holographic measurement of the acoustical 3d output by ...€¦ · “toole, f. (2008). sound...

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


Introductions


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


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


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


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


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 !


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



Accuracy of measured response

(phase !!) depends on

• microphone placement

• DUT positioning

• Turning around reference point

• Sound reflections on turntable

• Room absorption irregularities

Not practicalr


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


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 !!


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)


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)


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)

. . ..


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 !


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


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


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.


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)


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


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


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


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


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


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


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


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)


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


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)


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


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


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


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


Thank you !

holographic measurement of the acoustical 3d output by ...€¦ · “toole, f. (2008). sound...

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