Revised My Film Curve Graphing Spreadsheet

[ic-racer]

My prior film graphing spreadsheet was created back in 2011. I finally got around to revising it, as I had some film curves I needed to analyze.

The speed points are automatically determined. It can't actually measure 0.3G point, but it estimates it with Luther's equation and X-intercept and Delta-X.
It does not have the complete Delta-X functionality, it only evaluates Delta-X for the condition of Delta-D = 0.8 and Delta-X = 0.29*.


*Why that condition is important is explained in a monograph by Steve Benskin https://www.photrio.com/forum/threads/delta-x-criterion.192714/

 

[ic-racer]

This is the new version. I did this one in Apple Numbers.

 

[ic-racer]

This a screenshot of the old version from 2011. It is in Microsoft Excel and no longer works on my computer.

 

[Andrew O'Neill]

...and here I am STILL using pencil, paper, and flexible ruler! No Excel here, but Google Sheets seems to work well, when I tried it. Thanks for sharing!

 

[koraks]

Looks really need! Are you planning to share the actual template as well, or just the screenshots? Mind you, I'm personally fine with either because I'm not in the business of doing film plots. I can imagine others might want to know...

 

[ic-racer]

Still testing it so I don't inadvertently share something with errors.

One issue (for which I have PM'd Steven Benskin) is the discrepancy of 0.30 vs 0.29 for the Delta-X value of the ISO/ASA triangle condition. The equation shown assumes 0.3 (one stop).
ISO speed = 0.8/H vs Fractional speed = 0.4/Hfg are one stop apart.

His paper referenced above shows both. Depending on which version is used a speed might be 382 vs 392. Right now my spreadsheet is calculating both.

 

[ic-racer]

Steve replied that the actual number (for Delta-X when Delta-D = 0.8) is 0.296, so that makes it reasonable to round up to 0.30 for all the calculations.

 

[ic-racer]

...and here I am STILL using pencil, paper, and flexible ruler! No Excel here, but Google Sheets seems to work well, when I tried it. Thanks for sharing!

Nothing wrong with graphing. In fact someone should make some CAD files for the clear plastic overlays. All the math is just trying to duplicate those, in which case pencil graphing puts one ahead of the game!

 

[Bill Burk]

I’ve got those as PDF (source InDesign)

 

[ic-racer]

I will share the 'guts' of the program.

For the "W" speed determination we need "E", "Gamma"(Slope) and "A" (X-intercept). To find the "E" this IF-THEN statement is applied to each of the transmission densites.

D4 and D5 are two adjacent transmission densites recorded from the film

$H$33 is the X-intercept (easy to get with the "SLOPE" function)

C4 and C5 are the two adjacent step wedge densities (or millilux-sec) that are associated with the transmission densities D4 and D5.

In plain language, it asks if the Y-densities straddle the X-intercept. If so, it assumes the two points straddling the x-intercept form a straight line (rather than curved) and it calculates the near-exact Y value that will fall right above the X-intercept (below). First it calculates the slope of the two points (K22) and puts this in the cell. If not, then it puts "0" in the cell. Then add up all the cells with "SUM," they should all be zero except for the value we are seeking (slope of the two points, K22). (See columns K and L on the spreadsheet screenshot).

Next we need "W" which is easy to find as it is E/(1/2 Gamma).

Then we use the equation from the paper:

Where H37 is "W" that we calculated above.

This number that results is the deviation of 0.3G point from the X-intercept. So add or subtract this from the X-incercept and you have the 0.3G point.

That is a little different from the Delta-X method where one calculates the deviation from the 0.1 point. You see the X-intercept is easier to find.

However, I did go ahead and figure out how to solve for the 0.1 point...

 

[RalphLambrecht]

Looks really need! Are you planning to share the actual template as well, or just the screenshots? Mind you, I'm personally fine with either because I'm not in the business of doing film plots. I can imagine others might want to know...

Yes, please share the actual spreadsheet or a template for use in 'Numbers'.

 

[Sharktooth]

This thread brings back distant memories for me. Back in the early 80's I was doing D-Log E curves on the computer. I started with Fortran code on punchcards, and waited in line to feed my stack into the mainframe computer at the university. The following year I got access to a Commodore PET, and could enter Basic code via keyboard and green screen (no punchcards, Yippee!). Program files were stored on cassette tape. By the mid 80's I'd changed my career path and no longer needed to worry about this stuff.

