We can quantify how dense highlights and shadows are by measuring the fraction of light transmitted through the negative. Transmission density is defined as the log of the reciprocal of transmission:

A transmission densitometer is used to measure the transmission in log units. However, only the relative difference between shadow and highlight transmission densities is important, and so it is usually applicable to measure transmission relative to the clear negative material as ‘relative transmission density’ or just ‘transmission density’. In practice, a piece of clear film is placed under the densitometer and the meter reset to ‘0’. In the exceptional case when absolute negative densities are measured, for instance to measure the effect of development fogging, the results should be clearly marked as ‘absolute transmission density’.

The numbers representing lens apertures, shutter speeds and film sensitivity should become second nature to every photographer, but there is no need to do a lot of calculation to take good photographs. Nevertheless, it helps to be familiar with some of the terminologies of logs and densities, so one is able to interpret published or self-made film and paper characteristic curves, which contain a lot of useful information. Understanding a little bit more about the sometimes-complex techniques and processes of photography is not an absolute necessity, but it can be both rewarding and interesting at the same time.

fig.7       The percentage of incident light transmitted through a negative or reflected from a print can be expressed in density units. Every increase of 0.3 in density cuts light transmission or reflection in half.

 

Make Your Own Transfer Function

What you see is not always what you get

Typically, digital image manipulation is controlled and verified with the help of a calibrated monitor. It makes sense to manipulate individual image tones and overall contrast right on the screen, because a calibrated monitor provides reliable visual feedback immediately. However, this approach is of little value if the final print has little in common with what is shown on the screen. Ideally, we would like to have a perfect match between monitor and print tones (fig.1). This chapter shows why a perfect match is impossible, but how a well-designed transfer function produces a reasonably close match between monitor and print.

Tone Reproduction

Image science differentiates between objective and subjective tone reproduction. Luminance is defined as the amount of light emitted or reflected from a surface. It can be objectively measured with a lightmeter. Brightness is defined as a subjective sensation produced by light, and it can only be approximated by psychological scaling procedures. Applying these terms to our task of creating a perfect match between monitor and print, the purpose of an objective tone reproduction is to create a print in which all monitor luminances are accurately reproduced. In other words, after the print is made and properly illuminated, corresponding monitor and print measurements must return the same light readings. On the other hand, subjective tone reproduction is satisfied when it appears that monitor and print have the same brightness and overall contrast.

The Impossible Match

Monitors and prints are fundamentally different in the way they produce an image. A monitor creates image detail and tonality through a matrix of pixels, emitting light at a number of different luminance levels. The print image, on the other hand, is made up of small, high and low-density areas, which reflect light at different levels of intensity.

The fact that a monitor emits light and a print reflects light is no reason that the two images cannot be matched. After all, in both cases light intensities can be measured as luminance values and compared to each other. Furthermore, print illumination can be altered until both values match. For example, you can easily measure the monitor luminance of a specific image area with a spotmeter and record the reading. If you then adjust the print illumination until the corresponding image area returns the same reading, both images have an identical luminance value for that area. Nevertheless, the two images only match if they also have the same overall contrast.

Modern monitors feature an image contrast of at least 400:1. Some provide a contrast of 800:1 or more, which is sufficient to realistically render outdoor scenes of the highest contrast. Silver-gelatin papers have a theoretical contrast range of up to 125:1, and inkjet papers go up to 250:1, but if we deduct the tonal extremes of their characteristic curves, their practical contrast limit is about 80:1. This is roughly half of what is needed to faithfully reproduce an average outdoor scene. The contrast difference between monitors and photographic papers is the main reason why it is not possible to obtain an accurate objective tone reproduction from monitor to print. As with slides in the past, monitors provide a more vibrant image experience than any printed media.

The Rendering Intent

Fig.2 shows an example of a detailed subjective tone-reproduction study for a hypothetical imaging process. I am not suggesting that you conduct such a study just to make your own transfer function, because there is no need to do so, but fig.2 helps to understand how image tones are modified by the imaging process and how we can manipulate them to achieve a subjectively close match between monitor and final print.

fig.1       The purpose of a transfer function is to bring the subjective tone-reproduction cycle full circle, and closely match the final print to the digital image seen on the computer monitor.

(based on an illustration by White, Zakia and Lorenz, The New Zone System Manual, Morgan & Morgan, Inc. ISBN 0-87100-100-4)

A typical subjective tone-reproduction study is divided into four quadrants. Each quadrant (Q) represents one step of the reproduction cycle and illustrates the tonal modification during this step through a curve. In Q1, we see how digital image values are modified prior to image processing to achieve a close match between monitor and final print. Any undesired effect on image tonality by subsequent image processing is preempted through the curve in this quadrant. In other words, this quadrant is home to our transfer function, and we have full control over it, as we will see over the next few pages.

