# How to calculate a new print exposure time for a change in enlarger head height

Discussion in 'Enlarging' started by cornflower2, Dec 29, 2012.

1. ### cornflower2Member

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Hi! For years I thought about this problem of 'What exposure factor do I need - or more practically, what new exposure time -for a change in enlarger head height?' I was running a photo studio at the time and was wanting to display 20x24" b&w SGFB framed prints in my front window - and I was typically using about 5 (five!) whole sheets of paper just to get to my first 'excellent' or 'perfect' display print, going through the usual series of numerous test strips and whole sheet prints, pretty wasteful! And of course, not only was I chewing through my expensive stock of paper, but also all my chemistry was getting pretty quickly worn out as well, mostly on rubbish! So I decided that there must be a way to work out correctly - with total, utter accuracy - a new exposure time for a new enlarger head height, and I did work it out.

It's a mathematical thing, and what I came up with, as a perfectly functioning solution, was complicated! A spreadsheet or computer app runs 'the formula' in a snap, but if you had to work it all out every time you went to a new print using, say, a simple pocket calculator, you'd go nuts and probably make mistakes.

Forget about using the simple, pure 'inverse square law' as it applies only to a 'point light source', whereas our enlargers are not 'point light sources', but rather they are much more complicated multi-element optical systems comprising head casings or reflectors, a lamp, a condenser or diffusor; the negative; the enlarging lens - and finally, the print paper. For these reasons, the use of the Inverse Square Law (ISL) to calculate a new exposure time gives only a very rough approximate result, and our photographically sensitive print papers being what they are, you will always end up simply exposing a print that looks noticeably too dark or too light.

The ISL is the starting point for the calculation, but that's all. Then there's the second problem: As the enlarger head is re-positioned at different heights to make prints of different sizes, the relative 'error-to-ISL' changes. Why is this? Theoretically the enlarger head's internal reflector, lamp, condenser (or diffusor), negative, lens - and of course the print paper - should all change their corresponding positions relative to each other in order to to maintain the same equivalently focused 'conjugate' setup, or if you like, to simply maintain 'the same degree of divergence-from-ISL'. But they don't: our enlargers, even the best and most expensive, are relatively simple 'fixed boxes' in this respect, usually only the lens shifts relative to its distance between the neg and paper (correctly so), but everything above the neg tends to stay the same (incorrect operation) so there's a constantly changing 'degree of error' over the print magnification range.

In fact the initial degree of divergence-from-ISL doesn't matter, but 'the degree of change-through-the print-magnification range' is everything; and all we need to do is identify this 'degree of change through the range' over, say, a continuous range of 2.5X to 20X magnifications, and use this as the controlling value in a slightly modified ISL calc program.

When we do this, the enlarging process goes as follows (this is how I have been printing for the last 20+ years, since I first solved this math):

1) I start off by making a small (c.63x88mm or 'wallet size') print of my entire desired neg, or the part of it (the 'crop') that I'm interested in. I keep working on this tiny (wallet-sized) print until I think it's just "perfect". Typically I might get such a print, after several tries using different exposure times and contrast filters, at an exposure time of, say, 3.4 secs, with my lens set to its best-performing printing aperture of, say, f14.

Because I'm making a tiny print, my enlarger head is set fairly close to the print paper; we're in 'tiny print land' here, using very short exposure times and not using much paper or chemistry. Whilst doing this, I always notice how great it is to work with a complete image, rather than just a test-strip slice, and often, in the course of perfecting this first tiny print, I may realize that it's not such a great photo after all and I can abandon it early and move onto another neg before wasting large amounts of paper and associated chemistry on it. Finally, when I get my first tiny print right, I use a simple steel hardware-store measuring tape to measure the straight-line (eg. vertical) distance from the print paper (in practice, the surface of the print easel) up to the enlarger's negative plane: lets say this distance is 452 mm. I now enter this distance ('452') and my tiny print's perfected basic exposure time ('3.8') into the two waiting fields in my (pocket) computer screen app.

2) Next, I raise or lower the enlarger head to any distance I like (in practice, somewhere between 1X and 20X) to get the degree of print magnification that I want for my second (usually larger, but it could be smaller, program works both ways) print. I lock the enlarger head in this desired new position and refocus the lens sharply for the print, taking care not to touch or change the setting of the lens's aperture ring. I now measure the new straightline (eg. vertical) easel-to-negative distance once again with my tape measure - let's say it now measures 1125 mm - and I enter this new distance ('1125') into a third waiting field in my app. I hit the 'calc' button and my app instantly computes and displays the new exposure time; eg, '38.5 secs'. I now set my exposure timer to this new exposure time and expose the print. After processing for the same period of time as for the earlier perfect tiny print, the 2nd print looks absolutely identical to the first tiny print, and I'm talking no error, but a perfect match. Sounds too good to be true? You just need the right computing app.

