The establishment of a stable and well-defined reference axis is fundamental to precise optical alignment. Although the idea has been implicit in earlier chapters, it deserves explicit treatment because its practical implementation is not always obvious. Consider a point focus—such as the free-space output of a single-mode fiber or its image formed by upstream optics—located at height h above the optical table. The task is to define an axis that passes through this focus, is parallel to the tabletop, and is parallel to the table’s hole pattern so that subsequent optical elements may be aligned to it as shown in Fig. 1.
Fig. 1 Location of the required axis relative to the source and tabletop
If a pixelated, position-sensitive detector such as an autostigmatic microscope or Point Source Microscope (PSM) is used, the initial step is straightforward. The detector is first brought to the point focus and centered on it. Then, without altering any translational adjustments, it is moved along a rail fixed to the table to the far end of the desired axis. This establishes the detector at the correct height and parallel to the rail and tabletop. At this location the detector only sees dim, uniform illumination from the source at the other end of the desired axis.
By inserting an Axicon grating between the source and detector, the grating converts the spherical wave into a Bessel beam with a bright, narrow central core surrounded by concentric rings. When the grating is first inserted it may be tilted or decentered, but the Bessel beam always propagates along the line connecting the point source and the center of the grating’s pattern as shown in Fig. 2.
Fig. 2 Direction of the Bessel beam for a tilted and decentered Axicon grating
As the grating is adjusted so that its center approaches the intended axis, the Bessel beam correspondingly moves toward that axis and eventually becomes coaxial with it. While a small residual tilt of the grating relative to the Bessel beam leaves the beam ring pattern perfectly circular and suitable for alignment, larger tilts distort them into a characteristic four-lobed diamond pattern, indicating a large tilt that should be corrected for precise alignment.
Tilt of the grating can be corrected by adjusting it until the Bessel beam ring pattern is circular, which is sufficient for most work. For higher precision, the PSM may illuminate the grating from the opposite direction using its internal point source. When the reflected Bessel beam returns centered on the PSM detector plane, the grating is normal to the incident spherical wavefront at the center of the pattern to within approximately an arc second.
A key conceptual result of this method of establishing an axis is that the Axicon grating behaves, for alignment purposes, as a lens of arbitrary focal length. It can be placed anywhere between source and detector while still generating a usable Bessel beam that defines the reference axis. Practical considerations such as the numerical aperture of the source and the acceptance angle of the detector limit its useful locations; if placed far from a high-NA source, the illumination may be insufficient. Sensitivity to lateral translation also depends on the grating’s position, since the optical lever arm magnifies motions when the grating is closer to the source.
Once the grating is aligned and locked in place, the Bessel beam becomes the system axis. The PSM may then be removed from the far end of the table and used, as described in Chapter 15, to align individual optical elements. At the center of curvature of a surface of an element, the PSM simultaneously observes the Bessel-beam core and the autostigmatic reflection. When both are centered on the reticle, the element is aligned in both tilt and decenter relative to the established axis to on the order of 1 um and 1 second of arc. Each subsequent component is aligned in the same manner using the transmitted Bessel beam, ensuring complete centering of all elements throughout the system to the reference axis.
This method demonstrates that with only a point focus, a pixelated detector, and an Axicon grating, a precise reference axis can be generated and used for high-accuracy alignment. It should be noted that quad cells and continuous position-sensitive detectors are unsuitable, as the Bessel beam’s surrounding rings have nearly uniform intensity; a pixelated detector capable of centroiding the central peak is essential.