Collapsible Origami Pinhole Camera

Last year I played around a bit with pinhole photography.

A pinhole camera is the simplest form of a camera. It essentially consists of a box with a tiny hole (also called a camera obscura) , the tiny hole is often literally a pinhole, hence the name.

Light that shines through the hole and falls onto a photographic film of photosensitive paper where an image is recorded. This is schematically shown in Fig. 1.

Fig.1 - Schematic of a pinhole camera. Points P,Q and R are imaged through a pinhole on a sheet of photographic paper as the points P',Q' and R'.

There are plenty of resources on pinhole cameras a google search away, even though they are the simplest kind of camera, like all things you can go very deep on the subject; the optics of a pinhole is surprisingly complex on a fundamental level.

Pinhole cameras are very easy to use, they are at the same time quite inconvenient to use. They need long exposure times (up to multiple minutes depending on the light) due to the extremely small aperture.

Each time you take a picture, you need to develop the photography paper. So you need the typical a developer, stop and fixer baths. That's all quite easy (especially with photography paper) but the developer in your bath goes bad quite fast, and since you can essentially take only one picture at a time you can imagine it is not an ideal situation.

What about taking multiple pictures?  For that you need to be able to take your photosensitive paper out of the pinhole camera and put it in an envelope and put a fresh photographic paper back in the pinhole camera.  Since the paper is

sensitive to light, this has to happen in the dark, which is very cumbersome when you're outside for example. It is easy to make mistakes like putting the photosensitive paper in the wrong way around.

I needed a different solution. I thought, since I carried around my photographic paper in tiny envelopes anyway, could I make envelopes that "pop-up" into pinhole cameras?

Then I could just carry around a stack of envelopes, pop them open when I want to take a picture and collapse them again.

Turns out it was quite a puzzle to make it work, but it is possible and this is what I present in this instructable.

Supplies

Materials:

• Paper

Paper is the main material of the camera. There are many types of paper to a degree it is a personal choice, but there are some properties that are required.

• It has to be opaque to light.
• It must be thin
• Hold folds well

More correctly, it must be opaque to the light wavelengths at which the photography paper is sensitive. Black is the safest option, but photography paper is not very sensitive to red light, so red paper works fine as well.

Generally 120 - 160 GSM is fine. Shine a flashlight through it, if the light spot is red, or if you don't see a spot, it should be fine.

• Piece of thin sheet metal, e.g form a drink can.

Optimal are small circular apertures with a specific diameter. These can be made easily with a piece metal from a beverage can. Using paper one would have fuzzy edges and fibers sticking out which would diffract the light and make the picture less clear.

• Glue.

Regular white PVA glue is perfect.

• Black paint.

Mixed with the white glue it is a good option to fill up tiny holes. PVA glue by itself dries up transparent.

Tools.

• Something to cut paper.

I have cut some prototypes with a regular x-acto knife, it is precise work, but it can be done. Alternatively I had access to a'cutting plotter', an automatic cutting machine which is of course a far more convenient option. Of course a laser cutter would be the ideal tool, but I didn't have access to one of those sadly.

• Scoring tool

To fold thick paper cleanly it is best to first go over the folds with a scoring tool. There are dedicated tools with a metal ball at the end (as shown in the picture), but an empty ballpoint pen works fine too.

• Toothpicks

Very convenient to apply small blots of glue.

• Tin snips

To cut a piece out of a beverage can. I guess you can use regular scissors, but tin snips are of course more convenient.

• Needle

To create the pinhole

• Sanding paper

To neaten the pinhole

To actually make a photo:

This isn't really explained in this instructable, but there is a ton of information online about developing photographic paper. Besides, instructions should be attached to the specific kind of photographic paper you buy.

• Photographic paper

You may have to cut the photographic paper to 5x5 cm under red light

• Developer

After the photographic paper is exposed, nothing is visible yet. The developer makes the photo visible.

• Stopper

A chemical that as the name says "stops" the development of the picture.

• Fixer

A chemical that dissolves the unreacted silver halides.

• A red lamp

(Red LEDs from e.g. a bicycle light work great)

• A dark room

My dark room isn't very dark, so I have to develop the pictures at night.

Optional

• FreeCAD

I've designed everything in FreeCAD, because it's currently the only CAD software I have on this laptop, so if you want customize the design you can do it. All the files are also supplied in .svg and .pdf format, so you can use a wide range of softwares.

