Bo Gao
email: bgao@mail.ipc.ac.cn

Hui Chen

Dongxu Han

Pascal Gambette

Haiyang Zhang

Changzhao Pan

Yingwen Liu

Bo Yu

Ercang Luo

Mark Plimmer

Laurent Pitre

Realization of ppm level pressure stability for primary thermometry using a primary piston gauge

Keywords: Single-pressure refractive-index gas thermometry, Pressure control system, Piston gauge, Cryogenics

To achieve an uncertainty of 0.25 mK in single-pressure refractive-index gas thermometry (SPRIGT), the relative pressure variation of He-4 gas in the range 30 kPa to 90 kPa, should not exceed 4 ppm (k=1). To this end, a novel pressure control system has been developed. It consists of two main parts: a piston gauge to control the pressure, and a home-made gas compensation system to supplement the micro-leak of the piston gauge. In addition, to maintain the piston at constant height, a servo loop is used that automatically determines in real time the amount of extra gas required. At room temperature, the standard deviations of the stabilized pressure are 3.0 mPa at 30 kPa, 4.5 mPa at 60 kPa and 2 mPa at 90 kPa. For the temperature region 5 K-25 K used for SPRIGT in the present work, the relative pressure stability is better than 0.16 ppm i.e. 25 times better than required. Moreover, the same pressure stabilization system is readily transposable to other primary gas thermometers.

Introduction

The 1990 international practical temperature scale (ITS-90, T90) [START_REF] Preston-Thomas | The International Temperature Scale of 1990 (ITS-90)[END_REF] is used worldwide to approximate thermodynamic temperature T. The scale is based on the best thermodynamic temperature measurements that were available in 1990. To measure the temperature in the range 5 K to 24.5561 K (the neon triple point), three primary thermometry techniques are traditionally employed: constant volume gas thermometry (CVGT) [START_REF] Moldover | Advances in thermometry[END_REF][START_REF] Astrov | Precision gas thermometry between 2,5 K and 308 K[END_REF], dielectric constant gas thermometry (DCGT) [START_REF] Moldover | Advances in thermometry[END_REF] and acoustic gas thermometry (AGT) [START_REF] Moldover | Advances in thermometry[END_REF][START_REF] Pitre | New measurement of the Boltzmann constant k by acoustic thermometry of helium-4 gas[END_REF][START_REF] Pitre | Acoustic thermometry: new results from 273K to 77K and progress towards 4K[END_REF]. The core principle of CVGT is to measure the absolute pressure in a constant volume. In DCGT, the thermodynamic temperature is obtained from measurements of the dielectric constant of a gas. In AGT, it is the speed of sound in a monatomic gas that yields thermodynamic temperature. SPRIGT, by contrast, is as a relative primary gas thermometry method, whereby the thermodynamic temperature is determined by microwave frequency measurements in a gas-filled resonator. The resonance frequency is measured over the temperature range of interest first with the resonator under vacuum (in practice p =10 µPa). The thermometric gas is then admitted and its pressure maintained constant at the chosen value. Microwave resonant frequencies are measured with the gas present at different temperatures [START_REF] Gao | Feasibility of primary thermometry using refractive index measurements at a single pressure[END_REF].

Taking advantage of recent advances in the ab initio calculation of the thermophysical properties of He-4, SPRIGT has the potential to yield an uncertainty as small as 0.25 mK. A suitable cryostat for it was developed in our group and details of the temperature control system, thermal response characteristics of the cryostat and microwave measurement published [START_REF] Gao | Chinese SPRIGT realizes high temperature stability in the range of 5-25 K[END_REF][START_REF] Gao | Realization of an ultra-high precision temperature control in a cryogen-free cryostat[END_REF][START_REF] Chen | Thermal response characteristics of a SPRIGT primary thermometry system[END_REF][START_REF] Zhang | A high-stability quasi-spherical resonator in SPRIGT for microwave frequency measurements at low temperatures[END_REF]. However, stable long-term pressure is also required i.e. one constant to better than 0.12 Pa over periods of days or weeks, a considerable challenge for any pressure control system. The design, development and performance of such a system at both ambient and cryogenic temperatures are the subject of the present article, only a short report on the pressure control at room temperature only having been published up to now [START_REF] Han | Ultrastable pressure is realized for Chinese Single Pressure Refractive Index Gas Thermometry in the range 30 kPa to 90 kPa[END_REF].

The pressure stabilization scheme employed in our work exploits a piston gauge in two novel ways. Piston gauges (PGs) are traditionally used as primary and secondary pressure standards in national metrology institutes [START_REF] Ooiwa | Novel nonrotational piston gauge with weight balance mechanism for the measurement of small differential pressures[END_REF][START_REF] Schmidt | Primary pressure standards based on dimensionally characterized piston/cylinder assemblies[END_REF][START_REF] Bandyopadhyay | Characterization of a compact 200 MPa controlled clearance piston gauge as a primary pressure standard using the Heydemann and Welch method[END_REF][START_REF] Jain | A Primary Dead-Weight Tester for Pressures (0.05-1.0) MPa[END_REF][START_REF] Bowers | A capacitive probe for measuring the clearance between the piston and the cylinder of a gas piston gauge[END_REF][START_REF] Olson | A Gas Pressure Scale Based on Primary Standard Piston Gauges[END_REF]. To achieve long-term pressure stability, many researchers first calibrate a pressure transducer using a piston pressure balance, then use the calibrated gauge output as the input for a pressure control feedback loop [START_REF] Rourke | NRC Microwave Refractive Index Gas Thermometry Implementation Between 24.5 K and 84 K[J[END_REF][START_REF] Hill | The vapour pressure of caesium between 370 ℃ and 660 ℃[END_REF][START_REF] May | Quasi-spherical cavity resonators for metrology based on the relative dielectric permittivity of gases[END_REF][START_REF] Scherschligt | Pressure Balance Cross-Calibration Method Using a Pressure Transducer as Transfer Standard[END_REF]. By contrast, in the system described here, the piston gauge is used directly for pressure control, thereby omitting the intermediate steps of pressure value transfer, which leads to more accurate pressure measurement and closed-loop stability.

