Jacques Hinderer
email: jhinderer@unistra.fr

U Riccardi

S Rosat

J.-P Boy

B Hector

M Calvo

F L Littel

J.-D Bernard

A study of the solid earth tides, ocean and atmospheric loadings using an 8-year record (2010-2018) from superconducting gravimeter OSG-060 at Djougou (Benin, West Africa)

A study of the solid earth tides, ocean and atmospheric loadings using an 8-year record (2010-2018) from superconducting gravimeter OSG-060 at Djougou (Benin, West Africa)

Introduction

The superconducting gravimeter OSG-060 from GWR Instruments has been installed in Nalohou, close to Djougou in northern Benin (West Africa) in July 2010. This installation was done in the frame of the GHYRAF (Gravity and Hydrology in Africa) program that lasted from 2008 to 2012 [START_REF] Hinderer | Land water storage changes from ground and space geodesy: first results from the GHYRAF (Gravity and Hydrology in Africa) experiment[END_REF]. This gravimeter is part of the IGETS (International Geodynamics and Earth Tides Service) under the umbrella of IAG (International Association of Geodesy). Fig. 1 shows the location of the Djougou station (The geographical coordinates of the station are 9.7424 °N and 1.6056 °E) among the other stations of the international network of superconducting gravimeters (SG).

It is noticeable that only two stations exist in Africa (Djougou in Benin and Sutherland in South Africa) and, even more important, Djougou is the only equatorial station of the network to date since the end of operation of the Bandung and Cibinong stations in Indonesia. This means that Djougou station is especially valuable for studying the Earth's lunisolar tides, as well as the ocean tidal loading and atmospheric loading.

Before the installation of the SG, since no power was available, a 1.5 km line of medium voltage was first set up. Then several buildings shown on Fig. 2 were built with the generator building at a sufficiently large distance from the two buildings dedicated to the SG and the absolute gravimeter (AG) that episodically measures in parallel with the SG. The generators (one main + two spare equipments) turned out to be vital because of the numerous power shortages that range from a few hours to 15 days occurring in Djougou.

The choice of this location for installing the SG was driven by the fact that Nalohou is part of the Ara catchment, one of the key sites in the Sudanian region monitored by AMMA-CATCH hydrological and meteorological observatory (http://www.amma-catch.org/) with a high density of data available over a long time span of several decades.

Gravity data processing

The first results in terms of calibration and instrumental drift of OSG-060 have been reported by Hinderer et al. (2014a) for a period ranging from July 2010 to May 2011. The scale factor of OSG-060 was obtained from a parallel registration of 5 days (8-15 April 2011) with an absolute gravimeter FG5#206 which is the classical way to calibrate SGs (e.g. [START_REF] Hinderer | On the calibration of a superconducting gravimeter using absolute gravity measurements[END_REF][START_REF] Imanishi | Calibration of the superconducting gravimeter T011 by parallel observation with the absolute gravimeterFG5#210-a Bayesian approach[END_REF]. For a detailed discussion on various aspects of the AG/SG calibration, we refer to the recent studies by [START_REF] Riccardi | On the accuracy of the calibration of superconducting gravimeters using absolute and spring sensors: a critical comparison[END_REF] and [START_REF] Crossley | More Thoughts on AG-SG Comparisons and SG Scale Factor Determinations[END_REF].

We used a least square fit of the SG values to AG drop values every 10 s (second) yielding a value of -709 ± 4 nm s -2 /volt (precision of 5.6‰).

The phase experiment to determine the phase shift of the instrument (sensor + decimation filter) was done in July 2012 using the step method [START_REF] Wenzel | Precise instrumental phase lag determination by the step response method[END_REF] and led to a time delay of 10.6 ± 0.1 s.

The SG-060 gravity and air pressure data are sampled at both 1 and 60 s. As done classically, the gravity record is corrected for the major disturbances resulting in spikes, steps or gaps.

Some of these disturbances are caused by earthquakes (saturation of the sensor due to the arrival of seismic waves) or are man-made (in the case of instrumental maintenance for instance). We refer the reader to [START_REF] Hinderer | Influence of different processing methods on the retrieval of gravity signals from GGP data[END_REF] and [START_REF] Hinderer | Superconducting gravimetry, in treatise on geophysics[END_REF] for more details on the processing steps.

The cleaned pressure and gravity data sets are shown on Fig. 3 for the investigated period (2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018). The correction for lunisolar tides (solid Earth + ocean tidal loading), as well as for atmospheric effects and Earth's rotation leads to the gravity residuals (in black on Fig. 4). ) (in black) after correction for solid Earth and ocean tidal loading, atmospheric effects and Earth's rotation; corrected gravity residuals (in blue) after subtracting a linear instrumental drift (in red).

A further correction for the instrumental drift of the gravimeter (in red on Fig. 4) leads then to the corrected residual signal (in blue on Fig. 4) that is merely of hydrological origin and characterized by an annual periodicity (see Boy and Hinderer 2006;[START_REF] Hector | Hydro-gravimetry in West-Africa: first results from the Djougou (Benin) superconducting gravimeter[END_REF].

The instrumental drift is composed of an initial exponential term followed by a linear term that remains stable over the years. This is very classical for SGs and confirms the earlier results based on a 1.5 year record (Hinderer et al., 2014a(Hinderer et al., , 2014b)).

The fit to an exponential function g = g0 + A1*exp(-(x-x0)/T1), where g0 and x0 are the starting values of gravity and time, leads to an amplitude A1 of -147.6 ± 1.2 nm s -2 and a time delay T1 = 13.8 ± 0.3 days. It must be noted that this exponential drift had to be done on the residual gravity corrected for hydrological loading which mixes up with the instrumental part.

In our case, we used MERRA2 global hydrology model [START_REF] Reichle | Assessment of MERRA-2 land surface hydrology estimates[END_REF] available at the EOST loading service (http://loading.u-strasbg.fr). The linear drift is + 213.6 ± 0.1 nm s -2 /year, which is rather large for SGs [START_REF] Hinderer | Superconducting gravimetry, in treatise on geophysics[END_REF], but the linearity is very strong and apparently stable in time from our tests.

Tidal analysis and ocean tidal loading

We analyze the whole dataset of gravity records (nearly 8 years), using the [START_REF] Hartmann | The HW95 tidal potential catalogue[END_REF] tidal potential catalogue. Amplitude and phase tidal parameters (Fig. 5) for groups combining inseparable constituents as well as the air pressure admittance factors are adjusted in the long period, diurnal and sub-diurnal frequency bands by means of ET34-ANA v7.1 software [START_REF] Schüller | Theoretical Basis for Earth Tide Analysis and Prediction[END_REF]; the complete list of the adjusted tidal parameters is given in Annex A.

From the free Ocean Tide Loading Provider (Bos & Scherneck 2019) we retrieve the time invariant loading contribution to reduce the ocean loading effect in the collected gravity records. The computed contributions are resulting from nine different global ocean tide models: GOT00.2 [START_REF] Ray | A Global Ocean Tide Model From TOPEX/POSEIDON Altimetry: GOT99[END_REF], GOT4.7 (update of [START_REF] Ray | A Global Ocean Tide Model From TOPEX/POSEIDON Altimetry: GOT99[END_REF], TPXO8 [START_REF] Egbert | Efficient inverse modeling of barotropic ocean tides[END_REF], FES2004 [START_REF] Lyard | Modelling the global ocean tides: modern insights from FES2004[END_REF], FES2014b [START_REF] Carrère | FES2014, A New Tidal Model on the Global Ocean With Enhanced Accuracy in Shallow Seas and in the Arctic Region[END_REF], OSU12 [START_REF] Fok | Ocean Tides Modeling Using Satellite Altimetry[END_REF], DTU10 [START_REF] Cheng | Improvement in global ocean tide model in shallow water regions[END_REF], HAMTIDE [START_REF] Taguchi | Inferring deep ocean tidal energy dissipationfrom the global high-resolution data-assimilative HAMTIDE model[END_REF] and NAO99 [START_REF] Matsumoto | Ocean tide models developed by assimilating TOPEX/POSEIDON altimeter data into hydrodynamical model: a global model and a regional model around Japan[END_REF].

Finally, we calculate the corrected tidal parameters for the main eleven tidal constituents (Ssa, Mm, Mf, Q1, O1, P1, K1, N2, M2, S2, K2) by averaging the results of the nine ocean models to tackle the inaccuracies rising from the limited spatial resolution of the models which might be relevant especially at locations in coastal areas (e.g. [START_REF] Habel | A new tidal analysis of superconducting gravity observations in Western and Central Europe[END_REF]) (Fig. 6a,b).

It is noteworthy that ocean loading residual vectors can be used to get insight into calibration inaccuracies of gravimeters, both in amplitude and phase. Since the observed phase lags of the tidal parameters are routinely small (in the order of few degrees), inaccuracies in the calibration constants will map only on the real part (in-phase) of the residual vector. On the contrary, an inaccurate phase determination in the gravity observations, due for instance to a wrong filter delay or even a missing or inaccurate phase calibration, will only appear in the imaginary part (out-of-phase).

