# Exposure compensation

Discussion in 'Enlarging' started by emanded, Aug 21, 2008.

1. ### emandedMember

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I'm new to the darkroom and after much advice here I'm up and running with a Durst M670. The results are beyond my expectations - far better than my digi work (done with full frame Canon & L glass). The prints have far more depth and 'liquidity'- if that's the right word for it,
Now, my question is, I've done some prints on 10x8 that are worthy of going to 12x16 - what compensation do I need on the exposure for pulling the light further away, bearing in mind there will also be some dodging & burning. Or do I have to start again with test strips?
Joe

2. ### Steve SmithSubscriber

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If you keep everything else the same, it is exponential based on length of print or linear based on area of print. So doubling the dimensions from 10x8 to, for example 20x16 gives you four times the area which the same light is covering so it is getting a quarter of the strength. Therefore multiply the exposure time by four.

10x8 and and 12x16 are not the same aspect ratio so you could do a bit of maths to work it out. If we assume that the same linear length of image which fits the 10" side of the 10x8 is also going to fit on the 16" side of the 12x16 then we can do this:

Exposure multiplier = (large size squared)/(small size squared) = (16x16)/(10x10) = 256/100 = 2.56

So about two and a half times the original exposure will get you in the right sort of area.

Steve.

3. ### pentaxuserSubscriber

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I have a site provided by an APUGer in which you simply put in current exposure time and enlarger height plus new enlarger height and a hidden excel prog gives you the new time.

I cannot give you the URL for it as nothing shows up. I simply saved it from whatever was given on the post. Sorry to be so vague. Someone might refer to it here or the original poster will respond but if not do a search on enlarger posts and it should come up.

pentaxuser

4. ### David BrownSubscriber

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Do another test strip.

5. ### ic-racerMember

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This comes up all the time. Do as David Brown suggested and make a new test print.

If you like math the equation is:

new_time = old_time x (new_M +1)^2 / (old_M+1)^2

where M = new magnification (print/neg) and m = old magnification (print/neg)

The exposure time factor would be:

Factor = (M + 1)^2 / (m + 1)^2

The equation does follow the inverse square law for light but, since you re-focus the image, you also have to account for the change in your 'effective aperture.' Similar to 'bellows factors' used in macro photography. When doubling the size of the print, you will be about one stop off if you use the 'inverse square' equation alone.

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There is an f-stop print size exposure adjustment ruler on the Darkroom Automation web site.

It works with "f-stop timing", which is a good technique to start using early on in your darkroom work. To get started with f-stop timing and your present timer, an f-stop timing dial for a GraLab timer and f-stop timing table for digital timers are provided the Darkroom Automation web site. A true f-stop timer is the best way to control enlarger exposure.

The other way to compensate for changes is to use an enlarging meter. The Darkroom Automation Enlarging Meter will read the exposure change in stops. You can also use an Ilford EM-10 exposure comparator which will let you use the lens aperture to adjust for changes in print size.

7. ### Ben 4Member

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Do Both!

Because speed and contrast of different batches of paper are seldom exactly the same, you'll want to do a test strip (I'm assuming here that you'll be working from different boxes of paper). But you can use the formulae cited to get yourself in the ballpark. That's what I do!

--Ben

8. ### ic-racerMember

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This looks like a good idea. I consider myself easily in the 'double digit' IQ range but frankly, I don't understand how to use it. :confused:

9. ### pentaxuserSubscriber

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What! Don't know how to use it. Well let me explain.... that I am in exactly the same boat.

I have some vague idea about how it works but an amplification from Nicholas would be gratefully received. It looks great, avoiding as it does, I think, any calculations other than simple subtraction, I think, to arrive at the fstop increase/decrease which then of course if you haven't got a fstop timer has to be translated into actual time so a fstop table to time conversion is also required. Again I think but don't know.

pentaxuser

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To use it is simple:

Measure the size of the projected image and note the numbers. You dont measure from zero but from BASE. The difference in the numbers is the number of stops to add/subtract to the exposure time.

You can also use it to measure the easel-lensboard height if this is easier. The BASE is then the base of the yard-stick.

