The hyperfocal distance

[Doug Kerr]

For a setup with:
• A certain lens focal length
• A certain aperture (actual, or as an f-number)
• A certain adopted circle of confusion diameter limit (COCDL), the criterion we adopt as indicative of "acceptable" blurring from imperfect focus

there is a certain distance such that if we focus the camera at that distance, the far limit of the depth of field will be at infinity. That distance is called the hyperfocal distance for the parameters involved.

A corollary is that, again for focus at the hyperfocal distance, the near limit of the depth of field is exactly half the hyperfocal distance.

A related fact is that, for a certain set of those parameters, we focus the camera at infinity, the near limit of the depth of field will be at almost the hyperfocal distance (less than exactly half by the focal length, in fact).

We sometimes hear that this is the, or another, definition of hyperfocal distance, but it is not. It is just a fact. This is like "the diameter of a circle is the circumference divided by pi". That is a fact, but is not the definition of diameter.​

Especially in landscape photography, it may be advantageous to set the focus of the camera to the hyperfocal distance (based on the other applicable parameters).

That's not always so. If there are important objects nearby, and no "very distant" objects, or we can ignore a little "over our limit" blurring on those (or plan to correct such in post), we may wish to focus at a distance closer than the hyperfocal distance.​

How can we determine the hyperfocal distance without a specialized calculator at hand?

Well, the formula is:

Dh=f^2/Nc

where Dh is the hyperfocal distance, f is the focal length, N is the f-number, and c is the COCDL we adopt, with Hd, f, and c in consistent units.

But if we use f in mm and c in um (micrometers), then Dh will come out in meters (handy).

Common values of c that are adopted are (based on the guideline of 1/1400 of the frame diagonal dimension):

For a full-frame 35-mm format size: 31 um
For a "1.6x" format size: 19 um
For an "8x10" format: 232 um

Thus, if working with a "full-frame 35-mm" format size, for:

f=50 mm
N=2.8 (f/2.8 aperture)
c=31 um (based on the format size)

the hyperfocal distance is about 28.9 m (95 ft). With the camera focused (by focusing scale, presumably) at that distance, focus sharpness should be within the criterion defined by our COCDL for objects at distances from about 14.4 m (47.3 ft) to infinity.

Or, if working with a "1.6X" format size, for:

f=50 mm
N=2.8 (f/2.8 aperture)
c=19 um (based on the format size)

the hyperfocal distance is about 47.0 m (154.3 ft). With the camera focused at that distance, focus sharpness should be within the criterion defined by our COCDL for objects at distances from about 23.5 m (77.1 ft) to infinity.

Best regards,

Doug

 

[Steve Robinson]

But Doug, I was told there would be no math! Thanks for the info on calculating Dh. Aside from various charts or the DOF scales on older lenses I always wondered how to determine Dh. I think I'll find this helpful in the field. If only I could do the math! 8~D

 

[Asher Kelman]

But Doug, I was told there would be no math! Thanks for the info on calculating Dh. Aside from various charts or the DOF scales on older lenses I always wondered how to

If you have an iphone or a Nokia, for sure "there's an app for that!"

Asher

 

[Steve Robinson]

I guess I'll have to join the 21st century and get an iPhone!

 

[Doug Kerr]

Hi, Steve,

But Doug, I was told there would be no math!

Well, sometimes these recruiters lie!

Thanks for the info on calculating Dh. Aside from various charts or the DOF scales on older lenses I always wondered how to determine Dh. I think I'll find this helpful in the field. If only I could do the math! 8~D

Best regards,

Doug

 

[Steve Robinson]

So Doug, if I've done the math right the size of the circle on a 1D series, 1.2x, would be about 25 or 26um?

 

[Doug Kerr]

Hi, Steve,

So Doug, if I've done the math right the size of the circle on a 1D series, 1.2x, would be about 25 or 26um?

Remember that the COCDL is not a property of the camera. It is a value we choose.

But If we wish to use the "rule of thumb" of choosing a COCDL of about 1/1400 the frame diagonal, then yes, for an EOS 1D Mark IV, with sensor dimensions about 1/1.29 those of a full-frame 35-mm camera, that would lead us to choose about 24 um.

Best regards,

Doug

 

[Ken Tanaka]

Doug,
There are more "hyperfocal distance" calculators on the Internet (and now as apps for iPods/iPhones) than there are stars in the sky! DOFMaster is among the "oldest".

In actual daily photographic practice, however, these calcs are generally useless. It's much more practical to understand how zones of focus work than to delve into optical science with an HP calculator. (People generally create poor images long before they focus the lens.)

