I’m going outside of the normal dogma today to focus on a field that I am a bit of a hobbyist in: I’m sort of a photography nerd, primarily interested in the fascinating balance-of-compromises that are optics, so I’m in my domain a bit with this piece on photography and depth of field. There are many great articles on depth of field out there, but in this I’m primarily focused on the depth of field issue of smartphones, and the often futile quest for bokeh.
Bokeh is the photography effect where background lights and details are diffuse and out of focus, as seen in these Flickr photos. Often it’s contrasted against a sharply focused foreground subject, providing an aesthetically pleasing, non-distracting backdrop.
To photographers this has always been called a shallow depth of field: with a large aperture and a longer focal length it is the normal technique to isolate a subject from the background, and is the mainstay of photography. The term “bokeh” has taken root among many courtesy of a late-90s photography how-to magazine article, so you’ll come across it frequently. Some purists hold it to only talk specifically about blurred light patterns, while in general parlance it just means “out of focus background”.
The best known mechanism to control the depth of field on a given piece of imaging hardware is the aperture (aka the f-stops) and distance to subject (the closer to the lens, the shorter the depth of field), each new device seemingly offering a wider aperture to enhance the options.
The Nexus 6p has an f/2 capable camera. The iPhone 6S offers f/2.2 29mm equivalent, and the new iPhone 7 pushes new boundaries with an f/1.8 lens (28mm equivalent, with a second 56mm equivalent on the 7+).
The ultimate portrait lens in the 35mm world is an 85mm f/1.4 lens.
On a traditional SLR-type camera, f/1.8 is a very wide aperture (aside – a “small” aperture has a larger number, e.g. f/22, while a wide or “large” aperture has a smaller number, such as f/1.8). If the scene isn’t too bright, or you have some neutral filters handy, it is gravy for a dish full of bokeh.
By now you’ve probably learned that it’s really hard to achieve shallow depths of field with your smartphone unless the subject is unreasonably close to the device (e.g. fish eye distortion of someone’s face), despite those seemingly wide apertures: Most everything is always in focus, so while there isn’t the once endemic problem of the slightly out of focus shots (being sort of close in focus is often good enough), it makes the cool effects tough to achieve. Instead blurry smartphone photography is primarily caused by too low of a shutter speed coupled with moving subjects or a shaky photographer.
But why is that? Why does your f/2 smartphone yield such massive depths of field, making bokeh so difficult? Why isn’t f/2 = f/2? If you’re coming from the SLR world and install some great manual control photography app on your smartphone, you likely found yourself disappointed that your f/2 smartphone isn’t delivering what you’re accustomed to elsewhere.
Because of the f in f/2. While it is treated like a abstract value holder, it literally means “focal length / 2”.
And the focal length on smartphones is why you are separated from your bokeh dreams. While my Nexus 6p has a 28mm equivalent (compared to the 35mm camera benchmark) focal length, it’s actually a 4.67mm focal length. Courtesy of the physics of depth of field, its focal length means an f/2 on this device is equivalent to about an f/10 DoF on a 35mm lens when the subject is at the same distance from the lens. The iPhone 6 has a focal length of 4.15mm, while the iPhone 7 offers up lenses of apparently 3.99mm and 7.7mm.
This is easy enough to prove. Here’s an f/2 photo on my Nexus 6p. The subject is about 30cm from the lens.
Now here’s approximately the same scene, at the same distance, with a zoom lens set at ~28mm on a Canon T2i (approximating the zoom level of the Nexus 6p fixed focal length), the aperture set to f/10.
While each device has its own post-processing (the T2i in this case is set to neutral, while the 6p, like most smartphones, is fairly heavy handed with contrast and saturation), if anything the SLR features as much or more blurring, despite a significantly smaller aperture.
This is the impact of the focal length on the depth of field. Here the same subject shot from the same distance, the zoom lens set to 55mm, the aperture still at f/10. The depth of field collapses further (it isn’t just a crop of the above picture, but instead the DoF shrinks further).
And for comparison here it is at f/5.6-
So why is this?
First let’s talk about something called the circle of confusion (CoC) to get it out of the way as a parameter of the calculator following. In this discussion the CoC is the amount that a “focused” photon can stray outside of the idealized target before it leads to blur for a given sensor. There are many, many tables of static CoC values, and a lot are very subjective measures (e.g. “if you print this as an 8×10 photo and view it from 3 feet away, what amount of blur is indiscernible). For my calculations I am calculating the CoC as 2 x the pixel stride of the target sensor (via the nyquist theory), but you can use a table or your own mix of crazy as the CoC. I leave that open.
The Nexus 6p has a sensor that is 6.324mm wide, containing 4080 pixels per line (not all pixels are active, so this was measured via the SDK). So a pixel stride of 0.00152794mm, and doubling that we get 0.0030558. That is the CoC I’m using for the Nexus 6p.
We know the focal length (4.67mm), and we know the desired CoC (0.0030558), so let’s calculate something called the hyperfocal distance.
The hyperfocal distance is the focus distance where everything to infinity, and to approximately 1/2 the focus distance, will also be in effectively perfect focus for a given aperture. It is a very important number when calculating DoF, and the further the hyperfocal distance, the shallower the DoF will be for closer subjects.
|Focal length (mm)|
|Hyperfocal Distance (mm)|
Focusing beyond the hyperfocal distance does nothing to improve distant focus for this CoC, but instead simply unfocuses closer objects. Once again I have to note that CoC is not a fixed constant, and if you had a sensor with 4x the pixels, the CoC by my method would halve and the focus would need to be more precise. Others would argue, with good reason, that the CoC should be percentage of the total span such that the same effect amount is seen across devices, while my measure is achieving technical perfection for a given device.
The hyperfocal distance is the basis of the calculations that allow us to calculate the near and far of the depth of field. Let’s calculate the DoF for a given focus distance. Note that these values are in millimeters, as most things are in the photography world (so instead of 10 feet, enter 3048).
|Subject distance (mm)|
|Near Depth of Field (mm)|
|Far Depth of Field (mm)|
Beyond the near and far depth of field, of course the defocus increases as a multiple of the distance.
If you entered a focal length of 4.67, a CoC of 0.0031, an f-setting of 2.0, and a subject distance of 300 (30cm — the distance in the above picture), the near and far depth of field would calculate to about 276.454 mm to 327.931 mm, meaning everything within that distance from the camera should be focused perfectly on the device, and the further out of those ranges the more defocus is evident. Altering those values for the SLR, with a focal length of 28, a CoC of 0.0086 (the SLR has a much larger sensor), and an f-setting of 10.0, with the same subject distance of 300, yields a smaller depth of field of 290mm to 310mm. A significantly smaller aperture, yet an increased amount of bokeh at a given distance.
All f-stops are not created equal, which is why Apple is artificially simulating bokeh on their newest device (as have other vendors). Your f/1.8 smartphone might provide light advantages, but don’t expect the traditional depth of field flexibility. On the upside, this is the reason why almost all smartphone photography is sharp and in focus.
I love using my smartphone to take photos (or stabilized videos): It is the camera that is always with me, and an enormous percentage of the shots turn out great. When I’m looking for defocus effects I reach for the SLR, however.