Bit depth vs Dynamic Range

I’ve just started reading Bruce Fraser’s book on Camera RAW, and he uses an analogy of a staircase. Dynamic range is the height of the staircase from top to bottom, and bit depth is the number of steps. So, the two are somewhat independent. Large dynamic range combined with shallow bit depth gives the chopped-up looking histogram, because the limited luminosity values must be spread over a larger range.

This probably doesn’t answer your question, but I just learned it yesterday and thought I’d better type it out before I forget it.

So, the two are somewhat independent.

Not really.

If one attempts to digitize a particular range of analog amplitude values using a particular bit depth, the quantization errors for those particular choices are predictable and unavoidable. Quantization error is tantamount to noise. Your noise floor level, in turn, determines dynamic range because you cannot reliably quantize values that lie below the noise floor.

Hence, bit depth is directly related to dynamic range.

I’ve heard that good ol’ Kodachrome 25 delivers the equivalent of 56-bit dynamic range. I don’t know whether that’s true. To George’s question, I’m not certain that a simple comparison of intensity quantization to the f-stop scale can take into account differences such as the gamut limitations of the RGB model.

=-= Harron =-=

Harron is correct. 16 bit is minimum in audio, due to the dynamic range of sound levels needed to record. 16 bit gives a dynamic range of 96 db, where 8 bit is 48 db.

Now 8 bits is roughly equivalent to 8 stops on the camera, which most modern films can hold.

However, another consideration. Assume for the moment that the black level on a ccd is 0 and white is 1. You can divide that up into as many or as little steps you want, but you will never get more than the output of the ccd.

The key here is to fit the quantization to the requirements. Native noise sets the low end.

How low can you go? 😉

Personally, worrying over linear to non-linear conversion leads to excessive obsessions! I wear the conversion hat when working as a hardware engineer, I wear a cowboy hat when working as a photographer.:D

Bit depth controls the precision, not dynamic range.

8 bits black to white is the same dynamic range as 16 bits black to white — just with more precision on the values in between.

With all due respect, Chris, I think we define dynamic range differently.

If you convert a grayscale image to bitmap, you go from 8- or 16-bit to 1-bit. The appearance of the bitmapped version will depend on your conversion algorithm (50% threshold or some type of dithering), but in no case will I be convinced it has the same dynamic range as the original.

=-= Harron =-=

Dynamic range is the range from the black point to the white point. Yes, they all have the same dynamic range.

Google: High Dynamic Range

Google: High Dynamic Range

I just did. I have yet to find a hit that contradicts my assertion that dynamic range is directly related to bit depth. I’ll keep searching.

The relation is that to have enough precision for larger dynamic ranges, you do need more bits.

But bits alone only define precision, not dynamic range.

I am not asking about precision of the measurement. I am asking about relative ranges of sensitivity of film vs sensors in digital cameras. I concede that film has the greater dynamic range (ratio of lightest to darkest expressed as a logarithm). Still I can’t reconcile that superiority of film from allegations that the film range covers 8 F-stops (doublings of intensity) against other allegations that the best digital cameras can detect tonal differences requiring 12 bits. Since each bit is a doubling of color value, that’s 12 doublings compared to 8 for film.

As I said, I can reconcile this discrepancy if digital color values represent radiation E-vectors rather than Poynting vectors, i.e.,if they are the square root of intensity rather than intensity. That drops the digital camera DR below film DR. I do not think that color values are so defined, however, because if they were then I’d have new questions about gamma.

I fully agree with everyone that measuring shoe size with a micrometer is not going to help you fit your feet. The number of bits used to describe color value has no effect on the sensitivity of the sensor. But, of course, the measurement must be expressed in enough bits to match the sensor’s discriminatory power, else data is lost. If the sensor discriminates to 12 bits the measurement needs to be AT LEAST 12 bits. If 16 bits are uaed to define 12-bit sensor data, nothing is lost. Again, that is not the issue I raise.