Q2 stands for the hypothetical process we have chosen to get the digital image onto paper. The curve in this quadrant is process dependent. It may represent the characteristics of a halftone negative, an inkjet printer or a more complex sequence of processing steps such as in the copy-print process. The details of how image tones are processed and manipulated in this quadrant are of no concern to us and irrelevant for creating a transfer function. Nevertheless, this quadrant shows how the digital image data, corrected by the transfer function, is converted by our chosen process into ‘exposure’ of the print media. In this context, ‘exposure’ is used as a broad term, as it can refer to actual exposure of photographic paper through a negative, as well as to the amount of ink ejected by an inkjet printer to create density on inkjet paper.

fig.2       A typical subjective tone-reproduction study is divided into four quadrants (top). Each quadrant (Q) stands for one step of the reproduction cycle. In Q1, digital image values are modified through a transfer function (left). Q2 stands for the process characteristics to get the digital image onto paper, which are not required to create a transfer function. Q3 illustrates how the chosen paper responds to the chosen process. Q4 shows the author’s personal rendering intent (curve ‘a’) compared to typical monitor characteristics. To achieve a close contrast correlation between monitor and final print, highlight densities are over-laid and the curve is smoothly adjusted to account for the Dmax limitations of the print media. Midtone densities are maintained as much as possible. Once defined, this personal rendering curve can be used to create a transfer function for any digital/analog process, as long as the print media has the same Dmax.

Q3 shows the print media’s characteristic curve. It illustrates how the chosen paper responds to the chosen process. The curve in this quadrant is material dependent, and as in Q2, we cannot alter this curve, but we can replace it with others by choosing a different print media. I have selected the curve of a paper with a maximum print density of 2.1, which is a typical Dmax value for photographic paper.

In Q4, we get the opportunity to define our personal rendering intent. We already discussed why a perfectly objective tone reproduction is not possible. The green ‘typical monitor’ curve verifies this point. A monitor, calibrated to gamma 2.2, emits a luminance difference of about 2.2 f/stops between image values of 0 and 50% gray (0-50K), which is exactly the theoretical value. Approaching image values of 100K, the monitor deviates significantly from theoretical gamma values. Nevertheless, the Dmax equivalents are still far beyond the paper’s Dmax. The monitor image has more contrast than the print! To make up for this difference, and to create a print closely matching the on-screen image, we need to define what we feel is the most appropriate, subjective tone reproduction. We can do that by defining our personal rendering intent through a smooth curve.

Q4 shows the author’s personal rendering intent (curve ‘a’) compared to typical monitor characteristics. To achieve a close contrast correlation between monitor and final print, highlight densities are overlaid and the curve is smoothly adjusted to account for the Dmax limitations of the print media, while midtone densities are maintained as much as possible. Once defined, this personal rendering curve can be used to create a transfer function for any digital/analog process, as long as the print media has the same Dmax. It is your perceptual rendering intent. To make it all work, we need to close the subjective tone-reproduction cycle in Q1 with a smooth transfer function.

Creating the Transfer Function

The purpose of a transfer function is to bring the subjective tone-reproduction cycle full circle, and closely match the final print to the on-screen image. To do so, a transfer function must correct for the differences between the actual and the desired process characteristics. In order to design a transfer function, these differences must be clearly understood.

We already established our desired process characteristics with our personal rendering curve in Q4 of fig.2, which gives us a desired, absolute print reflection density for every on-screen value. These are listed as target densities in fig.4 for later use, and with the help of a step tablet, we are able to determine the actual characteristics of our chosen process.

A well-designed step tablet simplifies the development of a transfer function. The self-made example in fig.3 has a tonal spacing of 1% for the extreme highlight and shadow tones and a 2% spacing in the midtone area. It is available from our websites or can be constructed easily with any suitable drawing software.

Open the step tablet in your photo editing software, and run it through your process to bring it to paper. For example, if your process involves a digital halftone negative, send the file to a service bureau and have them produce such a negative of it. Once returned, produce a test print of that negative on your chosen photographic paper. Tone it, if that is part of your standard process, and check the actual densities for a few on-screen input percentage in the table of fig.4 with a densitometer. The measurements will most likely deviate from the target densities of your personal rendering intent. Now, find the patches on the test print that are closest in value to the desired target densities, interpolate if necessary, and list the actual percentages in the output column of fig.4.

The input and output values in fig.4 are entered into the ‘Curves’ adjustment dialog box of the photo editing software (fig.5) and saved as a transfer function for future use. From now on, this transfer function is applied to every digital image after final image manipulation, and just prior to committing it to the chosen process and the print media this transfer function was made for. This ensures that the final print will always be a close match to the on-screen image as seen on your monitor, even if process and paper changes, because all transfer functions designed this way are based on your personal rendering intent.

fig.3        A well-designed step tablet simplifies the development of any transfer function. This self-made tablet has a tonal spacing of 1% for the extreme highlight and shadow tones and a 2% spacing in the midtone area. It is available from our websites or can be constructed easily with any suitable drawing software.

fig.4        After running the step tablet in fig.3 through the chosen digital/analog process, the actual output values required to achieve the absolute target densities of our personal rendering intent are determined and listed against the digital, on-screen input values.

fig.5        The input and output values in fig.4 are entered into the ‘Curves’ adjustment dialog box of the Adobe Photoshop software and saved as a transfer function for future use. This transfer function is applied to every digital image after final image manipulation and just prior to committing it to the chosen digital/analog process and the print media this transfer function was made for.

 

Photographic Chemistry

An introduction for the non-chemist

Traditional photography combines art, technology and science, predominantly chemistry. From preparing light-sensitive emulsions to developing and creating permanent images, photographic chemistry is the backbone of traditional photography, controlling exposure, development and fixation.

During the exposure, light is directed onto the emulsion, where its radiation affects light-sensitive silver salts and produces a latent image. A chemical treatment, called development, turns the latent image into a visible image, by converting the silver salts that were affected by the exposure into metallic silver. All remaining silver salts, not affected by the exposure and, consequently, not changed by the developer, must subsequently be removed to produce a permanent image. This is accomplished through another chemical treatment, called fixing, which is followed by a final wash in plain water to remove chemical residue.

fig.1       As of this writing, in 2010, there are 118 elements known to exist, but only a few of them find significant use in silver-based photography.

