Creating complex interference figures with simple sources 3D printers that use Stereolithography usually have to build a 3D object layer by layer, each layer being constructed by having a laser travel across the surface until it has hardened all the layer's interesting parts.
Thus I was wondering if it would be possible to theoretically (I am aware that in practice that would probably be impossible), using a large amount of simple light sources, instantly build the layer using interference.
Say for instance that you have $n$ sources $s_k(d,t)=S_k\cos(kd+\omega t)$ where $d$ is the distance to the source, and any two sources have to be separated by a distance of at least $\epsilon$. If we consider a simple case, we could consider that all the sources are in 2D, and on a centered circle (or square). Let's suppose that our space is filled with resin, which becomes solid upon being under an intensity $S_r$. What is the optimal resolution one could get ?
If this problem is too complex to be answered here, has that been researched before ? I haven't managed to find relevant articles.
 A: In principle I think your idea is sound, but there are serious complications that you probably haven't recognized.  The complications have to do with "coherence".  So your n sources actually have functions 
$s_k = S_k \cos(kd + \omega t + \phi_k)$
where $\phi_k$ are phase constants associated with each source.  Even for "nice" sources like lasers they each have a different $\phi_k$.  What is more, the $\phi_k$ are actually time dependent.  This time dependence is generally very complicated, but can often be well modelled as constant but with random changes which occur at random times with some characteristic time, $\tau$, which we call the coherence time.
So, if you just walk down the hall to the lab, take two HeNe lasers and point them both at the same point on a smooth surface you won't see any evidence of interference because their coherence time (while longer than, say, an incandescent bulb) is much shorter than the time that your brain averages visual data over.  So on sufficiently short time scales interference patterns would exist.  But the patterns would change on a very short time scales.  There are ways around this (such as phase locking the lasers).
