metrology.comparison_calibration

Calibration of a measurement microphone by comparison with a reference microphone (IEC 61094-5:2016, pressure; IEC 61094-8:2012, free field).

A working standard microphone is not calibrated by reciprocity. It is put beside, or in place of, a reference microphone whose sensitivity is already known, both are exposed to the same sound pressure, and the ratio of their open-circuit output voltages carries the reference’s sensitivity over to it. IEC 61094-5 does this in a pressure field, in a coupler or a jig; IEC 61094-8 does it in a free field, in an anechoic room or behind a time window. Annex D of the first part writes the model once for both:

where $R_V$ is the ratio of the output voltages of the test and reference microphones and $R_P$ that of the effective sound pressures acting on them, reduced to unity by the procedure and the corrections. In sensitivity levels, the form every function here computes,

with $C_j$ the corrections the part asks for.

Simultaneous excitation (IEC 61094-5 5.1.2 and Annex C, IEC 61094-8 5.3). Both microphones sit in the field at once, each on its own measuring channel. The level reading difference between the channels, reference on channel 1, is Formula (C.1); after the microphones are interchanged it is Formula (C.2); and their difference cancels the gains of the two channels and the asymmetry of the field, Formula (C.3):

IEC 61094-5 requires the interchange in a coupler or a jig (“shall be used”, 5.1.2); simultaneous_comparison refuses a pressure calibration without it. IEC 61094-8 does not, and without it the channel difference is taken as read.

Sequential excitation (IEC 61094-5 5.1.3 and Annex B, IEC 61094-8 5.2 and Annex A). The microphones take the same place in turn. Either the exchange does not change the sound pressure significantly, or any change is detected and corrected, for example with a monitor microphone near the source: the ratio of each microphone’s output to the monitor’s, and the quotient of the two ratios, is the output ratio corrected for the drift (IEC 61094-8 A.2). sequential_comparison computes it, with the MonitorReadings of the monitor or without.

Corrections. IEC 61094-8 7.6 always corrects the reference’s sensitivity to the environmental conditions of the test. IEC 61094-5 6.6 does so when the two microphones are different models; for two of the same model it allows the result to be referred instead to the conditions at which the reference’s calibration is valid. Both parts allow the result to be referred to the reference conditions of clause 4 (23,0 °C, 101,325 kPa, 50 %) when reliable correction data are available. environmental_sensitivity_correction writes that correction to first order from the coefficients of the microphone, in the units IEC 61094-2 Annex D gives them. jig_diameter_correction returns the corrections of IEC 61094-5 Table A.1 for a type WS3 microphone calibrated against an LS2aP in the jig of Figure A.4, and diameter_sound_field_correction computes them for any test microphone smaller than its reference by the model 6.5 refers to, Barham, Barrera-Figueroa and Avison (2014), from which Table A.1 was calculated. A free-field calibration against a reference calibrated in a pressure field takes the reference’s free-field to pressure sensitivity level difference of IEC/TS 61094-7 (IEC 61094-8 Table 1 and 8.2).

Uncertainty. comparison_uncertainty_budget combines, on combine_uncertainty, the components of IEC 61094-5 Table D.1 or IEC 61094-8 Table 2, each with a sensitivity of 1 in the level model above, and multiplies the combined standard uncertainty by the coverage factor $k=2$ both parts report with (IEC 61094-5 7.9 and D.2, IEC 61094-8 8.8). The expanded uncertainty is then passed to the calibration, which draws it as a band.

The effective free-field region (IEC 61094-8 B.1). free_field_region gives the prolate spheroid inside which a time window of length $\tau$ simulates a free field, with the source and the microphone at its foci and the major diameter

at the speed of sound $c$ of IEC 61094-2 Annex F for the conditions of the test (air). Turned round, reflection_free_window_s gives the longest window that keeps a reflection of a known path outside it.

The phase of the sensitivity (IEC 61094-5 5.1.1, IEC 61094-8 5.1). Both parts carry the phase over with the modulus: IEC 61094-5 calculates “the sensitivity (both modulus and phase) of the test microphone”, and IEC 61094-8 “both the modulus and phase of the free-field sensitivity of the microphone under test”. The model of D.2 holds for the complex ratios, so the phase follows the level term by term:

and the interchange of Annex C cancels the phase shifts of the two channels and of the field just as (C.3) cancels their gains, ${\phi }_{\mathrm{ref}}-{\phi }_{\mathrm{test}}=\frac{1}{2}({\Phi }_{C12}-{\Phi }_{C21})$. In a free field the phases have to be referred to the acoustic centres of the microphones (5.1 of the second part), which 7.3 positions “at the measurement points”; in a sequential substitution both centres go to the same point in turn, and the pressures on the two microphones have the same phase there. The phase inputs of a calibration travel together, as a SimultaneousComparisonPhase or a SequentialComparisonPhase.

Different acoustic impedances (IEC 61094-5 7.4 and 7.5). Two microphones of different acoustic impedance do not see the same sound pressure; neither clause prints a model, and both ask for the effect to be assessed and taken into the budget. impedance_pressure_ratio writes it in one form, each microphone’s equivalent volume $V_{\mathrm{e}}$ (IEC 61094-1 6.2.2) against the equivalent volume $V_x$ of what it works into,

for two circuits: a closed coupler, the printed Formula (3) of IEC 61094-2, for a sequential substitution; and, for a simultaneous excitation, each microphone in series with the air between the two, as the “Microphone impedance” row of Table D.1 has it, by the circuit of its reference [2], Jarvis (1996), whose series impedance air_gap_series_impedance_pa_s_m3 gives. ReciprocityMicrophone.complex_equivalent_volume_m3 gives $V_{\mathrm{e}}$ from the lumped parameters of IEC 61094-2 E.4.

Validation (IEC 61094-5 6.7). Calibrations made in a jig or a coupler “shall be validated by comparison with calibrations performed in other jigs and couplers and alternative sound sources”, or, for a laboratory standard microphone, with its reciprocity calibration. verify_jig_or_coupler sets the two calibrations side by side; the clause prints no criterion, and the library reads it as their agreeing within the expanded uncertainty of their difference. Two calibrations that share a component entering both levels alike, the same reference microphone or the same measuring chain, are correlated, and the part they share cancels in the difference: with $u_{\mathrm{sh}}$ its standard uncertainty, the GUM law of propagation for correlated inputs (JCGM 100:2008 5.2.2, with the covariance $u_{\mathrm{sh}}^2$ of F.1.2.3 for two sensitivities of 1) gives

which shared_standard_uncertainty_db passes to it.

