Factor for enlarger head height adjustment?

Lee L · Dec 12, 2008

Just another thought that came to me. There are rulers printed on clear plastic (C-Thru makes nice ones in the US) that could be substituted for the negative at both degrees of enlargement, then magnification changes could be easily calculated against a ruler on the easel. Might be quick enough for those without an enlarging meter.

Lee

I may have pre-answered Dan's simultaneous post.

dancqu · Dec 12, 2008

ic-racer said:
I wonder if Nicholas could supply the
magnification in the above examples.

M&m; magnification. And how are the values for
the two established? I see that a ratio of squares
is involved. I'm suspicious. A "...correct conclusion."
is at stake. Dan

David Brown · Dec 13, 2008

OMG!

Make another test strip ...

Nicholas Lindan · Dec 13, 2008

David Brown said:
Make another test strip.

I just made and evaluated a test strip and it took 4 minutes, 45 seconds, 2 minutes of that time were in the developer.

Using the ruler took 30 seconds. Used no chemicals, paper or electricity.

Add 15 seconds if you don't have an f-stop timer and need to use a chart.

Saves yer money - saves yer time - takes yer choice.

A note on using Darkroom Automation's stops<->seconds chart: If you are only applying a stops correction to a time you can simply multiply your present exposure time by the number in the chart.

As an example:

your present exposure is 5 seconds and you want to add 1.4 stops
look up 1.4 stops in the chart and find 2.6
multiply 5 seconds by 2.6 => 13 seconds is the new time

Jean Noire · Dec 13, 2008

Nicholas Lindan said:
The negative carrier size is 9.2mm. The projection of the carrier outline was measured, this contributes somewhat to the error as the carrier is 3 dimensional and the lens was focused on the negative in the middle of the carrier.

Going from a negative size of 9.2mm to the following sizes, the exposure factor correction in stops is:

Size......Magnification...Metered...Formula...DA Ruler
11mm ...1.2
21mm ...2.3...............1.1..........1.1.........1.3
32mm ...3.4...............2.0..........2.0.........2.0
45mm ...4.9...............2.8..........2.9.........2.8

The ruler and the formula should provide identical results as the ruler is based on the same optical formula - I am not sure where the discrepancy arrises at the 21mm image size. Apart from that they all seem to agree within experimental and rounding error.

I have been following this thread with interest and thanks for posting.
I may have missed something but you are talking here of images in millimetre sizes and this seems really small, can you elaborate please?
Regards
John

Nicholas Lindan · Dec 13, 2008

John Roberts said:
millimetre sizes and this seems really small

Emmm, hrrrr, hummphh....

centimeters, it's centimeters -- change the 'mm' to 'cm'.

David Brown · Dec 13, 2008

Nicholas Lindan said:
- takes yer choice.

OK, I realize that I am in the minority here, but I have made a choice and simply stated my opinion (just like everyone else) :rolleyes:

I own and have used:

The old Kodak "computer" in their B&W dataguide.
Mr. Linden's ruler
an Ilford EM10
the enlarging attachment for a Gossen Luna pro
the algebra formula being discussed.

All of these got me close. "Close!" I still had to fine tune, and - in my experience - a test strip and/or a "work print" or two ended up being made anyway. Starting with a test strip is, for me, the quickest, cheapest and most efficient method.

YMMV

uwphotoer · Dec 13, 2008

David Brown said:
OK, I realize that I am in the minority here, but I have made a choice and simply stated my opinion (just like everyone else) :rolleyes:

I own and have used:

The old Kodak "computer" in their B&W dataguide.
Mr. Linden's ruler
an Ilford EM10
the enlarging attachment for a Gossen Luna pro
the algebra formula being discussed.

All of these got me close. "Close!" I still had to fine tune, and - in my experience - a test strip and/or a "work print" or two ended up being made anyway. Starting with a test strip is, for me, the quickest, cheapest and most efficient method.

