Richard D. Deslattes

Analytical modeling of the periodic nonlinearity in heterodyne interferometry.

The periodic nonlinearity that arises from nonideal laser sources and imperfections of optical components limits the accuracy of displacement measurements in heterodyne interferometry at the nanometer level. An analytical approach to investigating the nonlinearity is presented. Frequency mixing, polarization mixing, polarization-frequency mixing, and ghost reflections are all included in this investigation. A general form for the measurement signal, including that of the distortions, is given. The analytical approach is also applicable to homodyne interferometry.

Heterodyne interferometer with subatomic periodic nonlinearity

A new, to our knowledge, heterodyne interferometer for differential displacement measurements is presented. It is, in principle, free of periodic nonlinearity. A pair of spatially separated light beams with different frequencies is produced by two acousto-optic modulators, avoiding the main source of periodic nonlinearity in traditional heterodyne interferometers that are based on a Zeeman split laser. In addition, laser beams of the same frequency are used in the measurement and the reference arms, giving the interferometer theoretically perfect immunity from common-mode displacement. We experimentally demonstrated a residual level of periodic nonlinearity of less than 20 pm in amplitude. The remaining periodic error is attributed to unbalanced ghost reflections that drift slowly with time.

Remeasurement of γ-Ray reference lines

Abstract Over the last several years, we have established a new and significantly improved measurement chain connecting γ-ray lines with visible reference standards. This chain has three links: First, a Si lattice repeat distance is determined by combined X-ray and optical interferometry. Second, this crystal calibration is transferred to other specimens suited to γ-ray diffraction. Finally, these crystals are used in a transmission double-crystal instrument to determine γ-ray wavelengths via the Bragg-Laue equation. To obtain the required precision and accuracy, the spectrometer is fitted with angle interferometers of considerable sensitivity (∼0.05 marcsec) and these are calibrated by summing to closure the external interfacial angles of a 72-sided optical polygon. This report focuses on the apparatus and methodology of the third step but includes descriptions of the first two also. Results are presented from tests of closure using cascade-crossover relations and inter-order comparisons. Energies for γ-transitions in 198Au, 192Ir, 170Tm, 169Yb, together with the X-ray transition W Kα1 are included. γ-Ray wavelength accuracies are estimated to be near 0.5 ppm.

Description, Performance, and Wavelengths of Iodine Stabilized Lasers

A description is given of lasers stabilized to components of the (129)I(2) spectrum in the region of the 633-nm laser lines for (3)He-(20)Ne and (3)He-(22)Ne. Relationships between operational characteristics such as power output, peak size, and peak width are shown, along with their relationships to some of the controllable parameters such as excitation level, iodine absorption, and iodine pressure. We found an iodine pressure broadening of about 13 MHz/Torr with a 2.6-MHz zero-pressure intercept. The frequency shift associated with iodine pressure is roughly 2 x 10(-9) nu/Torr to the red. Power broadening and power shifts are small, about a 10% increase in width and about 2 x 10(-11) nu variation in frequency for a fivefold to sixfold increase in power. These lasers exhibit a frequency stability for 10-sec sampling time of about 2 x 10(-12) nu and a resetability of about 1 x 10(-10) nu. The absolute vacuum wavelength for one iodine component has been measured against the (86)Kr standard-(3)He-(20)Ne:(129)I(2), kappa lambda = 632 991.2670 +/- 0.0009 pm. The wavelengths of several other iodine components have been determined by measuring the frequency difference between them and the (129)I(2), kappa component. Among these are (3)He-(20)Ne:(129)I(2), i lambda = 632 990.0742 +/- 0.0009 pm: and (3)He-(20)Ne:(127)I(2), i lambda = 632 991.3954 +/-0.0009 pm. These results were obtained using the Rowley-Hamon model for asymmetry in the krypton line and assume that the defined value for the standard is axssociated with the center of gravity of the line profile. The indicated uncertainties are statistical. No allowance has been included for imperfect realization of the krypton standard or for uncertainty in the asymmetry model.

K‐Absorption Fine Structures of Sulfur in Gaseous SF6

Measurements are reported on the K‐absorption fine structure of sulfur in gaseous SF6. The results differ qualitatively from previous measurements on molecular gases of lower coordination. Comparison is also made with preliminary results on H2S.

Estimates of X-ray attenuation coefficients for the elements and their compounds

Some recent developments leading to improved knowledge of the distribution of oscillator strength in the photo-ionization continua of atoms are briefly reviewed. Selective comparisons between the experiments and calculations are indicated. Estimates for attenuation by compounds and solids, insofar as they depart from the mixture rule, require an understanding of X-ray fine structure or, at least, of its limiting form, which is not yet at hand. Some of the mechanisms leading to fine structure in solids and molecules are briefly reviewed.

World Year of Physics: A direct test of E=mc2

One of the most striking predictions of Einsteins special theory of relativity is also perhaps the best known formula in all of science: E=mc2. If this equation were found to be even slightly incorrect, the impact would be enormous — given the degree to which special relativity is woven into the theoretical fabric of modern physics and into everyday applications such as global positioning systems. Here we test this mass–energy relationship directly by combining very accurate measurements of atomic-mass difference, Δm, and of γ-ray wavelengths to determine E, the nuclear binding energy, for isotopes of silicon and sulphur. Einsteins relationship is separately confirmed in two tests, which yield a combined result of 1−Δmc2/E=(−1.4±4.4)×10−7, indicating that it holds to a level of at least 0.00004%. To our knowledge, this is the most precise direct test of the famous equation yet described.

Laser wavelength comparison by high resolution interferometry

High resolution interferometry has been used to determine the wavelength ratio between two molecularly stabilized He-Ne lasers, one locked to a methane absorption at 3.39 microm and the other locked to the k peak of (129)I(2) at 633 nm. An optical beat frequency technique gave fractional orders while a microwave sideband method yielded the integer parts. Conventional (third derivative) peak seeking servoes stabilized both laser and cavity lengths. Reproducibility of the electronic control system and optics was a few parts in 10(12), while systematic errors associated with curvature of the cavity mirrors limited the accuracy of the wavelength ratio measurement to 2 parts in 10(10). The measured wavelength ratio of the methane stabilized He-Ne laser at 3.39 microm [P(7) line, nu(3) band] to the (129)I(2) (k peak) stabilized He-Ne laser at 633 nm was 5.359 049 260 6 (0.000 2 ppm). This ratio agrees with that calculated from the (lower accuracy) results of earlier wavelength measurements made relative to the (86)Kr standard. Its higher accuracy thus permits a provisional extension of the frequency scale based on the cesium oscillator into the visible spectrum.

X‐RAY MONOCHROMATORS AND RESONATORS FROM SINGLE CRYSTALS

Single‐crystal specimens shaped so as to permit successive x‐ray diffraction by two nonparallel atomic planes are fixed wavelength monochromators. It is shown that certain plane pairs in Si and Ge pass wavelengths sufficiently close to strong characteristic lines to allow production of intense highly monochromatic beams. For tautozonal planes belonging to the same crystal form, resonators and retroreflectors are possible.

Single axis photoelectronic autocollimator

Several single axis, diffraction limited, monolithic autocollimators, capable of resolving less than 10−3 arc s have been designed and built. Their features include small size, lightweight, ruggedness, and ease of operation. Construction features and performance levels are given.