A thorough understanding of chemistry is not required to effectively operate a darkroom. One can successfully process film and paper, using commercially available photographic chemistry, by simply following the instructions, without ever giving the underlying chemical processes much thought. However, preparing your own processing solutions according to a chemical formula, using raw chemicals, makes you independent of commercial product availability and provides the opportunity for customized process optimizations. In the following chapter, you will find a basic set of formulae for developers, a stop bath, fixers and other processing chemicals. To better understand the purpose and function of their main ingredients, it will be beneficial to have a rudimentary understanding of photographic chemistry.

Elements and Compounds

For much of its history, chemistry was a relatively simple science with all matter divided into just four elementary materials: air, water, earth and fire. This changed in 1661 when Robert Boyle summarized a better understanding of matter and proposed that there is a difference between elements and compounds. Since then, an element is defined as the simplest form of matter (atom), indivisible and with individual characteristics, but, combined with each other, elements can create a number of compounds (molecules) with distinctively different properties. As of this writing, there are 118 known elements (fig.1), but only the first 94 elements occur naturally on earth. The rest are mainly short-lived by-products of nuclear reactions. The number of possible compounds, on the other hand, seems to be endless.

Compounds, created by chemical reaction, often have properties quite different from the elements they are made of. For example, the elements sodium and chlorine are both extremely dangerous, but when combined chemically, they produce harmless sodium chloride, which we know as ordinary table salt. The chemical equation for this reaction is written as:

Types of Compounds

Elements can be roughly divided into two groups: metals and non-metals. Compounds can be classified as being organic or inorganic. Organic compounds are mainly composed of hydrogen, carbon, nitrogen, oxygen and sulfur. Inorganic compounds usually contain metallic elements. Another useful classification of compounds (fig.2) differentiates four groups:

Oxides are compounds of oxygen and other elements. Examples are sulfur dioxide (S + O₂ = SO₂) and sodium oxide (₄Na + O₂ = ₂Na₂O). Many oxides are soluble in water, and, depending on the type of element combined with the oxygen, this results in either an acid or a base.
Acids are formed when the oxides of non-metallic elements are dissolved in water. For example, sulfur dioxide dissolved in water produces sulfurous acid (SO₂ + H₂O = H₂SO₃). Acids are sour and have a pH value < 7.
Bases are formed when oxides of metallic elements are dissolved in water. For example, sodium oxide dissolved in water produces sodium hydroxide (Na₂O + H₂O = ₂NaOH). Bases are alkaline and have a pH > 7.
Salts are typically combinations of acids and bases. For example, when sulfurous acid reacts with sodium hydroxide, sodium sulfite is formed (H₂SO₃ + ₂NaOH = Na₂SO₃ + ₂H₂O). Sodium sulfite is found in many photographic formulae.

pH

The ‘power of hydrogen’, or pH, is a measure of strength for an acid or alkaline solution (fig.3), and measured pH values typically range from 1 to 14. Roughly speaking, the pH value is the negative logarithm of the hydrogen ion concentration, but it is more important to remember that acids have pH values < 7 and bases have pH values > 7. Distilled water is said to be neutral with a pH of 7.

Precise pH measurements require sophisticated pH meters, but sufficiently accurate pH values can be obtained with a litmus test. Litmus is a water-soluble dye that changes its color depending on the pH value of the solution with which it comes into contact. Test papers, containing litmus, turn bright red in acid solution and deep blue in alkaline solutions. The actual pH value can be estimated by comparing the resulting color to a calibrated color chart.

A pH test is useful for darkroom workers, because the pH value of a photographic solution is often an indicator of its freshness or activity. For example, a fresh acid stop bath has a pH value of 4 or less, but when in use, it will be continuously contaminated with alkaline developers. The alkali carry-over raises the pH value of the stop bath, and by the time it approaches a pH value of 6, the stop bath has lost most of its usefulness and must be replaced. In another example, the pH value of a developer can be an indicator of its activity. A changing pH value, due to age or usage, will lead to process inconsistencies, which can be predicted and controlled, after the actual pH value has been determined.

Chemistry and Photography

In 1727, Johann Heinrich Schulze experimented with several compounds of silver and noticed that silver salts darkened under the influence of light. In 1802, Thomas Wedgwood and Humphrey Davy coated paper with a silver-salt solution and exposed it in a camera obscura to produce an image, which could only be seen for a limited time. In 1834, William Henry Fox Talbot suggested that a developer could amplify a weak exposure of silver salts, turning a latent image into a visible image, and in 1837, two years prior to the official invention of photography, John Herschel proposed sodium thiosulfate as a solvent for unexposed silver salts to create a permanent image.

Emulsion

A photographic emulsion is a thin layer of light-sensitive material suspended in photography-grade gelatin. The gelatin makes it possible for the emulsion to be coated onto a substrate of glass, plastic film or paper. Three silver salts have been found to be particularly sensitive to light: silver chloride (AgCl), silver bromide (AgBr) and silver iodide (AgI), and as a group, they are often referred to as silver halides.

fig.2    Chemical compounds can be divided into oxides, acids, bases and salts.

fig.3    The pH value is a measure of how strong an acid or alkaline solution is.

