ISO 16063-15:2006

INTERNATIONAL ISO
STANDARD 16063-15
First edition
2006-08-01

Methods for the calibration of vibration
and shock transducers —
Part 15:
Primary angular vibration calibration by
laser interferometry
Méthodes pour l'étalonnage des transducteurs de vibrations et de
chocs —
Partie 15: Étalonnage angulaire primaire de vibration par interférométrie
laser




Reference number
ISO 16063-15:2006(E)
©
ISO 2006

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ISO 16063-15:2006(E)
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ISO 16063-15:2006(E)
Contents Page
Foreword. iv
1 Scope . 1
2 Normative references . 2
3 Uncertainty of measurement . 2
4 Requirements for apparatus. 2
4.1 General. 2
4.2 Frequency generator and indicator . 3
4.3 Power amplifier/angular vibration exciter combination. 3
4.4 Seismic block(s) for vibration exciter and laser interferometer . 5
4.5 Laser. 5
4.6 Interferometer. 5
4.7 Instrumentation for interferometer signal processing. 8
4.8 Voltage instrumentation, measuring true r.m.s. accelerometer output. 9
4.9 Distortion-measuring instrumentation . 9
4.10 Oscilloscope (optional). 9
4.11 Other requirements. 9
5 Ambient conditions . 9
6 Preferred angular accelerations and frequencies . 10
7 Common procedure for all six methods. 10
8 Methods using fringe-counting (methods 1A and 1B). 11
8.1 General. 11
8.2 Common test procedure for methods 1A and 1B. 12
8.3 Expression of results . 12
9 Methods using minimum-point detection (methods 2A and 2B) . 16
9.1 General. 16
9.2 Common test procedure for methods 2A and 2B. 17
9.3 Expression of results . 17
10 Methods using sine approximation (methods 3A and 3B) . 21
10.1 General. 21
10.2 Procedure applied to methods 3A and 3B . 22
10.3 Data acquisition . 27
10.4 Data processing. 27
11 Reporting of calibration results . 29
Annex A (normative) Uncertainty components in primary angular vibration calibration of vibration
and shock transducers by laser interferometry . 30
Annex B (normative) Equations for the calculation of the angular quantities of rotational angle, Φ,
angular velocity, Ω, and angular acceleration, α, and of the sensitivities of angular
transducers: rotational angle transducers, S , of angular velocity transducers, S , and
Φ Ω
angular accelerometers, S . 36
α
Bibliography . 42

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ISO 16063-15:2006(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 16063-15 was prepared by Technical Committee ISO/TC 108, Mechanical vibration and shock,
Subcommittee SC 3, Use and calibration of vibration and shock measuring instruments.
ISO 16063 consists of the following parts, under the general title Methods for the calibration of vibration and
shock transducers:
⎯ Part 1: Basic concepts
⎯ Part 11: Primary vibration calibration by laser interferometry
⎯ Part 12: Primary vibration calibration by the reciprocity method
⎯ Part 13: Primary shock calibration using laser interferometry
⎯ Part 15: Primary angular vibration calibration by laser interferometry
⎯ Part 21: Vibration calibration by comparison to a reference transducer
⎯ Part 22: Shock calibration by comparison to a reference transducer
The following additional parts are under preparation:
⎯ Part 23, addressing the angular vibration calibration by comparison to reference transducers
⎯ Part 31, addressing the testing of transverse vibration sensitivity
⎯ Part 32, addressing the resonance testing
⎯ Part 41, addressing the calibration of laser vibrometers
⎯ Part 42, addressing the calibration of seismometers

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INTERNATIONAL STANDARD ISO 16063-15:2006(E)

Methods for the calibration of vibration and shock transducers —
Part 15:
Primary angular vibration calibration by laser interferometry
1 Scope
This part of ISO 16063 specifies the instrumentation and procedures used for primary angular vibration
calibration of angular transducers, i.e. angular accelerometers, angular velocity transducers and rotational
angle transducers (with or without amplifier) to obtain the magnitude and the phase shift of the complex
sensitivity by steady-state sinusoidal vibration and laser interferometry. The methods specified in this part of
ISO 16063 are applicable to measuring instruments (rotational laser vibrometers in particular) and to angular
transducers as defined in ISO 2041 for the quantities of rotational angle, angular velocity and angular
acceleration.
