Spherical interferometer

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The spherical interferometer is a two-armed Fizeau interferometer with spherical reference surfaces that was specially developed by the Physikalisch-Technische Bundesanstalt (PTB) to determine the absolute diameter topographies of the silicon spheres of the international Avogadro project .

Background of the development

Brief history of the international system of units

Since the first General Conference on Weights and Measures (CGPM) in 1889 agreed on a system of units with the three base units kilograms for mass , meters for length and seconds for time , the MKS system , there have been several changes in the field the definition and completion of an international system of units. In addition to the inclusion of the four quantities amperes for electrical current , Kelvin for temperature , candela for light intensity and moles for the amount of substance , the expanded MKS system was named the International System of Units (SI) in 1960 . Furthermore, the definitions of the basic quantities are subject to frequent changes in order to be able to adapt the uncertainties associated with the implementation of the respective definition to modern measuring equipment and to be able to break away from unit standards in the form of a prototype (cf. original meter , original kilogram ). Despite all efforts, this has not yet been achieved for all basic sizes, as the kilogram prototype from 1889 must still be used to define the size of mass. This is particularly uncomfortable for the guardians of the units, since comparisons of the mass of the original kilogram with different national copies showed a time-increasing difference.

In order to become independent of a prototype when defining the mass and to base the definition on a natural constant, two approaches are currently being pursued. On the one hand this is the Watt balance proposed by P. B. Kibble in 1975 , on the other hand a redefinition based on the Avogadro constant is to be carried out. The latter approach is being pursued within the framework of the international Avogadro project with the participation of PTB.

Avogadro project

The Avogadro project aims to redetermine the Avogadro constant via the precise measurement of mass and volume of a body, which consists of a material with a particle density and molar mass that must also be determined :

.

The high-precision determination of the volume requires the manufacture of a sphere with the smallest deviations in shape from silicon, the diameter of which is then measured in the spherical interferometer with nanometer accuracy. The spherical shape was chosen instead of a parallelepiped or cube, since corners can break out of the latter due to handling and the undefined loss of material prevents exact volume determination.

A sufficiently accurate determination of the particle density is possible using X-ray laser interferometry and requires a monocrystalline material. Because of the requirements for the accuracy of the material parameters, only chemically ultra-pure, isotopically pure silicon-28 is currently in question. With natural silicon, which is a mixture of three isotopes, the relatively poor determinability of the mean molar mass limits the overall accuracy. After setting the Avogadro constant to an exact value, a kilogram could finally be defined by a certain number of atoms of a certain type of atom (e.g. 12 C ).

Structure and measuring principle

Spherical interferometer

In the center of the spherical interferometer there is a three-point support for holding the silicon sphere to be measured. In addition to the latter, there are two opposing Fizeau lenses with spherical reference surfaces that are concentric to the sphere, so that the center of the sphere forms the center of the structure.

Three measurements are required to determine the diameter:

  1. Two to determine the distances between the individual reference surfaces and the corresponding surface segment of the sphere and for each arm of the interferometer and
  2. a measurement of the reference surface distance in the empty etalon.
Measuring principle

Consequently, the diameter of the ball results according to

During the measurement of the smaller distances and the ball rests on the three-point support inside the interferometer housing. Underneath the three-point support there is a rotating and lifting mechanism for orientation on the sphere section to be measured and for moving the sphere into a position above the beam path so that the size of the empty etalon can be determined. This inner part of the interferometer is surrounded by a vacuum chamber in order to reduce disruptive influences due to the refractive index of air. Outside the chamber there are two collimators with a focal length of 1.6 m, which shape the light emerging from the multimode fibers into a plane wave front to illuminate the lenses .

Due to the large mass and a weak thermal coupling between the interferometer frame and the vacuum chamber, very low temperature gradients and high temperature stabilities are achieved with this structure. The measurements are nominally carried out at 20 ° C. Any remaining fluctuations of a few millikelvin can be corrected later in the data evaluation. A Pt 25 resistance thermometer in a copper block, which is attached in the central area of ​​the interferometer, is used to determine the temperature precisely . Differential temperatures relative to this temperature are determined with the aid of thermocouple pairs . This precise logging of the temperature is a prerequisite for correcting the thermal expansion of the measuring object.

Exemplary measurement result

The animation shows the diameter topography of a measured silicon sphere as an example. Shown are the shape deviations around the mean diameter, the color scale being around 105 nm. The mean diameter itself is around 93 mm, six orders of magnitude more! In addition, a photo of an original ball in the transport container is shown for comparison.

See also

literature

  • G. Bartl: Interferometric determination of absolute spherical radius topographies. Dissertation, Technical University of Braunschweig, 2010 ( [1] , accessed on August 2, 2010).
  • A. Nicolaus, G. Bartl, A. Peter: Interferometry on spheres. In: PTB-Mitteilungen. 120, 2010, pp. 23-30.

Web links

Individual evidence

  1. ^ RA Nicolaus, G. Bönsch: A Novel Interferometer for Dimensional Measurement of a Silicon Sphere . In: IEEE Trans. Instrum. Meas. tape 46 , no. 2 , 1997, p. 563-565 , doi : 10.1109 / 19.571915 .
  2. a b c 10th CGPM 1954
  3. 14th CGPM 1971
  4. G. Girard: The Third Periodic Verification of National Prototypes of the Kilogram (1988-1992) . In: Metrologia . tape 31 , no. 4 , 1994, pp. 317-336 , doi : 10.1088 / 0026-1394 / 31/4/007 .
  5. P. Becker, H. Friedrich, K. Fujii, W. Giardini, G. Mana, A. Picard, H.-J. Pohl, H. Riemann, S. Valkiers: The Avogadro constant determination via enriched silicon-28 . In: Meas. Sci. Technol. tape 20 , no. 9 , 2009, p. 092002 , doi : 10.1088 / 0957-0233 / 20/9/092002 .
  6. G. Bartl, A. Nicolaus, E. Kessler, R. Schödel, P. Becker: The coefficient of thermal expansion of highly enriched 28 Si . In: Metrologia . tape 46 , no. 5 , June 24, 2009, p. 416-422 , doi : 10.1088 / 0026-1394 / 46/5/005 .