Adjusting the exposure is most easily done with an f-stop timer. Dials and tables for use with analog and digital and seconds timers are available on the web.

The ruler is in 0.1 stop increments because Darkroom Automation equipment works in a uniform system of decimal stops. If you have a timer that works in fractional stops you can make a ruler in any increment you wish. The equation for distance for each stop f is:

Inches = length of ruler * 2 ^ (-f / 2)​
= length of ruler * 10 ^ (-f / 6.6439)​

The 6.6439 converts from base 2 to base 10, and makes calculations easier in some spreadsheet programs.

The theory:

The ruler, like everything in f-stop land, is logarithmic in base 2.

The ruler is made inside out - you start with the f-stop and find the distance for the mark for that stop. As a result the equations use inverse functions: exponentiation and square roots rather than logarithms and squares. Subtracting the distances (logarithms) accomplishes division. Division by 2 (-f / 2) when calculating the position of the marks on the ruler takes the square root.

Subtracting the two numbers gives the result of:

R = log base 2 [(x ^2) / (y ^ 2)]​

where x and y are the linear distances at the two magnifications.

If the calculations started with distance and calculated the stops the resulting ruler would be filled with numbers that are hard to work with: 27 inches would be marked 0.642; 7 inches would be marked 4.53. The present method puts the marks at even stop intervals.

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It is rather hard to get one's head around the thing, but the 'effective aperture' concept is the same-old square law compensation in different clothing. A thought experiment is to imagine the square-law experiment with a point source: if it works for one point source, then it will work for two point sources next to each other; ditto three, four ...; and finally, ditto a circular aperture. This is why measuring lens to easel distance works for determining exposure compensation.

The biggest systematic error in a geometrical approach to print size compensation is because of the change in condenser "efficiency" - not the right word but I can't think of a better one. The distance from the condensers to the lens has to be held constant for a geometrical compensation scheme to really work well. You can do this on a Beseler 45 series enlarger (and on the 23 series). However, I have always used an enlarging meter when things get critical. Beseler has never mentioned this feature of their enlargers (and may not even be cognizant of it) - the condenser gauge on a Beseler should, ideally, be from the lens stage to the condenser and be fixed at the condenser focus. It's factory location, from the negative stage to the condenser, is wrong. A perfect diffusion enlarger should have no error due to diffuser-lens distance.

In practical work if the required compensation is less than 2 stops then a geometrical approach to adjusting exposure for magnification changes is more than accurate enough. With larger changes, errors due to stray light and flare become meaningful and it's test strip time.

As is often mentioned, the aesthetics of the print change with print size and often a much larger or much smaller print looks better if it is made lighter or darker or with more or less contrast than the original.

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12. ### Gary HollidayMember

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Personally I have no desire to turn a darkroom session into a maths session, so a test strip for me too. Papers can vary in batch, so a test will also give you the opportunity to check contrast also.

For reference, take a note of how much extra exposure was required and refer to it next time..that should spped things up a bit. Glad to hear you are noticing the qualities of darkroom printing.

13. ### Steve SmithSubscriber

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Neither do I and I personally would not do the equations other than very roughly in my head to get close. Then do a test.

Steve.

14. ### Martin AislabieSubscriber

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I'm with Steve

I do the maths - to get close to the size corrected exposure

But because paper varies batch to batch and with age, I do another set of test strips based bracketed around the size corrected exposure

Martin

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That's the whole reason for the ruler - there isn't any 'maths' to using it.

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Some examples may help. There is a table of stops to percentages below:

You want to increase the size of a print by a few inches:

1. Use the ruler to measure the size of the negative carrier opening projected on the easel - read 3.0 (~12 inches).
2. Change to the new size and measure again - read 2.5 (~14 inches).
3. The difference is 3.0 - 2.5 = 0.5, so you increase the exposure 1/2 a stop, about 40%. If you are using an f-stop timer you just change the exposure by 0.5.

You want to decrease the size of a print by a small amount:

3. The difference is .2 stops, about 15% or between 1/8 and 1/4 stop. If the old time was 20 seconds then remove 15% (3 seconds) and the new time is 17 seconds.

