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Imatest Documentation Lobj is the luminance at the Object plane (test chart) in candelas per square meter, N is the f-stop (aperture). The sensitivity standards contain two factors in addition to T that reduce the light passing through the lens. There are vignetting factor v, assumed to be 0.98 and cos 4 (Θ), where Θ is assumed to be 10 degrees. cos 4 (10 degrees ) = cos 4 (π/18 radians) = 0.9406. This number is somewhat high for typical Imatest test conditions. Using Θ = 6 degrees, cos 4 (Θ) = 0.9783. With these additional factors, I = πTvLobj cos 4 (Θ) ⁄ 4N 2 = π * 0.9 * 0.98 * 0.9783Lobj ⁄ 4N 2 = 0.6777Lobj ⁄ N 2 (3) Plugging I back into equation (1) gives Sensitivity = 10 ⁄ H = 10 ⁄ It = 10 N 2 ⁄ 0.6777 Lobj t = 14.76 N 2 ⁄ Lobj t (4) Note that for Θ = 10 degrees, Sensitivity = 15.4 N 2 ⁄ Lobj t , in agreement with the Kodak ISO Measurement document. Imatest modules that measure sensitivity analyze images of grayscale step charts, which consist of patches of known density d or reflectivity r, where d = -log10(r); r = 10 -d . The X-Rite Colorchecker and the major charts supported by Multicharts contain such patterns. For reference, pure white surfaces have r of about 90% (0.9), equivalent to d of about 0.05. The luminance of a chart patch is Lobj = I r ⁄ π where I is the illuminace of the test chart in Lux. (5) Reference: Basic Photographic Materials and Processes, Second Edition, by Stroebel, Current, Compton, and Zakia, Chapter 1, p. 27 (footnote), "Metric: A perfectly diffusely reflecting surface (100%) illuminated by 1 metercandle (... 1 lux) will reflect ... 1 ⁄ π candela per square meter." Illuminance in Lux is easily measurable by an incident light meter such as the inexpensive BK Precision 615. Saturation-based ISO sensitivity Ssat This measurement assumes the image is exposed using a standard gray card with 18% reflectivity (r = 0.18) and that the the sensor saturates (reaches its maximum output) at 141% reflectivity (well above the 90% reflectivity for pure white) in order to provide some "headroom". The patch (and corresponding luminance Lsat and saturation reflectance rsat) where the sensor saturates is calculated by extrapolating the brightest unsaturated patches. (If any patches are saturated they cannot used directly because they contain no real information. In such cases the extrapolated saturation luminance cannot be larger than the first saturated patch.) The equation is derived by assuming that Lobj is 18/141 of the value that saturates the sensor, Lsat = Irsat ⁄ π , where rsat and hence Lsat are determined by extrapolating patch pixel levels to locate the saturation point, i.e., at the test chart we must use Lobj = (0.18 ⁄ 1.414) Lsat = 0.1273 Lsat ISO Sensitivity = Ssat = 14.76 N 2 ⁄ Lobj t = 116 N 2 ⁄ Lsat t = 116 π N 2 ⁄ I rsat t = 364.6 N 2 ⁄ I rsat t (6) Saturation-based ISO sensitivity is not affected by signal processing, though measurement accuracy can be strongly affected. For best accuracy RAW files are recommended. Standard Output Sensitivity SSOS (from CIPA DC-004) This measurement assumes the image is exposed using a standard gray card with 18% reflectivity (r = 0.18), and that the normalized pixel level for this region is 0.18^(1 ⁄ gamma), where gamma is the display gamma corresponding to the color space. Many standard color spaces such as sRGB and Adobe RGB are designed for display with gamma = 2.2, so the normalized pixel level is 0.4586 (pixel level = 116 for 8-bit pixels where the maximum is 255). (0.461 or pixel level 118 is used in DC-004 because sRGB gamma is not exactly 2.2.) The patch density d46 = -log10(r46 ) and luminance Lobj = L46 where Lobj = I r46 ⁄ π , corresponding to this pixel level is found using a second order polynomial fit to the log pixel levels as a function of patch density. If Lobj is the patch luminance, Standard Output Sensitivity = SSOS = 14.76 N 2 ⁄ Lobj t = 46.37 N 2 ⁄ I r46 t (7) SOS is strongly dependent on signal processing. It is increased when a "shoulder" is present in the tonal response curve (TRC). 56 of 451
Imatest Documentation Shoulders are widely used to reduce the likelihood of highlight "burnout" (saturation). For files encoded with a straight gamma = 1/2.2 curve (what you get when you decode a RAW file with dcraw), SSOS = 0.71 * Ssat, i.e., the image is assumed to saturate at 100% reflectivity ( no headroom). When a shoulder is present, SSOS is generally larger than Ssat. Headroom Hdr Headroom is the amount of exposure available between the exposure for a 100% reflective patch and system saturation. When Exposure Index (EI) is set to the Saturation-based ISO Sensitivity, Ssat, headroom is always Hdrsat = 41.4% or 1/2 f-stop (or EV or Zone). Standard Output Sensitivity SSOS and its corresponding headroom HdrSOS are both strong functions of the response curve. Increasing the response "shoulder" (curvature near saturation) increases both SSOS and HdrSOS. The formulas are fairly simple: HdrSOS(f-stops) = log2( SSOS ⁄ Ssat ) + 0.5 (f-stops or EV or zones) (8) Using RAW files Saturation-based ISO sensitivity measurements are more accurate and reliable when a RAW file is converted using dcraw wth the following settings. Auto white level must be unchecked. dcraw input dialog box (appears when RAW files are opened) showing recommended settings for ISO sensitivity measurement Demosaicing should be set to Normal RAW conversion. (We haven't found the right combination of settings that produces reliable results with Bayer RAW files.) Output color space is normally set to sRGB. Output gamma should be set to sRGB or 2.2. 57 of 451
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