YMMV

Even with the EM-10 I still do a test strip...... have you priced cibachrome materials.... I would never just toss in a bigger sheet of paper and run a print like it would be a final.....

FilmIs4Ever · Dec 13, 2008

It should be possible to tweak the formula to be "spot on" at any enlarger height.

Things that probably aren't being taken into account are paper reciprocity, actual lens-to-print distance (not the hypotenuse of lens-to-print distance and chassis stalk angle), and the aforementioned contrast loss due to light scatter with increase in magnification factor.

Nicholas Lindan · Dec 13, 2008

Time for a real world test ...

Conditions: Beseler 45MX, condenser light source, Stouffer 4x5 31-step tablet, 150mm Rodagon, Ilford MGIV RC glossy, #2 1/2 filter, D-72 70F 2 min

Prints were made at 4x5 (1:1), 5x7, 8x10, 11x14 and 16x20.

In each case the #1 step was metered with the Darkroom Automation meter. Time was controlled with a DA f-Stop timer. A total of 10 stops of exposure (meter reading + timer setting = 10) was given in each case.

The results are as consistent as I could ever do with test strips. All the prints were made with the same contrast filtration - results would be a bit closer if contrast were tweaked.

Time to find new exposure and set it into the timer after changing magnification - less than 5 seconds.

declark · Dec 13, 2008

Why am I not surprised to find such thorough and thoughtful insight on such a niche APUG forum topic. There's a lot here that I need to still digest. It looks like making a test strip is probably the best bet, but at least the calculations will be useful to even get in the ballpark on the test strip. I find that sometimes I am way off base especially if proper exposure time goes from say 12s to 45s or so, the usual 3s test strip just isn't going to work at the longer exposure, so I will now know where to start with a certain base exposure.

Nicholas Lindan · Dec 14, 2008

Comparison of methods for determining the exposure correction required for magnification changes using a 50mm lens, Beseler 45 enlarger and condenser lamphousing

The ruler and the magnification formula provide the same result - the previous difugalty was due to not correctly locating the lens nodal point. In this case the point is 1.1" back from the front flange of a 50mm f2.8 El-Nikkor, FWIW.

However, although they agree, they both provide the wrong exposure correction - enough to create a shift of about 1/3 of a Zone in some cases. Intriguingly the error doesn't seem to follow any sort of pattern.

The error doesn't seem to be due to the variation in the distance from the lens to the condenser. Changing the distance by 1", a bit more than the lens travel in the above test, changes the light intensity by less than 0.005 stops. It might be interesting to repeat the test with a diffuse light source.

So far, it seems only a good meter will provide accurate compensation.

Curt · Dec 14, 2008

The old Kodak "computer" in their B&W dataguide.

A lot is/has been said about Kodak but the Data guides both BW and Color have probably helped more people than can be counted. In fact the data from the papers you could order were invaluable.

2F/2F · Dec 14, 2008

In all practicality, you are fine with an estimate. You will never be spot on via formula anyhow, so will end up wasting a full test print, when you could have just done a test strip. Going from one standard print size to the next (say from 8x10 to 11x14), I would add one stop of exposure as a general adjustment. Going to 16x20? Add two stops versus the 8x10. This is making the quite general estimate that each standard size contains twice as much surface area as the next smallest. This is not exactly true, but it is close enough to make a good test strip. One thing that is true is that when going from 4x5 to 8x10, or from 8x10 to 16x20, you exactly quadruple the surface area, therefore you end up with only one quarter the light. This means that you can theoretically compensate by increasing the amount of light by a factor of four, also known as adding exactly two stops of exposure.

Mike Crawford · Dec 14, 2008

David A. Goldfarb said:
Recognize these numbers--4, 5, 8, 11, 16? Both the standard sizes (4x5, 5x7, 8x10, 11x14, 16x20) and approximately the f:stop series. One stop more exposure for every standard increase in size.

