11institutetext: National Centre for Nuclear Research (NCBJ), Warsaw, Poland

# Measurement of $\mathbf{\phi_{s}}$ and $\mathbf{\Delta\Gamma_{s}}$ at LHCb

Varvara Batozskaya
on behalf of the LHCb Collaboration  11<EMAIL_ADDRESS>
###### Abstract

Determination of the mixing-induced $C\\!P$-violating phase $\phi_{s}$ and
decay width difference $\Delta\Gamma_{s}$ in $\bar{b}\to\bar{c}c\bar{s}$
decays is one of the main goals of the LHCb experiment. Thanks to the precise
prediction of the $\phi_{s}$ value within the Standard Model, it represents an
excellent probe to search for new physics. The measurements of $\phi_{s}$ and
$\Delta\Gamma_{s}$ at LHCb are reviewed including results from the 3.0 fb-1
dataset accumulated during 2011-2012. Further measurement improvement is
expected from the inclusion of results obtained using decay modes with smaller
branching fraction.

##  1 Introduction

The $C\\!P$-violating phase $\phi_{s}$ can be related to the angle $\beta_{s}$
of the unitary Cabbibo-Kobayashi-Maskawa (CKM) triangle of the $B^{0}_{s}$
meson system analogous to $\beta$ angle in $B^{0}$ meson decay Cabibbo:1963yz
. The interference between the direct decay of $B^{0}_{s}$ mesons to $C\\!P$
eigenstates via $\bar{b}\to\bar{c}c\bar{s}$ transitions and
$B^{0}_{s}-\bar{B}^{0}_{s}$ mixing allows to measure the phase $\phi_{s}$:

$\phi_{s}=\phi_{M}-2\phi_{D}=-2\beta_{s}+\Delta\phi^{Peng}_{s}+\delta^{NP}_{s}$
(1)

where $\phi_{M}$ and $\phi_{D}$ are the mixing and direct phases,
respectively. The value of $\phi_{s}$ can be shifted with respect to the
Standard Model (SM) value by the presence of higher order "penguin" diagrams
from non-perturbative hadronic effects (Fig. 1) and new physics (NP)
contributions that could be difficult to distinguish from "penguins". These
components start to play an important role when reaching high precision of the
$\phi_{s}$ measurement bib:Ligeti .

If only the dominant "tree-level" contributions are included (Fig. 1), the
phase $\phi_{s}$ within the Standard Model is predicted to be $-2\beta_{s}$
where $\beta_{s}=\arg(-V_{ts}V^{\ast}_{tb}/V_{cs}V^{\ast}_{cb})$ bib:Kobayashi
. An indirect determination of $\phi_{s}=-37.6^{+0.7}_{-0.8}$ mrad is obtained
using a global fit to experimental data Charles:2015gya .

(a)

(b)

(c)

(d)

Figure 1: Feynman diagrams: (a-b) $B^{0}_{s}-\bar{B}^{0}_{s}$ mixing and
contributions to the decay $B^{0}_{s}\to J/\psi h^{+}h^{-}$ within the SM,
where $h=\pi,K$: (c) "tree-level" and (d) "penguin" diagrams.

##  2 Status of $\phi_{s}$ and $\Delta\Gamma_{s}$ measurement

###  2.1 $B^{0}_{s}\to J/\psi\phi$ analysis and combination with $B^{0}_{s}\to
J/\psi\pi^{+}\pi^{-}$

The phase $\phi_{s}$ and the decay width difference $\Delta\Gamma_{s}$ are
extracted using a tagged time-dependent angular fit to $B^{0}_{s}\to
J/\psi(\to\mu^{+}\mu^{-})\phi(\to K^{+}K^{-})$ candidates as described in Ref.
bib:Aaij1 . The final state is decomposed into four polarization amplitudes:
three P-waves, $A_{0}$, $A_{\parallel}$, $A_{\perp}$ and one S-wave, $A_{S}$
accounting for the non-resonant $K^{+}K^{-}$ configuration. The angular
analysis is required to disentangle the interfering $C\\!P$-even and
$C\\!P$-odd components in the final state which arise due to total spin
conservation between two vector resonances coming from a pseudoscalar meson
decay.

A sample of 95 690 $\pm$ 350 signal $B^{0}_{s}\to J/\psi\phi$ candidates are
obtained after the trigger and off-line selection. The fit procedure takes
into account angular and decay time acceptances, decay time resolution as well
as the tagging efficiency. A simulated sample is used to determine the angular
acceptance. The decay time acceptance is defined from data, using a prescaled
unbiased trigger sample and a tag-and-probe technique. The decay time
resolution is estimated to be $\sim$45 fs using prompt $J/\psi K^{+}K^{-}$
combinations. The flavour tagging algorithms use the information from
additional same-side and opposite-side particles with respect to the signal
candidates optimised on simulated samples and calibrated on data using flavour
specific control channels. The obtained effective tagging power is
(3.73$\pm$0.15)$\%$ bib:Aaij1 .

A weighted unbinned likelihood fit is performed using a signal-only PDF as
described in Ref. bib:Xie . The signal weights are extracted using the sPlot
technique bib:Pivk . The fit is divided into six bins of $m(K^{+}K^{-})$
region to allow the measurement of the small ($\sim$2$\%$) S-wave amplitude in
each bin and to minimize correction factors due to the interference between
the different components of the final state. The projections of the decay time
and angular distributions are shown in Fig. 2. The measured results are
$\phi_{s}=-58\pm 49\pm 6$ mrad and $\Delta\Gamma_{s}=0.0805\pm 0.0091\pm
0.0032$ ps-1, where the first uncertainty is statistical and the second
systematic bib:Aaij1 . This measurement of the $C\\!P$-violating parameter,
$\phi_{s}$, is the single most precise to date and is in agreement with the SM
predictions Charles:2015gya ; Artuso:2015swg . The dominant source of
systematic uncertainty comes from knowledge of the angular and decay time
efficiencies, respectively.

Figure 2: Decay time and angle distributions for $B^{0}_{s}\to J/\psi\phi$
decays (black markers) with the one-dimensional projections of the PDF. The
solid blue line shows the total signal contribution, which is composed of
$C\\!P$-even (long-dashed red), $C\\!P$-odd (short-dashed green) and S-wave
(dotted-dashed purple) contributions.

The $B^{0}_{s}\to J/\psi\pi^{+}\pi^{-}$ decay analysis bib:Aaij3  is similar
to the $B^{0}_{s}\to J/\psi\phi$ one with a noticeable simplification. The
angular analysis is not needed because the final state has been found to be
$>97.7\%$ completely $C\\!P$-odd with $f_{0}(980)$ representing the dominant
component LHCb:2012ae . A combination of the $B^{0}_{s}\to J/\psi\phi$ and
$B^{0}_{s}\rightarrow J/\psi\pi^{+}\pi^{-}$ measurement gives the result of
$\phi_{s}=-10\pm 39$ mrad bib:Aaij1 .

###  2.2 $B^{0}_{s}\to\psi(2S)\phi$ analysis

The $B^{0}_{s}\to\psi(2S)(\to\mu^{+}\mu^{-})\phi(\to K^{+}K^{-})$ is another
decay mode with $\bar{b}\to\bar{c}c\bar{s}$ transition that has been exploited
by the LHCb collaboration to measure $\phi_{s}$ and $\Delta\Gamma_{s}$
Aaij:2016ohx . The formalism used for this analysis is very close to that of
$B^{0}_{s}\to J/\psi\phi$ decay bib:Aaij1  where the $J/\psi$ meson is
replaced with $\psi(2S)$. The number of signal candidates selected from a fit
to the data sample is $\sim 4700$ (Fig. 3). The decay time acceptance is
determined using a control $B^{0}\to\psi(2S)K^{\ast 0}(\to K^{+}\pi^{-})$
decay mode as shown in Fig. 3. The first measurement of the $C\\!P$-violating
parameters in a final state containing the $\psi(2S)$ resonance is
$\phi_{s}=-230^{+290}_{-280}\pm 20$ mrad and
$\Delta\Gamma_{s}=0.066^{+0.041}_{-0.044}\pm 0.007$ ps-1. The fit result is
consistent with $B^{0}_{s}\to J/\psi\phi$ measurement and the SM predictions.
The systematic uncertainty is less than 20$\%$ of the statistical uncertainty.

Figure 3: Distribution of the $m(\psi(2S)K^{+}K^{-})$ invariant mass for the
selected $B^{0}_{s}\to\psi(2S)\phi$ candidates and decay time acceptance in
arbitrary units.

###  2.3 $B^{0}_{s}\to J/\psi K^{+}K^{-}$ in high $m(K^{+}K^{-})$ range

The measurement of the $C\\!P$-violating parameters has been also performed in
the $B^{0}_{s}\to J/\psi K^{+}K^{-}$ decay with $K^{+}K^{-}$ invariant mass
higher than 1050 MeV/c2 Aaij:2017zgz  that is above the $\phi(1020)$ resonance
region. The important difference between both decay analyses is that modelling
of the $m(K^{+}K^{-})$ distribution is included to distinguish different
resonant and nonresonant contributions. The decay time acceptance is
determined with the same method as described in Aaij:2016ohx  by using a
control channel $B^{0}\to J/\psi K^{\ast 0}(\to K^{+}\pi^{-})$. The
$K^{+}K^{-}$ mass spectrum is fitted by considering the different
contributions found in the time-dependent amplitude analysis as shown in Fig.
4. The final fit has been performed allowing eight independent sets of
$C\\!P$-violating parameters: three corresponding to $\phi(1020)$ transversity
states, $K^{+}K^{-}$ S-wave, $f_{2}(1270)$, $f^{{}^{\prime}}_{2}(1525)$,
$\phi(1680)$ and the combination of the two high-mass $f_{2}(1750)$ and
$f_{2}(1950)$ states.

Figure 4: Distribution of the $m(J/\psi K^{+}K^{-})$ invariant mass with
contributing components.

The measurement result of $B^{0}_{s}\to J/\psi K^{+}K^{-}$ in the high
$m(K^{+}K^{-})$ region is $\phi_{s}=119\pm 107\pm 34$ mrad and
$\Delta\Gamma_{s}=0.066\pm 0.018\pm 0.006$ ps-1. The largest contribution to
systematic uncertainty results from the resonance fit model. The combination
with the $B^{0}_{s}$ decay fit results in the $\phi(1020)$ region gives
$\phi_{s}=-25\pm 45\pm 8$ mrad that improves the precision of the $\phi_{s}$
measurement by more than 9$\%$.

###  2.4 Global combination

The $C\\!P$-violating phase and lifetime parameters have been measured by
Tevatron and LHC experiments, namely four analysis using the $B^{0}_{s}\to
J/\psi\phi$ final state from CDF bib:CDF , D0 bib:D0 , ATLAS bib:ATLAS  and
CMS bib:CMS  collaborations and five analyses using different final states
performed by the LHCb collaboration. The world average result of $\phi_{s}$
and $\Delta\Gamma_{s}$ measurements shown in Fig. 5 is found to be
$\phi_{s}=-21\pm 31$ mrad and $\Delta\Gamma_{s}=0.085\pm 0.006$ ps-1
bib:MainPlot . It is dominated by the measurements from the LHCb collaboration
and is consistent with the SM predictions. However, the combined measurement
is still far from the SM precision thus leaving some room for NP effects. The
improvements on the sensitivity of $\phi_{s}$ are expected from the inclusion
of data collected in 2015-2018 at center-of-mass energy of $\sqrt{s}$ = 13
TeV. It will allow to use the $b\to c$ and $b\to s$ processes with very small
branching fraction to constraint the $\phi_{s}$ measurement.

Figure 5: 68$\%$ confidence level regions in $\Delta\Gamma_{s}$ and $\phi_{s}$
plane obtained from individual contours of CDF, D0, CMS, ATLAS and LHCb
measurements and the combined contour (solid line and shaded area)
bib:MainPlot . The expectation within the SM Charles:2015gya  is shown as a
black thin rectangle.