In addition to the main gravitational tidal waves, other tidal components are provided in the FES2014b model, including the diurnal S1 tide forced by air pressure. This allows testing the effect of ocean loading correction on the retrieval of solar tidal waves and related air pressure ones in the equatorial band (Fig. 11).

Except for S2 tide, where all ocean models exhibit large in-phase and out-of-phase components, all the other results mostly show a cluster around (0, 0). There is no significant systematic deviation in the in-phase component that would imply a calibration error or in the out-of-phase component related to a time delay error.

Free Core Nutation resonance in diurnal frequency band

Because of the existence of a slightly elliptical fluid core, the Earth possesses a normal mode called Free Core Nutation (FCN), which consists of a free wobble of the fluid Core around the Earth's rotation axis, with fluid pressure acting as a feedback mechanism. In a rotating terrestrial frame attached to the Earth's mantle, the FCN has a quasi-diurnal period but is retrograde with a 430-day period in an inertial frame. Under the forcing by tides at diurnal periods, we can observe a resonance effect in the Earth's gravimetric response. The FCN resonance effect has been widely studied in surface gravimetric observations [START_REF] Neuberg | Stacking gravity tide observations in Central Europe for the retrieval of the complex eigenfrequency of the nearly diurnal free wobble[END_REF][START_REF] Florsch | Bayesian estimation of the free core nutation parameters from the analysis of precise tidal gravity data[END_REF][START_REF] Ducarme | Determination of the free core nutation period from tidal gravity observations of the GGP superconducting gravimeter network[END_REF] but has been better determined through its resonance effect in VLBI nutation data [START_REF] Defraigne | Stacking gravity tide measurements and nutation observations in order to determine the complex eigenfrequency of the nearly diurnal free wobble[END_REF][START_REF] Mathews | Modeling of nutation and precession: new nutation series for nonrigid Earth and insights into the Earth's interior[END_REF][START_REF] Koot | Estimation of Earth interior parameters from a Bayesian inversion of very long baseline interferometry nutation time series[END_REF][START_REF] Rosat | Free core nutation resonance parameters from VLBI and superconducting gravimeter data[END_REF][START_REF] Rosat | Earth's core and inner core resonances from analysis of VLBI nutation and superconducting gravimeter data[END_REF]. An attempt has been done to retrieve FCN parameters even from very long-base hydrostatic tiltmeters [START_REF] Riccardi | Free core nutation parameters from hydrostatic Long-Base tiltmeter records in sainte Croix aux mines (France)[END_REF] and strainmeters (Amoruso et al., 2012). We refer to Rosat et al. (2009) for a summary of past FCN analyses.

U N C O R R E C T E D P R O O F
From the tidal analysis results, we perform a Bayesian inversion based on the Metropolis-Hastings algorithm with a Markov-chain Monte Carlo method (described in [START_REF] Rosat | Earth's core and inner core resonances from analysis of VLBI nutation and superconducting gravimeter data[END_REF] applied on the gravimetric complex δ factors corrected from the ocean tidal loading using a "mean" model (mean coming from the 9 ocean models previously quoted) and for various atmospheric corrections.

Since the ocean tides model do not provide amplitudes and phases for smaller diurnal waves, we have performed a spline interpolation of the tidal admittances of the main tides [START_REF] Munk | Tidal spectroscopy and prediction[END_REF]. In Fig. 7 one can see the diurnal gravimetric factors before and after ocean load reduction for the three atmospheric pressure reductions described below in the next section devoted to atmospheric loading.

It is well known from the tidal potential that the Ψ1 wave, the closest to the resonance, is very small and even smaller at the latitude of Djougou, close to the equator. The error bars are larger than the values. Consequently, inverting for the FCN parameters from tidal resonance at Djougou is very challenging. Indeed, it turns out that we cannot put any constraint on the period and damping of the FCN mode from Djougou data. In Annex B we have enclosed an example of the Bayesian inversion result applied on the δ factors using MERRA2 atmospheric correction. We obtain similar results using other sets of δ factors from various atmospheric corrections, with or without ocean tide loading reduction.

Atmospheric loading

As previously mentioned, the Djougou station is presently the only one of the IGETS network in operation in the equatorial band. It is hence of primary importance to study the air pressure effects on gravity in this region of the world. As can be seen in Fig. 8, the S1 and S2 waves of 1 and 2 cycle per solar day frequency respectively, have the largest amplitude in the equatorial band (e.g. [START_REF] Schindelegger | Surface pressure tide climatologies deduced from a quality-controlled network of barometric observations[END_REF] and we have an excellent opportunity to investigate their effects on gravity at Djougou station.

An example of the pressure changes in both time and frequency at Djougou is given by Fig. 9, where we also added the changes at the mid-latitude station Strasbourg.

In fact, S1 and S2 pressure waves are also strongly modulated in amplitude as shown by Fig. 10. The adjacent peaks around S1 (one cycle per solar day) and S2 (two cycles per solar day) are due to annual, semi-annual and ter-annual modulation. This modulation was already pointed out in another study [START_REF] Gegout | Influence of atmospheric pressure on the Free Core Nutation, precession and some forced nutational motions of the Earth[END_REF] and is known to alter some specific tidal waves like P1 and K1 (by annual modulation) and PSI1 and PHI1 (by semi-annual modulation) in the diurnal band and T2 and R2 (by annual modulation) and 2T2 and K2 (by semi-annual modulation) in the semi-diurnal band. The existence of the modulated S1 pressure field of large scale may even lead to perturbations in the Earth's luni-solar nutations by pressure torque effects as stated by [START_REF] Gegout | Influence of atmospheric pressure on the Free Core Nutation, precession and some forced nutational motions of the Earth[END_REF].

U N C O R R E C T E D P R O O F
The air pressure also exhibits long period features among which the annual component Sa (one cycle per year) is the largest and other terms at Ssa (2 cycle per year) and Sta (3 cycle per year) (see Fig. 11 ).

We have superposed onto the spectrum of the observed air pressure P obs the spectrum of the pressure P model used in the atmospheric model ERA5 (Copernicus Climate Change Service (C3S) (2017). Since the time span of the model pressure is much longer than the obser vation time span (2010-2018) the spectral definition is much better for all the waves.

The question of the atmospheric pressure effects on gravity has been widely investigated in the literature (see [START_REF] Hinderer | Superconducting gravimetry, in treatise on geophysics[END_REF] for a review). Usually one introduces the concept of barometric admittance (in nm s -2 /hPa) which can be either constant or time and frequency dependent [START_REF] Crossley | Effective barometric admittance and gravity residuals[END_REF][START_REF] Crossley | Using the atmosphere-gravity correlation to derive a time-dependent admittance[END_REF][START_REF] Crossley | Effective barometric admittance and gravity residuals[END_REF]. Observed gravity is then corrected for atmospheric effects using the computed barometric admittance. However the local pressure changes cannot account alone for the atmospheric loading as soon as the size of the coherent presure field exceeds a specific size [START_REF] Merriam | Atmospheric pressure and gravity[END_REF]. To overcome this difficulty one has to compute the atmospheric loading effect at each station from the worlwide pressure field using surface pressure values on a grid (e.g. [START_REF] Boy | Reduction of surface gravity data from global atmospheric pressure loading[END_REF] or, in the most sophisticated models, computing the 3D full effects where the changes of density with height are taken into account [START_REF] Boy | Precise evaluation of atmospheric loading effects on Earth's time-variable gravity field[END_REF][START_REF] Neumeyer | Gravity reduction with three-dimensional atmospheric pressure data for precise ground gravity measurements[END_REF][START_REF] Gitlein | Modeling of atmospheric gravity effects for high-precision observations[END_REF][START_REF] Klügel | Correcting gravimeters and tiltmeters for atmospheric mass attraction using operational weather models[END_REF].

In this study we do not further discuss the transfer function between gravity and air pressure as a function of frequency. This was previously done for Djougou station in Hinderer et al. (2014b) for frequencies between 0.01 cpd and 300 cpd using a 2.5 year time span and similar results can be infered from this 8 year analysis. In particular, we confirm the V shape (see Fig. 7 in Hinderer et al. (2014b) in the barometric admittance also seen elsewhere [START_REF] Zürn | On noise reduction in vertical seismic records below 2 mHz using local barometric pressure[END_REF][START_REF] Zürn | On the minimum of vertical seismic noise near 3 mHz[END_REF][START_REF] Zürn | Clear evidence for the sign-reversal of the pressure admittance to gravity near 3 mHz[END_REF].

We also added in Fig. 10 and Fig. 11 the spectra of the gravity changes (in nm s -2

) caused by the atmospheric load P load . At every spectral peak, there is an induced gravity load that will alter the tidal response. This gravity load is not a simple function of the local pressure (only the so-called local part is computed with a barometric admittance) but is more complicated because of the non-local part that involves the convolution of the pressure field worldwide with the atmospheric loading Green's function (see e.g. [START_REF] Boy | Reduction of surface gravity data from global atmospheric pressure loading[END_REF].