The second innovation concerns the mode of operation of the piston gauge. In the traditional working mode, the loaded piston rotates freely inside the cylinder, behaving as an aerodynamic bearing. Sutton and Fitzgerald have discussed the aspects of rotated gas-operated pressure balances that affect their performance [START_REF] Sutton | Performance aspects of gas-operated pressure balances as pressure standards[END_REF]. It is recommended that the piston gauge be operated with a small, reproducible falling rate [START_REF] Bandyopadhyay | Characterization of a compact 200 MPa controlled clearance piston gauge as a primary pressure standard using the Heydemann and Welch method[END_REF]. Izumi et al. [START_REF] Izumi | A high gas pressure calibration system using a liquidlubricated pressure balance[END_REF] evaluated the falling rate of a liquid-lubricated piston-cylinder (PC) assembly.

In the work of Sabuga et al. [START_REF] Sabuga | Design and Evaluation of Pressure Balances with 1. 10 -6 Uncertainty for the Boltzmann Constant Project[END_REF], the gap width of the PC assembly at PTB was adjusted to yield an optimal compromise between the rate of descent and sensitivity.

However, when the piston gauge employed in the present work (Fluke PG 7601) was used in rotating mode, unwanted peaks appeared in the pressure profile due to the acceleration of the rotating piston whenever its speed reached its lower limit. Moreover, each time the piston had fallen for one or two hours, it would reach its lowest permissible height and so no longer be able to control the pressure. (To add pressure to the system, the piston must drop). To prevent this from being a problem, therefore, we should not only isolate the pressure oscillation from the surroundings (external pressure-noise), but more importantly isolate the pressure change due to the piston gauge (internal pressure-noise). [START_REF] Bock | Reduction of the uncertainty of the PTB vacuum pressure scale by a new large area non-rotating piston gauge[END_REF] discovered that by using a large area non-rotating piston gauge, they were able to reduce the uncertainty of their vacuum pressure scale. This approach was followed in the present work. In addition, a novel piston suspension gas path compensation system was implemented to prevent the piston from reaching the bottom of the cylinder. This article presents experimental results for pressure control using this system.

Bock et al. at PTB

To gain a better understanding of the pressure control principle, the pressure control was first implemented using the internal height sensor of the commercial piston gauge.

For finer height measurement and control, an external laser interferometer was used to determine the height of the upper surface and enabled ultra-stable pressure control in the range of 30-90 kPa in a ballast volume at room temperature. Finally, results are given for different pressures (30 kPa, 60 kPa and 90 kPa) and low temperatures (5 K-25 K) when the pressure control system was connected to the resonator in the cryostat.

Apparatus

An overview of the apparatus is given in Fig. 1 (a). The three main components are the temperature control box, the piston gauge (Fig. 1 (b)) and the gas compensation system (ballast volume, mass flow controller, absolute pressure gauge).

Temperature control box

The temperature control box was designed to provide a stable working temperature for the instruments (24.5℃, temperature instability <1.5 mK) to reduce the impact of external temperature variation on the measured pressure, the temperature box is based on the description given in Berg et al [START_REF] Berg R F | Constant pressure primary flow standard for gas flows from 0.01cm3/min to 100cm3/min (0.007-74μmol/s)[END_REF].

Piston gauge

Piston gauges are oft-used standard instruments in pressure metrology [START_REF] Sharipov | Primary pressure standard based on piston-cylinder assemblies. Calculation of effective cross-sectional area based on rarefied gas dynamics[END_REF]. Fig. 1 (b) shows a schematic of a gas-operated piston gauge, which consists of a loaded piston in a close-fitting vertical cylinder. The piston moves vertically in the cylinder, changing the pressure in the volume beneath the piston until the gravitational force on the piston and its load are balanced by the force of pressure acting on the lower surface of the piston.

The absolute pressure PA beneath the piston is given by the force balance equation

where A θ, P the effective area of the piston-cylinder, M the mass load, P HA the fluid head correction, g the local gravitational acceleration and P vac the residual pressure above the piston.

In the present work, the piston gauge is a Fluke PG 7601 (piston surface area 980.49 mm 2 ). A turbomolecular pump (Pfeiffer Hipace 300) backed by a dry (oil-free) pump (Pfeiffer ACP 28) provides the vacuum above the piston (Pvac=0.1 Pa, u(Pvac)=0.1 Pa).

Gas compensation system

The gas compensation system (Fig. 1 (a)), is composed of the gas source, the pressure regulator, ballast volumes, mass flow controllers (MFC), absolute pressure gauge, the laser interferometer, pump together with the requisite pipes and valves.

The gas source is a bottle of high purity (>99.99999%) 4 He at high pressure (20 MPa). Using the pressure regulator, the gas pressure at the entrance to the 1 L ballast volume is reduced to 1.5 bars (0.15 MPa).

