Exposure tables/spreadsheets using incorrect actual f/stop and time values

Being new to pinhole photography, I was making a table of pinhole correction factors when I found a source of error in my calculation of the light meter time correction factor. My calculation was fine for the odd-numbered f/stops (assuming f/stop 1 is f-number 0), but a subtle error creeps in for the even numbered stops. The conventional numbers used for the even f/stops (like f/2.8, f/5.6 etc.) are NOT the precise numbers used internally by a light meter. If the displayed f-number on the light meter is used, and the f/stop happens to be an even number, the calculation of the factor will be incorrect. What should be done is to determine the f-number (0 for f/1.0, 1, for f/1.4, 2 for f/2.0 etc.), raise the square root of 2 to the f-number and use the resulting precise f/stop as the denominator in the time factor equation ( the square of (pinhole f/stop) / (meter f/stop) ).

Since the pinhole aperture calculation yields a precise f/stop value, a precise value (used internally by the meter) should be used. So, to figure the true f/stop for "f/11", you take the f-number for "f/11" (7) and raise the square root of 2 to the f-number. The result is 11.3137085, which should be used in the denominator of the time factor equation. For a pinhole with a calculated aperture of, say, 300, the time correction factor would be the square of 300/11.3137085 = 703.12. If the conventional "11" value were used, the result would be an incorrect factor of the square of 300/11 = 743.80.

Again, this only affects the even-numbered stops.

This gets even more confusing if your meter displays decimal f/stops, like my Minolta IVf. These are fractions of f-number to the next f/stop, not an added decimal value to be added to the displayed f/stop. So a displayed value of "11.0 6" on my Minolta means f/11 plus 6/10 of a whole stop to the next f/stop value (f/16). Since "f/11" is f-number 7, an additional 6/10 of a stop would be f-number 7.6. If you raise the square root of 2 to the power of 7.6, you will get the precise actual f/stop used internally by the meter, which is f/13.92880901. Obviously an Excel-generated table of time correction factors is the way to go!

Another "gotcha" is that some of the long exposure times displayed by a light meter, are not the times used internally! If you use one of these times as a reference, the exposure might be way off. Exposure times follow the power of 2 sequence 1, 2, 4, 8, 16, 32, 64, 128.... A light meter usually shows correct times for 1, 2, 4, and 8 seconds. However, most will display "30" seconds when it is actually using 32 seconds internally. The same for a displayed "60" seconds. The meter actually used 64 seconds. This is normally not an issue with a meter or camera, as the software knows how to do the right thing and use the real values. If the odd "conventional" displayed values for some of the times are used in the calculations, the pinhole exposure can be significantly off. The nominal numbers are OK for direct use from the meter, but when multiplied by a large factor for extrapolating pinhole exposures, the inaccuracies multiply as well.

Can anyone verify that my concerns have any validity? Many articles, tables, and calculators use the displayed light meter f/stops and times without regard to their precise value.

Regards,

Don

I'm not sure my aging mind is totally following where you're going with this, but my gut sense is you may be overthinking this stuff -- especially for pinhole work!

Once a pinhole is chosen and installed we are operating in "aperture priority" and the only exposure adjustment one can make is time. One way to work, supported by the Pinhole Designer utility, is to come up with a multiplier relating the pinhole as an f-stop to f/22. One then takes a meter reading, notes the exposure time for f/22 (another stop could be chosen, but that's what PD uses) and multiplies that time by the pre-calculated multiplier (which could be some odd-ball number like 117) or whatever (and throws in reciprocity adjustments perhaps). Even the 2x relationships of shutter speeds bend a little over the typical standard numbers ( half of 1/60 is not exactly 1/125 for example). I usually make a pocket sized card with a table of nominal shutter speed at f/22, multiplied speed, and sometimes a 3rd column with reciprocity adjusted times. And if I even bother to notice fractional stop readings I just make a quick mental interpolation from the surrounding table records. These days there are also smartphone apps one can use, although I have acquired a couple I haven't done much with them.

Given that pinhole cameras, especially those with a fairly wide angle of view, typically have noticeable light fall-off away from the central axis, any exposure is a compromise over the image area to begin with. There are also questions about the specification of reciprocity failure for many films at the multi-second (minute?) exposures frequently encountered. I tend to view my pinhole shooting along the lines of cooking without a recipe (which I also occasionally do!) and play it loose. A second or two out of an 18 second exposure really is not IMHO a big deal in the grand scheme of things.

