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# Thread: Algorithm to find characteristic curve

1. I've never built a densitometer, but my RH Designs Alalyser has the capability to work as one. I've checked it against an X-Rite one I have and it is right on (relative values only).

2. Originally Posted by Photo Engineer
The best method of fitting the characteristic curve comes from use of a cubic spline. Here is a reference:

http://en.wikipedia.org/wiki/Spline_(mathematics))

We use this in most all of our software, or at least did when I worked in the area.

PE
Thanks, that should be enough to get me started. Now I just need to figure out how to program it.

3. Originally Posted by L Gebhardt
I've never built a densitometer, but my RH Designs Alalyser has the capability to work as one. I've checked it against an X-Rite one I have and it is right on (relative values only).
I've no reason to believe that the aforementioned analyser is bad, but...

1) I'm, ahem, cheap!
2) I have a tight budget.
3) I have an itch.

4. Originally Posted by Anon Ymous
I've no reason to believe that the aforementioned analyser is bad, but...

1) I'm, ahem, cheap!
2) I have a tight budget.
3) I have an itch.
I should have expanded on this to say that the probe is a fairly simple looking thing and probably uses a cell like you mention. So, I'm sure it's possible. Just use the enlarger as a light source. You would need a calibrated step wedge to correlate the voltages to density.

5. Originally Posted by L Gebhardt
You would need a calibrated step wedge to correlate the voltages to density.
Maybe not. See post #10 in this thread.

6. You will find that Excel or most any spreadsheet program can make a quite good graph of sensitometric data. I have posted some of mine here.

PE

7. Originally Posted by Photo Engineer
You will find that Excel or most any spreadsheet program can make a quite good graph of sensitometric data. I have posted some of mine here.

PE
That's what I've found too. I also have the BZTS plotter program. But if I want to automate the process of reading a point off of a curve, say the exposure for 90% of DMAX I can't do that with Excel.

I figure if all these program can nicely plot the line it shouldn't be too hard to get a nice function for each data set.

8. Tough one. First, you have to choose whether you are setting out to predict, or describe, what the film is doing.

If you master the 'predictive' testing, you've made a lovely graph and cut off your creative future at your knees. Choose wisely. BTZS considered, it is just a beginning. Add imagination to the business of reproducing a perfect tone curve, and you will get photography, not numerology.

9. Well, you have to consider that many densitometers made nowdays have parallel and serial ports including USB. These can be connected to the computer to read the data, and a simple program can convert the data to row-column format for Excel. I've done this and it is fairly easy. I no longer have a copy of it, as it was written years ago (80s) and was used at Kodak for a number of chores including inverting row with column and sorting. This was before Excel or Lotus had those features.

PE

10. For me getting the curve is not the problem. Solving a polynomial or cubic spline to get some useful data from it would be helpful. For example solving (X) for, say (Y=0.1) is the difficulty I have encountered.

For example, I got a good 4th order polynomial fit with this Delta400 in T-max developer curve:
f(x) = 5.480380E-2*x^4 + -2.520940E-1*x^3 + 3.262913E-1*x^2 + -6.918132E-1*x + 1.568020E+0

But solving it for Y=0.1 is time consuming, even with a computer. I found it easier to just graph it and pick up any needed value off the graph.

But if you were to write some software to easily solve a polynomial like this or a spline, that would be great. It would also be nice to have it solve for the X-intercept of a least-squares fit through the straight-line portion (another way to estimate speed as PE has pointed out in a related thread).

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