Time-selective processing (IEC 61094-8 Annex B). A free field can be simulated by keeping only the direct sound of an impulse response: time_selective_response weights the response with a time window (B.1.3), with the “‘tapered’ edges” B.1.2 says it “normally has”, and transforms what is left by Formula (B.2), at any frequency. The impulse response comes from any of the methods of B.2 to B.6: stepped_sine_impulse_response takes a stepped-sine measurement to the time domain by Formula (B.3), and the sweeps, the maximum length sequences and the random noise of B.3 to B.5 are those of phonometry.room and phonometry.electroacoustics. For the direct impulse method of B.6, rectangular_pulse is the pulse of Formula (B.10) and rectangular_pulse_duration_s the duration whose first spectral zero lies an order of magnitude above the frequencies of interest.

IEC 61094-5 D.3. The root-sum-square of the eight components Table D.1 prints is 0,0437 dB, not the 0,040 dB D.3 states; with $k=2$ it is 0,087 dB rather than 0,08 dB. comparison_uncertainty_budget gives the sum of the printed components, and the defect is in docs/ERRATA.md.

IEC 61094-8 B.10. The spectrum of Formula (B.10) is that of a rectangular pulse of duration $2b$, although the text calls $b$ the duration. The formula and the first zero it puts at $1/(2b)$ agree, so the library follows them and reads $b$ as the half-duration: rectangular_pulse takes the whole duration $T=2b$. The defect is in docs/ERRATA.md.

Barham et al. (2014), Formulas (1), (2) and (4). With the inputs of its Table 1, the model as printed gives -0.986 dB at 20 kHz at 344,8 m/s, where its Table 2 (Table A.1 of IEC 61094-5) prints -1.443 dB. Read with the radial sensitivity of Formula (4) less 1, the deflection of a membrane under a uniform pressure, the annulus of Formula (2) from the test microphone’s overall radius, and $k_{n}r/a$ in Formula (1) as in (2) and (3), it gives every row of the table; diameter_sound_field_correction follows that reading. The defects are in docs/ERRATA.md.

Jarvis (1996), Appendix B. In the published scan the impedance of the first microphone reads $r_1+wm+1/(\mathrm{i}w{c}_1)$, its mass term without the imaginary unit the second microphone’s carries: blank space stands where the glyphs belong, as it does for others the scan loses on the same folio. Only $\mathrm{i}w{m}_1$ gives the graphs computed from it, and air_gap_series_impedance_pa_s_m3 is checked against that. The defect is in docs/ERRATA.md.

The IEC 61183 diffuse-field comparison of clause 5 (diffuse_field_sensitivity) is the same sequential comparison without a monitor, and computes its level difference and its sensitivity level through this module.

Auto-generated from the source docstrings by scripts/generate_api_docs.py (make api-docs). Do not edit by hand.

air_gap_series_impedance_pa_s_m3(
    frequencies_hz: ArrayLike,
    *,
    gap_length_m: float,
    gap_radius_m: float,
    temperature_c: float = 23.0,
    static_pressure_kpa: float = 101.325,
    relative_humidity_percent: float = 50.0,
    gas: Fluid | None = None,
) -> NDArray[np.complex128]

The acoustic impedance of the air between two microphones that each acts in series with, in a symmetric coupler driven at its middle (IEC 61094-5:2016 Table D.1 and 7.4, by the circuit of Jarvis 1996, reference [2] of the part).

“The acoustical impedance of the microphone acts in series with that of the air in the space between the two microphones. Microphones with different acoustic impedance therefore see slightly different pressures when simultaneously exposed to the same pressure field (see 7.4 and [2])” (Table D.1, “Microphone impedance”). Reference [2], NPL Report CIRA(EXT) 010, models the coupler in its Appendix B as a ladder: the source at the reference plane in the middle, and on each side a mass $Z_L$, the compliance $Z_c$ of that side’s half of the volume to ground, a second $Z_L$ and the microphone,

for a tube of length $L$ and radius $r$. It prints the ratio of the two pressures, $R=Z_{s1}{Z}_{m1}{Z}_{o2}(Z_L+Z_{m2})/[Z_{o1}(Z_L+Z_{m1})Z_{s2}{Z}_{m2}]$ with $Z_s=Z_c\parallel (Z_L+Z_m)$ and $Z_o=Z_L+Z_s$. Seen from each microphone, the pressure of the middle behind the ladder is a source of pressure $p_c{Z}_c/(Z_L+Z_c)$, common to both, behind the impedance this function returns,

so each diaphragm takes that pressure times $Z_m/(Z_m+Z_x)$, and the printed ratio is the divider of impedance_pressure_ratio given coupling_impedance_pa_s_m3 = $Z_x$, exactly.

Parameters

Returns: $Z_x$ at each frequency, complex, in Pa·s/m³, read-only.

Raises

comparison_uncertainty_budget(
    standard_uncertainties_db: Mapping[str, float | Quantity],
    *,
    frequency_hz: float,
    field: str = 'pressure',
    additional_components: Sequence[Quantity] = (),
    coverage_factor: float = 2.0,
) -> ComparisonUncertaintyBudget

The uncertainty budget of a comparison calibration at one frequency (IEC 61094-5:2016 Annex D; IEC 61094-8:2012 8.8 and Table 2).

Each component is given as a standard uncertainty in dB, the column Table D.1 prints, or as a Quantity whose standard uncertainty it takes: metrology.rectangular(0, 0.03) for a semi-range of 0,03 dB, say. They are keyed by the names of IEC61094_5_TABLE_D1 for a pressure calibration and of IEC61094_8_TABLE_2 for a free-field one; neither table is exhaustive (D.1, 8.1), so a component may be left out and additional_components adds the ones a set-up needs, such as the diameter correction of a WS3 microphone in the jig (Table D.1, special cases). The combination is combine_uncertainty on the level model, every component with a sensitivity of 1, which is the root-sum-square of D.3; the expanded uncertainty is $k=2$ times it, the coverage factor 7.9 and D.2 of the first part and 8.8 of the second report with.

With the eight components of Table D.1 at 2 kHz the combined standard uncertainty is 0,0437 dB and the expanded one 0,087 dB. D.3 prints 0,040 dB and 0,08 dB, which are not the root-sum-square of its own components (an erratum; see docs/ERRATA.md).

Parameters

Returns: The ComparisonUncertaintyBudget.

