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RE: filmscanners: brief density math lesson...

At 11:03 PM 6/15/01 -0400, Austin Franklin wrote:

 >The integer ratio values are what your scanner gives you.  14 bits means you
 >can represent an integer number from 0 to 16,383.  This means if your
 >scanner can record integer density ratio values from 1:1 (0) to 16,384:1
 >(16,383).  16,384:1 is a D value of 4.2 (log 16,384 = 4.2).  That is why
 >scanners that have 14 bit A/Ds claim to have a DMax of 4.2...all that means
 >is they can support integer density ratio values of 1:1 to 16384:1, but that
 >does not mean the scanner CCD and analog circuitry can provide that!  That's
 >another topic of discussion...

This is a common misconception - relating bit depth to dynamic range.

The CCD sensor, an analog device, determines the dynamic range as well as 
noise of a scanner or digital camera. It is connected to an A to D 
converter of some resolution (8 or 12 or 14 bits or more as technology gets 
better). The number of bits that the A to D converter produces determines 
how finely the range of the CCD is quantized, or to put it in photographic 
terms, how much tonal detail there is in the image. A good scanner will 
have a CCD sensor with wide dynamic range and low noise, and an A to D 
converter that is matched to the quality of the CCD sensor. There is no 
point in using a high resolution A to D converter with a CCD that has poor 
range or a lot of noise.

Let's take a silly example. Suppose we have a CCD that can cover a 1000 to 
1 range of light intensity. That's a DMax of 3. Provide an appropriate 
light source and some optics, and connect it to a four bit A to D converter 
(16 levels). Set the gain and offset so that the limits of CCD sensitivity 
correspond to values 0 and 15 (computer things count from zero, not one) of 
the A to D converter. We have a scanner with a DMax of 3, and four bits of 
resolution. The DMax has nothing to do with the number of bits in the A to 
D converter, just the range of the CCD sensor. We could use an A to D of 
any number of bits with this CCD sensor and capture its full range with any 
level of tonal precision we wish.

It is also worth noting that film is not linear in its response to 
exposure. The curve has an S shape, with not a lot being recorded near DMin 
and DMax. You can find D Log E curves (density as a function of the 
logarithm of exposure) in the film data sheets that Kodak and Fuji have on 
their web sites. The DMax of a film is the maximum density it can produce, 
but there is very little information in those deep tones. So it does not 
follow that if you are shooting UltraDmaxia with a DMax of 4 that you need 
a scanner with that range. 3.5 might be all you ever need to pull 
everything useful off the film.


Roy Smyth
Victoria, British Columbia, Canada


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