# How is f-stop a measure of dynamic range?

As far as I have read f-stop is a measure of the aperture. This affects the amount of area in the foreground and background which is in focus.

While having a look at the dynamic ranges of cameras I realised that it is also measured in f-stops. The more f-stops, the more the dynamic range — which means better Brightness:Darkness ratio in the photo.

Do these two "f-stops" mean the same thing? Does the aperture size control the dynamic range?

Also I read that f-stop or f-number=focal length/diameter of entrance pupil. When the f-stop is changed, does the focal length change or diameter of entrance pupil change?

Dynamic range is not measured in f-stops, it is measured in stops. A stop is often used to refer to a change that doubles the value or, in the case of cameras, the amount of light. Changing the aperture by one f-stop doubles to amount of light allowed in, so in the case of aperture, a stop is an f-stop. Similarly, cutting the shutter speed in half is a one stop change, however it is not an f-stop because it is not aperture.

When a camera is said to have 12 stops of dynamic range, it means that the brightest part of a scene can be 2^12 times brighter than the darkest part. (One stop is twice as bright, two stops is 4 times, etc).

• Hey thanks for the explanation. It was crystal clear. I was sort of confused when this cambridgeincolour.com/tutorials/… website used f-stop in 2 places while describing dynamic range. – jinkx Jan 8 '14 at 16:48
• Assuming the black point (the absence of any detail) is set at zero (2^0=1), a camera with 12 stops of DR can record a scene in which the brightest part rendered with any detail is 2^11 times brighter than the darkest part rendered with any detail. If the brightest part is 2^12 times as bright as the darkest, the bright part will be saturated in all color channels and rendered as pure white with no detail, regardless of the actual color. – Michael C Jan 8 '14 at 23:01
• 4094 (additional base units of light) is not quite 4095 (additional base units of light), yet is quite a bit more than 2048 (additional base units of light). 2^12 might be completely saturated, but 2^12 - n, where n < 2^11, is not. – user2719 Jan 9 '14 at 0:02
• cameras usually saturate to pink, and in software you then set a virtual saturation point to make it white. – Michael Nielsen Jan 10 '14 at 9:27
• @BrettSchneider - no, not at all. Bits per channel is resolution, not range. A camera with a lower dynamic range could have more bits per channel, it would just have smaller differences between the values. Dynamic range is a comparison of the absolute max and the absolute min that can be simultaneously recorded. It doesn't matter if it has a million possible values in between or 2. – AJ Henderson Mar 3 '18 at 2:15

Q: "How is f-stop a measure of dynamic range?". A: One Stop equals 6dB and theoretically can be represented by one bit (though in practice additional bits are necessary, see Link at end of this answer).

No other answer mentions a Unit of Measurement for Dynamic Range, let's define everything in comparable Units so an exact answer can be given.

The decibel (dB) is a logarithmic unit used to express the ratio of two values of a physical quantity.

A change in amplitude ratio by a factor of 2 (equivalently factor of 4 in power change) approximately corresponds to a 6 dB change in level.

The f-number (sometimes called focal ratio, f-ratio, f-stop, or relative aperture) of an Optical System is the ratio of the lens's focal length to the diameter of the entrance pupil. The "F" pertains to Lenses, so f/8 is the "fractional diameter" or Focal Number of the Aperture of an Optical System (Lens, Filter, etc., and not the Sensor, ADC, Bus or Memory width).

A "Stop" will halve or double the amount of light. A Len's F's are in Stops but could be fractional Stops too.

Dynamic range is a term used to describe the ratio between the smallest and largest signals that can be measured by a Data Acquisition System (a Sensor, ADC, Bus, and Memory - specifically, the Bit Width and accuracy), let's call that a Camera (but also applicable to 'Analog' or Film). Analog Electronic Cameras had a Tube that detected light and converted it to a range of voltages that was recorded on a Tape. Both Systems have a theoretical Dynamic Range which can be designed for or calculated, in practice the attained Dynamic Range will be less.

Digital Systems (as opposed to Analog) have a response that is more linear than film, which has characteristics (reciprocity failure) that tend to compress or "bend" the first and last stops. Film's nonlinearity makes it more forgiving of overexposure and permits capturing of shadow details slightly better than video.

This is why Digital Cameras have "Log" or in Sony's case, SLOG; there's fewer Bits for the middle and more available for the highest and lowest values (essentially the 'width' of the Bit is altered).

In Digital Systems the resolution (of the Dynamic Range) of a measurement system (a Digital Camera) is determined by the number of bits that the ADC uses to digitise an input signal (from the Sensor).

Most ADCs have either 8 bit to 24-bit resolution (not used in Digital Cameras). For a 16-bit device the total voltage range is represented by 2^16 (65536) discrete digital values. Therefore the absolute minimum level that a system can measure is represented by 1 bit or 1/65536th of the ADC voltage range. For a system with a voltage range of ±10V then the smallest voltage that the system can distinguish will be:

20 / 65536 = 0.3 mV

In decibels this dynamic range is therefore expressed as:

20 Log10 (65536) = 96dB

Therefore for a 16-bit ADC the dynamic range is 96dB. Using the same calculations the dynamic range of a 24-bit ADC is 144dB.

6 dB = 1 stop = 1 bit.

This is why people say they like 14-Bit RAW, and why you want to avoid an 8-Bit Camera - Dynamic Range.