Source: https://jmrplens.github.io/phonometry/signals/metrology/free-field-corrections/ # Free-field corrections of a sound level meter (IEC 62585) A periodic test of a sound level meter by IEC 61672-3 drives the microphone with a sound calibrator, a comparison coupler or an electrostatic actuator, and none of those is the plane progressive wave the meter is specified for. The test needs, at each frequency, the **correction** that turns what the meter indicates on that source into what it would indicate in a free field of the same level, and the manufacturer states it in the manual. IEC 62585:2012 gives the methods for finding those corrections, the uncertainty they may carry, and the adjustment value the manual quotes at the calibration check frequency. This page runs every step on a synthetic class 1 meter and on the two worked budgets the standard prints. ## The adjustment value at the calibration check frequency The manufacturer sets the sensitivity so that the free-field response deviates as little as it can from the incident level over the whole frequency range, then applies the calibrator and reads `L4`; the manual states `Delta L = L1 - L4` as a fixed number (Annex A, clause 8). The text prints no formula for the fit, and `metrology.adjustment_value` takes the least-squares reading, the adjustment `s = -sum(w d) / sum(w)` with weights `w = 1/t²` for the tolerance `t` at each frequency: ```python import numpy as np from phonometry import filters, metrology f3 = metrology.exact_frequencies(63, 16000, fraction=3) # 25 exact one-third octaves nominal, lower, upper = filters.weighting_class_limits(1) # IEC 61672-1 Table 3, class 1 band = (nominal >= 63) & (nominal <= 16000) tolerance = np.minimum(upper, -lower)[band] # the narrower side at each band x3 = f3 / 1000 response = 0.4 + 0.12 * np.cos(3 * np.log(x3)) - 0.3 * (x3 / 8) ** 2 # indication less field, dB a = metrology.adjustment_value( f3, 94.0 + response, 94.35, calibrator_level_db=94.0, tolerance_db=tolerance ) print(round(a.sensitivity_adjustment_db, 2), round(a.adjustment_db, 2)) # -0.37 0.02 print(round(a.check_frequency_offset_db, 2)) # 0.15 ``` The adjusted meter reads a free field 0,15 dB high at 1 kHz: the offset the fit chose so the response sits inside the tolerances everywhere else. ## How the measurement goes | Requirement | Value | Clause | | :--- | :--- | :--- | | Environment | 80 kPa to 105 kPa, 20 °C to 26 °C, 25 % to 70 % relative humidity; below 97 kPa an extra component enters the budget | 6 | | Free-field mounting | On a rod of the microphone's diameter; source more than 1 m away and at least six times the largest dimension of the meter | 6 | | Samples | Three calibrators, three microphones and one meter; five microphones for a typical response, five windscreens | 7 | | Source level | 70 dB to 125 dB in a calibrator or coupler; 80 dB to 105 dB on the display at 1 kHz with an actuator | 12, 13, 14 | | Frequencies | Exact base-ten frequencies of Annex H | 10, B.2, C.2 | ## The corrections for a calibrator, a coupler and an actuator Every method compares the meter with a type LS2P reference microphone, whose free-field correction `C_FF,RM` comes from IEC/TS 61094-7 and is an input. On a calibrator (Formula (D.7)), `C_FF,SLM = (L_ind1 - L_ind3) - (L_ind2 - L_ind4) - (L_p,F1 - L_p,F2) + (L_p,P1 - L_p,P2) + C_FF,RM`: ```python f = metrology.exact_frequencies(63, 16000, fraction=1) # the nine exact octaves x = f / 1000 c_ff_rm = 0.05 * x**1.3 # C_FF,RM of the reference: illustrative free = 0.1 * np.sin(np.log(x)) - 0.05 * x**1.2 # the meter in a free field, re the field pressure = -0.1 * x**1.5 # the meter on the calibrator, re its level spread = np.array([[0.0], [0.02], [-0.03]]) * x**0.8 # three microphones of the model c = metrology.sound_calibrator_correction( f, 94.0 + free + spread, # L_ind1: the meter in the free field 94.0 + c_ff_rm, # L_ind2: the reference in its place 94.0 + pressure + spread / 2, # L_ind3: the calibrator on the meter 94.0, # L_ind4: the calibrator on the reference reference_free_field_correction_db=c_ff_rm, ) print(c.correction_db.round(2)) # [-0.04 -0.09 -0.1 -0.05 0.05 0.23 0.63 1.72 4.95] print(c.clause, c.formula) # 12 D.7 ``` The three rows are three microphones on one calibrator. The nine determinations of D.2 step 6, three microphones on three calibrators, go in as nine rows with `microphones=[1, 1, 1, 2, 2, 2, 3, 3, 3]`, so that `range_db`, the range clause 12 judges, is taken over the three microphones' mean corrections and not over the calibrators as well. `metrology.comparison_coupler_correction` names its two readings in the coupler by what each is of, `slm_coupler_level_db` and `reference_coupler_level_db`, because Formulas (E.4) to (E.6) exchange the two labels Figure E.1 defines (an [erratum](https://jmrplens.github.io/phonometry/reference/errata/)). `metrology.electrostatic_actuator_correction` returns the correction of Formula (F.13), normalised