2
It is applicable to a frequency range from 1 Hz to 1,6 kHz and a dynamic range (amplitude) from 0,1 rad/s to
2
1 000 rad/s (frequency-dependent).
These ranges are covered with the uncertainty of measurement specified in Clause 3. Calibration frequencies
lower than 1 Hz (e.g. 0,4 Hz, which is a reference frequency used in other International Standards) and
2
angular acceleration amplitudes smaller than 0,1 rad/s can be achieved using method 3A or method 3B
specified in this part of ISO 16063, in conjunction with an appropriate low-frequency angular vibration
generator.
Method 1A (cf. Clause 8: fringe-counting, interferometer type A) and method 1B (cf. Clause 8: fringe-counting,
interferometer type B) are applicable to the calibration of the magnitude of complex sensitivity in the frequency
range of 1 Hz to 800 Hz and under special conditions, at higher frequencies. Method 2A (cf. Clause 9:
minimum-point method, interferometer type A) and method 2B (cf. Clause 9: minimum-point method,
interferometer type B) can be used for sensitivity magnitude calibration in the frequency range of 800 Hz to
1,6 kHz. Method 3A (cf. Clause 10: sine-approximation method, interferometer type A) and method 3B
(cf. Clause 10: sine-approximation method, interferometer type B) can be used for magnitude of sensitivity
and phase calibration in the frequency range of 1 Hz to 1,6 kHz. Methods 1A, 1B and 3A, 3B provide for
calibrations at fixed angular acceleration amplitudes at various frequencies. Methods 2A and 2B require
calibrations at fixed rotational angle amplitudes (angular velocity amplitude and angular acceleration
amplitude vary with frequency).
NOTE 1 The numbering 1 to 3 of the methods characterizes the handling of the interferometer output signal(s)
analogous to ISO 16063-11: number 1 for fringe counting, number 2 for minimum-point detection and number 3 for sine-
approximation. Each of these signal handling procedures can be used together with interferometer types A and B specified
in this part of ISO 16063.
Interferometer type A designates a Michelson or Mach-Zehnder interferometer with retro-reflector(s) located at a radius, R,
from the axis of rotation of the angular exciter. This interferometer type is limited to rotational angle amplitudes of 3°
maximum. Interferometer type B designates a Michelson or a Mach-Zehnder interferometer using a circular diffraction
grating implemented on the lateral surface of the circular measuring table. This interferometer type is not limited as
regards the rotational angle amplitude if the diffraction grating covers the whole lateral surface of the disk (i.e. 360°).
Usually, the maximum angular vibration is, in this case, limited by the angular vibration exciter.
NOTE 2 Though the calibration methods specified in this part of ISO 16063 are applicable to angular transducers
(according to definition in ISO 2041) and, in addition, to measuring instrumentation for angular motion quantities, the
specifications are given for transducers as calibration objects, for the sake of simplified description. Some specific
information for the calibration of rotational laser vibrometers is given in 4.11 and Figure 11.
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ISO 16063-15:2006(E)
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 266, Acoustics — Preferred frequencies
ISO 2041:1990, Vibration and shock — Vocabulary
ISO 16063-1:1998, Methods for the calibration of vibration and shock transducers — Part 1: Basic concepts
3 Uncertainty of measurement
The limits of the uncertainty of measurement applicable to this part of ISO 16063 shall be as follows:
a) for the magnitude of sensitivity:
⎯ 0,5 % of the measured value at reference conditions,
⎯ u 1 % of the measured value outside reference conditions;
b) for the phase shift of sensitivity:
⎯ 0,5° of the measured value at reference conditions,
⎯ u 1° of the reading outside reference conditions.
Recommended reference conditions are as follows:
⎯ frequency: 160 Hz, 80 Hz, 40 Hz, 16 Hz or 8 Hz (or radian frequency, ω: 1 000 rad/s, 500 rad/s, 250 rad/s,
100 rad/s or 50 rad/s);
2 2 2
⎯ angular acceleration: (angular acceleration amplitude or r.m.s. value): 100 rad/s , 50 rad/s , 20 rad/s ,
2 2 2 2
10 rad/s , 5 rad/s , 2 rad/s or 1 rad/s .
