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Calibration Approaches for Higher Order Ambisonic Microphones
Charles J Middlicott1,2 and Bruce J Wiggins1
1 University of Derby, Derby, UK. 2 Sky Labs Brentwood, Essex, UK.
Correspondence should be addressed to Charles J Middlicott
(charles@charlesmiddlicott.co.uk)
ABSTRACT
Recent years have seen an increase in the capture and production of ambisonic material due to companies such
as YouTube and Facebook utilising ambisonics for spatial audio playback. Consequently, there is now a greater
need for affordable high order microphone arrays due to this uptake in technology. This work details the
development of a five-channel circular horizontal ambisonic microphone intended as a tool to explore various
optimization techniques, focusing on capsule calibration & pre-processing approaches for unmatched capsule
1 Introduction
This paper expands on capsule calibration
approaches utilised in our previous work [1], where a
set of software tools were developed to aid ambisonic
microphone array design and evaluation.
Typically, low cost microphone capsules are not
mechanically matched at the production stage due to
cost-effectiveness resulting in inconsistencies from
capsule to capsule. This results in the user having to
match them after the fact.
The capture of ambisonic signals was developed by
Gerzon and Craven [2], where the notion of using a
tetrahedral array of capsules was described. Various
manufacturers have developed 1st order ambisonic
(FOA) microphones based on the same design
concepts such as those by Farrah [3], Core Sound [4]
and Sennhiesser [5].
Users have been able to synthesize higher order
ambisonic material in digital audio workstations
(DAWs) for some time. However, the need for
microphones capable of capturing such signals has
recently grown due to increasing demand from
content producers, as previously the use was confined
to those in academic institutions. Commercially
available arrays such as the mhAcoustics Eigenmike
[6] are capable of capturing up to 4th order signals with
CoreSound [7] and Brahma Microphones [8] having
recently developed 2nd order arrays. Yet, these are out
of reach of the everyday user due to the expensive
nature of such high-quality arrays.
When considering the development of a low-cost
alternative using inexpensive capsules for capturing
ambisonic material, any deviation in the response
between them will affect the quality of resulting the b-
format signals. Due to the isotropic nature of
ambisonics it is important that the capsule utilised
have a uniformity between them so as to not colour or
misrepresent the recorded sound-field.
Various approaches have been implemented in this
paper to investigate how we can overcome the pitfalls
of cheap unmatched capsules. The purpose of this
work is to ascertain which capsule calibration
approach is best utilised when working with low cost
ambisonic microphones. At this stage no post-filtering
of the B-Format signals has been investigated, this will
be considered separately in a future paper.
Middlicott & Wiggins Calibration Approaches for HOA Microphones
Page 2 of 11
Prototype array measurement has been undertaken
and associated signal processing implemented to
calibrate the individual microphone capsules. Details
of the implementation can be seen in section 4.
The frequency response and directivity are shown at
each stage of the process and this is compared to both
simulations and the uncalibrated capsule responses.
B-Format signals are generated from both the raw and
calibrated capsule data as a means to evaluate the
overall arrays performance.
2 Current Capsule Calibration Methods
Various approaches to capsule calibration for
ambisonic microphones are utilised across both
academic institutions and the commercial sector, due
to the nature of the commercial market it has proven
difficult to gather specifics on how manufacturers
arrays are specifically calibrated.
Rode & Sennhiesser have a rich heritage in
manufacturing microphones, the capsules both
companies choose to use in their 1st order arrays are
well matched in the first instance. Sennhiesser choose
to forgo individual array measurement and capsule
calibration opting to rely on the quality/matching of the
capsules from the production line. They utilise
generalised filtering in the supplied A/B conversion
software to optimise the B-Format signals [9].
mhAcoustics also utilize well-matched capsules from
Sennhiesser in the manufacture of the em32 array.
Measurement of all the capsules characterise the
array and additional calibration is implemented by
applying individual capsule calibration weights using
either of the supplied software packages eigenStudio
& eigenSetGain [10].