Perhaps one of our more dedicated number crunchers will have more helpful input.

DWThomas said:

I'm not sure my aging mind is totally following where you're going with this, but my gut sense is you may be overthinking this stuff -- especially for pinhole work!

Click to expand...

My thoughts exactly.
And I am not new to pinhole photography.

My experience is that exposures rarely need to be precise with slow or medium speed film.

I needed to make a 35 second exposure in a building lobby, but had to interrupt it after 10 seconds - it came out fine.

In a coffee shop, I made 45sec., 6 minute, and 18 minute exposures on different frames - the 45 sec one was a bit dark, but usable. Hardly any difference between 6min and 18min except for areas in deep shadows, which came out well on the longer exposure.

So, I don't fine-tune exposures for pinhole photography.

I use a Zero Image 2000, which is a 6x6 and has an f/138 aperture. The camera has a simple dial calculator on the back where you look at what a typical exposure might be (e.g. f/11 at 1/125) and the dial shows the time for the f/138 equivalent.

I also use this site for reciprocity estimation:

http://www.nancybreslin.com/pinholetech.html

Well, I did a back of the envelope example, and I think you guys are correct - The difference seems significant in absolute seconds, but doesn't amount to much in terms of overall change in exposure.

I figured a .3mm pinhole at 3.0 inch focal length (76.2mm). That's a pinhole f/stop of 76.2 / .3 = 254

Figure a light meter reading of f/45 at 15 seconds for ISO 3 paper. The real internal numbers used by the meter are f/45.25 and 16 seconds.

Using the displayed values, the square of 254 / 45 is 31.86 times 15 seconds is 477.9 seconds or 7 minutes and 58 seconds

Using the real internal meter values, the square of 254 / 45.25 is 31,51 times 16 seconds is 504.13 seconds or 8 minutes and 24 seconds.

That's a 26 second difference or about a 5% under exposure using the displayed values. That's much less than a single stop of difference. In this case, the light meter displayed time error helps offset the displayed f/stop error.

Virtually every pinhole calculator I have checked uses the displayed and rounded value, rather than the precise value.

I'm not particularly concerned about it, practically. It's just that I ran across the issue when making my own calculator and felt it best to use the correct value instead of historical but incorrect values.

Errors have a way of multiplying and it seems good practice to avoid them if the means exists.

A good discussion of the issue is here:

https://www.scantips.com/lights/fstop2.html

His tables of nominal and actual agree with my Excel calculator, BTW.

Best regards,

Don

I agree with others that exposure doesn't have to be so precise but however you want precision is easy. Set the meter to readout in EV and do the calculation with that.

A shutter speed error of 20% is acceptable to many of us. The formulae for determining optimum pinhole diameters varies that much among different sources. Only with Kodak Tech Pan film have I bracketed exposures in less than one stop increments. Most practical photography does not demand great precision.

Well, the commonly used f/stop and exposure time numbers produce NO error when used on regular photography equipment as the light meters and cameras/shutters use the correct "internal" value where there is a variance.Try setting a modern digital camera for a 30-second exposure and time it. It will expose for 32 seconds.

There IS an error with pinhole exposure calculation because there is no compensation on the camera side, which the light meter expects. Why introduce any error when the correct value can be used so easily, at least on the f/stops used in figuring the exposure factors. Kind of like deciding to make pi = 3.0 because it's easier and doesn't matter much when making ox cart wheels.

Best,

Don

Don, I get your math and think you're correct but, don't forget the purpose of photography over it!