Raises

ComparisonCalibration(
    frequencies_hz: NDArray[np.float64],
    reference_sensitivity_level_db: NDArray[np.float64],
    output_level_differences_db: NDArray[np.float64],
    pressure_level_difference_db: NDArray[np.float64],
    corrections_db: Mapping[str, NDArray[np.float64]],
    field: str,
    excitation: str,
    expanded_uncertainty_db: NDArray[np.float64] | None = None,
    *,
    reference_sensitivity_phase_deg: NDArray[np.float64] | None = None,
    output_phase_differences_deg: NDArray[np.float64] | None = None,
    pressure_phase_difference_deg: NDArray[np.float64] | None = None,
)

The sensitivity level of a microphone calibrated by comparison (IEC 61094-5:2016 D.2 for a pressure field, IEC 61094-8:2012 for a free field).

Attributes

property

${\sum }_j{C}_j$, in dB (0 without corrections).

property

The number of determinations averaged.

property

$20\lg R_V$, the mean over the determinations, in dB.

property

$\arg R_V$, the mean over the determinations, in degrees, or None for a calibration of the level alone.

ComparisonCalibration.plot(
    ax: Axes | None = None,
    *,
    quantity: str = 'level',
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Plot $L_{\mathrm{test}}$ and the reference’s level against frequency, with the expanded uncertainty as a band when it is known, or the two phases.

The reference’s level is $L_{\mathrm{ref}}$, or, in a free field against a pressure-calibrated reference, $L_{\mathrm{ref}}$ plus its free-field difference: the level the test microphone was compared with.

Parameters

Returns: The axes. Requires matplotlib (pip install phonometry[plot]).

Raises

property

$L_{\mathrm{test}}$, in dB re 1 V/Pa.

property

$M_{\mathrm{test}}=10^{L_{\mathrm{test}}/20}$ V/Pa, in mV/Pa.

property

${\phi }_{\mathrm{test}}={\phi }_{\mathrm{ref}}+\arg R_V-\arg R_P$, in degrees from -180° (excluded) to 180°, or None for a calibration of the level alone (IEC 61094-5 5.1.1, IEC 61094-8 5.1).

property

The designation the calibration follows.

ComparisonUncertaintyBudget(
    frequency_hz: float,
    field: str,
    names: tuple[str, ...],
    components: tuple[str, ...],
    standard_uncertainties_db: NDArray[np.float64],
    uncertainty: UncertaintyResult,
    coverage_factor: float = 2.0,
)

The uncertainty budget of a comparison calibration at one frequency (IEC 61094-5:2016 Annex D, IEC 61094-8:2012 8.8).

Every component is a standard uncertainty in dB and enters the level model with a sensitivity of 1, so the combined standard uncertainty is their root-sum-square (D.3), and the expanded uncertainty is $k=2$ times it (7.9 of the first part, 8.8 of the second).

Attributes

property

$u_{\mathrm{c}}$, the combined standard uncertainty, in dB.

property

$U=k{u}_{\mathrm{c}}$, in dB.

property

$u_{\mathrm{c}}$ combined in linear form, in dB.

Each component converted to a relative uncertainty, $r_i=10^{u_i/20}-1$, combined in quadrature and converted back, $20\lg (1+r_{\mathrm{c}})$: the “strict calculation” D.3 mentions and 8.8 prefers. For components of a few hundredths of a decibel it differs from combined_uncertainty_db in the fourth decimal at most, which is why both parts accept the logarithmic form.

ComparisonUncertaintyBudget.plot(
    ax: Axes | None = None,
    *,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Plot the standard uncertainty of each component, with $u_{\mathrm{c}}$, $k$ and $U$.

Parameters

Returns: The axes. Requires matplotlib (pip install phonometry[plot]).

property

The designation whose table the budget follows.

ComparisonUncertaintyRow(
    component: str,
    subclauses: tuple[str, ...] = (),
    stated_db: float | None = None,
    divisor: float | None = None,
    standard_uncertainty_db: float | None = None,
)

One row of the uncertainty table of IEC 61094-5 (Table D.1) or IEC 61094-8 (Table 2).

Table D.1 is a worked example at 2 kHz: seven of its eight rows state a value, the distribution it is read with and the standard uncertainty that follows; the repeatability row prints its standard uncertainty alone. Table 2 lists the typical components with the subclause that discusses each and prints no value.

Attributes

diameter_sound_field_correction(
    frequencies_hz: ArrayLike,
    *,
    reference_radius_m: float,
    test_diaphragm_radius_m: float,
    test_outer_radius_m: float,
    separation_m: float,
    reference_resonance_frequency_hz: float,
    test_resonance_frequency_hz: float,
    temperature_c: float = 23.0,
    static_pressure_kpa: float = 101.325,
    relative_humidity_percent: float = 50.0,
    gas: Fluid | None = None,
) -> DiameterSoundFieldCorrection

The correction for a test microphone smaller than the reference it faces in a jig (IEC 61094-5:2016 6.5 and A.2), by the model of Barham, Barrera-Figueroa and Avison (2014), the reference [1] of the part.

“The effect of a non-uniform pressure distribution over the surface of the diaphragm will be significantly greater if the test and reference microphones are of different diameters. A theoretical model which can be used to apply corrections and assess the uncertainties in this case is given in the literature (for example [1])” (6.5). The model is the origin of Table A.1: the space between the diaphragms is a cylinder of the reference’s front-cavity radius $a$ and length $L$, closed by the reference at $z=0$ and driven, in a radially symmetrical field, through the annulus around the smaller microphone at $z=L$. The pressure is a Fourier-Bessel series of the radial modes of the cavity, Formulas (1) to (3),

and each microphone reads it averaged over its diaphragm with its radial sensitivity, Formula (5), the reference at $z=0$ over $a$ and the test microphone at $z=L$ over $b$. The correction is the ratio of the two averages, $-20\lg |R_P|$.

As printed, the formulas with the inputs of the paper’s Table 1 do not give its Table 2, which is Table A.1 (an erratum in docs/ERRATA.md). They give it, every row to its printed rounding, read as follows, which is what this function computes: the radial sensitivity of Formula (4) is the deflection of a membrane under a uniform pressure, $J_0(j_{01}\varpi r/a)/J_0(j_{01}\varpi )-1$ (printed without the $-1$), with $\varpi$ the frequency over the diaphragm’s resonance frequency; the annulus that drives the gap starts at the test microphone’s overall radius, which Table 1 lists and no formula uses, while the average of Formula (5) runs over its diaphragm radius $b$; and the argument of Formula (1) is $k_{n}r/a$, as in (2) and (3). The paper prints no speed of sound: at the reference air of clause 4 the result is within 0,01 dB of every row of Table A.1, and at 344,8 m/s it is every row.

