Holographic Measurement of the Acoustical 3D Output by ...€¦ · “Toole, F. (2008). Sound Reproduction: The Acoustics and Psychoacoustics of Loudspeakers and Rooms” 1/r law
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LOGAN,NEAR FIELD SCANNING, 1
Holographic Measurement of the Acoustical 3D Output by
Near Field Scanning
2015
by Dave Logan, Wolfgang Klippel, Christian Bellmann, Daniel Knobloch
LOGAN,NEAR FIELD SCANNING, 2
Introductions
LOGAN,NEAR FIELD SCANNING, 3
AGENDA
1. Introduction to directivity measurement
2. Pro and Cons of conventional far field measurements
3. Near Field Measurements are beneficial !
4. Why do we need a holographic post processing ?
5. Critical evaluation of the new technique
6. Practical application and examples
7. Conclusion
LOGAN,NEAR FIELD SCANNING, 4
Conventional Far-Field Measurements
(a time line)
• Far-Field Measurement in Anechoic Chambers (1930’s, Beranek and Sleeper 1946)
– Realized as a half and full space
– Good absorptions of room reflections (> 100 Hz)
– High ambient noise isolation
– Controlled climate condition and avoids wind effects
• Far-Field Measurement under simulated free-field condition bygating or windowing the impulse response (Heyser 1967-69, Berman and Fincham 1973)
– Good suppression of room reflections at higher frequencies
– Lower SNR ambient noise separation (SNR)
– Limited low frequency resolution (depends on time difference betweendirect sound and first reflection
LOGAN,NEAR FIELD SCANNING, 5
Problems
• Low frequency measurements (accuracy, resolution)
limited by acoustical environment
• High frequency measurement requires far field
condition
• Phase response measured in far field depends on
temperature field and air movement
• An anechoic chamber is an expensive and long-term
investments which can not be moved
LOGAN,NEAR FIELD SCANNING, 6
Why are Far-Field Condition used ?
“Toole, F. (2008). Sound Reproduction: The Acoustics and Psychoacoustics of Loudspeakers and Rooms”
1/r law is not
applicable in
the near field
In the far field of the source the
sound level falls 6 dB per
doubling the distance (1/r law)
Used for extrapolation of the
measured sound pressure to a
larger distance
Conventional
far-field
measurements
LOGAN,NEAR FIELD SCANNING, 7
How to Ensure Far-Field Condition ?
Requirements:
• Distance rfar >> d
(geometrical dimension of
the DUT)
• Distance rfar >> λ
(wavelength of the signal)
• ratio rfar /d >> d/λ
region of validity only in the far field r>rfar
extrapolateextrapolate
extrapolate extrapolate
d
Large loudspeaker systems (e.g. line arrays) require large anechoic rooms !
LOGAN,NEAR FIELD SCANNING, 8
How to perform Directivity Measurements in the Far Field ?
P
U
S
H
A
M
PInput
Outpu
tTurntable
Multiplexer
Analyzer
Amplifier
Loud-
speaker
anechoic
room
The sound pressure is measured
multiple measurement points
located on sphere with radius r
according to the desired resolution:
5 degree 2592 points
2 degree 16200 points
1 degree 64800 points
Accuracy of measured response
(phase !!) depends on
• microphone placement
• DUT positioning
• Turning around reference point
• Sound reflections on turntable
• Room absorption irregularities
Not practicalr
LOGAN,NEAR FIELD SCANNING, 9
Problems of Far-field MeasurementsPhase response depends on air temperature
Phase error caused by temperature difference of 2°C during
smcC /4.34320 11
smcC /6.34422 22
)3.34( mmr
Far Field Measurement
required measurement
distance > 5m
Sound velocity is dependent from air conditions (e.g. temperature)
a temperature difference of ∆ϑ=2°C
will change the sound velocity by ∆c≈1.2 m/s
Dependent from the distance the temperature difference will influence the propagation time:
mst 1.0
smcC /345.824 33
Frequency
f=2kHz
f=5kHz
f=10kHz
Wave length
λ=171.7mm
λ=68.7mm
λ=34.3mm
Phase Error in 5 m distance
36° (0.1 λ)
90° (0.25 λ)
180° (λ)
Deviation:
Far field measurement are
prone to phase errors
LOGAN,NEAR FIELD SCANNING, 10
No anechoic room is perfect !How to cope with limited absorption at low frequencies ?