Typical emulsions contain a mixture of two or three silver halides, because they differ in light and color sensitivity. But, even as a group, they are mostly blue-sensitive and not able to record the entire visible spectrum. To make silver halides responsive to all wavelengths of light, complex organic chemicals, so-called optical sensitizers, are added to the emulsion. They act as an internal color filter, extending the color sensitivity from blue into green and red.

During the exposure, light energy is absorbed by the silver-halide crystals, which produces a chemical reaction within the salts. This creates a latent image, which is made visible through development.

Developer

Developers are able to differentiate between exposed and unexposed silver halides. They liberate exposed silver halides from their salts and reduce them to metallic silver, but unexposed halides remain untouched. The chemical process of development is rather complex, and an exact equation cannot be given, but in simple terms, the following reaction takes place:

Developer solutions contain a number of ingredients, which can be divided into four groups:

Developing Agents are relatively complex organic compounds, which provide the electrons required to reduce silver ions to metallic silver. The most commonly used developing agents are metol, hydroquinone and phenidone.
Accelerators increase the alkalinity of the developer and provide additional ions to create metallic silver. In general, the higher the pH value of the developer, the more active it is. Typical accelerators are sodium hydroxide, sodium carbonate and borax.
Preservatives are added to developer solutions to protect developing agents against oxidation. A frequently used preservative is sodium sulfite.
Restrainers suppress the formation of chemical fog, which is an unwanted silver production on unexposed silver halides. A minute amount of potassium bromide effectively reduces fog, but larger amounts affect the rate of normal development.

Stop Bath

Once the desired degree of development has been reached, the process must be stopped quickly to avoid overdevelopment. This can be achieved through a simple water rinse, but an acid stop bath is more effective in neutralizing the alkaline activators and stopping development almost instantaneously.

A dilute solution of acetic or citric acid makes for a powerful stop bath. However, with developers containing sodium carbonate, the acid concentration must be kept sufficiently low to avoid the formation of carbon-dioxide gas bubbles in the emulsion, because this may lead to ‘pinholes’ in the emulsion.

Fixer

After the stop bath has successfully terminated the development of exposed silver halides, all unexposed halides still remain in the emulsion, because they are not soluble in water. This is of great benefit during the development process, but during fixing, they must be removed completely, or they will eventually darken upon further exposure to light, and the image will not be permanent. This requires a fixing bath with a number of ingredients:

Fixation Agents must dissolve all remaining silver halides and convert them into water-soluble compounds. Only two chemicals, sodium and ammonium thiosulfate, are known to do that without negatively affecting the silver image or the gelatin layer. Since ammonium thiosulfate dissolves silver halides more rapidly than sodium thiosulfate, it is commonly known as ‘rapid fixer’.
Acids are optional fixer ingredients, separating fixers into acid and alkali solutions. Acid fixers have the benefit of neutralizing any residual developer solution and preventing emulsion swelling in the wash. Often, a combination of acetic and boric acid is used. Acid-free fixers produce a less objectionable odor and are easier to wash out of the emulsion.
Preservatives are used with acid fixers to prevent an accumulation of sulfur, due to a reaction of thiosulfate with acids. This is achieved by adding sodium sulfite, which quickly reacts with colloidal sulfur and creates fresh sodium thiosulfate.
Hardeners can be added to prevent excessive swelling of the emulsion during washing and protect against physical damage. The most widely used hardener is potassium alum. Hardeners impede washing and are not recommended for normal processing, but they find use in special application.
Buffers such as sodium sulfite and sodium carbonate are used to stabilize the pH value of acid and alkali fixers. If alkali fixers are preceded by an acid stop bath, sodium carbonate must be substituted with sodium metaborate or balanced alkali to avoid the formation of carbon-dioxide gas bubbles.

Washing Aid

After fixing, emulsion and film or print substrate contain a considerable amount of thiosulfate, which must be removed so not to adversely affect later processing operations and to optimize image longevity. Washing is a combination of displacement and diffusion, and consequently not a chemical but a physical process. However, certain chemicals can positively affect the rate of washing and its efficiency.

According to Modern Photographic Processing by Grant Haist, a salt bath prior to washing was suggested as early as 1889, and washing in seawater has been known to speed up the rate of washing since 1903. On a global average, seawater contains roughly 3.5% salt, mainly sodium chloride. Unfortunately, seawater cannot be left in the emulsion, because the remaining salts cause a fading of the silver image under storage conditions of high humidity and temperature.

The modern alternative to seawater is a washing aid, containing up to 2% of sodium sulfite. Applying a washing-aid bath prior to the final wash is standard practice with fiber-base print processing, and is also recommended for film processing. It makes residual fixer and its by-products more soluble and reduces the washing time significantly. Washing aids are not to be confused with hypo eliminators, which are no longer recommended, since recent research has shown that minute amounts of thiosulfate actually protect the silver image against environmental attack.

An alternative to using sodium sulfite alone is using it together with sodium bisulfite, which is done in commercial washing aids. This constitutes a compromise, as lower pH values reduce emulsion swelling in the wash, but lowering the alkalinity also reduces the rate of thiosulfate elimination. To prevent calcium precipitation and ‘print scum’, some sodium hexameta-phosphate, also known as Photo Calgon, may be added to the washing aid as a sequestering agent.

