Pinhole Cameras and Practical Camera

This instructable includes:

1. The design of a small pinhole camera
2. The design of a large pinhole camera
3. The design of a convex lens practical camera
4. Discussion and mathematical analysis of results

1. Cardboard
2. Tracing paper
3. Duct tape
4. Black paint and brush to apply
5. Convex lens

Two pinhole cameras were created, one larger than the other. Both models follow the same design process and are built with a cardboard box. A hole was punched at the center of one end of the box. The other end was cut out, such that a smaller, open-ended cardboard rectangular tube could be slid into the box.

The sliding mechanism allowed the focal length of the camera to be adjusted. One side of the rectangle tube was then taped over with tracing paper, so that the image may be projected onto a surface. The interior of the cameras were painted black as well to minimize any unwanted, internal diffraction of light.

Resulting images obtained from the pinhole cameras have been flipped right side up for readability. The above images were produced for the small pinhole model.

The large pinhole camera was cut from a larger box and constructed with the same steps as above. The image taken from the large pinhole camera are attached above.

The above images obtained from the pinhole cameras were the images that had the sharpest focus and obtained experimentally by adjusting the sliding inner rectangular tube. It was found that increasing the focal length resulted in larger but darker images (field of view narrowing), while decreasing the focal length made the image smaller but brighter.

Sharpness of the image depended on the pinhole size (which was adjusted with a piece of tape over the pinhole). When the pinhole was too large, geometric blur occurred and resulted in blurring. Likewise, when the pinhole was too small, blurring still occurred due to heightened diffraction blur.

The design of the practical camera is simply that of a lens replacing the small pinhole model as discussed in the previous section. By creating a hole and fitting a convex lens through the hole (taking extra care to fill the gaps with tape so as to avoid leaking in light), the lens effectively converges light rays to minimize geometric blur from the pinhole model. With a pinhole, multiple rays of light from a single object could still enter at slightly different angles, causing blurriness. A convex lens actively converges these rays of light to minimize the blur. The resulting images are thus a lot clearer than the previous pinhole models.

For the calculation of the optimal pinhole size, it was found that 0.4mm was the optimal pinhole diameter for a focal length of 18cm for the small pinhole camera. For the large pinhole camera, a pinhole that was 0.7mm in diameter was most suitable for a camera with a 46cm focal length. These were the measurements applied experimentally to obtain the above results.

Explain what you noticed about the large camera versus the small camera. What size pinhole works best for the large camera? What size pinhole works best for the small camera?

Given the general formula for the diameter of the aperture for a pinhole camera and applying it to the smaller versus larger model, it can be seen that as focal length increases, so does the diameter for the optimal pinhole. A larger camera will typically have a longer focal length and a smaller camera will have a shorter focal length. This is proven in the image below, where the focal lengths of both cameras are indicated by the black arrows.

As such, a larger pinhole will work best for a larger camera, and a smaller pinhole should work best for a smaller camera. In practice, this was found to be the case. When the same size pinholes were made for both cameras, the images in the smaller camera were blurrier and the pinhole of the smaller camera had to be partially covered or minimized by tape in order to sharpen the image. The optimal focal lengths for the pinhole size in the following image were found by experimentally adjusting the cameras and marking where that point for optimality was.

The larger camera was also able to produce clearer images than the smaller camera. This could be because the optimal pinhole size of the smaller camera was simply too small and more difficult to create than that of the large camera.

Explain why the inside of the camera should be black (apart from the opening and the screen).

A white or reflective interior would cause light to bounce around, making the image appear faint, blurry, or washed out. Light entering the camera from the scene should not bounce around the inside of the camera, but rather project directly onto the tracing paper screen. Otherwise the image may become less distinct, with poor edge definition and reduced contrast.

Explain what a camera does. Derive a mathematical relationship between planar subject matter and what is projected onto the camera image plane. For simplicity you may assume you're living in a 2-dimensional world and the image and subject matter are both 1-dimensional. Draw simple diagrams that show you understand what a camera is and what it does.

A camera is a device that captures an image by projecting a scene in the world frame onto an image plane. By simplifying the dimensions, the subject and the image are both lines, and the camera exists to project the subject line onto the image line. Assuming that the camera adopts a pinhole model the following calculations above could be made.

The final equation for the position on the image plane (in terms of focal length, the distance of the real-world object from the image plane and the position of the object in the real world with respect to the 2D x-y frame centered at the pinhole) is seen above. Additionally, the y-coordinate for all points on the image plane will be a constant and equal to the negative of the focal length due to flipping in the projection.

Is it better to have a large camera, i.e. does large-format pinhole photography produce better pictures, and if so, why?

Yes, generally it is better to have a larger camera. A large camera could make it easier to adjust the pinhole size (larger pinholes are easier to produce than smaller pinholes). Most importantly, larger pinholes avoid diffraction blur - which are common with smaller pinholes. A larger camera also produces a wider range of sizes for a field of view than smaller cameras, thus making the focus easier to adjust.

Provide the mathematical formulations in regards to a simple ideal pinhole camera model, and be prepared to discuss your camera in general.

Extending the 2D camera model (discussed in question 3) to a 3D model, there exists the following formulation as seen above. As seen in the formulations above, increasing the distance from the subject to the plane by increasing focal length causes the camera's field of view to widen, thus allowing for more to be seen. This effect is also attributed to increasing the size of the camera.