Step 1: Understanding the Concept

Requirements for a pinhole camera

A pop-up pinhole camera must satisfy 2 conditions to work.

*   It must be lightproof

*   It must pop up into a "stable" configuration. 

The first condition is quite evident, as you only want your photographic paper to be exposed by light coming through the pinhole.

With some googling you can find many examples of pop-up boxes in all shape and forms, but they all have holes, so totally unusable as a pinhole camera.

The second condition is more subtle, but very import. If you fold a sheet of paper or cardboard and unfold it again, the fold will behave as a spring and it will slowly refold itself again. Early cameras had a bellow that could expand to focus the lens, but an extra frame was needed to secure everything so that it doesn't collapse by itself.

Similarly, a pop-up-able pinhole camera shouldn't collapse again by itself, it must expand and then keep its shape. If the pinhole moves during the exposure, the picture will be blurred.

The box must be "bistable", it must collapse in a stable flat configuration A and pop up into a stable "box" configuration B . Like a switch.

Initially I remembered an episode of the mythbusters where they made a balloon out of lead. Therein they used an origami configuration that started from a flat shape and inflated into a cube. Being airtight, it is also is light proof.

Sadly it turns out this inflating is impossible with more rigid materials like paper. 

I'm generally interested in origami though and some time later I stumbled across a paper about "Deployable" origami which featured the kind of structure that I need. The authors als have an nice talk on youtube. (Actually the resulting structure that they made isn't collapsible with paper, they seem to use struts) It uses the exact same principle as the origami lead balloon, but with a hexagonal cross section instead of a square.

These structures are called "Triangulated Cylindrical Origami".

By twisting it, you can change such a triangulated segment from a flat state (A) into a popped up state (B).

Designing a pop-up triangulated Cylindrical Origami box

With some experimenting, this hexagonal configuration satisfied both criteria. It was lightproof and it was bistable, it popped up.

To adapt this concept to a functional pinhole, there are the following additional design criteria.

* The distance form the pinhole to the photographic film must be large enough.

* The internal "edges" of the origami structure must not cast a shadow on the photographic film.

* The size must not be much bigger than the photographic paper.

There two parameters that can be changed. The number of corners "N"and the angle of the parallelograms out of which the structure is built.

The origami deployable cylinder consists out of N parallelograms in a row with a fold in the long diagonal. You can't just use any parallelogram, there is a simple elegant relation between the polygon and the the parallelogram that makes it collapsable.

I used an octagon for this project so my explanation will use octagons, but it is applicable to whatever n-gon you desire.

Fig.2 - Schematic of two octagons with side length "a" rotated an angle δ with respect to ech other. On the right one can find the accompanying triangles with sides a and b, and angles 𝛼/2 and δ/ 2to construct the cylindrical triangulated origami.

This is schematically represented in Figure 1

On the left side you see a top-down view of a collapsed deployable octagonal structure. Being collapsed you know that every surface lies in the same plane so some simple geometry can be applied to find some relations.

In the collapsed form, the top red octagon is rotated an angle δ with respect to the bottom blue octagon.  The edges from the top octagon must be connected to those of the bottom octagon with a folded parallelogram.

Such a folded parallelogram is drawn in the octagons on the left, and drawn "unfolded" on the right. 

A first observation you can make is that all the corners of the triangles lie on corners of the octagon. Therefore they all lie on a circle. This means that all edges of the triangle are chords of a circle. 

Consider the green triangle first. In an octagon, an edge "a" will correspond to an angle 𝛼 in the center. With a being a chord, you can then use the "inscribed angle theorem" to find that the angle of opposite pointy corner of the triangle will be 𝛼 / 2.

One can see that the angle δ corresponds with the dashed line that connects a corner from the bottom octagon to the twisted top octagon. It is therefore also a chord, and again one can see that the opposite corner of the yellow triangle (with dashed lines) will have an angle of δ/2. It is maybe more difficult to see as this yellow triangle is partially obscured by the green one. 

As you make some prototypes, this all becomes much clearer very fast.

The general rule of thumb is, if you have an N-gon, you can create a "deployable" origami structure out of parallelograms consisting out of two triangles 𝛼/2  (= 360/N/2) and the "twist" angle δ/2.

This angle δ is still an important design choice. The bistableness of the origami structure depends strongly on this angle δ, a good value depends a bit on what you want and what paper you use.