Amplifier settings shall be selected for optimum performance with respect to noise, distortion and influence
from cut-off frequencies.
The uncertainty of measurement is expressed as the expanded measurement uncertainty in accordance with
ISO 16063-1, for the coverage factor k = 2 (referred to, in short, as “uncertainty”).
4 Requirements for apparatus
4.1 General
Clause 4 gives recommended specifications for the apparatus necessary to comply with the scope of Clause 1
and to obtain the uncertainties of Clause 3.
If desired, systems covering only parts of the ranges may be used, and normally different systems
(e.g. exciters) should be used to cover all the frequency and dynamic ranges.
NOTE The apparatus specified in Clause 4 covers all devices and instruments required for any of the six calibration
methods described in this part of ISO 16063. The assignment to a particular method is indicated (cf. Figures 2, 3, 4, 5, 6, 7,
8 and 10).
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ISO 16063-15:2006(E)
4.2 Frequency generator and indicator
A frequency generator and indicator having the following characteristics shall be used:
a) uncertainty of frequency: maximum 0,05 % of reading;
b) frequency stability: better than ± 0,05 % of reading over the measurement time;
c) amplitude stability: better than ± 0,05 % of reading over the measurement time.
4.3 Power amplifier/angular vibration exciter combination
4.3.1 General
A power amplifier/angular vibration exciter combination having the following characteristics shall be used:
a) total harmonic distortion: 2 % maximum;
NOTE 1 This specification relates to the input quantity for the transducer to be calibrated.
NOTE 2 If method 3A or method 3B is used, greater harmonic distortions can be tolerable.
b) transverse, and rocking angular acceleration: sufficiently small to prevent excessive effects on the
calibration results. For interferometer type A, a transverse motion of less than 1 % of the tangential
motion component at the minimum rotational angle displacement can be required. For interferometer
type B, a maximum lateral motion (including eccentricity) of 2 µm is tolerated, which can be achieved only
if the moving part (measuring table) of the angular exciter is carried in a high-precision rotational air
bearing;
c) hum and noise: 70 dB minimum below full output;
d) stability of angular acceleration amplitude: better than ± 0,05 % of reading over the measurement period.
4.3.2 Electro-dynamic angular vibration exciter
An electrodynamic vibration exciter is based on the Lorentz force acting on electric charge carriers when
these move through a magnetic field.
In analogy to common electrodynamic vibration exciters designed to generate rectilinear vibration, the coil
located in the magnetized air gap of a magnetic circuit can be so designed that the Lorentz force generates a
dynamic torque exciting the measuring table with the angular transducer to be calibrated to angular vibration.
In the working frequency range (i.e. 1 Hz to 1,6 kHz), the amplitude of angular acceleration is proportional to
the amplitude of the electric current carried through the coil. An example of an angular vibration exciter is
shown in Figure 1. The maximum rotational amplitude is in this case limited to 30° (i.e. double amplitude:
1 rad). Another example of an angular acceleration exciter (amplitude of 60°, i.e. 1 rad) is described in
Reference [14].
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ISO 16063-15:2006(E)

Key
1 angular accelerometer
2 diffraction grating
3 air bearing
4 housing
5 coil
6 magnet
Figure 1 — Example of an angular exciter (mode of function)
4.3.3 Angular vibration exciter based on a brushless electric motor
Special angular exciters have been designed and manufactured for angular transducer calibration using
commercial electric motors.
For the testing of inertial navigation sensors, so-called “rate tables” have been developed for many years.
These are often equipped with brushless, three-phase, hollow-shaft motors that are electronically commutated
and servo-controlled, in particular for the angular velocity, i.e. angular rate operating mode. Normally, a
constant angular velocity is generated. Often, sinusoidal angular velocities with low distortion are achieved.
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ISO 16063-15:2006(E)
The progress in control made over the last few years allows this exciter type to be used even to generate
angular acceleration. A basic requirement is the use of an air bearing as in the flat-coil exciter (cf. 4.3.2).