You want to go from a small work print to making a large final print:

3. The difference is 4.3 stops - increase the setting on the f-stop timer by 4.3
4. If you have a linear seconds timer, then from the table below, a 4.3 stop adjustment requires 19.7 times the exposure. If it was 10 seconds it is now about 197.
5. Because the size change is so large, it is a good idea to make a new test strip around the new time.

In the last example, the new time is too long. Instead you can open the lens up 2 stops, so now the time exposure only needs to change by 2.3 stops. From the table below you can see a 2.3 stop increase requires 4.9x the time, so set the timer from 10 seconds to 49 seconds. Or add 2.3 stops to the f-stop timer - less maths that way.

A table of stops to the time adjustment.

Examples:
• To add 0.2 stop, multiply the time by 1.15 or add 15%
• To remove 0.2 stop divide the time by 1.15 or subtract 15%.

0.1 1.07
0.2 1.15
0.3 1.23
0.4 1.32
0.5 1.41
0.6 1.52
0.7 1.62
0.8 1.74
0.9 1.87
1.0 2.00
1.1 2.14
1.2 2.30
1.3 2.46
1.4 2.64
1.5 2.83
1.6 3.03
1.7 3.25
1.8 3.48
1.9 3.73
2.0 4.00
2.1 4.29
2.2 4.59
2.3 4.92
2.4 5.28
2.5 5.66
2.6 6.06
2.7 6.50
2.8 6.96
2.9 7.46
3.0 8.00
3.1 8.57
3.2 9.19
3.3 9.85
3.4 10.56
3.5 11.31
3.6 12.13
3.7 13.00
3.8 13.93
3.9 14.93
4.0 16.00
4.1 17.15
4.2 18.38
4.3 19.70
4.4 21.11
4.5 22.63
4.6 24.25
4.7 25.99
4.8 27.86
4.9 29.86
5.0 32.00
5.1 34.30
5.2 36.76
5.3 39.40
5.4 42.22
5.5 45.25
5.6 48.50
5.7 51.98
5.8 55.72
5.9 59.71
6.0 64.00
6.1 68.59
6.2 73.52
6.3 78.79
6.4 84.45
6.5 90.51
6.6 97.01
6.7 103.97
6.8 111.43
6.9 119.43
7.0 128.00
7.1 137.19
7.2 147.03
7.3 157.59
7.4 168.90
7.5 181.02
7.6 194.01
7.7 207.94
7.8 222.86
7.9 238.86
8.0 256.00

17. ### Dave MillerMember

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Use a calculator! You lot do make life difficult for yourselves.
It really is level one math.
The new exposure time is the old exposure time divided by the old height, divided by the old height again, multiplied by the new height, and multiplied by the new height for a second time.
I measure the height from the paper to the lens and find the method simple, quick, and very accurate.
You may use rods, poles, perches, feet or inches for measurement, I use centimeters since they feed into my calculator easily.

18. ### Frank SzaboMember

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It's commonly known as the "Law of Inverse Squares" (a helluva lot simpler than Simpson's Rule), if age hasn't addled my mind too badly. It works well with setting studio light, both flash and continuous, calculating bellows extension factors, and the very problem before us.

However, when I had a wet darkroom, I always had a 4X5 box of whatever paper I was using laying around and would just throw a sheet onto the easel and check exposure. Trying to apply a definite (math) to a subjective (photograph) is very much like trying to mix apples and oranges.

Just guess and do a test print. Have a beer while you're at it.

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What a lot of math. How about "subtract - enter value into timer". That sounds a lot easier to me.

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"When mixing apples and oranges be sure to add a beer."
I'll drink to that.

21. ### Frank SzaboMember

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Last year when I went for a physical exam, I was having quite a bit of trouble with allergies that particular day.

My doctor, Lord love him, is a Chinese fellow - extremely thorough. Not really adept at American humor, he loves it when caught off guard with a wisecrack.

He made the mistake of asking "what I think wrong with me" and after a short hesitation I told him I had too much blood in my alcohol system. He laid his head down on the desk and laughed for about 2 minutes without a stop.

At that time, I hadn't had anything alcoholic to drink in over ten years.

By the way, Nicholas - I have and use regularly a little gadget that works in a manner similar to your instructions made by Sinar years ago - a bellows extension gage.

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