OSU College of Engineering
Introduction to Engineering
Camera Lab #3
Pre-Lab Assignment
Purpose
The purpose of this assignment is to have you read the attached material to get some understanding about optics and related issues prior to performing the Camera Lab 3 procedures.
What You Have To Do
1. Read the material for Camera Lab 3. If you like, you can even visit a library to find out more about these things.
2. Write a summary of the material, taking about a page. It would be nice if this was word-processed, but hand-written submissions are acceptable.
3. Submit the summary at the start of your Camera Lab 3
Introduction to Engineering
Camera Lab 3
Background Reading
The Camera as an Information Appliance
Design Issues – Optics
Introduction
The purpose of these notes is to present some of the basic theoretical points that underlie what we will be covering in Lab 3. In the lab session itself, we will be more concerned with the engineering design implications of this theory and how we can reverse engineer the camera, than with a lot of theory. This set of notes will therefore address mainly the theory behind what’s going on.
You don’t need to know a great deal of theory to understand this lab. However, you should have an understanding of the general idea of what the background theory is about, i.e. what it means and what it is used for, to help you understand this lab.
Choosing a Camera
When selecting a camera to use, you need to consider what it will be used for. Will you be taking very close-range photographs? Will it be used for photographing fast-moving objects? Will there be enough light or will we need to use a flash (or faster film)?
Professional photographers generally choose a number of camera bodies (mostly for specific film formats or other features), then select lenses and film to suit their needs. But when we are designing a general-purpose camera, like the single-use camera we are studying, we cannot be so flexible. We need to be able to have a camera that can take most of the photographs that most people want to take, with a minimum of fuss and hassle.
In the last 15 years or so, there has been developed and sold a range of pretty much automatic cameras. These tended to cost over $ 100 and to require some thought as to film, zoom settings, use of a flash, etc. But most have automatic focusing, flash use, film handling and some other settings. If we want to manufacture a general-purpose series of cameras that cover most people’s needs, we will have to skip a lot of the complexity of these cameras and focus on what most people’s photographs have to achieve. We want to avoid the issues of focusing, adjusting the aperture settings, deciding when to use the flash, the film speed required and the like.
Most people take photographs of subjects that are from about 2 meters away from the camera (e.g. the child drinking), up to as far away as one can see (termed infinity, which tends to mean more than about 20 meters). See the images on the next page, copied from a Kodak brochure. So we need to design a camera that can cover that range. We need a camera with a fairly wide field of view, because we need to fit in group shots (e.g. the little ballerinas’ behinds) and panoramic landscapes (like the forest). We need a camera that can work with a fairly quick shutter speed (to avoid shaking effects if held for very long during an exposure), and need flash only for shots in poor light (we don’t want the flash to be needed for landscapes on fairly bright days). All these needs place a lot of constraints on the optics of the camera we are designing.
Clearly we need a camera that can do a lot with a little, so we will have to have some compromises in the design. But we can do a lot with what we have.
The lab we will undertake is designed to let you see a little of the optics considerations that went into the design of these cameras. It doesn’t cover everything, but it should give you a basic understanding of how cameras work optically, and how you can apply that knowledge 
to some issues in camera design.
The first important issue is, of course, the lens. The power that a lens has to focus light is expressed in unit called dioptres. The larger the number of dioptres a lens has, the tighter it focuses light that comes into it. By tighter, we mean how close to the lens the image forms. For example, most common glasses that people wear have powers between about 2 and 10 dioptres. A 20 dioptre lens is starting to look like the bottom of the proverbial Coke bottle (which used to be made of very thick glass). It turns out that the focal length and the power in dioptres are related; each is the inverse of the other. So a 10 dioptre lens has a focal length of 0·1 meter; a 1 dioptre lens has a focal length of 1 meter. The classical 50 mm focal length camera lens is a 20 dioptre lens.
The focal length is an important characteristic of the lens, so we will examine it first.
Focal Length
In one view, the focal length is the distance away from the lens where a bundle of originally parallel rays intersect (come into focus). In reality, it is never so simple. Most complex cameras (not the Kodak Max Flash though) have lens systems made up of many individual lenses. Even the eye, a well-established camera-type system, is complicated by the fact that the refractive index of the material on one side of the lens system (it has two basic components) differs from that on the other side of the lens system.
One good way of thinking about focal length, especially in a camera designed for measurement work (a metric camera), is that the focal length is the distance from the lens system to a location from which you can see exactly what the camera sees. This means that we can treat the lens system as though it were a pinhole in a pinhole camera, and that pinhole would be the lens node. This is an ideal definition, but most real cameras come fairly close to this. If we assume that there is no distortion in either the lens system or the camera (never really true), then the image will meet this ideal about the focal length. We call this ‘ideal focal length’ the principal distance of the lens system, and it tends to get the symbol, ƒ.