Toner

Unprotected metallic image silver is subjected to constant attacks by reducing and oxidizing agents in our environment. The mechanisms of image protection are not entirely understood, but the positive influence of sulfide and selenium on silver image permanence is certain. Toning baths, containing sodium sulfide, polysulfide or selenium, convert the image forming metallic silver into more stable silver compounds, such as silver sulfide and silver selenide, and sodium carbonate buffers the pH value in polysulfide toners.

The information presented in this chapter was not designed to withstand scientific scrutiny. Instead, it was purposely oversimplified to provide a brief overview and basic understanding of chemistry and photographic processes, while trying to avoid getting hopelessly lost in scientific detail. I trust this will make some more comfortable with photographic chemistry and instigate others to deepen their studies. Much of what has been presented here can be found in far more detail in an excellent book, called Photographic Chemistry by George T. Eaton, which is unfortunately out of print. I highly recommend finding a secondhand copy of this book to anybody interested in the subject of photographic chemistry.

fig.4a     The crisscross method is a simple technique of mixing two compatible liquids into a target solution of desired strength. It can be used to create a working solution from two existing stock solutions, or it may help to determine how a stock solution must be diluted to create the working solution.

fig.4b     In this example, 50% acetic acid is mixed with water (0%) at a ratio of 28/22 to create 28% acetic acid, by subtracting the working strength (c=28) from the stock strength (a=50) and the diluting strength (b=0) from the working strength (c=28) and knowing how many parts of each are required for the mixture.

 

Basic Chemical Formulae

The bare necessities of a life in the darkroom

Among the plethora of developers, fixers and toners are an essential few, which will persevere through fashion and commercial profitability. The following is a complete set of basic formulae, which are essential for archival processing. We do not recommend to anyone to prepare their own chemistry as a means of ‘saving money’, but if you have a hard time obtaining darkroom supplies in your area, or if you like to modify proven formulae in order to obtain unique characteristics, the information presented is a good starting point. To see the whole gamut of darkroom alchemy with all its opportunities and alternatives, get yourself a copy of The Darkroom Cookbook by Steve Anchell and The Film Developing Cookbook by Anchell and Troop, and add them to your photographic library. These books contain an unrivalled collection of photographic formulae and easy-to-understand explanations on how to use them.

Many chemical suppliers do not sell directly to the public, but there are several suppliers of photographic chemicals around the world selling directly to photographers, including Silverprint in the UK, Artcraft Chemicals, Bostick & Sullivan and The Photographers Formulary in the USA. If you have difficulty finding a qualified local source, start by talking to your neighborhood drugstore or pharmacy. They will be able to either point you into the right direction or may actually sell you most of what you need.

Equipment you need to get started:

1.   an old fashioned chemical balance or a modern electronic scale, accurate to at least ±0.1 grams and weighing up to 100 or 200 grams

2.   plastic syringes of up to 1, 5 and 10 ml to accurately measure very small liquid volumes

3.   a set of graduated cylinders, ranging from 30 ml to 1 liter for measuring liquids and solids

4.   plastic scoops for measuring out chemicals

5.   one to three plastic beakers, holding 1 and 2 liters each, for mixing working solutions

6.   a small and a large plastic stirring rod to keep undissolved chemicals in motion

7.   plastic funnels for pouring liquids into bottles

8.   a selection of brown glass or plastic bottles to store the solutions and labels to identify them

Initial Shopping List for Basic Chemicals

acetic acid (28%)	500 ml
ammonium thiosulfate	2 kg
borax (sodium tetraborate, decahydrate)	500 g
boric acid (granular)	250 g
citric acid	100 g
hydroquinone	250 g
metol	100 g
phenidone	25 g
potassium bromide	100 g
potassium ferricyanide	250 g
potassium iodide	50 g
potassium permanganate	10 g
potassium polysulfide (liver of sulfur)	100 g
silver nitrate	5 g
sodium carbonate (monohydrate)	1 kg
sodium hexametaphosphate (Photo Calgon)	100 g
sodium sulfite (anhydrous)	2 kg

   D-76 is a fine-grain, general-purpose film developer for maximum shadow detail. It was formulated in 1926 by Kodak and still is the standard by which all other developers are judged, because it offers the best compromise between speed, sharpness and resolution. Many deviations from this original formula have been proposed over the years. A recent suggestion is to omit hydroquinone and raise metol to 2.5 g, creating D-76H, an environmentally friendly and more stable developer.

   D-72 is a neutral-tone paper developer for brilliant highlights and maximum blacks, very similar to Kodak Dektol. Standard dilution for this developer is 1+2, but it can be diluted 1+1 for a longer shelf life and slightly higher Dmax, or 1+3 for warmer tones and softer shadows. It has excellent keeping properties and an outstanding development capacity. Replace with fresh developer as soon as factorial development fails to create potential Dmax.

   ID-78 is a warm-tone paper developer with a formulation very close to Ilford Warmtone and Agfa Neutol WA. It works well with all modern neutral and warm-tone papers on the market. Dissolve the phenidone separately in 50 ml of hot water (>80°C). Standard dilution for this developer is 1+3, but it can be used as strong as 1+1 for richer shadows. Replace with fresh developer as soon as factorial development fails to create potential Dmax.

   SB-7 is an odorless acid stop bath for film and paper processing. It quickly neutralizes the alkaline developer and brings development to a complete stop. Its capacity is approximately ten rolls of film or 8×10-inch prints per liter. Use prior to acid fixers, and precede alkaline fixers with a plain water rinse instead.