The circular symmetry it assumes is the reason a calibration it corrects is made with a coaxial source in a free field or in a diffuse field averaged long enough (6.5, A.2). The radial sensitivity of Formula (4) divides by $J_0(j_{01}\varpi )$, which vanishes at the resonance, so the frequencies are held below the resonance frequency of each microphone, as the paper’s are (20 kHz against 22 kHz and 100 kHz). Near the half-wave resonances of the gap, $c/2L$ and its multiples, and near the cut-offs of its radial modes, the pressures of the lossless model grow without bound while $R_P$, their ratio, stays finite and is returned; the plane mode alone gives $R_P=-1$ at $c/2L$.

Parameters

Returns: The DiameterSoundFieldCorrection.

Raises

DiameterSoundFieldCorrection(
    frequencies_hz: NDArray[np.float64],
    ratio: NDArray[np.complex128],
    doubled_separation_ratio: NDArray[np.complex128],
    reference_radius_m: float,
    test_diaphragm_radius_m: float,
    test_outer_radius_m: float,
    separation_m: float,
    speed_of_sound: float,
)

The sound-field correction of a test microphone smaller than its reference, facing it across a narrow gap (IEC 61094-5:2016 6.5, by the model of Barham, Barrera-Figueroa and Avison 2014, reference [1] of the part).

$R_P$ is the ratio of the effective sound pressures on the test and the reference microphone of D.2, each the pressure of the cavity between them averaged over its diaphragm with its radial sensitivity, and the correction to add to the test microphone’s sensitivity level is $-20\lg |R_P|$, the form Table A.1 prints. The same correction at twice the separation, which A.2 names as what the 10 % uncertainty of Table A.1 approximately is, comes with it.

Attributes

property

$-20\lg |R_P|$, in dB: to be added to the sensitivity level of the test microphone, as Table A.1 is.

property

The correction with the diaphragms twice as far apart, in dB.

property

$\arg R_P$, in degrees.

DiameterSoundFieldCorrection.plot(
    ax: Axes | None = None,
    *,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Plot the correction and the correction at twice the separation against frequency.

Parameters

Returns: The axes. Requires matplotlib (pip install phonometry[plot]).

property

How much the correction changes when the separation is doubled, in dB, as a magnitude.

A.2 estimates the expanded uncertainty of the corrections of Table A.1 as 10 % of their value, “which is approximately the change observed by doubling the distance between the microphones”. This is that change, by the model, for any geometry. 6.5 offers the model “to apply corrections and assess the uncertainties” for microphones of different diameters and prints no rule for that assessment; A.2’s doubling is the one estimate the part gives, for Table A.1. Whether to take this change as the expanded uncertainty is the caller’s estimate to make.

environmental_sensitivity_correction(
    frequencies_hz: ArrayLike,
    *,
    static_pressure_kpa: float,
    temperature_c: float,
    relative_humidity_percent: float,
    static_pressure_coefficient_db_per_kpa: ArrayLike,
    temperature_coefficient_db_per_k: ArrayLike,
    humidity_coefficient_db_per_percent: ArrayLike = 0.0,
    reference_static_pressure_kpa: float = 101.325,
    reference_temperature_c: float = 23.0,
    reference_relative_humidity_percent: float = 50.0,
) -> EnvironmentalSensitivityCorrection

The correction of a sensitivity level from one set of environmental conditions to another (IEC 61094-5 6.6, IEC 61094-8 7.6).

IEC 61094-8 7.6 asks for the reference microphone’s sensitivity to be corrected to the conditions of the test in every case. IEC 61094-5 6.6 asks for it when the two microphones are different models, and for two of the same model allows the result to be referred instead to the conditions at which the reference’s calibration is valid. Both allow the result to be referred to the reference conditions of clause 4 when reliable correction data are available; neither prints a formula. This is the first-order one, a coefficient times a deviation for each of the three conditions,

with the coefficients in the units IEC 61094-2:2009 Annex D gives them: dB/kPa for the static pressure, dB/K for the temperature. Annex D of that part puts the low-frequency static pressure coefficient of LS1P microphones between -0,01 dB/kPa and -0,02 dB/kPa and of LS2P between -0,003 dB/kPa and -0,008 dB/kPa, the temperature coefficient within ±0,005 dB/K, and all three vary with frequency and from one microphone to another, so they are the microphone’s own and are required here. 6.5.3 of the same part observes no influence of humidity on a laboratory standard microphone, hence the default of 0 for its coefficient.

The reference conditions default to clause 4 of IEC 61094-5 and IEC 61094-8, 101,325 kPa, 23,0 °C and 50 %. The correction adds to a level known at the reference conditions to give it at the conditions of the test; simultaneous_comparison and sequential_comparison add it to the reference microphone’s level (reference_environment=) or subtract it from the result (test_environment=).

Parameters

Returns: The EnvironmentalSensitivityCorrection.

Raises

EnvironmentalSensitivityCorrection(
    frequencies_hz: NDArray[np.float64],
    static_pressure_kpa: float,
    temperature_c: float,
    relative_humidity_percent: float,
    reference_static_pressure_kpa: float,
    reference_temperature_c: float,
    reference_relative_humidity_percent: float,
    static_pressure_coefficient_db_per_kpa: NDArray[np.float64],
    temperature_coefficient_db_per_k: NDArray[np.float64],
    humidity_coefficient_db_per_percent: NDArray[np.float64],
)

The change of a microphone’s sensitivity level between two sets of environmental conditions, to first order in each.

with the static pressure coefficient ${\delta }_p$ in dB/kPa, the temperature coefficient ${\delta }_t$ in dB/K and the humidity coefficient ${\delta }_H$ in dB per percentage point, each one value or one per frequency. Added to a sensitivity level valid at $(p_{s,0},t_0,H_0)$, it gives the level at $(p_s,t,H)$.

Attributes

property

$C_{\mathrm{env}}$, the sum of the three terms, in dB.

property

${\delta }_H(H-H_0)$, in dB.

EnvironmentalSensitivityCorrection.plot(
    ax: Axes | None = None,
    *,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Plot $C_{\mathrm{env}}$ and its three terms against frequency.