If I were to do what you are doing I would set the meter up to display in EV instead of aperture and shutter speed. Instead of calculate the factor between the actual aperture and the aperture displayed by the meter and then multiply this factor with the time indicated by the meter I would do the following.
1. Set the meter to display EV.
2. Calculate the number of stops between f/1.0 and the pinhole aperture. For example f/300 is 16.46 and f/254 is 15.98
3. Subtract the above value from the EV displayed by the meter. Make this value X.
4. Calculate the exposure time using this value. T= 1/(log(2^X)/log(2))

In Excel I would use this formula. Substitute EV as the EV reading from the meter and substitute A for the pinhole aperture

Time=1/2^(EV-(log(A^2,2)))

The other thing to bear in mind with these "heavy analytics" is the issue of accuracy vs precision. With dirt cheap computing power available, it's not unusual to see numbers displayed with two and three decimal places, but alas, the measured quantity may well be +/-5% accuracy. It's my understanding that the highest speeds on nearly all mechanical leaf shutters were optimistic at best, and possibly 20% or more slow when new. Most light meters prior to maybe the 1990s were analog devices left to deal with non-ideal response of their sensors over a large dynamic range.

I'd suggest when you pick up an inexpensive consumer device incorporating a cascade of widgets and computations there is a string of possible errors cascaded and the end result may actually be pretty sloppy. I have a nice electronic bathroom scale that displays to tenths of a pound. Early on I noticed I never see an odd digit in that tenth location, so at best the resolution is 0.2 pounds. But I would not be at all surprised (if I had an accurate way to check) the sucker might be more like +/- three, four, five pounds in actual measurement accuracy. Hopefully in a reasonably stable temperature and humidity environment, its consistency is sufficient to monitor my weight gains and losses. (Yeah -- "repeatability" there's another gotcha out in the real world! )

Edit: Not that I mean to belittle these analytic efforts -- it's good to understand the links, levers and pinions behind the facade -- we all need brain teasers to stave off Alzheimers in our golden years.

Here's the practical output of my spreadsheet. I have a laser-drilled .3mm pinhole and use a 3.5 inch focal length with my Graflex Super Graphic.

For those values, I set my Minolta IVf meter (time priority only) to 1 second and take a reading at ISO 3 (optimal for my enlarger paper and reversal processing).

The meter reads the aperture for 1 second. I look up the decimal aperture value in the chart to get seconds or hh:mm:ss exposure times. All very precisely calculated!

For those interested in the full spread sheet that calculates the precise exposure time correction factors for any pinhole diameter and common focal lengths, I put it for download at:

http://projectmf.homelinux.com/Pinhole_Exposure_Table.xlsx

Accuracy is calculated for tenth stop intervals between f/90 and f/2.8 and focal lengths from 2 to 10 inches (50.8mm to 254mm) in 1/4 inch steps.

Just enter the pinhole diameter in mm in the yellow cell and the spreadsheet updates automatically. The numbers can be read directly for a 1 second exposure meter reading or applied as a correction factor for other time values on the meter.

The second tab is my worksheet for the individualized table below. Mostly, this was a sorting and formatting exercise.

Regards,

Don

I think you're overthinking this. Figure out the f/stop of your pinhole camera. Pinhole is simple and I try to keep it that way.
http://www.mrpinhole.com/calcpinh.php

I meter my exposure then I figure out reciprocity of my film, with an Iphone app. https://itunes.apple.com/us/app/reciprocity-timer/id459691262?mt=8

I've seen different reciprocity times for the same film but as mentioned before with the long pinhole exposure times I haven't found enough to make much in the way of differences in a final print. I use Ilford HP5 4x5 and either contact print platinum/palladium or scan the negatives. The Ilford website has a factor chart for their films. Enter the time you meter (Tc) multiply by the factor with a cellphone turned horizontal and calculator app by (Xy) and that will give you the exposure time. The "y" is above the "X" but my keyboard doesn't do that. No complicated math equations involved. What to change the development time is another issue. I'd rather err on developing a little too long than not long enough so unless the exposures have been rather long I stick to the normal time.

http://www.jeffreyglasser.com/

Reciprocity failure dictates that when a small enough amount of light quanta fall on film, exposure times verge on infinite.

Does anyone flash their film, to get it off the toe?

My incorrect method of metering for pinhole ends up over-exposing a bit, according to Don's calculations; which is probably okay, given I frequently use paper negatives. I would suspect that reciprocity failure of many films would be much more imprecise to account for than the otherwise straight exposure time uncorrected for reciprocity. In any event, thanks to Don for figuring this out. It's up to us to either ignore it or put it to good use.

