Pinhole Camera - What Is a Camera?

A camera, in essence, is a dark box with a small aperture to admit light. I will be building three variations of pinhole cameras to explore the effects of large vs. small focal lengths, and experimenting with the size of apertures. This project was completed for Lab 1 of ECE516: Intelligent Image Processing at the University of Toronto, with Professor Steve Mann.

Supplies

The materials for this project are very simple. A cardboard box, some black tape, white foam board or paper and black paint is all that is necessary. To take it a step further, I'll be using some plywood and a lens to experiment with different setups.

Step 1: Small Camera Obscura

Making The Box

I constructed the small camera obscura from a cube-shaped cardboard box, and sealed the edges with some black hockey tape to prevent light from leaking through. A piece of white foam board was cut to size and placed on one side of the interior of the box to act as the image plane. The white board makes it easy to reflect back incoming light to make the image clearer. I also painted all other sides black, of both the interior and exterior of the box. The colour black helps to mitigate reflections of the sides of the box that would diminish the quality of the image.

I cut two holes on the side of the box opposite the white board, one to act as the aperture, and another meant to fit the camera lens on my smartphone to take a picture of the picture seen in the camera obscura. This act of taking a "picture of a picture" has been referred to as metaphotography, metavision, or Through the View Finder photography.

Aperture Sizes

The formula for the optimal diameter of the aperture is given by d=c √(fλ), where d is the optimal diameter, f is the focal length, λ is the wavelength of light and c is a constant. I measured the distance from the aperture to the image plane to be 21cm. Choosing c to be 1.56, and using a λ of 550nm, I calculated d to be 0.53mm.

I wanted to be able to compare the effects of changing the aperture size on the quality of the image. I drilled a series of holes of varying diameters into a strip of thin plywood to act as a variable width aperture system. The size of the calculated optimal diameter was smaller than the smallest drill bit I had access to, so it was made by pressing a push pin into some electrical tape stretched over a larger hole. The resulting hole was approximately 0.5mm. By sliding the plywood strip across the larger opening in the box, I can adjust the aperture within the range of 0.5mm, 1mm, 1.6mm, 2mm, 2.4mm, and 2.8mm.

I used some cardboard strips and black hockey tape to create some pockets to hold the plywood strip as well as my phone in place for convenience.

Results

After taking multiple metaphotos with this camera, I found that the widest aperture produced the best results, both in terms of clarity and sharpness. The widest diameter (2.8mm) was able to produce clear images indoors, whereas the smaller sizes (0.5mm - 1mm) were only faintly visible even during daytime usage. I shot predominantly with a 30s exposure time on my iPhone 12 Pro, but I suspect I would need even longer exposures to capture images with my smaller sized apertures since the amount of light entering the box is very minimal.

Photos

The first image in the gallery above is myself standing before the camera taken with a 2.8mm diameter aperture.

The second is the box while the inside was being painted.

The third is the box fully painted on the inside with the hole cutouts.

The fourth is the strip of plywood with the various aperture sizes.

The fifth and sixth are the finished camera.

The seventh is a comparison of the different aperture sizes by taking a picture of a lamp up close. This was required to produce enough light for the smaller sizes.

Step 2: Large Camera Obscura

Turning a Room into a Camera

Next, I built a large camera obscura from a room. The functionality mirrors that of the smaller camera, just on a much larger scale. Ideally, a room with a window letting in lots of natural light would be ideal, as larger cameras typically need more light (more on this later!). Unfortunately, this type of room wasn't accessible to me, but I was able to locate a small room looking out into a larger space on the 12th floor of the Pharmacy Building at the University of Toronto. I blocked out the window in the door with some black bed sheets and black tape, leaving a small hole to act as the aperture. The cracks in the door were also covered to prevent light from leaking in the room.

Aperture Sizes

I started by using the inner radius of a roll of tape (3.5cm) as the aperture. With this setup, lots of light was being let in and the image produced was very blurry. I then used some tape to shrink the opening down to the optimal sized aperture. Using the same formula as above, I calculated the optimal diameter of the aperture for the room-sized camera to be 1.45mm, with the focal length of the room being 157cm, with c and λ chosen to be 1.56 and 550nm, respectively. The optimal aperture size produced much clearer images.

Results

The images clearly depict the conference room on the other side of the door. Although there were large windows letting in natural light into the room, I imagine an identical setup outdoors on a sunny day would produce superior results. Being limited by resources, I think that the room sized camera produced sufficient images.

Photos

The first image in the gallery above depicts a photo of a photo of me taking a photo of a photo.

The second is a view from inside the room, showing the blanket and tape used to block out the door window.

The third is a view inside the room, with the image displaying on the back wall.

The fourth is an image of the conference room.

The fifth is a closer look at the aperture.

Step 3: Practical Camera Obscura With Lens

Construction

I constructed another camera obscura, but this time with a lens. The lens helps to let more light in, but focus the light to create a sharper image. I designed this camera to have a focal length equal to the focal length of the lens, which I obtained simply by measuring the height of the point with the most magnification. Again, there's a piece of white board to reflect the light of the image, and all other sides are painted black. I created another variable aperture system, this time with a piece of tape sliding on a wooden dowel to act as a curtain and block more of the image.

Results

This camera produced the clearest images. I still had to block some of the opening with tape, but I was able to keep a much larger opening than I did with the first camera, which let more light through while not sacrificing sharpness.

Photos

The first image in the gallery above is a photo of myself.

The second is the top of the box with the lens in place and a cutout for the phone camera lens.

The third shows me painting the inside of the box.

The fourth is the box before the outside was painted.

The fifth is the final camera with the variable aperture system on visible on the top.

The sixth shows the measurement of the focal length of the lens.

The seventh shows me painting the outside of the box.

The eighth is a 'mirror selfie' showing myself taking the picture holding the camera.

The ninth is a photo of a map of Toronto to test its ability to capture detail.

The tenth is a GIF made from a video test.

Step 4: Mathematical Analysis and Discussion

What Does a Camera Do?

I'll first assume the camera is in a two dimensional world and the image and subject matter are both one dimensional. Let's derive the relationship between the planar subject matter and what is seen on the image plane. Firstly, we can construct an optical axis perpendicular to the image plane and passing through the centre of projection. Let X_1 represent the subject matter's distance above the optical axis, and let X_2 represent the corresponding image's distance below the optical axis. Likewise, let Z_1 be the subject matter's distance from the centre of projection, and let Z_2 be the image's distance from the centre of projection. Leveraging similar triangles, we can derive the relationship to be X_1 / Z_2 = X_2 / Z_2.

Does Large-Format Pinhole Photography Produce Better Pictures?

The large camera had a focal length almost 8 times longer than the small camera, but the optimal aperture size was only 2.9 times larger. The larger camera has a proportionately smaller aperture, so the image should appear with more detail. Additionally, due to the inverse square law, light entering a camera with a larger focal length is spread out more by the time it reaches the image plane, so it is dimmer. This means the larger camera should require more light to produce images than the small camera. This was observed experimentally.