Please help me with my photographic math.

Last night, just for fun, I did the Barnbaum safelight test and while I was at it tried to arrive at a good pre-flashing exposure for Ilfor MGFB, I used a LPL 6700 condenser enlarger which, to be quite honest, does not have great consistency in illumination edge to edge.

Anyway. I set my timer for 1.15 seconds which is the shortest time the Analyser pro will allow you to set. I started by exposing the whole sheet to 1.15 seconds and then progressively covered the paper until I had 7 separate exposures.

I assume the progression would be 1.15, 2.30, 3.45, 4.6, 5.75 etc

When I read the strip under the densitometer the values were 0.00, 0.06, 0.21, 0.38. 0.51, 0.62. 0.69.

So my question is, by moving across a strip in 1.15 sec increments, It looks as if I'm changing the exposure by half a stop, is that right? I know this is probably a dumb question but I'm actually a bit dyslexic when it comes to math.

Not! Using the same 1.15 sec the amount of exposure would be
Between the 1st and 2nd 1 stop different.
Between the 2nd and 3rd 0.58 stop different
between the 3rd and 4th 0.41 stop different
Between the 4th and 5th 0.32 stop different.
etc..
And you can see your result reflect that. You have less and less differences in densities.

Chan Tran said:

Not! Using the same 1.15 sec the amount of exposure would be
Between the 1st and 2nd 1 stop different.
Between the 2nd and 3rd 0.58 stop different
between the 3rd and 4th 0.41 stop different
Between the 4th and 5th 0.32 stop different.
etc..
And you can see your result reflect that. You have less and less differences in densities.

Click to expand...

So what would the exposure sequence have to be to get say 1/4 stop differences? I assume you'd have to cut out a hole in a card and give each strip a completely seperate exposure?

1 stop strips would be for instance:
1.15 seconds
2.30
4.60
9.20
etc.

Half stop is a multiplication of the square root of 2, so approx. 1.41, so it would go like this:
1.15
1.63
2.30
3.25
4.60
6.51
9.20
etc.

Quarter stops would be a multiplication factor of the square root of the square root of 2...so:
1.15
1.37
1.63
1.93
2.3
etc...

markbau said:

I assume you'd have to cut out a hole in a card and give each strip a completely seperate exposure?

Click to expand...

No, but the math gets boring & confusing unless you stick to full stops. For instance for a one stop range from 1.15 up to 2.30 seconds, you would do this:
Initial exposure (2.3-1.93) = 0.37 seconds. Move strip.
Expose for (1.93 - 1.63) = 0.3 seconds. Move strip.
Expose for (1.63 - 1.37) = 0.26 seconds (etc)
...................(1.37 - 1.15) = 0.22 seconds
Final exposure would be 1.15 seconds.
There are of course other ways to do the math. Doesn't have to be extremely complicated but as you can tell the risk of a small error gets pretty big pretty fast, and if you mess up halfway in your process, the error carries over to subsequent strips. Not to mention the minimum time of your clock apparently is an issue.

So for fractional stops it would indeed be a little easier to do separate strips for each time.

The Analyzer Pro has a test strip mode that will do the math for you. If it's calibrated accurately for your paper, it can also be used to calculate a pre-flash exposure directly. But I usually make a test strip just to be sure. If you don't have the manual, you can download it using this link:

https://rhdesigns.co.uk/wp-content/uploads/2020/04/Analyser_Pro_UM_v64.pdf

With respect to calculating fractional stops, I think about it like this:

Each full stop is a factor of 2. The number 2 can be broken down into a product of powers of 2, and since the exponents in such a productive are additive, you can break down 2 like this:

2 = 2^1

or

2 = 2^1 = 2^0.5 * 2^0.5 (half stops)

or

2 = 2^1 = 2^0.25 * 2^0.25 * 2^0.25 * 2^0.25 (1/4 stops)

This can be done for any fractional stop. Want to calculate 1/6 stops? Then 2 = 2^1 = 2^(1/6) * 2^(1/6) * 2^(1/6) * 2^(1/6) * 2^(1/6) * 2^(1/6)

Using your example:

base exposure time = 1.15s. 1/4 stop more would be 1.15 *2 ^0.25 = 1.63s. The next 1/4 stop is 1.63 * 2^0.25 = 1.93. To get the next sequence of 1/4 stops, just keep multiplying by 2^0.25.

For any fractional stop the multiplication factor is 2^fraction, so the multiplier for 1/6 stops is 2^(1/6), 1/12 stop is 2^(1/12), and so on.

The Analyzer Pro can do this math for you since you configure it for the fraction of a stop you want to work with.

markbau said:

So what would the exposure sequence have to be to get say 1/4 stop differences? I assume you'd have to cut out a hole in a card and give each strip a completely seperate exposure?

Click to expand...

1.15
0.218
0.259
0.308
0.366
0.435
0.518
0.615
0.732
0.870
1.035
1.231
1.464
1.741
2.070
2.462
2.928
3.481
4.140
4.923
5.855
6.963
8.280
9.847
11.710
That in 1/4 stop.

Thanks for those figures, even if I don’t understand the math. It looks like it would be simpler to make seperate exposures using the f stop timer.
I do use the Analyser Pros test strip feature often. I have tried the pre flash function but got a visible grey! Maybe it was something I did wrong.

Chan Tran said:

1.15
0.218
0.259
0.308
0.366
0.435
0.518
0.615
0.732
0.870
1.035
1.231
1.464
1.741
2.070
2.462
2.928
3.481
4.140
4.923
5.855
6.963
8.280
9.847
11.710
That in 1/4 stop.

Click to expand...

markbau said:

I have tried the pre flash function but got a visible grey! Maybe it was something I did wrong.

Click to expand...

That probably means your calibration is a bit off. Mine's not perfect either. I use the Analyzer to calculate a pre-flash exposure then make a test strip to fine tune it.