Film Developer (D-76 / ID-11)

distilled water 50°C / 120°F	750 ml
metol	2 g
sodium sulfite anhydrous	100 g
hydroquinone	5 g
borax decahydrate	2 g
cold distilled water to make	1,000 ml

---

dilute 1+1 for standard film development use as one-shot developer for processing consistency

Neutral Paper Developer (D-72)

water 50°C / 120°F	750 ml
metol	3 g
sodium sulfite anhydrous	45 g
hydroquinone	12 g
sodium carbonate monohydrate	80 g
potassium bromide	2 g
cold water to make	1,000 ml

---

dilute 1+2 for standard paper development very similar to Kodak Dektol

Warm-Tone Paper Developer (ID-78)

water 50°C / 120°F	750 ml
sodium sulfite anhydrous	50 g
hydroquinone	12 g
phenidone	0.5 g
sodium carbonate monohydrate	72 g
potassium bromide	4.5 g
cold water to make	1,000 ml

---

dilute 1+3 for warm-tone paper development very similar to Ilford Warmtone and Agfa Neutal WA

Stop Bath (SB-7)

water	750 ml
citric acid	15 g
water to make	1,000 ml

---

working solution for paper, dilute 1+1 for film

Acid Rapid Fixer (RF-1)

water 50°C / 120°F	750 ml
ammonium thiosulfate	120 g
sodium sulfite anhydrous	12 g
acetic acid 28%	32 ml
boric acid granular	7.5 g
cold water to make	1,000 ml

---

working solution for film and paper use two-bath fixing method for film and fiber-base paper with film, use as one-shot fixer for processing consistency

Alkaline Rapid Fixer (RF-2)

water 50°C / 120°F	750 ml
ammonium thiosulfate	120 g
sodium sulfite anhydrous	15 g
sodium carbonate monohydrate	0.7 g
cold water to make	1,000 ml

---

working solution for film and paper use two-bath fixing method for film and fiber-base paper with film, use as one-shot fixer for processing consistency

Hypo-Clearing Agent (HCA-1)

water 50°C / 120°F	750 ml
sodium sulfite anhydrous	100 g
sodium hexametaphosphate *	5 g
cold water to make	1,000 ml

---

dilute 1+4 for film or paper * add with hard water supplies to prevent calcium scum

Polysulfide Toner (T-8)

water	750 ml
potassium polysulfide	7.5 g
sodium carbonate monohydrate	2.5 g
water to make	1,000 ml

---

working solution for direct paper toning

   RF-1 is a non-hardening, acid, rapid fixer for film and paper. The omission of a hardener supports archival washing and makes it easier for spotting fluids to be absorbed by the print emulsion. Dissolve the boric acid separately in 80 ml of hot water (>80°C) and add last, or substitute with 9 g of sodium carbonate to create an almost odorless version of this fixer. We recommend using the two-bath fixing method for film and fiber-base paper, both at full fixer strength. The first fixing-bath capacity is approximately ten 8x10-inch prints per liter.

   RF-2 is a non-hardening, alkaline, rapid fixer for film and paper, supporting an odorless darkroom environment and significantly reducing washing times. To conduct an entirely acid-free process, do not use in combination with an acid stop bath. Instead, follow development by a 60s wash in plain water, and use the two-bath fixing method for film and fiber-base paper at full fixer strength. The first fixing-bath capacity is approximately ten 8x10-inch prints per liter.

   HCA-1 is a washing aid for film and paper, used subsequent to acid fixers. Treat films for 2 and papers for 10 minutes with slight agitation. Used after a preceding water rinse, the capacity is approximately twenty rolls of film or 8x10-inch prints per liter. With hard water supplies, add sodium hexametaphosphate (Photo Calgon) to prevent the formation of calcium scum on the emulsion surface.

   T-8 is a direct polysulfide toner for modern papers, similar to Kodak Brown Toner or Agfa Viradon, and can be used at room temperature. Wash fiber-base prints for 30 minutes without washing aid prior to toning. Please note that this toner produces toxic hydrogen sulfide gas, as well as the offensive odor that goes along with it. Only use with adequate ventilation.

   At this dilution, R-4 is a proportional reducer for film and paper. Apply with a brush to locally improve print highlights, or treat an entire film to reduce overall negative density. Use solutions in sequence or mix 1+1 just prior to use. Solution A will last for months, but if combined with solution B, the mixture will deteriorate within 10 minutes. Rinse film or paper thoroughly after use. Then, fix again and continue with normal processing.

   FT-1 is a fixer test solution when archival processing is not required. Add 1 ml to 10 ml of used fixer and stir, and discard the fixing bath if a cloudy, white precipitate forms in the mixture. For archival processing requirements, measure the silver content of the fixing bath with a professional silver estimator.

   HT-1 is a residual hypo test to verify the efficiency of film washing. 1 ml of the test solution is applied to 10 ml of the film’s last wash water. The resulting color change of the wash water depends on its thiosulfate content and becomes a rough measure of the emulsion’s residual thiosulfate level.

   HT-2 is a residual hypo test to verify the efficiency of print washing. The color stain left by the test solution is an indicator of the hypo level in the paper. HT2 contains light sensitive silver nitrate. Consequently, the entire test must be conducted under subdued tungsten light. Please note that silver nitrate requires 24 hours to completely dissolve.