Anechoic room
room correction curve
Simulated Free field
response
1. Select typical set of
loudspeakers
2. Measure Loudspeaker in
anechoic room and under
free-field condition
3. Calculate a room
correction curve
insufficiently damped for
frequencies below 100Hz
+
Free field
room
Room correction curve depends
on loudspeaker properties !!
LOGAN,NEAR FIELD SCANNING, 11
Comprehensive 3D-Directivity Data required:
• Home Audio Application
Specification for 360 degree polar measurements largely based on thetechniques developed by Toole and Devantier at Harman to predicthow a loudspeaker will sound in a typical listening room (CEA 2034 -2013)
• Hand Held Personal Audio Devices
The near-field generated by laptops, tablets, smart phones, etc. ismore important than the far field response (considered in newproposal IEC60268-2014)
• Studio Monitor Loudspeakers
Professional reference loudspeaker need a careful evaluation in thenear- and far-field
• Professional Stage and PA Equipment
Accurate complex directivity data are required for room simulation and sound system installation (line arrays)
LOGAN,NEAR FIELD SCANNING, 12
Measurements in the Near Field
Advantages:
• High SNR
• Amplitude of direct sound much greater than room reflections providing good conditions for simulated free field conditions
• Minimal influence air properties (air convection, temperature field)
Disadvantages:
• Not a plane wave
• Velocity and sound pressure are out of phase
• No sound pressure extrapolation into the far-field by 1/r law(holographic processing required)
LOGAN,NEAR FIELD SCANNING, 13
Short History on Near-Field Measurement
Single-point measurement
close to the source
Don Keele 1974
Application Note 38,39
On-axis
Multiple-point measurement
on a defined axis
Ronald Aarts (2008)
Scanning the sound field on
a surface around the source
Weinreich (1980)
Melon, Langrenne, Garcia (2009)
Bi (2012)
General approach
1. Measurement of the sound pressure distribution by using robotics (scanning process)
2. Holographic post-processing of the measured data (wave expansion)
3. Calculation of the sound pressure at any point in far- and near-field (Extrapolation)
. . ..
LOGAN,NEAR FIELD SCANNING, 14
How many points have to measured ?
Number of points required depends on
• Loudspeaker type (size, number of transducers)
• Assumed symmetry of the loudspeaker(axial symmetry)
• Application of the data (e.g. EASE data)
• Field seperation (non-anechoic conditions)
with reference
Measurement
sound power
Directivity
High resolution
Normal scan
1
100
1000
5000
Number of points
Note: Number of measurements points is
much lower than the final angular resolution
of the calculated directivity pattern !
LOGAN,NEAR FIELD SCANNING, 15
Moving the DUT or the MIC during near field measurements ?
Moving the Microphone(s) givesadvantages:
• Accurate positioning of Mic and heavy loudspeakers (hangingon a crane)
• Constant room and DUT interaction during scanning(required in a non-anechoicenvironment)
• Minimum gear (only a platformand a pole) within the scanningsurface
Loudspeaker
microphone
φ
z
r
LOGAN,NEAR FIELD SCANNING, 16
Scanning on a Single or Multiple Layers ?
First Prototype of a Near-Field Scanner
scanning in various
coordinates (cylindrical,
spherical, cartesian)
A double layer scan provides information about the incoming and
outgoing waves used for separating the direct sound radiated by DUT
and room reflections.
Direct sound
Room reflections
LOGAN,NEAR FIELD SCANNING, 17
Good SNR in the Near-Field !