If we think about the negative of the image, it and the lens system back node (that single point where all the light rays pass through the lens system on their way to the focal plane (film) form a duplicate of the relationship between the lens system front node and the object space being observed (photographed), with the only difference being one of scale. That is to say, the angle that a ray of light makes with the camera’s optical axis as it enters the lens system is the same as the angle it makes when it leaves the lens system on its way to the film. (In reality we get some distortion, but the relationship is generally pretty good.)
So, if we make a contact positive print of the film negative, which is at the same scale and size as the negative, we have a situation where we can use similar triangles to investigate things in the image and also the camera.
The determination of the focal length of the camera lens is important. The focal length is the most basic parameter of the camera’s design. It affects almost every other aspect of the camera design, so we have to know it. The lab exercise will address this aspect.
Depth of Field
Another of the critical issues in camera design and use is the depth of field. This is the range of distances (of objects) from the camera where the image is in focus, i.e. the image is sharp. This depends upon two main factors: the focal length of the lens and the size of the aperture. In general, the smaller the aperture, the longer the depth of field; and the larger the aperture, the shorter the depth of field.
Why is this the case? Without going into the theory too far, consider a lens system with a large aperture, and then the same system with a small aperture. When light from an object enters the large aperture, the light coming from the edges of the lens is coming in at a sharper angle and has a smaller range in which to focus. With a smaller aperture, the light never comes in from that far out, so has a larger range of focal positions. See the diagram below.
The range of acceptable focus is determined by how large a blur appears on the film. This blur is often termed the circle of confusion. We can translate this directly back into how wide a range of objects, in terms of distance from the camera, we can focus on the film. So a smaller aperture makes the camera more versatile as far as the depth of field is concerned.
The images below show the affect of different aperture sizes on a series of objects at different distances, photographed with two different aperture settings.
Photo taken with a very large aperture. Notice how the near and far objects are out of focus (a bit blurred), while the central figure is in sharp focus. The side view shows the depth of field.
Photo taken with a very small aperture. Notice how there is a very large depth of field, and that objects throughout the picture are in sharp focus. The side view shows the depth of field.
For our general purpose camera design, we should use as small an aperture as possible, to get the largest depth of field. But a small aperture means that we need either faster film or a longer exposure time. Faster film tends to appear a little ‘grainier’, while a slower exposure time leads to more chance of shaking the camera and blurring the image that way. Clearly we need to compromise here, but how can we decide what aperture to set for the camera to cover all its potential uses?
It turns out that there is a formula to cover the question of the relationship between focal length, aperture setting and depth of field. (Are you surprised?) We can compute the closest and furthest distance that will be in focus for a give focal length and aperture setting. We simply have to decide what level of poor focus we will accept. This ‘level of poor focus’ is determined by the circle of confusion. If we accept a certain sized circle of confusion, we can determine either the closest and furthest distances or, more useful in this case, given that we want certain distances and have some constraints as to the focal length of the lens (the camera cannot be too large), the size of the aperture we want to meet the constraints.
We can determine the depth of field by inspection of images. Basically, at what distances do objects appear out of focus. However, this is rather imprecise and it doesn’t help us in designing the camera.
We know that a lot of photographs are taken of objects at infinity, such as those shots of the mountains. So this must be the upper limit of the depth of field. We can also expect to take photographs of objects at two to three meters from the camera, especially when indoor shots with flash are contemplated. So we can set either of these distances (2 or 3 meters) as the minimum depth of field. We must decide about the size of the circle of confusion that we are prepared to accept, and we can then compute the size of the aperture we need.
We can also compute the setting for the lens itself, given that we know its focal length, so that the depth of field is correct. This affects the placement of the lens with respect to the plane of the film, and is a matter of the finer details of the design. We have to position the lens so that it will focus the correct distance perfectly and the full range of the depth of field acceptably, and this is based on the lens equations that affect the sharpness of the image.
Some Formulae
Looking at the diagram on the next page, if we have a lens that is imaging an object (which is in the ‘object plane,’ OP) onto the ‘image plane’, IP, when everything is in perfect focus, there will be a relationship between the distance from the front node of the lens (H) to the OP, termed s, and the distance from the back node of the lens (H') to the IP, termed s'. The relationship is called the lens equation:
Now, for a given s, there are two other distances to objects where the circle of confusion reaches a specific size, which we can call u. One of these will be nearer the camera, and termed sn, while the other will be further from the camera, and termed sf.
If we have the aperture set to a particular size, generally given as a diameter, d, this will allow us to determine the ratio of the focal length to the aperture, , which is also called the FNumber or F-Stop setting. Often this will get the letter k.
With some geometrical and algebraic shuffling and legerdemain, we can produce a pair of equations that will give us the near and far distances of the depth of field. These are: