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 2006
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©  ISO 2006
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ii © ISO 2006 – All rights reserved

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

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

iv © ISO 2006 – All rights reserved

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.
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
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
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.
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).
2 © ISO 2006 – All rights reserved

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].
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.
4 © ISO 2006 – All rights reserved

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.
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.
6 © ISO 2006 – All rights reserved

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
measuring beam, two linearly polarized beam components are obtained whose directions of polarization are
perpendicular to each other. After separation of the two components in space, two different interference
systems are derived having a phase shift of 90° with respect to each other. The two photodetectors transform
the relevant parts of the light intensities into electrical signals that show a sinusoidal and a cosinusoidal
dependence on the displacement of the measuring reflector.
4.6.3 Interferometer type B (diffraction-grating interferometer)
An interferometer with a diffraction grating as measuring reflector shall be used (e.g. a Michelson
interferometer) with a light detector for sensing the interferometer signal bands and with a frequency response
covering the necessary bandwidth (cf. 4.6.1).
For methods 1B and 2B, a modified Michelson interferometer with diffraction grating is used (cf. Figures 2, 4
and 6).
The angular acceleration, the angular velocity or the rotational angle are measured by a special diffraction
grating interferometer developed on the basis of a high-resolution grating (e.g. a sine-phase grating of
2 400 grooves/mm or 3 000 grooves/mm, manufactured by holography) (examples are described in
References [12] and [13]). An optical reflection grating is located on the air-borne measuring table of the
angular vibration exciter, concentrically to the axis of rotation (cf. Figure 2). The light beam emitted by a
frequency-stabilized single-frequency He-Ne laser is split into two parallel beams striking the grating
symmetrical to the axis of rotation at the angle at which the first-order beams diffracted by reflection
(according to the diffraction formula for oblique incidence) return into the direction of the incident beam. The
first-order diffracted light beams are superposed in the optical arrangement. When the moving part is rotated,
these light beams undergo a frequency change opposite in sign and of the same amount that is proportional to
the tangential velocity and, thus, also to the angular velocity. The interfering beams give rise to a light intensity
whose significant component shows a periodic dependence on the rotational angle.
For method 3B, a homodyne quadrature interferometer with diffraction grating is used (cf. Figure 8).
In the quadrature diffraction-grating interferometer in the single measuring beam arrangement, the light beam
is split into the reference beam and the measuring beam. The measuring beam strikes the grating at the angle
at which the first-order beam diffracted by reflection returns into the direction of the incident beam. The first-
order beam diffracted in accordance with the diffraction equation for oblique incidence and the reference
beam are superimposed in the optical arrangement. The interfering light beams yield a light intensity whose
significant component depends sinusoidally on the rotational angle.
For high-accuracy requirements (relative uncertainty of calibration smaller than 0,5 %), a grating
interferometer calibration procedure shall be carried out once for a measuring table with an individual
diffraction grating disk, to accurately determine the quantization intervals of the displacement, ∆s, and of the
rotational angle, ∆Φ (cf. procedure in Clause 7).
4.7 Instrumentation for interferometer signal processing
4.7.1 General
The instrumentation used has in common that the phase-modulated electric current or voltage at the output(s)
of the photodetector(s) is demodulated to extract the vibration parameter(s) of interest (e.g. amplitude and
initial phase of the sinusoidal rotational angle). Different techniques are to be used for methods 1A, 1B
(cf. 4.7.2), methods 2A, 2B (cf. 4.7.3) and methods 3A, 3B (cf. 4.7.4).
4.7.2 Instrumentation for fringe counting (for methods 1A and 1B)
The counting instrumentation shall have the following characteristics:
a) frequency range: 1 Hz to the maximum frequency needed (20 MHz is typically used);
b) maximum uncertainty: 0,01 % of reading.
The counter may be replaced by a ratio counter offering the same uncertainty.
4.7.3 Instrumentation for zero-point detection (for methods 2A and 2B)
A tunable bandpass filter or spectrum analyser with the following characteristics shall be used:
a) frequency range: u 800 Hz to W 1,6 kHz;
b) bandwidth: < 12 % of centre frequency;
c) filter slopes: equal to or greater than 24 dB per octave;
d) signal-to-noise ratio: greater than 70 dB below maximum signal;
e) dynamic range: greater than 60 dB.
Instrumentation for zero detection (not needed with spectrum analyser), with a frequency range from 800 Hz
to 1,6 kHz shall be used. The range shall be sufficient for detecting output noise from the bandpass filter.
4.7.4 Instrumentation for sine-approximation (for methods 3A and 3B)
A waveform recorder with a computer interface capable of analog-to-digital conversion and storage of the two
interferometer quadrature outputs and the accelerometer output shall be used. The amplitude resolution, the
sampling rate and the memory shall be sufficient for calibration in the intended amplitude range with the
uncertainty specified in Clause 3. Typically, an amplitude resolution of W 10 bits is used for the accelerometer
output. For the quadrature signal outputs of the interferometer, a resolution of W 8 bits is sufficient. A two-
channel waveform recorder may be used for the interferometer output signals, and another waveform recorder
(with higher resolution and lower sampling rate) for the angular transducer output signal. In each case,
conversion of the data from the interferometer and the angular transducer output signals shall begin and end
at the same time, with an uncertainty that meets the uncertainty requirements of Clause 3.
A sufficient number of samples (cf. 10.3) are required of the shortest period of the interferometer output signal
occurring at maximum velocity. For a particular angular acceleration amplitude, at decreasing frequencies,
larger displacement amplitudes occur that require higher sampling rates and larger memories. If such
capabilities are not available, the angular acceleration amplitude shall be reduced.
8 © ISO 2006 – All rights reserved