##  3 Future contributions for measuring $\phi_{s}$ and $\Delta\Gamma_{s}$

###  3.1 Observation of the $B^{0}_{s}\to\eta_{c}\phi$ decay

The $B^{0}_{s}\to\eta_{c}\phi(\to K^{+}K^{-})$ decay mode, with $\eta_{c}\to
K^{+}K^{-}\pi^{+}\pi^{-}$, $K^{+}K^{-}K^{+}K^{-}$,
$\pi^{+}\pi^{-}\pi^{+}\pi^{-}$ and $p\bar{p}$, has been observed by the LHCb
collaboration for the first time Aaij:2017hfc . This decay is an another
$\bar{b}\to\bar{c}c\bar{s}$ transition that could be used to measure
$\phi_{s}$. The interference between the $\eta_{c}$ and purely nonresonant
contributions is taken into account using an amplitude model to simultaneously
fit the four hadrons and $p\bar{p}$ mass distributions (Fig. 6). The branching
fraction is normalized to the $J/\psi$ mode and found to be
$\mathcal{B}(B^{0}_{s}\to\eta_{c}\phi)=[5.01\pm 0.53(\mathrm{stat})\pm
0.27(\mathrm{syst})\pm 0.63(\mathcal{B})]\times 10^{-4}$. First evidence for
the $B^{0}_{s}\to\eta_{c}\pi^{+}\pi^{-}$ decay mode has also been reported,
with a branching fraction of
$\mathcal{B}(B^{0}_{s}\to\eta_{c}\pi^{+}\pi^{-})=[1.76\pm
0.59(\mathrm{stat})\pm 0.12(\mathrm{syst})\pm 0.29(\mathcal{B})]\times
10^{-4}$.

Figure 6: Invariant mass distributions for selected $p\bar{p}$,
$K^{+}K^{-}\pi^{+}\pi^{-}$, $K^{+}K^{-}K^{+}K^{-}$ and
$\pi^{+}\pi^{-}\pi^{+}\pi^{-}$ combinations.

###  3.2 $B^{0}_{s}\to J/\psi\eta$ effective lifetime

The $B^{0}_{s}$ effective lifetime has been measured by the LHCb collaboration
using the $C\\!P$-even $B^{0}_{s}\to
J/\psi(\to\mu^{+}\mu^{-})\eta(\to\gamma\gamma)$ decay mode using Run1 data
Aaij:2016dzn . As $\phi_{s}$ is measured to be small and assuming $C\\!P$
conservation, the effective lifetime corresponds to the lifetime of the light
$B^{0}_{s}$ mass eigenstate, $\tau_{L}\propto\Gamma_{L}$. The invariant mass
resolution is approximately 48 MeV/c2 (Fig. 7) causing the overlap of the
$B^{0}_{s}$ signal mode with the $B^{0}\to J/\psi\eta$ background component.
The effective lifetime for $\sim$3000 signal candidates is measured to be
$\tau_{\mathrm{eff}}=1.479\pm 0.034\pm 0.011$ ps. The result is consistent
with, and has a similar precision to, the other $C\\!P$-even lifetime
measurements Aaij:2013bvd ; Aaij:2014fia .

Figure 7: Distributions of $J/\psi\eta$ invariant mass (left) and decay time
(right) for selected $B^{0}_{s}\to J/\psi\eta$ decays. Combinatorial
background (green), background from $B^{0}\to J/\psi\eta$ decays (blue) and
partially reconstructed background (orange) are shown.

###  3.3 Observation of the $B^{0}_{s}\to\phi\pi^{+}\pi^{-}$ decays

The first observation of the inclusive decay $B^{0}_{s}\to\phi(\to
K^{+}K^{-})\pi^{+}\pi^{-}$ has been performed by the LHCb collaboration
Aaij:2016qnm . Fig. 8 shows the result of the final fit to the
$m(K^{+}K^{-}\pi^{+}\pi^{-})$ distribution. The $B^{0}_{s}$ yield is found to
be around 700 signal candidates. Since the $\pi^{+}\pi^{-}$ spectrum includes
several resonances, an amplitude analysis to the $\pi^{+}\pi^{-}$ mass and
decay angle distributions is used to separate out exclusive contributions to
the $B^{0}_{s}$ meson decays (Fig. 8). The $B^{0}_{s}\to\phi\phi$ is used as a
normalization channel for both the inclusive and exclusive decays. The
measurement of their branching fractions is $\mathcal{B}(B^{0}_{s}\to\phi
f_{0}(980))=[1.12\pm 0.16^{+0.09}_{-0.08}\pm 0.11]\times 10^{-6}$,
$\mathcal{B}(B^{0}_{s}\to\phi f_{2}(1270))=[0.61\pm 0.13^{+0.12}_{-0.05}\pm
0.06]\times 10^{-6}$ and $\mathcal{B}(B^{0}_{s}\to\phi\rho^{0})=[2.7\pm 0.7\pm
0.2\pm 0.2]\times 10^{-7}$, where the first uncertainty is statistical, the
second is systematic, and the third is related to the knowledge of the
normalization channel branching fraction. The decays $\phi f_{0}(980)$, $\phi
f_{2}(1270)$ and $\phi\rho^{0}$ are observed with a significance of 8$\sigma$,
5$\sigma$ and 4$\sigma$, respectively. The measurements are consistent with
the SM predictions and, in case of the $B^{0}_{s}\to\phi\rho^{0}$, they
provide a constraint on possible contributions from NP effects Hofer:2010ee .

Figure 8: (left) Distribution of $K^{+}K^{-}\pi^{+}\pi^{-}$ invariant mass
where the (blue) dashed line is the $B^{0}_{s}$ signal, the (green) dotted
line shows the combinatorial background and the (black) dot-dashed line
indicates the $B^{0}$ component. (right) Distributions of $\pi^{+}\pi^{-}$
invariant mass with contributing components.

###  3.4 $C\\!P$ asymmetry measurement of the $B^{\pm}\to J/\psi\rho^{\pm}$
decays

The branching fraction and direct $C\\!P$ asymmetry of the $B^{\pm}\to
J/\psi(\to\mu^{+}\mu^{-})\rho^{\pm}(\pi^{\pm}\pi^{0})$ decay have been
measured by the LHCb collaboration Aaij:2018abc . The decay predominantly
proceeds via a $b\to c\bar{c}d$ transition involving tree and penguin
amplitudes. The measurement of $\mathcal{A}^{C\\!P}$ provides an estimate of
imaginary part of the penguin-to-tree amplitude ratio of the $b\to c\bar{c}d$
transition, which can be used to place constraints on penguin effects in
measurements of the $C\\!P$-violating phase $\phi_{s}$, assuming SU(3)
symmetry. The $B^{\pm}\to J/\psi K^{\pm}$ decay is used as a normalisation
channel for the branching fraction measurement. The fit to $B^{+}$ and
$\rho^{+}$ candidate mass has been performed to distinguish $J/\psi\rho^{+}$
from non-resonant $J/\psi\pi^{+}\pi^{0}$ decay as shown in Fig. 9. The
branching fraction and $C\\!P$ asymmetry are measured to be
$\mathcal{B}(B^{+}\to J/\psi\rho^{+})=(3.79^{+0.25}_{-0.24}\pm 0.32)\times
10^{-5}$ and $\mathcal{A}^{C\\!P}(B^{+}\to
J/\psi\rho^{+})=-0.045^{+0.056}_{-0.057}\pm 0.008$. The results are consistent
with BaBar measurement Aubert:2007xw . The measured value of $C\\!P$ asymmetry
is consistent with the corresponding measurement using $B^{0}\to
J/\psi\rho^{0}$ decays, as expected from isospin symmetry Aaij:2014vda .

Figure 9: (left) Distribution of $J/\psi\pi^{+}\pi^{0}$ invariant mass for
2012 data set. (right) Distribution of $\pi^{+}\gamma\gamma$ invariant mass
for 2012 data set for $m_{J/\psi\pi^{+}\pi^{0}}\in(5250,5310)$ MeV/c2 range.

##  4 Summary

The most precise measurement of $C\\!P$-violating phase $\phi_{s}$ and decay
width difference $\Delta\Gamma_{s}$ in the $B^{0}_{s}$ system has been
performed using Run1 data collected by LHCb experiment corresponding to an
integrated luminosity of 3 fb-1. So far all results are compatible with the SM
prediction. In order to reach an uncertainty of the measurement comparable or
even better than the theoretical uncertainty of the SM prediction aside from
improvements in available luminosity, inclusion of new decay modes has been
explored. For example, the $B^{0}_{s}\rightarrow J/\psi(\to e^{+}e^{-})\phi$
channel not only could bring about 10$\%$ of the $\mu^{+}\mu^{-}$ mode
statistics, but it will be also an important verification of the
$B^{0}_{s}\rightarrow J/\psi(\to\mu^{+}\mu^{-})\phi$ as kinematics for both
channels are expected to be identical. The statistical sensitivity to
$\phi_{s}$ after the LHCb upgrade, with an integrated luminosity of 50 fb-1,
is expected to be $\sim$9 mrad. As that will be close to the present
theoretical uncertainty bib:Upgrade . As the measurement precision improves,
the penguin pollution contributions to the $B^{0}_{s}$ meson decays need to be
kept under control. Current measurements constrain them to be smaller than 20
mrad Aaij:2015mea ; Aaij:2014vda ; Aaij:2015tza .

Acknowledgments

The talk has been supported by the MNiSW with grant DIR/WK/2016/16. I would
like to thanks the organizers of the CKM2018 workshop for the invitation to
present this work and my LHCb colleagues who helped in the preparation of this
talk.

## References

  * (1) N. Cabibbo, Phys. Rev. Lett. 10 (1963) 531.
  * (2) Z. Ligeti, M. Papucci and G. Perez, Phys. Rev. Lett. 97, 101801 (2006); P. Ball and R. Fleischer, Eur. Phys. J. C 48, 413 (2006); A. Lenz, Phys. Rev. D 76, 065006 (2007); R. Fleischer, eConf C 0610161, 020 (2006); U. Nierste, Int. J. Mod. Phys. A 22, 5986 (2007).
  * (3) M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49, 652 (1973).
  * (4) J. Charles et al., Phys.Rev. D91 (2015) no.7, 073007.
  * (5) A. A. Alves, Jr. et al. [LHCb Collaboration], JINST 3, S08005 (2008).
  * (6) R. Aaij et al. [LHCb Collaboration], Phys. Rev. Lett. 114, no. 4, 041801 (2015).
  * (7) Y. Xie, arXiv:0905.0724.
  * (8) Pivk M and Le Diberder F R, Nucl.Instrum.Methods Phys.Res., Sec.A 384 (2015) 491.
  * (9) M. Artuso, G. Borissov and A. Lenz, Rev. Mod. Phys. 88 (2016) 045002, arXiv:1511.09466 [hep-ph].
  * (10) R. Aaij et al. [LHCb Collaboration], Phys. Lett. B 736, 186 (2014).
  * (11) R. Aaij et al. [LHCb Collaboration], Phys. Rev. D 86 (2012) 052006, arXiv:1204.5643 [hep-ex].
  * (12) R. Aaij et al. [LHCb Collaboration], Phys.Lett. B762 (2016) 253.
  * (13) R. Aaij et al. [LHCb Collaboration], JHEP 1708 (2017) 037.
  * (14) T. Aaltonen et al. [CDF Collaboration], Phys. Rev. Lett. 109, 171802 (2012).
  * (15) V. M. Abazov et al. [D0 Collaboration], Phys. Rev. D 85, 032006 (2012).
  * (16) G. Aad et al. [ATLAS Collaboration], JHEP 1608 (2016) 147.
  * (17) V. Khachatryan et al. [CMS Collaboration], Phys.Lett. B757 (2016) 97.
  * (18) Y. Amhis et al., arXiv:1612.07233 [hep-ex].
  * (19) R. Aaij et al. [LHCb Collaboration], Phys.Rev. D90 (2014) no.5, 052011.
  * (20) M. Beneke, J. Rohrer and D. Yang, Nucl.Phys. B774 (2007) 64.
  * (21) M. Bartsch, G. Buchalla and C. Kraus, arXiv:0810.0249 [hep-ph].
  * (22) H. Y. Cheng and C. K. Chua, Phys.Rev. D80 (2009) 114026.
  * (23) R. Aaij et al. [LHCb Collaboration], JHEP 1707 (2017) 021.
  * (24) R. Aaij et al. (LHCb Collaboration), Phys.Lett. B762 (2016) 484.
  * (25) R. Aaij et al. (LHCb Collaboration), Phys.Rev.Lett. 112 (2014) no.11, 111802.
  * (26) R. Aaij et al. (LHCb Collaboration), Phys.Lett. B736 (2014) 446.
  * (27) R. Aaij et al. (LHCb Collaboration), Phys.Rev. D95 (2017) no.1, 012006.
  * (28) L. Hofer, D. Scherer and L. Vernazza, JHEP 1102 (2011) 080.
  * (29) R. Aaij et al. [LHCb Collaboration], submitted to Phys.Lett. B.
  * (30) B. Aubert et al. [BaBar Collaboration], Phys. Rev. D 76, 031101 (2007)
  * (31) R. Aaij et al. [LHCb Collaboration], Eur. Phys. J. C 73, no. 4, 2373 (2013).
  * (32) R. Aaij et al. [LHCb Collaboration], JHEP 1511 (2015) 082.
  * (33) R. Aaij et al. [LHCb Collaboration], Phys.Lett. B742 (2015) 38.
  * (34) R. Aaij et al. [LHCb Collaboration], JHEP 1506 (2015) 131.


