You are probably familiar with those thick postcards which look different depending on the viewing angle, allowing them to be autostereoscopic, display different phases of some action, or simply display different pictures. They can usually be found in the souvenir stores of art or science museums.

The common lenticular sheets laminated to the front of such postcards have riblets, giving this effect in one direction only. The original concept, however, photographies intégrales, or integral photography, used dots rather than riblets, which makes it closely related to light field display and photography. Light field displays and cameras are subject intensive development today, but the concept was invented by Gabriel Lippmann in 1908. He is perhaps better known for winning a Nobel prize in physics (the same year) for an ingenious method for colour photography.

This instructable will show you how the first hand-made integral painting ever was made. Ever? Well, such claims are always quite hard to prove. The artist Barbara Strasen for instance, has done something similar, but it looks as if she has scanned several paintings, i.e. views, and generated the final composite image with a computer. That is why I restrict my claim for fame with the quantifier hand-made. My integral painting is truly hand-made. I painted directly on the back of the lenses. In particular, no computer was involved.

p.s. Please leave a comment if you know of an earlier hand-made integral painting.

p.p.s. The original version of the image above is a GIF-animation. Try clicking it!

Step 1: The Basic Principle

The basic idea is to create a surface such that each point on it will have a colour which depends on the viewing angle. Lippmann's original design used a facet lens design which optically accurate, but somewhat out of reach for an impatient amateur. Since I wouldn't be able to paint the back very accurately anyway, I chose to be inspired by retro-reflective street markings paint.

Tiny glass spheres are embedded in retro-reflective paint. As shown in the two illustrations here, the spheres will first (almost) focus the light to a point at the back of the sphere, opposite to the source. There the light will be reflected by the paint. The lensing action now acts in reverse, and the reflected light is send back in (almost) the direction it came from.

The simplified version of Lippmann's concept which I have used isn't exactly new. See e.g. this publication by Sokolov from 1911.

Step 2: Where to Paint

When hand-painting "integrally", it is useful to be familiar with the concept of a voxel ("volume" + "pixel"). As illustrated by the first two pictures in this step, a each voxel of the 3D object to be part of the painting, corresponds to a specific pattern of paint on the back of the layer of glass spheres. As you can see, voxels behind as well as in front of the physical surface of the painting are possible. (The case where the voxel coincides with the layer of spheres, is left as an exercise to the reader.)

Naturally, a voxel-centric frame of mind is inappropriate when painting. The third illustration shows an object-centric view of how to apply paint. Painting object by object is slightly less taxing on your patience, than painting voxel by voxel.

Step 3: Stuff I Used

I put "Stuff I Used" rather than "What You Need" as a title, since the method I used was a bit flawed, and should be easy to improve on. I will come back to this later.

The most important item are the spheres. I managed to find an online shop which sells glass spheres by the kilo, in all sizes and qualities. I used 10 mm spheres of the "technical" quality. There is an "optical" quality too, but that will have to wait until I have honed my skills and perfected the method.

The picture was taken before I started. Some minor items are missing, but you will probably spot them as you read on.

Step 4: Preparing the Temporary Front Plate

The spheres have to be held in place during the painting, then transferred to the final back plate. This is the task of the temporary front plate.

As you can see on the pictures, I used a piece of picture frame glass. A glass pane has some good properties as a front plate, but the disadvantages seem too many. I will come back to this later.

Anyway, I used a water soluble, or "aquarellable", pen for tracing the outline of the back plate on the glass pane. The plumber's putty is then used to form a levee holding back the molten wax. (Ordinary modelling putty for children may not work, since it is softer and appear to have a lower "melting" point. Plumbers have stronger and warmer hands than kids.)

I achieve two things by heating the plate on top of a pot with some water in it. The temperature is fairly easy to control, and the top of the stove is usually fairly accurately levelled. My pane was to big for the oven, but I wouldn't have put it in there for these two reasons.

Step 5: Adding Spheres to the Front Plate

I started out with a reference furrow ploughed in the wax, but that was silly. The spheres stack nicely in a triangular pattern all by themselves. This is hard on your thumbs. Halfway through, I regretted not ordering larger spheres. Not only would a smaller number cover the same surface, but the radius of curvature would have made it less painful for my thumbs.

Initially, I considered adding the spheres when the wax was melted, but worried too much about the wax ending up on the parts which were to be painted later on. I was also worried that the spheres would roll all over the place, refusing to stay in their orderly pattern.

Step 6: Applying Paint

Painting in 3D is a bit like a crossing between enacting a hidden lines algorithm and painting an Ukranian/Russian Easter egg, a pysanka. I painted one colour at a time, painting objects close to the viewer first, finishing off with the most remote objects.

Each colour has to dry completely before the next one can be applied. After hunching over, and painting small dots on, several hundred tiny glass spheres, you start to appreciate the long drying time.

Step 7: Glueing the Spheres to the Back Plate

This is were the serrated filler spreader is needed. We definitely don't want any of the filler to squish up between the spheres, and we still want an adequate layer which will hug the spheres and secure them to the back plate.

After some algebra and geometry, it is possible to figure out that the maximum thickness of filler which will not come up between the spheres if they are pressed down all the way to the back plate, is a little less than 1/5th of the sphere diameter.

Step 8: Releasing the Painted Spheres From the Temporary Front Plate

As you can see in the first picture, I have moved the levee-perimeter outwards to let the wax escape from the spheres as it melts.

It worked so-so. Too much wax is left behind on the spheres.

First I tried using newspaper pages to absorbed the molten wax. This removed some, but not all of the residue. In the end, I washed the whole thing in hot water with dish-washing liquid and a brush.

Seven spheres had fallen off before the bath, so I was quite nervous before I dunked those man-hours of painting etc. into the sink.

Step 9: Setback

Well, as I said, seven spheres fell off, so they had to be put back again.

I will not describe the effort that went into this repair, but trust me on this, it was tedious. Try to avoid ending up there.

No, the integral painting fairy will not leave a coin under your pillow for every stray sphere you put there.

Step 10: Discussion

Well, the final result was shown up front. Here comes some thoughts on the method I used.

A glass pane as temporary front plate has several positive sides:

flatness
easy to clean
transparency

but it does not conduct heat very well, which, if the heating isn't perfectly even, will cause surface tension (Marangoni) effects. This will make it very difficult to achieve an even layer of wax. I guess this is what caused the imperfect bonding of the seven spheres near the centre of the painting; The wax was thicker near the levee boundary, making the centre (of the back) slightly concave. During my attempt to push the spheres into the epoxy filler, the spheres near the periphery were pushed much deeper into the filler than those near the centre.

To base the procedure around wax was maybe a mistake. Not only did I have some problems achieving a flat wax bed for the spheres, it tended to end up on the surfaces which were to be painted or glued. I would like to get rid of those tedious cleaning and degreasing sessions. Wood's metal, anyone? A vacuum plate with a pre-drilled hexagonal pattern of holes, perhaps? Surprise me!

I did not care much about aligning the sphere pattern to be parallel with the horizon. This was maybe a mistake, since it made it almost impossible to paint vertical or horizontal lines accurately. At least if you paint "ad lib", as I did.

Yes, some kind of computer-generated map, showing how each sphere backside should be painted, would probably have helped, but that would have killed the thrill and sport of it...