SPL over distance at 500 Hz
Near-field measurements give the following benefits:
• Higher SNR (20 dB typically) than far field measurement
• Measurement can tolerate some ambient noise (office, workshop)
• Speeding up the measurement by avoiding averaging required in the far field
far field (~ 1/r)
(near -field effects)
Noise Floor
Far field
Near Field
20 dB
Christian The left picture is stupid with 100 m please put 10 m maximum into that and use maybe higher frequencies
We have to indicated the two points.
LOGAN,NEAR FIELD SCANNING, 18
Avoiding Air Diffraction Problemscaused by a difference of 2 Kelvin in air temperature
Frequency Wavelength Phase Error @ 5 m
Phase Error @ 0.5 m
2 kHz 17.15 cm 36 3.6
5 kHz 6.8 cm 90 9.2
10 kHz 3.4 cm 180 18.5
Distance Deltatime
Deltadistance
5 m 50 µs 1.7 cm
0.5 m 5 µs 1.75 mm
Air temperature Speed of sound
20o C 343.4 m/s
22o C 344.6 m/s
Reduces requirements for air conditioning
(normal conditions in office, workshop are sufficient)
LOGAN,NEAR FIELD SCANNING, 19
2nd Step: Holographic wave expansion
General solutions of the wave equation
used as basic functions in the expansion
monopol
dipols
quadropols
)( fC
COEFFICIENTSBASIC FUNCTIONS
),( rB f+
Results
3rd Step: Wave
Extrapolation
SCANNING
DATA
),( rfH
LOGAN,NEAR FIELD SCANNING, 22
How to interpret coefficients ?
N > 2 N > 5 N > 10
frequency100 Hz 1 kHz 10 kHz
order of the expansion
),()(),( rBCr fffH
• The coefficients in vector C(f) are complex and frequency dependent and
weight each basic solution of the wave equation
• The number of coefficients depend on frequency
• Significant data reduction (measurement points coefficients)
• Truncation of the order Smoothing of the directional properties (lobes)
• Interpolation between measurement points based on wave propagation
LOGAN,NEAR FIELD SCANNING, 23
Sound field has a limited
complexity and can be
characterized by a limited
number of basic functions
Example: Woofer
N=0 N=2N=1 N=3 N=10
f in Hz
Sound P
ow
er
in d
B
Total Sound Power
Directivity pattern at 200 Hz
Total
sound field is completely described by order N=3 (16 Coefficients)
High Angular Resolution derived from a few measurement points ?
Higher orders
N=0
N=1
N=2
N=3
LOGAN,NEAR FIELD SCANNING, 24
Fitting E
rror
in d
Bf in Hz
How to Check the Accuracyof the wave field expansion ?
Fitting error truncated expansion (e.g. N=3)
bad SNRHigher order
terms are
missing-20dB = 1%
• Number of measurement points is larger than number of cofficients in C(f)
redundancy of information (fitting problem)
• The redundancy is use for calculating the fitting error in dB
• The fitting error would indicate potential problems (poor SNR, insufficient order, geometrical errors in the scanning
f in Hz
Sound P
ow
er
in d
B
Total Sound Power
N=0
N=1
N=2
N=3Higher orders
LOGAN,NEAR FIELD SCANNING, 25
How to find the maximum order N of the
expansion ?
Target N=0 N=5 N=10 N=20
Fitting E
rror
in d
B
f in Hz
Fitting error as a function of the maximum order N
bad SNR
-20dB = 1%
Dear Christian Please show for the
woofer how the fitting error goes
down with order 5, 10, 20
The measurement system
determines autiomatically the
optimum order N.
