Units of dynamic range

[TN Args]

Hi everyone, I would like to get some clarification please.

I have seen dynamic range described using various units, as a number of EV, stops, dB, bits.

Firstly, are all those units legitimate units of dynamic range?

Also, are there any conversion factors?

• 12 EV of dynamic range
• 12 stops of dynamic range
• 12 dB of dynamic range
• 12 bits of dynamic range
• 12=12=12=12?

Finally, does the appropriate unit vary with what is being measured?

• the live scene in front of me has 12 (unit) of dynamic range
• the sensor has 12 (unit) of dynamic range
• the image has 12 (unit) of dynamic range
• the PC monitor has 12 (unit) of dynamic range

As an aside, some PC monitors or video projectors seem to use a contrast ratio (like 5000:1) when they are describing what I would call the dynamic range. Can one convert from contrast ratio to EV / stops / dB / bits?

Thanks for any responses.

 

[J A C S]

Hi everyone, I would like to get some clarification please.

I have seen dynamic range described using various units, as a number of EV, stops, dB, bits.

Firstly, are all those units legitimate units of dynamic range?

Also, are there any conversion factors?

• 12 EV of dynamic range
• 12 stops of dynamic range
• 12 dB of dynamic range
• 12 bits of dynamic range
• 12=12=12=12?

Just by the sound of it, DR should be a range, like from X to Y (over which, say, SNR is acceptable). In math, it is a set, which may not be even an interval. The common way to report is as a ratio: Y/X, for example contrast ratio 1000:1 which simply means 1000. Another way to report it is on a log scale, like log_2(Y/X) and we call that stops. Decibels is another logarithmic metric which can be misleading since that notion depends on what is measured (power vs. field).

IMO, bits should be avoided unless we are really talking about files.

 

[Iliah Borg]

Hi everyone, I would like to get some clarification please.

I have seen dynamic range described using various units, as a number of EV, stops, dB, bits.

Firstly, are all those units legitimate units of dynamic range?

Also, are there any conversion factors?

• 12 EV of dynamic range
• 12 stops of dynamic range
• 12 dB of dynamic range
• 12 bits of dynamic range
• 12=12=12=12?

Finally, does the appropriate unit vary with what is being measured?

• the live scene in front of me has 12 (unit) of dynamic range
• the sensor has 12 (unit) of dynamic range
• the image has 12 (unit) of dynamic range
• the PC monitor has 12 (unit) of dynamic range

As an aside, some PC monitors or video projectors seem to use a contrast ratio (like 5000:1) when they are describing what I would call the dynamic range. Can one convert from contrast ratio to EV / stops / dB / bits?

Thanks for any responses.

1 EV = 1 stop

I'm not fond of measuring DR in bits, but theoretically 12 bits = 12 EV

1 stop (EV) ≈ 6.02 dB, 20 log base10 (2) * nEV

Just in case, 1D (density unit) ≈ 3.322 EV; typical gray scale chart like Q13 use 0.1D step, very close to 1/3 EV.

1:5000 -> log base2(5000/1) ≈ 12.3 EV

Dynamic range of a scene is usually measured in stops (EV), using a spotmeter, as difference between the brightest and darkest regions of the scene where details need to be preserved.

DR measurements for a shot are usually noise-based; for a scene they are brightness-based.

 

[57even]

Hi everyone, I would like to get some clarification please.

I have seen dynamic range described using various units, as a number of EV, stops, dB, bits.

Firstly, are all those units legitimate units of dynamic range?

Also, are there any conversion factors?

• 12 EV of dynamic range
• 12 stops of dynamic range
• 12 dB of dynamic range
• 12 bits of dynamic range
• 12=12=12=12?

Finally, does the appropriate unit vary with what is being measured?

• the live scene in front of me has 12 (unit) of dynamic range
• the sensor has 12 (unit) of dynamic range
• the image has 12 (unit) of dynamic range
• the PC monitor has 12 (unit) of dynamic range

As an aside, some PC monitors or video projectors seem to use a contrast ratio (like 5000:1) when they are describing what I would call the dynamic range. Can one convert from contrast ratio to EV / stops / dB / bits?

