W-Speed--Finally Did It: Spreadsheet to easily calculatre 0.3G speeds.

[ic-racer]

W-Speed--Finally Did It: Spreadsheet to easily calculate 0.3G speeds.

BACKGROUND:
Jones showed pictures to 200 people. They chose the best ones. The negatives from the best pictures were analyzed and all showed lowest useful density to be at the tangent of a line with slope zero point three times the gradient of the straight line portion. (0.3G). Current ISO standard is based on this work.

For reasons not to go into here, the modern ISO test involves development to exactly a specific slope, then testing for 0.1 above film base. That is fine, but in HOME TESTING, you would need to zero in on that exact slope with repeated development tests before your 0.1 point matches the ISO standard. (not a big deal for personal film speed testing, but if I want to make a post about how fast a Chinese film is compared to Tri-x I should use an ISO method).

Wouldn't it be great to have a way to test for relative film speed (for comparing emulsions) that you can get from a single curve of just about any gamma?

There are TWO ways in the literature to do that. The DELTA-X way and the less-known "W speed."

Steve has done a lot to explain the DELTA-X and indeed that is a fantastic way to do it. This method complements the work Steve has done promoting DELTA-X method and is presented as "another interesting way to do it."

Why did I embrace the "W speed?" Because it is based on SLOPE and X-Intercept which are the two parameters I have been using all along for my relative film speed testing. (See link to extensive discussion of various computerized methods of film analysis (there was a url link here which no longer exists)). Also, Steve has already posted extensively on Delta-X, so I wanted to do something a little different .

BTW I want to thank Steve the literature he sent me so I could research 'inertia.'

 

[ic-racer]

So, what is the "W-Speed?"

To understand it one needs to know a little bit about "INERTIA"

Inertia is the speed point used long ago by H&D. It is very easy to get. They just extended the gamma line from the straight portion down to the X axis (the horizontal axis of the H&D curve). They called the intersecting point "inertia" and used that as an indicator of the film's speed.

Much more work has been done since then, and even though the inertia is stupid-easy to obtain with just about any computer software, it is not as good as 0.3G.

What the "W-Speed" method does is to use some more parameters from the shape of the toe of the H&D curve to adjust the "inertia" speed point so that it matches the 0.3G speed point.

Why not just have the computer calculate the 0.3G speed point directly??? I wish it could but the math is beyond me and no one in that extensive thread posted anything in DeltaGraph or Excel that do it.

The W-Speed and the Delta-X were specifically developed to be easily obtained from the H&D curve by simple geometric means, originally with clear plastic overlays. What I am presenting here is a way it can be computed on an Excel spread sheet with simple mathematical terms.

 

[ic-racer]

"Simple Methods for Approximating the Fractional Gradient Speeds of Photographic Materials"
C.N.Nelson and J.L.Simonds, 1955

This is the paper that shows how to make the clear plastic overlays for calculating both Delta-X and W-Speed. Quote from the paper: "both methods are suitable for practical use..." so I hope not to start a "DELTA-X" vs "W-SPEED" war What I did was use the math included in the paper to have Excel do the work.

 

[Kirk Keyes]

Can you post the spread sheet so some of use can try it?

 

[Stephen Benskin]

Dale,

Congratulations! I'd love to see more on what you have.

I tended to stay away from W for two reasons, 1. the math. 2. the ISO standard went with Delta-X.

Steve

 

[ic-racer]

Dale,

Congratulations! I'd love to see more on what you have on it.

I tended to stay away from W for two reasons, 1. the math. 2. the ISO standard went with Delta-X.

Steve

Yes, when I first got the paper from you I discounted that 'w' method pretty quickly! But, after researching all the "inertia" papers, I came back to the W-speed. After reading the chapter a few times I realized all the difficult math from the Lutherian Equation Curve Fit was already done and incorporated into the final equation in the paper:

Difference between 0.3G and "Inertia" = -0.0948 + 0.0122w - 2.2945 w(squared)

So, all one needs to do is get Excel to figure out the 'w' term and plug it in.
The components of 'w' are gamma, inertia and 'E.' The gamma and inertia I'm already getting but the "E" has to be read from the graph. My solution was to get Excel to automatically get the "E" value with a clever use of IF(AND( ,),,) statement running down the column of values.