To calibrate an angular accelerometer at a vibration frequency of 10 Hz and an angular acceleration amplitude
of 1 000 rad/s , a memory of W 4 Mbytes should be used if a sampling frequency of W 20 kHz is applied.
A computer with data-processing program (for methods 3A and 3B) in accordance with the procedure for the
calculations stated in 10.4 shall be used.
4.8 Voltage instrumentation, measuring true r.m.s. accelerometer output
Voltage instrumentation, measuring true r.m.s. accelerometer output, having the following characteristics shall
be used:
a) frequency range: u 1 Hz to W 1,6 kHz;
b) maximum uncertainty: 0,1 % of reading.
The r.m.s. value shall be multiplied by a factor of 2 to obtain the (single) amplitude.
For methods 1A, 1B, 2A and 2B, an r.m.s. voltmeter shall be used. For methods 3A and 3B, special voltage-
measuring instrumentation in accordance with 4.7.4 shall be used; an r.m.s. voltmeter may be applied in
addition (optional).
4.9 Distortion-measuring instrumentation
Distortion-measuring instrumentation capable of measuring the total harmonic distortion of < 1 % to 5 % and
with the following characteristics shall be used.
a) frequency range: u 1 Hz to W 1,6 kHz, with the capability of measuring up to the fifth harmonic;
b) maximum uncertainty: 10 % of reading in the distortion range of 0,5 % to 5 %.
4.10 Oscilloscope (optional)
An oscilloscope for optimizing the interferometer and for checking the waveform of the interferometer and
accelerometer signals, with a frequency range from 1 Hz to 2 MHz minimum, may be used.
4.11 Other requirements
The transducer to be calibrated shall be structurally rigid. The base strain sensitivity, the transverse sensitivity
and the stability of the angular accelerometer/amplifier combination (if calibrated as a single unit) shall be
taken into account in the calculation of the uncertainty of measurement (cf. Annex A).
All effects influencing the measurement result shall be included in the uncertainty calculation.
Methods 1B, 2B and 3B can be applied to calibrate rotational laser vibrometers if the motion parameter is
sensed simultaneously by the standard device (cf. 4.6 and 4.7) and by the laser interferometer being
calibrated. If the motion sensing periods of both measurement systems are different, the rotational vibration
amplitude shall be sufficiently stable to meet the uncertainty requirement of Clause 3. An example of an
arrangement for the calibration of rotational laser interferometers is shown in Figure 11.
5 Ambient conditions
The calibration shall be carried out under the following ambient conditions:
a) room temperature: (23 ± 3) °C;
b) relative humidity: 75 % max.
Care should be taken that external vibration and noise do not affect the quality of the measurements.
6 Preferred angular accelerations and frequencies
The angular accelerations (amplitude or r.m.s. value) and frequencies equally covering the angular
accelerometer range should preferably be chosen from the following series;
a) angular acceleration (methods 1A, 1B, 3A and 3B):
2 2 2 2 2 2 2 2 2
⎯ 0,1 rad/s , 0,2 rad/s , 0,5 rad/s , 1 rad/s , 2 rad/s , 5 rad/s , 10 rad/s , 20 rad/s , 50 rad/s ,
2 2 2 2 2
100 rad/s , 200 rad/s , 500 rad/s , 1 000 rad/s (1 000 rad/s is valid for amplitude only);
b) frequency:
⎯ selected from the standardized one-third-octave frequency series (in accordance with ISO 266)
between 1 Hz and 1,6 kHz or the series of radian(s) frequencies evolving from ω = 1 000 rad/s.
7 Common procedure for all six methods
Methods A1, B1, A2, B2, A3 and B3 have in common that the interferometer (type A or B) senses a
displacement at a point situated at a distance, R, the “effective radius”, from the axis of rotation of the circular
ˆ
measuring table of the angular vibration exciter. From the displacement amplitude, s sensed by the
ˆ
interferometer, the amplitude of the rotational angle, Φ , is obtained using Equation (2):
ˆ
s
ˆ
Φ = (2)
R
where R is the effective radius whose value shall be determined from a special interferometer calibration
carried out once before the interferometer can be used for transducer calibrations. In all cases, the
ˆ
measurement of s is based on the comparison with an accurately known value of a very small length in the
sub-micrometer range. For interferometer type A, this is the wavelength λ = 0,632 81 µm of the laser of the
red helium-neon type, which is known a priori. In interferometer type B, this is the gating constant, g (groove
length, i.e. grating constant of 0,333 33 µm of a sine-phase diffraction grating having 3 000 grooves/mm). The
measure, g, shall be accurately known (from length measurements carried out by the manufacturer of the
diffraction grating).
NOTE If the grating constant is not known with sufficient accuracy, the angular quantization interval ∆Φ, which
corresponds to one interferometer signal period, can be determined by a special diffraction grating interferometer
[13]
calibration . Then, the expression ∆s = R ∆Φ with the displacement quantization interval ∆s (e.g. ∆s = g in a single-beam
arrangement of interferometer type B, cf. Figure 8) can be used to eliminate the radius, R; cf. Equation (2), which is no
ˆ
longer used to calculate Φ .
ˆ
All six methods apply the result for the rotational angle amplitude, Φ , obtained from Equation (2) to calculate
the following:
a) sensitivity (magnitude), S , of rotational angle transducers, using Equation (3):
Φ
uˆ
S = (3)
Φ
ˆ
Φ
b) sensitivity (magnitude), S , of angular velocity transducers, using Equations (4) and (5):
Ω
uˆ
S = (4)
Ω
ˆ
Ω
where
ˆ
ˆ
ΩΦ=π2 × f (5)
10 © ISO 2006 – All rights reserved