Both the CoreSound TetraMic & OctaMic use well
matched capsules and utilize a similar approach to
mhAcoustics in that each array is individually
characterised using a pseudo-anechoic measurement
procedure to generate individualised array capsule
calibration filters, these are applied by means of VST
plugins VVEncode and VVOctoEncode. [11]. Brahma
ambisonic microphones also use VVEncode to apply
the individual array calibration filters. Angelo Farina
has worked with Umashankar Manvathredi to
generate A/B format matrices for the Bramaha
microphones calibrating for microphone mismatch.
The SpHEAR* project is an array development study
aimed at DIY ambisonics enthusiasts. Lopez-
Lezcano’ two papers on the project [12] and [13]
discuss the capsule calibration and A/B conversion
approaches for two microphone designs, a 1st order
tetrahedral design and an eight capsule 2nd order
design original proposed by Benjamin [14].
When calibrating the tetrahedral SpHEAR design in
[12] Lopez opts to measure impulse responses of
each capsule using 8 to 16 equally-spaced
measurement points over the azimuth plane to
compensate for the low frequency response of the
capsules, differences in sensitivity and directivity, and
the effects of the non-coincident nature of the array.
When calibrating the 2nd order OctaThingy [13], Lopez
notes the need for physically matched capsules due
to differences in capsule gain and directivity causing
errors in the recovery of the 2nd order harmonics.
Stating that capsule equalisation by means of IR
measurement will improve this recovery where the
horizontal plane and low elevations are preferred for
capsule calibration measurements as it is the most
likely region of importance when recording with such
a microphone.
Farina proposed an approach to capsule calibration
for tetrahedral arrays in [15] as part of the A to B
Format conversion process, where axial impulse
response measurements of the capsules are taken
these are used to generate filters by means of Nelson-
Kirkeby inversion, where a measurement microphone
is used as a reference. The authors have taken a
similar approach to that of Farina regarding the
measurement process and use of axial responses as
a reference. The difference in our approach being that
we opt for a theoretical flat response opposed to using
a measurement microphone due to the obvious issues
with alignment to the prototype array.
Adriensen developed a suite of software called
TetraProc and TetraCal [16], An ambisonic
microphone processor and calibration tool. TetraProc
splits into three sections, compensating from any
mismatch in sensitivity and directivity, equalisation to
compensate for the non-coincident nature of the array
at mid to high frequencies and finally compensation in
the LF region to correct for the high-pass nature of
directional microphones. This calibration tool takes
eight 45˚ impulse response measurements in the
azimuth plane to compensate solely for deviation in
capsule sensitivity & directivity, additional the speaker
response is measured so that it can be compensated
for, A similar approach is taken in this work, but
measurements are captured at a higher resolution.
Middlicott & Wiggins Calibration Approaches for HOA Microphones
Page 3 of 11
3 Prototype Array Development
3.1 Array Design Considerations
A cost-effective 2nd order horizontal Ambisonic
microphone prototype has been developed as a
vehicle to evaluate several approaches to higher order
array calibration. It can be shown that the minimum
number of capsules needed to capture the horizontal
only 2nd order spherical harmonics using an equal
angle sampling distribution is 2N+1, where N is the
order [17]. This leads to an initial circular array
prototype that consists of five 14mm electret capsules
with a capsule spacing of 72° and an array radius of
25mm. This radius was calculated taking into account
the physical size of the JLI 140A-T capsules utilized
[18]. Figure 1 below shows the array geometry &
housing designed in SolidWorks. It was decided to
focus initially on an increased resolution in the
azimuth plane. Factors such as spacing, calibration
and filtering could then be evaluated with greater ease
with findings informing the development of a 3D
spherical array.
Figure 1 – Five Channel 3D Printed Housing in SolidWorks
3.2 Objective Measurement Process
Objective measurement took place in a hemi-
anechoic chamber, a set of measured impulse
responses (IRs) were captured at 2-degree
increments along the azimuth plane, from an on-axis
position to 180 degrees above which symmetry was
assumed. To both further the accuracy and minimize
the length of the measurement process, an Outline
ET250-3D [19] automated turntable was utilized.
Measurements were taken at a 2 metre distance from
the acoustic centre of the capsules under test. A total
set of 450 measured IRs were captured.
The measurement source material was a 15 second
20Hz to 20kHz logarithmic sine sweep, this was fed to
a DynAudio BX5a loudspeaker. An omnidirectional
Earthworks measurement microphone [20] was used
to capture the response of the loudspeaker.