Nowadays, Excel, Numbers, and related programs, make creating these graphs very neat and easy. The Numbers program you’ve created here makes perfect sense, and I agree with the way you’re doing the standard film speed calculation.

What’s not clear to me is the reason for the delta X calculation, and the 0.3 gamma slope point. To me, this seems like splitting hairs. No film speed methodology is going to be perfect, but they should at least give you a repeatable result, so I can’t see any real advantage to go beyond the conventional approach.

If you really want to find the 0.3 gamma slope point you could do something similar to what I did in the early 80’s. You can create a least-squares polynomial fit to your data set. A fifth or sixth order polynomial should be more than enough to smoothly capture even the lumpiest of characteristic film curves. The slope at any point on the curve is just the first derivative of the polynomial, which is easy to calculate.

I have an Excel file I made years ago to create polynomials from data sets, and tried that last night with the data you’ve provide here. It creates a nice curve through your data. If I have time today, I might try expanding on this to get the 0.3 slope point. I’m also thinking of doing it in Libre Office, since it’s free for Mac and Windows (and Linux?), so anyone could use it.

 

[pentaxuser]

...and here I am STILL using pencil, paper, and flexible ruler! No Excel here, but Google Sheets seems to work well, when I tried it. Thanks for sharing!

Nothing wrong with that, Andrew.The benefits of pencil, paper and flexible ruler are twofold:

1. It strengthens you arm muscles

2. It gives you some instruments of defence

Both 1 and 2 will be needed when you hire that holiday cabin in the Yukon for you and the wife then run out of food and she thinks you are a giant chicken

pentaxuser

 

[ic-racer]

I have an Excel file I made years ago to create polynomials from data sets, and tried that last night with the data you’ve provide here. It creates a nice curve through your data. If I have time today, I might try expanding on this to get the 0.3 slope point. I’m also thinking of doing it in Libre Office, since it’s free for Mac and Windows (and Linux?), so anyone could use it.

I have fitted film curves to polynomials in the 1980s, but then and now have been unable to solve a polynomial in either Excel or Numbers. I did once find a webpage that can do it, however. For example solving this for y=0.1

y=-0.987x^3+0.5376x^2-0.177x-0.0375

 

[Sharktooth]

You can solve this easily via the Newton-Raphson method. It should only take 3 or 4 iterations to get a good result, since the curve is well behaved.

 

[Sharktooth]

You can look up Newton-Raphson to get the details, but here is a brief description.

Choose a random x value to start with, but it's better if the chosen x is close to where the target is. Solve for y using the polynomial.
Now find the slope at that point. The slope will be the first derivative of the polynomial at x. Now you have a point and a slope, so this defines a straight line of the form y=mx +b, where m is the slope. b=y-mx.

Your second guess at x will now be x=(y-b)/m where y is your target (0.1). Each iteration of x should get you closer to the target y value.

 

[Sharktooth]

In the first screenshot I'm showing a fifth order polynomial fit to the data. Below that is the calculation of X for a Y value of 0.1. I used the Newton Raphson method with 4 iterations. It found X to 2 decimal points accuracy in only 3 iterations. I chose an initial starting point of X=0.6

To find the 0.3 gamma slope point you'd have to take the second derivative of the polynomial to get the slope change, and use the same Newton Raphson method to get the X value for the first derivative slope. It sounds complicated, but it's rather simple to do.

If you look at the data plot, there's a strange inflection happening around 0.5 Log E. It looks like the curve is offset upwards at that point

 

[Stephen Benskin]

This thread brings back distant memories for me. Back in the early 80's I was doing D-Log E curves on the computer. I started with Fortran code on punchcards, and waited in line to feed my stack into the mainframe computer at the university. The following year I got access to a Commodore PET, and could enter Basic code via keyboard and green screen (no punchcards, Yippee!). Program files were stored on cassette tape. By the mid 80's I'd changed my career path and no longer needed to worry about this stuff.

Nowadays, Excel, Numbers, and related programs, make creating these graphs very neat and easy. The Numbers program you’ve created here makes perfect sense, and I agree with the way you’re doing the standard film speed calculation.

What’s not clear to me is the reason for the delta X calculation, and the 0.3 gamma slope point. To me, this seems like splitting hairs. No film speed methodology is going to be perfect, but they should at least give you a repeatable result, so I can’t see any real advantage to go beyond the conventional approach.