〒630-0121 生駒市北大和２−１４−４
河原英紀 5 2

# Safeguarding test signals for acoustic measurement using arbitrary sounds

Measuring impulse response by playing music

Hideki Kawahara1<EMAIL_ADDRESS>Kohei Yatabe2
<EMAIL_ADDRESS>University1Wakayama University 930 Sakaedani
930 Sakaedani Wakayama Wakayama 640-8510 Japan
2Waseda University 640-8510 Japan
2Waseda University 3-4-1 Ookubo 3-4-1 Ookubo Shinjuku-ku Shinjuku-ku Tokyo
Tokyo 169-8555 Japan 169-8555 Japan

discrete Fourier transformation, periodic signal, impulse response, spurious
responses, entertaining test sounds, loop music

###### pacs:

43.20.Ye,43.55.Br,43.55.Mc,43.58.-e,43.58.Ry,43.58.Ta

##  1 Introduction

We propose a simple method to measure acoustic responses using any sounds by
converting them suitable for measurement. This method enables us to use music
pieces for measuring acoustic conditions. It is advantageous to measure such
conditions without annoying test sounds to listeners. In addition, applying
the underlying idea of simultaneous measurement of multiple-paths[3, 4]
provides practically valuable features. For example, it is possible to measure
deviations (temporally stable, random, and time-varying) and the impulse
response while reproducing slightly modified contents under target conditions.
The key idea of the proposed method is to add relatively small deterministic
signals that sound like noise to the original sounds. We call the converted
sounds as safeguarded test signals.

##  2 Safeguarded transfer function measurement

Let $x[n]$ be a periodic discrete-time signal with a period $L$. Convolution
of $x[n]$ and the impulse response $h[n]$ of the target system yields the
output $y[n]$. Because the signal is periodic, the DFT (Discrete Fourier
transform) of $x[n]$ and $y[n]$ segments (their length is $L$) are invariant
other than the phase rotation proportional to frequency. Let $X[k]$ and $Y[k]$
represent their DFT, where $k$, ($k=0,\ldots,L-1$), is the discrete frequency.
Then, the ratio $Y[k]/X[k]$ is independent of the location of the segment.
This ratio agrees with the DFT $H[k]$ of the impulse response $h[n]$, where
$X[k]\neq 0$ for all $k$ values is the condition of this relation to provide
physically meaningful results.

However, this simple solution is sensitive to noise when the absolute value
$\left|X[k]\right|$ is very small relative to absolute values
$\left|H[k]\right|$ of other $k$ values. We propose to limit the absolute
value $\left|X[k]\right|$ to have larger value than a threshold111Generally
the threshold is a function of discrete frequency $\theta_{L}[k]$. We use a
constant value here to make explanations simple.. We use the following
equation to derive the DFT $X_{\mathrm{s}}[m]$ of the safeguarded signal
$\tilde{x}_{\mathrm{s}}[n]$.

$\displaystyle X_{\mathrm{s}}[k]$
$\displaystyle=\left\\{\begin{array}[]{lll}\displaystyle\frac{\theta_{L}X[k]}{\left|X[k]\right|}&\mbox{for}&0<\left|X[k]\right|<\theta_{L}\\\
X[k]&{}&\theta_{L}\leq\left|X[k]\right|\end{array}\right.,$ (3)

where we set $X_{\mathrm{s}}[k]=\theta_{L}$ when $X[k]=0$. Then, we derive the
safeguarded transfer function $H_{\mathrm{s}}[k]$ as follows.

$\displaystyle H_{\mathrm{s}}[k]$
$\displaystyle=\frac{Y_{\mathrm{s}}[k]}{X_{\mathrm{s}}[k]},$ (4)

where $Y_{\mathrm{s}}[k]$ represents the DFT of the output of the target
system for periodic test signal $\tilde{x}_{\mathrm{s}}[n]$. Because the
safeguarded signal $\tilde{x}_{\mathrm{s}}[n]$ is periodic, we can make the
safeguarded test signal for acoustic measurement by concatinating it as many
times as required. For analyzing the safeguarded transfer function, we can
select the safeguarded test and the output segment anywhere, obeying one rule.
The segment has to have the length of exactly $L$ samples222Do not use the
initial segment of length $L$ samples (plus samples for propagation delay from
the sound source to the microphone), because it does not have the preceding
cycle..

##  3 Measurement of other responses

When the target system is an LTI-system (LTI: liner time-invariant), and no
observation noise exists, the calculated safeguarded transfer function
$H_{\mathrm{s}}[k]$ is identical, irrespective of the location of the
safeguarded test and the output segments. Also, $H_{\mathrm{s}}[k]$ is
independent of the used safeguarded test signals. However, it is not the case
in measuring acoustic systems in the real world. We can use these differences
of $H_{\mathrm{s}}[k]$ measured at different observation locations and using
different safeguarded test signals to separate the LTI-response and other
spurious responses. They are signal-induced deterministic responses and random
responses333In addition to background noise and observation noise (they are
source independent), there are source-related random noises. For example, they
are; turbulent noise caused by strong low-frequency airflow in the bass-reflex
port and high-frequency phase modulation noise due to the doppler effect
caused by air move[3]..

###  3.1 Separation of random responses

An additive noise $d[n]$ in output observation produces a deviation term
$D[k]$. We define the time-invariant response $H_{\mathrm{sTI}}[k]$ and the
squared absolute random response $|D_{\mathrm{sTV}}[k]|^{2}$ by measuring the
system $M$ times.

$\displaystyle H_{\mathrm{sTI}}[k]$
$\displaystyle=\frac{1}{M}\sum_{m=1}^{M}H_{\mathrm{s}}^{\\{n_{m}\\}}[k]$ (5)
$\displaystyle|D_{\mathrm{sTV}}[k]|^{2}$
$\displaystyle=\frac{1}{M-1}\sum_{m=1}^{M}\left|H_{\mathrm{s}}^{\\{n_{m}\\}}[k]-H_{\mathrm{sTI}}[k]\right|^{2},$
(6)

where use of superscript $a^{\\{n_{m}\\}}$ represents that the calculation of
$a$ uses the segment starting from the discrete-time $n_{m}$444It is better
not to overlap analysis segments..

###  3.2 Separation of signal-dependent responses

For LTI-systems, the time-invariant response $H_{\mathrm{sTI}}[k]$ is
identical, irrespective of the test signals. However, again, it is not the
case. We define the linear time-invariant response $H_{\mathrm{sLTI}}[k]$ by
averaging responses measured using different test signals. Then, we represent
the squared absolute signal-dependent responses $|H_{\mathrm{sSDR}}[k]|^{2}$
by averaging the squared absolute valued deviation from the time-invariant
response. We use an index variable $p$ to identify the member of the set of
test signals $\Omega_{\mathrm{P}}=\\{\tilde{x}_{\mathrm{s}}^{\\{p\\}}[n]\ |\
p=1,\ldots,P\\}$.

$\displaystyle H_{\mathrm{sLTI}}[k]$
$\displaystyle=\frac{1}{P}\sum_{p=1}^{P}H_{\mathrm{s}}^{(p)}[k]$ (7)
$\displaystyle|H_{\mathrm{sSDR}}[k]|^{2}$
$\displaystyle=\frac{1}{P-1}\sum_{p=1}^{P}\left|H_{\mathrm{s}}^{(p)}[k]-H_{\mathrm{sLTI}}[k]\right|^{2},$
(8)

where $a^{(p)}$ represents that we used the $p$-th member of the set
$\Omega_{\mathrm{P}}$ to calculate $a$.

##  4 Numerical simulation

We conducted a set of numerical simulations to check the feasibility of the
proposed method. We used white noise for the original test signal and studied
the effect of safeguarding by flooring the low-level absolute values.

###  4.1 Effect of flooring in LTI-response

Figure 1: The top panel shows power spectra of the original white noise,
safeguarded noise, and the background white noise (original and adjusted). The
middle panel shows the level distribution. The bottom panel shows the
estimated gains using the original signal and the safeguarded signal.

Figure 1 shows simulation results using additive white noise with 40 dB SNR.
We adjusted the noise level for the safeguarded signal because flooring
increases the signal power. The threshold $\theta_{L}$ value we used here is
the average absolute value of the original spectrum. The sampling frequency
was 44100 Hz, and the signal length was 100000 samples.

Figure 2: Effect of flooring on the maximum deviations from the ground truth
(0 dB) for different SNR conditions. Flooring level -50 dB does not change any
frequency bins and 20 dB changes all bins.

Figure 2 shows the maximum deviation of the safeguarded gain function for
different SNR settings. Flooring significantly reduces maximum deviations.

Safeguarding by flooring adds a deterministic signal that sounds like noise.
Regression analysis of the flooring level $\theta_{L}|_{\mathrm{dB}}$
(represented in dB) and the power of the deterministic signal
($\sigma_{\mathrm{dB}}$: also represented in dB) resulted in the following
experimental relation.

$\displaystyle\sigma_{\mathrm{dB}}\sim-10.321+1.995\
\theta_{L}|_{\mathrm{dB}},$ (9)

where the intercept and the slope indicates that 0 dB flooring adds 10 dB
smaller noise and the level decreases two times faster than the flooring level
decrease. For example, the -10 dB flooring level makes SNR 30 dB. This
relation suggests that safeguarding does not severely damage the quality of
the original signal (for example, a music piece).

Figure 3: Standard deviations of the smoothed gain estimated using safeguarded
signals. The flooring level is 0 dB and the smoothing width is one-third
octave.

The estimated gain using safeguarded signal still has random peaks and dips.
Spectral smoothing is a common practice to make spectral characteristics of
acoustical systems. Figure 3 shows the standard deviation of the smoothed gain
functions using one-third octave width rectangular smoothing. Comparison with
Fig. 2 illustrates that spectral smoothing significantly reduces deviations.

###  4.2 Random response

Measuring many times using the same test signal provides the random response
estimate by using Eq. 6.

Figure 4: Estimated rondom response level dependency on the flooring level.

Figure 4 shows the estimated random response level. Note that the estimate at
20 dB flooring provides the correct estimate of the noise level because the
test signal has a constant absolute value with randomized phase; in other
words, it is a periodic pseudo-random noise.555CAPRICEP and FVN also provide
correct estimate[3, 4].

###  4.3 Signal-dependent response

Measuring many times using the same test signal does not provide signal-
dependent deviations such as harmonic distortion and intermodulation
distortion caused by nonlinearity. We introduced an exsample non-linearity
using the following equation.

$\displaystyle y=\frac{1}{\alpha}\left(\exp(\alpha x)-1\right).$ (10)

We use Gaussian white noise as $x$ and added the other Gaussian noise to the
output $y$ with the given SNR. We prepared four types of the original segments
and repeated each segment four times, assuming a piece of typical loop music
having prospective application in mind.

Figure 5: Input level dependency of the random response and the signal
dependent response ($\alpha=0.4$).

Figure 5 shows the results. Colored lines represent the signal-dependent
response level calculated using Eq. 8. The black dashed lines represent the
random response level calculated using Eq. 6. The random response levels
normalized by the total output levels are virtually constant reflecting the
assigned SNR. The signal-dependent levels decreases as the input level
decreases. This decriment satulates at the effective (-3 dB for each doubling
of number of repetitions) random response level.

##  5 Example measurement using a loop music

We conducted example acoustic measurements in a connected Japanese room with
an area of about 40 m2. The sound source is a loudspeaker (Fostes FF85WK) with
a bass-reflex enclosure (Fostex BK85WB 2). To drive the loudspeaker, we used a
power amplifier (Fostex AP20d) connected to an audio interface (PRESONUS
STUDIO $2|6$). A wide-range omnidirectional condenser microphone (EARTHWORKS
M50) connected to the audio interface acquired reproduced sounds.

