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Eazy math inline
body\text{pixel level = (RAW pixel level)}^ \gamma \approx \text{exposure} ^ \gamma

There are actually two gammas:

  1. encoding gamma, which relates scene luminance to image file pixel levels, and

  2. display gamma, which relates image file pixel levels to display luminance. It is typically found in equations of the form,

    Eazy math inline
    body\text{log(display brightness)} \approx  \gamma \ \text{log(pixel level)}

The above equations (and equation,

Eazy math inline
body\text{log(pixel level)} \approx  \gamma \ \text{log(exposure)}
(above and in most references to gamma on this page) refer , refers to encoding gamma. Exceptions are for characterizing color spaces (such as sRGB, where display gamma is approximately 2.2) and when display gamma is explicitly referenced, as in the Appendix on Monitor gamma.

The overall system contrast is the product of the encoding and decoding gammas. More generally, we think of gamma as contrast.

Encoding gamma is introduced applied in the image processing pipeline because the output of image sensors, which is linear for most standard (non-HDR) image sensors, is never gamma-encoded. Encoding gamma is typically measured from the tonal response curve, which can be obtained photographing a grayscale test chart and running Imatest’s Color/Tone module (or the legacy Stepchart and Colorcheck modules).

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Note that this curve is not a straight line. It’s slope is reduced on the right, for the brightest scene luminance. This area of reduced slope is called the “shoulder”. It improves the perceived quality of pictorial images (family snapshots, etc.) by reducing saturation or clipping (“burnout”) of highlights, thus making the response more “film-like”. A shoulder is plainly visible in the lower-right of the Fujichorme Provia 100F curve, above. Shoulders are almost universally applied in consumer cameras; they’re less common in medical or machine vision cameras. [A region of reduced slope in dark regions is called a “toe”. It is common in film, but relatively rare in digital images.]

Because the tonal response is not a straight line, gamma has to be derived from the average (mean) value of a portion of the tonal response curve. 

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The chart on the right is designed for a visual measurement of display gamma. But it  rarely displays correctly in web browsers (and may never display correctly on this Atlassian page, where there is no way to set it to 100% size). It has to be displayed in the monitor’s native resolution, 1 monitor pixel to 1 image pixel. Unfortunately, operating system scaling settings and browser magnifications can make it difficult.

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To view the gamma chart (on the right) correctly, right-click on it, copy it, then paste it into Fast Stone Image Viewer.

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