# Introduction

The camera obscura is a device that takes advantage of the phenomenon in which one can project an image onto a surface by placing the surface in an environment where light only enters via a pinhole. Because light that reaches the target surface must pass through the pinhole, the image projected onto the surface is relatively focused. The optimal pinhole diameter is 1.9 * sqrt(f * lambda), where f is the orthogonal distance from the pinhole to the target surface and lambda is the wavelength of light (~550 nm).

# How a pinhole camera 'focuses' without a lens

Pinhole Camera Ray Diagram

Suppose we had an infinitesimally small pinhole. Using geometry (and ignoring the size of photons), we can see that any point from the source can only project onto one point on the target surface; there is a bijection between the source object and the projected image. However, this is not practical because this restriction would result in a very dark image. By using a small pinhole, we can approximate this effect and have a relatively focused image without compromising too much brightness.

# Design

We decided to use an Instant Pot® box to provide a dark enclosed environment for the target surface. The box has dimensions 30cm x 30cm x 30cm. Therefore, the optimum pinhole diamter is 1.9 * sqrt(550nm * 30cm) = 0.8mm. We poked two vertically-aligned holes on one side of the box -- the top hole is for the pinhole, and the bottom hole is for the smartphone camera to look into. We placed an aperture slider on top of the top hole so that we can adjust the aperture between three sizes: 0.8mm, and 5.0mm. To minimise as much unwanted light as possible, we spray painted the interior of the box with black paint, and covered the edges of the box with tape and alumnium foil. To take a picture, we placed a smartphone camera into the bottom hole and use an extended exposure time.

Box interior spray painted black Camera with aperature slider on it Aperature slider
Box interior screen Close up of aperature slider mechanism Using the Instant Pot® camera

We used the iPhone 6s Plus camera to take photos of the projected image within the camera obscura. Here are some pictures of our smartphone camera. It contains an optical image stabalisation unit to prevent motion blur.

# Results

The below images are example photos taken with our camera obscura device with pinhole diameter of 0.8mm, 3.0mm, and 5.0mm. As shown below, the images taken with a larger pinhole diameter are blurrier, though they required shorter exposure time since more light entered the box. On the other hand, images taken with a smaller pinhole diameter are sharper, but required a longer exposure time since less light entered the box. The calculated 0.8mm diameter seems to have the optimum picture quality. However, due to the limited amount of light entering the 0.8mm diameter pinhole, we had to boost the ISO to get a visible image, which led to a low SNR and thus a purple casted image.

ƒ2.2 15s ISO 1000
5.0mm
ƒ2.2 15s ISO 1600
3.0mm
ƒ2.2 30s ISO 2000
0.8mm
ƒ2.2 15s ISO 1000
5.0mm
ƒ2.2 30s ISO 1250
3.0mm
ƒ2.2 37s ISO 2000
0.8mm

# Freestyle

Using our camera obscura and iPhone 6s Plus, we experimented with multiple aperture, ISO, and exposure settings and took additional images. We also tried to incorporate artistic merits into the images. Although the 3.0mm aperture setting is blurrier than the 0.8mm, we decided to use the 3.0mm aperture to avoid the noisy effect created by the high ISO required in the 0.8mm setting.

ƒ2.2 24s ISO 1000 ƒ2.2 15s ISO 2000 ƒ2.2 30s ISO 1000
ƒ2.2 15s ISO 1000 ƒ2.2 1/3s ISO 2000 ƒ2.2 15s ISO 1000

# Alternative Box Design (Extra Credit)

For our first bells-and-whistles, we came up with new design for the camera obscura. Our original design involved having to place the smartphone camera underneath the pinhole, which makes camera operation quite difficult. In fact, using our Instant Pot® camera obscura, we had to take pictures while sitting or standing in uncomfortable positions. The images also come out as reversed. To fix this, we created a new camera obscura with a mirror at an angle in the interior. With this construction, the hole for the smartphone camera is placed on the top of the box, and the camera operator can stand behind the camera while looking down at the camera. Images also come out in the correct orientation.

Box interior with morror Box interior and screen Top hole for camera

### Results

ƒ2.2 15s ISO 1000 ƒ2.2 15s ISO 1000 ƒ2.2 30s ISO 800

# Light Painting (Extra Credit)

For our second bells-and-whistles, we decided to demonstrate light painting. Light painting is a technique in which the subject moves a bright hand-held light source, which is captured using an extended exposure time. This creates an effect in which the hand-held light source "paints" figures in the air.

'Fireworks'
ƒ2.2 1/120s ISO 2000
'Dandelion'
ƒ2.2 1/4s ISO 400
'Neuron Firing'
ƒ2.2 1/4s ISO 800

# Multiple Exposure (Extra Credit)

For our last bells-and-whistles, we experimented with combining multiple exposures into one image.

'Half Full or Half Empty' 'Squirrel on Lake' 'UFO Bottles'
*We are not affiliated with Instant Pot®