Thanks for any responses.

Dynamic range is just a ratio. You can convert a ratio into dB=20log(ratio) or EV/bits=log2(ratio) but its still a ratio.

Contrast range normally applies to a scene or display. It's also a ratio, so you can express it in any of the same units. 800:1 = 58dB = 9.64 bits/EV.

EV is really a way to compare the ratio with exposure. dB is used for sound because it matches our ear's logarithmic response.

But they are all just ratios at the end of the day. Maximum brightness/minimum brightness.

 

[TN Args]

My thanks to J A C S, Iliah Borg, and 57even

 

[TN Args]

Hi everyone, I would like to get some clarification please.

I have seen dynamic range described using various units, as a number of EV, stops, dB, bits.

Firstly, are all those units legitimate units of dynamic range?

Also, are there any conversion factors?

• 12 EV of dynamic range
• 12 stops of dynamic range
• 12 dB of dynamic range
• 12 bits of dynamic range
• 12=12=12=12?

Finally, does the appropriate unit vary with what is being measured?

• the live scene in front of me has 12 (unit) of dynamic range
• the sensor has 12 (unit) of dynamic range
• the image has 12 (unit) of dynamic range
• the PC monitor has 12 (unit) of dynamic range

As an aside, some PC monitors or video projectors seem to use a contrast ratio (like 5000:1) when they are describing what I would call the dynamic range. Can one convert from contrast ratio to EV / stops / dB / bits?

Thanks for any responses.

1 EV = 1 stop

Yes, this is the one I was most confident about. Thanks for confirming.

I'm not fond of measuring DR in bits, but theoretically 12 bits = 12 EV

Are there any situations where theory would not apply in real life photography? I was getting a bit uncertain whether this was 1:1.

1 stop (EV) ≈ 6.02 dB, 20 log base10 (2) * nEV

Thank you. Why is the multiplier 20 and not 10 like in normal conversion from Bels?

Just in case, 1D (density unit) ≈ 3.322 EV; typical gray scale chart like Q13 use 0.1D step, very close to 1/3 EV.

Another unit!

1:5000 -> log base2(5000/1) ≈ 12.3 EV

Thank you.

Dynamic range of a scene is usually measured in stops (EV), using a spotmeter, as difference between the brightest and darkest regions of the scene where details need to be preserved.

DR measurements for a shot are usually noise-based; for a scene they are brightness-based.

 

[dosdan]

Thank you. Why is the multiplier 20 and not 10 like in normal conversion from Bels?

Because, the ratio is ultimately between the powers of the two quantities. Normally though you are comparing two voltage levels. Actually, with the technical DR of a pixel we're comparing charge levels: the number of photoelectrons in a pixel at FS, (changes with the amount of gain applied in the PGA stage), compared to the output RMS noise floor of a pixel in equiv. photoelectrons. These charges are converted linearly to output voltages, so we can continue the DR discussion using voltages. P=V^2/R. So, if comparing two voltages, to get their power ratio you need to square their voltage ratio.

In Bels: log(Pmeasured/Pref)

A deciBel is 1/10th of a Bel so
In dB: 10 log(Pmeasured/Pref)

But if comparing voltages
In dB: 20 log(Vmeasured/Vref).

Multiplying a log of a ratio by 2 is equiv. to squaring the orig, ratio.

The noise floor used for the System DR will be different at different PGA gain levels as the noise floor is the quadrature combination of Pixel RN, PGA noise and ADC noise.

Dan.

 

[beatboxa]

I'm not fond of measuring DR in bits, but theoretically 12 bits = 12 EV

Are there any situations where theory would not apply in real life photography? I was getting a bit uncertain whether this was 1:1.

If data is not recorded linearly, this is not true. For example, if some sort of tone curve is applied at any point, all bets are off.

