Random pinhole plate for the characterization of laser focal spots

This project was conducted under the Dean's Research Award (DRA) program at the University of Alberta. The project was conducted under the Supervision of Dr Robert Fedosejevs.  The research conducted for this project was awarded the "Outstanding Research Award" under the DRA program.

 This project aimed to address the issue of laser beam attenuation.  Firstly, why do we need to attenuate a laser beam? Attenuation of a laser beam is desired in numerous research experiments involving lasers, where data collection involves imaging the beam. Most imaging methods have a limited saturation range, and laser beams have a much higher intensity. Hence, reducing the beam power is a desired practice in these experiments.  And secondly, why is that complicated? It's complicated because these beams are of such high intensity that normal ND filters could deform when placed in the beam path. Also, attenuation must be done in such a manner that the beam profile is preserved.   

Now, we know what the objective is and why we are doing it. The proposed idea of this project was to use a plate with random pinholes, which is then placed on the beam path and then using a converging lens to image the focal spot. In theory, the randomised sampling of the beam cancels out any diffraction patterns that would otherwise appear, and the focal spot of the random samples preserves the original focal spot of the beam. Why should this happen? Because the laser field is coherent, your random pinhole plate does not destroy the wavefront—it only sparsely samples it—so the surviving beamlets still carry the correct phase information and recombine in the Fourier plane (focus) to reconstruct the same Airy focal pattern, just with reduced intensity and added speckle noise. 

The project involved making an apparatus of 3-axis servo motors fixed perpendicular to each other, controlled by an Arduino, to puncture a sheet of aluminium foil with random holes. Moving on from early prototypes, the apparatus was moved and integrated with the titanium-sapphire laser to drill holes with the laser. This greatly improved the quality and reduced the size of the holes. This leads to the question of why smaller holes are preferred. Tiny holes act like near-point samples of the wavefront, so they minimally disturb the local phase and uniformly sample all spatial frequencies of the beam; this preserves the correct interference needed to reconstruct the Airy pattern. Larger holes introduce phase averaging and local wavefront distortion, which blurs and biases the reconstructed focal spot.  On the simulation side of this project, the airy disk pattern was generated by calculating the path difference from a hemispheric (simulation equivalent of a convex lens) laser source to our focal plane. Generating a random pinhole mask and projecting this to our sperical source allowed us to simulate the improvement in our airy pattern with increasing number of holes. 

All of the relevant results of this project are presented on the poster. 

Something that I found interesting in this project was that when I was writing code to generate the random pinhole position, I had to figure out a way to generate a string of random numbers. I went down numerous rabbit holes to find a good solution, one of them was to use the inbuilt python library, another was to use a function in Intel CPUs that gets random numbers from the thermal noise at the CPU. Eventually, I settled for the Python library for simplicity, but that leads to the question: Can anything be truly random? The Python library is termed pseudo-random, meaning if you know the input seed, the algorithm produces the same random numbers. And thermal noise in a CPU is just a really complicated thermodynamics problem. These are random enough for experiments but not truly random. Is anything in nature truly random? Einstein famously said this quote, "god does not play dice." This was his reaction to Quantum Mechanics where nature is fundamentally random. For example, when a photon hits a 50-50 non-polarizing beam spliter there is no way to predict if it reflected or transmitted. It is truly random based on probabilities. Numerous such examples exist due to quantum mechanics. Just like Einstein, though, this is truly such a disturbing reality.  How can this randomness be harnessed for potential experiments in the future? 

Cool pictures from the project-