Aperture, stops and f/22.6!

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DiG

DiG

DiG

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Hi,
I'm, trying to add the ability to use 1/2 and 1/3 stops in the my "Photographic Light Meter" Android app (ok, that was a bit of a plug!)

However, I'm struggling to understand the aperture naming system, as far as I understand it,

f-number = sqrt(2) ^ stop

so for stop 1, f = sqrt(2) ^ 1 = f/1
stop 5, f = sqrt(2) ^ 5 = 5.656 = f/5.6

So far so good, however it falls down when you get to stop 7, where
f = sqrt(2) ^ 7 = 11.313 = f/11.3, but its actually f/11. Same problem with 22.627 becoming f/22 not f/22.6!


So, where am I going wrong? What I want is a method which, given a stop (which could be a whole stop, a 1/2 stop or even 1/3 stop, so 5, 5.5 or 5.3, 5.6 etc) would give me a correct f/ value

Not a normal Photography & Video thread I know, but hoping someone understands this better that I do!
 
Well the usual figures of f/2.8, f/5.6, f/11, etc. are not exact; the actual numbers are of course irrational (being powers of sqrt(2), which is itself irrational) and therefore having infinite decimal expansions, so it needs some kind of rounding, but the photographic community is lazy and doesn't bother to do it properly, hence 22.6 being rounded down to 22 rather than up to 23 :p

I think your best bet is to do it heuristically by checking numerically which number is the closest and looking up a pre-rounded value. For example, for f/5.6, you'd calculate sqrt(2)^5, which gives 5.65685[...], then look up the closest number in some sequence of pre-determined display values, which would clearly by 5.6.

Note that if you were to try to do it automatically, you'd also need to know how many decimal places to round it to, since 5.6 is rounded to tenths, while 11, 22, etc. are rounded to units.

Also, let us know when the app is finished; sounds useful :cool:
 
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DiG said:
Hi,
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Click to expand...

Someone help this guy out! :o
 
Inquisitor said:
Well the usual figures of f/2.8, f/5.6, f/11, etc. are not exact; the actual numbers are of course irrational (being powers of sqrt(2), which is itself irrational) and therefore having infinite decimal expansions, so it needs some kind of rounding, but the photographic community is lazy and doesn't bother to do it properly, hence 22.6 being rounded down to 22 rather than up to 23 :p

I think your best bet is to do it heuristically by checking numerically which number is the closest and looking up a pre-rounded value. For example, for f/5.6, you'd calculate sqrt(2)^5, which gives 5.65685[...], then look up the closest number in some sequence of pre-determined display values, which would clearly by 5.6.

Note that if you were to try to do it automatically, you'd also need to know how many decimal places to round it to, since 5.6 is rounded to tenths, while 11, 22, etc. are rounded to units.

Also, let us know when the app is finished; sounds useful :cool:
Click to expand...

Ok so there is no logic to it, good to know thanks! Thats pretty much the way I do it at the moment, I have a hard coded map of stops -> display values. I wanted a automatic way of doing it so that I could let the user define the min and max apertures and just calculate all the steps in between, guess I will have to go the long way round! Thanks for the help
 
DiG said:
Hi,
I'm, trying to add the ability to use 1/2 and 1/3 stops in the my "Photographic Light Meter" Android app (ok, that was a bit of a plug!)

However, I'm struggling to understand the aperture naming system, as far as I understand it,

f-number = sqrt(2) ^ stop

so for stop 1, f = sqrt(2) ^ 1 = f/1
stop 5, f = sqrt(2) ^ 5 = 5.656 = f/5.6
Click to expand...
Mistake in the maths here - stop 1 is f/1.4, not f/1. f/1 should be stop 0.
 
Phate said:
Anyone else look at this thread and go

"oh **** maths?" ??
Click to expand...

Nope, it is very useful to know what the f-numbers actually mean and is part of learning exposure.

If you like it or not there is a hell of a lot of maths in photography. Luckily, you can mostly ignore it.
 
D.P. said:
Nope, it is very useful to know what the f-numbers actually mean and is part of learning exposure.

If you like it or not there is a hell of a lot of maths in photography. Luckily, you can mostly ignore it.
Click to expand...

I understand how exposure works without getting tangled up in the technicals such as displayed above thankfully :) - My maths is horrendous, sod trying to work it out on the spot :o
 
DiG said:
Hi,
f-number = sqrt(2) ^ stop

so for stop 1, f = sqrt(2) ^ 1 = f/1
stop 5, f = sqrt(2) ^ 5 = 5.656 = f/5.6

So far so good, however it falls down when you get to stop 7, where
f = sqrt(2) ^ 7 = 11.313 = f/11.3, but its actually f/11. Same problem with 22.627 becoming f/22 not f/22.6!