We used four loop-music (5 s each) pieces composed for this research. We mixed
the stereo track into a monaural track. The sampling frequency was 44100Hz.

###  5.1 Example-1: single test segment

For the first experiment, we located the microphone at 10 cm in front of the
center of the loudspeaker. The sound pressure level, measured using
A-weighting, at the microphone was 95.8 dB. The background noise level was 24
dB. We repeated each segment six times. We used the middle four segments for
calculation666For loop music, it is better to repeat each segment four times
and use three segments excerpted after expected reverberation time plus
propagation delay. As far as the length of the segment is exactly identical to
the length of the signal period, it is not necessary to match the location
with the beginning of the segment..

Figure 6: Absolute value distribution of a loop music segment. We set the
threshold $\theta_{\mathrm{s}}$ to the average value.

Figure 6 shows the absolute value distribution of the DFT $X[k]$ of the
original signal. We floored absolute values at the average absolute value of
the DFT.

Figure 7: The absolute value of DFT of the original signal and the safeguarded
signal.

Figure 7 shows the absolute DFT values of the original signal and the
safeguarded signal. The safeguarded signal sounds like the original signal
with a slight white noise.

Figure 8: The DFT of the measured segment and background noise segment.

Figure 8 shows calibrated sound pressure level (SPL) of DFT of the acquired
loudspeaker output and the background noise. Note that the loudspeaker output
at a high-frequency range reflects spectral flooring.

Figure 9: Separated responses with 1/3 octave smoothing.

Figure 9 shows the LTI-response, random and time-varying response, and the
effects of the background noise. We used 1/3 octave smoothing to clarify
essential features of the responses. This representation suggests that the
random component in the high-frequency region is the result of a high-sound
pressure level.

###  5.2 Example-2: multiple test segments

Figure 10: Measured responses with A-weighting SPLs 87.1 dB (upper plot) and
93.5 dB (lower plot).

Figure 10 shows the effects of playback levels. The upper plot shows the
results of the sound pressure level at A-weighting 87.3 dB. The lower plot
shows using 93.5 dB. The louder playback result777The LTI gain of Fig. 9 and
Fig. 10 are different because they were measured at a different time with
different sensitivity setting. shows that the signal-dependent distortion is
significantly higher than the random response. The signal-dependent random
noise mentioned before contributes to this difference.

##  6 Conclusion

We proposed a simple method for measuring attributes of acoustic systems using
arbitrary sounds by safeguarding them. This method enables us to use music to
measure room or concert acoustic conditions filled with the audience without
annoying their musical experience. This report is to demonstrate the
feasibility of the proposed method. This safeguarding makes even an arbitrary
pure tone possible to measure the LTI response in the whole audible frequency
range by adding a slight deterministic noise.

This method has a wide range of applications. For example, for assessing the
listening conditions of a classroom, we can use words and phrases. We are
planning theoretical and comprehensive investigations of this method and the
introduction of frequency-dependent flooring.

## Acknowledgement

This work was supported by JSPS (Japan Society for the Promotion of Science)
Grants-in-Aid for Scientific Research Grant Numbers JP21H00497 and JP20H00291.
The authors appreciate discussions and comments by Drs. Ken-Ichi Sakakibara,
Tatsuya Kitamura, Mitsunori Mizumachi, and Hideki Banno. The authors
appreciate the loop music composition and performance very much by Kazuki
Matsumoto.

## References

  * [1] N. Aoshima, “Computer-generated pulse signal applied for sound measurement,” JASA, 69(5), 1484–1488, (1980).
  * [2] M. Schroeder, “Synthesis of low-peak-factor signals and binary sequences with low autocorrelation,” IEEE Trans. Information Theory, 16(1), 85–89, (1970).
  * [3] H. Kawahara, K. -I. Sakakibara, M. Mizumachi, M. Morise and H. Banno, “Simultaneous measurement of time-invariant linear and nonlinear, and random and extra responses using frequency domain variant of velvet noise,” Proc. APSIPA ASC 2020, 174–183, (2020).
  * [4] H. Kawahara and K. Yatabe, “Cascaded All-Pass Filters with Randomized Center Frequencies and Phase Polarity for Acoustic and Speech Measurement and Data Augmentation,” Proc. ICASSP 2021, 306–310, (2021).


# Ferromagnetism of cobalt-doped anatase TiO2 studied by bulk- and surface-
sensitive soft x-ray magnetic circular dichroism

V. R. Singh<EMAIL_ADDRESS>Department of Physics,
University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan  K. Ishigami  Department
of Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan  V. K. Verma
Department of Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan
G. Shibata  Department of Physics, University of Tokyo, Bunkyo-ku, Tokyo
113-0033, Japan  Y. Yamazaki  Department of Physics, University of Tokyo,
Bunkyo-ku, Tokyo 113-0033, Japan  T. Kataoka  Department of Physics,
University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan  A. Fujimori  Department
of Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan  F.-H. Chang
National Synchrotron Radiation Research Center (NSRRC), Hsinchu 30076, Taiwan,
Republic of China  D.-J. Huang  National Synchrotron Radiation Research Center
(NSRRC), Hsinchu 30076, Taiwan, Republic of China  H.-J. Lin  National
Synchrotron Radiation Research Center (NSRRC), Hsinchu 30076, Taiwan, Republic
of China  C. T. Chen  National Synchrotron Radiation Research Center (NSRRC),
Hsinchu 30076, Taiwan, Republic of China  Y. Yamada  Institute for Materials
Research, Tohoku University, Sendai 980-8577, Japan  T. Fukumura  Department
of Chemistry, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan  PRESTO,
Japan Science and Technology Agency, Kawaguchi 332-0012, Japan  M. Kawasaki
Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
WPI-AIM Research, Tohoku University, Sendai 980-8577, Japan  Quantum-Phase
Electronics Center and Department of Applied Physics, University of Tokyo,
Tokyo 113-8656, Japan  CREST, Japan Science and Technology Agency, Tokyo
102-0075, Japan

###### Abstract

We have studied magnetism in anatase Ti1-xCoxO2-δ (x = 0.05) thin films with
various electron carrier densities, by soft x-ray magnetic circular dichroism
(XMCD) measurements at the Co $L_{2,3}$ absorption edges. For electrically
conducting samples, the magnetic moment estimated by XMCD was $<$ 0.3
$\mu_{B}$/Co using the surface-sensitive total electron yield (TEY) mode,
while it was 0.3-2.4 $\mu_{B}$/Co using the bulk-sensitive total fluorescence
yield (TFY) mode. The latter value is in the same range as the saturation
magnetization 0.6-2.1 $\mu_{B}$/Co deduced by SQUID measurement. The
magnetization and the XMCD intensity increased with carrier density,
consistent with the carrier-induced origin of the ferromagnetism.

Semiconductors partially substituted with magnetic ions are called diluted
magnetic semiconductors (DMSs) and are expected to be useful in spintronics
devices, where electron spins can be controlled by electric field and/or by
photons. Ferromagnetic DMS’s with Curie temperatures ($T_{C}$’s) higher than
room temperature are highly desirable for the development of spintronic
devices. To date, much work in this area has been done, mainly on II-VI and
III-V compounds doped with magnetic ions such as (Cd,Mn)Te 1  and (Ga,Mn)As 2
; 3 , but their $T_{C}$’s are far below room temperature. Ferromagnetism was
observed in Mn-based zinc-blende II-VI compounds such as (Cd,Mn)Te after the
result of carrier induced ferromagnetism 90 . Kuroda et al.50 ; 95  reported
that Cr rich phases of (Zn,Cr)Te showed room temperature ferromagnetism,
causing a stimulation of II-VI DMS. Ferromagnetism was also observed in
(Ga,Mn)As 2 ; 3 . It was theoretically suggested 40  that the co-doping of
magnetic semiconductors with shallow impurities affects the self-assembly of
magnetic nanocrystals during epitaxy, and therefore modifies both the global
and local magnetic behavior of the material. This concept was also
qualitatively corroborated by experimental data for (Cd, Mn, Cr)Te 45  and
(Ga, Mg, Fe)N 60 ; 70 ; 80 . However, origin of ferromagnetism at room-
temperature is controversial so far. Recently, Matsumoto et al.100 ; 105
reported the occurrence of room temperature ferromagnetism in Co-doped anatase
TiO2 films. According to Fukumura et al. 5 ; 7  the high electron carrier
densities and Co content favor the ferromagnetic phase in Co-doped rutile TiO2
at 300 K. Room-temperature ferromagnetism was also reported in such materials
as (Ga,Mn)N 22  and (Al,Cr)N 23 . The near edge x-ray absorption fine
structure study of Co-doped TiO2 by Griffin et al. 24  claims that
ferromagnetism is due to $d$-$d$ double exchange mediated by tunneling of $d$
electrons within the impurity band. Some studies that also claim the
ferromagnetism of Co-doped TiO2 is due to Co metal clusters 25 ; 26 ; 27 ; 28
. The recent theoretical study by Calderon et al. 29 , electric field-induced
anomalous Hall effect (AHE) study by Yamada et al. 15  and x-ray photoemission
spectroscopy study by Ohtsuki et al. 30  suggested the ferromagnetism of Co-
doped TiO2 is due to carrier mediated. However, direct information about the
magnetization as a function of carrier density has been lacking. Soft x-ray
magnetic circular dichroism (XMCD) at the Co 2$p\rightarrow 3d$ absorption (Co
$L_{2,3}$) edge is a powerful technique to clarify this issue because it is an
element-specific magnetic probe 28 . A previous XMCD study on rutile Co-doped
TiO2 by Mamiya et al. has revealed that the ferromagnetism is not due to
segregated Co metal clusters but is due to Co2+ ions in the TiO2 matrix 6 .
However, the XMCD signal intensities were an order of magnitude lower than
that expected from the bulk magnetization 6 . In a more recent work 7 , we
performed x-ray absorption spectroscopy (XAS) and XMCD studies on rutile Co-
doped TiO2 not only by the surface-sensitive total electron yield (TEY) mode
but also the bulk-sensitive total fluorescence yield (TFY) mode and found that
Co ions in the bulk indeed have a large magnetic moment of 0.8-2.2
$\mu_{B}$/Co.

In this work we have extended the same approach to anatase Co-doped TiO2 and
studied correlation between magnetism and transport properties. Magnetization
measurements of anatase Ti1-xCoxO2-δ thin films reveal ferromagnetic
hysteresis behavior in the M-H loop at room temperature with a saturation
magnetization. In the bulk region probed by the TFY mode, strong XMCD spectra
with similar spectral line shapes were obtained for all the samples. The
magnetization and the XMCD intensity increased with carrier density,
consistent with the carrier-induced origin of the ferromagnetism.

Anatase Ti1-xCoxO2-δ epitaxial thin films with $x$ = 0.05 were synthesized by
the pulsed laser deposition method on LaAlO3 (001) substrates at 523 K and
oxygen pressures ($P_{{\rm O}_{2}}$) of 5 $\times$ $10^{-7}$, 1 $\times$
$10^{-6}$ and 2 $\times$ $10^{-6}$ Torr. The resistivity increases in this
order and these samples are hereafter referred to metallic, intermediate,
insulating samples, respectively. The carrier densities $n_{e}$ were 4.1
$\times$ $10^{19}$, 1.1 $\times$ $10^{19}$ and 4.0 $\times$ $10^{18}$ cm-3,
respectively. Segregation of secondary phases were not observed under careful
inspections by x-ray diffraction (XRD) and transmission electron microscopy
(TEM) 15  of $\sim$40 nm thick films 15 . Reflection high-energy electron
diffraction was monitored during the in-situ growth. An intensity oscillation
was observed at the initial stage of the growth. We have confirmed that Co
distribution along the film thickness direction in our films is uniform using
TEM 15 , unlike the inhomogeneous distribution in films prepared on Si
demonstrated using atom probe tomography by Larde et al 31 . Ferromagnetism at
room temperature was confirmed by Hall-effect measurements and magnetization
measurements. XAS and XMCD measurements were performed at the BL-11A beamline
of the National Synchrotron Radiation Research Center, Taiwan. In XMCD
measurements, magnetic fields (H) were applied parallel to the direction of
anatase (001). XAS and XMCD spectra were obtained in the TEY and TFY modes and
probing depths were $\sim$5 and 100 nm, respectively.