Thanks, George

But bits alone only define precision…

On that we can agree. And it is the precision of the quantization that ultimately determines how accurately we can represent the differences between lightest and darkest — i.e., dynamic range.

Chris is essentially correct. The true dynamic range is defined by the source of that which one is trying to record (photography is first and foremost, a recording medium). In the case of light, generally it falls from the brightness of the sun, directly sensed, to a black coal bin at midnight. Now, if we are trying to photograph (record) the proverbial black cat in a coal bin at midnight, we really don’t have much of a dynamic range! If we try to include the sun in that shot, we really have a huge dynamic range! Inconsequential, for the most part, and leading to all kinds of difficulties for sure.

So, now we introduce some sort of sensor mechanism, microphones for sound, film or ccd/cmos devices for light. The first order of business is to ascertain the devices linearity, where it ceases to capture the energy faithfully.

There are other factors to consider as well, but linearity is what we are after. When both the ends of the linearity curve flatten out, we have defined, roughly a second dynamic range, that of the sensor.

Then other factors concerning processing get into the act. But, all we are concerned with here is the dynamic range of the device in question.

Once that is settled, it is a simple matter to determine what the specifications of the transfer system needs to be. Well, maybe not simple, but certain.

It’s true that the dynamic range of a digital processor, expressed as a logarithm, is a function of it’s bit depth. However, the dynamic range of the system is governed by the dynamic range if the signal provided, which in turn is defined by the linear range of the detector.

A pound of coarsely ground pepper is the same as a pound of finely ground pepper. The difference is in the details!

George – again, you’re confusing precision with range.

Negative film has better range (8 stops or more).

Digital cameras have better precision, but only about 2 stops of range (comparable to slide film).

Chris,

Then the 12 bits of RAW data from a single pixel site filtered to contain only a single color channel has really only x bits of tonal data read to a precision of 12 bits? If x were 6, that would give 64 tones or a Dynamic Range of 1.8 (log 64), and that would be more in the ball park. Taking x = 8 yields 128 tones or a DR of 2.1. For either x, DR=2 is a good rounded estimate.

Asuming 6-8 bits to be the sensitivity limit, what purpose is served by providing a 12-bit/pixel camera RAW output? A 6 or 8 bit output could be jacked up externally to 16 bits to preserve it through editing. The higher bit depth is not needed until and unless the input/ouput curve is manipulated and that is done externally for RAW data. Why saddle the camera AD converter with unneeded precision?

George

Sorry for going off-topic, George.

The true dynamic range is defined by the source of that which one is trying to record (photography is first and foremost, a recording medium).

Lawrence, let’s not confuse various dynamic ranges — source, recording device, digitization process — by lumping them all into one.

I’m only talking about the assertion, which I consider to be erroneous, that in the quantization process dynamic range is independent of bit depth. Perfect quantization can’t always be achieved (e.g., using your audio examples, 48dB for 8-bit and 96dB for 16-bit) because other factors, such as source and recording device, will always intervene. Bit depth, however, does place an upper limit on the theoretically achievable dynamic range for that quantization process.

Those who would have you believe that both a bitmapped version of a 16-bit grayscale image and the original actually have the same dynamic range want you to assign 16-bit values to the light and dark pixels of the bitmap. And all I’m saying is you can’t do that. The only values available for you to assign in that case are 0 or 1.

When you view that bitmap on a 24-bit monitor, the actually white and black points can be very far apart on the contrast scale, but that has nothing to do with the intrinsic dynamic range of the quantized data.

=-= Harron =-=

Separating the various ranges is not lumping them together! In the final analysis, they do lump together, and certainly you know the differences. But to keep track of what is what, it is necessary to take apart the system and looking at the components.

Why you call it "Lumping all into one" is beyond me.

I also understand that the numbers are theoretical, so far as quantization is concerned. I don’t expect them to be met in practice.

Zero and one are all the values you can assign anywhere specific on a bitmap, not only at the end points. I never viewed the assignment of values any other way.