Nelson/Kirkeby inversion [21] was utilized to generate
an inverse of this speaker response shown in Figure
2 using Eq. 4 . The resultant filter is convolved with the
captured IRs thus compensating for the frequency
response of the loudspeaker.
Figure 2 - Speaker / Inverse Filter in the Frequency Domain
3.3 Raw Measured Responses
To evaluate the feasibility of using these capsules
within a prototype ambisonic array, the deviation in
frequency evident between the five capsules on-axis
responses was considered. This was to ascertain how
matched the capsules were from the production line.
The initial on-axis response measurements show a
deviation of approximately +/- 1.5dB between 50Hz
and 6.5kHz, above which the deviation increases to
+/- 2dB and the sensitivity ranges quite significantly
between the capsules above this frequency. This can
be below shown in Figure 3.
Figure 3 - Measured On-Axis Capsule Frequency Response
Figure 4 - Polar Response of Capsule 1
The raw capsule directivity shown above in Figure 4
exhibits a cardioid like response up to 1kHz, at 2kHz
the response mirrors more of a super-cardioid pattern
as shown by the -15dB figure at 180˚ this is opposed
to -27 to -33dB below 1kHz.
Middlicott & Wiggins Calibration Approaches for HOA Microphones
Page 4 of 11
The higher frequency regions of 8kHz and above
exhibit an increase in directivity response, albeit not
as smooth as with the lower frequencies, this can be
attributed to the design of the capsules housing.
The remaining four capsules exhibit a similar
response as above, where at frequencies below 6kHz
they are within a +/- 1.5dB range. Above 6kHz the
responses deviate from capsule to capsule quite
dramatically. This can be seen for on axis positions in
Figure 3. Additional polar responses for the remaining
capsules can be reviewed in an appendix available
online [22].
4 HOA Microphone Array Calibration
Approaches & Implementation
Due to the low cost per unit of the capsules utilised,
matching at the production stage isn’t a viable option.
Thus, we must develop an approach to calibrate the
capsules that culminates in a desired matched
response for all transducers within an array. In the
following section, four approaches to capsule
calibration are investigated for use with Ambisonic
microphone arrays.
4.1 Calibration by 1/3rd Octave Average
Gain Matching
The first method considered utilizes gain matching of
the capsules within an array. This is arguably the
simplest of the approaches being evaluated, in that
some form of gain or attenuation is applied to each
transducer to level match the signals.
Gain matching of the capsules could be implemented
using only this time domain signals as a reference,
however this has no dependency on the frequency
response of the capsules. To successfully gain match
these capsules it was deemed necessary to analyze
each capsules response in the frequency domain by
apply a Fast Fourier Transform (FFT) to each
capsules on-axis impulse response.
To increase the flexibility of this method the authors
chose to average over 1/3rd octave bands instead of
over all frequencies. This was so that some of the
octaves can be omitted when generating the
correction factor at the discretion of the operator. thus,
gain matching for a frequency range of interest.
The equations 1 & 2 below show how the frequency
index (k), which corresponds to the upper and lower
limits of each 1/3rd octave band were calculated.
Respective of the size of the FFT being applied which
was 2048 points.
!"#$%&'()* )+,-.)
+/ ++01234
5
)))))))))))))))))))))))))))))))
(1)
#6#$%&'()* )+,78)
+9++0:7;<
5
))))))))))))))))))))))))))))))))
(2)
Where
=>?@)
= Upper 1/3rd Oct. Frequency Limit in Hz
=>AB
= Lower 1/3rd Oct. Frequency Limit in Hz
=C)
= Sampling Frequency (48kHz)
==DEAFG
= Length of the FFT to be applied (2048)
Once the frequency indices for each set of octave
limits, are calculated the magnitude of the capsules
on-axis response is averaged per each 1/3rd octave
band. This is shown in equation 3 below.
HIJKL)MNO)PQR
&
ST'
(
)*) H
!"#$%
&
'
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'
(VW
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(3)
Where
`
= Capsule Index
a
= Frequency Index
bcdA>&a(
= Upper Limit Index Per Octave
dedA>&a(
= Lower Limit Index Per Octave
==D&`(
= On Axis FFT Data for Capsule (
N
)
Once each capsules response has been averaged.
