# Using multiplier of area to scale print size and adjsting for print density

Discussion in 'Enlarging' started by tkamiya, Feb 28, 2011.

1. ### tkamiyaMember

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I just want to confirm what I am seeing is real.... not some error in my process.

Paper in question is Ilford MGIV FB Glossy in 8x10 cut and 11x14 cut. These were purchased at the same time from the same vendor. (no way to tell if they came from the same master roll)

I have a negative which prints exactly the way I want on 8 x 10 paper with 1/4" borders using #1 1/2 filter, f/8, and 21 seconds.

When I wanted to print this on 11 x 14 with the same border, I calculated the ratio of surface area and used that multiplier for 21 seconds, then came up with computed figure of 42 seconds exposure.

Comparing the results, the larger version has shadow area is about 1/6EV darker.

Is it correct that this method will give me fairly accurate figure but fine tuning is still required?

2. ### keithwmsMember

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Well, normally you just compute a linear magnification number, i.e. 8 inches becomes 11 inches, and compute the exposure difference from that. Did you try that and compare?

I wouldn't recommend working in terms of areas. That'd take more math.

Try this:

http://www.fineart-photography.com/xc.html

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3. ### Dan HendersonMember

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I learned to use changes in enlarger height to calculate exposure for a new print size, using the following formula:

(new height+1) squared / (old height+1) squared.

I found a tape measure with a sticky back side at the local home improvement store that I attached to the column of my enlarger to facilitate height measurement, and keep a small calculator in the darkroom to do the math.

4. ### jeffreygSubscriber

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Years ago Kodak published a darkroom guide that as I recall had a dial that would give exposure changes for enlarging from one size print to another. As for myself, I prefer to make a new test print when increasing print size. Different sizes can give a different feel to an image and depending on the size a different viewing distance.

http://www.jeffreyglasser.com/

5. ### Dave MartinyMember

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I would think that finding an accurate measurement of the two projected areas, and then using their ratio as a multiplier, would give the best approximation of the new exposure. 8x10 and 11x14 have aspect ratios that are darn close, but I would still use the true projected areas outside of the easel arms, not the areas within the easel arms. Beyond that, I think the answer to your question about tweaking is "yes". Probably due to the granular nature of film, the tonality, micro contrast and overall contrast of a print can sometimes change in subtle ways as it is enlarged.

Regards,

Dave

6. ### tkamiyaMember

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Thanks everybody. Just to clarify, two prints are very close. I found some subtle differences in deep shadow where on larger print, the details aren't as clear as the smaller. I'd bet the adjustment is only a few seconds worth (out of 43 second exposure).

I may just dodge that area a bit as everything else looks about right.

Thanks again.

7. ### wiltwSubscriber

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Kodak Black-and-White Darkroom Dataguide
...
'School solution' says that 8x10 at 10 sec. becomes 18 seconds for 11x14

For the OP's numbers, 21 second 8x print becomes 38 sec 11x print

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What you are seeing is real: ratioing the areas will give the wrong answer, as you have found out. Sometimes very wrong, sometimes not terribly so.

There is a long drawn-out convoluted sticky thread at the top of this forum that resolves this topic.

The correct correction can be calculated as either:
• The ratio of magnifications (m + 1) ^ 2 / (M + 1) ^ 2
• The ratio of lens heights h ^ 2 / H ^ 2. When using lens height it is important to use the position of the diaphragm in the lens (there is a further tweak, but it can be ignored).

A scale for calculating exposure correction using lens height is available on the Darkroom Automation web site support files section, about 2/3 the way down the page:
http://www.darkroomautomation.com/support/index.htm

9. ### 2F/2FMember

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Using difference in enlarger height to figure this out is theoretically accurate in a single step, not area...but this is what test strips or for. IMHO, there is no point in trying to go for broke on the first print after changing the enlargement. You can calculate to you heart's content, but this is analog photography. Something will always be slightly different from your calculations. I would use enlarger height to get close, but still use test strips before devoting a whole piece of paper to the enlarged print.

10. ### tkamiyaMember

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I appreciate everybody for comments. Experimentally, I found 8x10 print at 21 seconds can be matched EXACTLY to 11x14 print at 38 seconds. Margin of error is +/- 1 second at 11x14 scale.

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11. ### keithwmsMember

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Yes, well the calculator I linked gives 37.3 sec. So you're off by 0.7 sec

12. ### tkamiyaMember

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Oh no! I'm off! Waaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa!!

13. ### Ronald MoravecMember

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Be careful you do not run into reciprocity error when scaling up or down.

Actually you will be very close if you remember from 35mm only, 3.5x5 5x7 8x10 11x14 16x20 all one f stop apart if you open or close the lens.

You can prove this with an enlarging meter if you take care to get the cell EXACTLY on the plane of focus. It will not work if you drop it op to of the easel.

14. ### Ian CMember

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With respect to posts #10, 11, 12:

The difference in going from a calculated exposure of 37.3 seconds to 38 seconds is 0.03 f.

In either case, could anyone tell the difference?

15. ### David A. GoldfarbModeratorStaff MemberModerator

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The standard sizes are about one stop apart, corresponding approximately to the f:stop series--4x5, 5x7, 8x10, 11x14, 16x20, 20x24. There will be differences, because the proportion of the frame is different, so the composition might change slightly, unless you are printing full frame or changing the proportion of the border to maintain the composition independent of the aspect ratio of the frame.

When you go larger, though, you may also find there is more light scattering from various sources, the lens, the reflection of the image from the paper onto the walls of the darkroom and back, etc., so it's not unusual to find that you need a little more contrast as you go larger, and depending on the exposure time, there may be reciprocity effects, so there's always a little fine tuning to do, and I wouldn't count on being able to calculate the new exposure precisely.

16. ### krakerSubscriber

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I agree. This is indeed the way I do it. (new height)^2/(old height)^2 gives an estimate of the extra factor, 2log of that gives the difference in f-stops, but that merely gives me a new starting point for test strips, not an absolute truth for a good print. I don't even consider the height of the easel nor the exact height of the lens; I just read the heights from the enlarger column and do the math to give me an estimate; nothing more than an estimate.

17. ### tkamiyaMember

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I didn't expect it to be exactly right based on calculations only. But getting them as close as possibly can with calculations help. For one, I don't think paper response is exactly linear. Also they may be technically identical but different size gives different visual impressions.

I got it pretty close and to my liking - visually that is.

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Geometric correction - if done carefully - is within a few hundredths of a stop. From the sticky post at the top of this forum:

Unless the exposure time is greater than 100 seconds there is no measurable reciprocity failure with paper.

The old adage 'open up a stop for each paper size' is good to 1/10th of a stop - as long as you are printing from 35mm negatives, using a 50mm lens, cropping to the central 1 inch/25mm (length) of the negative or so, only changing one print size, and going no smaller than 5x7. For most prints made from 35mm negatives these aren't onerous conditions. More exact results can be had by using 0.9 stops correction per print size. However, with a 4x5 negative/150mm lens the error can be 0.25 to 0.35 of a stop, or a print zone of density.

There is no debating the physics of the matter concerning geometric correction - it is exact. However, exact correction doesn't tell the whole story as the aesthetics of small prints and large prints are different. A small test strip won't uncover the changes needed and a full size work print is needed.

Metering will take into account the effects of changing flare levels. Flare levels don't play much of a part until print size gets really big - over 20x24 in my darkroom. If your darkroom is painted with titanium white and your enlarger leaks light like a sieve then things can be different.

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