The dynamic range of the data being quantized sets the dynamic range of the output, so far as I can see. As Chris states, only the precision changes.

We are taking information from analog sources, processing that data digitally, then presenting that data as analog again. We need to be careful of how we consider analog data and digital data.

The dynamic range of the data being quantized sets the dynamic range of the output, so far as I can see.

The mind boggles.

You cannot so conveniently separate dynamic range from precision as you seem to claim.

It is the very fact that the only values assignable to the samples of a bitmap are 0 or 1 — i.e., its very limited precision — that defines its very limited dynamic range.

Why do you think it is impossible to achieve more than 48dB dynamic range with 8-bit PCM audio? By your argument, if the source had wider range, say 60dB, the bit depth should be immaterial. We can still capture that range with 8 bits, just at reduced precision.

But what does reduced precision mean? It means more quantization error. That means a higher noise floor. It means 48dB is the maximum dynamic range that can be achieved, assuming all things work out perfectly. It’s the math. I’m not making it up.

Now, during replay (or viewing) that 48dB can be put through an expander so that the difference between softest (darkest) and loudest (lightest) is exaggerated in terms of SPLs. Have you recaptured that original 60dB of source dynamic range? No way.

=-= Harron =-=

Thanks for all the insights. I’m seeing the dawn but I’m not at daybreak. Still groping but I can now see alternative interpretations of dynamic range. Is the following analogy viable? Imagine an elevator with a cab that spans 3 floors in a shaft that extends 20 floors. The cab height represents the dynamic range and the shaft height the total range (jet black on floor 1, pure white on floor 10). The cab can be open to 3 floors, but which three floors depends on its position. Compare this elevator system to another with cab height of 4 and shaft height of 10. The latter has greater dynamic range but a smaller total range. Might these elevators correspond to digital and film cameras?

George

Look, if the dynamic range is 0 to 1 volt, and you assign 0 volts bit 0, and 1 volt as bit 1, you have 0 volts to 1 volt dynamic range, but no precision. If the entire Beethoven ninth is contained in that 0 to 1 volt range, you have just stuffed Beethoven to nothing. This is clearly evident in streaming audio, where the quantization is selected by the provider. The higher quantization levels are much cleaner, but the sound level changes (dynamic range) remain the same. Don’t confuse dynamic range with total information content. You must have both dynamic range and bandwidth in the equation.

It seems a no- brainer to me, and the only mind that boggles is….never mind! 😉

Very good analogy, George. Similar to the black cat in a coal bin at midnight. The cat probably would get on and off at the same floor!

Hmmm, why do cats wind up in analogies?

This is clearly evident in streaming audio, where the quantization is selected by the provider. The higher quantization levels are much cleaner, but the sound level changes (dynamic range) remain the same. Don’t confuse dynamic range with total information content.

Lawrence, I have no further argument with you, but please do not obfuscate the issue.

Do not confuse bit rate with bit depth. Compare linear to non-linear encoding if you’d like, but, then, make that the point of your discussion, not the relation of quantizing precision to dynamic range.

Streaming audio via lossy-compression perceptual encoding techniques has little to do with our discussion. It’s like bringing JPEG into the argument all of a sudden, claiming the existence of user-selectable compression levels somehow proves dynamic range is independent of bit depth.

You must have both dynamic range and bandwidth in the equation.

Bandwidth is a function of sampling frequency and has nothing whatsoever to do with bit depth. But you knew that.

In the end, I think my difference with Chris is mostly that of terminology. We’ll both look at a source. He’ll say "Let’s capture it with reduced precision." I’ll say, "Let’s capture it with compressed dynamic range." In the world of digitization, we’d essentially be saying the same thing.

=-= Harron =-=

That’s right. I was stretching to make a point. Streched to much in this case!

I brought it in as an example of how one parameter alone does not define the totality of the result. Bad example!!

Interesting discussion, however. Thanks for all the input.