The first mass flow controller MFC1 (S48 300/HMT) is used to fix the mass flow rate transfer to the upstream, usually a small value around 2 sccm 1 . The gas flow is split into two parts using a tee: one part going to supplement the piston gauge leakage while the other is evacuated by a dry pump (Pfeiffer ACP 15). The second mass flow controller MFC2 (S48 300/HMT) is used to control the amount of gas evacuated. Thus, the extra quantity corresponds to the difference in flow difference between the two controllers. A four-way cross is used to connect ballast volume 2 (1 L), the pressure vessel and the piston gauge. In normal operation, since the flow rate from the four-way 1 Sccm=standard cubic centimeters per minute, corresponding to 1.6667×10 -8 m 3 •s -1 in the International System of Units (SI). We define the volumetric flow 1 sccm as the flow of 1 cubic centimeter per minute of argon at the pressure 103 kPa and temperature 20℃.

cross to the piston gauge is very small (about 10 -2 sccm) with almost no gas flowing to the pressure vessel and ballast volume 2, the pressure in the whole system is nearly uniform aside from some hydrostatic head difference. All the test experiments were performed at room temperature (about 24.5 ℃), independently of the microwave resonator. The latter was isolated from the system by closing valve 2 and the volume of the pressure vessel simulated using the 1 L ballast volume 2. Upon completion of the test experiments, valve 2 was opened and the pressure control system used to control the pressure within the microwave resonator. To estimate the stability of the controlled pressure, two absolute pressure transducers (Paroscientific Digiquartz 745) of range 0-23 psig with nano-i.e. parts-per-billion (10 -9 ) resolution, were used to track the pressure in real time.

During normal operation, MFC1 is used to fix the flow rate at 2 sccm (or some other small value) while the flow rate through MFC2 is determined by the piston height.

When the piston height lies above the set value, the set-point of MFC2 is reduced, causing the piston to rise to the chosen height. The reverse happens whenever the piston height lies below the set value. Thus, the piston height remains almost constant with only a very small oscillation. Servo-control using a proportional-derivative (PD) feedback loop is implemented via a control program written in LabVIEW software.

The piston height is measured by the LVDT height sensor internal to the piston gauge (resolution 10 µm) and an external laser interferometer (Keyence LK-G80, resolution 0.1 µm).

3 Experimental results and discussions

Comparisons between rotation and non-rotation behaviour of PG 7601

When the piston gauge is in operation, the piston must float freely without friction due to contact between the piston and cylinder. Thus, it is recommended that, during pressure measurements, the piston should be in permanent rotation. To supply gas pressure for pressure control, the piston must fall. As times goes by, the piston slows down due to viscous damping by the surrounding gas. Whenever the piston reaches its lower rotational speed threshold, the control electronics of the gauge add some angular acceleration, which causes the pressure to jump. In the case of the present experiment, this happens every 30 minutes, which is unacceptable. It was thus decided to operate the gauge without rotation.

To test this approach, the rotational and non-rotational behaviours of the pistoncylinder assembly were compared with the piston falling. The procedure as follows: (1)

Close valve 2 and set the flow through MFC2 to 0 sccm. (2) Apply a flow of 2 sccm to MFC1 and wait until the piston reaches its highest point. (3) Set the value of MFC1 to 0 sccm and let the piston fall freely. For the rotation experiment the "auto-rotation function" was enabled with minimum and maximum rotation speeds of 20 rpm and 100 rpm respectively. For the non-rotation experiment, the "auto-rotation function" was disabled.

Fig. 2 shows the results of experiments with and without rotation under a nominal pressure 60 kPa, i.e, for a nominal load mass of 6 kg. Fig. 2 (a) shows the rate of descent of the piston for the two modes of operation where the piston height was measured using the internal height sensor. Both curves are linear and show similar rates of descent (90 µm/min for rotating mode and 97 µm/min for non-rotating mode). Fig. 2 (a) also includes two zooms for different heights. In the zoom on the right, one can see that the curve for the non-rotating piston is smooth while that for the rotating mode exhibits some fluctuations. The reason is that the rotation of the piston is not strictly co-axial so its height varies slightly as it wobbles. This fluctuation interferes with the servo-loop used to stabilize the piston height. On the zoom on the left-hand side, a different zone is visible for the experiment in rotation mode. The reason can be found in Fig. 2 (b):

every time the piston is re-accelerated by the driving motor after reaching its minimum permissible rotation speed, the contact between the motor and piston causes the piston to jump upwards.

The contact also upsets the force balance of the piston, thereby causing a significant pressure shift (Fig. 2 (c)). After one minute of acceleration, the piston becomes free once again and a stable pressure is restored. This scenario repeats itself every 1.5 hours. By contrast, the non-rotational mode exhibits no such behaviour. Fig

(d)

gives comparisons of pressure between the rotating and non-rotating piston experiment. One sees that the pressure increases as the piston falls. The pressure difference between the heights of +2.5 mm and -2.5 mm is 0.75 Pa. According to the calculation of Sharipov et al. [START_REF] Sharipov | Primary pressure standard based on piston-cylinder assemblies. Calculation of effective cross-sectional area based on rarefied gas dynamics[END_REF], this difference arises from additional forces on the piston due to the gas flow in the crevice between piston and sleeve. Moreover, the gas pressure beneath the piston and filling the crevices causes an elastic deformation of both sleeve and piston. Though small, it modifies the dimensions, so its effect should be included in the calculation of the effective area.