That's really interesting and something I had never realised. However, trust us pesky Europeans to come along with our 12 x 16 paper and ruin the sequence!!

Keith Tapscott. · Dec 14, 2008

Mike Crawford said:
That's really interesting and something I had never realised. However, trust us pesky Europeans to come along with our 12 x 16 paper and ruin the sequence!!

9.5 x 12 inches and A4 also to be included.:confused:

ic-racer · Dec 14, 2008

Nicholas Lindan said:
Comparison of methods for determining the exposure correction required for magnification changes using a 50mm lens, Beseler 45 enlarger and condenser lamphousing...

Fantastic!

Nicholas Lindan · Dec 14, 2008

The flies over this well flogged dead horse get thicker and thicker and the horse keeps twitching.

For making moderately cropped 4x5, 5x7, 8x10 and 11x14 prints from 35mm and 4x5 negatives, the exposure correction factors for changes in magnification follow no discernible pattern. The geometric methods [either the DA correction ruler or the (M+1)^2/(m+1)^2 method] can result in answers that range from exact to 0.2 stops off from the metered values. The previous tests show the metered values are the correct values. All the meter readings and correction values are in stops.

Also included are test results with an opal diffuser over the negative. The results with the diffuser are close to identical to those with the normal Beseler condenser lamp housing. The conclusion is that the same behavior will be exhibited by diffusion, cold-light and dichroic enlargers.

The cropping is for the central 2/3's of the negative to be enlarged to the full size of the print - the central 1" for 35mm, the central 3" for 4x5.

dancqu · Dec 16, 2008

ic-racer said:
The equation I use 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)

My quick study of this matter a few years ago had
me turn my attention to the purchase of an OM-10.
A more thorough study this pass confirms the
equation you use to be THE one to use. Print
size divided by negative size is specified
to be the method for deriving M&m.

Although a + 1 in each term appears to compensate
for aperture changes and the equation is described
as being accurate, I've not encountered any claims
of it being exact. So I wonder if the equation is
the last word?

Without the + 1s results will equal those of the
equation Nt = Ot x Ne^2/Oe^2; where the terms
are Old, New, time, and edge.

For more information on this subject and derivation
of other exposure related variables search Google
for, exposure enlargement calculations . Dan

dancqu · Dec 16, 2008

Pardon me. That should be EM-10. I think Darkroom
Automation's combination Enlarging Meter/Densitometer
a good value. I'd have one except for it's appearance of
being bulky and lacking a narrow up front sensor; good
for metering small prints and any size print's corners.

Any chance of a redesign Mr. Lindan? Dan

Nicholas Lindan · Dec 16, 2008

dancqu said:
I think Darkroom Automation's combination Enlarging Meter/Densitometer a good value. I'd have one except for it's appearance of being bulky

It is 1" shorter and a 1/2" wider than an EM-10, with the same thickness. It is the size of a slightly long pack of 100's cigarettes (an obsolete unit of measure, I know).

Its silicon-blue photodiode sensor is 0.008 sq in, a bit less than 3/32" on a side, comparable in size to the EM-10's CdS cell. Spots much smaller than that probably aren't important metering tones and a very small sensor is noisy because it starts to pick up grain and very fine image detail.

It comes with a 30 day money back guarantee, if it fails to satisfy then send it back.

Nicholas Lindan · Dec 16, 2008

Sanity and grace ...

After a somewhat sleepless night, and a distracted day, I went over the magnification exposure correction calculations and measurements and found a pair of dumb errors that caused the results to get skewed.

The (M+1)^2/(m+1)^2 formula and the metered values all agree within a few hundredths of a stop -- which is what they are supposed to do.

The 'square law', beloved of all 7th grade science students, does still work. The law doesn't work on magnification but on distance from the light source to the screen. In this case the light source is the illuminated aperture of the lens and the screen is a point on the photographic paper (or you can turn it around, projecting a point on the paper onto the area of the aperture). The DA magnification exposure correction ruler works on this principle. An error in it's use can arise if the position of the lens' apparent aperture isn't located properly.