Lawrence

George – again, quit trying to get dynamic range numbers out of the bit count: they’re not directly related!

The camera needs the extra precision.

But the dynamic range doesn’t have much to do with the precision used by the camera.

You can change the dynamic range of your camera image just by changing the exposure. But the number of bits doesn’t change.

Digital cameras have better precision, but only about 2 stops of range (comparable to slide film)

Hmm? What kind of digital cameras are you referring to Chris? 7-8 stops would be more like it for respectable DSLR.

I’m not into “measurebating” all that much but it’s been my experience that correctly exposed (for the highlights) and processed RAW file can yield considerably more shadow detail than slide film.

Here are comparison charts for DSLRs with Nikon lens mount compiled by Thom Hogan, who definitely IS into measuring these things. Check out dynamic range of tested cameras.

<http://www.bythom.com/dslrcomp.htm>

Chris, Ok, I accept that and thanks for your patience. Now, if you’ll stick with me a little longer let me take it from there to fit this into the overall picture. Correct me where I am wrong.

Depending on the camera’s pizazz, the camera creates anywhere from 10 to 14 bits per pixel (typically 12 bits, so let’s assume 12 bits) all in a single, filtered channel at each pixel site but changing channels from pixel to pixel depending on the pattern of filters (typically Bayer).

If TIFF or JPEG formats have been chosen by the user, the camera then internally interpolates this data to transform it to 8 bits in each of three color channels. It compresses JPEG but passes TIFF along uncompressed. If RAW format has been chosen by the user, the camera passes along the initial 12 bits, leaving all processing for external editing.

Now, here’s my shaky, conjectural part: If the dynamic range can be covered by 8 bits, then it seems that 8 bits is all RAW needs, since it can be externally converted to 16 bits for processing without loss of detail when edited. The 12 bits are needed for TIFF and JPEG because they ARE processed internally. The same 12 bits, although not needed for RAW, are passed through simply because they are there. The conclusion (which I do not trust because it’s so weird) is that TIFF and JPEG formats demand more sensing precision than RAW.

George

Interesting read.

I’ve always understood bit depth being tied to how many DIFFERENT bits/levels of information that can be captured. Not quantity or tonal width=dynamic range.

It’s not the blackest black that can be captured but how many levels of detail transitioning between black and viewable tone that is bit depth. You may capture the whites white and the blackest black ever seen, but it’s crap if you start seeing posterization in certain tonal transitions anywhere in between.

Exposure, lens quality and what it brings to the CCD/CMOS chip and software determines how many different levels of data that are IMPORTANT in conveying the illusion of depth in an image.

George, do a Google check for "dynamic range bit depth". Lots of info, although it is mosly about scanners. Scanners are cameras, right? 😉

George – the range could be covered by 8 bits, if you had perfect lighting and perfect expsosure, and perfect white balance, and…. yeah, like that’s gonna happen.

The extra bits of precision allow you to make corrections later without losing the image detail.

It’s the same as working from a 16 bit scan instead of an 8 bit scan….

Also, because the camera capture is linear (gamma 1.0), you need some extra bits (2, preferably 4 more) to preserve details when converting to a gamma encoded colorspace.

Lawrence,

Googling on that subject is definitely the way to go and I’ve done that although, surely, not thoroughly enough. At some time, however, you should be able to back off from all the background and tutorials and succinctly make sense out of all you’ve read well enough to answer simple direct questions like why you need more bits than called for by the sensor’s dynamic range even before you begin to distort the input/output curve by editing. The answer may very well be that you don’t.

"…Scanners are cameras, right?…"

Yeah, except scanners don’t have to record data at all sites in the image simultaneously and can directly measure the color intensity at each site in all three channels, therefore eliminating the need to augment the actual measurements with interpolated values. Insofar as dynamic range (a sensor characteristic) is concerned, they ought to essentially equivalent.