Parameters

Returns: The axes. Requires matplotlib (pip install phonometry[plot]).

property

${\delta }_p(p_s-p_{s,0})$, in dB.

property

${\delta }_t(t-t_0)$, in dB.

free_field_region(
    source_distance_m: float,
    window_time_s: float,
    *,
    temperature_c: float = 23.0,
    static_pressure_kpa: float = 101.325,
    relative_humidity_percent: float = 50.0,
) -> FreeFieldRegion

The effective free-field region of a time window (IEC 61094-8:2012 B.1).

Formula (B.1), $A=d+\tau c$, with $c$ “the speed of sound at the prevailing environmental conditions”, which is taken from the IEC 61094-2:2009 Annex F air of air. The conditions default to the reference conditions of clause 4, 23,0 °C, 101,325 kPa and 50 %.

Parameters

Returns: The FreeFieldRegion.

Raises

FreeFieldRegion(
    source_distance_m: float,
    window_time_s: float,
    speed_of_sound: float,
)

The effective free-field region of a time-selective calibration (IEC 61094-8:2012 B.1, Formula (B.1) and Figure B.1).

A prolate spheroid generated by an ellipse with the acoustic centres of the source and of the microphone at its foci, $d$ apart, and the major diameter $A=d+\tau c$. A reflection from any point on its surface arrives $\tau$ after the direct sound, at the end of the window; the device measured is inside, and any reflecting surface or obstacle has to be outside.

Attributes

property

$A=d+\tau c$, Formula (B.1), in m.

FreeFieldRegion.plot(
    ax: Axes | None = None,
    *,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Plot the region in a plane through the axis, as Figure B.1 draws it.

Parameters

Returns: The axes. Requires matplotlib (pip install phonometry[plot]).

property

$(A-d)/2=\tau c/2$, how far the region reaches behind the microphone along the axis, in m: the mounting rod “should be sufficiently long so that the end opposite to the microphone is completely outside” it (B.1).

property

$b=\sqrt{(A/2{)}^2-(d/2{)}^2}$, the radius of the region at mid-way between the source and the microphone, in m: the clearance a surface parallel to the axis needs to be outside it.

Constant (mapping).

IEC61094_5_TABLE_A1 = {1000.0: -0.004, 1250.0: -0.006, 1600.0: -0.009, 2000.0: -0.015, 2500.0: -0.023, 3150.0: -0.036, 4000.0: -0.059, 5000.0: -0.092, 6300.0: -0.146, 8000.0: -0.235, 10000.0: -0.367, 12500.0: -0.572, 16000.0: -0.933, 20000.0: -1.443}

Constant (mapping).

IEC61094_5_TABLE_D1 = {'reference': ComparisonUncertaintyRow(component='Sensitivity of reference microphone', subclauses=(), stated_db=0.05, divisor=2.0, standard_uncertainty_db=0.025), 'capacitance': ComparisonUncertaintyRow(component='Microphone capacitance', subclauses=(), stated_db=0.01, divisor=1.7320508075688772, standard_uncertainty_db=0.006), 'non_linearity': ComparisonUncertaintyRow(component='Non-linearity', subclauses=(), stated_db=0.03, divisor=1.7320508075688772, standard_uncertainty_db=0.017), 'impedance': ComparisonUncertaintyRow(component='Microphone impedance', subclauses=(), stated_db=0.005, divisor=1.7320508075688772, standard_uncertainty_db=0.003), 'polarizing_voltage': ComparisonUncertaintyRow(component='Polarising voltage', subclauses=(), stated_db=0.008681549586371858, divisor=1.7320508075688772, standard_uncertainty_db=0.005), 'repeatability': ComparisonUncertaintyRow(component='Repeatability', subclauses=(), stated_db=None, divisor=None, standard_uncertainty_db=0.025), 'drift': ComparisonUncertaintyRow(component='Drift in reference microphone sensitivity since last calibration', subclauses=(), stated_db=0.03, divisor=1.7320508075688772, standard_uncertainty_db=0.017), 'rounding': ComparisonUncertaintyRow(component='Rounding of reported results', subclauses=(), stated_db=0.005, divisor=1.7320508075688772, standard_uncertainty_db=0.003)}

Constant (mapping).

IEC61094_8_TABLE_1 = {'primary_free_field': ReferenceCalibrationRow(microphone_types='LS', method='Primary free-field calibration', references=('IEC 61094-3',), expanded_uncertainty_1khz_db=0.25, expanded_uncertainty_10khz_db=0.1), 'primary_pressure': ReferenceCalibrationRow(microphone_types='LS', method='Primary pressure calibration with the addition of a free-field to pressure sensitivity level difference', references=('IEC 61094-2', 'IEC/TS 61094-7'), expanded_uncertainty_1khz_db=0.12, expanded_uncertainty_10khz_db=0.4), 'secondary_pressure': ReferenceCalibrationRow(microphone_types='LS', method='Secondary pressure calibration with the addition of a free-field to pressure sensitivity level difference', references=('IEC 61094-5', 'IEC/TS 61094-7'), expanded_uncertainty_1khz_db=0.15, expanded_uncertainty_10khz_db=0.5), 'secondary_free_field': ReferenceCalibrationRow(microphone_types='LS and WS', method='Secondary free-field calibration', references=('IEC 61094-8',), expanded_uncertainty_1khz_db=0.2, expanded_uncertainty_10khz_db=0.5), 'electrostatic_actuator': ReferenceCalibrationRow(microphone_types='LS and WS', method='Electrostatic actuator calibration with the addition of a free-field to actuator response level difference', references=('IEC 61094-6',), expanded_uncertainty_1khz_db=0.3, expanded_uncertainty_10khz_db=0.6)}

Constant (mapping).

impedance_pressure_ratio(
    frequencies_hz: ArrayLike,
    *,
    reference_equivalent_volume_m3: ArrayLike,
    test_equivalent_volume_m3: ArrayLike,
    coupling_equivalent_volume_m3: ArrayLike | None = None,
    coupling_impedance_pa_s_m3: ArrayLike | None = None,
) -> ImpedancePressureRatio

The ratio of the sound pressures that the different acoustic impedances of two microphones cause (IEC 61094-5:2016 7.4 and 7.5).