The atmospheric gravity loading is computed using ECMWF (European Centre for Medium Range Weather Forecasts) operational and reanalysis (ERA interim) pressure data, assuming either an inverted barometer response of the oceans or a dynamic response using TUGO-m [START_REF] Carrère | Modeling the barotropic response of the global ocean to atmospheric wind and pressure forcingcomparisons with observations[END_REF]. The use of the TUGO-m model has shown significant improvement in terms of reduction of the amplitude of the gravity residuals compared to the classical inverted barometer assumption [START_REF] Boy | High-frequency non-tidal ocean loading effects on surface gravity measurements[END_REF][START_REF] Boy | Modelling atmospheric and induced non-tidal oceanic loading contributions to surface gravity and tilt measurements[END_REF].

The gravity loading is composed of 3 terms:

• a "local" contribution (integration within 0.10°or 0.25°around the gravimeter) using nominal admittances of -2.2105 nm.s-2 / hPa (radius of 0.10°) and -3.0668 nm.s-2 / hPa (radius of 0.25°)

• a "non-local" contribution • the sum of the previous two, i.e. the complete loading model.

In the spectra shown by Fig. 10 and 11, the pressure loading in gravity P load for the period 2010-2018 was computed from the ERA5 model using a 1 h sampling rate (derived by linear interpolation from the original 3 h time resolution) together with a 0.10°local zone and inverted barometer ocean response.

The long-period part of the amplitude spectra of air pressure and gravity loading is shown on Fig. 11. The largest component is the annual term Sa followed by the semi-annual Ssa and ter-annual harmonics Sta.

Bearing in mind that, as shown by a number of authors (e.g. [START_REF] Riccardi | On the efficiency of barometric arrays to improve the corrections of atmospheric effects on gravity data[END_REF][START_REF] Hinderer | Superconducting gravimetry, in treatise on geophysics[END_REF], the single admittance concept is far from being a realistic account for the air pressure effect, we have tested two possible approaches, other than a single admittance coefficient, to correct the atmospheric effect on gravity: a) an a priori cor rection based on global load calculations (ERA5, MERRA2) available at (http://loading.u-strasbg.fr/GGP/); b) using a hybrid approach.

U N C O R R E C T E D P R O O F
In a nutshell, the hybrid corrections are computed by retaining the modelled non-local component and replacing the local one with the observed air pressure multiplied by the nominal admittance coefficient coherently with model resolution. The hybrid method enables us to account both for very local atmospheric effects, as probed by the surface pressure observations, and larger scale contributions to gravity. Some of the considered loading models also include atmospheric and induced oceanic loading and makes use of the ECMWF reanalysis (ERA interim) surface air pressure, assuming a barotropic ocean model forced by air pressure and winds (MOG2D, [START_REF] Carrère | Modeling the barotropic response of the global ocean to atmospheric wind and pressure forcingcomparisons with observations[END_REF].

Interpolating 3 h pressure data, 1 h resolution air pressure loading models are retrieved by splitting the contribution from the models into local and non-local components.

Performances of the different corrections are tested against the capability of an actual resolution of the tidal solar waves (Fig. 12). Notice that in Fig. 12 the gravity observations have been corrected for ocean tidal loading using the mean of the various ocean models available.

It is very clear that the classical admittance reduction based only on local pressure are clearly failing for Sa and S1. Global atmospheric models work better but the best results i.e. the smallest discrepancy between the reduced tidal amplitude factors and the solid Earth theoretical value [START_REF] Dehant | Tides for a convective earth[END_REF] are found using the hybrid models. A similar conclusion for S1 was obtained on other superconducting gravimeters of the international GGP network in a previous study (Boy et al., 2006).

Conclusion

Using an 8-year record (2010-2018) of the superconducting gravimeter OSG-060 at Djougou (Benin, West Africa) we investigated the solid Earth tides and ocean tidal loading. The tidal analysis was performed using ET34-ANA v7.1 software and led to the gravimetric amplitude and phase factors for all separable waves in various frequency bands ranging from the long period band to the quart-diurnal one.

Ocean tidal loading was computed from nine available global ocean tide models and allowed us to calculate the real and imaginary parts of the residual vector for the main eleven tidal constituents (Ssa, Mm, Mf, Q1, O1, P1, K1, N2, M2, S2, K2).

Because of the equatorial location of the Djougou station, atmospheric loading is dominated by the thermal waves S1 and S2. We have shown the annual and semi-annual amplitude modulations in the S1 and S2 pressure signals, as well as in the associated gravity loading using the global atmospheric model ERA5. In addition to S1 and S2, there are additional components in the long period band where the annual term SA dominates the semi-annual Ssa and ter-annual Sta terms.

We have shown how the amplitude gravimetric factors for the waves Sa, Ssa, S1 and S2 vary according to different air pressure cor rections. In particular, there is a large discrepancy between the classical single admittance pressure reduction and the hybrid model using global atmospheric models like ERA5 and MERRA2 everywhere except in the local zone where the model pressure is replaced by the observed pressure.

U N C O R R E C T E D P R O O F

Uncited references

Baker and Bos (2003), Boy et al. (2003), Boy and Hinderer (2006), Copernicus Climate Change Service (C3S) (2017), Hinderer et al. (2002), Ray and Egbert (2004), [START_REF] Ray | A Global Ocean Tide Model From TOPEX/POSEIDON Altimetry: GOT99[END_REF]Ponte (2003), Rodell et al. (2004), [START_REF] Warburton | The influence of barometric pressure fluctuations on gravity[END_REF] and Wenzel (1996) CRediT authorship contribution statement (Dehant andZschau, 1989. Dehant et al., 1999).

Annex A

Adjusted parameters (δ and k) of a tidal analysis carried out with ET34-ANA-v71 software [START_REF] Schüller | Theoretical Basis for Earth Tide Analysis and Prediction[END_REF] on the data set spanning 22 July 2010 -31 March 2018 (Recorded days in total: 2809). Instrumental drift, hydrological and atmospheric effects are reduced before applying the analysis. Hydrological effects are modelled by MERRA2, while the atmospheric effects are accounted by following the hybrid MERRA2 approach (see the main text for details).

Annex B. Bayesian inversion results for the FCN resonance parameters

We employ the same inversion algorithm as in [START_REF] Rosat | Earth's core and inner core resonances from analysis of VLBI nutation and superconducting gravimeter data[END_REF] with the resonance equation defined as where N 2 is the resonance strength, δ 0 is the tidal response far from the FCN resonance taken here as the mean value of the observed gravimetric factors for Q1 and OO1. s 2 is the complex frequency of the FCN and the quality factor is obtained from the real and imaginary parts of the frequency by . σ is the frequency of the forcing tidal constituent.

We assume uniform prior distributions for the parameters that we inverse. A priori information, particularly in ill-posed inverse problem like the current one, is of critical importance because it is conditioning the a posteriori solution. In other words, a completely unresolved parameter has a posteriori marginal density function that follows the a priori one. So the more the a posteriori density function differs from the a priori one, the more the parameter has been resolved. We can see in Fig. B1 that the strength of the resonance is well constrained since the a posteriori distributions are Gaussian. However, the complex frequency of the FCN spans the full range of the a priori distribution without converging to a preferred value: the complex frequency is not resolved from the data. The dot distribution between and shows a tilted shape that is characteristic of a correlation between both parameters (e.g. [START_REF] Florsch | Bayesian estimation of the free core nutation parameters from the analysis of precise tidal gravity data[END_REF].

U N C O R R E C T E D P R O O F

Fig. 1 .

 1 Fig. 1. A map of the superconducting gravimeter stations contributing to IGETS (International Geodynamics and Earth Tides Service, http://igets.u-strasbg.fr ). The operational stations in 2018 are in red and former stations now stopped are in blue.

Fig. 2 .

 2 Fig. 2. A picture of the three buildings belonging to the Djougou gravity station in Nalohou.

Fig. 3 .

 3 Fig. 3. Gravity (in nm s -2) and barometric pressure (in hPa) recorded at the Djougou station from 2010 to 2018.

Fig. 4 .

 4 Fig. 4. Residual gravity signal (in nm s -2

Fig. 5 .

 5 Fig. 5. Tidal gravimetric factors retrieved from tidal analysis; a) δ amplitude factors, b) phase (°).

Fig. 6 .

 6 Fig. 6. Residual X vectors after ocean tide loading correction applied to the adjusted delta factors: a) amplitude of the residual vector (% of adjusted amplitude). Real (in-phase) and Imaginary (out-of-phase) part of the residual vector for: b) diurnal, long period waves and c) semi-diurnal waves.

Fig. 7 .