The bistableness comes from the fact that to open it, the paper is bent a bit, so some energy is needed to bend the paper in between the stable configurations, just like a light bends a piece of metal or plastic so it doesn't want to stay

in between the on and off positions. This is illustrated in Figure 3, the bump represents some energy you must overcome to switch from state A to state B. The fact that state A isn't at 0 is because the paper has some thickness. It will never be perfectly flat. When in state B, the paper won't go back to the folded state A by itself.

Fig.3 - To go from a flat state A to a flat state B one must overcome a small energy bump caused by the bending of paper. At some threshold the paper breaks.

It turns out this angle δ has a big influence on this "bump" in energy required to go from one configuration to another. If δ is too small, the bump disappears and there is only one stable configuration. The origami structure behaves as a spring.

If δ is too large, the bump is too high and too much force is required to cross the bump. The paper starts ripping or crumbling as you twist it. (This was the problem with the paper version of the leas balloon).

The choice of paper also has an impact on the position and height of the stable positions, and the height of the bump. Paper has a thickness, and the folds can't be perfect so you will not be able to fold it completely flat.

If the paper is too thin however, it will just crumble if you twist it.

Fig.1 - The graph depends on many factors, it mainly depends on the angle δ of the design. If δ is too small, there is no bistability, if δ is too big, the model will be destroyed while twisting.

This is schematically represented in figures X and Y.

Generally, for hexagons to octagons δ/2 angles from ~35 - 50 degrees seem to resut in deployable structure. I chose an angle of 45 degrees as the two octagons then match nicely in the collapsed form.

Step 2:

To actually begin constructing the pinhole camera you need the different parts.

In the attachments you can find a .svg and a .pdf file of all the paper parts needed. You can use these files directly or you can rescale them if you want different sizes of photography paper. The parts here are for a paper size of 5 x 5 cm.

As said in the part list, black or otherwise opaque paper is used. Either you can use the .svg or .pdf file to cut the shapes out using a lasercutter or a cutting plotter. I have access to a cutting plotter, so that was the most convenient option for me.

As an alternative, if your paper is not too thick, you can print the pattern on the paper and cut it out with an x-acto knife. This may be difficult with thicker papers or difficult to see on black paper.

While making some prototypes I've printed it on regular printing paper and then transfered the shape to the thick paper by marking all the corners with a needleprick. It is then pretty easy to cut the shapes going from hole to hole.

Step 3: The Triangulated Bellow

In the attachments you can find a separate file for the "deployable origami bellow" which has to be cut out of paper.

When this is done, you have to crease it with a set of mountain and valley folds according to the design. I represent mountain folds with a solid blue line, and valley folds with a dotted red line as shown in the schematic.

Befere the creasing, it is a good idea to score the paper where the folds will be. This can be done with a scoring pen or with an empty ballpoint pen. (though considering the paper is black, it doesn't have to be empty)

Score the mountain folds on one side and and the valley folds on the other side. Keep in mind that the diagnals are mirrored when you flip your paper over! If you score the wrong diagonal, it will not be collapsable. This is not something you want to realise when you finish your model. (happened to me more than once)

When all the folds are prescored the model folds very easily. The last part of this step is to glue the "glue flap" on one end onto the other end. The bottom end of the glue flap should more or less coincide with one of the folds. This step has to be done as accurate as possible.

Step 4: The Envelope

This pinhole camera is actually an envelope that pops up into a pinhole camera. The actual envelope is thus a crucial component.

Initially I tried to use a classic style envelope where only the "seal flap" opens up. This worked fine, but it would be useful to be able to access the pinhole which is on a piece of metal sheet on the inside of the camera.

Therefore I designed an envelope that can fold open completely so one can reach in and replace the pinhole.

Unlike a normal envelope, the bottom flap of this envelope can open up completely. Once you fold all the folds it becomes pretty clear how everything fits together and it is shown in the pictures.

The back of the envelope is open because the photographic paper in it has to be exposed by the pinhole. Around the opening there is an edge on which you can apply some glue and glue it onto the "bottom" octagon with the two square holes aligned.

Step 5: Front Octagon

The front octagon consists out of 2 parts.