That said, I think I’ll go back through the Google offerings as you suggest and pan for new gold 🙂

George

Chris,

That’s an acceptable explanation and I’ll settle for it! 🙂

George

George,I know nearly not enough to comment on your perceived differences between camera sensors and scanners. I would expect differences. One of those is what Chris mentioned, the linearity of the camera capture.

Anyway, I hope these answers, especially Chris’s will light the Aha! in you!!:-)

Chris, I’m glad you have a good explanation. I just came back from a short trip up the North side of Mt. Hood and I actually did spend some time thinking about expanations. Question: How do you explain anything?

Good teachers are among the people I greatly admire!

Too bad I’m not a good teacher…

A search on CCD technology, Bayer filtering and Foveon, leads to other scientific articles giving insight on bit depth and dynamic range and issues trying to control and precisely map it with digicams.

There’s a lot of software interpolation going on under the hood with Bayer filtering that I wasn’t aware of and this CCD technology is in most scanners and digicams.

I’ve been looking at sample images taken with a Foveon CCD digicam and I was impressed with the amount of sensitivity with low noise it could capture.

Zoom in on these images at this site:

<http://www.sjphoto.com/>

Laurence,

"…I would expect differences [between cameras and scanners]. One of those is what Chris mentioned, the linearity of the camera capture…"

Hoping not to come across as pedantic yet trying to clarify a point:

Camera sensors respond linearly to input light intensity and so too do scanner sensors. Camera and scanner sensors are fundamentally the same. Linearity of response should not be cited as a difference between cameras and scanners. Scanners were nowhere in the context of Chris’s remark.

George

Sticking my nose in where it doesn’t belong <again>, you may find this interesting:

Wayne Fulton – 24 bit or 36 bit color depth in scanners <http://www.scantips.com/basics14.html>. There, dynamic range v. bit depth is discussed in some pretty easy to understand terms.

For the sake of clarification, precision basically relates to the distribution of values from repeated measurements. IOW, the ability of a measurement to be consistently reproduced.

Tony,

"…Sticking my nose in where it doesn’t belong <again>…"

Needless to say, all points of view, and particularly yours, are welcome. Yes, Wayne Fulton has been most articulate on this and related subjects and, deservedly, his treatise is the first one cited of 76,900 Google hits under "Bit Depth vs Dynamic Range".

George

Well, thanks George. I say that I "don’t belong" because I don’t know squat about cameras. I was just following the technical discussion because "Dyanmic Range" and "Precision" are terms I am intimately familar with, albeit from a different field of study.

I found it most interesting to relate bit-depth to precision and am still trying to connect the dots on that one, although dynamic range is pretty clear. So in short, I’m learning, although your original question still makes my eyes gloss over <grin>.

Peace,
Tony

So when my neg scans written to cd from my local Fuji minilab show a histogram with data covering RGB level 5 to 248 but the preview has all my shadow detail plugged up, is that low dynamic range, bad scan or neg exposure or wrong gamma correction curve?

The reason I ask is, if I assign a 1.0 gamma profile to the untagged jpeg all that plugged shadow detail reveals itself. A closeup shot of flowers in grass now shows the ground underneath where before it was just blades of grass surrounded by flat black globs of shadow.

How is dynamic range related to this issue?

That’s a new definition of precision, Tony. Precision to me is the measure of exactness of a parameter, the degree of refinement or the tightness of tolerance. Repeatability is not necessarily a factor. I can make one measurement to the tolerance specified, or I can make many. (One shot measurements are a case in point). Precision, resolution and accuracy are related but not the same.

George, I was referring to the gamma mentioned by Chris. Linearity and gamma are not the same. One can have a linear transfer function and not have a 1 to 1 correspondence in the output. Gamma 1 indicates a slope of 45°, correct? Also, I lump cameras and scanners here as image transfer devices, with specialized considerations for each.

Chris, you are a good teacher, sometimes a bit impatient, but you know your stuff!

