Holographic Measurement of the Acoustical 3D Output by Near Field Scanning by Dave Logan, Wolfgang Klippel, Christian Bellmann, Daniel Knobloch

Transcription

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, 1

2 Introductions LOGAN,NEAR FIELD SCANNING, 2

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, 3

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 by gating or windowing the impulse response (Heyser , 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 between direct sound and first reflection LOGAN,NEAR FIELD SCANNING, 4

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, 5

6 Why are Far-Field Condition used? 1/r law is not applicable in the near field Conventional far-field measurements 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 Toole, F. (2008). Sound Reproduction: The Acoustics and Psychoacoustics of Loudspeakers and Rooms LOGAN,NEAR FIELD SCANNING, 6

7 How to Ensure Far-Field Condition? Requirements: extrapolate region of validity only in the far field r>r far extrapolate Distance r far >> d (geometrical dimension of the DUT) d Distance r far >> λ (wavelength of the signal) ratio r far /d >> d/λ extrapolate extrapolate Large loudspeaker systems (e.g. line arrays) require large anechoic rooms! LOGAN,NEAR FIELD SCANNING, 7

8 t P U S H How to perform Directivity Measurements in the Far Field? The sound pressure is measured multiple measurement points located on sphere with radius r according to the desired resolution: anechoic room 5 degree 2592 points 2 degree points 1 degree points Not practical Amplifier Loudspeaker r Accuracy of measured response (phase!!) depends on microphone placement DUT positioning Turning around reference point Sound reflections on turntable Room absorption irregularities A M P Outpu Input Turntable Analyzer Multiplexer LOGAN,NEAR FIELD SCANNING, 8

9 Problems of Far-field Measurements Phase response depends on air temperature 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 1 20 C c m / s 2 22 C c m / s 3 24 C c m / s Dependent from the distance the temperature difference will influence the propagation time: Far Field Measurement required measurement distance > 5m Deviation: t 0. 1ms ( r 34.3mm) Phase error caused by temperature difference of 2 C during Frequency f=2khz Wave length λ=171.7mm Phase Error in 5 m distance 36 (0.1 λ) f=5khz f=10khz λ=68.7mm λ=34.3mm 90 (0.25 λ) 180 (λ) Far field measurement are prone to phase errors LOGAN,NEAR FIELD SCANNING, 9

10 No anechoic room is perfect! How to cope with limited absorption at low frequencies? Anechoic room + Simulated Free field response insufficiently damped for frequencies below 100Hz room correction curve Room correction curve depends on loudspeaker properties!! 1. Select typical set of loudspeakers 2. Measure Loudspeaker in anechoic room and under free-field condition 3. Calculate a room correction curve room Free field LOGAN,NEAR FIELD SCANNING, 10

11 Comprehensive 3D-Directivity Data required: Home Audio Application Specification for 360 degree polar measurements largely based on the techniques developed by Toole and Devantier at Harman to predict how a loudspeaker will sound in a typical listening room (CEA ) Hand Held Personal Audio Devices The near-field generated by laptops, tablets, smart phones, etc. is more important than the far field response (considered in new proposal IEC ) Studio Monitor Loudspeakers Professional reference loudspeaker need a careful evaluation in the near- 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, 11

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, 12

13 Short History on Near-Field Measurement Single-point measurement close to the source Multiple-point measurement on a defined axis Scanning the sound field on a surface around the source On-axis.... Don Keele 1974 Application Note 38,39 Ronald Aarts (2008) 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, 13

14 How many points have to measured? Number of points with reference Measurement sound power Directivity Normal scan 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) High resolution Note: Number of measurements points is much lower than the final angular resolution of the calculated directivity pattern! LOGAN,NEAR FIELD SCANNING, 14

15 Moving the DUT or the MIC during near field measurements? microphone r z Loudspeaker φ Moving the Microphone(s) gives advantages: Accurate positioning of Mic and heavy loudspeakers (hanging on a crane) Constant room and DUT interaction during scanning (required in a non-anechoic environment) Minimum gear (only a platform and a pole) within the scanning surface LOGAN,NEAR FIELD SCANNING, 15

16 Scanning on a Single or Multiple Layers? First Prototype of a Near-Field Scanner Room reflections Direct sound 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. LOGAN,NEAR FIELD SCANNING, 16

17 Good SNR in the Near-Field! Christian The left picture is stupid with 100 m please put 10 m maximum into that and use maybe higher We have to indicated the two points. SPL over distance at 500 Hz (near -field effects) far field (~ 1/r) Near Field Far field 20 db Noise Floor 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 LOGAN,NEAR FIELD SCANNING, 17