Farmer’s Reducer (R-4)

Solution A
potassium ferricyanide	10 g
water to make	1,000 ml
Solution B
rapid fixer working solution	1,000 ml

---

use solutions in sequence or mix 1+1 just prior to use

Fixer Test Solution (FT-1)

water	80 ml
potassium iodide	5 g
water to make	100 ml

---

add 1 ml to 10 ml of used fixer

Residual Hypo Test (HT-1)

distilled water	80 ml
potassium permanganate	0.1 g
sodium carbonate monohydrate	0.2 g
distilled water to make	100 ml

---

add 1 ml to 10 ml of the film’s last wash water

Residual Hypo Test (HT-2)

water	80 ml
acetic acid 28%	12 ml
silver nitrate	0.8 g
water to make	100 ml

---

apply a drop to a damp print border for 5 minutes

 

Tables and Templates

A collection of useful look-up and conversion tables, and some templates to support your work

© 2008 by Thomas Bertilsson, all rights reserved

A considerable amount of scientific work and care has gone into the preparation of this book. All authors made an effort to take nothing for granted and challenged many photographic myths. To prove out these challenges, numerous tests were conducted, evaluated and archived. However, some material and processing conditions and their combinations are either not predictable, or depend entirely on the individual setup and material choices. Consequently, you may wish to conduct your own tests, which allows for individual calibration and provides you with confidence and knowledge about your own materials and techniques. Testing should be kept to a minimum; after all, the main purpose of our efforts is to create beautiful images and get them ready for display. Nevertheless, a few basic tests save time, material and frustration in the long run, while improving and assuring quality results and making our photography more enjoyable.

The tables and templates in this chapter are prepared to help you run a few experiments using your own photographic papers and films. Feel free to copy the individual pages from the book for your own test records and evaluations, but take care not to damage the book. Some templates are used as overlays and must be the same scale as the data sheets evaluated. If possible, copy overlays onto transparent material. Otherwise, use them in combination with the data sheets on a light table or against a window.

To obtain accurate and repeatable results, many tests rely on the availability of a reflection and transmission densitometer. We realize that such an instrument is a serious investment for any photographer, but its many uses will soon justify the purchase. Densitometers are often available from a friend or on the secondhand market. If all else fails, every 1-hour photo-lab has one to calibrate their systems, and the owner may be willing to take a few readings for you.

Standard Values for Negatives, Prints and Monitors

fig.1       Standard, normal development, Zone System density values for relative negative transmission and absolute print reflection, as well as digitally representative grayscale values for computer monitors set to 2.2 gamma, are shown in 1/3-stop increments.

f/stop Timing Table [s]

fig.2

Circle of Confusion / Typical Enlargements / Required Resolution

fig.3       Throughout the book, we make several references to standard and critical viewing conditions, the minimum circle of confusion, typical print enlargements and the lens, film or sensor resolutions required. The data compiled in these two tables are the foundation of our references.

Enlarger Magnification

fig.4       Negative magnification during enlargement depends on the distance between negative and paper as well as the focal length of the enlarging lens. Measure the negative-to-paper distance after focusing. Select this distance on the vertical axis and find its intersection with the focal length of the enlarging lens. Drop the intersection to the horizontal axis to find the magnification of enlargement.

Enlarger-Height Exposure Compensation

fig.5       Any adjustment to the enlarger height requires a change in the print exposure. This chart provides the means to determine the exposure compensation required without calculations. Measure the lens-to-paper distances before and after the adjustment to the enlarger. Then find the upper lens-to-paper distance on the vertical axis and the lower lens-to-paper distance on the horizontal axis of the chart. The intersection of the two will indicate the exposure compensation in f/stops. A previously verified exposure will have to be increased by the compensation if the enlarger was raised and decreased if it was lowered. The compensation can be applied either to the aperture of the enlarger lens or to the exposure time. The use of a separate f/stop timing table may be advantageous if a modification of the exposure time is preferred. It is recommended, and more practical, to make small modifications by changing the exposure time. Larger changes of 1 or 2 stops are easier made by modifying the aperture of the enlarger lens. This will also keep exposure times at manageable levels.

Temperature Conversion

fig.6       Celsius is a temperature scale named after the Swedish astronomer Anders Celsius (1701–1744), who developed it two years before his death. The Fahrenheit scale is named after the physicist Daniel Gabriel Fahrenheit (1686–1736) who proposed his scale in 1724. On the Celsius scale, 0 and 100°C are defined as the freezing and boiling points of water, both measured at standard atmospheric pressure. The Celsius scale has replaced Fahrenheit in most countries, with the exception of the USA and a few other nations, where most people are still accustomed to measuring temperatures in Fahrenheit.

Film Development Temperature Compensation

fig.7       To achieve consistent film development at different temperatures, a temperature coefficient (c) is used to calculate a new development time (t2) for a new temperature (T2) from an old development time (t1) and an old temperature (T1). For the table shown here, a coefficient of 2.5 was used to account for the temperature effect on D-23, D-76 and ID-11. In the column with your standard development temperature, find the row with your target development time. Follow that row, left or right, until you reach the column with the actual processing temperature and find the new development time. For example, if 10 minutes at 20ºC is your standard film development process, you need to reduce the development time to 6 minutes and 20 seconds if the processing temperature changes to 25°C.

Paper Characteristic Curves

fig.8       This template is used to chart paper characteristic curves. First, record the paper specifications and contrast-filtration method. Then, conduct the test as described in ‘Measuring Paper Contrast’ and chart the data on one of these sheets. Use the template in fig.12 as an overlay to measure the log exposure range and the table in fig.9 to determine the corresponding ISO grade.