 7 Fig. 7. Diurnal gravimetric tidal factors obtained with ET34-ANA v7.1 software (Schüller, 2018) tidal analyses and after atmospheric pressure reduction using either a nominal admittance (black asterisk), or MERRA2 loading model (magenta full circle) or ERA5 (C3S, 2017) loading model (blue diamond). (a) Real (upper plot) and imaginary (lower plot) parts before ocean loading reduction; (b) real (upper plot) and imaginary (lower plot) parts after ocean loading reduction.

Fig. 8 .

 8 Fig. 8. Amplitude (in Pa) and phase (in degree) of the S1 and S2 atmospheric pressure deduced from ECMWF latest reanalysis (ERA5) hourly surface pressure and for the 2000-2017 period.

Fig. 9 .

 9 Fig. 9. Time and frequency changes of the atmospheric pressure at Djougou and Strasbourg (from Hinderer et al., 2014a).

Fig. 10 .

 10 Fig. 10. Diurnal and semi-diurnal amplitude spectra of air pressure and induced gravity loading in Djougou. P load is expressed in nms -2 , P obs and P model are in hPa. The spectra are normalized and use Hanning window filtering.

  Jacques Hinderer: Conceptualization, Methodology, Investigation, Supervision, Project administration. U. Riccardi: Methodology, Formal analysis, Investigation, Visualization. S. Rosat: Methodology, Formal analysis. J.-P. Boy: Methodology, Data curation. B. Hector: Investigation. M. Calvo: Data curation. F. Little: Resources. J.-D. Bernard: Resources.

Fig. 11 .

 11 Fig. 11. Long-period amplitude spectra of air pressure and induced gravity loading in Djougou. P load is expressed in nms -2 , P obs and P model are in hPa. The spectra are normalized and use Hanning window filtering.

Fig. 12 .

 12 Fig. 12. Amplitude gravimetric factors (Delta) according to different air pressure corrections. The red square uses the classical single admittance coefficient. Blue and green circles use the global atmospheric models ERA5 and MERRA2 respectively. Blue and green triangles replace in ERA5 and MERRA2 the model pressure in the local zone by the observed pressure. The black cross is the theoretical value predicted for a slightly inelastic Earth's model(Dehant and Zschau, 1989. Dehant et al., 1999).

Fig. B1 .

 B1 Fig. B1.A posteriori distributions for the inversion of the gravimetric tidal factors corrected for ocean loading and from MERRA2 atmospheric loading effects. On the diagonal, we have plotted the a posteriori distributions for each parameter. We have plotted the joint probability density functions for the four parameters as bi-dimensional distributions sampled by dots. The boxes represent the 95 per cent probability intervals estimated from the Markov-chain Monte-Carlo a posteriori distribution. and are respectively the real and imaginary parts of the resonance strength. and are respectively the real and imaginary parts of the complex FCN frequency. is given in deg/h.

Acknowledgments

We acknowledge the financial support of INSU-CNRS for operating SG 060 in Djougou as part of the French Observatory Service (SNO Gravimétrie).


Songtao Hu

Hongwei Xu

Bingshuai Zhou

Shihan Xu

Bo Shen

Biao Dong
email: dongb@jlu.edu.cn

Ze Yin

Liheng Sai

Sun

Jiekai Lv

Jiahe Wang

Wen Xu

Xue Bai

Lin Xu

Svetlana Mintova

Hongwei Song
email: songhw@jlu.edu.cn

Double Stopband Bilayer Photonic Crystal Based Upconversion Fluorescence PSA Sensor

Keywords: Upconversion fluorescence enhancement, double stop band, photonic crystal, tumor marker detection

Precise detection on tumor markers is significant for the early diagnosis on cancer. Upconversion fluorescence probes are ideal for tumor marker sensing, but still subject to bottleneck problems of low emission efficiency/strength. In this work, a novel bilayer of poly(methyl methacrylate) opal photonic crystal (PMMA OPC) with double photonic stop bands was fabricated to match the excitation field and emission field of the upconversion nanoparticles (UCNPs) at the same time, and greatly enhance their upconversion fluorescence intensity. Herein, NaYF4:Yb 3+ ,Er 3+ UCNPs and NaYF4:Yb 3+ ,Er 3+ @NaYF4:Yb 3+ ,Nd 3+ UCNPs with a core-shell structure were employed as a core, which could be excited by 980 nm and 808 nm light, respectively.

With the optimized geometry structure, the upconversion emission intensity was enhanced over 150 folds under the excitation of both 808 nm and 980 nm laser.

Through the NaYF4/OPC biochip and florescence resonant energy transfer (FRET) sensing strategy, the lowest detection limit of 0.01 ng/mL with good linear relationship was obtained ranging from 0.1 ng/mL to 10 ng/mL. The power density of the pumping light was as low as 1.7 W/cm 2 . This enhanced upconversion tumor marker biochip sensor provides a promising and powerful tool for facile early diagnosis on cancer markers.

Introduction

Cancer is one of the main diseases that endanger human life and health.

Conventional detection methods, such as magnetic resonance imaging, and computed tomography, are mainly applied in clinical diagnosis with high sensitivity but restricted by complex equipment, high cost and time-consuming. [START_REF] Wu | Cancer biomarker detection: recent achievements and challenges[END_REF][START_REF] Wang | Recent Advances in Glucose-Oxidase-Based Nanocomposites for Tumor Therapy[END_REF][START_REF] Hou | Hydrogenated Titanium Oxide Decorated Upconversion Nanoparticles: Facile Laser Modified Synthesis and 808 nm Near-Infrared Light Triggered Phototherapy[END_REF][START_REF] Liu | 808-nm-Light-Excited Lanthanide-Doped Nanoparticles: Rational Design, Luminescence Control and Theranostic Applications[END_REF][START_REF] Wang | New advances on the marrying of UCNPs and photothermal agents for imaging-guided diagnosis and the therapy of tumors[END_REF][START_REF] Dai | 808 nm near-infrared light controlled dual-drug release and cancer therapy in vivo by upconversion mesoporous silica nanostructures[END_REF][START_REF] Zhang | Tailored Synthesis of Octopus-type Janus Nanoparticles for Synergistic Actively-Targeted and Chemo-Photothermal Therapy[END_REF] It's important to design convenient and efficient methods for early detection of tumors, especially for home-based self-screening. Note that the occurrence of cancer is closely associated with the abnormal expression of tumor markers, and the precise identification of potential cancer biomarkers in patient samples is a key factor in the early cancer diagnosis and an estimation of the cancer development stage. [START_REF] Bray | Global cancer statistics 2018: GLOBOCAN estimates of incidence and mortality worldwide for 36 cancers in 185 countries[END_REF][START_REF] Wu | Biomedical and clinical applications of immunoassays and immunosensors for tumor markers[END_REF][START_REF] Perfezou | Cancer detection using nanoparticle-based sensors[END_REF][START_REF] Zheng | Multiplexed electrical detection of cancer markers with nanowire sensor arrays[END_REF][START_REF] Zhang | Electrochemical prostate specific antigen aptasensor based on hemin functionalized graphene-conjugated palladium nanocomposites[END_REF] Recent years, different kinds of innovative tumor marker detection methods have been developed. Among them, biochip-based device for biomarker detection is an important assay not only in clinical diagnostic fields, but also in home-based self-screening, due to the portability, flexibility, and short processing time on samples.