And that's it. I have since bundled this calculating program up into a proper app that runs on practically any PalmOS organizer (Zire22, TX, T5), sorry, it isn't available in any other format. You do need to calibrate it to your specific enlarger rig (thus inform it of your rig's 'slope') before you print, not hard, takes 20 minutes of your time and a few tiny scraps of paper in the wet darkroom. The app stores several different rig profiles and has extra features: it can automatically compensate for print dry-down, it can handle up to four different burn/dodge pockets; it can handles up to 9 split exposures with automatic reciprocity compensation; and it can help you to execute a (focal-length) lens-change mid-print. Great for making up sets of differently sized but otherwise identical prints! Send me your PalmOS device user name (eg 'thomasK' or whatever you call it) and I'll send you a full unlocked version on the house. I originally packaged this app, which I call 'enLARGE for PalmOS', about 5 years ago but nobody was interested, everyone too interested in going digital. Well, who says you can't use a computer in the darkroom? As they say, "Add a little computer to your darkroom!"

2. ### Ken NadvornickSubscriber

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Or just make a new test strip, which by design factors in all of the variables you mention. Only takes a moment. And doing so puts you in closer touch with the materials you are working with, instead of inserting additional layers of indirection and logically abstracting you further away from them.

Just sayin'...

Ken

3. ### Denis P.Member

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Or, if you are not that much mathematically inclined, you could simply use something like Ilford EM10 exposure monitor (or a similar device).
Nowadays you can find those Ilford devices, used, almost for free - I presume even "down under".... It s particularly suited for just this purpose, e.g. if you have a known good print on a certain enlargement and want to have the same amount of exposure on a different size of paper (i.e. change of enlarger head height). Much faster and less error-prone than fiddling with numbers in the darkroom. Also less prone to fogging paper than an electronic organizer/iphone/whatever screen.

Although, I do admit that I still use my Palm in the darkroom. However, when making prints or test strips, it's stowed away in the (light-proof) cupboard, and started using a foot switch:
see HERE.

4. ### Steve SmithSubscriber

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It does work if you use the ratio of the areas of the print rather than the enlarger height squared (although that will get you to a good starting point for further experimentation).

Steve.

5. ### pentaxuserSubscriber

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This post is really for others' benefit as you believe you have successfully got an App but in another thread an APUGer was kind enough to give a link to his own site which simply requires that you input enlarger height or length measurement. The link is: home.centurytelnet/dwilder57/timeAdjust.html

Each time I experimented with the height I checked the exposure reading given by a probe on the same spot with what the site gave me and each time the figure was identical.

pentaxuser

6. ### ic-racerMember

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I came up with something similar when I got my ATARI computer back in the 1980s. As I got older I realize that with that method, after making the perfect small print I was not done, but only beginning. Now I just make the perfect big print then I'm done.

There is a thread on this topic every year, here is one if the better ones: http://www.apug.org/forums/forum41/53417-exposure-compensation.html

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7. ### Worker 11811Member

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That's how I used to do it. Factor by the change in the size (area) of the paper then make a test strip. Then you have to also consider that your contrast is going to change, too.
I made up a chart for my most-used print sizes: 4x5, 5x7, 8x10, 11x14. Just multiply by the factor from the chart and add or subtract contrast as indicated.

But, it's been months since I did all that. I don't even know where my chart is. I think I tossed it out.
Since I got an Analyser Pro, I don't putz around with that stuff anymore. I just take two readings then push the "Print" button.

Seriously! Pull your Christmas gift card money together and get one!

8. ### Steve SmithSubscriber

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Why would the contrast change?

Steve.

9. ### Jim JonesSubscriber

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It almost works. When you change the enlarger height, you have to refocus. This changes the effective aperture number, and therefore the required exposure. Dials and charts have been published over many decades to let us get the precise exposure after changing enlarger height without metering or test strips. A google search should point to some of them.

10. ### Bill BurkSubscriber

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The price is right, and it sounds like a genuine offer made in good faith.