Tim, I am interested in how others, especially Chris, will answer your question. Hazarding a SWAG, I would say the practical dynamic range is what you have, about 243. The gamma doesn’t change that, it simply changes the distribution of the data within the dynamics presented. How does the histogram change when you change the gamma?

Lawrence,

That’s a new definition of precision

Uh, new to you, but certainly not new, all due respect.

Precision to me is the measure of exactness of a parameter,

Common misconception. Precision is the repeatability and the variance from a mean in a given distribution. Accuracy is the measure of the exactness.

Here’s the example. I shoot a rifle at a target. My sites line up with the center, and every time I hit the outside edge. Very tight grouping. The rifle is precise, but not accurate, since you’re aiming for the center.

I vaguely (very vaguely) recall a discussion of precision vs. accuracy in college physics. I believe the instructor used a watch as an example. A watch that averages the correct time (as defined by the NIST atomic clock, I guess) over the long haul, but may vary by seconds on any given day, is accurate but not precise. A watch that is exactly 10 seconds fast, and is repeatedly 10 seconds fast at all times, is precise but not accurate.

Sorry for the O/T, I’ll shut up now.

Edit: I cross-posted with you Tony. I think we’re on the same page.

A watch that is exactly 10 seconds fast, and is repeatedly 10 seconds fast at all times, is precise but not accurate.

Yes, precision.

I think we’re on the same page

Yep, we are.

Lawrence,

The histograms on Fuji jpegs don’t change when I assign a 1.0 gamma profile which is one of the canned Kodak film profiles installed with my Agfa flatbed scanner driver.

Because of the different exposure latitudes during shooting, each image will have a different histogram. I find the one that has the widest distribution of data and assign the 1.0 gamma profile just to get a glance of the shadow detail captured. Standard 1.8 and 2.2 gamma profiles hide quite a bit of shadow detail but retain balanced hue/saturation while the linear profile washes the image out.

Even the canned Fuji Neg Scan profile off their site is around a 2.0 gamma and does the same thing to the shadows. These are just 8 bit files shot outdoors/no flash from a fairly good quality Olympus point and shoot, but look nowhere near the balanced tonal quality I’ve seen captured off even the cheapest digicam point and shoots.

Most of the images need severe S-curve adjusts to get them to the quality of digicam exposure. But man, the detail that S-curve does bring out, though, at the expense of some histogram levels. I can get visable transition detail from 250 and down in the highlites and 5 to 25 in the shadows where beginning at level 10 and down transitions begin to look a bit grainy like dirt.

I did mean new to me, Tony. I wasn’t very clear on that!

I looked up the definition in the dictionary, and one current definition does include repeatability. Another, older one does not.

So, I went to my favorite reference on such matters, "The Art of Electronics" by Horowitz and Hill. There om p391 is a discussion of precision vs dynamic range, along with several examples. If you can lay your hands on a copy, it makes a good read. Repeatability didn’t seem to have a place in the discussion.

Tony, are you saying repeatability in terms of that each time I use a given measuring device to measure a known value, the device returns the same reading within specified tolerance? If so, I agree. If what I thought you to be saying is "repeated measurements are necessary to assure precision", then I disagree, as single shot measurements would therefore be impossible to validate.

The one place that repeated measurements do seem to be necessary are measurements that are done with respect to time, such as speed. Measurements always compare a starting point to an end point, and since we cannot wind the clock back, the starting point in time is lost forever.

Lawrence,

Accuracy is defined as, "The ability of a measurement to match the actual value of the quantity being measured"

Precision is the ability of a measurement to be consistently reproduced or the number of significant digits to which a value has been reliably measured, depending on what we’re referring to.

It has to do with time, only in as much as we measure at one point, and then measure again. You can test the pH of a liquid, with a precision of 4 decimal places, but if you test it 10 times, it is only precise when the coefficient of variation falls within an expected range.

Single shot measurements have precision, but in a single measurement, preceision means the number of significant digits.

