Connecting Visible Wavelength Standards With X Rays and Rays

The 1996 centenary of W. K. Röntgen’s discovery of x rays celebrated the penetrating visions offered by these “strange rays.” Aside from their ubiquitous application to imaging the interior structure of visually opaque systems, x rays continue to have important applications in elucidating the geometrical and electronic structure of matter. In addition to the synchrotron radiation facilities, conventional x-ray sources available in modest laboratory environments have wavelengths well suited to reveal the arrangements of atoms in crystalline solids and biological molecules. In addition, spectroscopy of absorbed and emitted x rays reveals the electronic structure of atoms, molecules and materials. In a similar way, nuclear -rays reflect the energy level structure of nuclei in a wavelength range that extends as far beneath the scale of x-ray wavelengths as x-ray wavelengths lie below visible wavelengths. X-ray diffraction, first reported in 1912, connects x-ray wavelengths with the dimensions of crystal lattices, but fails to connect either of these scales with the dimensions of macroscopic objects. From the early 1930’s to the early 1970s, x-ray spectroscopy was an important contributor to the determination of fundamental constants such as NA, h/e, and hc/e. These measurements were, however, limited by uncertainty in the connection between the x-ray scale and visible reference wavelengths. Up to the mid-seventies, the only well established direct connection was by means of ruled grating diffraction of long wavelength x-ray lines, a procedure that even in its late development was not sufficiently accurate. The paper X-ray to Visible Wavelength Ratios [1] represents the first results of a more direct and robust connection between these disparate spectral domains. Because relative measurements of x-ray wavelengths were more accurate than those linking x-ray wavelengths to macroscopic standards, early workers in the x-ray region introduced local reference standards that approximated sub-multiples of optical units, but were more sharply defined. The local unit in the x-ray region was called the xu, a unit that was intended to approximate 0.001 Å (0.1 pm). Although originally defined by assigning a conventional value to the lattice spacing of rock salt, and later that of calcite, the x-unit was more often specified by assigning particular values (in xu) to the wavelength of one of the widely used reference lines in the x-ray region. It was not until around 1930 that the 1926 demonstration of x-ray diffraction by a ruled optical grating achieved a refinement capable of providing a useful conversion factor between x-ray and optical units. Results from this work were at variance with the local x-ray unit calculated by making use of the electron’s charge determined by Millikan’s oil drop experiment. The disagreement (>0.2 %) remained controversial for over a decade. In the end, it was shown that the oil drop measurement of e contained an error arising from the viscosity of air. Realization of the first x-ray interferometer by Bonse and Hart in 1965[2] opened another route to x-ray wavelengths, and subsequently to the -ray region. The path to a significant measurement began with Hart’s “Ångström ruler” [3], an articulated silicon monolith able to scan over an extended, though limited, range. Subsequently, Bonse and TeKaat demonstrated the quasi-static re-assembly of separated components while retaining favorable intensity contrast [4]. The first combined x-ray and optical interferometer was realized at the NBS [5]. The subject paper [1] reported combined X-Ray and Optical Interferometry (XROI) of the lattice period of a silicon crystal, followed by accurate spectrometry to determine the two most commonly used x-ray reference wavelengths, Cu K 1 and Mo K 1. This measurement plan connected manifestly invariant quantities. The crystal spacing was determined with respect to the optical reference in the XROI measurement and then used, through absolute angle measurement, to link the optical “standard” to x-ray transition wavelengths. Although it has been proposed that the lattice period of silicon (at specific temperature, pressure and purity) should be treated as a “constant of nature” [6], we restrict such usage to transitions between atomic energy levels (x rays), or between nuclear energy levels ( rays). The subject paper describes both parts of the measurement (for x rays) with an emphasis on the XROI component owing to its perceived difficulty and novelty. The original cartoon illustration shown in Fig. 1 has been widely reproduced in textbooks and elsewhere, possibly on account of its deceptive simplicity. The stationary and moving platforms were supported by a flexure stage. In actual data taking, the mechanical stage was “locked” to an optical interference maximum by means of a piezoelectric actuator situated in the drive.