Bessel beams are useful for alignment because they create a small diameter, bright, straight line image in space perpendicular to the Axicon, or Axicon grating, producing the beam that is an exact analog of a single ray in a ray tracing program. Here we limit our discussion to Bessel beams produced by plane gratings whose pattern is evenly spaced concentric circles that are illuminated by a point source of light on the grating axis. The gratings produce a more nearly ideal Bessel beam than a lens type Axicon, and the plane grating serves as a plane mirror as well in an alignment setup so the combination define four degrees of freedom in space rather than the usual two. Most discussions of Bessel beams assume illumination with collimated light. We have found it advantageous to use a point source for illumination because it is easy and less expensive to use a single mode fiber as a source than a precision collimating lens the diameter of the Axicon. Besides, collimated illumination produces a Bessel beam of finite length in transmission while in theory a beam of infinite length is created using a point source. With these assumptions about how the beams are produced and details about the grating diameter and line spacing it is easy to calculate the useful length of the Bessel beam in reflection from the grating, the usual matter of concern when using the grating for alignment purposes in a double pass test setup. Other practical matters are also discussed such as lens centering with a test apparatus with no moving parts.
|