Figure 1: (Color online) M-H curves of Ti0.95Co0.05O2-δ at 300 K. (a)
Metallic, intermediate and insulating anatase samples. (b) Metallic rutile
sample.

Figure 1(a) shows the magnetization curves of anatase Ti1-xCoxO2-δ ($x$ =
0.05) at 300 K for various carrier densities ($n_{e}$). The $n_{e}$ for
metallic, intermediate and insulating samples were 4.1 $\times$ $10^{19}$, 1.1
$\times$ $10^{19}$ and 4.0 $\times$ $10^{18}$ cm-3, respectively. That of
metallic rutile thin films which has the carrier density of 7 $\times$
$10^{21}$ cm-3 is also shown in Fig 1(b). The saturation magnetization of the
anatase sample is 0.6-2.1 $\mu_{B}$/Co with a coercive force of $\sim$100 to
200 Oe. In the M(H) measurements, magnetic field was applied parallel to the
the direction of anatase (001). Anomalous Hall-effect (AHE) measurements for
anatase Ti1-xCoxO2-δ with various $n_{e}$ also show similar magnetic field
dependences 15 . From Fig. 1, it is clear that the magnetization of the
anatase thin films is larger than the rutile thin films, which may be
attributed to the fact that anatase films in this study have a mobility
$\sim$2-11 cm2V-1s-1 which is two orders of the magnitude higher than the
mobility of rutile thin films 5 .

Figure 2: (Color online) Co $L_{2,3}$-edge of anatase Ti0.95Co0.05O2-δ taken
in the TEY mode at T = 300 K and H = 1 T. (a) XAS. (b),(c) XAS and XMCD
spectra of the metallic anatase Ti0.95Co0.05O2-δ sample. The XAS and XMCD
spectra of Co metal by Kim et al.28  are shown for comparison.

In Fig. 2(a), we show the Co $L_{2,3}$-edge XAS (metallic, intermediate and
insulating thin films) and Fig. 2(b)-(c) XAS and XMCD spectra of (metallic
thin film) anatase Ti1-xCoxO2-δ obtained in the TEY mode. In the figure,
$\mu_{+}$ and $\mu_{-}$ refer to the absorption coefficients for photon
helicity parallel and antiparallel to the Co majority spin direction,
respectively. The XMCD spectra $\Delta\mu$ = $\mu_{+}$ \- $\mu_{-}$ have been
corrected for the degree of circular polarization. The XAS and XMCD spectra of
the metallic anatase Ti1-xCoxO2-δ sample showed multiplet features as shown by
Fig 2(a)-(c), which is similar to Mamiya et al. 6  and agree with our $D_{2h}$
high-spin crystal-field symmetry cluster model calculations using the
parameter values : Charge-transfer energy ($\Delta$)= 4 eV, On-site 3$d$-3$d$
Coulomb energy ($U_{dd}$)=5 eV, 3$d$-2$p$ Coulomb energy ($U_{dc}$)= 7 eV,
Hopping integral between the Co 3$d$ and O 2$p$ orbitals of Eg symmetry
($V_{{\rm E}_{g}}$)= 1.1 eV and Crystal-field splitting (10Dq)= 0.9 eV. The
multiplet features of the XMCD spectra show almost one-to-one correspondence
to those in the XAS spectra. The spectral line shapes of the XAS and XMCD
spectra for the metallic and intermediate anatase Ti1-xCoxO2-δ samples are
also similar to those of rutile Co-doped TiO2 results which were reported in
our previous work 6 ; 7 . For the insulating sample, we observed an XAS
spectrum similar to those of the metallic and intermediate samples. The
estimated magnetic moments for all samples obtained from XMCD in the TEY mode
were $<$ 0.3 $\mu_{B}$/Co. These values are larger than the 0.1 $\mu_{B}$/Co
which is reported by Mamiya et al. 6 , but they are still smaller than the
saturation magnetic moments 0.6-2.1 $\mu_{B}$/Co deduced from magnetization
measurements. The XAS and XMCD spectra of Co metal is also shown at the bottom
of Fig. 2 (a)-(c) for comparison. It is demonstrated that the present XAS and
XMCD spectra of Co-doped TiO2 are distinctly different from Co metal.

Figure 3: (Color online) Co $L_{2,3}$-edge of anatase Ti0.95Co0.05O2-δ taken in the TFY mode at T = 300 K and H = 1 T. (a) XAS. (b),(c) XAS and XMCD spectra of anatase Ti0.95Co0.05O2-δ for metallic sample in the TFY mode. The XAS and XMCD spectra of Co metal by Kim et al. 28  are shown for comparison. (d),(e) Comparison of XAS and XMCD spectra shown in (b) and (c) with cluster-model calculation 34 . Table 1: Electronic structure parameters for anatase Co-doped TiO2 thin film used in the cluster-model calculations in units of eV to analyze. Crystal-field symmetry | Spin | $\Delta$ | $U_{dd}$ | $U_{dc}$ | $V_{{\rm E}_{g}}$ | 10Dq | Weight(%)
---|---|---|---|---|---|---|---
$D_{2h}$ | Low | 4 | 5 | 7 | 1.1 | 1.1$-$1.2 | 35
$O_{h}$ | Low | 3 | 6 | 7.5 | 1.1 | 1.1$-$1.2 | 35
$O_{h}$ | High | 2 | 5 | 7.5 | 1.1 | 0.8$-$0.9 | 30

Figures 3(a),(b) and (c) show the Co $L_{2,3}$ XAS and XMCD spectra of the
same samples taken in the TFY mode. From the figure, it is clear that the XMCD
intensities are much higher than those taken in the TEY mode. The large
difference between the bulk-sensitive TFY mode with $\sim$100 nm probing depth
and the surface-sensitive TEY mode with $\sim$5 nm probing depth suggests that
there is a magnetically dead layer of $\sim$5 nm thickness or more at the
surface of the samples as in the case of rutile 6 ; 7 . The presence of a
surface dead layer of $\sim$5 nm thickness is consistent with the recent
measurements of the film-thickness dependence of AHE 32 . The spectral line
shapes of the XAS and XMCD spectra of all the samples taken in the TFY mode
show broad features with spectral line shapes similar to those of rutile Co-
doped TiO2 7 . Both magnetization and XMCD intensity increased with carrier
density. This is consistent with spin alignment arises due to the interaction
of local spins with the spin polarized free carriers, in which carrier-
mediated ferromagnetism and ferromagnetic ordering is realized. Yamada et
al.15  have also demonstrated electrically induced ferromagnetism at room-
temperature in anatase Ti1-xCoxO2-δ, by means of electric double layer gating
resulting in high density electron accumulation ($>$1014 cm-2). By applying a
gate voltage of a few volts, a low-carrier paramagnetic state was transformed
to a high-carrier ferromagnetic state. This also supports theoretically as
well as experimentally the idea that the ferromagnetism originates from a
carrier-mediated mechanism 15 ; 29 . The broadening of the TFY spectra may be
due to the randomly displaced positions of Co atoms, which leads to in various
local structures as suggested by the anomalous X-ray scattering study of
Matsumura et al. 33 . The experimental XAS and XMCD spectra are distinctly
different from Co metal and show qualitatively good agreement with the
calculated spectra for the Co2+ in random crystal fields 34 , where the
calculations were done using the various electronic structure parameters as
listed in Table I.

Figure 4: (Color online) Magnetization as a function of magnetic field
obtained from the XMCD intensities of anatase Ti0.95Co0.05O2-δ compared with
M-H curves obtained using a SQUID.

Figure 4 shows magnetization versus magnetic field curves estimated from the
XMCD spectra obtained in the TEY and TFY modes using sum rules 6 , as compared
with the M-H curves measured using a SQUID. We have divided the obtained spin-
magnetic moment by a correction factor of 0.92 given by Teramura et al.35 .
The Co magnetic moment is found to be obviously much larger in the bulk region
than in the surface region. These results are also consistent with the x-ray
photoemission spectroscopy study by Yamashita et al. 14 . Since we know that
TFY suffers from self-absorption and therefore it will saturate the XAS
signal. This saturated XAS signal will reduce XMCD signal. Because of this
very fact, we can conclude that the real value of magnetic moment in bulk
should be even higher than the measured TFY value in metallic and intermediate
samples which are reported in the present work. Accordingly, our observation
by using the TEY and TFY modes are validated. The magnetic moment obtained
from cluster-model calculation (Fig.3) is 1.6 $\mu_{B}$/Co, which is similar
to the magnetization of $\sim$2 $\mu_{B}$/Co deduced from the TFY results and
the SQUID measurement. These results suggest that the Co ions in the bulk
region are responsible for the ferromagnetism in anatase Ti1-xCoxO2-δ.

In conclusion, we have studied the ferromagnetism of cobalt-doped anatase TiO2
thin films using element-specific XMCD at the Co $L_{2,3}$ edges in both the
surface-sensitive TEY and bulk-sensitive TFY modes. The large magnetic moment
of the Co ions, 0.6-2.4 $\mu_{B}$/Co, was observed by the TFY method. The
carrier-induced origin of ferromagnetism at room-temperature in anatase
Ti1-xCoxO2-δ is supported by the XMCD study of the samples with different
carrier concentration. According to the spectra taken in the TFY mode, the
positions of Co2+ atoms seem to be displaced from the regular Ti4+ sites,
resulting in random crystal fields. Good agreement is demonstrated not only in
magnetization and AHE but also in the magnetic field dependences of XMCD. The
magnetic moment values deduced with the TEY mode was $<$ 0.3 $\mu_{B}$/Co,
indicating the presence of a magnetically dead layer of $\sim$5 nm thickness
at the sample surfaces.

This work was supported by a Grant-in-Aid for Scientific Research in Priority
Area “Creation and Control of Spin Current” (19048012) from MEXT, Japan,
Grant-in-Aid for Scientific Research (S 22224005) from JSPS and TF was
supported by the Funding Program for Next Generation World-Leading
Researchers.