18 Avoiding Air Diffraction Problems caused by a difference of 2 Kelvin in air temperature Air temperature Speed of sound Distance Delta time Delta distance 20 o C m/s 22 o C m/s 5 m 50 µs 1.7 cm 0.5 m 5 µs 1.75 mm Frequency Wavelength Phase 5 m Phase 0.5 m 2 khz cm khz 6.8 cm khz 3.4 cm Reduces requirements for air conditioning (normal conditions in office, workshop are sufficient) LOGAN,NEAR FIELD SCANNING, 18

19 2nd Step: Holographic wave expansion SCANNING DATA H ( f, r) + BASIC FUNCTIONS B( f, r) COEFFICIENTS C( f ) monopol dipols Results quadropols General solutions of the wave equation used as basic functions in the expansion 3rd Step: Wave Extrapolation LOGAN,NEAR FIELD SCANNING, 19

20 How to interpret coefficients? H ( f, r) C( f ) B( f, r) 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 N > 2 N > 5 N > 10 order of the expansion 100 Hz 1 khz 10 khz 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, 22

21 Sound Power in db High Angular Resolution derived from a few measurement points? Example: Woofer Total Sound Power Sound field has a limited complexity and can be characterized by a limited number of basic functions N=0 N=1 N=2 N=3 Higher orders f in Hz Directivity pattern at 200 Hz Total N=0 N=1 N=2 N=3 N=10 sound field is completely described by order N=3 (16 Coefficients) LOGAN,NEAR FIELD SCANNING, 23

22 Sound Power in db Fitting Error in db How to Check the Accuracy of the wave field expansion? Total Sound Power N=0 N=1 N=2 Higher orders N=3 Fitting error truncated expansion (e.g. N=3) bad SNR -20dB = 1% Higher order terms are missing f in Hz f in Hz 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 LOGAN,NEAR FIELD SCANNING, 24

23 Fitting Error in db How to find the maximum order N of the expansion? Dear Christian Please show for the woofer how the fitting error goes down with order 5, 10, 20 Fitting error as a function of the maximum order N The measurement system determines autiomatically the optimum order N. Additional scanning can be required to provide sufficient points for the wave expansion. bad SNR -20dB = 1% N=3 f in Hz Target N=0 N=5 N=10 N=20 LOGAN,NEAR FIELD SCANNING, 25

24 3rd Step: Extrapolation of the Sound Pressure COEFFICIENTS C( f ) + BASIC FUNCTIONS B( f, r) Reconstructed Transfer Function H ( f, r) Loudspeaker characteristics Independent of the loudspeaker at any point outside the scanning surface 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 H ( f, r) C( f ) B( f, r) between the input signal u(t) and the sound pressure output p(t,r) at measurement point r at a distance r= r r ref from the reference point r ref which is larger than the validity radius a Region region of validity S s S 1 LOGAN,NEAR FIELD SCANNING, 26

25 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, 27

26 Anechoic Environment vs Reverbent Room SPL Comparison Using Line Array excited 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 Not excited (boundary Condition) LOGAN,NEAR FIELD SCANNING, 28

27 Practical Evaluation of Near field Scanning Anechoic Chamber vs. Reverberant Room 7 m 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 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 LOGAN,NEAR FIELD SCANNING, 29

28 More Resolution with less Points? 2.5 khz 5 khz Far-Field Measurement in anechoic room (assuming axial symmetry) 8 khz 10 khz Near-Field Scanner + Far- Field Extrapolation (full 3D resolution) 90 0 LOGAN,NEAR FIELD SCANNING, 31

29 o in your office and diagrams versus teta and phi gle plots 2nd Example Studiomonitor Near-field scanning in an ordinary office room 500 points Order of expansion N LOGAN,NEAR FIELD SCANNING, 34

30 Fast Near-Field Measurements 1 measurement point + Correction curve Assumption: Loudspeakers with similar geometry (e.g. same type) similar directivity Single Point measurement in nonanechoic room room Near field Near field response + + Extrapolated Near field far field PROBLEMS: 1 point is insufficient for holografic processing No field separation No far field extrapolation room correction curve correction curve for extrapolation room complete Scan in the near field a DUT with similar geometry (in the same room) Direct sound near field LOGAN,NEAR FIELD SCANNING, 36

31 How to Measure Transducers? Far Field Measurement baffle can t be rotated Change microphone Position Near Field Scanning microphone positioning in front of a baffle using same hardware 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 ) BENEFITS: Deflections are outside the surface can be separated by holographic field separation Perfect half-space measurement LOGAN,NEAR FIELD SCANNING, 41 in out

32 A New and Better Way Summary Near-field scanning + holografic wave expansion + Field separation gives 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, 42

33 Thank you! LOGAN,NEAR FIELD SCANNING, 43