More importantly, the difference in mean pressure value with and without piston rotation is less than 50 mPa, as is obvious from Fig. 2 (d). This means the choice of non-rotational mode has only a small effect on the measured pressure. Given this and the fact that the non-rotational mode is immune to periodic jumps in piston height that hinder servo-control, this mode was adopted in the remainder of the experiments described here.

Comparison of falling and regulatory behaviour of the piston cylinder gauge

It is generally recommended that the piston gauge be operated at a small, reproducible falling rate. In the present application, however, the fall of the piston causes two problems. First, after dropping for one or two hours, the piston reaches its lowest height below which it can no longer control the pressure. Second, the pressure changes by 10 -1 Pa (Fig. 2 (d)) as the piston falls, which makes it generate an additional pressure instability. To solve these problems, the gas compensation system mentioned in section 2.2 was installed to regulate the piston height.

To compare the falling and regulation modes of operation of the piston gauge. The piston was regulated in non-rotation mode at different heights between +2.5 mm and -2.5 mm in steps of 0.5 mm. Fig. 3 shows the results of the regulation and falling piston experiments.

As shown in Fig. 3 (a), for regulation mode, the generated pressure increases as the height decreases. The behaviour follows the same trend as for the falling piston experiment. However, the regulated pressure is always a little larger than that measured in the latter. To quantify the pressure difference, we fitted the pressure measured in falling mode by a second-order polynomial and compared the pressure values for the different regulated heights. It is apparent from Fig. 3 (b) that the pressure difference between regulation and rotation-falling modes is less than 0.1 Pa. This difference is very small, almost the same as that between h =2.5 mm and h = -2.5mm in falling mode. From the above discussions, it is found that, for the piston gauge, the "regulation non-rotation mode" yields a pressure that differs from that measured in the "falling rotation mode" by less than 0.1 Pa.

Since the "regulation non-rotation mode" avoids the problems caused by piston fall and rotation stated above, and provides a stable long-term pressure, the remaining experiments were all carried out using it. For completeness, the corresponding uncertainty arising from the small pressure difference between the two modes is included in the uncertainty budget (section 4.1).

Pressure regulation at room-temperature using a ballast volume

The main goal of the pressure control system was to provide a stable pressure for SPRIGT, i.e. primary thermometry at cryogenic temperatures (4 K-24.5 K). Indeed, this was achieved, as described later. In a first instance, however, pilot experiments were performed at room temperature and some improvements made as a result of them.

For the room temperature studies, the pressure vessel containing the microwave resonator in the cryostat was isolated by closing valve 2 (Fig. 1 (a)). The setpoint of mass flow controller MFC1 was chosen to be 2 sccm set point while that of MFC2 was determined in real time by feedback control software written in LabVIEW. The purpose of the feedback loop is to stabilize the piston at a constant height. In this experiment, the feedback signal is derived from the height measured by the internal sensor of the piston gauge with a resolution of 10 μm. shows that the pressure, measured by the absolute pressure gauge with an integration time of 44 ms, fluctuates with a relative standard deviation of 0.4 ppm. To measure the real noise, namely the instability, the white noise should be removed. This is easily achieved by increasing the integration time of the absolute pressure gauge. Figs. 4 (d),

(e) and (f) show the pressure measured with integration times of 178 ms, 700 ms and 1400 ms. The noise decreases as the integration time is increased, but the noise changes rarely between results for integration times of 700 ms and 1400 ms. This means the noise measured with an integration time 700 ms corresponds to the real noise. One can see in Fig. 4 that some points lie far from the mean, no matter how long the integration time. The excursions are caused by the sudden flow changes due to the aforementioned low resolution (10 μm) of the LVDT height sensor. This means a better resolution is required for piston height control.

To measure piston height more precisely, a laser interferometer (Keyence LK-G80, resolution 100 nm) was installed above piston gauge. Specifically, a mirror the upper surface of the piston forms part of the optical path. Fig. 5 shows the pressure control results obtained using it. The piston height is stabilized to within 4 μm of the set point, a clear improvement upon the use of the internal LVDT sensor. As a result, the pressure is controlled with instability of 0.075 ppm, clearly better than that shown in Fig . 4 (b).

Low-temperature regulation of the microwave resonator gas pressure

Following the test experiments at room temperature, the pressure regulation system was connected to the resonator in the cryostat to provide a stable pressure at low temperature. The resonator was connected by opening valve 2 shown in Fig. 1(a). As

with the experiments at room temperature, the flow through the mass-flow controller MFC1 is fixed while that through MFC2 is determined in real time by the feedback signal derived from the height of the piston gauge. Before the pressure control system is connected to the cryostat, the pressure system should be initially under vacuum, after which the gas is slowly introduced into the pressure system and the resonator in the cryostat. As shown in Fig. 6, the relative fluctuations at pressures near 30 kPa, 60 kPa 90 kPa and 120 kPa in the temperature range 5 K-24.5561 K are all less than 0.16 ppm, i.e. 25 times lower than the 4 ppm pressure stability required for SPRIGT at the 0.25 mK level of uncertainty. The values and uncertainties calibrated by the National Institute of Metrology of China used in the determination of pressure p are listed in Table 1. The area of the piston gauge was calibrated at TIPC by NIM in 2019 at 24.5 ℃. A correction for thermal expansion of piston and cylinder calibrated by NIM is applied to calculate the Aθ, p. The combined standard uncertainty for PA is obtained by quadratic summing of the estimated uncertainty components listed in Table 2. Under the present absolute mode of operation of the piston gauge, the pressure reproducibility is not only related to the masses of load and piston, gravity and piston effective area, but also affected by the vacuum in the region above the pressure balance, the thermal expansion coefficients of piston and cylinder and their temperature. Once the pressure control system is connected to the cryostat, the uncertainty in the hydrostatic head correction PHA must also be included. In the uncertainty budget for pressure measurements at room temperature, this sub-component will be neglected. Eq. ( 1) and Eq. ( 2) give the mathematical model used to deduce the pressure using the PG7601 piston gauge, taking into account the aformentioned effects. The effective area of the piston is given by 6 , 24.5,0 P C nom 10 [1 ( 24.5)( )](1 )