## References

  * (1) A. E. Turner, R. L. Gunshor, and S. Datta, Appl. Opt. 22, 3152, (1983).
  * (2) H. Ohno, F. Matsukura, and Y. Ohno, Solid State Commun. 119, 281, (2001).
  * (3) H. Ohno, J. Magn. Magn. Mater. 200, 110, (1999).
  * (4) A. Haury, A. Wasiela, A. Arnoult, J. Cibert, S. Tatarenko, T. Dietl, and Y. Merle d Aubigne, Phys. Rev. Lett. 79, 511 (1997).
  * (5) S. Kuroda, N. Nishizawa, K. Takita, M. Mitome, Y. Bando, K. Osuch, and T. Dietl, Nat. Mater. 6, 440 (2007).
  * (6) N. Samarth, Nature Mater. 6, 403 (2007).
  * (7) T. Dietl, Nat. Mater. 5, 673 (2006).
  * (8) K. Ishikawa and S. Kuroda, AIP Conf. Proc. 1399, 705 (2011).
  * (9) A. Navarro-Quezada, N. Gonzalez Szwacki, W. Stefanowicz, Tian Li, A. Grois, T. Devillers, M. Rovezzi, R. Jakiela, B. Faina, J. A. Majewski, M. Sawicki, T. Dietl, and A. Bonanni, Phys. Rev. B 84, 155321 (2011)
  * (10) A. Bonanni, A. Navarro-Quezada, T. Li, M. Wegscheider, Z.Matej, V. Holy, R. T. Lechner, G. Bauer, M. Rovezzi, F. D Acapito, M. Kiecana, M. Sawicki, and T. Dietl, Phys. Rev. Lett. 101, 135502 (2008).
  * (11) M. Rovezzi, F. D Acapito, A. Navarro-Quezada, B. Faina, T. Li, A. Bonanni, F. Filippone, A. A. Bonapasta, and T. Dietl, Phys. Rev. B 79, 195209 (2009).
  * (12) Y. Matsumoto, M. Murakami, T. Shono, T. Hasagawa, T. Fukumura, M. Kawasaki, P. Ahmet, T. Chikyow, S. Kohsihara, and H. Koinuma, Science 291, 854 (2001).
  * (13) Y. Yamada, T. Fukumura, K. Ueno, and M. Kawasaki, Appl. Phys. Lett. 99, 242502 (2011).
  * (14) T. Fukumura, H. Toyosaki, K. Ueno, M. Nakano, and M. Kawasaki, New J. Phys. 10 , 055018, (2008).
  * (15) V. R. Singh, Y. Sakamoto, T. Kataoka, M. Kobayashi, Y. Yamazaki, A. Fujimori, F.-H. Chang, D.-J.Huang, H.-J. Lin, C.T. Chen, H.Toyosaki, T. Fukumura and M.Kawasaki, J. Phys.: Condens. Matter 23, 176001, (2011).
  * (16) M. L. Reed, N. A. El-Masry, H. H. Stadelmaier, M. K. Ritums, M. J. Reed, C. A. Parker, J. C. Roberts, and S. M. Bedair, Appl. Phys. Lett. 79, 3473, (2001).
  * (17) S. G. Yang, A. B. Pakhomov, S. T. Hung, and C. Y. Wong, Appl. Phys. Lett. 81, 2418, (2001).
  * (18) K. A. Griffin, A. B. Pakhomov, C. M. Wang, S. M. Heald, and K. M. Krishnan, Phys. Rev. Lett 94, 157204, (2005).
  * (19) S. R. Shinde, S. B. Ogale, S. Das Sarma, J. R. Simpson, H. D. Drew, S. E. Lofland, C. Lanci, J. P. Buban, N. D. Browning, V. N. Kulkani, J. Higgins, R. P. Sharma, R. L. Greene, and T. Venkatesan, Phys. Rev. B 67, 115211, (2003).
  * (20) P. A. Stampe, R. J. Kennedy, Y. Xin, and J. S. Parker, J. Appl. Phys. 92, 7114, (2002).
  * (21) D. H. Kim, J. S. Yang, K. W. Lee, S. D. Bu, T. W. Noh, S.-J. Oh, Y.-W. Kim, Y.-S. Chung, H. Tanaka, H. Y. Lee, and T. Kawai, Appl. Phys. Lett. 81, 2421, (2002).
  * (22) J. -Y. Kim, J. H. Park, B. -G. Park, H. -J. Noh, S. -J. Oh, J. S. Yang, D. -H. Kim, S. D. Bu, T.-W. Noh, H. -J. Lin, H. -H. Hsieh, and C. T. Chen, Phys. Rev. Lett. 90, 017401 (2003).
  * (23) M. J. Calderon, S. Das. Sarma, Ann. Phys. 322, 2618, (2007).
  * (24) Y. Yamada, K.Ueno, T. Fukumura, H. T. Yuan, H. Shimotani, Y. Iwasa, L. Gu, S. Tsukimoto, Y. Ikuhara, and M. Kawasaki, Science 332, 1065 (2011).
  * (25) T. Ohtsuki, A. Chainani, R. Eguchi, M. Matsunami, Y. Takata, M. Taguchi, Y. Nishino, K. Tamasaku, M. Yabashi, T. Ishikawa, M. Oura, Y. Senba, H. Ohashi, and S. Shin, Phys. Rev. Lett. 106, 047602, (2011).
  * (26) K. Mamiya, T. Koide, A. Fujimori, H. Tokano, Appl. Phys. Lett. 89, 062506, (2006).
  * (27) R. Larde, E. Talbot, P. Pareige, H. Bieber, G. Schmerber, S. Colis, V. Pierron-Bohnes, and A. Dinia, J. Am. Chem. Soc. 133, 1451 (2011).
  * (28) M. Nakano, Y. Yamada, T. Fukumura, K.Ueno, and M. Kawasaki, unpublished.
  * (29) T. Matsumura, D. Okuyama, S. Niioka, H. Ishida, T. Satoh,1 Y. Murakami, H.Toyosaki, Y. Yamada, T. Fukumura, and M. Kawasaki, Phys. Rev. B 76, 115320 (2007).
  * (30) The calculated spectra are the weighted sum of 35% of $D_{2h}$ low spin (LS), 35% of $O_{h}$ low spin (LS), 30% of $O_{h}$ high spin (HS).
  * (31) Y. Teramura, A. Tanaka, and T. Jo, J. Phys. Soc. Jpn. 65, 1053, (1996).
  * (32) N.Yamashita, T. Sudayama, T. Mizokawa, Y.Yamada, T. Fukumura, and M. Kawasaki, Appl. Phys. Lett. 96, 021907 (2010).


Copyright for this paper by its authors. Use permitted under Creative Commons
License Attribution 4.0 International (CC BY 4.0).

PhysioCHI: Towards Best Practices for Integrating Physiological Signals in
HCI, May 11, 2024, Honolulu, HI, USA

[1] [1] [1] [1]These authors contributed equally. [1]Corresponding author.

# Camera-Based Remote Physiology Sensing for Hundreds of Subjects Across Skin
Tones

Jiankai Tang  Tsinghua University, Beijing, China  Xinyi Li  Jiacheng Liu
Xiyuxing Zhang  Zeyu Wang  Yuntao Wang

(2024)

###### Abstract

Remote photoplethysmography (rPPG) emerges as a promising method for non-
invasive, convenient measurement of vital signs, utilizing the widespread
presence of cameras. Despite advancements, existing datasets fall short in
terms of size and diversity, limiting comprehensive evaluation under diverse
conditions. This paper presents an in-depth analysis of the VitalVideo dataset
[1], the largest real-world rPPG dataset to date, encompassing 893 subjects
and 6 Fitzpatrick skin tones. Our experimentation with six unsupervised
methods and three supervised models demonstrates that datasets comprising a
few hundred subjects(i.e., 300 for UBFC-rPPG, 500 for PURE, and 700 for MMPD-
Simple) are sufficient for effective rPPG model training. Our findings
highlight the importance of diversity and consistency in skin tones for
precise performance evaluation across different datasets.

###### keywords:

rPPG Physiological Sensing VitalVideo

##  1 Introduction

Convenient and accurate access to vital signs is crucial for assessing health
states and preventing diseases. Traditional methods for measuring
physiological parameters, such as pulse waves, heart rate, and blood oxygen
levels, often rely on wearable devices. While effective, these methods pose
risks of cross-infection and may not be suitable for infants due to their
delicate fingers. In contrast, camera-based physiological sensing offers a
novel, contactless, and non-invasive approach that is both rapid and
accessible, leveraging the ubiquitous nature of cameras to transform health
signal measurement into a more user-friendly experience for everybody. This
technology has the potential to be applied in various scenarios, including
remote patient monitoring [2], fitness and wellness tracking [3], and in
situations where traditional wearables are impractical or undesired [4].

Figure 1: Standard procedure. Pipeline for predicting rPPG waveforms from
facial frames, utilizing configuration settings consistent with the rPPG-
Toolbox [5]

The underlying principle of camera-based physiological sensing, particularly
remote photoplethysmography (rPPG), utilizes pixel information from video
recordings to detect changes in light modulated by blood flow beneath the
skin. These changes, reflecting the volumetric variations of oxygenated and
deoxygenated hemoglobin, enable the measurement of the peripheral blood volume
pulse (BVP), with rPPG signals closely correlating with heart rate [6, 7].
Leveraging advanced computer vision and time series analysis techniques, rPPG
signal extraction emerges as a viable path for non-invasive health monitoring.
The standard process for extracting rPPG signals from facial footage
encompasses several critical steps [5]: selecting the region of interest
(ROI), performing signal normalization, training the neural network,
conducting model inference, and signal processing, as depicted in Fig 1.

Despite the potential, the application of rPPG in real-world scenarios faces
challenges, including body motion, varying lighting conditions, and poor-
quality recordings. Moreover, accurately extracting pulse signals from
individuals with darker skin tones remains difficult due to their lower light
absorption and the risk of overexposure [3, 8, 9]. These challenges highlight
the need for extensive research across diverse subjects and conditions. The
emergence of the VitalVideo dataset [1] presents an opportunity to explore the
boundaries of rPPG technology with respect to subject size and skin tone
diversity. This dataset offers a solid foundation for research, yet,
intriguingly, it has not been utilized for comprehensive benchmarking or
classification studies, including by its own creators. The availability of the
VitalVideo dataset opens new avenues for addressing the aforementioned
challenges, promising advancements in the accuracy and applicability of rPPG
technologies across diverse populations and environments.

This paper enhances the understanding of camera-based health monitoring by
making key contributions in a clear and straightforward manner: 1) We are the
first to train and test on the VitalVideo dataset, sharing our code
openly111https://github.com/Health-HCI-Group/Largest_rPPG_Dataset_Evaluation
and confirming the dataset’s reliability for research. 2) By employing four
datasets that include around 1000 individuals across 6 skin tones, we enhance
benchmark efforts and underscore the importance of diverse data for model
training. 3) Our analysis shows that optimal rPPG model training can be
achieved with data from just a few hundred individuals. Additionally, we find
that models are more sensitive to consistency in darker skin tones,
highlighting the impact of data volume and skin tone diversity on model
performance.

##  2 Related Works

###  2.1 Dataset

Figure 2: Datasets Samples, including PURE [10],UBFC-rPPG [11], MMPD [3],
VitalVideo [1]

From the multitude of available rPPG datasets, we carefully chose four
representative datasets for our data training and testing, as depicted in Fig
2. The PURE [10] and UBFC [11] datasets stand out as the most commonly used in
rPPG research due to their reliability. MMPD [3] distinguishes itself as the
largest rPPG dataset captured using mobile phones, whereas VitalVideo [1]
boasts the greatest number of subjects and all Fitzpatrick skin tones.

PURE [10]: Captured using an RGB eco274CVGE camera from SVS-Vistek GmbH, the
dataset comprises recordings from 10 subjects, with a distribution of 8 males
and 2 females. Video footage, obtained at a frequency of 30Hz and a resolution
of 640x480, presents subjects positioned around 1.1 meters away from the
camera. Illumination is provided by natural light filtering through a window,
ensuring front-facing illumination. Gold-standard PPG and SpO2 data, sampled
at 60Hz, are acquired through a CMS50E pulse oximeter affixed to the subject’s
finger. Across six recordings per participant, variations in motion conditions
yield a diverse dataset reflecting different physiological states.

UBFC-rPPG [11]: Recorded using a Logitech C920 HD Pro webcam at 30Hz, the
dataset features RGB videos with a resolution of 640x480, stored in an
uncompressed 8-bit RGB format. Reference PPG data, serving as the gold-
standard validation, is collected via a CMS50E transmissive pulse oximeter.
Subjects, positioned approximately one meter from the camera, are recorded
under indoor conditions illuminated by a combination of natural sunlight and
artificial light sources.

MMPD [3]: Comprising 660 one-minute videos captured using a Samsung Galaxy S22
Ultra mobile phone, the dataset is recorded at 30 frames per second with a
resolution initially at 1280x720 pixels and later compressed to 320x240
pixels. Ground truth PPG signals, obtained simultaneously at 200 Hz using an
HKG-07C+ oximeter and downsampled to 30 Hz, accompany the videos. The dataset
encompasses Fitzpatrick skin types 3-6, four lighting conditions (LED-low,
LED-high, incandescent, natural), and diverse activities including stationary,
head rotation, talking, walking, and exercise scenarios.

VitalVideo [1]: Utilizing a high-resolution Basler acA1920-40uc camera paired
with a Basler C11-1220-12M lens, this dataset captures videos at 1920x1200
pixels, 30 fps. Participants, positioned 50 to 70 cm away, were recorded under
varied indoor lighting, including artificial and natural sources, ensuring a
minimum illumination of 150 lux with additional ring light support when
needed. Accompanying physiological data were collected using a Contec CMS50D+
pulse oximeter and an Omron M7 blood pressure monitor, offering comprehensive
multimodal data. Video clips, 30 seconds in length, recorded twice for each
subject, were encoded in MP4 format, each approximately 2GB. The dataset,
enriched with PPG waveforms, heart rate, SpO2, and blood pressure
measurements, spans multiple indoor environments from libraries to shopping
malls across ten locations in Western Europe, encompassing a diverse range of
six skin tones and age groups ranging from 5 to 95 years. VV100, a subset with
100 subjects showcasing maximal demographic diversity, and the entire VVAll
set with around 900 subjects were utilized for analysis.