to the calibration check frequency, where it is zero. ## The uncertainty budget of Annex I `metrology.correction_uncertainty_budget` takes the fifteen components of Table I.1 as Table I.2 states them, divides each by its divisor (`√3`, 2 for `C_FF,RM`, 1 for the repeatability), combines them on `metrology.combine_uncertainty` and takes the coverage factor from the Welch-Satterthwaite effective degrees of freedom at 95 %: ```python table_i2 = { "a1": 0.005, "a2": 0.005, "a3": 0.005, "a4": 0.005, "a5": 0.05, "a6": 0.0, "a7": 0.06, "a8": 0.025, "a9": 0.025, "a10": 0.029, "a11": 0.013, "a12": 0.013, "a13": 0.0, "a14": 0.005, "a15": 0.03, } b1 = metrology.correction_uncertainty_budget(table_i2, repeatability_dof=2, frequency_hz=1000) print(round(b1.combined_uncertainty_db, 4), round(b1.effective_dof, 2)) # 0.059 29.98 print(round(b1.coverage_factor, 2), round(b1.expanded_uncertainty_db, 2)) # 2.04 0.12 ``` Tables I.2 and I.3 both reproduce. Table I.2 prints `k = 2,11`, which is not the factor its own 29,98 degrees of freedom give: at 95 % that is 2,04, and 2,11 is the one for about 17 (an [erratum](https://jmrplens.github.io/phonometry/reference/errata/)). ## The maximum permitted uncertainty, and the verdict | Clause | Correction for | Maximum expanded uncertainty | | :--- | :--- | :--- | | 9 | Reflections from the case, diffraction round the microphone | 0,25 dB up to and including 4 kHz; 0,35 dB above | | 10 | The microphone's deviation from a uniform response | 0,25 dB from 63 Hz to 4 kHz; 0,35 dB to 8 kHz; 0,45 dB above | | 11 | Windscreens and similar accessories | 0,20 dB up to and including 4 kHz; 0,30 dB above | | 12, 13, 14 | A calibrator, a coupler, an actuator | 0,25 dB up to and including 4 kHz; 0,35 dB below 10 kHz; 0,50 dB from 10 kHz | `metrology.verify_correction_uncertainty` judges the expanded uncertainty at each frequency against the maximum of the clause, and for clauses 12 to 14 the range of the corrections over the microphones too; the verdict carries `passes`, and `bool()` of it raises. `.report()` renders the documentation of clause 15 n) and o) as a one-page fiche: ```python v = metrology.verify_correction_uncertainty( f, 0.12 + 0.02 * x**0.8, clause=c.clause, correction_db=c.correction_db, correction_range_db=c.range_db, ) print(v.passes) # True ``` [](https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/reports/iec62585_free_field_correction_example.pdf) ## Exact frequencies Annex H gives the exact base-ten frequencies by Formula (H.1), `f_x = 1000 · 10^(3x/10b)` Hz, with `b = 12` for one-twelfth octaves: ```python h = metrology.exact_frequencies(1000, 10000) # the 41 rows of Table H.1 print(h.size, (h[[1, 31, 40]] / 1000).round(6)) # 41 [ 1.059254 5.956621 10. ] ``` All 41 values of Table H.1 reproduce; its exponent column prints `10^(31/80)` for index 31, where the value is `10^(31/40)` (an [erratum](https://jmrplens.github.io/phonometry/reference/errata/)). ## What this guide covers Implemented: the adjustment value of Annex A (the least-squares fit is this library's reading of a text that prints no formula); the free-field corrections for a multi-frequency calibrator, a comparison coupler and an electrostatic actuator (Formulas (D.7), (E.6) and (F.13)), averaged over the determinations with their range over the microphones kept; the uncertainty budget of Annex I with the fifteen components of Table I.1, the static-pressure component of clause 6 and the Welch-Satterthwaite coverage factor; the maxima of clauses 9 to 14 as a verdict and a fiche; and the exact frequencies of Annex H. Not implemented: the measurements themselves, the techniques of Annex G, the free-field correction of the reference microphone (an input from IEC/TS 61094-7), the corrections of clauses 9 to 11 (the set-up differences of Annexes B and C, the typical microphone response over five microphones and the rotational means of clauses 10 and 11, whose maxima are judged but which are not computed), and the comparison of the corrections with the IEC 61672-1 acceptance limits that clause 15 p) asks for separately. ## See also - [Random-incidence and diffuse-field response (IEC 61183)](https://jmrplens.github.io/phonometry/signals/metrology/random-incidence/): the response of the meter to sound from every direction. - [Measurement uncertainty](https://jmrplens.github.io/phonometry/signals/metrology/gum-uncertainty/): the GUM law of propagation and the Welch-Satterthwaite degrees of freedom the budget is built on. - [Compliance and verification](https://jmrplens.github.io/phonometry/signals/metrology/compliance-verification/): what the IEC 61672-1 class of a meter asserts. - [Errata in published sources](https://jmrplens.github.io/phonometry/reference/errata/): Table I.2, Table H.1 and Formulas (E.4) to (E.6). - API reference: [`metrology.free_field_corrections`](https://jmrplens.github.io/phonometry/reference/api/metrology/free-field-corrections/).