P A A P             (2)
where A 24.5,0 (in mm 2 ) is the effective piston area at 24.5 ℃ and zero pressure; θ the piston temperature, ℃; α p and α c the respective thermal expansion coefficients of piston and cylinder, ℃ -1 ; λ the elastic deformation coefficient of the piston-cylinder assembly, MPa -1 ; and P nom is the nominal pressure, MPa.

Pressure regulation of the resonator at cryogenic temperature

When the pressure control system is connected to the resonator in the cryostat, one must include the uncertainty in the thermodynamic temperature due to the pressure measuement. This contains two contributions: the absolute value of the pressure and the noise due to imperfect regulation.

The uncertainty due to the absolute pressure is calculated by quadrature summation of two sub-components assumed to be statistically independent. The first is due to the calibration of the piston gauge which is the same as the calculation for room temperature measurements. The second sub-component is the uncertainty in the hydrostatic head correction from the gas line. For the present study, the hydrostatic head corrections are calculated using Eq. ( 3). The gas line was divided into n straight segments. The thermal gradients along the gas line inside the cryostat between these measured endpoint temperatures are estimated using a simple linear approximation. The uncertainty in the hydrostatic head correction contribution from the pressure tube dominated by the uncertainty in the height change (calculated from the uncertainties in the length measurements), and multiplied with the average gas density in the segment.

Thus, the segments that contribute most strongly to the overall hydrostatic head correction uncertainty are those near the low-temperature end of the gas line that has large height-change uncertainties. The uncertainty due to imperfect pressure regulation varies with temperature, and is calculated using the standard deviation of the pressure regulation results:

  HA ii i P g h      ( 3
)
where ρi is the average gas density in segment i; Δhi is the change in height of the i th segment.

As shown in Table 3, the dominant uncertainty component due to pressure for SPRIGT thermodynamic temperature measurement at all temperatures arises from the uncertainty in the pressure calibration of the piston gauge and the pressure stability.

Conclusion

A high stability pressure regulation system for helium-4 gas based on a micro-flow compensation system has been developed and applied at both room temperature and cryogenic temperatures (5-25 K). Its purpose is to allow single-pressure refractive index gas thermometry in the latter range at the 0.25 mK level of accuracy. Since the refractive index is a function of both temperature and pressure, the latter must be controlled to better than 4 ppm. The main conclusions are as follows:

1. The pressure control system incorporates a piston gauge (Fluke PG 7601) whose operation in both rotation (falling) mode and non-rotating (regulation) mode was investigated in this paper. It was found that the mean pressure difference is less than 0.05 Pa, and that the non-rotation mode avoids large pressure jumps caused by the speeding up of piston rotation whenever it reaches the low revolution threshold.

2. Active servo control to maintain the piston gauge at constant height was studied using both the internal height sensor of the gauge and an external laser interferometer. The results for room temperature showed that the pressure instability, defined by standard deviation, was of order 3 mPa at 30 kPa, 4.5 mPa at 60 kPa and 2 mPa at 90 kPa, while in the range 5 K-24.5561 K, it is better than 0.16 ppm.

3. The uncertainty budget for the pressure of piston gauge determinations and the uncertainty contribution to SPRIGT were all analyzed. The dominant component (less than 0.032 mK) is that due to the measurement of absolute pressure.

Fig. 1

 1 Fig. 1 The schematic diagram of the pressure control system (a) Gas compensation system (b) Gas-operated piston gauge

Fig. 2

 2 Fig. 2 Descent of the piston in rotation and non-rotation experiments (a) Height profile (b) Speed profile (c) Pressure profile of rotation experiment (d) Comparisons of pressure between rotation and non-rotation experiment ("Each point corresponds to a 44 ms integration time.")

Fig. 3

 3 Piston falling and regulation experiments (a) Original pressure profile (b) mean pressure values for different piston heights (The regulation is performed in at non-rotation mode using the internal LVDT height sensor. All pressure values are measured by the absolute pressure transducer with an integration time 44 ms )

Fig. 4

 4 Fig.4shows the results. In Fig.4(a), the piston height appears very steady with small jumps (0.01 mm). In reality, the piston rises or falls very smoothly. Since the resolution of LVDT is 10 μm, its reading number is deceptive. Because, via the PID program, the set-point of MFC 2 is determined by the piston height signal with small jumps, sudden changes can occur in the flow through MFC2 (see Fig.4 (b)). Fig.4 (c)

Fig. 4

 4 Fig. 4 Piston height control results based on piston heights measured by the internal sensor (a) Piston height (b) Flow of mass flow controller 2 (c) 44 ms (d) 178 ms (e) 700 ms (f) 1400 ms ((c), (d), (e) and (f) are the controlled pressures measured by the absolute pressure transducer (Digiquartz1) at 60 kPa for the different integration times)

Fig. 5

 5 Fig. 5 Piston height and pressure control results based on piston heights measured by external interferometer (a) Piston height (b) Controlled pressure near 60 kPa (c) Idem near 30 kPa (d) Idem near 90 kPa

  Fig. 6 Pressure stability at different pressures for temperatures from 5 -25 K

  The dominant uncertainty component at all pressures measured in the present study arises due to the 5 ppm (k=1) uncertainty in the effective area of the balance piston. The uncertainty in the regulation experiment for different piston heights is estimated from the descending rotating piston experiments. A drop in piston height from +2.5 mm to -2.5 mm corresponds to a pressure difference of less than 0.1 Pa. Therefore, the different height regulation correction corresponds to a 0.06 Pa uncertainty. The value of the local gravitational acceleration g and its uncertainty were measured and calculated by the National Institute of Metrology of China.