Thanks, Joe. It was your excellent YouTube video that got me interested in fooling with the aperture numbers. I liked that a time correction constant could be so easily calculated, just by squaring the aperture ratios. There’s not a thing wrong with your method! You just used the conventional f/stop value in your example calculation. The method is quite elegant.

I just decided that since the pinhole effective aperture could be calculated, I would explore how regular f/stops were calculated when I made the sheet, and was surprised when only the odd f/stops seemed correct. I ended up learning a thing or two, which to me is as least important as any practical use.

Best,

Don

Don, just out of curiosity, how precise is that laser drilled .3mm pinhole? Laser drilling is a method of fabrication with perhaps a bit of salesmanship, not a guarantee of accuracy. Long ago I used a hand-held microscope with a measuring reticle to check home-made pinholes. Now a properly exposed high resolution scan of a pinhole on a desktop scanner might be more convenient for most photographers. At 2400dpi one should be able to measure to a few percent accuracy, good enough for practical photography.

Jim Jones said:

Don, just out of curiosity, how precise is that laser drilled .3mm pinhole? Laser drilling is a method of fabrication with perhaps a bit of salesmanship, not a guarantee of accuracy. Long ago I used a hand-held microscope with a measuring reticle to check home-made pinholes. Now a properly exposed high resolution scan of a pinhole on a desktop scanner might be more convenient for most photographers. At 2400dpi one should be able to measure to a few percent accuracy, good enough for practical photography.

Click to expand...

That's an interesting idea!

I tried it and found the lateral distortion of my inexpensive scanner was pretty bad. Plus, the pinhole mounting prevented contact of the copper foil with the scanner bed. Backlighting the pinhole with a portable light table, inverted seemed to give the clearest results. I scanned at 2400dpi in close zoom and enlarged further in Photoshop so the pixel blocks could be seen. I boosted the contrast to reduce the fuzzy boundaries and drew a circle using the vertical axis to set the diameter, as there seemed to be less distortion. I counted the pixel blocks and came up with 29.

That's 29/2400 of an inch or .012 inch x 25.4 = 0.304mm for a pinhole with an advertised 0.3mm diameter. That's a pretty good result.

Best,

Don

DonF said:

Thanks, Joe. It was your excellent YouTube video that got me interested in fooling with the aperture numbers. I liked that a time correction constant could be so easily calculated, just by squaring the aperture ratios. There’s not a thing wrong with your method! You just used the conventional f/stop value in your example calculation. The method is quite elegant.

I just decided that since the pinhole effective aperture could be calculated, I would explore how regular f/stops were calculated when I made the sheet, and was surprised when only the odd f/stops seemed correct. I ended up learning a thing or two, which to me is as least important as any practical use.

Best,

Don

Click to expand...

Don,
Can you just ignore the aperture and shutter speed displayed by the meter. These values are rounded off and not rounded off in a manner that is not mathematically correct. It's best to calculate the exposure time using the pinhole aperture and the EV number displayed by the meter. I think I know what you were trying to do and correct me if I am wrong. Since the meter can not display the aperture in the range of the pinhole so you would have it displays a larger aperture like f/11 and the corresponding shutter speed for the light level. You would then calculate the correction factor using the aperture number on the meter which is not correctly rounded off and then using this factor to multiply by the shutter speed from the meter which is also not rounded off correctly. While the error doesn't matter for the purpose of exposure but it it bothers you use the method I suggested.

Chan Tran said:

Don,
Can you just ignore the aperture and shutter speed displayed by the meter. These values are rounded off and not rounded off in a manner that is not mathematically correct. It's best to calculate the exposure time using the pinhole aperture and the EV number displayed by the meter. I think I know what you were trying to do and correct me if I am wrong. Since the meter can not display the aperture in the range of the pinhole so you would have it displays a larger aperture like f/11 and the corresponding shutter speed for the light level. You would then calculate the correction factor using the aperture number on the meter which is not correctly rounded off and then using this factor to multiply by the shutter speed from the meter which is also not rounded off correctly. While the error doesn't matter for the purpose of exposure but it it bothers you use the method I suggested.

Click to expand...

Well, that is exactly the point I was making in my original post! A quick review:

The precise (assuming accurate pinhole measurement) effective f/stop of a pinhole is pinhole diameter divide by pinhole to film distance.

