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I have a question concerning the sensitometry of photographic/radiographic films.

Anywhere I look about sensitometry and Hurter-Driffield curves, be it radiology books, medical physics books or even technical standards, I keep seeing a limited version of the Hurter-Driffield curve being described, that is, they never actually show the entire curve of a film (from base+fog all the way up to 100% film saturation), which can have a gamma value of way over 9.0 optical density. They usually keep it as low as 5.0 or so, why is that?

A more specific question is why do most books and standards always use the same optical density interval to evaluate the average gradient of a film, which usually goes from an optical density of 0.25 above base + fog all the way up to 2.00? Why is it defined this way?

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Actually film can have a gamma of 1. This is a measure of the straight line angle and then finding it's tan (trig). The tan of a 45 degree straight line is 1. When making paper, we wish to match the contrast of the film to the contrast of the paper. It was discovered that making the film contrast bases on a straight line angle of about 38 degrees = gamma 0.80 is a best fit for a grade 2 paper. A lower gamma has too little contrast and an higher gamma has too much contrast. This is a film to paper fit thing. It is based also on the fact that we view prints by reflected light that passes through the developed emulsion and then returns through the same emulsion. In other words light makes two passes. Because of this, one stop change of exposure on paper is double the blacking that would occur if you increased the exposure to film. 1 stop plus on film what a gamma of 1 = 0.30 density units. With a gamma of 0.8, one stop change is 0.8 X 0.30 = 0.24 density units. Paper with a gamma of 2 yield 0.60 density delta for 1 stop of exposure increase. Again, paper reacts twice as fast as film due to the two light passes and the gamma of both film and paper are adjusted to make a best fit as to contrast.

The ASA method of testing for film speed and now the ISO method is based on 0.10 above base fog. The film is sluggish as this is about the threshold of exposure. Best to start measuring just above this toe area. After all, the straight line area is due to a uniform density change induced by uniform changes in exposure.

2.00 is about the maximum blacking you can get on film. X-ray film is coated both sides and goes up to 4.00. The density of 2.00 is a log value base 10. It is 100 in decimal notation. A 100 watt lamp appears as if it is only 1 watt when viewed a film with a density of 2.00. Some pictorial films go to Dmax at 2.50 density.

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    \$\begingroup\$ Sir, first of all I'd like to thank you for your rapid and straightforward input. I'm mostly concerned with x-ray films (for research purposes), but I wasn't so sure where to ask about this on StackExchange. I learned about StackExchange Photography so I tried to make an analogy as best as I could with regular photographic film, although you're right, image viewing in one works by light reflection and in the other by light transmission. But I believe (please correct me if I'm mistaken) when it comes to sensitometry... \$\endgroup\$ May 23, 2017 at 23:56
  • \$\begingroup\$ ...the same equations for the parameters (average gradient, speed/sensitivty, contrast etc) applies to both, right? So why is it that most medical physics books (WEBB, S.; HENDEE & RITENOUR etc) and standards (ISO 5799, ISO 9236-1, ISO 9236-3, ISO 7004 etc) that deal with sensitometry always display the characteristic curve up for any given film up to a certain optical density when in reality such films can display a much higher optical density (and thus greater curve) if you fully expose them? \$\endgroup\$ May 24, 2017 at 0:01
  • \$\begingroup\$ Just a guess, but why give a patient a higher dose of x-rays than is necessary to expose the film enough to give a readable image? Thus the curves don't matter if the film is never exposed beyond that density. \$\endgroup\$
    – Michael C
    May 24, 2017 at 0:06
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    \$\begingroup\$ Likely the literature is behind the curve in densitometer design. When I built the ones that would read 4.00, about 15 years ago, this was state of the art. Also I think most diagnoses were visual examination of the X-ray place on a light box. The light box was not bright enough to work those elevated densities. Now days, likely you can diagnose with scan and computer. All this above my pay grade. \$\endgroup\$ May 24, 2017 at 0:38
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    \$\begingroup\$ A film density of 9.0 = 1,000,000,000 in decimal notation. A 1000 watt lamp viewed through this 9.0 area of the film appears to be 1 minus 6 - watts -- I don't think you can see any light coming through. \$\endgroup\$ May 24, 2017 at 1:04

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