In addition, new technological progress in the biomarker analysis occurs with recent innovations on optical detection methods with fluorescence readout. [START_REF] Das | Cancer biomarker determination by resonance energy transfer using functional fluorescent nanoprobes[END_REF][START_REF] Shang | How to produce white light in a single-phase host?[END_REF] Unlike traditional luminescent materials, such as quantum dots and dyes, [START_REF] Chan | Luminescent quantum dots for multiplexed biological detection and imaging[END_REF][START_REF] Medintz | Quantum dot-based resonance energy transfer and its growing application in biology[END_REF][START_REF] Smith | Semiconductor Nanocrystals: Structure, Properties, and Band Gap Engineering[END_REF][START_REF] Noor | Paper-Based Solid-Phase Multiplexed Nucleic Acid Hybridization Assay with Tunable Dynamic Range Using Immobilized Quantum Dots As Donors in Fluorescence Resonance Energy Transfer[END_REF] rare earth doped upconversion nanoparticles (UCNPs) are able to transform NIR light into visible light, [START_REF] Huang | Enhancing solar cell efficiency: the search for luminescent materials as spectral converters[END_REF][START_REF] De La Mora | Materials for downconversion in solar cells: Perspectives and challenges[END_REF][START_REF] Goldschmidt | Upconversion for Photovoltaics -A Review of Materials[END_REF][START_REF] Zhang | Observation of efficient population of the red-emitting state from the green state by non-multiphonon relaxation in the Er3+-Yb3+ system[END_REF][START_REF] Qin | Multi-ion cooperative processes in Yb3+ clusters[END_REF][START_REF] Hou | 808 nm Light-triggered and hyaluronic acid-targeted dual-photosensitizers nanoplatform by fully utilizing Nd3(+)-sensitized upconversion emission with enhanced anti-tumor efficacy[END_REF][START_REF] Yang | Current advances in lanthanide ion (Ln(3+))-based upconversion nanomaterials for drug delivery[END_REF][START_REF] Hou | UV-Emitting Upconversion-Based TiO2 Photosensitizing Nanoplatform: Near-Infrared Light Mediated in Vivo Photodynamic Therapy via Mitochondria-Involved Apoptosis Pathway[END_REF] with less damage on biospecimen, meanwhile, avoids background fluorescence during detection in comparison with conventional fluorescence probes. [START_REF] Wang | Microscopic inspection and tracking of single upconversion nanoparticles in living cells[END_REF][START_REF] Liu | Poly(Acrylic Acid) Modification of Nd3+-Sensitized Upconversion Nanophosphors for Highly Efficient UCL Imaging and pH-Responsive Drug Delivery[END_REF][START_REF] Li | Multifunctional Upconversion Mesoporous Silica Nanostructures for Dual Modal Imaging and In Vivo Drug Delivery[END_REF][START_REF] Yang | Hollow structured upconversion luminescent NaYF4:Yb3+, Er3+ nanospheres for cell imaging and targeted anti-cancer drug delivery[END_REF][START_REF] Hou | Electrospinning Preparation and Drug-Delivery Properties of an Up-conversion Luminescent Porous NaYF4:Yb3+, Er3+@Silica Fiber Nanocomposite[END_REF] Furthermore, UCNPs can be applied as a suitable energy donor in fluorescence resonant energy transfer (FRET) for the detection on tumor markers, and lots of biochip-based diagnostics of cancer for point-of-care (POC) applications were developed. [START_REF] Das | Cancer biomarker determination by resonance energy transfer using functional fluorescent nanoprobes[END_REF][START_REF] Shang | How to produce white light in a single-phase host?[END_REF] The goal of the POC diagnosis is to detect biomarkers with the requisite sensitivity and accuracy to meet the needs of clinical diagnosis and home-based self-screening. However, low fluorescence quantum yield of UCNPs probe limits their clinical applications on biochip devices for tumor marker analysis. Nowadays, enhancing the intensity of upconversion fluorescence is a challenge to expand their biological applications. To regulate upconversion florescence, core-shell structure and local field effect became the main means to enhance the intensity of upconversion fluorescence. Normally, the fluorescence intensity can be improved [START_REF] Deng | Temporal full-colour tuning through non-steady-state upconversion[END_REF][START_REF] Wang | Tuning upconversion through energy migration in core-shell nanoparticles[END_REF][START_REF] Wang | Enhancing multiphoton upconversion through energy clustering at sublattice level[END_REF][START_REF] Li | Rare earth fluoride nano-/microcrystals: synthesis, surface modification and application[END_REF][START_REF] Li | Controlled Synthesis of Ln(3+) (Ln = Tb, Eu, Dy) and V5+ Ion-Doped YPO4 Nano-/Microstructures with Tunable Luminescent Colors[END_REF] by preparing passivation shell, which, however, may cause the increasing size of UCNPs.

In biological detection, small size NPs with large specific surface area are preferred for the enough active sensing site, and meanwhile, low power density of the excitation light is applied on specimens, [START_REF] Chen | Size-dependent downconversion near-infrared emission of NaYF4:Yb3+,Er3+ nanoparticles[END_REF] both of which limit the emission intensity of UCNPs. [START_REF] Li | Ultra-small fluorescent inorganic nanoparticles for bioimaging[END_REF][START_REF] Liu | Magnetic/Upconversion Fluorescent NaGdF4:Yb,Er Nanoparticle-Based Dual-Modal Molecular Probes for Imaging Tiny Tumors in Vivo[END_REF] To enhance the emission intensity, various methods based on local field effect are developed, including photonic crystal effect [START_REF] Liu | Highly plasmon-enhanced upconversion emissions from Au@beta-NaYF4:Yb,Tm hybrid nanostructures[END_REF][START_REF] He | Plasmonic enhancement and polarization dependence of nonlinear upconversion emissions from single gold nanorod@SiO2@CaF2:Yb3+,Er3+ hybrid core-shell-satellite nanostructures[END_REF][START_REF] Sun | Plasmon-Enhanced Energy Transfer for Improved Upconversion of Infrared Radiation in Doped-Lanthanide Nanocrystals[END_REF] and surface plasma effect [START_REF] Noda | Spontaneous-emission control by photonic crystals and nanocavities[END_REF][START_REF] Yin | Remarkable enhancement of upconversion fluorescence and confocal imaging of PMMA Opal/NaYF4:Yb3+, Tm3+/Er3+ nanocrystals[END_REF][START_REF] Ding | Spectral and Directional Reshaping of Fluorescence in Large Area Self-Assembled Plasmonic-Photonic Crystals[END_REF]. They have been proved as effective ways to enhance fluorescence intensity, especially for small size NPs and with a low excitation power. For upconversion based biochips, local field effect with the advantage on the fluorescence enhancement, might greatly improve the detection performance and satisfy the clinical requirements for patient sample assays.

Since the discovery of the photonic crystal effect, it has received extensive attentions on optical regulation, especially for the intensity enhancement excited by the low-power light. Opal photonic crystal (OPC) with photonic stop bands can prevent or scatter the light that falls into the band gaps. [START_REF] Zhou | 320-fold luminescence enhancement of Ru(dpp)(3) Cl-2 dispersed on PMMA opal photonic crystals and highly improved oxygen sensing performance[END_REF] Once photonic stop band matches with the excitation light or emission light wavelength, upconversion emission intensity of UCNPs could increase over dozens of folds, [START_REF] Zhou | Modulation of upconversion white light emission in PMMA/NaYF4:Yb3+, Er3+, Tm3+ composite photonic crystals[END_REF] with putting UCNPs on the surface of OPCs. In our previous work, through combining PMMA OPC effect and surface plasma effect, the enhancement factor of upconversion emission of NaYF4:Yb 3+ ,Er 3+ NPs reached 1000-fold [START_REF] Yin | Local Field Modulation Induced Three-Order Upconversion Enhancement: Combining Surface Plasmon Effect and Photonic Crystal Effect[END_REF]. The photonic crystal stop band coupling with the upconversion excitation field has been proved to greatly increase the upconversion fluorescence intensity. Until now, synchronous coupling the upconversion excitation and emission fields has not been reported yet.

In this work, in order to promote the potential clinical utility of upconversion based biochip devices, a novel bilayer PMMA OPC with double photonic stop band was designed. In this biochip, based on the previous research results, bilayer photonic crystal structure was used to regulate the stop band to match the excitation field and emission field of the upconversion fluorescence, respectively. Because NaYF4:Yb 3+ ,Er 3+ and core-shell structure NaYF4:Yb 3+ ,Er 3+ @NaYF4:Yb 3+ ,Nd 3+ UCNPs were chose for the energy donor, which can be excited by 980 nm and 808 nm light, respectively. The double stop bands were regulated to 980 nm and 808 nm (excitation) and 545 nm (emission) band of UCNPs respectively (Fig. 1). Through the NaYF4/OPC hybrid structure, the upconversion emission intensity was enhanced over 150 folds under excitation of both 808 nm and 980 nm, which was superior to the conventional monolayer OPC. The geometry of the dual photonic crystal was also investigated. Utilizing the optimized structure, an upconversion fluorescence sensor was fabricated to detect a tumor marker, prostate specific antigen (PSA). The detection limit of 0.01 ng/mL with good linear relationship in the range of 0.1~10 ng/mL was obtained under the excitation power density of 1.7 W/cm 2 . Since the upconversion fluorescence is greatly enhanced, in the same condition, the excitation power density can be lowered with minimal damage on the sample. The remarkable performance of our PSA-detection biochip could lead to further development in clinical diagnostic applications, as well as in home-based self-screening.

Experimental

Preparation of double stop band OPC: PMMA OPC consisted of PMMA microsphere was prepared through a MMA polymerization process. Clean glass substrate was put into PMMA colloidal suspension (5% solid content) vertically and placed in 35℃ for 24h, the PMMA microsphere would be assembled orderly on glass substrate by surface tension along with the evaporation process. After this, OPC was put into 120℃ for 1h to enhance its physical strength. The position of PSB could be controlled by changing the size of PMMA microsphere. In this work, three kinds of OPC with PSB at 545 nm, 808 nm, and 980 nm were prepared. Next, we fixed OPC in beaker vertically and injected deionized water into beaker slowly by micro syringe pump with rate of 10 mL/h, OPC film on glass substrate would be peeled by surface tension. After OPC was peeled, we used another OPC to fish it, and strengthened it in 60℃ for 2h.