###  2.2 Existing Methods

Recent advances in computer vision have significantly propelled the
development of camera-based physiological vital sign measurements, introducing
an expanding realm characterized by both unsupervised and supervised
methodologies [12]. Unsupervised methods utilize traditional signal processing
and linear algebra to deduce PPG signals from RGB videos through techniques
such as exploiting the green channel information (Green [13]), Independent
Component Analysis (ICA [14]), chrominance-based signals (CHROM [15]), the
plane orthogonal to skin (POS [6]), blood volume pulse extraction (PBV [16]),
and motion-invariant features analysis (LGI [17]). On the other hand,
supervised methodologies employ neural networks, including DeepPhys [18],
PhysNet [19], TS-CAN [20], and video transformer-based PhysFormer [21], to
improve accuracy through deep learning techniques and optimized training
protocols. These advancements have been further bolstered by innovative data
generation [22], parallel computing [23] and augmentation strategies [24], as
well as meta-learning [25, 26], federated learning [27], and unsupervised
pretraining [28, 29, 30, 31], significantly elevating the state-of-the-art in
non-invasive physiological measurement.

###  2.3 Benchmarks

Current benchmarks in the rPPG field concentrate on equitable evaluations
across datasets for the task of heart rate estimation, comparing various
networks and models [5, 32]. The rPPG-Toolbox includes six unsupervised
methods and six supervised networks for datasets such as PURE [10], UBFC-rPPG
[11], and MMPD [3]. Nevertheless, there is a scarcity of research dedicated to
analyzing each scenario in-depth to comprehend its limitations and optimal
performance. MMPD [3] stands out by offering eight labels for detailed
examination, yet it lacks data for Fitzpatrick skin tone types 1 and 2. We
have incorporated a data loader and label filter in the toolbox to facilitate
the selection of all subset combinations (i.e., gender, skin tone, location,
movements, and talking) for the VitalVideo dataset [1]. To the best of our
knowledge, our study is the first to conduct research on the largest
VitalVideo dataset [1] and examine skin tone label combinations across
VitalVideo [1] and MMPD [3].

##  3 Experiments

###  3.1 Setup

For our experiments, we utilized an NVIDIA GeForce RTX 3090 graphics card,
CUDA Version 12.2, and PyTorch version 2.1.1. We integrated the VitalVideo [1]
dataset with the rPPG-Toolbox [5], introducing a label selector specifically
for VitalVideo [1] to streamline data extraction. The implemented code has
been open-sourced at GitHub: https://github.com/Health-HCI-
Group/Largest_rPPG_Dataset_Evaluation. The dataset was divided into VVAll
[1](893 subjects), encompassing all data, and VV100 [1](100 subjects), a more
balanced subset. The VitalVideo [1] dataset labels skin tones from type 1 to 6
according to Fitzpatrick rules. We selected MMPD’s simplest subset(MMPD-
Simple) [3] by excluding natural lighting and motion conditions while
preserving skin color variations. We chose settings like "LED-Low," "LED-
High," and "Incandescent" for lighting, "Stationary" for motion, "False" for
exercise, covering all skin tone types.

This study primarily focuses on cross-dataset training and testing, utilizing
the VitalVideo [1] dataset in conjunction with three other datasets: PURE
[10], UBFC [11], and MMPD [3]. Our methodology commenced with applying six
unsupervised methods [5] on the VitalVideo [1] dataset. Subsequently, we
conducted training sessions on various skin tones within the VV100 [1] and
executed tests on the PURE [10], UBFC [11], and MMPD [3] datasets. Meanwhile,
training was performed on the PURE [10], UBFC [11], and MMPD [3] datasets,
followed by testing on each distinct skin tone category within VV100 [1].

In our research, we selected six widely utilized unsupervised methods: ICA
[14], POS [6], CHROM [15], GREEN [13], LGI [17], and PBV [33]. These methods
represent a broad spectrum of approaches in the field of rPPG technology, each
with its unique advantages and applications. Additionally, we employed three
state-of-the-art networks that are representative of the most advanced
architectures in the domain: TS-CAN [20], which exemplifies 2D CNNs; PhysNet
[19], a representative of 3D CNNs; and PhysFormer [21], which utilizes the
Transformer architecture. These selections were made to encompass a
comprehensive range of methodologies, from traditional unsupervised techniques
to cutting-edge neural networks, ensuring a thorough investigation into the
capabilities and performance of camera-based physiological measurement
technologies.

###  3.2 Unsupervised methods on VV100 and VVAll [1]

Figure 3: Results of Unsupervised Methods on VitalVideo [1]. Line colors get
deeper as skin tone varies from type 1 to type 6. MAE = Mean Absolute Error in
HR estimation (Beats/Min).

As demonstrated in Fig 3, the mean absolute errors (MAE) for both VV100 and
VVAll [1] exhibit an ascending trend as the skin tones range from type 1 to
type 6 with POS [6] demonstrating the best performance in most cases. The
similar trend observed in both subgraphs underscores the ability of the VV100
subset to effectively represent the larger VitalVideo dataset [1],
demonstrating its comprehensiveness and relevance. Moreover, VV100 [1] not
only mirrors the characteristics of VVAll [1] but also has a more balanced
distribution(e.g., skin tone), making it a suitable subset for subsequent
experiments.

###  3.3 Supervised methods trained on VV100 [1]

Table 1: Supervised methods trained on VV100 [1]. Test result on PURE [10],
UBFC-rPPG [11] and MMPD-Simple [3] trained on VV100 [1] and three subsets of
VV100 [1] using TS-CAN [20], PhysNet [19], and PhysFormer [21].

Training Set | VV100 [1]
---|---
Testing Set | PURE [10]
Method |  TS-CAN [20] |  PhysNet [19] |  PhysFormer [21]
Metric | MAE | RMSE | MAPE | $\rho$ | MAE | RMSE | MAPE | $\rho$ | MAE | RMSE | MAPE | $\rho$
Training Skin Tone |  |  |  |  |  |  |  |  |  |  |  |
1 2(num:23) | 6.22 | 17.25 | 7.41 | 0.69 | 3.98 | 13.96 | 3.44 | 0.81 | 4.74 | 16.01 | 4.67 | 0.74
3 4(num:23) | 8.30 | 21.22 | 9.05 | 0.48 | 5.60 | 15.35 | 7.58 | 0.75 | 6.00 | 15.94 | 7.26 | 0.73
5 6(num:23) | 9.21 | 21.03 | 10.84 | 0.51 | 7.23 | 19.72 | 6.34 | 0.60 | 15.06 | 24.06 | 21.83 | 0.17
1 2 3 4 5 6(num:100) | 6.40 | 15.99 | 8.87 | 0.74 | 6.04 | 17.86 | 5.78 | 0.66 | 5.47 | 15.84 | 6.11 | 0.74

Training Set | VV100 [1]
---|---
Testing Set |  UBFC-rPPG [11]
Method |  TS-CAN [20] |  PhysNet [19] |  PhysFormer [21]
Metric | MAE | RMSE | MAPE | $\rho$ | MAE | RMSE | MAPE | $\rho$ | MAE | RMSE | MAPE | $\rho$
Training Skin Tone |  |  |  |  |  |  |  |  |  |  |  |
1 2(num:23) | 3.58 | 10.72 | 3.37 | 0.83 | 5.63 | 14.64 | 5.01 | 0.68 | 6.36 | 15.64 | 5.72 | 0.67
3 4(num:23) | 4.62 | 11.95 | 4.42 | 0.80 | 2.03 | 5.91 | 2.05 | 0.95 | 5.34 | 13.36 | 4.98 | 0.78
5 6(num:23) | 11.26 | 21.14 | 10.64 | 0.57 | 7.49 | 16.25 | 6.57 | 0.61 | 20.84 | 27.89 | 19.50 | 0.23
1 2 3 4 5 6(num:100) | 1.70 | 3.69 | 1.83 | 0.98 | 7.62 | 18.78 | 6.52 | 0.48 | 2.64 | 7.05 | 2.49 | 0.93

Training Set | VV100 [1]
---|---
Testing Set |  MMPD-Simple [3]
Method |  TS-CAN [20] |  PhysNet [19] |  PhysFormer [21]
Metric | MAE | RMSE | MAPE | $\rho$ | MAE | RMSE | MAPE | $\rho$ | MAE | RMSE | MAPE | $\rho$
Training Skin Tone |  |  |  |  |  |  |  |  |  |  |  |
1 2(num:23) | 4.23 | 8.59 | 5.51 | 0.73 | 5.14 | 10.10 | 6.60 | 0.58 | 6.90 | 12.36 | 8.54 | 0.37
3 4(num:23) | 5.67 | 11.98 | 7.54 | 0.42 | 5.49 | 10.83 | 8.51 | 0.53 | 10.59 | 16.91 | 15.43 | -0.02
5 6(num:23) | 4.07 | 9.36 | 5.50 | 0.68 | 4.62 | 10.33 | 5.44 | 0.59 | 12.52 | 16.66 | 16.83 | 0.12
1 2 3 4 5 6(num:100) | 4.73 | 11.96 | 6.48 | 0.48 | 4.70 | 9.93 | 5.87 | 0.62 | 5.49 | 11.58 | 6.96 | 0.44

MAE = Mean Absolute Error in HR estimation (Beats/Min), RSME = Root Mean
Square Error, MAPE = Mean Percentage Error (%), $\rho$ = Pearson Correlation
in HR estimation.

To investigate the variances in supervised neural network training across
different skin tones, we divided the VV100 [1] dataset into three segments,
each containing 23 subjects. Given the uneven distribution of skin tones, we
created subsets pairing type 1 with type 2 skin tones, type 3 with type 4, and
type 5 with type 6. Subsequently, we utilized three supervised learning
methods to train on the entire VV100 [1] dataset and its three subsets
individually. Table 1 presents the outcomes obtained by training on VV100 [1]
and testing on three presentative datasets: PURE [10], UBFC-rPPG [11], and
MMPD-Simple [3]. The best MAE indexes for PURE [10], UBFC-rPPG [11], and MMPD-
Simple [3] are 3.98, 1.70, and 4.07 beats per minute in remote heart rate
estimation task.

Test results on PURE are more accurate [10] when models are trained on lighter
skin tones, outperforming those trained on the entire VV100 [1] dataset. For
UBFC-rPPG [11], which consists of type 1 to 3 skin tones, models trained on
similar skin tones significantly outperformed those trained on darker skin
tones. Notably, models trained on type 5 and type 6 skin tones showcased
remarkably best test results on MMPD [3], especially with TS-CAN [20] and
PhysNet [19]. This underscores the pivotal role of maintaining consistency in
skin color between the training and test sets, as it can significantly enhance
test accuracy. Furthermore, skin tone diversity appears to contribute to more
stable performance, achieving the best test results with TS-CAN [20] on UBFC-
rPPG [11].

###  3.4 Supervised methods test on VV100 [1]

The results presented in Table 2 on VV100 [1] delineate the performance of
models trained across three datasets, with evaluations conducted on both
aggregated and individual skin tone categories within the VV100 [1] dataset.
Clearly, all models showed notable effectiveness on lighter skin tones,
particularly TS-CAN [20] and PhysNet [19]. However, a discernible degradation
in performance was observed as the skin tone deepened. Notably, the models
trained on the MMPD-Simple [3] dataset exhibited no superior performance on
darker skin tones compared to its counterparts likely due to the compression
of mobile phone shots.

Table 2: Supervised methods test on VV100 [1]. MAE on each single skin tone of
VV100 [1] and entire VV100 [1] with models trained on PURE [10], UBFC-rPPG
[11], and MMPD-Simple [3].