c) sensitivity (magnitude), S , of angular accelerometers, using Equations (6) and (7):
α
uˆ
S = (6)
α
αˆ
where
ˆ
αˆ=π4 × f Φ (7)
where
uˆ is the amplitude of the angular transducer output, u, (e.g. output voltage of an angular
accelerometer);
ˆ
Ω is the amplitude of the angular velocity, Ω ;
αˆ is the amplitude of the angular acceleration, α .
As the phase shift of the complex sensitivity of angular transducers can be measured only by methods 3A
and 3B, the common procedures used for phase shift calibrations are specified in Clause 10.
8 Methods using fringe-counting (methods 1A and 1B)
8.1 General
This method is applicable to sensitivity magnitude calibration the frequency range from 1 Hz to 800 Hz.
NOTE At the frequency of 800 Hz and an angular acceleration amplitude of 1 000 rad/s , the rotational angle
−5
amplitude is 4 × 10 rad. This corresponds to a displacement amplitude of 2 µm if a retro-reflector or a diffraction grating
is arranged in a distance of 50 mm from the axis of rotation (i.e. a diffraction grating at the lateral surface of a disk 100 mm
in diameter). Using the fringe-counting method without special means to suppress the quantization error (see
References [1] and [11]), displacement amplitudes down to 2 µm can be measured with an uncertainty specified in
[1], [11]
Clause 3. Methods 1A and 1B can also be applied at smaller amplitudes if the quantization error is suppressed .
This allows calibration at a specified angular acceleration amplitude (e.g. 1 000 rad/s ) to be performed at higher
frequencies.
In both interferometer types A and B (i.e. in methods 1A and 1B), the number of signal periods (e.g. intensity
maxima), N, is given by Equation (7):
ˆ
Ns=∆4/s (8)
resulting in Equation (9)
f
∆s
f
sˆ=× (9)
4 f
where
sˆ is the displacement amplitude sensed by the laser interferometer, required to apply Equations (2)
to (7);
∆s is the quantization interval, equal to λ/2, specified by Equations (10) and (11) for the two versions of
interferometer type A and by Equations (12) and (13) for the two versions of interferometer type B;
f is the frequency of the angular vibration exciter;
f is the (mean) fringe frequency.
f
Inserting the relevant expression for ∆s, i.e. Equations (10) or (11) for the type A interferometer and
Equations (12) or (13) for the type B interferometer and using Equation (2) to transform the displacement into
ˆ ˆ
a rotational angle, the rotational angle amplitude, Φ , is obtained. The angular velocity amplitud
...