The mean per capsule is used to generate a correction
factor. This is achieved by taking the lowest mean
figure as a reference. Applying attenuation to the
remaining capsules relative to the difference between
each capsule and the reference.
The authors opted to use the lowest capsules average
magnitude as a reference, so as to not add any excess
gain preferring to match by attenuation. The result of
this attenuation is shown in Figure 5.
Middlicott & Wiggins Calibration Approaches for HOA Microphones
Page 5 of 11
Figure 5 – On Axis Response (Pre/Post Gain Matching)
4.2 Calibration to a Specific Capsules
On-Axis Frequency Response
The following approach matches all the capsules
within an array to whichever capsules axial frequency
response is deemed more desirable by the user.
This target response is ascertained by observing the
axial frequency response each capsule. Once a target
response is chosen it is used in conjunction with the
remaining axial responses to invert between one
another resulting in an inverse filter which can be
calculated using the following equation.
f2gh&i()*)jk-lm<n
&
'
(
)o)p_gq
r
j
&
'
(s
)
p_gq
r
j
&
'
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)o)j
&
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tu
&
'
(
)))))))))))))))))))))))))))))
(4)
Where
v
&
a
( is the measured response,
vD?wxGy
&
a
(
)
is
the desired target response,
z
&
a
( is the frequency
dependent regularisation parameter and
i
)
is the
frequency index. The generated filters are then
convolved with its respective measured response so
as to exhibit a close approximation to the desired
target response.
Frequency dependent regularisation
z
&
a
( was used
throughout this work, as to not generate large
increases at the extremities of the frequency range of
interest. four points were chosen at which the
regularisation figure would change. The limits were
set as follows, 20Hz and 200Hz for the lower
frequency region and 8kHz and 16kHz for the higher
frequency region. Between the inner limits (200Hz -
8kHz) the regularisation parameter was set a 0.01,
outside of which the regularisation was set to 1.
Between these inner and outer limits (20Hz to 200Hz
and 8kHz to 16kHz) the regularisation parameter
decreased in the LF region from 1 to 0.01 in a linear
fashion and increased from 0.01 to 1 in the HF region
as shown below in Figure 6.
Figure 6 – Frequency Dependent Regularization
Figure 7 – Effect of Using Frequency Dependent vs.
Frequency Independent Regularization
Figure 7 illustrates the effect of using frequency
dependent regularisation over a fixed frequency
independent approach. The trace showing a blue
dotted line is the calculated inverse filter using
frequency independent regularisation of 0.01. In can
be shown that this would result in a large increase of
~20dB at 20Hz and a similar increase at 16kHz. The
red trace shows the effect of using frequency
dependent regularisation where it is evident that the
linear change in value positively impacts the result of
the invert filter. The lower of the two axes shows the
result of applying both regularisation approaches. The
frequency independent approach results in a flat
response over 20Hz/20kHz at the expense of
excessive increases in the LF/HF range due to the ill-
conditioned nature of the filters. The pink trace shows
the result of using frequency dependent
regularisation, where a flat response is evident
between the inner frequency limits (200Hz to 8kHz),
outside of which there is a roll off evident, showing no
excessive increase in the extremities.
Figure 8 - Calibrated to a Capsules Axial Response
Middlicott & Wiggins Calibration Approaches for HOA Microphones
Page 6 of 11
The resultant axial frequency response is shown
above in Figure 8, where between the inner
regularisation limits of (200Hz - 8kHz) the target
response is achieved. The LF/HF roll-off can be
attributed to using frequency dependent regularisation
which causes some differences to that of the target
response in this region.
4.3 Calibration to a Flat Frequency
Response
The third calibration approach investigated is one in
which the capsules are calibrated to a flat frequency
response. This is achieved by the on axis measured
responses being inverted as in equation (1) to a target
that is a Dirac’s delta function δ opposed to an optimal
measured response shown in section 4.2.
Figure 9 – Calibrating to a Flat On-Axis Response with
Frequency Dependent Regularization
The resultant axial frequency response of each
capsule is shown above in Figure 9, where a flat
frequency response is evident between 120Hz/8kHz.
The LF/HF roll-off can be attributed to using frequency
dependent regularisation.
4.4 Calibration by Diffuse Field
Equalization
The final approach implemented in this work utilizes
diffuse field equalization. Approximation of the
average diffuse field response is calculated by using
a large set of measured free-field responses taken
from the measurement procedure outlined in section
3.2. The inverse of this response is used as a target
in which individual calibration filters are generated.
Averaging the array response over a diffuse field,
rather than relying on a single on axis free-field
response for calibration. The averaged diffuse-field
calculation is shown in Equation 5. A similar approach
was taken by Heller [23] for the post filtering of 1st
order ambisonic components.
{|}&~()*)
•
€
•
‚W
XXY&STƒT'(
W
„
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ƒ…€ ))))
(5)
Where
†
= Number of Measurement Directions
‡
= Measurement Position Index (1 to D).
`
= Capsule Index
a
= Frequency Index of FFT
==D&`T‡Ta(
= FFT of Measured Responses
The calculated diffuse-field responses are shown in
Figure 10 below. The inverse of which is applied to the
measured responses the resulting in the axial
responses shown in Figure 11.
Figure 10 – Calculated Diffuse Field Response
Figure 11 – Calibrating with Diffuse Field Equalization
5 Microphone Array Simulation
A simulation routine developed previously in [1] was
used to derive a theoretical response, mirroring the
characteristics of an array in anechoic conditions.
The cardioid directivity response of each capsule is
shown in Figure 12.
Figure 12 – Directivity of the Simulated Five Channel Array
Middlicott & Wiggins Calibration Approaches for HOA Microphones
Page 7 of 11
5.1 Generating Spherical Harmonics
To accurately assess the performance of the
prefiltering methods considered in this paper, it was
critical that we evaluate the prototype arrays response
in the spherical harmonic domain.
Figure 13 shows the ideal response of the spherical
harmonics (SH) needed to derive 2nd order
ambisonics. In this case the minimum number of
harmonics is five (2N+1). The ambisonic channel
number (ACN) naming convention is used throughout
this work and the directivity in the azimuth plane can
be seen below.
Figure 13 - Ideal Harmonics (2nd Order Horizontal)
To generate the desired B-Format signals a set of SH
coefficients must be calculated and applied to each
microphone capsule. The coefficients for each SH are
generated using the following equation, modified from
[24].
ˆg
]
&
q
T
f
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‰ Šg
‹
]
‹
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‹
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(6)
Where
M
q
= The angular capsule azimuth in radians
M
F
= The angular capsule elevation in radians
n = The order (0 to the max order N)
m = The degree (-n to n)
•B
>)
= The associated Legendre polynomial
–B
>)
= Gain value for a given normalisation
scheme
Once calculated for a given SH they must be
convolved with each respective capsules IRs. These
are then summed together to create the desired SH
signal.
The simulated B-Format Signals for Ambisonic
Channel Number (ACN) 3 & 4 and shown below in
Figure 14.
It should be explicitly noted that no post-filtering has
been applied to the B-Format Signals at this stage as
the purpose of this work is to focus solely on capsule
pre-filtering strategies.
Figure 14 - Simulated B-Format Signals (ACN 3 & ACN 4)
When comparing the ideal harmonics against its
simulated counterpart, (which use perfect cardioid
responses) It can be observed that several factors
affect the array response, most notably the non-
coincident nature of the array at higher frequencies.
This is a direct consequence of the array design,
where the radius (25mm) and capsule spacing (72˚)
cause the array response to deteriorate above a
specific frequency. Above which the directivity is
skewed to the individual capsules look direction. This
is known as the spatial aliasing frequency, this begins
to affect the array response above 4.3kHz. This is
approximated below by using equation 7.
—˜Ž™•Ž•š)|›œ•žœ•~Ÿ *) ŠN)
¡K
(7)
Where
N = Is the Ambisonic Order (2nd Order)
c = Speed of Sound (343m/s)
r = Is the Array Radius (25mm)
Due to the above, in the remaining figures the array
responses will be shown up to 4kHz only, as the scope
of this paper isn’t to consider post filtering.
Middlicott & Wiggins Calibration Approaches for HOA Microphones
Page 8 of 11
6 Evaluation of Calibration Approaches
To accurately assess the performance of each
calibration method implemented, the following section
considers both the calibrated capsule directivity and
the directivity of the generated B-Format signals for
each approach investigated. These are compared to
both simulated and raw measured responses for
analysis. Additional results and figures for all capsules
and B-Format responses not included in this paper,
are freely available in appendix online [22].
The ideal & simulated B-Format responses are
considered when evaluating the performance of the
calibration approaches. However, the raw measured
directivity of each capsule differs quite drastically from
a perfect cardioid response at HF. Thus, the B-Format
responses generated would typically suffer. Due to
this the authors have chosen to display the raw B-
Format signals as a benchmark on which to assess
the difference between the calibration approaches.
6.1 Raw Measured B-Format Responses
Figure 15 – Raw Measured B-Format Signals
ACN 3 response shown in Figure 15 mirrors the
simulated response in Figure 14 up to 500Hz where
the null at 1kHz (90˚) deviates by 12dB, above this
frequency the response deteriorates. The response of
ACN 4 in comparison tracks below 1kHz with a distinct
exception between 180˚/270˚ where the expected
nulls in the pattern as per the simulation are non-
existent and the directivity deteriorates.
6.2 Calibration by Avg. Gain Matching
Averaged gain matching is the simplest of the
methods considered in this paper, due to attenuation
of the capsules input signals instead of filtering in the
frequency domain. The directivity response over the
five capsules shows no obvious difference the raw
directivity responses aside from a minor change in
gain, this can be seen for the axial positions in Figure
5.
In the SH domain, shown in Figure 16, ACN 3 loosely
mirrors the ideal response up to 1kHz above which it
deteriorates. The directivity of ACN 4 mirrors its
simulated counterpart below 500Hz where a decrease
of ~6dB per octave is observed due to the size of the
array and the directional nature of the capsules. A
slight improvement is observed at 270˚ when
compared to the Raw ACN 3 response at 1kHz in
Figure 15. However, ACN 4 shows a vast
improvement below 1kHz between 180˚/270˚ where
the accuracy of the derived pattern improves
compared to the raw response mirroring the
simulation, at 2kHz the nulls are more prominent at
both 0˚ and 180˚.
Figure 16 – Gain Matched B-Format Signals
6.3 Calibration to a Specific Capsules On-
Axis Frequency Response
When matching the 2nd capsules axial response to the
target response of capsule one it reaches the desired
response for the on-axis position (0˚ and 72˚
respectively). this is shown in Figure . Both capsules
two and three exhibit a minor increase in gain of about
1dB whereas capsules four and five exhibit a
decrease of about 2dB and 1dB respectively in
comparison to the raw directivity. This can be
observed by comparing the axial responses from
Figure 3 with the responses in Figure 8. When
considering the HF region of 8kHz and above there is
a decrease of ~2dB from the target response across
all capsules due to the effect of the frequency
dependent regularization.
Middlicott & Wiggins Calibration Approaches for HOA Microphones
Page 9 of 11
Figure 17 – Capsule 2 Calibrated to Capsule 1 On-Axis
ACN 3 in Figure 18 loosely mirrors both the ideal and
simulated responses up to 250Hz, above which it the
response deteriorates. The directivity of ACN 4
exhibits the ~6dB per octave decrease at 1kHz in line
with the simulated directivity response where the
cardinal direction is observed.
Comparing ACN 3 to the raw response the nulls at
500Hz are less pronounced and at 1kHz severe
deterioration at both 90˚ and 270˚ is evident where a
null is typically expected. Below 500Hz ACN 4 exhibits
more pronounced nulls than the raw response and the
directivity in Figure 16 is skewed between 0˚/90˚ with
~4dB decrease in sensitivity at the cardinal direction.
Both calibration methods tested so far have
successfully derived a more accurate directivity
pattern between 180˚ and 270˚ when comparing the
raw ACN 4 response, in this implementation the
directivity lacks consistency at 45˚ below 1kHz due to
a decrease in sensitivity. ACN 3 exhibits a similar
directivity in the cardinal direction but suffers due to
the decrease or lack of nulls at 90˚/270˚ respectively.