As Joe V. has instructed, an exposure time compensation factor can be calculated from a light meter reading by dividing the effective pinhole aperture by the meter-indicated f/stop and squaring the result.

This factor is inaccurate for even-numbered f/stops as the meter-indicated value is incorrect.

Precise f/stops values can be calculated by assigning a number to each whole f/stop number (f/1 = 0, f/1.4 = 1, f/2 = 2, f/2.8 = 3, f/4 = 4 and so on), the raising the square root of 2 (1.414) to the power of the f/stop number.

Example: f/2.8 is f-number 3. 1.414 raised to the power of 3 is 2.8284, which is the precise value of "f/2.8".

The precise value rather than the conventional f/.stop value should be used when calculating exposure time factors (although the error is small).

Using f-numbers as I am suggesting is (I think) the same as your method of using EV, except your method requires doing the complicated math every time.

Best,

Don

Chan Tran said:

Don,
Can you just ignore the aperture and shutter speed displayed by the meter. These values are rounded off and not rounded off in a manner that is not mathematically correct. It's best to calculate the exposure time using the pinhole aperture and the EV number displayed by the meter. I think I know what you were trying to do and correct me if I am wrong. Since the meter can not display the aperture in the range of the pinhole so you would have it displays a larger aperture like f/11 and the corresponding shutter speed for the light level. You would then calculate the correction factor using the aperture number on the meter which is not correctly rounded off and then using this factor to multiply by the shutter speed from the meter which is also not rounded off correctly. While the error doesn't matter for the purpose of exposure but it it bothers you use the method I suggested.

Click to expand...

You know, I read over your original post once again and I like the idea of using metered EV. Just to educate myself, I'll try to come up with a chart with your formula and see how it compares. How did you calculate a pinhole EV number from the effective aperture??

Best,

Don

DonF said:

You know, I read over your original post once again and I like the idea of using metered EV. Just to educate myself, I'll try to come up with a chart with your formula and see how it compares. How did you calculate a pinhole EV number from the effective aperture??

Best,

Don

Click to expand...

Using the effective aperture (diameter/distance from pinhole to film) as A, T as exposure time and EV as the EV reading from the meter. Just put this formula into Excel and you get it
T=1/2^(EV-(log(A^2,2)))

For the EV value of aperture do this. For example you have f/300. It's log2 of 300^2. If you use excel then the formula is EV= log(300^2, 2). If you use a regular calculator that generally doesn't have log base 2 then you can do this log(300^2)/log(2)=16.45.
Say if you have a sunny 16 condition an you're on ISO 100 the meter should read EV 14.7
14.7-16.45= -1.76. Next the exposure time is 1/(2^-1.76)=3.39 sec. You can shorten this calculation by changing the sign of the -1.76 first then raise 2 to the 1.76 power. That is 2^1.76=3.39 sec.

Chan Tran said:

Using the effective aperture (diameter/distance from pinhole to film) as A, T as exposure time and EV as the EV reading from the meter. Just put this formula into Excel and you get it
T=1/2^(EV-(log(A^2,2)))

For the EV value of aperture do this. For example you have f/300. It's log2 of 300^2. If you use excel then the formula is EV= log(300^2, 2). If you use a regular calculator that generally doesn't have log base 2 then you can do this log(300^2)/log(2)=16.45.
Say if you have a sunny 16 condition an you're on ISO 100 the meter should read EV 14.7
14.7-16.45= -1.76. Next the exposure time is 1/(2^-1.76)=3.39 sec. You can shorten this calculation by changing the sign of the -1.76 first then raise 2 to the 1.76 power. That is 2^1.76=3.39 sec.

Click to expand...

This seemed to work well! I created a spreadsheet that allows entering the pinhole diameter and "focal length" distance, then calculates the exposure time for EV values > 0 and up to 10. If you have a moment, could you look it over?

http://projectmf.homelinux.com/Pinhole_Exposure_by_EV.xlsx

Best,

Don

DonF said:

This seemed to work well! I created a spreadsheet that allows entering the pinhole diameter and "focal length" distance, then calculates the exposure time for EV values > 0 and up to 10. If you have a moment, could you look it over?

http://projectmf.homelinux.com/Pinhole_Exposure_by_EV.xlsx

Best,

Don

Click to expand...

I looked it over and it looks great!