Table 1 Uncertainty budget for pressure using the piston gauge determinations (k=1)

 1

	Mean	Standard deviation

Table 2 Uncertainty budget for the pressure of piston gauge determinations (k=1)

 2

			u(x) / Pa
		P=30 kPa	P=60 kPa	P=90 kPa	P=120 kPa
	Mass_piston / kg	0.006	0.006	0.006	0.006
	Mass_carryingbell / kg	0.005	0.005	0.005	0.005
	Mass_weights / kg	0.030	0.08	0.087	0.11
	g/ m•s -2	0.003	0.006	0.009	0.012
	A24.5,0/mm 2	0.15	0.30	0.45	0.6
	θ/℃	0.002	0.004	0.006	0.009
	αp /℃ -1	0.006	0.012	0.018	0.024
	αc /℃ -1	0.006	0.012	0.018	0.024
	Pvac/Pa	0.1	0.1	0.1	0.1
	ΔPregulation/Pa	0.06	0.06	0.06	0.06
	uPA / Pa	0.20	0.33	0.47	0.62

Table 3 Uncertainty budget of P for SPRIGT T determinations (P = 60 kPa, k=1)

 3

		PA /mK	PHA /mK
	T / K			p stability /mK	ptotal /mK
		Calibration	Hydrostatic
	26	0.008	0.00053	0.0015	0.008
	24.5561 (Ne triple point)	0	0	0.0025	0.002
	23	0.008	0.00057	0.0013	0.008
	22	0.012	0.00092	0.0012	0.012

ACKNOWLEDGEMENTS

This work was supported by the National Key Research and Development Program of China (grant n° 2016YFE0204200), the National Natural Science Foundation of China (grant n° 51627809), the International Partnership Program of the Chinese Academy of Sciences (grant n° 1A1111KYSB20160017) and the European Metrology Research Program (EMRP) Joint Research Project 18SIB02 "Real K". The authors are also grateful for the expert technical assistance of Zhen Zhang and Ying Ma.

NOMENCLATURE


Dojat Michel

Delon-Martin Chantal

Warnking Jan

Segebarth Christoph

Bullier Jean

Moving illusory contours activate primary visual cortex: an fMRI study

Keywords: Adult, Brain Mapping, Female, Form Perception, physiology, Humans, Magnetic Resonance Imaging, Male, Optical Illusions, physiology, Photic Stimulation, Visual Cortex, physiology ' é

Identifying the cortical areas activated by illusory contours provides valuable information on the mechanisms of object perception.

We applied fMRI to identify the visual areas of the human brain involved in the perception of a moving Kanizsa-type illusory contour. Our results indicate that, in addition to other cortical regions, areas V5 and V1 are activated. Activity in area V1 was particularly prominent.

Introduction

One of the essential operations carried out by the visual system is the segmentation of the visual scene into different components. This process requires the identification of borders between different surfaces which may be signaled by differences in luminance, in texture and/or in chrominance. Border perception can also be induced between distant colinear discontinuities that signal the presence of an opaque object with the same optical characteristics as the background (

). Borders which are perceived in the Petry and Meyer, 1987 absence of differences in luminance or chrominance are usually called illusory or subjective contours. One class of illusory contours ( ) is generated by the alignment of high contrast borders that act as inducers of the illusory perception of a dark shape placed over Figure 1a a set of white disks (

). [START_REF] Kanizsa | Organization in vision[END_REF] Illusory contours have been extensively used to test different hypotheses about how the information is processed within the visual system (see ( ; ) for an extended bibliography). Illusory contours provide good models, in Purgh and Coren, 1992 é Spillman and [START_REF] Spillmann | Phenomena of illusory form: can we bridge the gap between levels of explanation?[END_REF] particular, for investigating the mechanisms involved in perceptual grouping (

) and in the segregation of forms and objects from Marr, 1982 a background ( ). [START_REF] Kojo | Spatial and temporal properties of illusory figures[END_REF] One of the issues which are currently debated is the level at which illusory contours are encoded ( ; Gregory, 1972 Smith and Over, ; ; ; ; ; ; ; 1975 [START_REF] Rock | Illusory contours as the solution to a problem[END_REF][START_REF] Der Heydt | Illusory contours and cortical neuron responses[END_REF][START_REF] Grosof | Macaque V1 neurons can signal illusory contours[END_REF]Shapley, 1994[START_REF] Hirsch | Illusory contours activate specific regions in human visual cortex: evidence from functional magnetic resonance imaging[END_REF][START_REF] Ffytche | Brain activity related to the perception of illusory contours[END_REF]. Imaging studies in humans have suggested that static illusory contours activate neuronal populations at the earliest [START_REF] Mendola | The representation of illusory and real contours in human cortical visual areas revealed by functional magnetic resonance imaging[END_REF] levels of cortical processing. In a PET study, activation was shown mostly in area V2 (