But take that a step further, to exemplify my point. If I take a single shot measurement, I can measure with a precision of, say, 8.5549 (4 places behind the deicmal). But is it a precise measurement? What if I measure again and the value is 10.8891? Is it any less precise?

You are measuring with a precision of 4 places behind the decimal, but because there is no repeatability in the measurement, the precision is low. Now I measure a third time and the value is 10.8894, then you might say that the second two measurements are precise and have precision.

Another way to think about precision is by measuring the coefficient of variation. Within certain fields of study, certain systems have specific expected precision ranges, or CV’s. That basically means, how much deviation from the mean values were there in a specific set of measurements. It’s a way, to say, "I don’t care what the values are, how much deviation is there?"

If a measurement is precise, it is repeatable, regardless of the precision of the device used to measure it.

As I think this out now, I think that when Chris referred to bit depth being related to precision, I suspect he was referring to the number of places behind the decimal kind of precision, rather than repeatable values. IOW, a higher bith depth gave more significant digits, so-to-speak, and thus, more data upon which calculations could be performed. In that example, we know that the more data that goes into an algorithm, usually, the better, because the number of significant digits is higher.

Frankly, I may be picking gnat poop out of pepper here…

Peace,
Tony

The number of places behind the decimal point refers to it’s resolution, and of course, your argument is the same as the one that says resolution is not accuracy. I agree with that.

If I specify a parameter such as voltage to a tolerance of, say 0.0001%, I expect that when I measure against a known very accurate standard volt that my measurement will be within that 0.0001%, or +/-1 microvolt of that standard. In order to assure that reading, I would need to resolve at least 100 nanovolts, one more decimal place beyond 1 microvolt, and most likely I would try to resolve it to 10 nanovolts. After assuring that resolution, my next task is to reconcile the accuracy of that that number. Only then would I be in the position to validate my measurement.

Now,if my measuring device has an offset of say 10 millivolts, and I don’t know that, I am really out in left field. It’s been known to happen, and is the reason people who validate to such close tolerances do think in terms of gnatpoop!

Precision has a relative nature to it. A device, like the common oscilloscope, has a tolerance of around +/- 3% or so. If my standard is less than +/- 1%, I would consider that a precision source, for that measurement. It’s no damn good for the 0.0001% device. Therefore, knowing the precision without knowledge of the tolerance has little meaning to me.

The more I think of it, the more I realize that the term "precision" is descriptive rather than absolute. I deal in accuracy and resolution, so the description of a highly accurate device might state:

"This is a precision voltage (current, resistive etc) instrument, accurate to 0.xxx% and able to resolve )0.xxxxx volts, (ohms amps, whatever)". Sometimes, an offset max value is also specified. That value becomes more significant as the actual value measured decreases to zero.

Translating all this to digital, well, do you start with a 32 bit processor?

Lawrence,

I’m not in electronics so there may be some terminology differences, but where biological and physical sciences are concerned, the number of places behind refers to the precision of the measurment, not the precision of the instrument. If you want to call it resolution, fine, I can accept that.

Now maybe different fields of study have different ways to describe things, but I can tell you with absolute conviction, that in statistics, chemistry, physics, and even meteorology, the definitions go like this:

Accuracy is how close to the actual "real" value, Precision is how repeatable your measurement is, with the added note that some instruments can perform very precise measurements, but not necessarily with high precision. This latter concept refers to the number of significant digits being measured v. how repeatable a measurement is.

Now I can’t relate to electronics. I know there are electrons, and I know that Ohm is not a meditative chant, but that’s about as far as my knowledge goes in electronics. So it’s entirely possible that we’re saying the same thing with different terms.

Try this: google "what’s the difference between accuracy and precision". You’ll find I think, that regardless of absolute definitions, the common way of describing these terms by reputable sources are reasonably consistent with what I’ve been saying.

Fwiw, I have been tested on these definitions in national board exams for Medical Technology (to receive a board registered certification, much like nurses or radiologists have to take board exams), by the College of American Pathologists. Of course, I was young then, so I had to get out my reference books to check <grin>.

