I have implemented an initial version of this algorithm (versions of internal codes that I use are Zernike_Module 0.49 and Zernike_parameter_estimation 0.45). This version only fits two spots in the same fiber at the same time. 

The optimization algorithm works so that parameters that should be the same for two spots are kept the same, while others are allowed to be free. So, for each spot, there is a separate swarm of particles - but each particle in one swarm has a ``twin'' particle that has the same parameters which described the fiber properties. At each step, I order the particles that are exploring the parameter space according to their quality. I find the particle which has the best ordering for both spots (the sum of their ordering position is the lowest), and this is declared the best particles for the next step. I then continue in ``standard'' fashion (I assign velocities to other particles that gravitate to the best particle and therefore explore the parameter space.)

After the first implementation, I am noticing some problems in both defocused and focused models.

Defocused images show some structure in their residuals (see example_in_defocus.png). In addition to the stronger residuals around structures, I am observing stronger residuals in the general area of the donut. 

The focused images also show some peculiar residuals (see example_in_focus.png). In this example, obviously, the ``cross'' feature seen in the data is not explained.  

I believe that a fraction of these problems is due to poor sampling of the parameter space and algorithm not finding the optimal solution. I am currently investigating this, and I believe that this can be made better.
Some fraction of problems might be indicative of the deeper issues - when we constrain the freedom in parameters, the algorithm struggles to explain the data. This might be indicative of wrong assumptions of deficiency of the algorithm - which were masked when we had more freedom. When I analyze more images at once the problems might get even more glaring. 

The basic implementation has been achieved. The further improvements are in the follow up tickets (PIPE2D-928 and PIPE2D-929)