So, for example, in an "HDR" image, many stops of dynamic range from the scene are squeezed into fewer bits. Or pretty much any JPEG.

One way to think about this is to take a step back: each bit doubles the effective number of potential values, since these are binary.

1-bit = 2 values = 0 or 1

2-bit = 4 values = 00 or 01 or 10 or 11

3-bit = 8 values = 000 or 001 or 010 or 011 or 100 or 101 or 110 or 111

(etc.)

This doubling per bit can be thought of as stops if all values are linear. 2-bit can get twice as bright as 1-bit, 3-bit can get twice as bright as 2-bit, and so on.

 

[JimKasson]

Hi everyone, I would like to get some clarification please.

I have seen dynamic range described using various units, as a number of EV, stops, dB, bits.

Firstly, are all those units legitimate units of dynamic range?

Also, are there any conversion factors?

• 12 EV of dynamic range
• 12 stops of dynamic range
• 12 dB of dynamic range
• 12 bits of dynamic range
• 12=12=12=12?

Finally, does the appropriate unit vary with what is being measured?

• the live scene in front of me has 12 (unit) of dynamic range
• the sensor has 12 (unit) of dynamic range
• the image has 12 (unit) of dynamic range
• the PC monitor has 12 (unit) of dynamic range

As an aside, some PC monitors or video projectors seem to use a contrast ratio (like 5000:1) when they are describing what I would call the dynamic range. Can one convert from contrast ratio to EV / stops / dB / bits?

Thanks for any responses.

I see what you're getting at. Dynamic range has no dimensions. As others have said here, it is the ratio of two quantities. In photography, those quantities have the same dimensions (like volts), so the dimensions cancel when the ratio is created, and you are left with a dimensionless number. That number can be expressed in many ways. Say it's 5000, which is the example you used in your original post.

log2(5000) = 12.29. Since each stop is a doubling of light, that's 12.29 stops, or that many EV. Since one bit position is also a doubling, you could call that 12.29 bits.

If we're talking voltage, 20*log10(5000) = 74 decibels (dB). See how the dB number is different? That's because dB is based on log base 10, not log base 2.

Jim

 

[John Sheehy]

Others have mostly addressed your query so far, but I'd like to mention a couple other things you might want to consider.

Noise-limited DR is not an opaque, solid value like the brightness of black on a monitor. It is an abstraction. It is about an acceptably low interference of noise with the perception of relatively fine details in an image. For coarser details, the DR is actually higher, and theoretically unlimited with enough pixels of finite "DR" for fine details. This is especially true when the noise character is spatially random. All real cameras have spatially-correlated read noise at low frequencies which obfuscate even coarser details, hiding from us the fact that when noise is spatially random, we can reduce magnification and downsample such that any desired DR per unit of sensor area is possible.

As far as "bits" as units are concerned, bits are like EV and stops, with each additional bit doubling the number of linear values. Bits are something that don't need measuring, though, and are actually the carrier of information; just a number system. Literally, 12 linear bits can only express 0 through 4095.

With read noise over most of the range of these 4095 values, quadrupling the sensor area will double the DR of the resulting image, with 4x as many pixels of the same pixel quality. However, if the standard deviation of black frame noise at the pixel level drops below about 1.3 12-bit levels, this property of increasing DR with further extension of the pixel array to a larger area fails, because the noise becomes posterized and can no longer dither local mean values between the integer levels of black and one level above black. So, the premise upon which something like DxOMark shows greater "Print" (whole image) DR than "Screen" (pixel) DR for cameras with significantly more than 8MP relies on pixel DR being measured at no more than about 0.4 stops less than there are bits, ideally, but failure drops off slowly until about 0.2 stops more DR than bits, and after that, measured noise-limited DR becomes gibberish, as there is too much posterization to define a lowest signal in a meaningful way, with large areas of contiguous values which have no dithering ability. It's a capture like a display's lowest values, but a display can dither to get past itself. An undithered capture, however, can not be fixed.