That said, an instrument may perform precise measurements (your term for resolution) but it may not have a high precision as measuring the same thing under the same conditions may yield wildly different values.

<shrug>

I’m sorry to be argumentative, I took a "jerk" pill today and the dose is apparently higher than I’m used to.

No, you are not a jerk, Tony. You are very well informed as to your view of these considerations. I appreciate your position well. What is perplexing is that the definitions in electronics would depart from the definitions you supplied, as electricity is branch of physics.

What is really unnerving is your statement: "Precision is how repeatable your measurement is, with the added note that some instruments can perform very precise measurements, but not necessarily with high precision." Very precise is high precision to me. Otherwise, the definition is imprecise. When is precision not precision? When it is resolution?

The way out is to separate resolution, which is a commonly used term in electronics, from precision. Now your statement would read: "Precision is how repeatable your measurement is, with the added note that some instruments can perform with high resolution, but not necessarily with high precision." That makes perfect sense, as precision now relates to accuracy. Again an offset to the measurement blows precision right out the window, but the resolution remains. I can resolve 1 part in 10^6, is the way it is stated. But, if I resolve, say 1 part in 10^-6, but have an offset of 10^-3, you can see how far off from an accurate measurement I am.

This may not apply to pH measurements, perhaps, as no reasonable pH offsets seem likely. About the rest of the studies cited, I have as much knowledge of them as you do of electronics, no, less! (Yes, ohm is not a chant! However, I’m sure you have heard of "Ohm sweet ohm" or the famous song "There’s no place like Ohm" <G>):D

I am somewhat of a jerk about definitions. Metamerism sets me off! 😉

Repeatability: Now, if I am designing an instrument in the range of precision I specified, I would of course make multiple measurements of the same standard source to determine it’s repeatability. And, if I found that repeatability was an order of magnitude lower than the level of accuracy needed, I would have to spec it at that lower value, or find another solution. When you obtain my spanking new instrument, I would not expect or demand that you do repeated measurements to your DUT, except maybe to see if I really do live up to the numbers. If I do, one measurement will suffice, if I don’t, buy someone else’s!

In fact, when I do repeated measurements of the DUT, it is to ascertain the characteristics of the DUT, not to average out the meter’s problems. That would really confuse matters!

I would have royally flunked those exams.

Ok, I did the Google search, and I also searched the difference between resolution and precision. You are right Tony, and the way it was used in my process is sloppy, to say the least. All I can say is that’s the way it came down years ago, which shows how easy it is to get off base, and how hard it is to turn the corner.

For me, I found that the discrepancy between your use and mine, both in science, could differ so greatly, so I needed to resolve the matter.

I will expunge the casual use of resolution in place of precision, although how very precise measurements can be performed without high precision is still perplexing! I still have to noodle that one.

I went back to "The Art of Electronics" Chapter heading "Precision Circuits and Low Noise Techniques" p391. Here are some statements:

"In the field of measurement and control there is a need for circuits of high precision. Control circuits should be accurate, stable with time and temperature and predictable….we always have the desire to do things more accurately….Even if you don’t always actually need to the highest precision…."

<Sigh!>

Heh. Well, I didn’t mean to be such a stickler, but I certainly see your point about the term "resolution" when it comes to the issue of significant digits, and in fact, am noodling on that myself. It’s an interesting and possibly more accurate term, possibly especially when distinguishing between precision and precise <grin>.

But what I find interesting is Chris’ relation of precision to bit depth. And someone mentioned the "stair" analogy, whereby dynamic range would be the length of the staircase, and the bit depth would be the number of stairs. I think that’s a reasonably sound representation, and when coupled with the idea that bit depth represents, in a way, the number of significant digits in an image, it may actually make sense to me – still working on it though.

Again, sorry to beat the idea to death. I had been reading along trying to learn, and then "popped my hand up" with something.

Move along folks, nothing to see here…<grin>

Peace,
Tony