Exposure Calculator

One of the first tasks when getting a properly calibrated digital negative is to find the exposure time that has just enough exposure to create the maximum black tones that the process is capable of delivering.

Materials and equipment

Inkjet negative material

You will need a small piece of the transparent inkjet negative material you plan to use for making the negatives. There are several alternatives such as Pictorico Premium OHP, Pictorico Ultra OHP, Fixxons, and Lexjet polyester transparent film. The choices here will be determined by the anticipated maximum ink load for your negatives and cost. For most processes short of those requiring very density range negatives, pick something cheap that has predictable quality. Some processes such as salt prints fall into the category of processes that need very high inkloads, and transparency material able to absorb very high inkloads without smearing will be necessary.

Paper to be calibrated

To conduct this test, you will need a coated/sensitized piece of paper that is ready to expose. This paper should be ready to go and created in exactly the same way you intend to make all your future prints in the process you have chosen.

Consistent and repeatable light source

You will need a light source appropriate for exposing your process, and way of measuring the duration of the exposure. If you have a fluorescent or LED UV light box, generally a timer can be used making consistent exposures. One note on fluorescents: they have a little bit of a warm-up ramp where the light intensity increases for a short amount of time right after they are turned on. To get consistent exposures, I find it helpful to turn on the light in the box and leave it on during any printing session.

UV-LED boxes don’t have this same ramp-up of light intensity and can be switched on and off.

If you have a plateburner-type exposure unit, it has built in light integrator that measures the total amount of light for a given exposure. These units typically have metal-halide lamps which have considerable light intensity variations that change both during the exposure and also longer term as the bulbs age.

If the sun is the planned exposure light source, pick a sunny day and try to expose between 10AM and 2PM when the sun’s UV intensity is it at its peak and relatively stable. For the most repeatable results, get a Light Measure UV exposure meter from here, and use it to measure the total dose of UV light your printing frame is receiving. These are super handy items because they allow you to expose your photos on cloudy days and at either end of the day where the UV light emitted by the sun is reduced.

Stouffer’s step wedges - an extended explanation

A Stouffer’s tranmission step wedge is the final item you need to acquire. These come in 21, 31, and 41 step varieties. They can be purchased directly from Stouffer’s here. Another source for the 31-step variety is from Mark Nelson at Precision Digital Negatives here. Either the 21 step or the 31 step will be all you need for this test. (Stouffer’s T2115 or T3110).

The main difference in these two varieties is the amount of transmission density change between each step. The 21 step wedge has a density difference of 0.15 between each step. The 31 step wedge has a difference of 0.10 between each step.

Most photographers are familiar with the term ‘stop’, which when talking about the aperture on a camera indicates a halving or doubling of the amount of light as the aperture is reduced or increased. On a camera’s aperture ring, going from F/8 to F/11 is reducing the amount of light by half, whereas going from f/8 to f/5.6 doubles the amount of light reaching the film (or sensor in the case of digital).

Photography is awash in procedures that depend on this halving and doubling of exposure values. This is the reason that almost all transmission measurements are done in log_{base 2} units. You will see many references to measurements in log_D units.

This means that we are dealing with exponents on a base number of 2. A ‘stop’ is simply the exponent part of this number. A 2-stop increase in the amount of light is therefore \(2^2\) or 4 times the exposure. A 4-stop increase is \(2^4\) or 16 times the exposure!

On a transmission step wedge, a full-stop change is represented by the a change in transmission density of 0.3. Therefore, a 21 step wedge will have two steps for each stop \((0.15 \times 2)\), whereas a 31 step tablets will have three steps per stop \((0.10 \times 3)\).

Procedure

Figuring out the correct minimum time for maximum black exposure value is straightforward. Coat or prepare a print using your chosen process. Arrange the ready-to-expose print with the inkjet transparency material you intend to use covering half of the sensitized print surface. Place the step wedge on top of those two materials so that it straddles the line between the part of the print that is covered by the inkjet material and the part that is not.

We can take advantage of this predictable progression of densities to enable us to figure out the exposure value (time or units) that will be the bare minimum necessary to generate the darkest black tone from light going through the inkjet material and striking your sensitized printing paper.

If we radically overexpose the print through both the step tablet and the inkjet material, we can find the first step in the progression of solid black steps that is located just before a step that has a lighter tone of gray. By counting the number of steps, we can use that information to calculate an exposure factor to multiply times the exposure value used to over-expose the print material.

For instance, say we are using a 21-step tablet, and the last solid black tone before the tones go from black to dark-dark gray is step 4. That means that we have \((0.15 \times 4 = 0.60)\) exposure difference between the actual overexposed exposure value and the smaller amount of exposure that is needed to make a convincing black tone.

The math on calculating this is this:

\[\text{where } ET = \text{ target exposure value}\] \[\text{and}\] \[OT = \text {the overexposure test exposure value}\] \[s = \text{the number of steps to last full black value}\] \[sv = \text{the number of steps per stop, i.e. 2 for a 21-step or 3 for a 31-step tablet}\] \[ET = OT \times {2^{\large{-{s \over sv}}}}\]

So, for instance, if you exposed the strip for 15 minutes, and the last step that is pure black is step 4 on a 21-step tablet, then:

\[ET = 15 \times {2^{\large{-({4 \over 2})}}} = 15 \times {2^{-2}} = 15 \times 0.25 = 3.75\space minutes\]

The exposure time necessary to generate a solid black in your chosen print medium is 3.75 minutes ( 3 minutes and 45 seconds).

The following is a link to a very rudimentary Excel spreadsheet where the values can be entered and the new exposure is calculated : link.