"A" in the diagram is the same as the "Inertia" point of H&D.
From the paper. The "w" term I calculated as "C" minus "A" where "A" is the X-intercept of the straight line and C is calculated by geometry from point "E" and one half the slope of the straight part. For practical reasons I use a simple 'two point geometric interpolation' to get E from my data, rather than some extensive curve fit.

 

[ic-racer]

Here is a screenshot. I'm not sure how to post the real thing. But its still pretty rough.

The one thing I don't like is that it is based on the LINEST function. This requires you to re-set the boxes around 4 datasets with each new film test. Then you have to remember to use "Command & Return" after setting the columns in the LINEST equation otherwise you get an error saying that "Arrays can't be changed"

The 'guts' are all hidden but you can get an idea of how it works. The clever part was to make the IF(AND( ,),,) equation to step down the dataset and find the two points in-between which the "E" is going to be located. Then zeroing in on E with a little triangle based on the slope between the two points. Its not perfect because it assumes a straight line between each one of the datapoints (rather than a curve) but it should be close enough for home testing.

Well, already I see I got the labels I added for clarity for Gamma and Intercept in the yellow box wrong. The math is all still OK.

 

[htimsdj]

I can see that I have a lot to learn - because I have no idea what you are talking about here!

I think I'll go back to figuring out where I will put this enlarger!

 

[ic-racer]

I can see that I have a lot to learn - because I have no idea what you are talking about here!

I think I'll go back to figuring out where I will put this enlarger!

Nothing you need to worry about

Bottom line is I'm lazy. With this method if, you get a hundred rolls of unmarked film on fleabay, I can fire off a SINGLE test strip, process it in MY DARKROOM, and tell you how much slower or faster it is than T-max 400. And it would not matter how your are going to process it in your darkroom.

 

[ic-racer]

This is an enlargement of the toe (plotted in junk Excel, with its known bug of not show vertical chart line divisions).

The red dot is where the spread sheet automatically calculated "E" to be. As you can see, its a good estimation. (See figure 3 above for where "E" is supposed to be).

 

[Stephen Benskin]

Dale,

Would you mind going over the spreadsheet in detail?

 

[Lee L]

To add a spreadsheet as an attachment to a post:

click on Reply to Thread

and you'll get the "quick reply" frame shown in the attached image.

Then click on the "Go Advanced" button (circled in red in the attached screenshot) and that will bring you to a page that allows you to manage and upload attachments for that post. Valid file extensions (and one would assume the properly associated formats) are: bmp doc gif jpe jpeg jpg ods pdf png psd txt widget xls

So you can upload the .xls file without compression or modification. I'd love to see a copy of the spreadsheet as well. (But I'll be converting to .ods)

Lee

 

[ic-racer]

Would you mind going over the spreadsheet in detail?

"E" is defined as the point where the inertia (X-intercept) would intersect the toe of the curve if a straight vertical line were drawn up from the inertia point.

I make the assumption that there is a straight line between my data points (rather than a curve) this simplifies the math quite a bit.

The spreadsheet locates the two horizontal datapoints between which the inertia lies. It calculates the slope of these two points.
It makes a right triangle (not shown on the graph from the paper). The base is the horizontal distance between the inertia and right datapoint. The slope is calculated above. The unknown vertical segment is then easily calculated (slope = rise over run). So, after calculating this vertical segment, I subtract it from the vertical density of the right hand datapoint and this gives me the unknown vertical density of "E," or the distance E to A on the graph.

If you look at the graph from the paper you will see another right triangle ECA. We know by definition that the unknown "w" is equal to the distance C to A. We know the slope of E to C, which is by definition one-half the gamma. Therefore "w" is equal to "E" over "one-half gamma."

Now that "w" is known, it can be put in the equation from the paper to easily solve for our correction factor that is added to the inertia to get our 0.3G point.

 

[ic-racer]

I noticed that this thread (as almost every informational thread I posted since 2007) has lost all the photographs that were hosted on PhotoBucket. I'll try to post some of the images, but it is hard to know what is missing without practically re-doing the entire thread.
Here is one graph from the W-Speed paper, showing how the W parameter is computed from the H&D curve toe.

 

[Eric Rose]

Thanks for keeping this information fresh.