20. - 22. 10. 2009, Rožnov pod Radhoštěm, Česká Republika HIGH-PRECISION INTERFEROMETRY IN THE NANOSCALE WITH COMPENSATION OF FLUCTUATIONS OF REFREACTIVE INDEX OF AIR Josef Lazar, Ondřej Číp, Martin Čížek, Jan Hrabina, and Zdeněk Buchta a a ÚSTAV PŘÍSTROJOVÉ TECHNIKY AV ČR, v.v.i., Královopolská 147, 612 00 Brno, Česká republika, [email protected]Abstract We present a concept of an interferometric system which is compensated for varying refractive index of air in the measuring axis. The main idea is based on a principle where the wavelength of the laser source is derived not from an optical frequency of the stabilized laser but from a fixed length being a base-plate or a frame of the whole measuring setup. This will result into stabilization of the wavelength of the laser source in atmospheric conditions to mechanical length of suitable etalon made of a material with very low thermal expansion. There are glass ceramics available on the market with thermal expansion coefficients on the level 10 -8 which significantly exceeds the limits of uncertainty posed by independent evaluation of refractive index of air. This approach represents a contribution to high-precision dimensional metrology in the nanoscale. 1. INTRODUCTION Measurement of geometrical quantities with direct link to primary etalon is a task for laser interferometry. This is a method where a highly precise wavelength generated by an etalon laser is used as a scale for real distance evaluation. Relative uncertainty of interferometric measurements is clearly given by the precision/stability of the laser source. In case of measurement done by single wavelength (interference fringe) counting this can be the case only over large distances where counting quantization error is negligible. With advanced electronic signal processing it is possible to resolve and interpolate even very small fractions of the fringe. The limit seems to be a technical problem where noise of the laser, dynamics of the analog-to-digital conversion and bandwidth being the decisive factors. Thus modern systems can boast with resolutions on the level of tens of picometers, deep in the nanoscale. The immense dynamic range of incremental length measuring interferometer make it a primary choice where precision really matters being it measuring or calibrating large displacements in mechanical engineering or miniature positioning of a sample in local probe microscopy in nanotechnology applications. Tackling the problems with interferometric measurements in air has been the metrologic evergreen ever since the interferometer appeared. In the laboratory environment where the calibrations and comparisons of interferometers are performed the real refractometer is a must-have. The simplest configuration is a differential interferometer measuring with high resolution the difference between an air and vacuum path within a known distance of an evacuated cell [1, 2]. Further various arrangements of refractometers appeared trying to find a compact and precise way of measurement where the value of refractive index would be available on-line or at least more often than once the cell is evacuated and filled again. The systems covered movable triangular cells, flexible cells that could be elongated, and others [3, 4]. All measurements of the refractive index of air performed by refractometers or by evaluation of the Edlen formula suffer one principal limit which is the fluctuations of air along and around the laser beam axis. Furthermore there are always thermal gradients in the air mostly in the vertical direction. The sensors, primarily thermal, can be put only close to the beam, not into it and they measure only in certain points.
Transcript
20. - 22. 10. 2009, Rožnov pod Radhoštěm, Česká Republika
HIGH-PRECISION INTERFEROMETRY IN THE NANOSCALE WITH COMPENSATION OF FLUCTUATIONS OF REFREACTIVE INDEX OF AIR
Josef Lazar, Ondřej Číp, Martin Čížek, Jan Hrabina, and Zdeněk Buchta a
a ÚSTAV PŘÍSTROJOVÉ TECHNIKY AV ČR, v.v.i., Královopolská 147, 612 00 Brno, Česká republika, [email protected]
Abstract
We present a concept of an interferometric system which is compensated for varying refractive index of air in
the measuring axis. The main idea is based on a principle where the wavelength of the laser source is
derived not from an optical frequency of the stabilized laser but from a fixed length being a base-plate or a
frame of the whole measuring setup. This will result into stabilization of the wavelength of the laser source in
atmospheric conditions to mechanical length of suitable etalon made of a material with very low thermal
expansion. There are glass ceramics available on the market with thermal expansion coefficients on the level
10-8
which significantly exceeds the limits of uncertainty posed by independent evaluation of refractive index
of air. This approach represents a contribution to high-precision dimensional metrology in the nanoscale.
