Preamble
I prepared the following article some time ago, not knowing if it would go on my blog or be published elsewhere. I tentatively submitted it to an online magazine but heard nothing back. I am sure it needs work, so treat it as a draft!
The audience is likely the photographer who is not quite a beginner but not so expert as to have figured all this out for themselves. I hope this structuralist approach can clarify some oft-misunderstood terms and concepts.
Nine-Dimensional Photography
How many dimensions does a photograph have? Seems like a pretty simple question. And the simple answer would be two: width and height. The paper it's printed on (if indeed it
is printed... in this day and age that is not a given) also has a negligible depth, but the photo itself has two significant dimensions. This much is a commonplace.
The photograph is the end result of a photographic
process. How many dimensions does this process have? By the end of this article we will be able to answer this question. And the answer is: Nine!
Have you ever wondered why photography is so challenging... enough to keep generations enthralled with the science and art of taking pictures? It's because the photographer faces the complex and subtle task of controlling a nine-dimensional process in order to render a two-dimensional result. Read on and I'll explain.
Framing An Image
What do you do when you take a picture? You point a camera at your subject and look through the viewfinder (or look at an LCD screen... same thing). The important thing is, you choose where to point. Changing your position or direction changes your
perspective on the subject. Perspective is basically a vector, which we can represent as the distance from the photographer to the subject,
z[1], and the angle of view, theta.
(Read notations like
z[1] as
z sub 1, that is, the "1" should be a subscript. Unfortunately I do not think that markup is supported in BBcode.)
Using a lens of a different focal length gives you a different
field of view on your subject. (Twisting a zoom lens does the same thing.) Field of view is what angular slice of the subject we can see, so that's appropriately
delta theta. This defines an arc from
theta[1] to
theta[2], centred on
theta (assuming you are focusing in the centre of the frame).
Turn the camera ninety degrees and you have a portrait; keep it as it is and you have landscape
orientation. You might also be able to change your
aspect ratio, the ratio of width to height, either in camera or by choosing a different camera format in the first place. Ditto for the absolute number of pixels or inches or parsecs the image will have on a side. That's the
image size.
Orientation, aspect ratio and image size all boil down to
width and
height. I'll call these the
x and
y dimensions, since those are the letters my physics professor always used.
These four dimensions mentioned so far define what falls within the frame of the picture. The choice of framing is one of the most important a photographer can make.
Note that so far we haven't discussed anything that's reliant on technology. If you form a rectangle with your hands and stare through it, the problem is the same.
Time and Spatial Parameters
The next four photographic parameters require a camera, though any camera will do. Two are time-based, two are spatial.
The first temporal parameter is the
shutter actuation. When you press the shutter you start the time slice that defines the picture. This I'll represent by
t[1]. The second temporal parameter is
shutter speed. The faster the shutter speed, the more effectively we can freeze subject motion. This parameter,
delta t, determines the end of the photo time slice.
t[1] + delta t = t[2]. At
t[2] the shutter closes and our photo is done.
Blink and you have the process in reverse. You decide when to start blinking (
t[1]) and how long to keep your eyelids down (
delta t). The length of time you
cannot see is equivalent to the length of time the camera
does see... but now we're entering the realm of metaphysics! To avoid this philosophical abyss, I recommend you do not blink while taking photos.
The next spatial parameter under consideration is the lens
aperture. The larger the aperture the smaller the
depth of field (DOF). What is DOF? It dictates how near objects must be to the
focal distance to be in focus. Oh, it looks like we just sneaked in the other spatial parameter -- you did remember to focus the lens, didn't you?
But we have seen focal distance before -- it is the distance to the subject along the axis of the lens, that is,
z. If you choose to focus on a slightly different point you've chosen a different subject, as far as we're concerned here. So it turns out we've discussed not four new photographic parameters in this section, but only three.
Those last two spatial dimensions are analogous to the temporal domain. The DOF dictates
delta z, the distance around
z that will be in focus, that is, the distance from
z[1] to
z[2]. This is not
quite the same as the case of shutter actuation and shutter speed since
z[1] is slightly
in front of
z and
z[2] is behind it. But that's a technicality we can gloss over for now.
We'd say mathematically that
z[1] < z < z[2] and
delta z = z[2] - z[1].
Sensitivity
There's one last photographic variable and it's purely technological. To understand, it helps to remember that the faster the shutter speed (the smaller
delta t), the less light into the camera. Likewise the smaller the aperture, the less light gets into the camera (the larger
delta z). As a general principle, we want to capture as much light as possible. The more light that's dissipated or distorted on its way through the camera to the substrate that captures the picture, the less true our image.
Put in terms of information theory, the more light the less noise.
Since we rarely have an ideal amount of light, we must trade off image accuracy for noise. We do this using the last photographic parameter, which goes by the annoying name of
ISO. Annoying, because the ISO is an international organisation that is responsible for setting thousands of standards, this being only one. (In fact it's ISO 5800.)
If the photographic substrate is film, ISO measures how sensitive the film is to light. Back in the old days we could refer to this dimension simply as film speed. If the photographic substrate is a bunch of light sensors on a computer chip, however, the term "film speed" makes little sense. I suppose "substrate sensitivity" is the most accurate term, but no-one says that, they say "ISO", as if it means something.
(And since everyone says it, it does mean something. Oh no, now we're into the realm of philosophy of language!)
I'll call this dimension
s, because
sensitivity is the word to emphasise.
Summary
Let me summarise the nine photographic dimensions in a list.
- spatial dimensions:
- frame:
- perspective:
- angle of view: theta
- field of view: delta theta
- depth:
- focal distance: z[1]
- DOF: delta z
- temporal dimensions:
- shutter actuation: t[1]
- shutter speed: delta t
- information dimension:
I find this structuralist approach to photography useful to clarify the complexities of the terminology. Before I worked this out for myself I was forever being confused by sloppy use of terms in the literature and on the net.
Postscript
Before anyone decides to mention dimensions not covered here, I will point out that the geometry I have covered is valid for SLR cameras. Those with front or rear plane controls add more dimensions, since the sensor/film plane is no longer required to be parallel to the lens focal plane. Maybe I will get to that in some other article!