Synthesis of NaYF4:Yb 3+ , Er 3+ core nanocrystals: 0.78mmol YCl3, 0.20mmol YbCl3 and 0.02mmol ErCl3 were added into a 100mL flask containing 6 mL oleic acid and 15 ml 1-octadecene. The mixture was stirred at 160°C for 60 min to form the lanthanide-oleate complexes and then cooled down to 40°C. Next, dropwise adding 6 mL of methanol solution containing 4mmol NH4F and 2mmol NaOH into flask and the resultant solution was gently stirred for 30 min. After fully stirred, the solution was heated to 120℃ to remove methanol. Finally, the solution was further heated to 300℃ for 90min to obtain NaYF4:Yb 3+ , Er 3+ nanoparticles. The whole preparation took place with the nitrogen protection. Then the solution was cooled down to room temperature. The resulting NPs were collected by centrifugation in ethanol at 9,500 rpm for 15min, washed with absolute ethanol-cyclohexane (1: 3 v/v) two times and dispersed in cyclohexane for the following experiments.

Synthesis of NaYF4:Yb 3+ ,Er 3+ @NaYF4:Yb 3+ ,Nd 3+ core-shell nanocrystals: 0.70mmol YCl3, 0.15mmol YbCl3 and 0.15mmol NdCl3 were added into a 100mL flask containing 6 mL oleic acid and 15 ml 1-octadecene. The mixture was stirred at 160°C for 60 min to form the lanthanide-oleate complexes and then cooled down to 40°C. Next, 6 mL cyclohexane solution was added to coat 1mmol NaYF4:Yb 3+ , Er 3+ NPs. After fully stirred for 30min, the solution was heated to 90℃ to remove methanol cyclohexane and then cooled down to 40°C. Next steps are the same with the last part.

Preparation of gold nanoparticles: Gold NPs were prepared through sodium citrate reduction method. Firstly, 50mL HAuCl4 solution (1mM) was added into flask, the solution was stirred and heated in oil bath to boiling, then rapidly added sodium citrate solution (39mM). The whole progress required condensation reflux. After a few minutes, the solution turned to wine red. Being heated 15min continually, and then the solution was cooled down to room temperature. Gold NPs prepared through sodium citrate reduction method could be modified with antibody through electrostatic adsorption. Take 1mL gold NPs solution, collected by centrifugation at 12,000 rpm for 15min and re-dispersed in 1mL deionized water. Then add 60µL 0.1 mg/mL detection anti-PSA. After shaking for 1h and storing at 4℃ for 10h, detection anti-PSA modified gold NPs were collected by centrifugation at 12,000 rpm for 15min again.

Fabrication of PDA/NaYF4/OPC hybrid film: Glass and OPC films were vertically dropped into NaYF4 cyclohexane solution (0.1 mg/mL) and placed at 28℃ for 6h. With the volatilization of cyclohexane, the NaYF4 UCNPs will self-assemble onto the surface of glass and OPC films. Vertically putting hybrid films into dopamine TRIS solution (0.6 mg/mL, pH=8.0) for 1h and let dopamine self-polymerization at the surface of hybrid films for binding antibody.

Detection Section: PSA、capture antigen and detection antigen were purchased from Shanghai Linc-Bio science company(Basic information in Supplementary Material). The capture anti-PSA (0.1 mg/mL) was modified onto the surface of hybrid film. Next, the samples with different concentration of PSA were added onto the surface of hybrid film sensor, after incubation for 10 minutes, detection area was washed adequately by PBS buffer, then BSA blocking buffer and gold NPs modified with detection anti-PSA were orderly added and modified onto the surface of hybrid film sensor. It also needed 10 minutes for incubation in each step. Finally, detection area was washed by PBS buffer again. In next step, the emission spectra of detection area were recorded with fluorescence spectrometer equipped with 980 and 808 nm excitation lasers. For the tumor marker detection with confocal microscope, we just chose one detection area and added excessive capture anti-PSA, and then orderly added PSA sample and detection anti-PSA modified GNPs for multi times. The amount of capture anti-PSA was calculated to be enough to meet the requirement of six experiments. 0, 0.01, 0.1, 2, 5, 12.5 ng/mL PSA was added to the same detection area and the GNPs with same amount was added after each PSA sample addition. The real time tumor marker detection images in the sensing area and the corresponding spectra were recorded and scanned with confocal microscope.

Results and discussions

PSA is an important tumor marker of prostatic cancer, and the value of healthy person is 4 ng/mL. Above this value, the risk of tumor increases, and accurate detection of this tumor marker is important for early screening of prostatic cancer.

Figure 1 shows the design of bilayer upconvesion sensor and the principle of PSA detection. Through antibody-antigen-antibody combination, UCNP fluorescence donor can be linked with gold nanoparticles (NPs) receptor, and then the concentration of antigen can be quantified through measuring the decreased emission intensity due to the fluorescence quenching. After modifying the UCNPs on the surface of the photonic crystal, poly-dopamine (PDA) was further modified on the surface of UCNPs film for connecting with capture anti-PSA. Next, gold NPs with absorption peak at 560 nm was prepared, which matched with green emission peak of Er 3+ , and the anti-PSA was further modified on gold NPs by electrostatic adsorption for detection. [START_REF] Chen | Aptamer-based sensing for thrombin in red region via fluorescence resonant energy transfer between NaYF4:Yb,Er upconversion nanoparticles and gold nanorods[END_REF][START_REF] Long | Upconversion nanoparticle-based fluorescence resonance energy transfer assay for organophosphorus pesticides[END_REF][START_REF] Peng | A new biosensor for glucose determination in serum based on up-converting fluorescence resonance energy transfer[END_REF] In this system, we detected the concentration of PSA in PBS buffer solution under both 980 nm and 808 nm excitation. In the process, dropping capture anti-PSA, sample, BSA blocking buffer, and gold nanoparticles modified with detection anti-PSA onto fluorescence film in order, then testing the emission spectra of the detection area. BSA blocking buffer plays the function of anti-fouling to prevent the nonspecific adsorption of detection anti-PSA. Both capture anti-PSA and detection anti-PSA can target the PSA to form a sandwich structure that shortens the distance between the UCNPs and the gold NPs. Since the green emission from UCNPs and the plasma absorption of gold NPs overlap, efficient energy transfer can happen. The emission intensity of 545 nm light would reduce as the concentration of PSA increases. Fig. 2a-d shows the SEM images and transmittance spectra of 980/545 nm and 808/545 nm double stop band OPC, respectively. The bilayer structure of OPC is composed of PMMA spheres with two different sizes. From the SEM images, it can be observed that PMMA spheres are uniform and regular in arrangement, and both of the layers maintain good integrity. In Fig. 2a andb, the photonic crystals with band gaps around 980 and 808 are both in the upper layer, and the photonic crystals with band gaps around 545 are at down layer. It should be mentioned that, through the photonic crystal grafting method mentioned in experiment section, the photonic crystals of different sizes can be geometrically arranged separately, and this method is also applicable for flexible substrate, such as polyethylene glycol terephthalate (PET) substrate. [START_REF] Yin | Local Field Modulation Induced Three-Order Upconversion Enhancement: Combining Surface Plasmon Effect and Photonic Crystal Effect[END_REF] The bilayer photonic crystal films can match both the excitation field and the emission field together, which is important for studying the interaction between the excitation field and the emission field with the photonic band gap, and exploring the optimal fluorescence enhancement mode. From transmittance spectra, two photonic stop bands matching the excitation light and emission light, can be observed and the position of photonic stop band could be regulated by adjusting the size of PMMA spheres. The black and red lines correspond to the transmittance spectra of a single-layer photonic crystal, and the stop band position corresponds to the size of the PMMA. When the two photonic crystals are combined, transmission spectra (blue line) with double stop bands are obtained, which further suggests the successful preparation of double stop band bilayer photonic crystal structure. It is worth mentioning that, in the 980/545 nm bilayer photonic crystal structure, although the stop band of 545 nm is relatively shallow, it still provides contribution to the fluorescence enhancement.

From the TEM images of UCNPs (Fig. 2e,f), NaYF4:Yb 3+ ,Er 3+ UCNPs are ~23 nm, and the NaYF4:Yb 3+ ,Er 3+ @NaYF4:Yb 3+ ,Nd 3+ UCNPs are ~34 nm, both of which have good morphology of hexagonal, uniform sizes and good dispersion. The size of UCNPs can be tuned by changing the reaction temperature from 280℃ to 320℃ and the size of UCNPs increases with the increasing reaction temperature. The size of NaYF4:Yb 3+ ,Er 3+ @NaYF4:Yb 3+ ,Nd 3+ UCNPs increased, due to the modification of the shell, and the thickness of the shell was about 5 nm. Both UCNPs can emit strong green light under the excitation of 808 and 980 nm lights. The 980 nm excitation can generate upconversion emission of Er 3+ by the two-step sensitization of Yb 3+ ions.

The emission process under 808 nm excitation is more complicated, in which the Nd ions in the shell absorbs the 808 nm photon and then transfers energy to nearby Yb 3+ .