1. INTRODUCTION
Measurement of geometrical quantities with direct link to primary etalon is a task for laser interferometry.
This is a method where a highly precise wavelength generated by an etalon laser is used as a scale for real
distance evaluation. Relative uncertainty of interferometric measurements is clearly given by the
precision/stability of the laser source. In case of measurement done by single wavelength (interference
fringe) counting this can be the case only over large distances where counting quantization error is
negligible. With advanced electronic signal processing it is possible to resolve and interpolate even very
small fractions of the fringe. The limit seems to be a technical problem where noise of the laser, dynamics of
the analog-to-digital conversion and bandwidth being the decisive factors. Thus modern systems can boast
with resolutions on the level of tens of picometers, deep in the nanoscale. The immense dynamic range of
incremental length measuring interferometer make it a primary choice where precision really matters being it
measuring or calibrating large displacements in mechanical engineering or miniature positioning of a sample
in local probe microscopy in nanotechnology applications.
Tackling the problems with interferometric measurements in air has been the metrologic evergreen ever
since the interferometer appeared. In the laboratory environment where the calibrations and comparisons of
interferometers are performed the real refractometer is a must-have. The simplest configuration is a
differential interferometer measuring with high resolution the difference between an air and vacuum path
within a known distance of an evacuated cell [1, 2]. Further various arrangements of refractometers
appeared trying to find a compact and precise way of measurement where the value of refractive index
would be available on-line or at least more often than once the cell is evacuated and filled again. The
systems covered movable triangular cells, flexible cells that could be elongated, and others [3, 4].
All measurements of the refractive index of air performed by refractometers or by evaluation of the Edlen
formula suffer one principal limit which is the fluctuations of air along and around the laser beam axis.
Furthermore there are always thermal gradients in the air mostly in the vertical direction. The sensors,
primarily thermal, can be put only close to the beam, not into it and they measure only in certain points.
20. - 22. 10. 2009, Rožnov pod Radhoštěm, Česká Republika
Laser beam of the refractometer can again be only close to the measuring path. While the evaluation of the
refractive index of air through direct refractometery can be on the level of uncertainty between 10-7
and 10-8
,
the 10-8
seems to be a practical limit for determining the refractive index of air in stable laboratory conditions
due to thermal gradients and air fluctuations.
Practical interferometric measurements occur in the atmosphere where the speed of light differs by the factor
called index of refraction. All associated problems with the refractive index of air gave rise to a whole branch
of metrology – the refractometry. In case of all commercial interferometric systems the compensation of
index of refraction of air is done by measuring of the fundamental atmospheric parameters – temperature,
pressure and humidity of air, accompanied sometimes by the measurements of concentration of carbon
dioxide. The value of refractive index is extracted by evaluation of empirical Edlen formula [5, 6]. The limits of
the Edlen formula together with problems with measuring close to the interferometer laser beam result in
relative uncertainty achievable this way on the level of approx. 10-6
. This is quite a poor value compared to
the relative stabilities of modern laser etalons being about 10-13
(Nd:YAG iodine stabilized laser) or even
better.
The effort to put together a distance measuring interferometer and a refractometer into one setup which
could evaluate the influence of the refractive index of air during measurement or directly compensate for it
has been present in the metrology for quite a long time. There were arrangements presented where a
complex set of two separate interferometers evaluate the refractive index of air and measure the distance
[7]. This system can compensate for the refractive index but is unable to overcome the problem of
determination the refractive index in the laser beam axis. A method linking the wavelength of the laser
source to the mechanical length of some frame or board is proposed by [8]. This suggests again a set of two
identical interferometers where one is fixed in length and serves as a reference for the laser wavelength.