Using a meter requires you having the neg in carrier at one setup, then moving the setup and metering again. There are those factors of changing heads and changing lenses that don't show up on the Kodak wheel calculators.

And it doesn't hurt to get a ballpark number to center your test strip on if nothing else.

11. ### Worker 11811Member

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I don't know why but it does, sometimes. Smaller prints need less contrast to look the same. Larger prints need more.

When going from, for instance, 5x7 to 8x10, it might not be noticeable. Even if it is, it might not be objectionable but, if going from 4x6 to 11x14, I usually lose at least a grade of contrast. (Reverse if going from large to small.)

Again, it's not always noticeable or objectionable but it does happen often enough that I have to be aware of it and check for it. If not using an Analyser or some kind of meter, all it takes is a test strip to solve this. If using an Analyser or meter, all you need to do is double check but 9 times out of 10, it comes out right because the device makes that adjustment for you in the process of re-metering.

12. ### Ian CMember

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With respect to post #10:

I find it easier to meter the projection through an empty carrier for maximum brightness to find the difference in stops. I use the aperture wide open for the brightest projection.

I first focus the smaller projection, remove the negative, replace the empty carrier, meter the center of the projection, and record the reading.

Then I replace the negative, resize the image, focus, remove the negative, replace the empty carrier, and meter as before. The difference in readings is Δf. Then the time factor is

2^Δf

The new exposure time is

(2^Δf)*original time

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13. ### ic-racerMember

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Contrast can change by a number of theoretic mechanisms:
1) psychologic impression of the image
2) More fog from a leaky head. A 150 second exposure can fog the paper more than a 5 second exposure if your enlarger head leaks a little light (they all leak some).
3) More fog from stray light bouncing off the paper and coming back on your highlights. 16x20" print (320 square inches of white paper) reflects more stray 'white light' into your darkroom than 4x5" (20 square inches).
4) Slight variations in the paper batch for a different size
5) Potential for less developer activity on 320 square inches of paper vs. 20 square inches
6) If you have to open the lens from its 'sweat spot' it will have more flare.
7) A bigger print requires one to use the far edges of the lens' image circle. The MTF is lower out there and contrast can be lower also.

On the positive side there could be less flare in the enlarger head because the bellows is collapsed more.

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15. ### clivehSubscriber

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I'm with Steve here, as you are clutching at straws. Contrast shoudn't change.

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16. ### nworthSubscriber

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The inverse square law works, but as you get bigger, some other factors kick in. One is reciprocity. With exposure times greater than a minute, it can be a considerable factor. With really long exposures, reciprocity can affect contrast as well as exposure time. Another is flare, which can lower contrast and generally make things muddy. As you get further away, there are just more things for the light to bounce off of, and there is more chance of stray light and safelight fog affecting the image. Condenser enlargers may work better than diffusion types for big prints.

17. ### David A. GoldfarbModeratorStaff MemberModerator

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I'm with ic-racer--contrast often has to be increased as print size increases. You may not notice it from 5x7 to 8x10, but 8x10 to 16x20, it's noticable. Sometimes it could just be because you're changing the way you view the print, and you might need more contrast for the image to be effective from a greater viewing distance. It's fairly common for me at least to print large at a grade higher than I print small for the same image.

To get a ballpark exposure time, figure one stop for every standard print size. You'll notice they follow the f:stop series approximately: 4x5, 5x7, 8x10, 11x14, 16x20, 20x24.

18. ### Steve SmithSubscriber

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Whilst I asked why the contrast would change, I didn't actually express an opinion that it wouldn't.

Steve.

19. ### Ken NadvornickSubscriber

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Impressions of contrast change as a dependency of print size must be some sort of general visual artifact. I experience the same thing even in the electronic reproductions of the APUG Galleries.

How often have you seen at a thumbnail that looked like it had wonderful tonality, only to click and see the image go flat at its full uploaded size? Or seen a thumbnail that looked like it had way too much contrast, only to click and see a beautifully appropriate full range of tones from white to black?

For some reason if your goal is a full palette of shades of gray, it seems your thumbnails must look too contrasty. And that seems true even with the inevitable compromises inherent in electronic reproduction technologies.

Ken

20. ### ic-racerMember

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WTF is a 'sweat spot'
Thank you spell checker...

21. ### Steve SmithSubscriber

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Don't use a spell checker. It just reassures you that the wrong words you used were spelled correctly!

Steve.