With more demanding definitions of DR that include other noises than blackframe noise, like Bill Claff's PDR, there is more dithering available due to the inclusion of photon noise, too, but that just makes the PDR metric itself less problematic, but the shadow posterization is still there. Noise/DR measurements can be made by allowing such artifacts to alter results, or they are knowingly worked around, but do not predict what happens to signals approaching black, which is still sometimes damaged.

 

[D Cox]

Hi everyone, I would like to get some clarification please.

I have seen dynamic range described using various units, as a number of EV, stops, dB, bits.

Firstly, are all those units legitimate units of dynamic range?

Also, are there any conversion factors?

• 12 EV of dynamic range
• 12 stops of dynamic range
• 12 dB of dynamic range
• 12 bits of dynamic range
• 12=12=12=12?

Just by the sound of it, DR should be a range, like from X to Y (over which, say, SNR is acceptable). In math, it is a set, which may not be even an interval. The common way to report is as a ratio: Y/X, for example contrast ratio 1000:1 which simply means 1000. Another way to report it is on a log scale, like log_2(Y/X) and we call that stops. Decibels is another logarithmic metric which can be misleading since that notion depends on what is measured (power vs. field).

IMO, bits should be avoided unless we are really talking about files.

Bits define the number of steps in a range, not the amplitude of the range. You can have a one bit image with a huge difference in brightness between the black and the white.

You can have a 4 bit image with identical maximum and minimum brightness but with 14 intermediate shades of grey.

 

[jonas ar]

Hi everyone, I would like to get some clarification please.

I have seen dynamic range described using various units, as a number of EV, stops, dB, bits.

Firstly, are all those units legitimate units of dynamic range?

Also, are there any conversion factors?

• 12 EV of dynamic range
• 12 stops of dynamic range
• 12 dB of dynamic range
• 12 bits of dynamic range
• 12=12=12=12?

Finally, does the appropriate unit vary with what is being measured?

• the live scene in front of me has 12 (unit) of dynamic range
• the sensor has 12 (unit) of dynamic range
• the image has 12 (unit) of dynamic range
• the PC monitor has 12 (unit) of dynamic range

As an aside, some PC monitors or video projectors seem to use a contrast ratio (like 5000:1) when they are describing what I would call the dynamic range. Can one convert from contrast ratio to EV / stops / dB / bits?

Thanks for any responses.

I see what you're getting at. Dynamic range has no dimensions. As others have said here, it is the ratio of two quantities. In photography, those quantities have the same dimensions (like volts), so the dimensions cancel when the ratio is created, and you are left with a dimensionless number. That number can be expressed in many ways. Say it's 5000, which is the example you used in your original post.

log2(5000) = 12.29. Since each stop is a doubling of light, that's 12.29 stops, or that many EV. Since one bit position is also a doubling, you could call that 12.29 bits.

If we're talking voltage, 20*log10(5000) = 74 decibels (dB). See how the dB number is different? That's because dB is based on log base 10, not log base 2.

Jim

This might be a silly question, but what is the motivation for the 20x multiplier in the dB scale?

 

[D Cox]

Hi everyone, I would like to get some clarification please.

I have seen dynamic range described using various units, as a number of EV, stops, dB, bits.

Firstly, are all those units legitimate units of dynamic range?

Also, are there any conversion factors?

• 12 EV of dynamic range
• 12 stops of dynamic range
• 12 dB of dynamic range
• 12 bits of dynamic range
• 12=12=12=12?

Finally, does the appropriate unit vary with what is being measured?

• the live scene in front of me has 12 (unit) of dynamic range
• the sensor has 12 (unit) of dynamic range
• the image has 12 (unit) of dynamic range
• the PC monitor has 12 (unit) of dynamic range

As an aside, some PC monitors or video projectors seem to use a contrast ratio (like 5000:1) when they are describing what I would call the dynamic range. Can one convert from contrast ratio to EV / stops / dB / bits?

Thanks for any responses.