So, where am I going wrong? What I want is a method which, given a stop (which could be a whole stop, a 1/2 stop or even 1/3 stop, so 5, 5.5 or 5.3, 5.6 etc) would give me a correct f/ value
Click to expand...

In my understanding you are not far off.

x ^ 1 = x so as a previous poster has said sqrt(2)^1 = 1.414 (or f1.4)
x ^ 0 = 1 so stop 0 is f1

As a previous poster has also said f22.6 is close enough to f22 in terms of the light passing through that f22 is 'close enough'.

The other way of thinking about it is that each stop represents a halving of the light. so if I have a hole 1 unit in area, then to halve the light I need a hole 1/2 units in area, then 1/4, then 1/8 etc. The f number is the ratio of the focal length to the aperture size which is done to make sure that f4 on a 24mm lens is the same as f4 on a 300mm lens in terms of the light captured.

If we assume a circular aperture, then the ratio of the diameter of the aperture for each halving of the light is 1, sqrt(2) = 1.414, sqrt(4) = 2, sqrt(8) = 2.8, sqrt(16) = 4, sqrt(32) = f5.6 - see the pattern emerging ?

The difference in light between f22 and f22.6 is 22^2 / 22.6^2 or 0.947 which is a difference between a shutter speed of 1/500 to 1/473 in other words pretty well undetectable.

Hopefully this makes things less confusing rather than worse !

In terms of your app, I would suggest having a lookup table of all the full, half and third stop values as you want them displayed and taking the nearest value after whatever calculation you perform.
 
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DiG said:
Its the one in the Market, would be interested to hear any opinions?
Click to expand...



Not used it in practice yet, I shall attempt to more often now and give you feedback, although I'll say I like the design of the UI, is simple and effective.
 
I like the layout and the idea. :)

I started to write a very similar app for calculating ND exposures based on the current shutter speed / aperture / iso but couldn't be bothered to learn how to write the frontend stuff :D
What I wanted to be able to do was input the shutter speed / aperture / iso, and the number of stops to adjust by, and use that to find the new exposure and how much to adjust shutter speed. Then fiddle with the output exposure, with the app showing how each change affects the overall exposure of the new image (in the same style as the in-camera ev metre, for example), or locking one of the values to always keep the correct exposure.*

Only problem with your app is that it doesn't work (desire), the calculated ev never goes above 1. The first couple of times it gave me the light sensor timed out error as above.


And the other photography app that would really be good (combined with a little hardware) is a bluetooth shutter release :D, with an exposure timer as well. Wishful thinking... :D
edit: apparently this actually exists now for iPhone / nikon! two platforms I don't use :s

*not sure any of that made sense
 
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This thread pretty much reminds me why I never went beyond Pascal and Visual Basic at uni! :o
 
Zogger said:
I like the layout and the idea. :)

I started to write a very similar app for calculating ND exposures based on the current shutter speed / aperture / iso but couldn't be bothered to learn how to write the frontend stuff :D
What I wanted to be able to do was input the shutter speed / aperture / iso, and the number of stops to adjust by, and use that to find the new exposure and how much to adjust shutter speed. Then fiddle with the output exposure, with the app showing how each change affects the overall exposure of the new image (in the same style as the in-camera ev metre, for example), or locking one of the values to always keep the correct exposure.*
Click to expand...

All of that could easily be done in a spreadsheet if you have a spreadsheet app. Sure it may not look so nice but it would do the job. :)
 
Zogger said:
I started to write a very similar app for calculating ND exposures based on the current shutter speed / aperture / iso but couldn't be bothered to learn how to write the frontend stuff :D
What I wanted to be able to do was input the shutter speed / aperture / iso, and the number of stops to adjust by, and use that to find the new exposure and how much to adjust shutter speed. Then fiddle with the output exposure, with the app showing how each change affects the overall exposure of the new image (in the same style as the in-camera ev metre, for example), or locking one of the values to always keep the correct exposure.
Click to expand...

I guess I'm lucky in that I've always been able to that sort of stuff in my head... I guess you kind of remember the full stop values after a bit. You can always use the clicks on the aperture/shutter adjustment to keep count.

For example if your camera adjusts in 3rds. And you want to use a 10 stop ND filter. Just count the stops - aperture at f8, click, click, click ONE, click click click TWO etc then shutter 1/125, click click click THREE etc etc. Stop when you get to 10 !

Lots easier than film when you had to take into account reciprocosity failure as well !
 
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