Getting the measure of tiny angles

Diamond is one of the most advanced scientific facilities in the world; its pioneering capabilities are helping to keep the UK at the forefront of research. Diamond’s scientific and technical staff are constantly pushing the boundaries of what's possible, including developing new techniques and equipment, moving to ever higher resolution, and enabling users to conduct previously unimaginable experiments.

One of the fundamental pillars underlying all of Diamond's work is the need for accurate measurement. For example, if you are operating a micro- or nano-positioning stage on the beamline that scans or rotates your sample through the X-ray beam in incredibly tiny increments, how do you know it's working as expected? Similarly, when you assemble a new X-ray mirror system, how can you be confident that its surface profile has the accurate shape required to correctly focus the X-ray beam?

Recently, scientists from the Optics and Metrology (O&M) group at Diamond and the National Physical Laboratory (NPL) used an NPL Small Angle Interferometer to characterise and extend the angular performance of Diamond’s nano-angle generator (NANGO). An article describing this work has been accepted for publication in Metrologia, the Institute of Physics’ flagship journal for fundamental metrology.

For the first time, they demonstrated that NANGO could generate angles smaller than 1 nanoradian (equivalent to ~ 57 billionths of a degree) which were measurable by an external instrument. Traceability of NANGO to the International System of Units (SI), via the NPL Angle Interferometer, provides the accuracy required to calibrate a wide range of angle generating or measuring devices to benefit Diamond’s beamlines. 

Traceable calibration of scientific instruments is required for Diamond’s beamlines and labs to produce world-class science. Traceability is a fundamental concept of metrology relating a measurement to a national or international reference standard through a documented, unbroken chain of calibrations. Crucially, this is the only way the accuracy of a measurement can be determined. For length measurement, the metre definition is based on the fundamental constant, c, the speed of light. The most direct route to high-accuracy length measurement is via optical interferometry, which measures distances in terms of the wavelength of light. Angle measurements can be obtained as a combination of several length measurements.

The Optics and Metrology group (O&M) at Diamond provides expert support to the beamlines in the design, procurement, acceptance testing and optimisation of all beamline optics. They operate several state-of-the-art measurement labs, including the Precision Metrology Lab (PML) and the Optics Metrology Lab (OML). These facilities enable the O&M team to engage in research and development of novel X-ray optics and related instrumentation to benefit Diamond’s beamlines.

Dr Rabia Ince, Nanopositioning Specialist, who runs the PML with her colleague Hiten Patel, says:

To push the boundaries of Diamond’s dimensional nanometrology capabilities, Diamond partnered with the National Physical Laboratory (NPL), the UK's National Metrology Institute. NPL is a world-leading national metrology Institute that provides cutting-edge measurement science, engineering, and technology and traceability to SI units.

Diamond’s beamlines require precise and versatile micro- and nano-positioning systems to quickly move or rotate important beamline components including optics and samples.

In 2015, the O&M group collaborated with Diamond's Engineering group to develop and build NANGO: a nano-angle generator capable of making 1 nanoradian angle steps (which is the change in angle required to rotate a telescope to switch looking between the heel or toe of a footprint on the Moon!). O&M use NANGO to evaluate rotary positioning systems and calibrate the angle metrology testing of X-ray optics. However, there has been no traceable evaluation of the performance limits of NANGO.

Today’s state-of-the-art X-ray mirrors have slope deviations from the ideal form of < 50 nanoradians. Similarly, the two crystals in X-ray monochromators need to be stabilised in angle to < 50 nanoradians. Within the next few years, both values will reduce to < 25 nanoradians. Ever improving specifications, including faster movements, means we must develop and calibrate metrology instruments capable of accurately measuring them. The adage holds true: “if you can’t measure it, you can’t make it!”.

Since the O&M already use an NPL traceable interferometer to verify linear systems, the collaboration was extended in 2022 to cover angle metrology. The PML team and Andrew Yacoot from NPL used an NPL Small Angle Interferometer in the PML to measure the angular motion of NANGO. For the first time, one nanoradian steps made by NANGO were traceably measurable and the instrument’s performance independently verified. The 200 kHz acquisition rate of the interferometer also revealed unexpected dynamic information about NANGO's angular motion and the performance of its control system. The team demonstrated that NANGO can make: distinct steps of 500 picoradians; sinusoidal oscillations at 0.4 Hz with an amplitude of 125 picoradians; or 1 nanoradian oscillations at 40 Hz.

Dr. Simon Alcock, Senior Metrology Scientist in the O&M group, says:

Traceability of NANGO to the SI through National Metrology Institute instrumentation allows the accuracy of NANGO to be used for a wide range of angle metrology applications at Diamond, including metrology feedback for ion beam polishing of the next-generation of improved quality X-ray mirrors, and dynamic characterisation of nano-positioning stages.

Dr. Andrew Yacoot, Principal Research Scientist and leader of NPL’s Dimensional Nanometrology work, says;