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

[Bob-D659]

Only one comment to Mr. Lindan's post, red walls are bad idea if you print RA4 paper, I found that a brown shiny bookshelf unit is bad too. Go for black, paint or cloth.

 

[Nicholas Lindan]

... red walls are bad idea if you print RA4 paper ...

I don't know that I hold with that newfangled color stuff.

Yeah, red (or OC orange, even brighter) only work for black and white. I once used a darkroom with black-painted enlarger cubicles. Couldn't see a thing. I
would have wanted a dedicated Thomas safelight in each cubby. No, that wouldn't work, the ceiling was black.

I knew an outfit that painted their darkrooms blue. Now that has to be the worst color for darkroom walls.

 

[mr rusty]

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!

+1

 

[cornflower2]

Now an app that does the enlarger exposure computation for you, look for enLARGE on Apple AppStore

 

[cliveh]

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


Steve.

Well perhaps you should get off the fence and express your opinion.

 

[RalphLambrecht]

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!"

look at page 291 or fig.11

 

[Chan Tran]

Calculating new exposure time for new enlarger height isn't all that difficult. However, the problem is that I don't know where the nodal planes of the lens are.

 

[cornflower2]

look at page 291 or fig.11

A very impressive body of work!

 

[cornflower2]

Why would the contrast change?

There is no change in contrast with differences in print magnification. The contrast will be identical.


Steve.

There

 

[cmaldonados]

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!"

Do you still have this program?. Not that I have a Palm device but I'd be interested in the involved calculations; as you said "who says you can't use a computer in the darkroom?..."
I'm looking for a easy solution instead of having to spend thousands of dollars on a density meter –I couldn't find cheap ones like Ilford EM-10 Density Meter.

 

[Nicholas Lindan]

I'm looking for a easy solution instead of having to spend thousands of dollars on a density meter

Err, not to belabor the obvious, but http://www.darkroomautomation.com/em.htm

 

[cmaldonados]

Err, not to belabor the obvious, but http://www.darkroomautomation.com/em.htm

oh, this is great!... I'll look into it.

thank you!

 

[RalphLambrecht]

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!"

You can certainly do thismathematically every time, or you can do this once and turn the math into a table from which you look up theresult. the attached includes such a table (and the math ) on page 511. for more detail read the entire pdf.

 

[RalphLambrecht]

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

I never noticed a contrast change but then, I prefer making anew test strip anyway.

 

[Sirius Glass]

I would just make test strips of the negatives, just as I normally would.

 

[RalphLambrecht]

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.

In my view, the Ilford EM10 is a practical device with the drawback that it depends on changing the aperture to adjust the exposure setting. Once I set the f/stop, I like to keep it there.

 

[Andrew O'Neill]

By the time I got the EM10 out and checked illumination, I would have a test strip already made. I didn't cry when the EM10 was stolen...

 

[MattKing]

I use the EM10 to determine the middle time on my test strip - it works very well.
I also use it if I do a work print in one darkroom (say at home) and a subsequent print or prints in another darkroom (say my Darkroom Group) - it gets me right into the ballpark with the first test at the second darkroom.

 

[RalphLambrecht]

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.

very good explanation by Nicholas! Thanks.

 

[Ian C]

The Ilford EM-10 is useful in determining the proper exposure at a new magnification based on the exposure used on a prior print at a different magnification—provided that both prints are made on paper from the same package. That’s because two different packages of the same paper type can give different speed and contrast. Different packages of color papers can vary in color balance as well.

Here is an example. Suppose that you want a 16” x 20” print and that you want to use the enlarging lens’s optimum aperture of f/5.6. You want to do this with the minimum waste of paper and chemicals. So, you decide to first make an 8” x 10” print on paper cut from your box of 16” x 20” paper. Since this is approximately a doubling of print size, you know that the difference in exposures is roughly 4X or 2 stops.

Make the 8” x 10” print with the aperture closed 2 stops at f/11. Choose a midtone area in the projection and adjust the calibration knob on the EM-10 to light the green LED only. Record the calibration number on the EM-10 and leave it at that setting. Now resize the projection and focus for a 16” x 20” print. Initially, set the aperture to f/5.6 and use the EM-10 to measure the projection of the same reference area as you fine-tune the aperture position until you get the green LED lit only.

The light intensity falling on the reference area of the projection is the same as used for the smaller print. You’re also using the same paper, and the timer is set to the same value as used for the smaller print. Too, the lens is used at, or close to, its optimum aperture of f/5.6. When you expose and process the print, it should be identical to the smaller print.

No calculator? No problem.

For an odd integer or non-integer number of stops difference between two print exposures, some calculation is necessary, even with the aid of the EM-10.

 

[snusmumriken]

The Ilford EM-10 is useful in determining the proper exposure at a new magnification based on the exposure used on a prior print at a different magnification—provided that both prints are made on paper from the same package. That’s because two different packages of the same paper type can give different speed and contrast. Different packages of color papers can vary in color balance as well.

Here is an example. Suppose that you want a 16” x 20” print and that you want to use the enlarging lens’s optimum aperture of f/5.6. You want to do this with the minimum waste of paper and chemicals. So, you decide to first make an 8” x 10” print on paper cut from your box of 16” x 20” paper. Since this is approximately a doubling of print size, you know that the difference in exposures is roughly 4X or 2 stops.

Make the 8” x 10” print with the aperture closed 2 stops at f/11. Choose a midtone area in the projection and adjust the calibration knob on the EM-10 to light the green LED only. Record the calibration number on the EM-10 and leave it at that setting. Now resize the projection and focus for a 16” x 20” print. Initially, set the aperture to f/5.6 and use the EM-10 to measure the projection of the same reference area as you fine-tune the aperture position until you get the green LED lit only.

The light intensity falling on the reference area of the projection is the same as used for the smaller print. You’re also using the same paper, and the timer is set to the same value as used for the smaller print. Too, the lens is used at, or close to, its optimum aperture of f/5.6. When you expose and process the print, it should be identical to the smaller print.

No calculator? No problem.

For an odd integer or non-integer number of stops difference between two print exposures, some calculation is necessary, even with the aid of the EM-10.

Some enlarger lenses (such as the Rodagon I have) allow the click stop to be disengaged, giving continuous aperture adjustment.

 

[Carnie Bob]

You can certainly do thismathematically every time, or you can do this once and turn the math into a table from which you look up theresult. the attached includes such a table (and the math ) on page 511. for more detail read the entire pdf.

We use to calculate using a mathematical formula for all our mural printing very precise .

 

[Sharktooth]

It's an interesting challenge. It's a little harder to calculate the exposure time when measuring the head height instead of the lens height, but it's still quite doable. I made up a little Excel sheet to do the calculation. You input the enlarging lens focal length in mm, the distance (or height) of the negative carrier from the paper, as well as the best exposure time at the lower position. Next raise the head to the higher position, and input the new distance from the negative carrier to the paper. That's it. The Excel file shows you the image magnifications at both head positions, as well as the exposure correction factor and the new exposure time.

Here's a screenshot:

I've also attached the Excel file (I think). It's just a tiny file, since there's just a few calculations and text.

The calculations are based on the standard lens formula: 1/f = 1/u + 1/v
and the related calculations for magnification and extension factors. You don't need to know any of this to use it.

 

[wiltw]

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).

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.

I have two different generations of Kodak Master Darkroom guide (about 1966, and in 1988), and putting 4x enlargement at same time (10 sec.) the suggested 8x enlargement time ends up DIFFERENT (38 sec vs 33 sec.)! ...and neither seems to follow Inverse Square suggesitons.

 

[wiltw]

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

...when you forgot to use deodorant?!