If you really want to find the 0.3 gamma slope point you could do something similar to what I did in the early 80’s. You can create a least-squares polynomial fit to your data set. A fifth or sixth order polynomial should be more than enough to smoothly capture even the lumpiest of characteristic film curves. The slope at any point on the curve is just the first derivative of the polynomial, which is easy to calculate.

I have an Excel file I made years ago to create polynomials from data sets, and tried that last night with the data you’ve provide here. It creates a nice curve through your data. If I have time today, I might try expanding on this to get the 0.3 slope point. I’m also thinking of doing it in Libre Office, since it’s free for Mac and Windows (and Linux?), so anyone could use it.

I believe ic-racer's concern was more about the accuracy of the constant and not just the single value of ΔX.

The default reason to use Delta-X is because the ISO standard uses Delta-X. The equation is built into the conditions laid out in the standard, but the fixed density method is only in good agreement with the fractional density method when the ISO parameters are followed. The fixed density criterion tends to underrate films that are developed to a lower average gradient and to overrate films that are developed to a higher average gradient. Ic-racer also appears to use a number of different criteria to compare. I'm assuming he's also interested in theory. If a person is only planning on using one film and developer, it really doesn't matter what they do, but if they go to the trouble of writing a program, they probably have additional uses in mind.

 

[ic-racer]

I got the Delta-X working. Since both the "W"(X-intercept) and "Delta-X" calculations in my spreadsheed make some assumptions (for example, the points are connected by straight lines, not curves), it is nice to be able to compare the results of the two estimates of 0.3G.

I did find that for high gamma (1.3 in my case) the Delta-X is so small that the calculated speed seems too slow. But, that is a very high gamma, even outside the bounds in the table in Stephen's Delta-x paper.

Otherwise, for films in the usual gamma range (below), the two tests are reasonably close. According to the paper by Nelson and Simonds, both tests should be less than 0.1 log D from the actual 0.3G point*.

Interessting the similarity in the structure of the equations*:

X-intercept (W) equation:

Approximate 0.3G point = Delta-W + X-intercept

Delta-W = -0.0948 + 0.0122*W - 2.2945 * W^2​

Delta-X equation:

Approximate 0.3G point = Delta-X - 0.1 point

Delta-X = 0.83 - 0.86 * Delta-D + 0.24 * Delta-D^2​

Nelson and Simonds Simple Methods for Approximating the Fractional Gradient Speeds of Photogrphic Materials 1955

 

[ic-racer]

One thing I have noticed in the last decade or so of doing film tests is that some manufacturers (like Ilford below) don't put much weight in ISO testing anyway. It is more about 'what works for you.'

ILFORD HP5

Kodak Tmax 400

 

[Stephen Benskin]

One thing I have noticed in the last decade or so of doing film tests is that some manufacturers (like Ilford below) don't put much weight in ISO testing anyway. It is more about 'what works for you.'

ILFORD HP5

View attachment 391809
Kodak Tmax 400

View attachment 391810

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.

 

[ic-racer]

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.

Yes, maybe they just downplay it a little. Anyway, thank you for your comments in this thread!

 

[Sharktooth]

I believe ic-racer's concern was more about the accuracy of the constant and not just the single value of ΔX.

The default reason to use Delta-X is because the ISO standard uses Delta-X. The equation is built into the conditions laid out in the standard, but the fixed density method is only in good agreement with the fractional density method when the ISO parameters are followed. The fixed density criterion tends to underrate films that are developed to a lower average gradient and to overrate films that are developed to a higher average gradient. Ic-racer also appears to use a number of different criteria to compare. I'm assuming he's also interested in theory. If a person is only planning on using one film and developer, it really doesn't matter what they do, but if they go to the trouble of writing a program, they probably have additional uses in mind.

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.

 

[RalphLambrecht]

Still testing it so I don't inadvertently share something with errors.

One issue (for which I have PM'd Steven Benskin) is the discrepancy of 0.30 vs 0.29 for the Delta-X value of the ISO/ASA triangle condition. The equation shown assumes 0.3 (one stop).
ISO speed = 0.8/H vs Fractional speed = 0.4/Hfg are one stop apart.

His paper referenced above shows both. Depending on which version is used a speed might be 382 vs 392. Right now my spreadsheet is calculating both.

View attachment 391557

will you grant us access to the spreadsheet files?

 

[ic-racer]

Try this: