Digital BW, The Print

Thanks Martin,

Bottom line to me is that when someone here (except for Austin, because he's
made it completely clear what he means by the term) or elsewhere says
'dynamic range' to me in reference to inkjet printing I will (safely) assume
they are talking about the range of paper base to max black, whether it's
technically correct or not. And, furthermore, that usage will be more than
adequate for conveying the thoughts and ideas under discussion the great
majority of the time.

Larry



-----Original Message-----
From: Martin Wesley [mailto:mwesley250@...]
Sent: Wednesday, March 27, 2002 1:00 AM
To: DigitalBlackandWhiteThePrint@yahoogroups.com
Subject: [Digital BW] Dynamic Range Definitions and Print Tones


I realize this may be of little interest to most but some have expressed
interest. So here is some additional information. This is long. You have
been warned.



Since we are on the Internet a web search seemed like the thing to do. Here
is some of what I found plus an additional text reference. Be careful of
long web addresses that wrap from one line to the next. You may need to cut
and paste the pieces into your browser to get them to work.



Dynamic Range, Some Definitions:



From Merriam-Webster's Dictionary:

Main Entry: dynamic range
Function: noun
Date: 1949
: the ratio of the strongest to the weakest sound intensity that can be
transmitted or reproduced by an audio or broadcasting system

http://www.m-w.com/cgi-bin/dictionary



From NASA website:

"The dynamic range of an image is the ratio between the maximum and minimum
brightness levels in the image."

http://nasatech.com/Briefs/Aug98/NPO20254.html



From the Cornell University Library:

"DYNAMIC RANGE is the range of tonal difference between the lightest light
and darkest dark of an image."

http://www.library.cornell.edu/preservation/tutorial/intro/intro-05.html



From Digital Photography Review:

"Dynamic range is the ratio between the brightest and darkest recordable
parts of an image or scene."

http://www.dpreview.com/learn/Glossary/Digital_Imaging/Dynamic_Range_01.htm



From X-rite's "The Color Guide and Glossary"

"Dynamic Range: An instrument's range of measurable values, from the lowest
amount it can detect to the highest amount it can handle."



From Mix Magazine:

"Dynamic range, generally measured in dB, is the ratio of maximum
undistorted signal (full-scale or onset of clipping) to residual noise
(noise floor)."

http://industryclick.com/magazinearticle.asp?releaseid=5828&magazinearticlei
d=72693&siteid=15&magazineid=141



From CCD Direct:

"The dynamic range is often represented as a log ratio of well depth to the
readout noise in decibels. For example, a system with a well depth of 45,000
electrons and a readout noise of 15 electrons would have a dynamic range =
20 log (45,000/15), or 69dB."

http://www.ccddirect.com/online-store/scstore/dynamic.html



From outer space. [Caution, viewing this page may be hazardous to your
sanity!] <G>

http://utam.geophys.utah.edu/UTAMtheses/JingChen/latex_2_html/node13.html



So what we have is a variety of definitions that seem to vary depending upon
what field you are in but the common element is that they are looking for a
meaningful way to describe a relationship between the minimum and maximum as
a ratio.



I have to wander into some math here to clear up a point. Sorry but I just
don't see any way around it.



Some people say the dynamic range is the difference between the min and max
and some say it is the ratio. The interesting thing is that they are both
sometimes correct. Some things such as sound volume, CCD response and image
density are not direct measurements of a physical property but are
calculated values from actual properties given in logarithmic form.



The log of a number is the value of that number as a power of a base number
which is most commonly 10. The Log10 of 100 is 2, (10 raised to the 2nd
power) the log10 of 10,000 is 4, (10 raised to the 4th power) the log10 of
112.3 is 2.0504, (10 raised to the 2.0504th power).



Now one of the nice things about logs is that if you add them the result is
the same as multiplying the original numbers and if you subtract them the
result is the same as dividing the original numbers when you convert the log
values back to their original form. This is the reason logs were so widely
used because they reduce complex multiplication and division problems to
simple addition and subtraction. Very handy before we had pocket calculators
and computers.



Photographic materials are usually measured in density. If it is a
transparency or negative the density is the log of 1 divided by the
percentage of light that passed through the film. If it is a print the
density is the log of 1 divided by the percentage of light that was
reflected from the print.




So if a print has a white paper base reflectance of 95% (95% of the light
shining on this spot bounces off toward your eye) and the deepest black has
a reflectance of 4% (only 4% of the light falling on this dark spot bounces
off and the rest is absorbed or scattered away from your eye.) The dynamic
range would be the maximum value of 95% divided by the minimum value of 4%,
which is 23.75. Here taking the ratio is proper because we are talking about
direct measurements of a physical property and not calculated values. The
difference would be 91percentile, which is the range of the reflectance.



Usually in photography we do not talk about reflectance but instead use
density. So for this case the paper base would have a density of 0.0223 (the
base 10 log of 4%)and the darkest black 1.3979 (the base 10 log of 95%).
Since these are log values calculated from the reflectance you find the
dynamic range by subtracting them. 1.3979 minus 0.0223 is 1.3757 the dynamic
range and the range of the Density.



Now if you take this Density dynamic range and raise 10 to the power of
1.3757 you get 23.75! The same number you got by dividing the maximum
reflectance by the minimum reflectance.



So if you are talking about image density (a log value) the dynamic range
and the range are the same. If you are talking about reflectance or
transmission they are not the same. One is the ratio and the other is the
difference.



It is interesting to note that if the reflectance range is 1% to 92% the
range stays the same at 91 but the dynamic range goes up from 23.75 to 92.
If the range shifts up to 8% to 99% (still a range of 91) the dynamic range
drops to 12.38. This suggests to me that the simple range of reflectance
with the min and max values is of more interest than the dynamic range when
looking at a print or judging print medium quality.



Noise generally does not seem to be used in the calculation of the dynamic
range but it may be a factor in determining the minimum or weakest value.
The best example would be in audio systems where there is a background hum
or hiss. This is what is known as the noise floor and in audio the weakest
or minimum value is this noise level since you cannot hear any sounds that
have a volume lower than the noise. So in this field taking noise as the
minimum value makes sense. In the CCD definition above it seems that this is
similar to the audio example and the noise is equal to the weakest signal
you could measure or use. (Notice that they take the log of the ratio of max
to min which is the same as subtracting the log of the minimum from the log
of the maximum.)



There is noise in the process of making a print since information is lost or
degraded as you move from scene to camera to print, but once the print is
finished the concept of noise does not appear to apply unless it is the
transfer of the light from the print to my eyes (which have a lot of noise)
to my brain (which has even more noise). In any case this would vary from
person to person and there would be nothing meaningful to measure.



For all practical purposes a print existing as an object separate from the
process that produced it seems to be noiseless and the dynamic range is the
ratio of the min and max reflectance or the difference of min and max
density.



Finally the "number of tones" present in a print does not depend upon the
dynamic range or the range or the min and max. A print is an analog image
and by definition has continuous tones that flow from one to another without
any step change or gaps. Just as the sun sets in a smooth motion and not in
increments, so the shades of gray flow in a continuous tone print.



A silver print or negative is continuous tone by the nature of the chemical
processes that produced it and an inkjet print is continuous tone by virtue
of the dither pattern, variable droplet size, etc. that are used to produce
it from a stepped digital file. By the definition of continuous tone there
are no steps and any tone value between the limits of min and max can be
created. Even though our eyes and instruments cannot distinguish between two
tones, if they are too close together in value, does not change the fact
that an infinite number of tones are available to the print maker in either
silver or ink to create their image.



For the sake of an example let's assume that we can only distinguish a 1%
change in reflectance and this is the same at all levels of light and dark.
So in my earlier example of a print with a min of 4% and a max of 95% and a
range of 91 percentile we would be able to distinguish between the two tones
that have 4% and 5% reflectance, or 5% and 6%, or 6% and 7%, and so on. This
would tend to make you think that you could only get 92 shades of gray out
of this range. What you have to keep in mind is that if you can distinguish
between 4% and 5% you can distinguish between 4.1% and 5.1%, and between
4.001% and 5.001%, and between 4.0000001% and 5.0000001%. Which leads to the
conclusion that there are an infinite number of distinguishable tone pairs
within any tonal range of a continuous tone image. If there are an infinite
number of tone pairs then there must be an infinite number of tones.



This then comes back to my original assertion that all continuous tone
photographic mediums have an infinite number of tones whether they are ink
jet or silver based. Which then means that an ink jet print cannot have more
tones than a silver print. They may be easier to control since the source is
a digital file. It may be possible to achieve better tonal compression and
map a wider real life scene into a digital file then onto film or photo
paper but the end result is not more print tones.



Thank you for your patience if you got this far. <G>



Martin Wesley



[Non-text portions of this message have been removed]



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