Q-13 Stepchart

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

Results are more detailed than those provided by Colorcheck. Transmission step charts are required for measuring dynamic range.

To run Q-13 Stepchart, load the image file, crop it (if needed), then specify the target density step (if different from the default value of 0.1 for reflective targets).

The two Figures below illustrate the results of analyzing a Q-13 image photographed with the Canon EOS-10D at ISO 100.

The first figure

contains basic tonal response and noise measurements.

The horizontal axis for both plots is the chart zone— proportional to the distance along the chart. Density (–Log Exposure) increases by a fixed step (0.10 or 0.15, depending on the target) for each zone.

The upper plot shows the normalized pixel level of the grayscale patches (black curve) and first and second order density fits (dashed blue and green curves). Gamma is derived from the first order fit.

The lower plot shows the RMS noise for each patch: for R, G, B, and Y (luminance) channels, 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 average noise for each channel (excluding the lightest and darkest zones) is displayed.

The second Figure

contains the most important results:

The horizontal axis for all three plots on the left is Log Exposure, which equals (–) the nominal target density (0.05 - 1.95 for the Q-13/Q-14).

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.

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 f-stop noise. This measurement corresponds to the response of the eye and has important consequences for the calculation of practical dynamic range. The vertical axis is logarithmic for clear display of low noise values.
EXIF data is shown in the middle right region (JPEG files only).
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.

Why measure noise in f-stops?

Because the human eye responds to relative luminance differences. That's why we think of exposure in terms of zones, f-stops, or EV (exposure value), where a change of one unit corresponds to halving or doubling the exposure.

The eye's relative sensitivity is expressed by the Weber-Fechner law,

    ΔL ≈ 0.01 L   –or–   ΔL/L ≈ 0.01

where ΔL is the smallest luminance difference the eye can distinguish.
(This equation is approximate; ΔL tends to be larger in dark areas of scenes due to visual interference from bright areas.)

Expressing noise in relative luminance units, such as f-stops, corresponds more closely to the eye's response than standard pixel or voltage units. Noise in f-stops is obtained by dividing the noise in pixels by the number of pixels per f-stop
. (I use "f-stop" rather than "zone" or "EV" out of habit; any of them are OK.)
noise in f-stops = noise in pixels / (d(pixel)/d(f-stop))
d(pixel)/d(f-stop) is the derivative of the pixel level with respect to luminance measured in f-stops (~log2(luminance) ).
The above-right image illustrates how the pixel spacing between f-stops (and hence d(pixel)/d(f-stop)) decreases with decreasing brightness. This results in an increase of f-stop noise with brightness, visible in the middle-left plot of the second figure, above.

Because luminance noise (measured in f-stops) is referenced to relative scene luminance, independently of electronic processing or pixel levels, it is a universal measurement that can be used to compare digital sensor quality.

Dynamic range

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

Dynamic range is measured using transmission step charts because they have density ranges of at least 3.0: a 1000:1 ratio (10 f-stops), sufficient for digital cameras. Reflective charts such as the Q-13 have a density range of only around 1.90; an 80:1 ratio (6.3 f-stops).

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 1/3 f-stop.

The figure below illustrates results for the Canon EOS-10D, taken from a JPEG image acquired at ISO 400 and converted with Canon Zoom Browser set for low contrast. A Kodak step tablet (density from 0.05 to 3.05 in steps of 0.15) was used. The total dynamic range is 8.6 f-stops. Total dynamic range changes little for 48-bit TIFF conversion or ISO 100. But 48-bit TIFF conversion has lower noise, hence higher dynamic range at any given quality level.

Because the maximum noise is 0.44 f-stops (in the darkest region), a medium quality image can be achieved when the full dynamic range (8.6 f-stops) is utilized. When a high quality image is required (maximum noise = 0.1 f-stops), the dynamic range is reduced to 6 f-stops (indicated by the yellow line on the middle left plot). High quality slide film has a total dynamic range of 5 to 6 f-stops.

Dynamic range detail for transmission stepchart
The second plot contains all important Stepchart results.

The shape of the response curve depends strongly on the conversion software and settings.

Compact digital cameras have much higher noise levels, hence lower useful dynamic range, even though their total dynamic range may be quite large.

Scanner results

Here are the results of scanning the Kodak step tablet with the Epson 3200 scanner set for negatives.

A few observations on the scanner results: