Introducing Q-13 Stepchart

Q-13 Stepchart analyzes the tonal response, noise, and dynamic range of digital cameras and scanners using

Q-13 Stepchart produces more detailed results than Colorcheck.

The Kodak Q-13 Gray Scale is an 8 inch long chart consisting of 20 zones, labeled 0-19, which have optical densities from 0.05 to 1.95 in steps of 0.1 (reflectances from 0.891 to 0.011). The chart is printed on a (semigloss) surface. The Jessops chart, from the UK, is similar to the Q-13, except that it has only 18 zones.

This image of the Q-13 Gray Scale was photographed slightly out of focus to minimize noise. Image of the Q-13 Gray scale

The Q-13 has finer steps and a higher maximum density than the GretagMacbeth ColorChecker (Dmax = 1.95 vs. 1.5), mostly because of its glossier surface. It considerably less expensive. Kodak also makes a 14 inch long Q-14, which is identical with the Q-13 except for its length. It can be used in exactly the same way. It's well suited for photographing next to slanted-edge SFR test targets.

Iliah Borg has analyzed the Q-13 Gray Scale. He says, "I'm pretty sure it's screen-printed, most likely with automotive enamel. The spectral response is flat from 420 to 730nm, similar to titanium dioxide mixed with carbon in different proportions to achieve different reflectivities. The layer is pretty thick, to isolate from the substrate."

Q-13 Stepchart also analyzes transmission (i.e., film) charts, which have higher maximum densities than reflective charts, making them valuable for measuring the dynamic range of digital cameras and scanners, as discussed below, in the section on Dynamic range.

Photographing the chart and running Q-13 Stepchart

Output

The example was photographed with the Canon EOS-10D at ISO 100 and converted from RAW format using Capture One with default settings (no curves applied).

The results include tonal response and noise. Colorcheck produces a similar result, but with less tonal detail. Two figures are produced.


First Figure

The upper plot shows the average density of the Q-13 grayscale patches (black curve) and first and second order density fits (dashed blue and green curves). The horizontal axis is the distance along the target. A portion of the patches themselves are shown just above the plot. The equations for the density fits are given in the Algorithm section, below. The second order fit closely matches the patches. The light cyan spikes are the differentiated and smoothed steps used to find the boundaries between zones.

The lower plot shows the RMS noise for each patch: R, G, B, and Y (luminance), expressed as the percentage of the range of pixel levels corresponding to a target density range of 1.5: the same as the white - black patches on the ColorChecker. The high levels of Red and Blue noise in zones 1-6 may be due to imperfections in the target. These imperfections are completely swamped by the noise at ISO 1600, below. Noise is largest in the dark areas because of gamma distortion: In the conversion from the sensor's linear output to the color space (sRGB, here) intended for viewing at gamma = 2.2, the dark areas are amplified more than the light areas, hence their noise appears to be greater.

The second Figure contains the most important of the results: the response curve (displayed on a log scale, similar to film response curves), the noise expressed in two different ways (most meaningful as a fraction of an f-stop or EV), and the dynamic range (for transmission step charts). The horizontal axis for the three plots on the left is Log Exposure, which equals (minus) the nominal target density (0.05 - 1.95 for the Q-13).

The upper left plot shows the density response (gray squares), as well as the first and second order fits (dashed blue and green lines). It resembles a traditional film density response curve. Dynamic range is grayed out because the reflective Q-13 target has too small a dynamic range to measure a camera's total dynamic range. See Dynamic range, below.
The upper right box contains dynamic range results: total dynamic range and range for several quality levels, based on luminance (Y) noise. It is shown in gray when a reflective target is selected.
Second figure
The middle left plot shows noise in f-stops (or EV) , i.e., noise scaled to (divided by) the difference in pixel levels between f-stops, which decreases as brightness decreases. The darkest levels have the highest noise. This measurement corresponds to the workings of the eye and has important consequences for the calculation of practical dynamic range. The vertical axis is logarithmic to display low noise levels clearly. Dynamic range information is displayed when the range for a specific quality level (defined by maximum noise) is within the range of the plot..
EXIF data is shown in the middle right region.
The bottom left plot shows the noise scaled to the difference in pixel levels between the maximum density level and the patch corresponding to a density of 1.5 the same density range as the GretagMacbeth Colorchecker. It may be less visually meaningful then the middle plot.
The lower right plot shows the noise spectrum. Digital camera images with excessive noise reduction will have an unusually rapid falloff of the noise spectrum.

Here are the results for ISO 1600. Tonal response is similar to ISO 100, but the noise is greatly increased— enough to swamp out any imperfections in the target. The noise is highly visible. It wouldn't be suitable for portraits and other high quality work, but it would be acceptable when a grainy "Tri-X" or "available light" look is desired. Neat image can do an excellent job of reducing it. The middle-left plot displays dynamic range for several quality levels, specified by the maximum noise within the range. The dynamic range for low quality (L; blue) has a maximum noise of 1 f-stop; the dynamic range for high quality (H; yellow) has a maximum noise of 0.1 f-stop.


