8x10in, 6x6cm, 35mm apertures

[Sizam]

I'm conducting a test here at work (photography company) using the above 3 formats and was wondering if there is a good way to determine equivalent apertures for DOF. Lets say the base is f8 (for the 35mm camera) what would be a similar aperture for 6x6 and 8x10? Feel free to point to some trig functions :)

Thanks

[venchka]

There are several online DOF calculators. Some go up to 4x5. I'm not sure about 8x10.

Since I own 105mm lenses for 35mm, 6x7 & 4x5 I used one of the online calcualtors for all 3 formats. The hyperfocal distance for a given aperture increased as the format increased. Not sure if that's what you're after.

[BradS]

This one is fun to play with...

http://www.dof.pcraft.com/dof.cgi

[David A. Goldfarb]

I like f/calc, which calculates DOF, field of view, hyperfocal distances, and other useful things for a variety of formats. Google should turn it up for you.

[Sizam]

Wow, thanks for all the quick responses.

[jon.oman]

Here is a free DOF calculator that I wrote. It will go up to 8x10 inches, and supports many other formats.

http://gogebic-pc.home.comcast.net/~gogebic-pc/dofcalc/win/

Jon

[aduncanson]

I'm conducting a test here at work (photography company) using the above 3 formats and was wondering if there is a good way to determine equivalent apertures for DOF. Lets say the base is f8 (for the 35mm camera) what would be a similar aperture for 6x6 and 8x10? Feel free to point to some trig functions :)

Thanks

You do not say if you will hold the final print and viewing distance size constant for each format. Those parameters come into play in determining the correct circle of confusion for each.

[Steve M Hostetter]

I always thought that hyperfocal distance verys with focal lenth ...

[venchka]

I always thought that hyperfocal distance verys with focal lenth ...

With a fixed format, yes. With a fixed focal length, hyperfocal distance varies with format.

[Emmanuel BIGLER]

if there is a good way to determine equivalent apertures for DOF.

Sorry but no need for any trig functions ! ;) And, yes, there is a very good & simple model to answer your question !

DOF is in fact not directly related to a certain format; in the classical model of geometrical blur (diffraction being neglected, this is a strong point not to forgotten), everything is contained in the formula of the classical hyperfocal distance H :

H = f^2/(N c)

where f is the focal length, N the f-number as engraved on the lens and c the diameter of the acceptable circle of confusion. If the model is considered as OK, hence everything derives from H under the form of the near (p_1) and far (p_2) distances of acceptable sharpness in object space:

1/p_1 = 1/p + 1/H . (1-f/p)
where p is the distance between the object and the front principal plane of the lens;
1/p_2 = 1/p - 1/H . (1-f/p)

Those formulae are valid even in the close-up range and for magnification ratios above unity, as high as you wish like in a microscope.

Actually there is no need to compare the actual values for p_1 or p_2, in order to get the same DOF you only need to get the same value for H.
No reference is made to any format nor any distinction is made between silver halide-on-gelatin or silicon sensors !

Now if we trust the formula as H = f^2/(N c) we eventually find an interesting paradox : Dof can be made independant from the format under certain operating conditions !

Before examining this paradox, let's start by scaling "c" like "f" i.e. we scale the value of "c" in proportion of the focal length and as a first approach we restrict ourselves to standard lenses for which f = diagonal D of the format. This makes sense, usually a good starting value for "c" is D/1720 where D is the diagonal of the image format. The 1720 factor comes from the angle of 2 minutes of arc supposed to be the limit of angular resolution for a regular human eye looking at a good print, at a distance of 300mm (12") for a contact print in 8x10", or any other enlarged print from any smaller fromat seen from 12"- 300mm with a 8x10" final enlarged print size.
(2 minutes of arc, this is not really the same performance as a jet fighter pilot, credited of 1 minute of arc or even better).