“Differences in the acoustic impedance between the test and reference microphones can cause the sound pressure at the test and reference microphones to differ” (7.4), most where a pressure and a free-field response microphone meet above 10 kHz (7.5). Neither clause prints a model; both refer the effect to the uncertainty, and 7.4 to the literature for a model. This function writes two circuits: the closed coupler that IEC 61094-2 prints as Formula (3), and the series divider of the simultaneous excitation of Table D.1, the circuit of its reference [2], Jarvis (1996). Each microphone enters by its equivalent volume $V_{\mathrm{e}}={\kappa }_{\mathrm{r}}{p}_{s,\mathrm{r}}/(\mathrm{j}\omega Z_{\mathrm{a}})$ (IEC 61094-1 6.2.2, with ${\kappa }_{\mathrm{r}}=1,40$ and $p_{s,\mathrm{r}}$ = 101,325 kPa):

• A closed coupler, sequential substitution. In a coupler small against the wavelength, the source drives the sum of the admittances of the gas and of every microphone in it, IEC 61094-2:2009 Formula (3), $1/Z=\mathrm{j}\omega [V/(\kappa p_s)+\sum V_{\mathrm{e}}/({\kappa }_{\mathrm{r}}{p}_{s,\mathrm{r}})]$, so putting the test microphone in the place of the reference changes the pressure by $R_P=(V_x+V_{\mathrm{e},\mathrm{ref}})/(V_x+V_{\mathrm{e},\mathrm{test}})$, with $V_x$ the rest of the load: the gas volume referred to the reference conditions, $V{\kappa }_{\mathrm{r}}{p}_{s,\mathrm{r}}/(\kappa p_s)$, and the equivalent volumes of the source and of any monitor. A monitor that “accurately sense[s] changes in the sound pressure at the test/reference microphone position” (5.1.3) corrects for this ratio; without one it is the correction. Pass coupling_equivalent_volume_m3.
• The air between the microphones in series, simultaneous excitation. “The acoustical impedance of the microphone acts in series with that of the air in the space between the two microphones. Microphones with different acoustic impedance therefore see slightly different pressures when simultaneously exposed to the same pressure field” (Table D.1, “Microphone impedance”). The row refers to [2], Jarvis (1996), whose Appendix B draws the coupler as a ladder from a source at its middle; seen from each microphone, that is a common pressure $p_0$ behind one series impedance $Z_x$, so each diaphragm takes $p_0{Z}_{\mathrm{a}}/(Z_{\mathrm{a}}+Z_x)$ and the ratio of the two is the one Appendix B prints, exactly. Written with volumes this is the same ratio, $V_x$ being the equivalent volume of $Z_x$, ${\kappa }_{\mathrm{r}}{p}_{s,\mathrm{r}}/(\mathrm{j}\omega Z_x)$. Pass coupling_impedance_pa_s_m3, which air_gap_series_impedance_pa_s_m3 gives for a coupler of known length and radius; Table D.1 still asks for the effect to be “established experimentally” when the impedances differ significantly.

Parameters

Returns: The ImpedancePressureRatio.

Raises

ImpedancePressureRatio(
    frequencies_hz: NDArray[np.float64],
    ratio: NDArray[np.complex128],
    coupling: str,
    coupling_equivalent_volume_m3: NDArray[np.complex128],
)

The ratio of the sound pressures on the test and the reference microphone that their different acoustic impedances cause (IEC 61094-5:2016 7.4 and 7.5).

with $V_{\mathrm{e}}$ the equivalent volume of each microphone and $V_x$ that of what it works into. Its level, level_difference_db, is the pressure_level_difference_db of a comparison, and its phase the pressure_phase_difference_deg.

Attributes

property

$20\lg |R_P|$, in dB: what the test microphone hears more than the reference.

property

$\arg R_P$, in degrees.

ImpedancePressureRatio.plot(
    ax: Axes | None = None,
    *,
    quantity: str = 'level',
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Plot $20\lg |R_P|$ and its standard uncertainty, or $\arg R_P$, against frequency.

Parameters

Returns: The axes. Requires matplotlib (pip install phonometry[plot]).

Raises

property

The level difference taken as the semi-range of a rectangular distribution, $|20\lg |R_P||/\sqrt{3}$, in dB.

This is how Table D.1 of IEC 61094-5 carries the effect, a semi-range of 0,005 dB at 2 kHz giving 0,003 dB, and how 7.5 asks for it when no reference of similar impedance is available: “the size of the error caused should be estimated and added to the uncertainty budget”. It is the "impedance" component of comparison_uncertainty_budget; a calibration that corrects for $R_P$ instead takes only what is left of it. The same row of Table D.1 warns that “when microphones have significantly differing impedances (for example WS2F microphone compared against LS2P at frequencies above 10 kHz), the measurement uncertainty can be considerably larger and should be established experimentally”: there this value is an estimate of the model’s, not a substitute for that experiment.

jig_diameter_correction(
    frequencies_hz: ArrayLike | None = None,
) -> JigDiameterCorrection

The corrections of IEC 61094-5:2016 Table A.1 for a type WS3 microphone against a type LS2aP reference in the jig of Figure A.4.

The table gives them at the preferred one-third-octave frequencies from 1 kHz, -0,004 dB, to 20 kHz, -1,443 dB, calculated for a radially symmetrical field and the 0,5 mm diaphragm separation of Figure A.4, “the only one for which the corrections specified in Table A.1 are valid”. A frequency within 2 % of a row, such as an exact base-ten one-third-octave frequency, reads as that row. Pass .correction_db to the comparison as one of its corrections_db and .standard_uncertainty_db to the budget as an additional component.

Parameters

Returns: The JigDiameterCorrection.

Raises

JigCouplerVerification(
    frequencies_hz: NDArray[np.float64],
    calibration_level_db: NDArray[np.float64],
    calibration_uncertainty_db: NDArray[np.float64],
    validation_level_db: NDArray[np.float64],
    validation_uncertainty_db: NDArray[np.float64],
    validation: str,
    unvalidated_frequencies_hz: NDArray[np.float64],
    *,
    shared_standard_uncertainty_db: NDArray[np.float64] = ...,
)

A calibration made in a jig or a coupler set against another calibration of the same microphone (IEC 61094-5:2016 6.7).

The difference of the two sensitivity levels at each frequency both calibrated, $\Delta =L_{\mathrm{cal}}-L_{\mathrm{val}}$, is judged against the expanded uncertainty of that difference: the jig or coupler agrees at a frequency where $|\Delta |\le U_{\Delta }$. 6.7 asks for the validation and prints no criterion; this is the library’s reading of it.