One of the most concisely informative online sources I've seen for this topic is presented by a fellow named Sean McHugh at Cambridge Colour. It's a brief walk-through with practical tips. (Yes, the page also includes a requisite calculator for the anal retentive crowd).

No math required.

 

[Andrew Stannard]

But If we wish to use the "rule of thumb" of choosing a COCDL of about 1/1400 the frame diagonal

Doug - thanks for this interesting article. Would I be correct in that the 'rule-of-thumb' historically has something to do with acceptable sharpness on an 8x10 print at a 'normal' viewing distance?

It strikes me that a more 'useful' value would be related to the pixel-pitch of the camera - thus allowing us to ensure that we make maximum use of the available pixels in any given camera (if we are looking to print large with good sharpness). Of course this raises questions about airy-discs and the like - does it matter if our airy disk is slightly larger than our pixels?


Regards,

 

[Doug Kerr]

Hi, Andrew,

Doug - thanks for this interesting article. Would I be correct in that the 'rule-of-thumb' historically has something to do with acceptable sharpness on an 8x10 print at a 'normal' viewing distance?

Yes, that was the basic premise (taking into account the angular resolution of the eye).

It strikes me that a more 'useful' value would be related to the pixel-pitch of the camera - thus allowing us to ensure that we make maximum use of the available pixels in any given camera (if we are looking to print large with good sharpness). Of course this raises questions about airy-discs and the like - does it matter if our airy disk is slightly larger than our pixels?

Yes, there is a good argument for doing that. But it has some peculiar side effects. For example, if we consider moving to a camera with the same format size and a smaller pixel pitch, we find that the calculated depth of field performance (for a certain focal length and aperture) will be "worse". That's of course because we now "expect more" of the whole system owing to the smaller pixel pitch. But it can take one aback before springing for the new body!

The important to remember is that this is only an approach to planning how to deploy our available resources within the workings of the laws of optics.

So of course it really depends on what we want to achieve. If we want the optical system to support the potential resolution of the sensor, then a COCDL based on pixel pitch makes sense. If we want to plan our shots to produce a result that will have "negligible" blurring to the viewer, making certain assumptions about the viewing context, and remembering that there is a price for doing better than "adequate", then perhaps the traditional guideline is useful.

Most important of course is to recognize what this result is, and isn't. The old rule about an ideal girlfriend having half one's age plus 10 years may not apply if we are thinking of the heiress to a large fortune.

Best regards,

Doug

 

[Bart_van_der_Wolf]

If we want the optical system to support the potential resolution of the sensor, then a COCDL based on pixel pitch makes sense.

Indeed, why bother with more sensels (and larger storage sizes) anyway if we don't need to enlarge the output size beyond a postcard?

If we want to plan our shots to produce a result that will have "negligible" blurring to the viewer, making certain assumptions about the viewing context, and remembering that there is a price for doing better than "adequate", then perhaps the traditional guideline is useful.

Using a circle of confusion of e.g. 24 micron for a 1D Mark IV would result in 2.83x magnification potential to reach true 300 PPI (5.9 line pairs / mm) resolution, or 79 x 53 millimetres output size. In my book that is (too) small, so I don't agree with the mentioned 'traditional guideline'. It would require something like an 8x10 inch output at 300 PPI (as a minimum) viewed at normal viewing distance to qualitfy as negligible blurring in a usable output size, IMHO of course.

For a quick guideline I prefer the suggestions as done by Paul van Walree in the COC criteria used for his VWDOF tool:
C= V / (1000 x Q x Mp)

Where:
C = COC in millimetres
V = viewing distance in centimetres
Q = quality factor (1 = conventional, 2 = demanding, or 3 = critical)
Mp = Print magnification, i.e. output divided by sensor dimensions

Cheers,
Bart

 

[Doug Kerr]

Hi, Bart,

For a quick guideline I prefer the suggestions as done by Paul van Walree in the COC criteria used for his VWDOF tool:
C= V / (1000 x Q x Mp)

Where:
C = COC in millimetres
V = viewing distance in centimetres
Q = quality factor (1 = conventional, 2 = demanding, or 3 = critical)
Mp = Print magnification, i.e. output divided by sensor dimensions

Interesting.

For a camera with a 36 x 24 mm sensor, and a print size of 12" x 8" (Mp=5.64), viewed at a distance of 24" (V=60.96 cm), and for the "normal" quality factor Q=1), that would suggest a COCDL, C, of about 0.011 mm.

