>> Thanks, but I would like to know how to calcuate this gamma value I hear so much about. <<(posted 8461 days ago)Hi Russell. Gamma is actually the slope of the "straight part" of the characteristic curve. You don't have enough data points to know if it's "straight" or not, so you can NOT actually confirm gamma. However, I'll describe how to figure it. BTW, there is no guarantee that a given film will have a straight line portion, which has something to do with Kodak's invention of a concept called "contrast index" quite a few years ago.
I'm not a zone system guy, so bear with me on definitions. I presume you consider that a Zone I exposure produces only a very small film density above base + fog density (note: 0.06 or 0.10 are both fairly small densities). Second, I presume that each additional zone number doubles the previous exposure. Everything else I say is based on these assumptions, so if these are wrong, disregard any further.
Assuming the above, here's what we can do:
To calculate slope of the characteristic curve, you need to have compatible units for both axes of a graph. Traditionally, in sensitometry you would use density of the negative for the vertical axis and the base 10 log exposure for the horizontal axis. You already have density values for your negative. Don't get scared about the other term; It's just technical mumbo-jumbo whereby each f/stop exposure change is equivalent to a 0.30 change on the log exposure axis where more exposure makes the number get larger. It can be a relative scale for your purposes, meaning that you can just make up a number for a starting point.
I would suggest you just call your lowest density patch (Zone I exposure) an exposure value of 0. If you do so, the doubled exposure (Zone II) has a log exposure value of 0.30; doubling exposure again (Zone III) is log exposure 0.60, etc, etc. So Zone V is equivalent to log exposure 1.20 and Zone VIII is like log E = 2.10.
Now, IF Zone I to Zone V were a straight line response, the gamma would be: change_in_density / change_in_log_exposure. Your density changed from 0.10 to 0.70 = 0.60. At the same time, your log exposure changed from 0.0 to 1.20 (Zone I to Zone VIII). As Joe H indicated, gamma (provided there is a straight line response) is density change divided by log E change = 0.60/1.20 = 0.50 for a gamma value.
For your second set of data points, Zone V (log E =1.20) to Zone VIII (log E = 2.10), you have density change of 1.00 - 0.70 = 0.30. This divided by the log E change of 2.10 - 1.20 = 0.90 gives 0.30/0.90 = 0.33 for the gamma value.
Now, clearly the the two "gamma values" of 0.50 and 0.33 ARE NOT THE SAME; this proves that they are NOT on the same straight line and cannot both be legitimate gamma values. It sounds very much like either A) your response curve (slope) is "shouldering off" on the top end or B) your zone exposure system (or my interpretation of f/stop film exposure changes per zone) is not legitimate. I really doubt option "A" unless you are really doing what I would consider underdevelopment.
I hope that this is more helpful than the other responses; feel free to email if necessary.