Testing Set |  VV100 [1]
---|---
Training Set | PURE [10] |  UBFC-rPPG [11] |  MMPD-Simple [3]
Method |  TC [20] |  PN [19] |  PF [21] |  TC [20] |  PN [19] |  PF [21] |  TC [20] |  PN [19] |  PF [21]
Testing Skin Tone |  |  |  |  |  |  |  |  |
1(num:5) | 0.22 | 0.00 | 0.59 | 0.66 | 0.66 | 0.59 | 0.00 | 0.00 | 0.59
2(num:35) | 3.24 | 1.58 | 2.26 | 1.39 | 5.50 | 2.26 | 2.67 | 3.02 | 4.10
3(num:21) | 9.24 | 1.35 | 7.57 | 4.33 | 5.68 | 7.57 | 6.70 | 7.32 | 6.90
4(num:17) | 6.15 | 4.34 | 10.62 | 5.49 | 3.46 | 10.62 | 7.03 | 6.26 | 7.69
5(num:13) | 13.00 | 13.02 | 11.91 | 10.11 | 9.35 | 11.91 | 10.23 | 8.60 | 14.94
6(num:9) | 14.26 | 14.65 | 17.23 | 12.40 | 11.33 | 17.23 | 15.72 | 16.11 | 15.12
1 2 3 4 5 6(num:100) | 7.23 | 3.78 | 7.29 | 4.86 | 6.08 | 7.83 | 6.36 | 6.30 | 7.58

TC, PN, and PF stand for TS-CAN [20], PhysNet [19], and PhysFormer [21]. MAE =
Mean Absolute Error in HR estimation (Beats/Min)

##  4 Discussion

###  4.1 Supervised methods on VVALL [1] and UBFC-rPPG [11], PURE [10], and
MMPD-Simple [3] for data volume

We investigated the impact of different proportions of training data in the
VVAll [1] dataset analysis. Specifically, we trained models on datasets
comprising 100%, 70%, 50%, 30%, 10%, and 1% of the VVAll [1] dataset,
corresponding to 893, 625, 446, 267, 89, and 8 subjects respectively,
subsequently tested them on UBFC-rPPG [11], PURE [10], and MMPD-Simple [3],
using TS-CAN [20]. Notably, for the 10% and 1% proportions, we divided the
dataset into five distinct parts and averaged their outcomes to minimize the
impact of random selection. It is evident from Fig 4(a) that an increased
volume of training data does not necessarily lead to improved model
performance. Instead, a threshold exists beyond which adding more subjects to
the training set ceases to significantly improve model performance.
Importantly, this threshold varies with the complexity of the testing dataset
but remains below 1000.

(a) Training on VVAll [1] using different proportions of data. Comparison of
test results on PURE [10], UBFC-rPPG [11], and MMPD-Simple [3] from training
on different proportions of VVAll [1].

(b) Training on VV100 [1] and testing on MMPD-Simple [3] by single skin tone.
Comparison of test results on each single skin tone on MMPD-Simple [3] with
models trained on three subsets of VV100 [1].

Figure 4: Training on VV100 [1] and VVAll [1] with TS-CAN [20]. MAE = Mean
Absolute Error in HR estimation (Beats/Min)

###  4.2 Supervised methods on VV100 [1] and MMPD-Simple [3] for diversity

In addition to quantity, the dimension of diversity also merits attention.
Specifically, we conducted tests on various skin tones within the MMPD-Simple
[3] dataset in isolation, utilizing a model trained on the VV100 [1] dataset.
The results are illustrated in Fig 4(b). For lighter skin tones (i.e. types 3
and 4), diversity proves more crucial than skin tone consistency. Conversely,
for darker skin tones (i.e., types 5 and 6), training on similar skin types
often yields better results than training with a larger number of subjects.

###  4.3 Limitation

We recognize the presence of certain limitations within our study and are
committed to addressing these in future research efforts. The primary
limitations identified are as follows: 1) New neural network modifications
necessary for achieving state-of-the-art performance were not implemented. 2)
There is an absence of a detailed exploration into the optical and medical
principles that could explain the models’ underperformance in challenging
scenarios.

##  5 Conclusion

This study marks the inaugural exploration of the VitalVideo dataset [1], the
most extensive rPPG dataset to date. Leveraging its vast array of subjects and
diverse skin tones, we embarked on a comprehensive series of experiments
employing six unsupervised methods alongside three supervised models. Our key
findings include: 1) Our pioneering training and testing on the VitalVideo
dataset, coupled with the open sharing of our code, underscores the dataset’s
reliability for advancing research in this field. 2) Optimal rPPG model
training is achievable with datasets comprising just a few hundred
individuals, demonstrating the efficiency of smaller, well-curated datasets.
3) We discovered a pronounced sensitivity to skin tone consistency,
particularly with darker skin tones, highlighting the critical need for
careful consideration of skin tone diversity in model development and
evaluation.

##  6 Acknowledgments

This work is supported by National Natural Science Foundation of China (No.
62132010 and No. 62002198), Young Elite Scientists Sponsorship Program by CAST
(No. 2021QNRC001), and Beijing Natural Science Foundation (No. QY23124).

## References

  * Toye [2023] P.-J. Toye, Vital videos: A dataset of face videos with ppg and blood pressure ground truths, 2023. arXiv:2306.11891.
  * Yan et al. [2020] B. P. Yan, W. H. Lai, C. K. Chan, A. C. Au, B. Freedman, Y. C. Poh, M.-Z. Poh,  High-throughput, contact-free detection of atrial fibrillation from video with deep learning,  JAMA cardiology 5 (2020) 105–107.
  * Tang et al. [2023] J. Tang, K. Chen, Y. Wang, Y. Shi, S. Patel, D. McDuff, X. Liu, Mmpd: Multi-domain mobile video physiology dataset, 2023. arXiv:2302.03840.
  * Villarroel et al. [2019] M. Villarroel, S. Chaichulee, J. Jorge, S. Davis, G. Green, C. Arteta, A. Zisserman, K. McCormick, P. Watkinson, L. Tarassenko,  Non-contact physiological monitoring of preterm infants in the neonatal intensive care unit,  npj Digital Medicine 2 (2019) 1–18.
  * Liu et al. [2022] X. Liu, G. Narayanswamy, A. Paruchuri, X. Zhang, J. Tang, Y. Zhang, Y. Wang, S. Sengupta, S. Patel, D. McDuff,  rppg-toolbox: Deep remote ppg toolbox,  arXiv preprint arXiv:2210.00716 (2022).
  * Wang et al. [2016] W. Wang, A. C. den Brinker, S. Stuijk, G. de Haan,  Algorithmic principles of remote ppg,  IEEE Transactions on Biomedical Engineering 64 (2016) 1479–1491.
  * Xu et al. [2014] S. Xu, L. Sun, G. K. Rohde,  Robust efficient estimation of heart rate pulse from video,  Biomedical optics express 5 (2014) 1124–1135.
  * Takano and Ohta [2007] C. Takano, Y. Ohta,  Heart rate measurement based on a time-lapse image,  Medical engineering & physics 29 (2007) 853–857.
  * Nowara et al. [2020] E. M. Nowara, D. McDuff, A. Veeraraghavan,  A meta-analysis of the impact of skin tone and gender on non-contact photoplethysmography measurements,  in: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, 2020, pp. 284–285.
  * Stricker et al. [2014] R. Stricker, S. Müller, H.-M. Gross,  Non-contact video-based pulse rate measurement on a mobile service robot,  in: The 23rd IEEE International Symposium on Robot and Human Interactive Communication, IEEE, 2014, pp. 1056–1062.
  * Bobbia et al. [2019] S. Bobbia, R. Macwan, Y. Benezeth, A. Mansouri, J. Dubois,  Unsupervised skin tissue segmentation for remote photoplethysmography,  Pattern Recognition Letters 124 (2019) 82–90.
  * McDuff [2021] D. McDuff,  Camera measurement of physiological vital signs,  ACM Computing Surveys (CSUR) (2021).
  * Verkruysse et al. [2008] W. Verkruysse, L. O. Svaasand, J. S. Nelson,  Remote plethysmographic imaging using ambient light.,  Optics express 16 (2008) 21434–21445.
  * Poh et al. [2010] M.-Z. Poh, D. J. McDuff, R. W. Picard,  Advancements in noncontact, multiparameter physiological measurements using a webcam,  IEEE transactions on biomedical engineering 58 (2010) 7–11.
  * De Haan and Jeanne [2013] G. De Haan, V. Jeanne,  Robust pulse rate from chrominance-based rppg,  IEEE Transactions on Biomedical Engineering 60 (2013) 2878–2886.
  * De Haan and Van Leest [2014] G. De Haan, A. Van Leest,  Improved motion robustness of remote-ppg by using the blood volume pulse signature,  Physiological measurement 35 (2014) 1913.
  * Pilz et al. [2018] C. S. Pilz, S. Zaunseder, J. Krajewski, V. Blazek,  Local group invariance for heart rate estimation from face videos in the wild,  in: Proceedings of the IEEE conference on computer vision and pattern recognition workshops, 2018, pp. 1254–1262.
  * Chen and McDuff [2018] W. Chen, D. McDuff,  DeepPhys: Video-Based Physiological Measurement Using Convolutional Attention Networks,  arXiv:1805.07888 [cs] (2018). URL: http://arxiv.org/abs/1805.07888, arXiv: 1805.07888.
  * Yu et al. [2019] Z. Yu, W. Peng, X. Li, X. Hong, G. Zhao,  Remote heart rate measurement from highly compressed facial videos: an end-to-end deep learning solution with video enhancement,  in: Proceedings of the IEEE/CVF International Conference on Computer Vision, 2019, pp. 151–160.
  * Liu et al. [2020] X. Liu, J. Fromm, S. Patel, D. McDuff,  Multi-task temporal shift attention networks for on-device contactless vitals measurement,  Advances in Neural Information Processing Systems 33 (2020) 19400–19411.
  * Yu et al. [2022] Z. Yu, Y. Shen, J. Shi, H. Zhao, P. H. Torr, G. Zhao,  Physformer: Facial video-based physiological measurement with temporal difference transformer,  in: Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, 2022, pp. 4186–4196.
  * McDuff et al. [2020] D. McDuff, J. Hernandez, E. Wood, X. Liu, T. Baltrusaitis,  Advancing non-contact vital sign measurement using synthetic avatars,  arXiv preprint arXiv:2010.12949 (2020).
  * Liu et al. [2024] M. Liu, J. Tang, H. Li, J. Qi, S. Li, K. Wang, Y. Wang, H. Chen, Spiking-physformer: Camera-based remote photoplethysmography with parallel spike-driven transformer, 2024. arXiv:2402.04798.
  * Wang et al. [2022] Z. Wang, Y. Ba, P. Chari, O. D. Bozkurt, G. Brown, P. Patwa, N. Vaddi, L. Jalilian, A. Kadambi,  Synthetic generation of face videos with plethysmograph physiology,  in: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2022, pp. 20587–20596.
  * Liu et al. [2022] X. Liu, Y. Wang, S. Xie, X. Zhang, Z. Ma, D. McDuff, S. Patel,  Mobilephys: Personalized mobile camera-based contactless physiological sensing,  Proc. ACM Interact. Mob. Wearable Ubiquitous Technol. 6 (2022). URL: https://doi.org/10.1145/3517225. doi:10.1145/3517225.
  * Liu et al. [2021] X. Liu, Z. Jiang, J. Fromm, X. Xu, S. Patel, D. McDuff,  Metaphys: few-shot adaptation for non-contact physiological measurement,  in: Proceedings of the Conference on Health, Inference, and Learning, 2021, pp. 154–163.
  * Liu et al. [2022] X. Liu, M. Zhang, Z. Jiang, S. Patel, D. McDuff,  Federated remote physiological measurement with imperfect data,  in: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2022, pp. 2155–2164.
  * Sun and Li [2022] Z. Sun, X. Li,  Contrast-phys: Unsupervised video-based remote physiological measurement via spatiotemporal contrast,  in: European Conference on Computer Vision, Springer, 2022, pp. 492–510.
  * Gideon and Stent [2021] J. Gideon, S. Stent,  The way to my heart is through contrastive learning: Remote photoplethysmography from unlabelled video,  in: Proceedings of the IEEE/CVF International Conference on Computer Vision, 2021, pp. 3995–4004.
  * Speth et al. [2023] J. Speth, N. Vance, P. Flynn, A. Czajka,  Non-contrastive unsupervised learning of physiological signals from video,  in: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2023, pp. 14464–14474.
  * Yang et al. [2022] Y. Yang, X. Liu, J. Wu, S. Borac, D. Katabi, M.-Z. Poh, D. McDuff,  Simper: Simple self-supervised learning of periodic targets,  arXiv preprint arXiv:2210.03115 (2022).
  * Wang et al. [2023] K. Wang, Y. Wei, M. Tong, J. Gao, Y. Tian, Y. Ma, Z. Zhao, Physbench: A benchmark framework for remote physiological sensing with new dataset and baseline, 2023\. arXiv:2305.04161.
  * de Haan and van Leest [2014] G. de Haan, A. van Leest,  Improved motion robustness of remote-PPG by using the blood volume pulse signature,  Physiological Measurement 35 (2014) 1913–1926. URL: https://doi.org/10.1088/0967-3334/35/9/1913. doi:10.1088/0967-3334/35/9/1913.