On the print, that would be a diameter of about 0.061 mm.

At specified the viewing distance, this would subtend an angle of exactly 0.1 milliradian. (Not a coincidence - this is inherent in the equation.)

It is generally considered that the angular resolution of the human eye is on the order of 0.33 milliradian.

Thus the circle of contusion on the print, as viewed from the stipulated distance (for this case, with the "normal" quality criterion) would subtend about 1/3 the resolution of the human eye.

That would certainly qualify as "negligible".

If we instead adopted the "critical" quality criterion (Q=3), then the circle of contusion on the print would subtend exactly 1/10 of the commonly-accepted value of the angular resolution of the human eye.

By way of reference, if the camera is an EOS 1Ds Mark III, its pixel pitch is about 0.0064 mm; its reported resolution is about 0.0088 mm.

So in this case, the "critical" quality factor would lead us to adopt a COCDL that was about 0.4 times the reported resolution of the camera.

Best regards,

Doug

 

[Doug Kerr]

It is important to think in terms of the effect on our practice of the choice of various COCDLs. After all, the choice of a COCDL has no effect on the photographic result - it just may influence what "settings" we choose to use for a shot, and that will influence the photographic result.

Now, this thread started out being about the hyperfocal distance.

Note that if we decide to use a more strict COCDL than we might otherwise (perhaps per van Walree's rule of thumb, vs. 1/1400 of the frame diagonal or such), the effect is that the calculated hyperfocal distance will be greater.

Assuming that we decide to focus at this "new" hyperfocal distance, the result is that less blurring will occur for distant objects, but for closer objects there will be greater blurring. We may not want that.

For example, consider this situation:

Format: full-frame 35-mm
Focal length: 50 mm
Aperture: f7/3.5

We will first calculate the hyperfocal distance using a COCDL of 1/1400 the format diagonal (0.031 mm). The hyperfocal distance is 23.09 m.

We set the focus to that distance. Now, for objects at infinity, the diameter of the circle of confusion is 0.031 mm (as we would expect).

At a distance of 15 m, the diameter of the circle of confusion is 0.0167 mm.

At a distance of 10 m, the diameter of the circle of confusion is 0.0406 mm.

Next we will calculate the hyperfocal distance using a COCDL of 0.01 mm. The hyperfocal distance is 71.48 m.

We set the focus to that distance. Now, for objects at infinity, the diameter of the circle of confusion is 0.01 mm (again as we would expect).

At a distance of 15 m, the diameter of the circle of confusion is now 0.0377 mm.

At a distance of 10 m, the diameter of the circle of confusion is 0.0615 mm.

Best regards,

Doug

 

[Bart_van_der_Wolf]

Hi, Bart,



Interesting.

For a camera with a 36 x 24 mm sensor, and a print size of 12" x 8" (Mp=5.64), viewed at a distance of 24" (V=60.96 cm), and for the "normal" quality factor Q=1), that would suggest a COCDL, C, of about 0.011 mm.

On the print, that would be a diameter of about 0.061 mm.

At specified the viewing distance, this would subtend an angle of exactly 0.1 milliradian. (Not a coincidence - this is inherent in the equation.)

Indeed, and that's what I like about the simple formula. The C criterion scales with viewing distance and output magnification, and is flexible enough to accommodate personal preference for quality. Another factor is that if a print looks good at normal reading distance, say 10-12 inches in well lit viewing conditions, then it can be enlarged as much as needed, as long as the viewing distance scales proportionally.

It is generally considered that the angular resolution of the human eye is on the order of 0.33 milliradian.

Thus the circle of contusion on the print, as viewed from the stipulated distance (for this case, with the "normal" quality criterion) would subtend about 1/3 the resolution of the human eye.

That would certainly qualify as "negligible".

At the viewing distance you used for the example, yes. Another thing to note is that the 'traditional' quality (Q=1) was based on film, which has a higher intrisic resolution than sensors with less than approx. 16 megapixels, especially when using large format contact prints or high resolution scans of low ISO film.

If we instead adopted the "critical" quality criterion (Q=3), then the circle of contusion on the print would subtend exactly 1/10 of the commonly-accepted value of the angular resolution of the human eye.

By way of reference, if the camera is an EOS 1Ds Mark III, its pixel pitch is about 0.0064 mm; its reported resolution is about 0.0088 mm.

Which comes close to the 1.5x sensel pitch rule of thumb I've advocated for a long time for high quality enlarged output. For small output sizes and downsampling, things are much less critical or to put it in another way; quality can/should be very high given modern sensors.

Cheers,
Bart