(do not change the scale of this template)

Paper Log Exposure Range / Standard ISO Paper Grade

fig.9       There is a numerical relationship between standard ISO paper grades (ISO) and the paper’s log exposure range (log ER or LER).

Film Characteristic Curves

fig.10     This template is used to chart film characteristic curves. First, record the film and development specifications. Then, conduct the test as described in ‘Customizing Film Speed and Development’ and chart the data on one of these sheets. Use the template in fig.13 as an overlay to measure the average gradient and the table in fig.11 to determine the corresponding zone modification.

(do not change the scale of this template)

Film Average Gradient, Zone System and Subject Brightness Range

fig.11     There is a numerical relationship between the average gradient, the zone modification (N) and the potential subject brightness range (SBR).

Paper Range and Grade Meter

fig.12     This template is used as an overlay to measure a paper’s log exposure range in combination with fig.8.

(copy onto transparent material but do not change the scale of this template)

Film Average Gradient Meter

fig.13     This template is used as an overlay to measure a film’s average gradient in combination with fig.10.

(copy onto transparent material but do not change the scale of this template)

Film Test Summary

fig.14     Serious Zone System practitioners want to calibrate their favorite film/developer combinations to customized conditions. Once accomplished, most lighting conditions can be mastered with confidence and ease, rendering any negative a hassle-free printing assignment, while leaving paper grade latitude to imagination and providing maximum flexibility for creative interpretation. In ‘Customizing Film Speed and Development’, a detailed description of custom calibration was given, and figures 10, 11 and 13 provide the table and templates required to create the required information, so they can be summarized and completed here.

Bellows Target and Rulers

fig.15     View camera users copy the target (top) and the two rulers (below) onto separate pieces of heavy paper stock. Assemble the rulers back-to-back, and laminate each piece with clear tape to make a more durable tool. For close-up photography, place the target into the scene, and measure the diameter of the outer circle on the view screen with the bottom ruler. Determine subject magnification and f/stop correction to adjust exposure by opening lens aperture or extend shutter exposure. The inner circle, in combination with the top ruler, is provided for extreme close-up photography.

(do not change the scale of these templates)

The Zone Dial

fig.16     The Zone Dial provides a visual reference to the way subject brightness will be represented in the final print. Zone III and VII are marked to place shadow and highlight details, and the tonality extremes of Zone I•5 and VIII•5 are identified as black and white points. All scales are in standard shutter speeds, f/stops and EVs. Meter the subject values in EVs, and correlate them to the intended Zones on the dial. This will give you an overview of the subject brightness range and several exposure recommendations. However, potential reciprocity failure has not been accounted for.

Exposure, Development and Printing Record

fig.17     Keeping accurate exposure and printing records are bureaucratic tasks many photographers avoid due to the initial workload required to obtain them. They do, however, provide significant clues to the ‘things gone wrong’ and allow for a certain repeatability of the overall photographic process. In ‘Exposure, Development and Printing Records’, we explained how to take them. This template provides the means to keep them.

The Paper-Grade Dial

fig.18     The Paper-Grade Dial provides a simple method to calculate the overall paper contrast required to transfer the negative density range to the print density range. Using a densitometer or a simple enlarger meter, take a textural highlight reading and set the negative density or measured exposure time on the dial. Then, take a textural shadow reading, and next to its location on the dial, read off the required ISO paper grade to capture the entire textural negative density range on paper.

Pinhole and Zone Plate Pattern

fig.19     Photon sieves and diffraction zone plates (bottom) are worthwhile alternatives to plain pinholes, but they cannot be cut or drilled like a simple hole. The best way of making them is to take an enlarged, tone-reversed design and photograph it onto high-contrast B&W film thus reducing it to the desired size. The two designs shown here have a center pinhole diameter of 25 mm. Using the equations above, photograph these designs with a focal length (f) from a lens-to-design distance (u), or a film-to-design distance (a), in order to reduce the patterns by a known magnification (m), and create the required size on transparent film.

The Pinhole Dial

fig.20     The Pinhole Dial provides a visual reference to the way subject brightness will be represented in the pinhole print. Zone III and VII are marked to place shadow and highlight details, and the tonality extremes of Zone I•5 and VIII•5 are identified as black and white points. All scales are in standard shutter speeds, f/stops and EVs. Meter the subject values in EVs, and correlate them to the intended Zones on the dial. This will give you an overview of the subject brightness range and several exposure recommendations. However, potential reciprocity failure has not been accounted for.

Drawing for Laser-Jig Housing

fig.21     With some ingenuity and help from a local machine shop, a do-it-yourself laser-alignment tool is brought from concept to reality. Three adjustable screws level the unit and align the laser module until it projects a perfectly vertical laser beam.

Transfer Functions

fig.22     The purpose of a transfer function is to bring the subjective tone-reproduction cycle full circle, and closely match the final print to the on-screen image. To do so, a transfer function must correct for the differences between the actual and the desired process characteristics. These are listed as absolute target densities for two different rendering intents. Target density curve ‘2.2a’ (left) is designed for normal processing with normal shadow detail, followed by moderate archival toning. Target density curve ‘2.2c’ (far left) compensates for heavy toning or provides emphasized shadow detail. Once collected, the input and output values are entered into the ‘Curves’ adjustment dialog box of your photo editing software and saved as a transfer function for future use.