1 EV = 1 stop

I'm not fond of measuring DR in bits, but theoretically 12 bits = 12 EV

No, it doesn't. You can map a 12 EV range onto any number of steps.

1 stop (EV) ≈ 6.02 dB, 20 log base10 (2) * nEV

Just in case, 1D (density unit) ≈ 3.322 EV; typical gray scale chart like Q13 use 0.1D step, very close to 1/3 EV.

1:5000 -> log base2(5000/1) ≈ 12.3 EV

Dynamic range of a scene is usually measured in stops (EV), using a spotmeter, as difference between the brightest and darkest regions of the scene where details need to be preserved.

DR measurements for a shot are usually noise-based; for a scene they are brightness-based.

 

[Iliah Borg]

Hi everyone, I would like to get some clarification please.

I have seen dynamic range described using various units, as a number of EV, stops, dB, bits.

Firstly, are all those units legitimate units of dynamic range?

Also, are there any conversion factors?

• 12 EV of dynamic range
• 12 stops of dynamic range
• 12 dB of dynamic range
• 12 bits of dynamic range
• 12=12=12=12?

Finally, does the appropriate unit vary with what is being measured?

• the live scene in front of me has 12 (unit) of dynamic range
• the sensor has 12 (unit) of dynamic range
• the image has 12 (unit) of dynamic range
• the PC monitor has 12 (unit) of dynamic range

As an aside, some PC monitors or video projectors seem to use a contrast ratio (like 5000:1) when they are describing what I would call the dynamic range. Can one convert from contrast ratio to EV / stops / dB / bits?

Thanks for any responses.

I see what you're getting at. Dynamic range has no dimensions. As others have said here, it is the ratio of two quantities. In photography, those quantities have the same dimensions (like volts), so the dimensions cancel when the ratio is created, and you are left with a dimensionless number. That number can be expressed in many ways. Say it's 5000, which is the example you used in your original post.

log2(5000) = 12.29. Since each stop is a doubling of light, that's 12.29 stops, or that many EV. Since one bit position is also a doubling, you could call that 12.29 bits.

If we're talking voltage, 20*log10(5000) = 74 decibels (dB). See how the dB number is different? That's because dB is based on log base 10, not log base 2.

Jim

This might be a silly question, but what is the motivation for the 20x multiplier in the dB scale?

d stands for deci-, factor of 10x.

2x is because log(V^2) = 2*log(V)

 

[Iliah Borg]

I'm not fond of measuring DR in bits, but theoretically 12 bits = 12 EV

No, it doesn't. You can map a 12 EV range onto any number of steps.

"I'm not fond of measuring DR in bits". "Theoretically" - if DR is converted to number of bits.

 

[J A C S]

Hi everyone, I would like to get some clarification please.

I have seen dynamic range described using various units, as a number of EV, stops, dB, bits.

Firstly, are all those units legitimate units of dynamic range?

Also, are there any conversion factors?

• 12 EV of dynamic range
• 12 stops of dynamic range
• 12 dB of dynamic range
• 12 bits of dynamic range
• 12=12=12=12?

Just by the sound of it, DR should be a range, like from X to Y (over which, say, SNR is acceptable). In math, it is a set, which may not be even an interval. The common way to report is as a ratio: Y/X, for example contrast ratio 1000:1 which simply means 1000. Another way to report it is on a log scale, like log_2(Y/X) and we call that stops. Decibels is another logarithmic metric which can be misleading since that notion depends on what is measured (power vs. field).

IMO, bits should be avoided unless we are really talking about files.

Bits define the number of steps in a range, not the amplitude of the range. You can have a one bit image with a huge difference in brightness between the black and the white.

You can have a 4 bit image with identical maximum and minimum brightness but with 14 intermediate shades of grey.

That is why I do not like them in this context. Also, what is the meaning of 12.3 bits?

 

[JimKasson]

Hi everyone, I would like to get some clarification please.

I have seen dynamic range described using various units, as a number of EV, stops, dB, bits.