Two independent calibrations give $U_{\Delta }=\sqrt{U_{\mathrm{cal}}^2+U_{\mathrm{val}}^2}$. Two that share a component, the same reference microphone or the same measuring chain, are correlated: each depends on the shared quantity with a sensitivity of 1, so the covariance of the two levels is its variance $u_{\mathrm{sh}}^2$ (JCGM 100:2008 F.1.2.3, Formula (F.2)), and the law of propagation for the difference (5.2.2, Formula (13)) is

the shared part cancelling in the difference. With the coverage factor $k=2$ both expanded uncertainties are reported with (IEC 61094-5 7.9 for a comparison, IEC 61094-2:2009 7.5 for a reciprocity calibration), $U_{\Delta }=\sqrt{U_{\mathrm{cal}}^2+U_{\mathrm{val}}^2-2(k{u}_{\mathrm{sh}}{)}^2}$, the root-sum-square of the parts of the two expanded uncertainties that are each calibration’s own. Only a component that enters both levels with the same sign and size can be shared this way; one that enters them with opposite signs makes the covariance negative and widens the band beyond the root-sum-square, which this verification does not represent.

Attributes

property

Whether $|\Delta |\le U_{\Delta }$ at each frequency, both sides settled to a nanodecibel before they meet.

property

$r=u_{\mathrm{sh}}^2/(u_{\mathrm{cal}}{u}_{\mathrm{val}})$, the correlation coefficient of the two levels (JCGM 100:2008 5.2.2, Formula (14)), at each frequency: 0 for two independent calibrations, and towards 1 as the shared part outweighs what each calibration adds to it (F.1.2.3, Example 2). 0 where a calibration carries no uncertainty, and so shares none.

property

$\Delta =L_{\mathrm{cal}}-L_{\mathrm{val}}$, in dB.

property

$U_{\Delta }=\sqrt{U_{\mathrm{cal}}^2+U_{\mathrm{val}}^2-2(k{u}_{\mathrm{sh}}{)}^2}$, the expanded uncertainty ($k=2$) of the difference, in dB: the root-sum-square of the two expanded uncertainties when the calibrations share nothing.

property

The frequencies where the two calibrations disagree, in Hz.

property

$\Delta /U_{\Delta }$, the difference in units of its expanded uncertainty: within $\pm 1$ where the two agree.

property

The verdict: the two calibrations agree within the expanded uncertainty of their difference at every frequency they share.

True says the jig or coupler is validated for this type of microphone over these frequencies, and no wider: 6.7 asks for “a separate validation […] for each different type of microphone”, and the frequencies in unvalidated_frequencies_hz are not covered.

JigCouplerVerification.plot(
    ax: Axes | None = None,
    *,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Plot the difference of the two calibrations against the expanded uncertainty of the difference, marking where they disagree, with the frequencies the validation does not cover as dashed vertical lines.

Parameters

Returns: The axes. Requires matplotlib (pip install phonometry[plot]).

JigDiameterCorrection(
    frequencies_hz: NDArray[np.float64],
    correction_db: NDArray[np.float64],
)

The corrections of IEC 61094-5 Table A.1 at the frequencies asked for.

Added to the sensitivity level of a type WS3 microphone calibrated against a type LS2aP reference in the jig of Figure A.4, they account for the radial sensitivity of the two diaphragms and for the smaller one of the test microphone. Their expanded uncertainty is 10 % of their value (A.2 and the NOTE to Table A.1), a component of the budget of Table D.1. None of the three places that give the 10 % states its coverage factor; the library reads it as $k=2$, the factor 7.9 and D.2 report every expanded uncertainty with.

Attributes

property

The expanded uncertainty of each correction, one tenth of its magnitude, in dB (read as $k=2$, 7.9 and D.2).

JigDiameterCorrection.plot(
    ax: Axes | None = None,
    *,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Plot the corrections with their expanded uncertainty.

Parameters

Returns: The axes. Requires matplotlib (pip install phonometry[plot]).

property

The standard uncertainty of each correction, the expanded one over $k=2$ (a reading of 7.9 and D.2, since the 10 % comes without a coverage factor), in dB: the special-case component of Table D.1.

MonitorReadings(
    *,
    reference_level_db: ArrayLike,
    test_level_db: ArrayLike,
    reference_phase_deg: ArrayLike | None = None,
    test_phase_deg: ArrayLike | None = None,
)

The readings of the monitor microphone that watches the source of a sequential calibration (IEC 61094-5:2016 5.1.3, IEC 61094-8:2012 A.2).

They travel together because they are one instrument’s: the monitor is read in the measurement of each microphone, and each microphone’s output is taken re the monitor reading taken with it, so a source that drifts between the two measurements cancels in the quotient of the two ratios. Its phases are read with its levels when the calibration carries the phase. Pass one to sequential_comparison as monitor.

Parameters

Raises

rectangular_pulse(
    duration_s: float,
    *,
    amplitude_v: float = 1.0,
) -> RectangularPulse

The rectangular pulse of the direct impulse method (IEC 61094-8:2012 B.6.1).

“A signal that approximates an idealized unit impulse (delta function) can be directly applied to the sound source”, and “in order to have a flat spectrum in the frequency range of interest […] the duration of the input signal needs to be sufficiently short”: its spectrum is Formula (B.10). Give the whole duration $T$; Formula (B.10) writes it as $2b$ (docs/ERRATA.md). rectangular_pulse_duration_s gives the duration for an upper limit of frequency.

Parameters

Returns: The RectangularPulse.

Raises

rectangular_pulse_duration_s(
    upper_frequency_hz: float,
    *,
    zero_ratio: float = 10.0,
) -> float

The duration of a rectangular pulse whose first spectral zero lies a given factor above the frequencies of interest (IEC 61094-8:2012 B.6.1).

The first zero, $1/(2b)=1/T$, “must be approximately an order of magnitude higher than the upper limit of the frequency range of interest, leading to a requirement for the duration, $b$ of just a few microseconds”:

with $r$ the factor, 10 by default. For 20 kHz that is 5 µs, a half-duration $b$ of 2,5 µs, at which the spectrum has fallen by 0,14 dB.

Parameters

Returns: $T$, in s.

Raises

RectangularPulse(duration_s: float, amplitude_v: float = 1.0)

The rectangular pulse of the direct impulse method (IEC 61094-8:2012 B.6.1, Formula (B.10)).

A pulse of amplitude $a$ lasting $T$ has the spectrum

Formula (B.10), whose first zero is at $f=1/(2b)=1/T$. The standard calls $b$ the duration; the formula and its first zero are those of a pulse lasting $2b$ (docs/ERRATA.md), and the library follows them.