Through the core-shell structure, this energy can be effectively transferred to the Yb 3+ ions in the core and this migrated energy is finally transferred to the Er ions by two-step energy transfer, as shown in the schematic diagram. (Fig. 3)

The SEM image of the UCNPs/OPC hybrid films (Fig. 2g) shows that uniform distribution of UCNPs in the crevices between PMMA spheres. When the position of stop band matches with excitation wavelength, the excitation field can be amplified, and even with low-power excitation, upconversion fluorescence will be enhanced.

Especially when UCNPs are located in the interstices between PMMA spheres, the luminescent intensity of UCNPs in those interstices could be further enhanced. The PMMA photonic crystal prepared by the self-assembly method is very sensitive to water, and water can damage the photonic crystal structure. In this process, the surface of the photonic crystal is modified with a thin hydrophobic layer, which can protect the photonic crystal structure when detecting aqueous solutions. In order to verify the role of the hydrophobic protective layer, we tested the transmittance spectra of UCNPs/bilayer OPC hybrid film before and after placed in water for 4 hours.

Benefit from hydrophobic oleic acid ligands on the surface of UCNPs (Fig. S1), UCNPs/bilayer OPC hybrid film shows good structural integrity after placed in water and the transmittance spectra of bilayer OPC base keeps intact, demonstrating the well water stability of UCNPs/bilayer OPC hybrid film. After modified with poly-dopamine, SEM image and Fourier Transform Infrared Spectroscopy (FTIR) spectra of hybrid film was tested (Fig. 2k,l). Contrast with Fig. 2g, a dense film in SEM image could be observed. In FTIR spectra, the new absorption peak between 3100 nm and 3500 nm is assigned to the N-H bond from poly-dopamine, which can be further used to connect with capture anti-PSA.

When studying the photonic crystal effect on the upconversion fluorescence enhancement, it is necessary to determine that the amount of UCNPs on the photonic crystal and the glass substrate are equal, so it is meaningful to compare the upconversion fluorescence enhancement. In the experimental process, same UCNPs solution were modified on the surface of photonic crystal and glass substrate at the same time, to ensure the comparability of their optical properties. In addition, we tested transmittance spectroscopy of glass substrate, UCNPs/glass, OPC film, and UCNPs/OPC hybrid film as shown in Fig. 2h. In the calculations of enhancement factor, it is necessary to avoid the influence of PSB, so the OPC with PSB of 780 nm is chosen and the transmittance at 980 nm is tested. Through Beer-Lambert law (Ei=log(1/Ti),i=1,2), the values of extinction were calculated (E1=1.79 and E2=1.97). This result indicates that the amount of UCNPs on glass substrate and OPC film are quite close. Thus the influence of the amount of UCNPs on different substrates can be neglected on calculation of the upconversion enhancement factors.

As the energy acceptor, gold NPs in Fig. 2i show uniform size and good dispersion. The absorption peak locates at 560 nm, which overlaps with the green emission of Er 3+ (Fig. S2a). To confirm the appropriate concentration of gold NPs, the concentration of prepared gold NPs was adjusted to be 0.002, 0.02, 0.2, 0.6, 1.0mg/mL, then 4uL PBS and five kinds of adjusted gold NPs were respectively added onto fluorescence film and the emission spectrum of every detection area was tested. In our detection system, when the concentration of gold NPs progress was between 0.02mg/mL to 0.2mg/mL, most of emission light was quenched and the FRET progress reached saturation point (Fig. S2b,c). So gold NPs with concentration of 0.2mg/mL was chose to process subsequent experiment. To demonstrate that the detection anti-PSA was connected with gold NPs, six controlled trials were conducted.

Firstly, 0, 40µl, 60µL, 80µL, 100µL, and 120µL 0.1 mg/mL detection anti-PSA were added into 1mL prepared gold NPs solution, respectively. After uniformly oscillating for 1h, gold NPs were centrifuged and re-dispersed in 1mL deionized water. Finally adding 100µL 1 mg/mL NaCl solution in each sample and test their absorption spectra (Fig. 2j). After mixed with NaCl solution, the absorption spectra of pure gold NPs solution were broadened obviously due to the agglomeration of gold nanoparticles.

More antibodies were connected with gold NPs as their concentration increased, which further weakened the agglomeration of gold NPs, so that the absorption spectra broaden disappeared gradually. This absorption trend indicates that the antibody was successfully modified on the surface of gold NPs. In our previous work, [START_REF] Yin | Remarkable enhancement of upconversion fluorescence and confocal imaging of PMMA Opal/NaYF4:Yb3+, Tm3+/Er3+ nanocrystals[END_REF][START_REF] Yin | Local Field Modulation Induced Three-Order Upconversion Enhancement: Combining Surface Plasmon Effect and Photonic Crystal Effect[END_REF][START_REF] Xu | A novel strategy for improving upconversion luminescence of NaYF4:Yb, Er nanocrystals by coupling with hybrids of silver plasmon nanostructures and poly(methyl methacrylate) photonic crystals[END_REF] remarkable enhancement on the intensity of upconversion fluorescence was realized in the coupling of the photonic crystal stop band with the upconversion excitation field. Upconversion fluorescence is a multiphoton process, therefore the fluorescence efficiency is relatively low. In biological detection, it is important to increase the fluorescence intensity. In this work, we use the local field effect of PMMA OPC to increase the upconversion fluorescence intensity. The band gap of the photonic crystal structure can be adjusted by the size of the PMMA sphere. When the photonic stop band is consistent with the wavelength of the incident light, the light will scatter many times on the surface of OPC, especially in the crevices between PMMA spheres. Since UCNPs are placed in the crevices of photonic crystal microspheres, when the excitation light intensity on the surface of OPC is greatly enhanced, then the up-conversion fluorescence is greatly enhanced.

According to this principle, the emission light of UCNPs can also be enhanced, as long as the position of the upconversion emission light and the photonic crystal stop band overlaps. Therefore, we have designed double-layer photonic crystal structure, so that their stop bands can be respectively coupled with the excitation light and emission light of UCNPs, causing that the excitation field and emission field of UCNPs can be simultaneously enhanced, and the intensity of up-converted fluorescence can be further improved. We found that when the photonic stop band is coupled with the excitation field, the better fluorescence enhancement can be obtained, so the upper photonic crystal stop band is set at 980 and 808 nm, and the down layer is at 545 nm couping with emission field, to obtain the best upconversion fluorescence.