Firstly, are all those units legitimate units of dynamic range?

Also, are there any conversion factors?

• 12 EV of dynamic range
• 12 stops of dynamic range
• 12 dB of dynamic range
• 12 bits of dynamic range
• 12=12=12=12?

Finally, does the appropriate unit vary with what is being measured?

• the live scene in front of me has 12 (unit) of dynamic range
• the sensor has 12 (unit) of dynamic range
• the image has 12 (unit) of dynamic range
• the PC monitor has 12 (unit) of dynamic range

As an aside, some PC monitors or video projectors seem to use a contrast ratio (like 5000:1) when they are describing what I would call the dynamic range. Can one convert from contrast ratio to EV / stops / dB / bits?

Thanks for any responses.

I see what you're getting at. Dynamic range has no dimensions. As others have said here, it is the ratio of two quantities. In photography, those quantities have the same dimensions (like volts), so the dimensions cancel when the ratio is created, and you are left with a dimensionless number. That number can be expressed in many ways. Say it's 5000, which is the example you used in your original post.

log2(5000) = 12.29. Since each stop is a doubling of light, that's 12.29 stops, or that many EV. Since one bit position is also a doubling, you could call that 12.29 bits.

If we're talking voltage, 20*log10(5000) = 74 decibels (dB). See how the dB number is different? That's because dB is based on log base 10, not log base 2.

Jim

This might be a silly question, but what is the motivation for the 20x multiplier in the dB scale?

d stands for deci-, factor of 10x.

2x is because log(V^2) = 2*log(V)

Iliah is correct. Let me unpack that for you, Jonas.

One Bel is one factor of ten in power. The relationship between power, P, and current, I, and voltage, V, is as follows:

P = E * I

Now, let's assume that the voltage is measured across a resistance of R. Ohm's law states that:

E = I * R

Let's solve that for I:

I = E / R

Now let's plus that into the power equation:

P = E * E / I, or P = E^2 / I

That's where the V^2 that Iliah is talking about comes from. Some engineers, like me, use E to indicate a voltage. Some, like Iliah, use V. Po-tay-to, po-tah-to.

So 1 Bel is a factor of ten in power (log10(10) = 1), and a factor of 3.162 in voltage (2*log10(3.162) = 1.

A decibel is one tenth of a Bel, so, if we have a power ratio of x, it's

10 * log10(x) decibels

If we have a voltage ratio of y, it's

20 * log10 decibels

If we raise the voltage to 3.162 times what it was before, the power goes up by:

20*log10(3.162) = 10 dB

If we raise the power to 10 times what it was before, the relationship is:

10*log10(10) = 10 dB

Jim

 

[John Sheehy]

That is why I do not like them in this context. Also, what is the meaning of 12.3 bits?

It's a way to refer to about 5042 levels.

Many real cameras don't use all of the RAW levels, so a 12-bit precision allows RAW numbers from 0 to 4095, but many cameras will clip below 4095, and the range of used values below black have kind of a special status, because they only exist as individual samples, but shouldn't as means, and may not be used all the way down to original 0. In fact, no 12-bit-DAC camera has 4095 levels between black and highlight clipping. Those which seem to, have stretched the histogram to make black 0 and maintain 4095 as a used level, and left gaps in the histogram.

 

[J A C S]

That is why I do not like them in this context. Also, what is the meaning of 12.3 bits?

It's a way to refer to about 5042 levels.

Yeah, and an incorrect one. The standard use of a bit is either a variable taking two values or the number of binary digits. In the latter case, it is an integer. In the former one, it is not even a number.

 

[JimKasson]

That is why I do not like them in this context. Also, what is the meaning of 12.3 bits?

It's a way to refer to about 5042 levels.

Yeah, and an incorrect one. The standard use of a bit is either a variable taking two values or the number of binary digits. In the latter case, it is an integer. In the former one, it is not even a number.

In another context, fractional bits are OK:

Shannon (unit) - Wikipedia

en.wikipedia.org

Jim