). In one fMRI investigation, [START_REF] Ffytche | Brain activity related to the perception of illusory contours[END_REF] activation of extrastriate areas has been reported with a possible weak participation at the border of areas V1 and V2 (

). [START_REF] Hirsch | Illusory contours activate specific regions in human visual cortex: evidence from functional magnetic resonance imaging[END_REF] In another fMRI study, similar static illusory contours have been shown to induce mainly activation of higher-order organized areas including V3A, V4v, V7 and V8. The activation of low level areas (V1 and V2) however was not ruled out (

). [START_REF] Mendola | The representation of illusory and real contours in human cortical visual areas revealed by functional magnetic resonance imaging[END_REF] It is well known that processing within the visual system occurs along two main pathways, the occipito-temporal ventral stream and the occipito-parietal dorsal stream. Previous studies of cortical activation by illusory contours have used static stimuli which are likely to preferentially trigger neurons of the ventral stream ( ; ;

). [START_REF] Hirsch | Illusory contours activate specific regions in human visual cortex: evidence from functional magnetic resonance imaging[END_REF][START_REF] Ffytche | Brain activity related to the perception of illusory contours[END_REF][START_REF] Mendola | The representation of illusory and real contours in human cortical visual areas revealed by functional magnetic resonance imaging[END_REF] Much less is known concerning the processing of moving illusory contours and the involvement of the dorsal stream. Two imaging studies have focused on the perception of illusory movement during viewing of static stimuli ( ; ). [START_REF] Zeki | Going beyond the information given: the relation of illusory visual motion to brain activity[END_REF]Tootell et al., 1995b Strong activation was found within and around area V5, a cortical region known to be important for the perception of motion. In another imaging study, the apparent motion of illusory contours ( ) has been reported to evoke activation in V5 [START_REF] Ramachandran | Apparent motion of subjective surfaces[END_REF][START_REF] Goebel | The constructive nature of vision: direct evidence from functional magnetic resonance imaging studies of apparent motion and motion imagery[END_REF] It was therefore of interest to assess whether moving illusory contours mainly activate area V5, as most moving stimuli do, and/or whether they activate areas V1 and V2 like at least some of the static illusory contours do ( ; ). Hirsch et al., 1995 Ffytche and[START_REF] Ffytche | Brain activity related to the perception of illusory contours[END_REF] Moving illusory contours were generated by means of rotating pacman inducers (

) configured in such a way that the [START_REF] Bravo | Cats see subjective contours[END_REF] subject perceives an illusory rectangle moving vertically across the visual field in a saccadic fashion (

). Activations were assessed Figure 1a by means of functional fMRI. Part of this work has previously appeared in abstract form (

). Seghier et al. 1999

Materials and Methods

Subjects

Thirteen healthy volunteers (age 32 10) were examined. All subjects (twelve males and one female) gave their informed consent to ± participate to the study. They had normal (n 11) or corrected-to-normal (n 2) vision. Nine among the volunteers were trained fMRI

= =
subjects.

Experiments

All subjects performed a first fMRI experiment (Experiment 1) aimed at identifying the functional responses to a moving illusory rectangle. Three additional control experiments were performed on two subjects: one to obtain the responses to stationary illusory contours (Experiment 2), another to localize the border between functional areas V1 and V2 (Experiment 3) and a third to identify with certainty the functional area V5 (Experiment 4). On these two subjects, whom we will refer to as the Control subjects C1 and C2, the four experiments were performed during the same session, without repositioning.

Paradigms

For all experiments, a block paradigm was applied, which alternated between reference and stimulation epochs.

" " " "

Visual stimuli

Visual stimuli were generated by means of a PC equipped with VisionWorks software (Vision Research Graphics, Durham, USA).

They were transmitted to the subjects by means of an LCD videoprojector (Eiki LC 6000, Eiki Industrial Company, Japan), a backprojection screen and a system of mirrors. The visual field spanned by this setup was approximately 15 and 11 in the horizontal and °°vertical directions respectively.

Experiment 1

The visual stimuli presented during the stimulation epochs aimed at inducing the perception of an illusory rectangle moving " "

vertically (

). Ten white pacman inducers (henceforth referred to as pacmen) were positioned on a dark background on the edges Figure 1a of a rectangular grid. Four adjacent pacmen among them were configured so as to induce the perception of the illusory Kanizsa rectangle. Vertical movement of this rectangle was achieved by the sequential display of four different configurations of the ten pacmen. Sequential configurations differed in a 90 rotation of the individual pacmen, clockwise for those in the left column and counterclockwise for those in °the right column. Thus, while individual pacmen rotated, the illusory rectangle appeared to move downwards, in a saccadic fashion (Figure ). Refreshment rate of the sequential configurations was 1.7 Hz, corresponding to an angular velocity of the illusory rectangle as viewed 1a by the subjects of 3.2 /s. °During the reference epochs, sequential configurations of pacmen were presented which were similar to those displayed during the " " "

stimulation epochs ( ). The sequential configurations differed from those presented during the stimulation epochs mainly in that "

Figure 1b

" " most of the pacmen were tilted. In the experiments on the control subjects (C1 and C2) they were tilted by 10 and in all other experiments °by 45 . Thus, the perception of illusory staircase shapes during the reference epochs was avoided. As during the stimulation epochs, °" " " " " " sequential configurations differed in a 90 clockwise rotation of the individual pacmen in the left column and a 90 counterclockwise °°rotation of those in the right column. In order to reduce possible visual aftereffects, a black transition screen was presented when

" "
switching from stimulation to reference epochs. The MR measurements performed while viewing the transition screen were discarded " " " " " "

during data processing. A white fixation dot was presented all over the experiment.

