Measuring very small angles with high precision from a distance on the order of meters or more, as is needed in applications such as calibrating coordinate measuring machines (CMMs), or aligning gravitational wave detector or particle accelerator components, currently requires the use of laser interferometry, and involves making use of a minimum of two beams for either pitch or yaw.

In this invention, the problem of measuring very small angular changes is transformed into that of measuring more readily detectable changes in incident optical power on a photosensor, in this case, a PSD, or Position-Sensing Device.

Furthermore, both pitch and yaw can be measured simultaneously utilizing a single laser beam.

The system relies on a novel dissipative optical fiber bundle (DOFB), i.e., a straight section of fiber bundle that is modified so that the core and/or the cladding of constituent multimode fibers **attenuate** the reflected or passing mode. Thus, the bundle acts as a collimator whose parameters can be designed to achieve very small numerical aperture.

Using geometrical optics as a first approximation, it can be demonstrated that dissipative waveguides with cylindrical symmetry, made of suitably chosen opaque and absorbtive core and cladding materials, diameters, and length, have the capacity to exhibit very strong dependence of the ratio (transmitted/incident) power on incidence angle. This is because both the number of internal reflections and the length of ray paths, and thus attenuation, increase exponentially as the angle between the waveguide axis and incident ray increases.

In the configuration shown in figure 1, the laser is a specially designed, diode laser-based, unpolarized source optimized for beam straightness and pointing stability, with residual instability measured in real-time using an auxiliary subsystem. The author of this invention has unique practical expertise in laser beam stabilization for position measurement applications (either in vacuum or in the atmosphere under laboratory conditions), attained while working in metrology research.

The auxiliary beam-angle measuring system consists of a beam splitter, mirrors for path folding the reference beam (to amplify beam spot displacement due to small angular deviation at the source), and a greyscale imaging sensor which allows for the processing of images in order to more accurately determine beam spot position, as well as monitor changes in beam power.

The target will have a PSD/DOFB pair affixed to it. The ends of the fiber bundle should be polished and coated with an anti-reflective coating.

Optical filters and shields are used to exclude ambient and extraneous light. A beam amplitude modulation scheme may also be used to better isolate the laser signal from external optical noise.

The power of the beam passing through the fiber bundle will be changed significantly in response to small angular offsets, and these changes in beam power will be detected by the PSD. After correcting for calibration errors, atmospheric effects, and source instability, they serve as a measure of the angular change. Shifting of the position of the spot will also be detected by the PSD and will serve to differentiate pitch from yaw.