Attributes

property

$X(0)=2ab$, the area of the pulse, in V·s.

property

$1/(2b)$, the first zero of the spectrum, in Hz (B.6.1).

property

$b$ of Formula (B.10), half the duration, in s.

RectangularPulse.level_db_at(
    frequencies_hz: ArrayLike,
) -> NDArray[np.float64]

$20\lg |X(f)/X(0)|$, how far the spectrum has fallen from its value at 0 Hz, in dB (minus infinity at a zero).

Parameters

Returns: The level at each, in dB.

RectangularPulse.plot(
    ax: Axes | None = None,
    *,
    upper_frequency_hz: float | None = None,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Plot $|X(f)/X(0)|$ in dB up to past its second zero, with the first zero and, when given, the upper limit of the frequencies of interest.

Parameters

Returns: The axes. Requires matplotlib (pip install phonometry[plot]).

RectangularPulse.spectrum_at(
    frequencies_hz: ArrayLike,
) -> NDArray[np.float64]

$X(f)$ of Formula (B.10), in V·s, the transform of the pulse centred on the time origin, where it is real.

Parameters

Returns: $X(f)$ at each.

Raises

ReferenceCalibrationRow(
    microphone_types: str,
    method: str,
    references: tuple[str, ...],
    expanded_uncertainty_1khz_db: float,
    expanded_uncertainty_10khz_db: float,
)

One row of IEC 61094-8:2012 Table 1: a way the reference microphone’s free-field sensitivity can be known, and the expanded uncertainty ($k=2$) it typically carries.

Attributes

reflection_free_window_s(
    source_distance_m: float,
    reflected_path_m: float,
    *,
    temperature_c: float = 23.0,
    static_pressure_kpa: float = 101.325,
    relative_humidity_percent: float = 50.0,
) -> float

The longest time window that keeps a reflection outside the effective free-field region (IEC 61094-8:2012 B.1 and B.1.3 a)).

A point on the boundary of the region of Formula (B.1) reflects along a path of the major diameter $A=d+\tau c$, from the source to it and on to the microphone, so a reflection whose path is $L$ stays outside the region, and out of the window, while

with $\tau$ measured from the arrival of the direct sound. B.1.3 places the window by “the relative distance between source and microphone […] and from the source to the walls or other reflecting objects”; for a plane reflector the path is that of the image of the source in it. The tapered edge the window “normally has” (B.1.2) has to fall within this time too.

Parameters

Returns: $(L-d)/c$, in s.

Raises

sequential_comparison(
    frequencies_hz: ArrayLike,
    reference_sensitivity_level_db: ArrayLike,
    reference_output_level_db: ArrayLike,
    test_output_level_db: ArrayLike,
    *,
    monitor: MonitorReadings | None = None,
    field: str = 'pressure',
    pressure_level_difference_db: ArrayLike = 0.0,
    corrections_db: Mapping[str, ArrayLike] | None = None,
    reference_environment: EnvironmentalSensitivityCorrection | None = None,
    test_environment: EnvironmentalSensitivityCorrection | None = None,
    reference_free_field_difference_db: ArrayLike | None = None,
    expanded_uncertainty_db: ArrayLike | None = None,
    phase: SequentialComparisonPhase | None = None,
) -> ComparisonCalibration

Calibration by comparison with the microphones put in the field in turn (IEC 61094-5:2016 5.1.3 and Annex B; IEC 61094-8:2012 5.2 and Annex A).

The reference and the test microphone take the same place one after the other. Either the exchange does not change the sound pressure significantly, or any change is detected and corrected (IEC 61094-5 5.1.3, IEC 61094-8 5.2), for example with a monitor microphone near the source: the ratio of each microphone’s output to the monitor’s output, and the quotient of the two ratios, “gives the ratio of the microphone under test output voltage to the reference microphone output voltage, corrected for any variation in the sound pressure generated by the source” (IEC 61094-8 A.2). With $V_{\mathrm{ref}}$ and $V_{\mathrm{mon},1}$ the outputs of the reference and the monitor in the first measurement, and $V_{\mathrm{test}}$ and $V_{\mathrm{mon},2}$ those of the second,

and without a monitor $20\lg (V_{\mathrm{test}}/V_{\mathrm{ref}})$, the plain difference of the two output levels. The sensitivity level of the test microphone then follows by D.2.

Each reading may be one value per frequency or a matrix of one row per determination; the calibration averages the determinations.

Phase (IEC 61094-5 5.1.1, IEC 61094-8 5.1). With the phase of the reference’s sensitivity and the phases of the two outputs, given together as a SequentialComparisonPhase and read against the monitor’s output (its phases in the MonitorReadings) or against the signal driving the source, the calibration carries the phase of the test microphone too, the quotient of the ratios written for their phases:

In a free field the phases are those at the acoustic centres of the microphones (IEC 61094-8 5.1); with each centre placed in turn at the same measurement point (7.3), $\arg R_P$ is 0.

Parameters

Returns: The ComparisonCalibration.

Raises

SequentialComparisonPhase(
    *,
    reference_sensitivity_phase_deg: ArrayLike,
    reference_output_phase_deg: ArrayLike,
    test_output_phase_deg: ArrayLike,
    pressure_phase_difference_deg: ArrayLike | None = None,
)

The phase inputs of a calibration by sequential excitation (IEC 61094-5:2016 5.1.1, IEC 61094-8:2012 5.1).

They travel together because the phase of the test microphone needs all of them at once: the phase of the reference’s sensitivity it is carried over from, and the phases of the two outputs, read against the monitor’s output or against the signal driving the source; $\arg R_P$ completes them where the pressures on the two microphones differ in phase. The monitor’s own phases are read with its levels, in MonitorReadings. Pass one to sequential_comparison as phase.

Parameters

simultaneous_comparison(
    frequencies_hz: ArrayLike,
    reference_sensitivity_level_db: ArrayLike,
    channel_difference_db: ArrayLike,
    interchanged_channel_difference_db: ArrayLike | None = None,
    *,
    field: str = 'pressure',
    pressure_level_difference_db: ArrayLike = 0.0,
    corrections_db: Mapping[str, ArrayLike] | None = None,
    reference_environment: EnvironmentalSensitivityCorrection | None = None,
    test_environment: EnvironmentalSensitivityCorrection | None = None,
    reference_free_field_difference_db: ArrayLike | None = None,
    expanded_uncertainty_db: ArrayLike | None = None,
    phase: SimultaneousComparisonPhase | None = None,
) -> ComparisonCalibration