Saving the results

When the Q-13 Stepchart calculations are complete, the Save results? dialog box appears, which allows you to choose where to save them. The default is subdirectory Results in the data file directory. After you click on Yes or No, the Imatest main window reappears.

Dynamic range of cameras and scanners

Dynamic range is the range of tones over which a camera responds. It is usually measured in f-stops, or equivalently, zones or EV. It can be specified in two ways:

A camera's (or scanner's) dynamic range can be accurately measured using a transmission step chart. A reflection step chart, such as the Kodak Q-13 or Q-14 is inadequate because its density range of 1.9 is equivalent to 1.9 * 3.32 = 6.3 f-stops, well below that of most digital cameras.

The table below lists several transmission step charts, all of which have a density range of at least 3 (10 f-stops). Kodak Photographic Step Tablets can be purchased calibrated or uncalibrated. Uncalibrated is usually sufficient. The Stouffer charts are attractively priced.

 
Product Steps Density increment Dmax Size
Kodak Photographic Step Tablet
No. 2 or 3
21 0.15 (1/2 f-stop) 3.05 1x5.5" (#2)
larger (#3)
Stouffer Transmission Step Wedge T2115 21 0.15 (1/2 f-stop) 3.05 0.5x5"
Stouffer Transmission Step Wedge T3110 31 0.1  (1/3 f-stop) 3.05 3/4x8"
Stouffer Transmission Step Wedge T4110 41 0.1  (1/3 f-stop) 4.05 1x9"

To measure dynamic range,

The Imatest algorithm for finding dynamic range is remarkably accurate. Imatest detects chart zones using the smallest density step that results in uniformly spaced detected zones (see Algorithm). For smaller steps, noise can be mistaken for zone boundaries. For larger steps, fewer zones are detected.

The dynamic range is the difference in density between the zone where the pixel level is 98% of its maximum value (250 for 24-bit color, where the maximum is 255), estimated by interpolation, and the darkest zone that meets the measurement criterion. The repeatability of this measurement is better than 1/4 f-stop.

Here is a result for the Canon EOS-10D at ISO 400, converted from RAW format with Capture One LE.

The total dynamic range of the Canon EOS-10D is 8.6 f-stops. Total dynamic range improves slightly for 48-bit TIFF conversion but very little for ISO 100. But the lower noise in 48-bit TIFF conversion and ISO 100 results in improved dynamic ranges for given quality levels.


The shape of the response curve is a strong function of the conversion software settings. The plot on the right is for Canon Zoom Browser with Contrast set to Low: the transfer curve is very different from Capture One LE, but the dynamic range is quite close— the result of slightly different noise reduction processing.

 
Algorithm
  • Locate the distinct zones in the image. This is done by taking the derivative of the pixel level averaged vertically, then smoothing it, illustrated by the light cyan spikes in the upper left plots in the above figures. A boundary between zones is detected if this function goes above a threshold. The threshold is adjusted to the lowest value that gives evenly spaced, regular intervals. This is an optimum detection algorithm: a lower threshold detects false boundaries (i.e., noise), while a higher threshold can miss valid zones.
  • Find regions of interest (ROIs) for each zone, which comprises the central 2/3 of the zone.
  • Calculate statistics for the ROIs, including the average pixel level and a second order polynomial fit to the pixel levels inside the ROIs this fit is subtracted from the pixel levels for calculating noise. It removes the effects of nonuniform illumination.
  • Calculate the noise in each ROI.
  • Using the average pixel values of the regions whose value is 10% below the maximum and above theminum, the average pixel response is fit to a mathematical function (actually, two functions). This requires some explanation.
  • Using the average pixel values of grayscale zones for densities between approximately 0.1 and 0.9 (omitting the extremes near white and black), the average pixel response is fit to a mathematical function (actually, two functions). This requires some explanation.

  • A simplified equation for a capture device (camera or scanner) response is,
      normalized pixel level = (pixel level/255) = k1 exposuregamc
    Gamc is the gamma of the capture device. Monitors also have gamma = gamm defined by
      monitor luminance = (pixel level/255)gamm
    Both gammas affect the final image contrast,
      System gamma = gamc * gamm
    Gamc is typically around 0.5 = 1/2 for digital cameras. Gamm is 1.8 for Macintosh systems; gamm is 2.2 for Windows systems and several well known color spaces (sRGB, Adobe RGB 1998, etc.). Images tend to look best when system gamma is somewhat larger than 1.0, though this may not hold for contrasty scenes. For more on gamma, see Glossary, Using Imatest SFR, and Monitor calibration.
    Using the equation, density = - log10(exposure) + k,
      log10(normalized pixel level) = log10( k1 exposuregamc ) = k2 - gamc * density
    This is a nice first order equation with slope gamc, represented by the blue dashed curves in the figure. But it's not very accurate. A second order equation works much better:
      log10(normalized pixel level) = k3 + k4 * density + k5 * density2
    k3, k4, and k5 are found using second order regression and plotted in the green dashed curves. The second order fit works extremely well.