We get something like H = constant . f/N i.e. when comparing lenses of same angular coverage at different formats, the f-number that gives you the same DOF is obtained when f/N is kept constant, I.e. N scales like the focal length. e.g. a standard lens of 80mm in 6x6 stopped down to f/8 yields the same DOF as a 160mm = 2x80 in 4x5 stopped down to N=16 = 2x 8 (hence stop down to f/16)

Now, imagine that, after many hours browsing through this forum you discover that medium and large format lenses can be stopped down to a f-Number much higher than a lens designed for 35 mm photography. Imagine that there would exist a rule-of-thumb obtained by compiling the best f-number of standard lenses of all formats from 35mm to 8x10", a rule stating that the best f-number for all standard focal lengths (focal length equal to the diagonal D of the format) stating:
N_best = best f-number = (standard_f = D (in mm)) / 8 (mm)
This does makes sense, we find N_best about 5.6 for a 50mm in 35mm photography ; N_best about 8-11 in 6x6, N_best about 11-16 in 6x9, N_best about 16--22 in 4x5" ; N_best = 22-32 in 5x7" and N_best = 32-45 in 8x10".

Substituting c=D/1720 and f=D, for standard lenses all formats we get, after
all simplifications are made :

H(standard lens, all formats at best F-number) = 1720 x 8 mm = 15.5 m = 50 feet 3 inches.

Now you are free to use wide-angle and telephotos any formats and recompute everything ;
You are also free not to use your lens at its best f-number ;
You are even 100% free to stop down to f/64 in 35 mm photography like Saint Ansel did.. but He did it in 8x10" only !

[aduncanson]

As always, I appreciate Emmanuel Bigler's insights and contributions. His suggestion that the circle of confusion be taken as equal to negative diagonal/1720 reflects the approach of holding print size and viewing distance constant irrespective of format. Which, to me is how a fair comparison would be done, but your applications could require otherwise, for example if the small format image was to be made for a magazine or brochure and the LF image for a mural. The context of your question will determine if this is a good assumption for you.

My only quibbles with Emmanuel would be to emphasize that the rule of thumb that optimal F number equals negative diagonal/8 will not be universally true and in any event, as he acknowledges, one frequently shoots at other than the optimal F number (particularly in small formats or when trying to limit depth of field as in portraiture), but my biggest problem is that every time I multiply 8mm x 1720 I get 13.76m or 45.14 ft, not 50.25 ft. ;)

Obviously you do not need to take focal length as equal to negative diagonal as Emmanuel did, but could generalize it to some constant of proportionality (k) times the diagonal and, leaving the F number independent, you still find that hyperfocal distance H = 1720*k^2*D/N. So that for constant H: N = 1720*k^2*D/H, meaning that the necessary F number is proportional to the negative diagonal and proportional to the square of the ratio of focal length to negative diagonal.

[Sizam]

I see. Well the final outputs here are going to be around 97x120 or 97x240 inches. But the argument here at work started to go beyond that to sharpness, dynamic range and tonal gradations (we're all measurebators). So the plan is to use an 8x10 camera for the shot but now we kind of want to see the justification for it so I'm setting up a test shot to show differences in detail/sharpness,dynamic range and tonal gradations btw a:

8x10
--trying Kodak E100G, Portra 160NC and Fuji Pro 160S
--and trying a Imicon and a drum scanner
Hasselblad H3D-50
Canon 1DsIII,5DII
Nikon D3

I'm trying to keep DOF and coverage consistent, hence the search for calculations. We'll also look at stitching several images from the 35mm cameras but the Hassy and 8x10 will be one shot only though I hate doing stitched images.

The constants will be a 10' distance from the subject, f8 on the 35mm cameras and either 210 or 480mm on the 8x10 camera.

[ic-racer]

Physically look at your aperture. If it is the same size, DOF will be the same. (Normal lens on both cameras, or 'equivalent proportion to film diagonal' lens length on both cameras).

So, for me, I like about 6.5mm across all formats (normal lens).