Glossary

In Foveon sensors (used in Sigma cameras), each pixel site is sensitive to all three colors. Foveon sensors are less susceptible to color aliasing than Bayer sensors; they can tolerate greater response above Nyquist with fewer ill effects.

      1 f-stop (1 EV) = 0.301 density units;   1 density unit = 3.32 f-stops (EV).

When an object is photographed, Log₁₀ Exposure = –density + k. (Constant k is generally ignored.)

1. In Imatest results, “exposure” is the amount of light reaching a region of the sensor. Imatest plots often use Log Exposure (where Log is log₁₀ in this context) because the human eye’s response is roughly logarithmic. For test chart images, Log exposure is proportional to −optical density.

2. In other contexts “exposure” may refer to the combination of exposure time and lens aperture, which can be expressed quantitatively in EV.

(Here in Boulder, Colorado, residents prefer to use “enlightenment”, which is based on natural logarithms (log_e, where e = 2.71828…). Boulderites strongly prefer products labeled “natural”, “organic”, or “green”, or prefixed “eco-“, “enviro-“, etc. 1 Enlightenment Unit (€) = 0.4343 Density units = 1.443 EV.)

F-stop = focal length / aperture diameter. The notation, “f/8,” implies (aperture diameter = ) focal length/8. The larger the f-stop number, the smaller the aperture. F-stops are typically labeled in the following sequence, where the admitted light decreases by half for each stop: 1, 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, 32, 45, 64, … Each f-stop is the previous f-stop multiplied by the square root of 2.

Gamma is equivalent to contrast. This can be observed in traditional film curves, which are displayed on logarithmic scales (typically, density (log₁₀(absorbed light) vs. log₁₀(exposure)). Gamma is the average slope of this curve (excluding the “toe” and “shoulder” regions near the ends of the curve), i.e., the contrast. See Kodak’s definition in Sensitometric and Image-Structure Data. For more detail, see the descriptions of gamma in Using Imatest SFR and Monitor calibration.

For digital cameras, log pixel level is plotted as a function of log exposure (– chart density). Gamma is the average slope of this curve, excluding the brightest (often saturated) and darkest (not visually significant) patches. For example, for the Colorchecker, patches 2-5 of the bottom row (patches 20-23 of the entire chart; light to dark gray) are used.

Confusion factor: Digital cameras output may not follow an exact gamma (exponential) curve: A tone reproduction curve (usually an “S” curve) may be superposed on the gamma curve to boost visual contrast without sacrificing dynamic range. Such curves boost contrast in middle tones while reducing it in highlights and shadows. Tone reproduction curves may also be adaptive: camera gamma may be increased for low contrast scenes and decreased for contrasty scenes. (Hewlett-Packard advertises this technology.) This can affect the accuracy of SFR measurements. But it’s not a bad idea for image making: it’s quite similar to the development adjustments (N-1, N, N+1, etc.) Ansel Adams used in his zone system.

Noise is measured as an RMS value (root mean square; an indication of noise power, equivalent to standard deviation, sigma).
It is usually expressed in volts, millivolts, or pixel levels (in a digital file). In Stepchart and Colorcheck, noise is converted to relative luminance units (f-stops), which may provide a more meaningful indication of its visual impact.

Software noise reduction, used to reduce the visual impact of noise, is a form of lowpass filtering (smoothing) applied to portions of the image that to not contain contrasty features (edges, etc.). It can cause a loss of low contrast detail at high spatial frequencies. The Log F-Contrast module was designed to measure this loss.

The visual impact of noise is also affected by the size of the image— the larger the image (the greater the magnification), the more important noise becomes. Since noise tends to be most visible at medium spatial (actually angular) frequencies where the eye’s Contrast Sensitivity Function is large, the noise spectrum has some importance (though it is difficult to interpret). To learn more, go to Noise in photographic images.

The highest spatial frequency where a digital sensor can capture real information. Nyquist frequency f_N = 1/(2 * pixel spacing) = 0.5 cycles/pixel. Any information above f_N that reaches the sensor is aliased to lower frequencies, creating potentially disturbing Moire patterns. Aliasing can be particularly objectionable in Bayer sensors in digital cameras, where it appears as color bands. The ideal lens/sensor system would have MTF = 1 below Nyquist and MTF = 0 above it. Unfortunately this is not achievable in optical systems; the design of anti-aliasing (lowpass) filters always involves a tradeoff that compromises sharpness.

In this simplified example, sensor pixels are shown as alternating white and cyan zones in the middle row. By definition, the Nyquist frequency is 1 cycle in 2 pixels. The signal (top row; 3 cycles in 4 pixels) is 3/2 the Nyquist frequency, but the sensor response (bottom row) is half the Nyquist frequency (1 cycle in 4 pixels)— the wrong frequency. It is aliased.

A large MTF response above f_N can indicate potential problems with aliasing, but the visibility of the aliasing is much worse when it arises from the sensor (Moire patterns) than it is when it arises from sharpening (jagged edges; not as bad). It is not easy to tell from MTF curves exactly which of these effects dominates. The Nyquist sampling theorem and aliasing contains a complete exposition.

The best way to be sure an image file faithfully resembles the RAW file— that it has no sharpening or noise reduction— is to read a RAW file into Imatest, which uses Dave Coffin’s dcraw to convert it to a standard format (TIFF or PPM).

Imatest documentation sometimes distinguishes between camera RAW files— camera manufacturer’s proprietary formats, and Bayer RAW files— undemosaiced files that contain the same data as camera raw files, but are in standard easily-readable formats such as TIFF or PGM. Dcraw can convert camera RAW files into Bayer RAW files. Starting with version 2.7, several Imatest Master modules can measure camera RAW files directly.