22. ### pinholerMember

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For my black and white prints I just make a test strip where I am changing the times by a quarter stop per strip. For example 10, 12, 14, 17, and 20 seconds. This gives me a better spacing between exposures than a 5, 10, 15, 20 second strip.

For color I have a spread sheet printed out using the formula T2 = T1 (H2/H1)^1.94 where H1 is the original height from the center of the lens to the baseboard, H2 is the new height measured the same way, T1 is the exposure for H1, and T2 is the new exposure. I am using Omega enlargers and found that an exponent of 1.94 works better than the exponent of 2 required by the inverse square law. I adjust the aperture so that my exposures stay in the 10 to 20 second range.

Prior to this, again for color, I calibrated an EM10 exposure monitor so that it read directly in seconds and filed out the edge of my negative carrier so that I could always take a reading off the blank film between frames. Both systems have worked well for me.

23. ### tkamiyaMember

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I've struggled with this for a while now.

What I have right now is both mathematical and seat-of-the-pants method combined. When I go from 8x10 to 11x14 to 16x20, simply doubling exposure each step will get me close. Then, I'll often have to bump up contrast by 1/4 to 1/2 grade each time to get each print to look similar. While contrast shouldn't change when the size change, how we perceive the contrast to be change depending on size. When I print larger, I print larger because I want the print to look larger. I don't necessary back up farther from the print to look at larger print looking the same size as before. With that in mind, I usually tweak contrast as well. I also need to change my dodge and burn schedule if I'm going larger by say 2 stops worth. Large patch of dark shadow look far more oppressive at 16x20 than did so at 8x10.

So I basically gave up on math to give me the answers. It will get me close and sometimes close enough. Then my gut and eye tells me what to change and by how much.

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25. ### Nicholas LindanAdvertiserAdvertiser

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There is a long interminable sticky thread on this subject at the top of the forum.

My view is that the need to increase contrast as print size goes up is largely perceptual. There isn't much physical effect with modern enlargers and lenses when combined with a blacked-out (or redded-out) enlarger alcove.

AA had a terrible time getting contrast on his mural prints. They were 5x7's - but measured in feet. The reason does seem to have been stray light. His darkroom was painted white and the enlarger was homemade, with an unknown amount of light leakage. And the lens wasn't multicoated.

If physical effects are contributing to contrast loss then:

Stray light from the enlarger can be dismissed (unless yours leaks like a sieve). The greatest stray light source is lite bouncing off the paper. The second greatest contribution is stray light from the lens - peer up at the lens and you can see quite a bit of illumination that shouldn't be there. To see the enlarger proper's contribution you can make an experiment: Turn on the enlarger and look at the illumination on the walls, then cover the lens and look at the contribution of light leaking from the enlarger; it's not night and day, exactly, but the enlarger's contribution to total stray light is tiny in comparison.

A lens hood on the enlarger might not be a bad idea. A multicoated lens will also reduce stray light.

If the aperture is opened to compensate for larger print size then printing time stays the same and the fog from the enlarger and the lens doesn't change.

The greatest contribution to lowered contrast, fog from light bouncing off the paper, will increase with print size: this was probably AA's greatest contribution to reduced contrast. The total amount of light from the lens is constant with print size, assuming you are using time to compensate. A certain percentage of the lens output bounces from the paper, then to the walls and back on to the print. So the total bounced light is independent of print size. However, as print size increases the exposure time increases and thus the effect of this bounced light increases. Using the aperature to compensate won't help here: if you open the aperture then the amount of bounced light increases (more total light).

Painting the walls and ceiling around the enlarger matte bright red (or black) is the only way to mitigate the effect of bounced-light fogging. It also reduces any effects from stray lens and enlarger light.

Reciprocity failure increases contrast. It's the same with paper as it is with film, but rather than the shadows going empty it's the highlights.

Using an EM-10 requires that you use the lens aperture to compensate for print size. If you are using an EM-10 then it is a good idea to make your work prints at a small aperture, so that the lens is at optimum when opened up to make the final print. The EM-10 was designed for use with Ilfochrome printing, where changing the exposure time would shift the color balance. There is another company (cough) that makes a meter better suited to this purpose, this meter has 1/100th of a stop of resolution and can meter any contrast changes accruing to the larger print size.

My experience is that small work prints are fine if they are no more than 1 size smaller: 11x14 for a 16x20, say. But that is still reducing paper wastage by half.

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26. ### Nicholas LindanAdvertiserAdvertiser

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Your darkroom is too warm.