The human vision perspective:
F-stop noise and scene (or scene-referenced) SNRThe 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 a factor of 2 change in exposure. The eye’s relative sensitivity is expressed by the Weber-Fechner law,  Image Modified 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 (flare light) from bright areas. When light is encoded by a camera into pixel levels, the scene contrast is usually altered, as explained in Gamma, Tonal Response, and related concepts. Low contrast encoding would tend to have lower noise (and better Signal-to-Noise Ratio, SNR) than higher contrast cameras. Because dynamic range is based on the scene, we need to remove the camera’s encoding. The result is called scene-referenced noise or SNR with units proportional to the luminance level. 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 = Nf-stop is obtained by dividing the noise in pixel level units by the number of pixel levels per f-stop. (We use “f-stop” rather than “zone” or “EV” out of habit; any are OK.) Note that 1 f-stop = 0.301 Optical density units = 6.02dB (decibels) = log2(luminance). Nf-stop is the scene noise in (logarithmic) units of f-stops, and must be distinguished from linear scene noise, Nscene, which has the same linear units as scene luminance Lscene. For signal in pixels = S, | Eazy math inline |
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| body | \displaystyle \text{F-stop noise } = N_{f-stop} = \frac{N_{pixels}}{dS/d(\text{f-stop})} = \frac{N_{pixels}}{dS/d(\log_2 ( L_{scene})} |
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| body | \displaystyle\text{Using }\ \frac{d(\log_a(x))}{dx} = \frac{1}{x \ln (a)} \ ; \ \ \ \ \ d(\log_a(x)) = \frac{dx}{x \ln(a)} |
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| body | \displaystyle N_{f-stop} = \frac{N_{pixels}}{dS/dL_{scene} \times \ln(2) \times L_{scene}} ≅ \frac{N_{pixels}}{dS/dL_{scene} \times L_{scene}} |
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where Npixels is the measured noise in pixels and | Eazy math inline |
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| body | d(\text{pixel})/d(\text{f-stop}) |
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is the derivative of the signal (pixel level) with respect to scene luminance (exposure) measured in f-stops = log2(luminance). ln(2) = 0.6931 has been dropped to maintain backwards compatibility with older Imatest calculations. Noting that luminance (exposure) is the signal level of the scene, | Eazy math inline |
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| body | \displaystyle \text{Scene noise} = N_{scene} = \frac{N_{pixels}}{dS/dL_{scene}} ≅ N_{f-stop} \times L_{scene} |
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The key to these calculations is that the scene-referenced Signal-to-Noise Ratio, calculated from the measured signal S and noise Npixels must be the same as the scene SNR, which is based on Nscene, which cannot be measured directly. | Eazy math inline |
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| body | \displaystyle \text{Scene Signal-to-Noise Ratio} = SNR_{scene} = \frac{L_{scene}}{N_{scene}} = \frac{1}{N_{f-stop}} = \text{Scene-referenced SNR} = SNR_{scene-ref} |
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the equation for Scene-referenced noise, , which enables | Eazy math inline |
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| body | SNR_{scene-ref} = SNR_{scene} |
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to be calculated directly from is given above.Displays in Stepchart, Color/Tone Interactive, and Color/Tone Auto offer a choice between f-stop noise or Scene-referenced SNR (expressed as a ratio or in dB). Note that SNRscene-ref decreases as the slope of the tonal response curve decreases (often the result of flare light in dark patches). 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 figures above. Since f-stop noise and scene-referenced SNR are functions of scene luminance, largely independent of image signal processing and fogging from flare light, they are an excellent indicators of real-world camera performance. They are the basis of Imatest Dynamic Range measurements. | 
