Color Depth vs. Image File - S Cameras

[davidmknoble]

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So the discussions about the New S3 has prompted me to do a little research.  Also, some other comments have shed some light for me on these Technical Data Sheets for the various cameras.  First, I did quick research and so if you see something I miscalculated, please say something.

Color is stored in computer bits, 1's and 0's.  So, the number of bits used to represent a color determines how many colors can be represented.  If we store color in 1 bit, it has two choices, 1 and 0, which is 2^1 (representing 2 choices and 1 bit).  If we store color in 8 bits, there are 2^8 colors represented, or 256.  For 12 bits, 8^12 or 4,096 colors are represented, 14 bits, 2^14 or 16,384 and finally, 16 bits, 2^16 or 65,536. (https://petapixel.com/2018/09/19/8-12-14-vs-16-bit-depth-what-do-you-really-need/)

To complicate matters, if each pixel (R, G & B ) stores its values in the same manner, then an 8 bit color would be represented by 256 R, 256 G and 256 B values, or 256 x 256 x 256 = 256^3 = 16.7 million colors.  Using the same theory, 14 bit color, or 16,385^3 = 4.3 trillion color values and 16 bit color is 65,536^3 or 280 trillion color values. (https://www.peachpit.com/articles/article.aspx?p=1709190&seqNum=2)

So, the first question to ask might be, is the S sensor (or any camera sensor used today) capable of distinguishing between  4.3 trillion color values or 280 trillion color values?  This question does not ask can the sensor display all 4.3 trillion colors at one time (even high end monitors I looked at only display about 1.07 billion of the 4.3 trillion colors at one time).

That is just recording colors.

Recording differences in light value is also part of the sensor's job.  If the S sensor has a 15 stop dynamic range, that means it can effectively record differences in light values for 2^15, or 32,768 different luminance values. (https://www.dpreview.com/articles/4653441881/bit-depth-is-about-dynamic-range-not-the-number-of-colors-you-get-to-capture)

When the RAW data, which is now luminance value for each pixel, defined as red, green or blue, is written to the DNG file, it is stored in a 16-bit file.  However, if uses 14+1 bits, or 15 bits, there is still at least 1 bit unused in the file.

So far I have ignored sensor read noise and whole host of other variables, most of which affect the deepest shadows.

The point here is that reading the specifications can be misleading between camera manufacturers, depending on what they are trying to say and some data might not even be available.

1. A 16-bit RAW, DNG, TIFF or other type of file, is only a box to hold the data.  It means that there could be room in the box for future data if the sensor can fill it, without having to change current software reading, storage, etc.

2. A 14-bit color representation is either 16,384 colors, or 4.3 trillion if it is stored with one bit for red, blue and green.

3. A sensor that can capture 15 stops of brightness, can differentiate between 32,768 level of brightness, much more levels of brightness than can be printed, but allows for more choices.

I think I got this right, but open to criticism.  Just trying to put these all in some kind of perspective.

 

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[albertknappmd]

interesting calculations and they seem to be correct but..... THE RATE LIMITING FACTOR are your eyes, optic nerve and cortex........

Albert

[davidmknoble]

39 minutes ago, albertknappmd said:

interesting calculations and they seem to be correct but..... THE RATE LIMITING FACTOR are your eyes, optic nerve and cortex........

Albert

Spoken like a doctor, and oh so true!

[Chaemono]

Very interesting and mind-spinning analysis in theory but for all practical purposes read noise cannot be ignored when talking about the visual difference between 14 and 16 bit raw precision, not only in the deepest shadows: https://blog.kasson.com/gfx-100/visual-comparisons-of-fuji-gfx-100-14-and-16-bit-raw-precision/

BTW, Jim Kasson’s conclusion is that OSPDAF banding with mirrorless MF cameras may be so strong that it makes any subtle differences in read noise quality between 16 and 14 bit inconsequential.

[paulsydaus]

10 hours ago, davidmknoble said:

(even high end monitors I looked at only display about 1.07 billion of the 4.3 trillion colors at one time).

Actually depending on the resolution of your monitor, most monitors can display no more than about 20 Million megapickle colors at a time 😉

Edited March 11, 2020 by paulsydaus

[paulsydaus]

David,

What you wrote is correct from a theoretical standpoint in so far as digital quantization effects (the effect that sampling/storing the signal has on the overall signal quality).

The reality is though that errors accumulate all the way through the signal chain starting from the interaction of light with the sensor itself and the circuitry by which these signals are routed and measured.

Most cameras have actual dynamic ranges in the range of 10-13 stops.  The S007 has a DR of 11.5.  The S3 will hopefully be around 12, maybe approaching 12.5.

Most of the noise appears therefore to be related to sensor design and signal routing and measurement, not digital quantization.

This tells me that 14 stops is sufficient and 16 is marketing overkill...

There is some good info on the website below.  I tried to read it once but fairly quickly realized it doesn’t help my photography to worry about this stuff.  Remember 10 stops was good enough for Ansel Adams...

http://www.photonstophotos.net/Charts/PDR.htm