Additional scanning can be required
to provide sufficient points for the
wave expansion. N=3
LOGAN,NEAR FIELD SCANNING, 26
3rd Step: Extrapolation of the Sound Pressure
Ss
region of validity
S1
Loudspeaker
characteristics
)( fC
COEFFICIENTS BASIC FUNCTIONS
),( rB f+
The coefficients C(f), the order N(f) depending on frequency
f, the validity radius a and the general basic functions B(f,r)
of the wave expansion describe the directional transfer
function
between the input signal u(t) and the sound pressure output
p(t,r) at measurement point r at a distance r=| r –rref | from the
reference point rref which is larger than the validity radius a
),()(),( rBCr fffH
Reconstructed
Transfer Function
),( rfHIndependent of
the loudspeakerat any point outside the
scanning surface
Region of
validity
LOGAN,NEAR FIELD SCANNING, 27
Examples
1. Professional loudspeaker (top) for line arrays
• Large size, heavy, long distance between transducers
• Accurate phase data required for EASE data
• Typical far field measurement at 7 m
2. Small Studio Monitor
• Similar dimensions of Consumer Home Loudspeakers
• Near field important in small studios
3. Laptop
• Represents personal audio equipment
• Large distance between left and right speaker
• Complex near field properties important for 3D sound
LOGAN,NEAR FIELD SCANNING, 28
Anechoic Environment vs Reverbent Room SPL Comparison Using Line Array
– Input stimulus only applied to the middle element
– Large physical dimensions: stacked elements of 70cm x 30cm x 40 cm each
– Multiple horns
– Horn area approx. 30cm x 30cm
excited
Not excited (boundary
Condition)
LOGAN,NEAR FIELD SCANNING, 29
Practical Evaluation of Near field ScanningAnechoic Chamber vs. Reverberant Room
Far-field in the anechoic room(half space at RWTH Aachen
•Half space (2π) measurement
(microphone on ground)
•DUT rotated by robotics arm
•4050 points measured on a quarter
sphere at 7m (axial symmetry on two axis
assumed to avoid measuring 16200
points)
Near-field scanning in the
reverberant room at the TU
Dresden.• DUT placed at fixed position
• Microphone moved by near field scanner
• 4000 points full scan (no symmetry
assumed)
• Maximum order N=30
7 m
LOGAN,NEAR FIELD SCANNING, 31
More Resolution with less Points ?
2.5 kHz 5 kHz
10 kHz
0°
90°
8 kHz
Far-Field Measurement in anechoic room
(assuming axial symmetry)
Near-Field Scanner + Far-
Field Extrapolation
(full 3D resolution)
LOGAN,NEAR FIELD SCANNING, 34
2nd Example Studiomonitor
• Near-field scanning in an ordinary officeroom
• 500 points
• Order of expansion N
photo in your office and diagrams versus teta and phi
angle plots
LOGAN,NEAR FIELD SCANNING, 36
Fast Near-Field Measurements 1 measurement point + Correction curve
Assumption:
• Loudspeakers with similar geometry (e.g. same type) similar directivity
PROBLEMS:
• 1 point is insufficient for
holografic processing
• No field separation
• No far field extrapolation
Single Point measurement in non-
anechoic room
• complete Scan in the near
field a DUT with similar
geometry (in the same room)
room
Near field
Near field
response
+ Extrapolated
far field+
correction curve
for extrapolationroom correction curve
room
Direct sound near field
Near field
LOGAN,NEAR FIELD SCANNING, 41
How to Measure Transducers ?
Near Field Scanning
microphone positioning in front of a baffle using
same hardware
BENEFITS:
• Deflections are outside the
surface
• can be separated by
holographic field separation
• Perfect half-space
measurement
PROBLEMS:
• Acoustic short cut for low frequencies
(measurement range limited)
• Deflection effects from the edges of the
baffle
• Reduction of deflection effects by placing
driver out of the center (norm baffle - DIN EN
602648-5)
Far Field Measurement
baffle can’t be rotated
Change microphone Position
out
in
LOGAN,NEAR FIELD SCANNING, 42
A New and Better WaySummary
Near-field scanning + holografic wave expansion + Field separationgives the following benefits:
• More information about acoustical output
• Sound pressure at any point outside scanning surface (complete 3D space)
• Improved accuracy compared to conventional far-field measruements(coping with room problems, gear reflections, positioning, air temperature, ...)
• Higher angular resolution with less measurement points
• Simplified handling (moving of heavy loudspeakers)
• Dispenses with an anechoic room
• Self-check by evaluating the fitting error
• Comprehensive data set with low redundancy
LOGAN,NEAR FIELD SCANNING, 43
Thank you !
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