Digital Sensor “Characteristic Curves”?

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NateW Forum Member • Posts: 66
Digital Sensor “Characteristic Curves”?

Digital cinema cameras use film-like logarithmic transfer curves for their 10 or 12 bit log-gamma recording modes and I noticed that a log exposure graph of Sony’s S-Log3 has almost the exact same shape as the photon transfer curve for the A7III (which uses the same sensor as their recent cinema cameras that record in SLog-3), other than the vertical scaling. This got me thinking about the “characteristic curve” published in film data sheets (which is a graph of log-exposure against log-density) and wondering how they relate to the log-gamma curves in the digital data sheets and the photon-transfer curves published on photonstophotos.net? Does every digital camera have a “native” logarithmic transfer function that can be derived from its photon transfer curve in some way?

Obviously a digital cameras linear signal can be converted from linear to logarithmic encoding values, but the noise floor and quantization issues at low exposure levels would induce a “toe” of sorts right?

How would one derive this curve? Maybe by converting the linear sensor values to logarithmic (at what scale for a 16 bit linear tif? 14 or 16 bit?) but transitioning to linear values based on where the PTC value transition from the read to the photon noise regimes?

Would it perhaps make sense to shape a “film-like” log transfer function using the photon noise regime portion of the PTC curve as the “straight-line” part of the film curve, and roll off the shadows and highlights in the read noise and non-uniformity noise dominated regions?

Also, I noticed that the ratio of the DNS between the x and y axis on the PTC curve (A7III) is almost exactly the same as the ratio of (channel noise floor normalized) exposure to density in film curves. Is this just coincidence, or are these curves actually that strongly connected?

Here are the log-gamma transfer curves for several digital cinema formats. If you compare them to the respective manufacturers PTC curves at PTP they all match very closely in shape:

A7III PTC

Canon PTC (compare to Sony and cinema log-gamma curves Above)

here’s a cinema film stock curve:

Here’s the Arri Alexa log-gamma curve:

A7RIII Noise vs standard deviation:

Another thought, what does this say about how ISO is rated for digital cameras vs cinema cameras vs film? Seems like film and cinema cameras count from the noise floor up 5 stops to middle gray, while digital still cameras count from sensor saturation down 3 stops to middle gray. Interesting!

its also interesting that the film curves are more logarithmically linear (and over a wider range) than the digital log-gamma specs and have a much quicker transition from the “straight line” to the noise floor. That seems to imply that digital sensors are really linear in the shadows, but that noise raises the values below middle gray so a linearized, Black subtracted film negative would actually be more linear in the shadows than digital, and digital would be more linear in the highlights. I guess that makes sense! Does digital “black point subtraction” take this into account, or is additional contrast needed in the shadows to give a film like response?

Thanks for your thoughts and help!

Sony a7
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