Figure 18 – B-Format Signals Calibrated to Capsule 1
6.4 Calibration to a Flat On-Axis Response
Calibration to a flat axial response has shown to
exhibit the smallest deviation between capsules thus
far, below 8kHz the axial response matches the target
as desired, with a minus 3dB beam width of +/- 30˚.
Again, as a product of the regularization used, above
8kHz a decrease in magnitude of ~4-5dB from a
theoretical flat response is observed in Figure 19.
Figure 19 – Calibrated to a Flat On-Axis Response
This translates to the SH domain in a very similar
manner as in the previous calibration approach. It can
be observed when comparing Figures 18 and 20 that
in both cases ACN 3 exhibits poor attenuation at the
null directions at 1kHz, potentially due to the fact that
this calibration method optimised for the capsules
axial positions, this results a directivity that is less
desirable than the raw B-Format response.
Although ACN 4 exhibits a more desirable response
than its uncalibrated counterpart, the same issues
arise as with the last calibration method where at the
cardinal direction between 0˚ to 90˚ the response in
decreases in amplitude by ~6dB at 500Hz and below
thus skewing the directivity.
Figure 20 – B-Format Signals Calibrated to Flat (On-Axis)
Middlicott & Wiggins Calibration Approaches for HOA Microphones
Page 10 of 11
6.5 Calibration by Diffuse Field
Equalization
Previous approaches optimize based on axial
responses, these have shown to have a negative
impact for off-axis positions in some cases, see
Figures 18 and 20. Averaging over the diffuse-field
attempts to negates this issue by having no bias on a
specific angle of incidence. From a capsule
perspective this has shown to offer a near flat
response below 4kHz at the axial position but above
8kHz exhibits a roll-off where frequency deviation is
evident, see Figure 11. This calibration approach
resulted in a slight decrease in the directionality of the
polar responses, exhibiting a more sub-cardioid
directivity at lower frequencies compared to the
uncalibrated capsules This can be confirmed by
observing the directivity responses in Figure 21.
Figure 21 – Calibrated Using Diffuse Field Equalization
Of the approaches implemented in this paper, diffuse-
field equalization yields the most accurate B-Format
responses in respect to the simulated counterpart,
nulls in both responses shown in Figure 22 are largely
improved over the raw measured responses and there
is greater consistency in the cardinal directions in
comparison to the previous calibration approaches.
Figure 22 – Diffuse Field Equalized B-Format Signals
7 Future Work
Research results show some interesting points
regarding capsule calibration and optimization
approaches, leaning towards optimizing with no bias
to one particular angle of incidence, as opposed to an
on-axis based approach. these approaches also
highlight the importance of effective pre and post-
filtering.
The work conducted has shown scope for further
investigation; specifically, the expansion to include the
full 3D spherical arrays. Consequently, development
of several array prototypes is under construction and
these prototypes will be measured imminently,
including an investigation into the generation of B-
Format signals and associated post filtering
approaches.
Worthy of notation the microphone array simulation
routine utilized in this work, although useful, would
benefit from additional features such as frequency
dependent capsule directivity, along with the updates
to the associated applications [1].
8 Conclusions
The implementation of several capsule calibration
approaches for ambisonic microphone arrays has
been outlined and evaluated. Analysis of the array
response at each stage of the calibration process has
shown that when calibrating with inexpensive
microphone capsules all of the approaches
considered in this paper have offered some degree of
improvement upon the raw B-Format, but when the
calibration approach optimizes for an axial capsule
response a correlation between this dependency on a
fixed angle and the deterioration of the B-Format
directivity response at certain off-axis angles is
evident. When an approach such as Average Gain
Matching or Diffuse Field Equalisation is utilised the
resultant array response observed exhibits a more
robust B-Format directivity than if optimising for an
axial position by filtering in the frequency domain. It
should be noted, the ability to accurately derive the
desired directivity above 2kHz has continually been
sub-optimal regardless of the approach used, this re-
affirms the need for effective post-filtering when
calibrating ambisonic microphones, especially when
using low cost capsules.
Middlicott & Wiggins Calibration Approaches for HOA Microphones
Page 11 of 11
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