The geometric forms - the ruler and (M+1)... formula - are based on thin lens formulations. The actual light fall off will deviate slightly as the size of the front entrance pupil - the effective aperture - changes a bit with lens to paper distance. You can see this by looking into a wide-open lens at several distances. In practical terms this slight error can be ignored.

The meter has one great advantage - no math and transcription errors.

The horse is finally dead, the flies have gone.

ic-racer · Dec 17, 2008

Thanks for spending the time on this!

Jimpix · Sep 5, 2009

Hi boys & girls.
I'm new here & checked out the original question about print exposures & formulas etc....
then came to this last page to see how long it went on for. mmmmm?
So, just in case no-one has mentioned this method. Read on.

I haven't done any printing for a couple of years now. But I have always used the guide told to me by my darkroom manager when I was a young lad starting in BW photo-printing.
Based on knowing the correct exposure for an SS print (e.g. 5x4 neg to 5x4 print).
If you measure the length of the print for a 10x8 - 10 inches (twice as long as 5 inches).
You just open up the lens 1 f-stop. Giving twice the light strength.
Then with the same neg do a 20x16 print (20 inches long = 4 x the original length) you open up 3 stops from original exposure.
For example: SS exposure of 5x4 neg to 5x4 print is, say 10 sec @ f32,
So 5x4 to 10x8 = 10 sec @ f22, & @ 15 inches long = F16 & 20 inches long = f11 @ 10 sec.
When you run out of f-stops, you then increase the time comparable to f-stops to suit the magnification.(open up 1 stop for every 5 inches) (that's what she said?).
This method flies in the face of the Inverse Square Law. However, it does work. I have used it since 1976 & it is usually on the button or within a 1/4 of a stop on massive blowups. But it is a very easy quick guide to save time. It also takes the 'Brain Damage' out of the job.
BTW. 5x4 to 20x16 I open up 3 stops (equal to 8 times the illumination. Whereas Inverse Square Law would say the area is 16 times as big as the original 5x4. Thus indicating a 4 stop difference. So anyone who would like to try that little experiment & see how it pans out, please do. sometimes it can be that simple. Honest.
Like a 10x8 neg to 15x12 print in this instance would be either 10 sec @ f22.1/2 or 15 sec @ f32 (same thing).
And so on throughout all the percentage ranges.
So a 10x8 neg printing to 5x4 (50% print size) would need to shut down 1 stop to f45 ( or 5 sec @ f32).
Remember though. Start with a really good neg to form your basis. Then you can up or down the corrective exposures for heavy or thin negs accordingly.
I think i've been quite thorough there.

Happy printing.

Jim

hoffy · Dec 6, 2009

Bruce Osgood said:
You're dealing with the Inverse Square Law. Moving a light source farther from the subject it diminishes proportionately to the distance.

I've worked out a simple Excel program that I simply plug in three variables and come up with New Elevated Exposure

New elevated exposure equals:

((New elevation / Old Elevation) ^2) X Original Exposure

Supposing your 8x10 elevation from lens to paper was 24 inches @ 16 seconds and your New elevation is 30
inches, then: ((24/30)^2) = 2.44
2.44 X Original Exposure (16 seconds) = 39.4 New Elevated Exposure.

I read this thread last night and decided to put this theory in practice.

While I don't agree with your example(!?), I found that the formula worked fine. Well, fine enough to be a pretty good starting point (I always test strip regardless).

I also found this one elsewhere on the net. Same formula in essence:

(ot/oh^2)*nh^2=nt, (old time divided by square of old height) times square of new height equals new time.

So, thanks to this thread, I am now saving a lot more time in the darkroom!!

Cheers

Factor for enlarger head height adjustment?

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