Revised My Film Curve Graphing Spreadsheet

Sharktooth said:

I was asking about Delta-X because I don't have any information about it. I'm just making educated guesses about what's trying to be done. The standard documentation for film speed doesn't mention it, so there's obviously some higher level analysis that I'm interested in finding out about.

This thread peaked my interest, since the Delta-X and 0.3 gamma points appear to be looking for a point on the toe of the characteristic curve that has a specific slope. That can't be found using a straight line point to point analysis, but it can be found with a polynomial or spline fit to the data. The conventional speed analysis can be well analyzed using the simple straight line point to point analysis, but it's the higher level analysis that might benefit from creating a mathematical function of the characteristic curve.

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Bill Burke used to have a server with Stephen's paper and the "Simple Methods" paper, though I can't find it anymore.

I did run across a shared curve plotter software developed by photrio member RafalLukawiecki that I had forgot about: https://github.com/RafalLukawiecki/film_tests

Member aparat was also working on software but "Last seen Jun 27, 2023" according to the photrio server.

Sharktooth said:

I was asking about Delta-X because I don't have any information about it. I'm just making educated guesses about what's trying to be done. The standard documentation for film speed doesn't mention it, so there's obviously some higher level analysis that I'm interested in finding out about.

This thread peaked my interest, since the Delta-X and 0.3 gamma points appear to be looking for a point on the toe of the characteristic curve that has a specific slope. That can't be found using a straight line point to point analysis, but it can be found with a polynomial or spline fit to the data. The conventional speed analysis can be well analyzed using the simple straight line point to point analysis, but it's the higher level analysis that might benefit from creating a mathematical function of the characteristic curve.

Click to expand...

The Delta-X Criterion is a mathematical approach to approximate the same results as the fractional gradient method. It uses a fixed density of 0.10 over film base plus fog. The value of ΔX represents the difference between the fixed density point and the approximate fractional gradient point. It's value is dependent on the value of ΔD which is the density above 0.10 found Δ1.30 to the right of the fixed density point. When ΔD = 0.80, ΔX always equals 0.296. So when the ISO contrast parameters are followed (Figure 1) ΔX equals 0.296 and there is no need for the equation. Determining a speed value outside the ISO parameters requires the use of the equation or a look-up table.

Bill Burk has generously made a number of papers available on a server, but the site is currently down. If you are interesting in doing additional research, two of the key papers are:

Nelson, C.N. and Simonds, J.L., Simple Methods for Approximating the Fractional Gradient Speeds of Photographic Materials, JOSA, Vol 46, No. 5, May 1956.
Nelson, C.N., Safety Factors in Camera Exposures, Photographic and Science Engineering, Vol. 4, No. 1, Jan-Feb 1960. (attached)

ic-racer said:

Bill Burke used to have a server with Stephen's paper and the "Simple Methods" paper, though I can't find it anymore.

I did run across a shared curve plotter software developed by photrio member RafalLukawiecki that I had forgot about: https://github.com/RafalLukawiecki/film_tests

Member aparat was also working on software but "Last seen Jun 27, 2023" according to the photrio server.

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I opened a ticket with my provider, the page should be up shortly beefalobill.com/benskin then add content or contents something like that

Stephen Benskin said:

The Delta-X Criterion is a mathematical approach to approximate the same results as the fractional gradient method. It uses a fixed density of 0.10 over film base plus fog. The value of ΔX represents the difference between the fixed density point and the approximate fractional gradient point. It's value is dependent on the value of ΔD which is the density above 0.10 found Δ1.30 to the right of the fixed density point. When ΔD = 0.80, ΔX always equals 0.296. So when the ISO contrast parameters are followed (Figure 1) ΔX equals 0.296 and there is no need for the equation. Determining a speed value outside the ISO parameters requires the use of the equation or a look-up table.
View attachment 391871
Bill Burk has generously made a number of papers available on a server, but the site is currently down. If you are interesting in doing additional research, two of the key papers are:

Nelson, C.N. and Simonds, J.L., Simple Methods for Approximating the Fractional Gradient Speeds of Photographic Materials, JOSA, Vol 46, No. 5, May 1956.
Nelson, C.N., Safety Factors in Camera Exposures, Photographic and Science Engineering, Vol. 4, No. 1, Jan-Feb 1960. (attached)

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Thanks for that info about the delta x calculation. I don't understand how it was derived, but I've added that to the analysis file I've created. I'll post that shortly.

I'm showing a couple of images from the Excel program I created to create and graph a polynomial from raw data. The Excel file is also attached below. If you don't have Excel, you can download LibreOffice for free. LibreOffice has no problem with most Excel files, other than some minor formatting differences.

The original reason for creating the file was to analyze raw data using a simple representative function for the data. A polynomial is simple to use for analysis, and can represent some types of data very well. The characteristic curves for photographic film seem to work reasonably well with a higher order polynomial fit. In this particular case, it is well suited to find slopes at any point of the curve, since the slope at any point is the first derivative of the function. The first derivative of a polynomial is easy to calculate, as is the second derivative. This means that you can easily find the X position of any target slope (such as the 0.3 Gamma slope).

The basic form of a polynomial is aX^4 + bX^3 + cX^2 + dX + e (of fourth order). where a, b, c, d, and e are the coefficients of the polynomial

The first derivative is 4aX^3 + 3bX^2 + 2cX + d

The second derivative is 3*4aX^2 + 2*3bX +2c

Higher order polynomials are handled in a similar fashion, and it's simple and straightforward.

Stephen Benskin said:

I wouldn't say they don't put much weight into the ISO speed but consider it as more of a guideline when it comes to exposure. In other words, there is a distinction between film speed and film exposure. Also, they are probably being responsive to public opinion.

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A lot also has to do with broader social expectations (away from those who spend too much time sweating over densitometers) for what people expect Tri-X to look like when exposed at 400 - not that it necessarily be an absolute '400' speed film - and the same for the original HP5, where Ilford wanted to claim that it would hit 640 in Microphen for Tri-X at 400 equivalency in 'look'.