1. On the back: A holder for the pinhole
2. On the fornt: A holder for the shutter (the part that looks like an alien)

The pinhole holder

The pinhole holder is the smallest part of the whole assembly. The rectangular flaps of this pinhole holder are creased in with a shallow "L" shape it forms a sort of shallow "box" or pocket. This is necessary to be able to shove the pinhole in it (described in the next step). The bottom parts of the "L" edges are then glued onto the octagonal part. The orientation doesn't matter that much, just make sure that the holes are more or less aligned.

The shutter

Next, this shutter holder has to be folded. It has 2 main functions, like the name describes it holds the shutter, you can slide a piece of paper (the shutter) in and out behind it to expose the pinhole and therefore the photosensitive paper behind it to light. A second functionality is to create a stable "foot" onto which the pinhole camera can stand. The overall shape of the camera is an octagon with a point facing down. The pinhole shutter has some extra paper that can be folded backwards to create a flat surface onto which the camera holder can stand stably.

When closing everything up, the little can be secured in the little slits that look like eyes. This serves as a sort of extra shutter which you can close while you shove the real shutter in place.

Step 6: The Pinhole

The pinhole camera of course needs a pinhole which describes itself pretty well. It is a tiny hole made by a pricking a pin trough some opaque surface.

Some theory

You can read a brief overview on Wikipedia: https://en.wikipedia.org/wiki/Pinhole_camera#Selection_of_pinhole_size

In a nutshell, there are two things that impact the maximum achievable resolusion of a pinhole camera. The shape of the pinhole and its size.

An ideal pinhole is perfectly round. Light is a wave and like water or sound waves it can diffract around edges and make the final image blurry. Therefore you can't really make a good pinhole out of paper as there will be many fibers sticking out around which the light can diffract and blur the image. You can make a good pinhole out of thin sheet metal from a can.

Just prick the point of a pin trough a piece of metal, you will see that the metal will potrude a bit and the hole won't be nice and round. You can then sand it flat again which should clean up the hole somewhat and finish it of by sticking in the needle and twisting it. Check with a magnifying glass till you think the hole is nice and round.

For the size:

As the wikipedia article mentions, if the size of the pinhole is too large more rays will be able to go through it and overlap on the image. (the "circle of confusion" is the size of the pinhole) If the pinhole is too small however, diffraction starts to become a factor again. Before i started writing this, I thought the optimal pinhole size was the sweetspot in the middle where both effects together are minimal. However, by reading the wikipedia article I learned that at a specific size diffraction can "collimate" the light a little bit! This is called Fresnel refraction. To keep a long story short, the optimal pinhole diameter "d" seems to be:

With f the "focal length" which in a pinhole camera is just the distance from the pinhole to the photographic paper. You can just measure this, it is the length of the origami bellow which should be ~ 43 mm when extended.

And λ is the wavelength for which the pinhole is optimal. Generally the peak wavelength of sunlight is 550 nm. You could choose a bluer (smaller wavelength) since the pinhole is not sensitive to red light, but it doesn't matter that much.

If you plug in the values, or your own values for your own pinhole camera, you get an optimal pinhole diameter of ~ 0.3 mm.

Well, I don't actually have a way of accurately measuring it, but with a magnifying glass and a ruler I just eyeball it. It is a paper pinhole camera after all.

Making the actual pinhole

As you can imagine making a pinhole can come with some experimentation, as I mentioned before, that is why the envelope was designed in such a way that it could open completely.

The pinhole is held in place in a kind of pocked glued on the inside of the front octagon.

These are the steps:

1. Trim a piece of can so that it fits in the pinhole pocket which you attached in the last step.
2. Mark the center of the circle with a needle.
3. Take the metal sheet out again and pierce the point of a needle trough it to make a small hole
4. Sand the protrusion you made on the other side down to make the metal flat again
5. Clean the hole by sticking the needle in and twist
6. Check with a magnifying glasss that it is nice, smooth and round and about ~0.3 mm in diameter
7. Stick the pinhole back in the pocket, and secure it, trim it a bit more if necessary and secure with a piece of tape.

Note: Only prick the tip a needle trough it, remember that the hole needs to be ~0.3 mm

Step 7: Combining Everything

The back and front octagon are glued onto the origami bellow.

This is actually a simple but annoying step. The origami bellow has many glue flaps which have to be glued onto the origami octagons. I do this in an "exteded" state one flap at a time and let it dry each time to be able to do it somewhat neatly.

Keep in mind that the front and back must be aligned in an extended state. The head of the "alien" and the top triangle of the envelope are aligned.