2. REFERENCING IN DIMENSIONAL METROLOGY
The system of dimensional metrology follows the definition of the metre and is based on primary etalons.
Length id defined as a quantity derived from the unit of time and the speed of light as a physical constant.
This is sufficient in vacuum conditions. In practice the fundamental etalons are in fact highly stable lasers
emitting light of a precise frequency. Again, in vacuum conditions the stable frequency is transferred into
stable wavelength which can be counted and used as a precise and high-resolution ruler to measure real
length. In any other environment the refractive index has to be considered and the inhomogeneity or
variability of the environment limits precision and causes the wavelength to vary (Figure 1).
Referencing the primary etalon to a wavelength has not been considered due to complications with
comparisons of etalons and availability of reference atomic transitions representing optical frequencies. In
practical interferometry where the 633 nm He-Ne laser based systems still dominate the reference is Doppler
broadened transition in Ne and relative stabilities of optical frequencies of such lasers are in the range of 10-
8. This is at the same level as the coefficient of thermal expansion of the best stable materials such as
Zerodur from Schott or ULE from Corning. There seems to be a chance to use mechanical etalons made
from these materials as a reference for stabilization of the wavelength under conditions of varying refractive
index.
20. - 22. 10. 2009, Rožnov pod Radhoštěm, Česká Republika
Fig. 1. Varying wavelength in Michelson interferometer with laser with stabilized optical frequency (A) and
interferometer with stabilized wavelength (B).
The proposed arrangement in Figure 1 represents a Michelson interferometer where the position of the main
beamsplitter and mirrors is fixed by a baseplate made of a low thermal expansion material. Constant length
of the measuring arm can be used to stabilize the laser wavelength through a constant integer number of
wavelengths within the length and detection of a stable interference fringe.
3. EXPERIMENTAL ARRANGEMENT
To prove the principle we assembled an experimental arrangement where the fixed reference length
represents a measuring range of the one-dimensional Michelson interferometer. To get the information of the
position of the movable reflector and together to have the value of the reference length in real time we
arranged a set of two counter-measuring interferometers positioned in one axis with the same both sides
reflecting plane mirror as a measuring reflector. The thickness of the mirror is also included in the overall
length and influences the resulting reference value so it has to be also made of a low thermal expansion
material. Both interferometers have to be supplied from a single laser source. Value from any of them gives
the information of the position of the movable reflector and the sum of the two output values of both
interferometers is a control value for the laser source. In Fig. 2 the principal configuration shows simplified
Michelson interferometers with semireflecting mirrors as beamsplitters, steering mirrors for light delivery and
wavelength control signals.
The configuration of the interferometric units chosen for the experiment is of a two-beam setup where both
the measuring arm and the reference arm are passing through corner-cube retroreflectors ensuring that both
output beams remain parallel without dependence on the angle deviation of the measuring plane mirror. This
does not mean that the system is insensitive to mirror angle errors. The configuration of the interferometric
unit is in Figure 3. The double beam configuration further improves optical resolution. Mechanical design of
the setup is a simple set of optics fixed to a baseplate of Zerodur ceramics and positioning of the movable
measuring mirror is in a 100 mm range through precision linear stage. Interferometric signal detection is
homodyne with polarization optics and transfer of the interference state into sine-cosine signals by means of
LASER
M
A)
B)
const.const.
n l n )= n ( c /x
SM M
LASER
M
const.
const.
n l )= n ( c /( 1 / ) x
l = N x L
nL
SM M
20. - 22. 10. 2009, Rožnov pod Radhoštěm, Česká Republika
retardation plate. This detection though more complicated compared to heterodyne electronic systems
operate with single-frequency lasers and are easy to implement when a tunable laser source in needed.
Fig. 2. Principal schematics of the inteferometric system with two countermeasuring Michelson
Interferometers and stabilization of the laser wavelength to mechanical etalon. D: detection unit, M: mirror,
