# Under The Dome

A project log for Affordable Reflectance Transformation Imaging Dome

A simple and inexpensive way to image and analyze subtle surface details on objects.

Leszek Pawlowicz 05/30/2016 at 21:480 Comments

RTI requires you to take photographs from a fixed position above the object of interest, but at multiple lighting angles all the same distance from the center point of the object. All points at the same distance from a single center point => sphere. But you're only photographing one side of the object => dome. Attaching lights to the inside of the dome, pointing inwards, is probably the easiest way to handle the lights, and certainly the most common. There are alternate ways to get lights in an equiradial pattern without a dome, but those usually involve quite a bit more work and expense. Feel free to explore alternatives if you like, but from this point on, I'll only deal with domes.

I'll talk more about the kind of domes I've been using in the next post, and what to look out for when ordering one, but for now the important question you have to ask yourself is, how big a dome do I need? To answer that question, you have to think about what an ideal light source would be for RTI. It would be at a constant incident intensity across the entire object you were imaging, and also all the light rays would be parallel. But unless your light source is infinitely far away from the object, that's virtually impossible to achieve. For a perfect point light source, the intensity will drop off inversely proportional to the square of the distance (the classic inverse-square law, describing how a spherical intensity changes with distance). But LEDs are not a perfect light source in that their output light varies with angle. For the LEDs I'm using, maximum intensity occurs at an angle of 0 degrees, and drops off essentially with the cosine of the angle ( the Lambertian distribution).

Lambertian distribution of light intensity with angle in one dimension (Source: ledsupply.com)

The further away the light is from an object, the less important both of these effects become. The radius of the sphere of light becomes larger and flatter, so that the variation in light across the object decrease; the angular width relative to the light position also decreases, so you're up at the flatter part of the Lambertian curve centered around zero degrees. So, ideally, you'd want a dome of nearly infinite radius. Not only is this not practical, but then you have to increase the power of the light source so that some reasonable amount of it is still available to hit the object and light it up - also not practical. So you're going to have to live with some non-uniformity of lighting, but the bigger the dome, the relatively more uniform the light will be over a larger area.

Cultural Heritage Imaging says, based on their experience, that the maximum object size you can get good results from is roughly half the radius of the dome, e.g. a 12" diameter dome would have a radius of 6" and a maximum object size of about 3"; 18" dome has a 9" radius and a 4.5" max object size; a one-meter dome would have a radius of 50 cm, and a maximum object size of 25 cm (just shy of 10"). My personal opinion is that these are conservative numbers, and you can get useful results from objects that are up to 25% larger than these, but YMMV. I'm working on some ideas to extend these size limitations, but they're not ready yet.

So bigger is better? In terms of light uniformity over a larger area, yes. But there are trade-offs:

1. Larger domes mean that the light intensity will be lower at the object, since it's further away from the light source. For my 12" dome, exposure times are typically on the order of 1/15th second, while they're about 1/5th second for my 18" dome. Extrapolate out to a meter-size dome, and you get a one second exposure. This is with a compact point-and-shoot at 3.1x zoom (f/5.6) at ISO 100, and you would get better results with a better camera using a faster lens, larger aperture, higher ISO, etc.. The camera is in a fixed, rigid position so you don't have to worry about camera shake limiting exposure. Still, at some size, the exposure times may become longer than you're willing to live with.
2. Larger domes will cost more. I've bought all my domes from EZ Tops, and been very happy with them. If you check their website and price domes, the listed price of a 24" dome is only about \$20 more than a 12" dome. But it's the shipping costs that will kill you - they're about \$35-40 for a 12" dome, and over \$100 for a 24" dome. Plus, a 12" dome only has room for 48 LEDs (15" minimum for 56 LEDs, 18" minimum for the maximum 64 LEDs supported by my controller design), so you'll save some money by not needing as many LEDs.
3. Larger domes require larger stands and more space, and are less portable.
4. If you want to do high-magnification RTI, working either with a USB microscope or a DSLR with a macro lens, you'll need to have a smaller dome for maximum magnification. Typical working distances for macro lenses are on the order of 6", as are typical lengths for USB microscopes, so a 12" diameter dome would probably be the optimum size for that application. Note 1: My controller can work with any size dome, so budget allowing, you could build multiple domes of different sizes, and run them with the same controller (not all at the same time). Note 2: Distances for macro lenses are often given as the distance from the object to the camera's focal plane, which is not the same as the working distance, the distance from the front of the lens to the object you're photographing.

All a long-winded explanation leading to some basic rules:

• If the most important factor to you is the size of the objects you want to image, measure the largest dimension of the largest object you need to image, multiply by 2 or a bit less, and that's the minimum dome diameter you'll need.
• If you need to do high magnification imaging with a macro lens or USB microscope, I'd recommend 12" diameter as the optimum size. I wouldn't go smaller, as you rapidly run out of room to install LEDs inside if you use domes smaller than that.