Muse S Athena: EEG scale factor appears to be the 12-bit constant (1650/4095) applied to 14-bit samples; midpoint not subtracted

[meanmod3]

Summary

MUSE_ATHENA_EEG_SCALE_FACTOR appears to be the 12-bit-era Muse LSB applied to 14-bit Muse S Athena samples, making BrainFlow's Athena EEG output ~4.55× too large in µV. Additionally, the Athena path does not subtract the 14-bit midpoint, so the output carries a large DC pedestal.

BrainFlow originally shipped the value that matches Interaxon's published spec, and it was changed later without discussion.

The constant

Current (src/board_controller/muse/inc/muse_athena_constants.h):

#define MUSE_ATHENA_EEG_SCALE_FACTOR 0.40293040293040294

At introduction in #779 (commit 7b2e41d3) it was:

#define MUSE_ANTHENA_EEG_SCALE_FACTOR (1450.0 / 16383.0)   // = 0.0885064

It was replaced with the bare literal in commit aa4c3226 ("generic muse improvements", #828). That commit also touched the accelerometer and gyro constants, but those were precision refinements to the same values:

constant	before	after	ratio
accelerometer	0.0000610352	0.00006103515625	×0.9999993
gyro	-0.0074768	-0.007476806640625	×1.0000009
EEG	1450.0/16383.0	0.40293040293040294	×4.5526

The EEG change is a different value, not a refinement, and I couldn't find any discussion of it (the PR body is empty and there are no review comments).

Note 0.40293040293040294 == 1650/4095 exactly — a 12-bit denominator. The Athena samples are extracted as 14-bit (extract_lsb_bits(data, bit_start, 14) in muse_athena.cpp), which has been unchanged since #779.

Why 1450/16383 looks correct

Interaxon's published Muse S Athena specification states:

Sample Resolution: 14 bits / sample
Aux Channel Connection: Input range: 725uV AC signal (1.45mVp-p) with 1.45V DC offset; Aux channels are amplified like all other EEG channels

1450 µV p-p ÷ 2^14 = 1450/16383 — i.e. the original constant is exactly the published input range divided by the published bit depth.

For contrast, the Muse 2 spec sheet (v1.0) states "12 bits / sample" with a "1.5mV p-p" input range, giving an LSB of ~0.37–0.41 µV. 0.40293 sits in that Gen-2 range — it looks like a correct previous-generation constant carried onto Athena.

Empirical check against hardware

I recorded 90 s of eyes-closed EEG from a Muse S Athena (fw 3.1.19, Athena_RevE) and used the ADC clipping level as a calibration reference. Channels that rail hit exactly ±8192 counts:

constant	implied clipping level
1450/16383	±725 µV = 1.45 mVpp — matches the published input range
0.40293…	±3300 µV = 6.60 mVpp — no Interaxon document states this

Plausibility of the resulting signal (band-limited 1–40 Hz RMS, same recording, verified 10.0 Hz alpha peak at TP9/TP10):

channel	counts	1450/16383	0.40293…
TP9	227	20.1 µV	91.5 µV
AF8	235	20.8 µV	94.8 µV
TP10	290	25.7 µV	116.9 µV
AF7 (poor contact, 15–38% railed)	1043	92.3 µV	420.3 µV

Under 1450/16383 the three well-contacted channels land in the normal range for a referential temporal derivation and the known-bad channel is the outlier. Under 0.40293 every channel — including ones carrying a clean alpha rhythm — reads well above physiological amplitudes.

Second issue: missing midpoint subtraction

muse_athena.cpp (~lines 785, 793) scales the raw unsigned value directly:

package[...] = (double)raw * MUSE_ATHENA_EEG_SCALE_FACTOR;

Since raw is an unsigned 14-bit value, the output sits on a DC pedestal of roughly half full-scale rather than being zero-centred. BrainFlow's own legacy Muse path does subtract its midpoint ((val - 0x800) * 125.0/256.0), and muse-lsl / OpenMuse / BlueMuse all subtract 1 << 13 before scaling for Athena.

Suggested fix

#define MUSE_ATHENA_EEG_SCALE_FACTOR (1450.0 / 16383.0)
#define MUSE_ATHENA_EEG_MIDPOINT     8192.0   // 1 << 13

package[...] = ((double)raw - MUSE_ATHENA_EEG_MIDPOINT) * MUSE_ATHENA_EEG_SCALE_FACTOR;

Caveat / open question

Interaxon's Athena sheet gives 1.45 mVpp, while an older Muse developer doc gives the EEG range as 1682.815 µV — a ~16% spread (LSB 0.0885 vs 0.1027). That ambiguity doesn't affect the 4.55× question but does mean the absolute figure carries ~±16% until someone injects a known-amplitude signal and reads the counts (100 µV p-p should give ~1130 counts p-p under 1450/16383). I don't have a calibration source to do that yet; happy to run it if I get access to one.

Related discussions elsewhere: muse-lsl PR #228 flags the same 4.55× disagreement as unresolved, OpenMuse issue #2 asks for the scalings to be checked, and BlueMuse PR #83 identifies 0.40293040293040294 as 1650/4095, the legacy 12-bit scale.

Environment: BrainFlow 993cb6ca, macOS 26.5 arm64, Muse S Athena fw 3.1.19.

[github-actions]

Welcome to BrainFlow project and thanks for your contribution! We will try to fix your issue ASAP. Make sure that you have read about issue format in the docs.

[Andrey1994]

hi and thanks for catching this one up.

scaling factor is fixed in #855 and I will add it to the new release
will fix midpoint calculations also