Stepchart

Measures tonal response, noise, and dynamic range using step charts

Imatest™ Stepchart analyzes the tonal response, noise, and dynamic range of digital cameras and scanners using

• reflection step charts such as the Kodak Q-13 and Q-14 Gray Scales (below, right), the Jessops Colour & Mono Separation Guide (UK), or any of several charts from Danes-Picta (Czech republic),
• transmission step charts from Stouffer, Kodak, Danes-Picta, Esser Test Charts, or
• Charts from Applied Image and additional ISO charts, shown below. (Imatest Master only; starting with version 1.7)

Stepchart can also measure veiling glare (lens flare) using reflection step charts. Results are more detailed than those provided by Colorcheck. Transmission step charts are recommended for measuring dynamic range. Full instructions can be found on Using Stepchart. Noise is explained in Noise in photographic images.

Applied Image and ISO charts: Imatest Master only
QA-61 ISO- 16067-1 Scanner	QA-62	ST-51 EIA Grayscale	ST-52 ISO-14524 12-patch OECF target	ISO-15739 Noise target
	20-patch OECF targets	ITE Grayscale

To run Stepchart, photograph the chart, taking care to avoid glare (shiny reflections). Scale the image for 50 pixels per zone for greatest noise analysis accuracy; 20 pixels per zone is adequate in most cases. Fewer are OK for tonal response curves. Load the image file, crop it (if needed), then specify the target density step and type (reflective or tramsmission). The default is a reflective target with density step = 0.1.

The two Figures below illustrate the results of analyzing a Q-13 image photographed with the Canon EOS-10D at ISO 100. A third figure (not shown here) displays density response for all channels (Y, R, G, and B) in color images.

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 acvite areas used for the analysis is shown as think pale pink bars. The lower plot shows the RMS noise for each patch: R, G, B, and Y (luminance), expressed as the percentage of the pixel level difference corresponding to a target density range of 1.5: the same as the white - black patches on the GretagMacbeth ColorChecker. For this camera, the pixel difference is 197.5. Noise measured in pixels can be calculated by multiplying the percentage noise by 197.5. Noise can also be normalized to the maximum pixel level (255). The average noise for each channel (excluding the lightest and darkest zones) is displayed. See Noise in photographic images for a detailed explanation of noise.

The second Figure

contains the most important results:

• the response curve displayed on a log scale, similar to film response curves,
• noise expressed units of f-stops (the same as EV), explained below, or SNR (Signal-to-Noise Ratio), explained here,
• noise in normalized pixel levels
• dynamic range (for transmission step charts),
• the noise spectrum.

The horizontal axis for the three plots is Log Exposure, which equals (–) the nominal target density (0.05 - 1.95 for the Q-13/Q-14). This axis is reversed from Figure 1.

SNR (S/N = 1/f-stop noise), in middle-left plot in place of f-stop noise.

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; effective ΔL tends to be larger in dark areas of scenes and prints 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)) = 1/SNR where  d(pixel)/d(f-stop) is the derivative of the pixel level with respect to luminance measured in f-stops (~log2(luminance) ).           SNR is the Signal-to-Noise Ratio. The above-right image illustrates how the pixel spacing between f-stops (and hence d(pixel)/d(f-stop)) decreases with decreasing brightness. This causes f-stop noise to increase with decreasing brightness, visible in the middle-left plot of the second figure, above. Since 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 when sensor RAW data is unavailable.

Dynamic range

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

• The total range. Stepchart measures a camera's total dynamic range, including noisy dark areas.
• A range of tones over which the RMS noise, measured in f-stops, is under a maximum specified value. The lower the maximum noise value, the better the image quality, but the smaller the dynamic range. Noise tends to be worst in the darkest regions. Imatest calculates the dynamic range for several maximum noise levels, from RMS noise = 0.1 f-stop (high image quality) to 1 f-stop (relatively low quality).
  

Dynamic range is measured using transmission step charts, which have density ranges of at least 3.0: a 1000:1 ratio (10 f-stops). Reflective charts such as the Q-13 have a density range of only around 1.90; an 80:1 ratio (6.3 f-stops), insufficient for digital cameras. Two charts are recommended for digital SLRs, which can have over 10 f-stops of total dynamic range.

• The Stouffer T4110 transmission step wedge, which has a maximum density of 4.05 (41 steps, 0.1 density increment, 13.3 f-stops dynamic range)
• The Danes-Picta TS28D (on their Digital Imaging page), which has a maximum density of 4.2 ( 28 steps, 0.15 density increment, 13.6 f-stops dynamic range)

The dynamic range is the difference in density between the zone where the pixel level is 98% of its maximum value (250 our of 255 for 24-bit color), estimated by interpolation, and the darkest zone that meets the measurement criterion. The repeatability of this measurement is around 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 8.58 f-stops (probably limited by the target; the Stouffer T4110 or Danes-Picta TS28D would have done a better job). It is displayed at the bottom of the upper-left plot (Density response). 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.

A medium quality image can ge achieved over a range of 8.21 f-stops out of a total dynamic range of 8.58 f-stops. When a high quality image is required (maximum noise = 0.1 f-stops), the dynamic range is reduced to 5.97 f-stops (indicated by the yellow line on the middle left plot). The best slide films have a total dynamic range of 5 to 6 f-stops.

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. Roger N. Clark, a space scientist and avid photographer has done a study of dynamic range. He finds digital (SLRs) to be superior to film.

Scanner results

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

A few observations on the scanner results:

• All 20 steps of the Kodak step tablet were detected. The total dynamic range is greater than 3 density units (the 10 f-stop range of the tablet). To determine the true total dynamic range we would need the Stouffer T4110 step wedge, which has a maximum density of 4.
• The response closely follows an exponential curve with gamma = 0.506. No "S" curve has been superposed.
• The practical dynamic range is limited by noise. It is 9.62 f-stops (2.9 density units) for a medium quality image.
• The flat noise spectrum indicates that no software noise reduction has been applied. Most digital cameras have rolloffs in their noise spectra due to Bayer interpolation and noise reduction.