As for the important factors related to fluorescence enhancement, it should be the position of the photonic band gap and the power of the excitation light. The position of the photonic band gap is controlled by the size of the PMMA microsphere. Once the optical band gap position mismatches with excitation light or emission light wavelength, the enhancement factor will decrease rapidly. Regarding excitation power and enhancement factor, we found that when the lower excitation power density is employed, greater enhancement factor can be obtained. In addition, the size of fluorescence nanoparticles also influences the enhancement factor. Bigger size of nanoparticles results in lower enhancement factor. Although clear quantitative relation is hard to get, we can build a more appropriate enhancement system for detection according to the variation trend. Normally, low power density of excitation light is meaningful and necessary for biological detection, which is needed to avoid damage to biological samples. Interestingly, our test system can obtain higher fluorescence enhancement when low power is used, showing that this system is suitable for biological detection which can protect biological samples and improve detection accuracy. In this work, we further introduced a bilayer photonic crystal and synchronously coupled the excitation and emission fields to enhance upconversion fluorescence. The work of synchronizing to couple the upconversion excitation and emission fields has not been reported yet. The difficulty lies in not only the fabrication, but also the spatial configuration and regularity, which are still unclear. The photonic crystal effect has a certain working distance, and UCNPs can obtain the maximum enhancement on the surface of the photonic crystal. With this bilayer photonic crystal, it is necessary to study the spatial order structure. In this work, as mentioned above, different spatial order of photonic crystals is designed to optimize the enhancement of upconversion emission. Fig. 3a-d shows emission spectra of two kinds of UCNPs excited by 980 nm and 808 nm laser, tested by spectrograph. Emission spectra and enhancement factor of UCNPs films on glass substrate, 545 nm OPC, 980/808 nm OPC, and double stop band OPC was compared. From spectra, compared with glass substrate, 545 nm emission intensity increased 12, 98, 156 folds under 980 nm excitation and 28, 122, 171 folds under 808 nm excitation. Light of corresponding wavelength was prevented by photonic stop band and was scattered on the surface of OPC, especially in the crevices between PMMA spheres. Obviously this effect was more effective to excitation light than emission light, and double stop band OPC showed much stronger enhancement performance than monolayer OPC. To confirm the influence of the spatial sequence of bilayer OPC with PSB of 545 nm and 980/808 nm, controlled trial was conducted. From emission spectra, the trend of fluorescence enhancement of 980 nm part and 808 nm part is the same. When the 545 nm OPC located on the upper side and 980/808 nm OPC on the down side, the enhancement factor was the same level with single 980/808 nm OPC. When the 980/808 nm OPC was on the upper side and the 545 nm OPC was on the down side, the enhancement factor was much higher than another sample. To get available light signal on glass substrate, these spectra were tested under a relatively high excitation light of 5 W/cm -2 . Fig. 4 (a-e) upconversion emission spectra of detection area, linear fitting and fluorescence lifetime result under 980 nm and 808 nm excitation in antigen detection. (f) specificity test result of PSA and other common substance in the blood. Fig. 4 shows the PSA detection results tested by spectrograph. We chose 545 nm emission peak of Er 3+ as detection position, and the emission intensity decreases as the increase of the concentration of PSA in sample (Fig. 4a,c). The correlation between emission intensity and PSA concentration was also calculated (Fig. 4b,d), which showed satisfactory linear relationship within the range of 0.1~10 ng/mL and the limit of detection (LOD) is 0.01 ng/mL. When sample concentration is 20ng/mL, signal response showed a saturation trend and deviated from the fitting curve. Note that the PSA content of normal people is below 4ng/mL, and if PSA concentration is above 10ng/mL, risk of prostate cancer will significantly increase, our detection system meets the requirement of clinical detection well. Fig. S3 shows the detection result in PBS and blood sample. To test blood sample with low PSA concentration, blood sample with PSA concentration of about 2ng/mL was diluted to 1/10 of its original concentration and blood sample with PSA concentration of 0.2, 2.2, 5.2, 10.2, 20.2ng/mL was prepared, respectively. Compared with PBS solution, detection result of blood sample also shows very good linear relationship with a little slop change in the range of 0~10ng/mL, indicating that the detection system is promising for PSA detection in blood sample. When sample concentration is 20ng/mL, signal response showed a saturation trend and deviated from the fitting curve, which was consistent with previous result (Fig. 4b,d). The signal response of blood sample was slightly higher than that in PBS solution, which can be attributed to that, in our detection system, antigen-antibody reaction in blood sample might be impeded by viscosity of blood. Compared with PBS solution sample at the same concentration, less PSA in blood sample can be attached with capture antibody due to the viscosity of blood, so that less fluorescence quenching occurred in detection, which resulted in the difference in signal response. These results were tested under excitation light of 1.7 W/cm -2 . It should be mentioned that, the same amount of GNPs were added to each test, while excessive GNPs did not affect the results of the assay. The upconversion fluorescence intensity is only related to the amount of PSA, indicating that this sandwich structure is effective for narrowing the distance between the donor and the acceptor, and that other kind of contacts do not lead to energy transfer. Fig. 4e shows the fluorescence lifetime in each detection area. The lifetime decreases as the increase of the concentration of PSA in sample. However, compared with emission intensity, the descend range of lifetime is much smaller. The reason may be that under present testing condition, emission spectra could be tested in a very low excitation power, so only surface layer UCNPs were excited and quenched by gold nanoparticles. However, the pulsed laser required in lifetime testing was more powerful, and when more and deeper UCNPs were excited, the change of statistical lifetime was not obvious since the deeper UCNPs were out of the range of FRET. Fig. 4f shows the result of specificity test, and the concentration of each control group is the same of 20 ng/mL.

From the result, PSA quenches fluorescence intensity significantly, indicating good selectivity of this detection system. This biochip for the detection of tumor marker is promising to be applied for home self-screening, since the upconversion emission is greatly enhanced, and the change in fluorescence under a fluorescence microscope can be clearly seen in the range of 0.1~20 ng/mL. Fig. 5 shows the detection result tested by confocal microscope with 980 nm excitation. We coupled a 980 nm laser to a confocal microscope, and the upconversion emission can be observed through a microscope. In addition, the spectra can be tested through a microscope. Fig. 5a is a schematic diagram of the overall sensing system. In this sensing system, the results also show remarkable sensing performance with the detection limit of 0.01 ng/mL, in the range of 0.1~12.5 ng/mL. We made a comparison between our detection method and the reported methods within Table 1, which indicates the remarkable detection performance of this tumor marker sensor among the various methods. Fig. 5(b-c) shows the emission spectra and corresponding photograph tested by confocal microscope with 980 nm excitation. In the green fluorescent region of the photonic crystal (Fig. 5c), when the PSA is added, the brightness of the green fluorescent region is gradually decreased. Note that the color in the figure is pseudo color and visual image of the detection can be realized through the gray value. Since excessive GNPs made no difference to fluorescence quenching, in this section, the same area on the biochip was selected for the multi-detection of PSA. Enough amount of capture anti-PSA was added firstly, the amount of capture anti-PSA was calculated to be enough to meet the requirement of six experiments.

After PSA and detection anti-PSA modified GNPs was subsequently added, through this sandwich detection method, PSA with different concentrations can be tested multiple times.

Conclusion

In summary, a novel bilayer structure OPC is designed which simultaneously matches with the excitation wavelength and emission wavelength of the UCNPs.

According to the emission spectra of UCNPs on different substrates which are prepared in the same condition, this novel structure shows significantly higher upconversion enhancement factor than the conventional single OPC. With low excitation power density and enhanced emission intensity, the upconversion based PSA sensor was fabricated using NaYF4:Yb 3+ , Er 3+ UCNPs and NaYF4:Yb 3+ , Er 3+ @NaYF4:Yb 3+ UCNPs, respectively. Under 980 nm and 808 nm laser excitation, this detection shows a good linear relationship within the range of 0.1 ng/mL~10 ng/mL and LOD of 0.01 ng/mL. Since the upconversion fluorescence was greatly enhanced, this system could excited by the NIR laser with low power density of 1.7

W/cm 2 . This enhanced upconvesion based strategy can be extended to design a universal biomaterial sensor, and applied in the areas of health assessment and disease diagnosis.

Fig. 1

 1 Fig. 1 Schematic illustration of detection system. (a) UCNPs/bilayer OPC hybrid fluorescence film. (b) Fluorescence film modified by poly-dopamine film and capture anti-PSA, excited by 980/808 nm laser. (c) After connecting with PSA and detection anti-PSA modified gold nanoparticles, emission light intensity of UCNPs quenches.

Fig. 2

 2 Fig. 2 (a-d) SEM image and transmitted spectra of 980/545 nm and 808/545 nm double stop band OPC. (e-f) TEM image of UCNPs NaYF4:Yb 3+ , Er 3+ and NaYF4:Yb 3+ ,Er 3+ @NaYF4:Yb 3+ ,Nd 3+ . (g) SEM image of UCNPs/OPC hybrid film. (h) Transmitted spectra of glass substrate, UCNPs/glass, OPC film, and UCNPs/OPC hybrid film. (i) TEM image of gold nanoparticles. (j) Absorption spectra of gold nanoparticles, they are modified by different amount of detection antibody and then adding NaCl solution. (k) SEM image of PDA/UCNPs/OPC hybrid film. (l) Fourier infrared spectra of PDA/UCNPs/OPC hybrid film. (l) FTIR spectra of poly-dopamine modified fluorescence film.

Fig. 3

 3 Fig. 3 Emission spectra, enhancement factory and schematic diagram of energy transfer progress of four kinds of fluorescence films. (a)UCNPs/980 nm OPC/545 nm OPC (b)UCNPs/545 nm OPC/980 nm OPC (c)UCNPs/808 nm OPC/545 nm OPC (d)UCNPs/545 nm OPC/808 nm OPC.

Fig. 5

 5 Fig. 5 (a) schematic diagram of detection process tested with confocal microscope. (b-c) emission spectra and corresponding photograph tested by confocal microscope under 980 nm excitation (Concentration of PSA in sample is 0, 0.01, 0.1, 2, 5, 12.5 ng/mL, respectively).

Table . 1

 . Comparison of different strategies used for PSA detection.

	Detection structure Sensor principle	Linear range	LOD	Ref.
	MWCNT	ECL	2.25~11.3ng/mL 0.88ng/mL [53]
	Nanomagnetic beads Fluorescent	0.05~100ng/mL 0.05ng/mL [54]
	CdTe QDs	Fluorescent	1~40ng/mL	0.4ng/mL	[55]
	Gold NPs	SERS	4~10ng/mL	0.012ng/mL [56]
	MOFs	Electrochemical	0.1~100ng/mL	0.06ng/mL [57]
	Mesoporous silica	Electrochemical	1~300ng/mL	0.28ng/mL [58]
	/gold film
	gold film	SPR	0.1~50ng/mL	0.091ng/mL [59]
	Gold nanodisk	LSPR	1.7~20.4ng/mL 1.49ng/mL [60]
	OPC/UCNPs	FRET	0.1~10ng/mL	0.01ng/mL Present work

Acknowledgements

This work was supported by the National Key Research and Development Program (2016YFC0207101), the National Natural Science Foundation of China (Grant Nos. 61775080, 11874181, 61874049, 11704056) and the Key Program of NSFC-Guangdong Joint Funds of China (U1801253), Research Project of Jilin Provincial Department of Education (JJKH20200975KJ).