Step 8: Making It Light Tight

Even if you work very neatly, you will probably notice tiny light specks at the corners of the origami bellow. These will cause stray light and reduce the contrast of your picture. And if they are big enough they can behive like (bad) pinholes themselves!

Filling them up with PVA glue doesn't help becasue PVA becomes transparent as it dries. Therefore I just mix some PVA glue with black paint and put a tiny dot on every corner. This seems to work very well.

Step 9: Actually Taking a Pictures

Now that the pinhole camera is fully made one can make pictures with it. This can be done in a few steps:

1. Loading the photosensitive paper

I've attached a little video among the videos of me loading some paper (5x5 cm) photo paper in the envelope of the pinhole camera.

I did it in daylight and used a developed picture for demonstration purposes only. Obviously this step has to happen in the dark (under a red lamp).

2. Measure the light to calculate the exposure time.

This needs some experimentation before you can do this properly. The exposure time depends on the brightness of your scene. The more light, the less the exposure time. I use a luxmeter (aimed at the scene) of my cell phone camera. This is not the good way to do it, ideally you use a dedicated light meter (spot meter) used for photography, but I don't have one.

Essentially you need to find a value C so that

exposure time x lux value = C

(Again, you want to use a spot meter and not a luxmeter)

With some experimentation you can find a good value for C, but this is just a guide, it will depend on temperature, or even bright or dark objects in your scene.

3. Take the actual picture

There is also a small video of this process. It involves positioning the pinhole camera by folding over the "alien legs" and removing the shutter.

Everything is closed back up by putting the "alien legs" back in the eyes and reinserting the shutter.

4 Develop the picture.

This instructable is already quite long.

There are many resources online about pinhole photography that describe the process of developing pretty well. There are also instructions attached to the photographic paper an bottles of chemicals.

• You dump your exposed photography paper in the developer for a certain number of seconds
• Transfer it to the stopper bath
• Transfer it to the fixer for a minute or so
• Rinse with water and dry.

The results

I live in Belgium, the past few weeks (or rather months) here were quite dark stormy and rainy. I had hoped to take some pictures outside, and the few days that were nice I was a bit ill because of my booster shot.

Nevertheless I managed to take some pictures, I don't want to show my home on the internet, but I have a nice picture of a still life of a glass with some water and some cups.

You'll notice that the picture is actually negative. Even though direct positive photographic paper exists, I just use regular photographic paper. Everything exposed to light becomes black. You can make a positive image by placing another paper on top and shining light throug it. Or you can do more complex stuff if you have the material.

I have included some failed pictures. Some were under exposed, some were over exposed. I only have made 3 of these pinhole cameras and i can only develop by at night because my dark room isn't dark enough (It is just a regular room with window blinds closed) . So essentially I can only develop 3 pictures a day. There are 3 pictures attached which are the result of my attempt today to develop pictures by day, but too much light crept apparently and all pictures are grey.

Finally i've attached some pictures made last summer with an other type of pinhole camera with exact the same dimensions, but it isn't foldable. The camera had a cylindrical shape, maybe you can see the barrel distortion. This is just to show the type of pictures you can make. I hope to add some extra pictures besides the single good one made with the actual pinhole cameras of this instructable.

Step 10: Extra & Customisation

Everything in this instructable was designed in FreeCAD as it is currently the only CAD softwere I have.

FreeCAD is a free CAD software used generally to design 3D objects but like most CAD progarms it has a nice sketch editor. You can find an example in the pictures of the sketch for the envelope.

The sketches are all quite simple, so you should be able to replicate it pretty quickly in your CAD software of choice if you want.

Everything is designed parametrically, you can change the shape of the film (though maybe keep the width and height the same, that is a relic from previous experiments), paper thickness and a border on which the film rests. The model will upload automatically. You can find these parameters in the "Params" spreadsheet.

If you want to try it yourself, the FreeCAD file is attached below. Change the "txt" extension to "zip". Apparently we can't upload .zip files here. In the .zip file you'll find the FreeCAD file for which you of course need FreeCAD (a recent version because it has changed a lot the past years).

With this you can make for example very small versions. I made a tiny one out of red paper, there is no pinhole in it so I haven't tried it. It is a bit dirty because it satisfyingly snappy and I've played with it a lot. (there is no pinhole so air can rush in easily.) I could use a laser cutter for that one but it is a previous version, a bit different than the one shown in this instructable.

In hindsight, you can also just rescale all the .svg files