Epson R-D1: depth of field compared with that of 35 mm film cameras

First, I would like to dispel some commonly encountered myths about using lenses on digital cameras and depth of field (DOF). After that, the technical underpinnings of DOF are briefly touched on, and, at the end, a rule of thumb given on how to use the lens distance markings to estimate DOF on the Epson R-D1.

Myth 1: DOF is a lens property and can never change

It is often argued that DOF is dependent solely on the physics of a lens, and, therefore, the DOF of a lens remains unchanged regardless of the camera it is used on.

This misunderstands what DOF is. Yes, DOF is dictated by the focal length of a lens – but not wholly. Sharpness in a photograph gradually tails off in front of and behind the subject on which the lens is focused, so the larger we print a photograph, the more obvious these out-of-focus areas become, and what is sharp on a 6-inch print can look blurred on a 10-inch print.

So, DOF is dependent on both the lens and the final size of the photograph (whether as a print or viewed on screen).

Myth 2: a 35 mm film lens becomes a telephoto lens on a digital camera

A common mistake when estimating the DOF for digital cameras is to multiply the focal length of the lens by the crop factor (i.e. the factor by which 35 mm film is larger than the digital sensor – 1.5 in the case of the Epson R-D1), on the basis that lenses on digital cameras simply behave as if they have longer focal lengths, e.g. a 50 mm lens becomes a 75 mm one.

This is a fundamental error, as it’s physically impossible for the focal length to change – a 50 mm lens is a 50 mm lens regardless of the camera it’s on. The term ‘crop factor’ gives the clue.

Let’s imagine we have a 35 mm film camera (e.g. a Leica M7), an Epson R-D1 and a 50 mm lens set to f/8, and take a photograph of the same subject from the same position. If we print the two photographs at the same scale, the images will be identical in every way (including DOF), except that the digital image is smaller, i.e. the central two-thirds (i.e. 1/1.5) of the film image. In other words, the only difference is the field of view: owing to the crop factor, the field of view of our 50 mm lens is equivalent to 75 mm on the R-D1 (1.5 × 50 mm).

If we enlarge the R-D1 photograph to the same size as the film print, the perceived DOF in the image becomes shallower, of course, since the out-of-focus areas are magnified, appearing less sharp. Now, let us take another photograph of the same scene as before using our 35 mm film camera, but with a 75 mm lens at f/8, and make a print the same size as our enlarged R-D1 print. They look identical, as the field of view is now the same, and, according to the myth, the DOF in each should also match – but it doesn’t: the digital image has a visibly greater DOF!

So, this erroneous assumption – that the DOF of a lens on a digital camera is equivalent to a longer focal length lens – will give shallower DOFs and longer hyperfocal distances than are actually the case.

Myth 3: a digital camera has greater depth of field than a 35 mm film camera

Well, yes and no – or, rather, no and yes …!

In the scenario described above for myth 2, assuming you don’t move, the photographs captured with the R-D1 and on 35 mm film using the same lens will, of course, differ in their fields of view, owing to the crop factor of the former. As nothing material has changed, the DOF is the same in both photographs, provided they are printed or viewed at the same magnification, as explained above.

But if you want the view in the R-D1 image to be identical to that captured by the 35 mm film camera, then you either have to move the R-D1 further from the subject or use a wider lens on the R-D1 – in both cases the DOF will increase. A digital camera thus does have greater DOF than a 35 mm film camera – but only if the angles of view in both are identical. As a rule of thumb, for identical fields of view:

digital DOF = 35 mm DOF × the crop factor

So, for example, the R-D1 will have about 50% more DOF than 35 mm film.

Digital DOF in detail – what affects it

Some background: the circle of confusion (CoC)

A lens is only sharp at one distance: any nearer or further results in tiny out-of-focus circles on a photograph, called circles of confusion (CoCs): the larger your printed photo, the more you’re enlarging these circles, and the more blurred the out-of-focus areas will appear. So, the larger the print, the smaller the CoC needs to be to keep the photo looking sharp. It is the CoC that is affected by the crop factor of a digital camera.

Let’s now examine the difference between the apparent DOF in our two example photographs described above taken with a 35 mm film camera and the Epson R-D1 using a 50 mm lens from the same position and at the same aperture. If we print the two images at the same size (i.e. enlarging the R-D1 print by the exact crop factor, 1.53), the apparent DOF of the digital print will be shallower, as explained.

So, how do we make the two images appear equally sharp? The solution is reduce the CoC in R-D1 images by the crop factor (i.e. 1/1.53 = 65%).

The relationship between CoC and aperture

So, if an R-D1 print is to match the DOF of a print of the same size from a 35 mm film camera (owing to the crop factor), we now know that we need to have a greater DOF, and hence must use a smaller aperture (i.e. a larger f number). But what f number should we use to achieve this DOF?

The relationship between aperture and DOF is dependent on the CoC. The choice of the upper limit for the CoC for a particular format can vary quite a bit – values for 35 mm film are typically in the range 0.025–0.050 mm for prints up to A4 in size. A widely used value is 0.030 mm. Applying the R-D1 crop factor to this CoC gives 65% × 0.030 mm = 0.020 mm. There are a number of DOF calculators on the web into which you can plug this CoC to create tables for your lenses (e.g. johnhendry.com).

Referring to DOF tables is not very practicable when you’re out taking photos! Luckily, the relationship between the DOF for 35 mm film and the R-D1 can be summarised conveniently:

The DOF and hyperfocal distance for a digital camera with an APS-sized sensor are approximated by the next widest whole stop on the DOF scale of a lens.

For example, if you set the aperture to f/8, the DOF is the distance between the f/5.6 marks; and to set the lens at the hyperfocal distance for f/8, the infinity symbol on the distance scale should be aligned with the f/5.6 mark.

The following DOF tables were derived using the online calculator at johnhendry.com:

Download DOF tables for the R-D1 (Word file, 50 kb)

That’s not the whole story ...

Well, I went out and took some photos using the DOF scale on my lens and the aperture closed up one stop to compensate for the shallower DOF, as I’ve described above, and printed some A4-sized photographs. They looked awful – the DOF was shallower than expected, and horizons were out of focus in photos taken with the lens set to the hyperfocal distance. What had gone wrong?

The answer is nothing. It’s down to the ~0.030 mm CoC standard for 35 mm film, which we used above. This CoC value dates from well before World War II, and is based on lens and film resolutions of that time (both of which have improved vastly). Like the inefficient QWERTY keyboard, the 0.030 mm CoC DOF scale has become a worldwide standard simply through widespread use, and is still used by all lens manufacturers (Zeiss: Camera Lens News, No. 1, 1997), partly because 90% of all photographic prints are still 4 × 6 in., for which the 0.030 mm CoC is sufficient.

The solution

If you’re going to be printing photos at A4 (10 × 8 in.) or larger, a 35 mm film CoC of 0.0015 mm is a sensible choice (i.e. half the standard CoC). Translating this to a crop-factor digital camera like the Epson R-D1, the CoC becomes 0.0009 mm, and when using the DOF scale on a lens:

select an aperture mark on the lens DOF scale that is two stops wider than the actual aperture

For example, when setting the hyperfocal distance for an aperture of f/8, align the infinity symbol with the f/4 mark.