As the distortion increases after differentiation, the calibration of angular accelerometers can require a
frequency-selective measurement of the transducer output signal, which is ensured by the use of method 3A
or 3B (i.e. sine-approximation).
4.4 Seismic block(s) for vibration exciter and laser interferometer
The angular vibration exciter and the interferometer shall be mounted on the same heavy block or on two
different heavy blocks so as to prevent relative motion due to ground motion, or to prevent the reaction of the
vibration exciter's support structure from excessively influencing the calibration results.
When a common seismic block is used, this should have a moment of inertia at least 2 000 times that of the
moving mass. This causes less than 0,05 % reactive angular vibration of angular transducer and
interferometer. If the moment of inertia of the seismic block is smaller, its motion generated by the vibrator
shall be taken into account.
To suppress disturbing effects of ground motion, the seismic block(s) used in the frequency range of 1 Hz to
1,6 kHz should be suspended on damped springs designed to reduce the uncertainty component due to these
effects to less than 0,1 %.
4.5 Laser
A laser of the red helium-neon type or a single-frequency laser with another wavelength of known value shall
be used. Under laboratory conditions (i.e. at an atmospheric pressure of 100 kPa, a temperature to 23 °C and
a relative humidity of 50 %), the wavelength of a red helium-neon laser is 0,632 81 µm.
If the laser is provided with a manual or automatic atmospheric compensation device, this shall be set to zero
or switched off.
4.6 Interferometer
4.6.1 General
The interferometer may be used to transform
⎯ the rotational angle, Φ(t), into a proportional phase shift, ϕ (t), of the interferometer output signal,
M
⎯ the angular velocity, Ω(t), into a proportional frequency shift, f (t) (Doppler frequency), of the
D
interferometer output signal.
For both transformations, a homodyne or a heterodyne interferometer (cf. Figures 3 to 8 and 10) and a one-
channel or two-channel arrangement (cf. Figures 3 to 8 and 10) may be used.
The first transformation of Φ(t) into ϕ (t) is specified in this part of ISO 16063 as a standard procedure
M
whereas the latter transformation of Ω(t) into f (t) is given as an option with reference to detailed descriptions
D
in the literature.
The interferometer types A and B basically have in common that the measuring beam senses a translational
displacement motion component so that an interferometer arrangement designed for rectilinear vibration
measurements can be used. To make the application of such conventional interferometers possible, the
quantity of rotational motion to be measured is converted into a representative translational displacement
motion component using retro-reflector(s) as measuring reflector(s) for interferometer type A, and a diffraction
grating arranged on the rotary measuring table for interferometer type B. In the latter case, an optically
reflecting diffraction grating is to be arranged on the lateral surface of an air-borne rotary table to meet the
requirement of the tolerable eccentricity of 2 µm.
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ISO 16063-15:2006(E)
For methods 1A, 1B (see Figures 3 and 4) and Methods 2A, 2B (see Figures 5 and 6), a common Michelson
interferometer with a single light detector is sufficient.
The Michelson interferometer can be realized with a single measuring beam or with two measuring beams.
For methods 3A, 3B, (see Figures 7 and 8), a modified Michelson interferometer with quadrature signal
outputs, with two light detectors for sensing the interferometer signal beams, shall be used. The modified
Michelson interferometer may be designed according to Figure 9. A quarter wavelength retarder converts the
incident, linearly polarized light into two measuring beams with perpendicular polarization states and a phase
shift of 90°. After interfering with the linearly polarized reference beam, the two components with
perpendicular polarization shall be separated in space using appropriate optics (e.g. a Wollaston prism or a
polarizing beam splitter), and detected by two photodiodes.
The two outputs of the modified Michelson interferometer shall have offsets of less than ± 5 % in relation to
the amplitude, relative amplitude deviations of less than ± 5 % and deviations of less than ± 5° from the
nominal angle of 90°. To comply with these tolerances, appropriate means shall be provided to adjust the
offset, the signal level and the angle between the two interferometer signals.
