My Pinhole Camera
 
Purpose:
A pinhole camera is not just kids stuff. The pinhole camera is a simple system that demonstrates the nature of light and images. The working principles of the simple pinhole camera can be expanded to explain the working of a camera and human eye.
 
 
Table of contents

 
Workings of a pinhole camera
A pinhole camera projects the light from a viewed image onto the screen inside the camera; in Figure one the object is light bulb. Every point on the viewed object emits light rays in every direction, which allow us to see the object with our eyes. However, the pinhole of the camera only allows those light rays into the chamber that pass straight through and project onto the screen, as shown in Figure 1. Figure 1 also illustrates that the result of all entering rays will produce an upside down image. The variables shown in Figure 1 will be used to mathematically describe the projection in the next section. The screen in a camera would be film that captures the image. On the other hand, the screen can also be translucent, in which case projection can be seen with your eyes from the opposite screen side. The screen has to be in a dark chamber, to allow viewing of the dim projected image (idea from Andrea Mantler).

Figure 1 – Workings of a pinhole camera 


 
A practical pinhole camera
The pinhole camera I made is intended to view the projection with your eyes, rather than a camera to take pictures. The camera is made of two chambers (like in Figure 1). The pinhole is on the first chamber opposite of which is the translucent projection screen. Viewers look into the second chamber on the side opposite the pinhole to see the image that is captured on the translucent screen. In my version of the camera, the second chamber with the screen can be slid toward and away from the pinhole (see Figure 2); this sliding is like that of a pirate's compacting telescope. This demonstrates the influence of different focal lengths (distance from pinhole to screen) on the image projected on the screen. In addition, the screen chamber can be used to experiment with the effects of different pinhole sizes on the image (see Figure 4). The pinhole used for my camera in chamber one is bigger than would be good for a photo-camera in order intensify the projected image for the human eye. 
 


Figure 2 – Sliding screen changes focal length

Figure 3 - The 2 chamber separated. The screen of the second chamber is shown. The second chamber fits inside the first.

Figure 4 – Changing pinhole size. The are four different size pinholes. The screen is on the opposite side of the holes. The room should be dark and a flashlight used to project the image when using the camera like this.

The best projections are achieved with a bright light source. A flashlight is used to project an image into the camera. Shining the flashlight through a colored transparence creates a color image. Viewing the world with the camera at noon (brightest out side) gives the clearest contrast between big objects, such as a patch of green grass next to black pavement. 


 
Mathematical Evaluation of projected image
This section evaluates the parameters, such as pinhole size and focal length, that influence the projected image. All variables in the equations below are illustrated in Figure 1. This information is summarized from an excellent scientific report from Max Young and the "Pinhole Camera Design Center" web-site that has a calculator for the listed equations. In addition, the bolded numbers give a perspective to relative sizes, such as the pinhole radius (s) and focal length (f).

Image resolution (listed first to define aprox. sizes for f and s.
  

Image resolution is most enhanced by a small pinhole (at the expense of image intensity). In addition, the focal length is optimal at the given equation. The given focal length optimizes the effects of near-field and far-field diffraction (see Max Young’s discussion). An average pinhole is 0.5 mm, which makes the optimal focal length 11.3 cm (average wavelength 550 nm). My camera demonstrates that exaggerating the pinhole diameter blurs the image. Image sharpness changes corresponding to focal length changes could not be observed with my camera. In addition, an image can be enlarged and still keep that same sharpness (at the cost of image intensity.)


Image Size
  

Object size and image size are related by the similar triangles created by the pinhole seen in Figure 1. Magnifying the image is demonstrated in my camera by sliding the screen toward and away from the pinhole, which decreases and increases the image respectively. Increasing the image size is at the cost of decreasing the image intensity. In addition, the image can be magnifyied by moving the image infront of the pinhole. This has only noticeable change when the viewed object is closer than a meter.
Image Intensity
  
Overall, Intensity decreases at the given proportion as do gravity and other forces in other situations. For photographers, the intensity is measured by the f-stop, which determines the exposure time for film. Sliding the screen in my camera demonstrates some change in intensity.
Field of view
  

 

Field of view is proportional to the screen space (max edge of image) and focal length as shown (beta in figure 1). An average field of view (fov) is 40 degrees (focal length 10 cm and screen 20 mm). The edge of the image is reached when  the image decreases to minimal amounts (as compared to the center). The intensity from the center of the images decreases proportional to (cos(theta))^4. This comes from the angle of the object with the pinhole and the angle at which light strikes the screen. The field of view can be improved by using a curved screen, which allows the light ray a more perpendicular intersection with the screen. This comes at a cost of distorting the image.
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dorian miller, 8/29/2000