The road to using a Bessel beam for optical alignment
Experiment on left, simulation using KostaCloud
Most ideas in optics don't arrive in a single Eureka moment. The idea of using a Bessel beam for optical alignment took me decades to recognize, beginning with work I did during the Sputnik era measuring the radii of optical test plates with an autostigmatic microscope. (The full story is in supplementary material under preparation; this is the condensed version.)
The journey became more serious while developing methods for centering cemented doublets. The traditional approach requires moving between two centers of curvature, or between a center of curvature and a focus. The problem is that moving the detector introduces centration errors unless the translation stage is exceptionally precise, and therefore expensive.
Inspired by work from Jim Burge and his student Laura Coyle, who used CGH Fresnel zones to simulate a spherical mirror, I designed a computer-generated hologram with two concentric Fresnel-zone patterns. One zone focused on the detector for aligning the first element, while the second focused at the same detector position after the second element was added.
The concept worked exactly as intended. I could perform precision alignment without ever moving the detector. Unfortunately, it wasn't practical for production because every new doublet design required its own custom CGH. What I really needed was a universal method based on the same underlying principle.
That experiment did provide an important insight: concentric Fresnel zones of different radii could serve as reference markers in space. I realized that a regular array of such zones could be used to calibrate an entire measurement volume.
Arizona Optical Metrology fabricated a prototype CGH for me, which I later took to UNC Charlotte. Working with Jesse Groover and his advisor, John Ziegert, we used it to map the volumetric accuracy of a CNC machine by mounting the detector in the tool spindle and the CGH on the machine table. The experiment again worked as expected. We mapped a 150 mm cube with approximately 1–2 μm precision and published the results in a Precision Engineering conference proceeding.
That success naturally led to another question: How can this work over a much larger volume?
As I explored ways to extend the range, I realized that in the limit, uniformly spaced concentric rings, rather than conventional Fresnel spacing, might produce the effect I wanted. It seemed worth testing, so I ordered a grating consisting of 10 μm chrome rings separated by 10 μm transparent spaces.
Illuminating the grating with a laser diode coupled into a single-mode fiber produced significant benefits. I could follow the bright central core and surrounding rings of the diffraction pattern for the entire 10-meter length of the laboratory.
About a year passed before I had time to investigate further experimentally. During that time, however, I discovered that the grating behaved like an axicon, producing what is known as a Bessel beam. More interesting, several theoretical papers, well beyond my mathematical abilities, showed that such a beam propagates through optical systems according to ABCD optical matrix theory. Another paper described generating a Bessel beam using a spherical rather than a using plane wavefront as is usually done.
At the time, I filed those papers away without fully appreciating their significance. Eventually it dawned on me what they implied: unlike a conventional focused beam, a Bessel beam can be observed anywhere along its propagation path. You are not confined to working only at a focal plane or a center of curvature.
When I returned to the lab, I wanted an experiment that would be difficult to reject. A ball lens was the perfect test object because it cannot be tilted. It can only be decentered with respect to the incident beam. Once again, experiment and theory agreed within experimental uncertainty.
By then, Professor Daewook Kim and his student Zac Chen had become interested in the idea that a Bessel beam behaves like an ABCD ray in optical design. Zac carried out an independent theoretical study, and together with collaborators published a paper confirming that this interpretation was correct.
With both experimental and theoretical validation in hand, I've continued developing Bessel-beam-based alignment methods.
What makes the approach attractive is that the beam remains well defined far beyond the focal point of a lens. That provides much greater sensitivity to alignment errors than measuring only at focus. Just as importantly, the alignment axis can be established before any optics are inserted into the beam, eliminating the need for a precision rotary axis. This makes high-precision alignment in tilt and decenter practical even on simple tabletop systems where rotary tables are impractical or impossible.
Because the setup remains fixed in a Cartesian coordinate system, every alignment adjustment produces immediate, useful feedback. That also makes automation more straightforward than with traditional rotational alignment methods.
Looking back, this has been a long journey. Each experiment answered one question while suggesting the next. Piece by piece, the concept of using Bessel beams for optical alignment has taken shape.
The journey is far from over. In fact, I believe we're only beginning to see the possibilities. The evidence so far suggests that Bessel-beam alignment can produce better optical performance while making precision alignment both simpler and faster than current practice.
I'd be interested to hear what others think, especially anyone who has worked in the field of precision optical alignment and lens centering.