At large rotational angles, it can be difficult to maintain the tolerances stated above for the deviations of the
two outputs of the modified Michelson interferometer. To comply with the uncertainty of measurement of
−2
Clause 3, the above tolerances shall be complied with at least for small rotational angles of up to 2 × 10 rad.
For greater amplitudes, greater tolerances are permitted.
−2 2
EXAMPLE For a rotational angle of 2,5 × 10 rad (i.e. angular acceleration amplitude of 1 rad/s at a frequency of
1 Hz), the tolerances can be extended to ± 10 % for the offsets and for the relative amplitude deviations, and to ± 20° for
the deviation from the nominal angle of 90° (see also NOTE 1 of 10.2).
The tolerances stated above are valid without correction of quadrature fringe measurement errors in
[6]
interferometer. If the correction procedure after Heydemann is applied, greater tolerances are permitted.
For methods 1A, 1B, 2A, 2B, 3A or 3B, another suitable interferometer, e.g. a (modified) Mach-Zehnder
heterodyne interferometer (cf. Figure 10) may be used in the place of the (modified) Michelson interferometer.
An interferometer of type A (cf. 4.6.2) or B (cf. 4.6.3) shall be used with a light detector to sense the
interferometer signal bands and with a frequency response covering the bandwidth necessary. The maximum
bandwidth (frequency f ) needed can be calculated from the maximum angular velocity amplitude, Ω
max max
using Equation (1):
Ω R
max
f = (1)
max
∆s
where
R is the effective radius (cf. 4.6.2 for the definition for interferometer of type A and 4.6.3, for
interferometer of type B);
∆s is the displacement quantization interval of the interferometer.
For interferometer type A, ∆s = λ/2 in the single measuring beam arrangement and ∆s = λ/4 in the two-beam
arrangement with the laser wavelength, λ. For interferometer type B, ∆s = g in the single measuring beam
arrangement and ∆s = g/2 in the two-beam arrangement with the grating constant, g.
4.6.2 Interferometer type A (retro-reflector interferometer)
For methods 1A and 2A, an interferometer of the Michelson type with retro-reflector(s) as measuring
reflector(s) shall be used with a light detector for sensing the interferometer signal bands and a frequency
response covering the necessary bandwidth (cf. 4.6.1). To compensate the influence of the disturbing motion,
a two-beam arrangement (for an example, cf. Figures 3 and 5) shall be used with two retro-reflectors mounted
symmetrically (i.e. shifted by 180°) at a distance, R, from the axis of rotation.
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ISO 16063-15:2006(E)
The laser beam emitted by the laser passes to a beam splitter which splits up the beam into two components
that are fed in parallel to the retro-reflectors. The reflected beams are superimposed on each other and the
relevant part of the resulting light intensity is transformed by the photodetector into an electrical signal (briefly
referred to as interferometer signal).
NOTE The two-beam arrangement leads not only to compensation of the disturbing motion (e.g. from ground
vibration) but also to doubling of the sensitivity (quantization interval of λ/4 instead of λ/2). The retro-reflectors (instead of
plane mirrors) compensate (in a certain range, cf. Appendix B) for the tilting effect of the rotational motion. Moreover, the
interferometer accommodates (in a certain range) disturbing motion in the transverse direction without the uncertainty of
measurement being affected.
For method 3A, a quadrature interferometer with retro-reflectors, measuring and reference reflectors shall be
used. In the homodyne interferometer version shown in Figures 7 and 9, the light source is a stabilized single-
frequency laser. The diameter of the laser beam is expanded by lenses to reduce the divergence of the beam.
The polarized laser beam is split by the beam splitter into a measuring beam and a reference beam. The
reference beam is reflected and shifted in parallel by a retro-reflector (reference reflector). As the λ/8
retardation waveplate is traversed twice, a path difference of λ/4 is obtained. At the same time, the reflected
laser beam is split into two beams, each with a direction of polarization orthogonal to the other, that show a
phase shift of 90° (i.e. circular polarization). The measuring beam is also shifted in parallel when reflected by
the retro-reflector mounted on the measuring table, retaining its linear polarization. The linearly polarized
reflected measuring beam and the circularly polarized reference beam are superimposed. When passing the
Wollaston prism, which is inclined by 45° with reference to the direction of polarization of the reflected
...