The illusory rectangle as viewed by the subjects extended over 2 and 1.7 in the horizontal and vertical directions respectively. They °°were displayed symetrically with respect to the vertical meridian. The radius of the pacmen extended over 0.45 . Thus the support ratio of °these contours ( ), i.e. the ratio of the total length of the borders actually drawn to the perimeter of the rectangle, Shipley and Kellman, 1992 is 0.48. Luminances of the pacmen and of the dark background were respectively 201 and 56 cd/m , as measured on the projection screen.

2

Experiment 2

The visual stimulus presented during the stimulation epochs was a single static Kanizsa rectangle, centrally placed. During the " " "

reference epochs, the four pacmen were tilted by 10 to avoid the perception of the illusory rectangle. During stimulation and reference

" °" " " "
epochs, the pacmen flickered synchronously at 4 Hz ( ). [START_REF] Hirsch | Illusory contours activate specific regions in human visual cortex: evidence from functional magnetic resonance imaging[END_REF] In this experiment, the illusory contour as viewed by the subjects (C1 and C2), extended over 3.3 and 2.6 in the horizontal and °°vertical directions respectively, the radius of the pacmen extended over 0.7 , and the support ratio was 0.48. Luminances of the pacmen °and of the dark background were respectively 201 and 56 cd/m , as measured on the projection screen.

Attentional tasks

In order to maintain the subject s attention, attentional tasks were built into the paradigm in Experiments 1 and 2. The fixation point ' (0.09 ) was intermittently dimmed and subjects were instructed to report the occurrence of these (rare) events by means of a button press.

°Furthermore, during the stimulation epochs in Experiment 1, the vertical movement of the illusory rectangle, while occurring usually " "

from top to bottom, occurred four times from bottom to top. Subjects were also instructed to report these reversals.

Experiment 3

The visual stimulus presented during the stimulation epochs aimed at inducing functional responses at the borders of areas V1 and " "

V2. This was achieved by using a hourglass-shaped stimulus centered on the vertical meridian. The latter is known to be represented at the border between areas V1 and V2. The stimulus was composed of two segments filled with a contrast-reversing checkerboard pattern (8 Hz flickering). The two segments had their apices at the fixation point and were centered on the upper and lower vertical meridian respectively. The angle of the segments was 40 . Maximum eccentricity was 7 ( , ). During the °°Hasnain et al., 1998[START_REF] Engel | Retinotopic organisation in human visual cortex and the spatial precision of fMRI[END_REF] " reference epochs, only the fixation point was displayed.

"

Experiment 4

The visual stimulus presented during the stimulation epochs aimed at inducing robust functional responses in V5. A stimulus

" "
composed of a set of low-contrast (gray on white, 16 contrast), continuously expanding, concentric rings was presented ( % Tootell et al.,

). Maximum eccentricity of the rings was 10 . The expansion rate of the rings was 7 /s. During the reference epochs, a snapshot of 1995b

°°" "

the rings was shown continuously. In order to prevent the perception of a motion aftereffect ( ), a transition screen was Tootell et al 1995b presented during the first 4 s of each reference epoch. The screen presented the same concentric rings, this time continuously contracting.

" "

MR acquisition

Subjects were examined at 1.5T on a clinical MR scanner (Philips ACS II). The body coil was used for excitation. A circular surface coil (diameter 13 cm) was used for detection. This coil was centered just beneath the occipital pole of the subject s head. Positioning of = '

the volume was performed on scout images acquired in the sagittal plane.

Subsequent to the functional MR scans, a high resolution 3D phase-contrast (PC) ( ) MR angiography scan was [START_REF] Dumoulin | Three dimensional phase contrast angiography[END_REF] eventually ran from the volume functionally examined. This scan provided anatomical (T1-weighted) as well as vascular information about the volume of interest.

For the 11 subjects having performed Experiment 1 only, the volume of interest imaged in the functional scans was composed of 6 adjacent, axial, slices (5mm thickness each). It was oriented parallel to the bicommissural plane and centered so as to encompass most of the calcarine sulcus. The volume was measured five and four times during the reference and stimulation epochs respectively. This

= = = × = × 2 = °= ×
volume of interest imaged in the functional scans was composed of 8 adjacent, coronal, slices (5mm thickness each). This volume was oriented orthogonal to the bicommissural plane and also centered so as to encompass most of the calcarine sulcus. In experiments 1 and 2, the volume was measured seventeen times during each of the reference , stimulation and transition screen epochs. This sequencing was " " " " " " repeated five times (total measurement time 8 36 ). In experiments 3 and 4, the volume was measured sixteen times during the control

′ ″ " "
and stimulation epochs. This sequencing was repeated four times (total measurement time about 4 22 ).

" " ′ ″

Data processing

MRI images were analyzed off line by means of a software package developed under the IDL 5.2 programming language (Research Systems Inc., Boulder, USA). Following image coregistration ( ) and pixelwise baseline correction, functional responses [START_REF] Roth | Coregistration of 2D MR images by means of a direct Fourier method applied in k-space[END_REF] were detected by means of cross correlation analysis (

). The cross-correlation coefficient was calculated pixelwise [START_REF] Bandettini | Processing strategies for time-course data sets in functional MRI of the human brain[END_REF] between a box-car function (representing the paradigm) and the set of measurements. In practice, we first identified pixels which presented a cross-correlation coefficient above a predefined threshold (typically .4). We retained only the pixels which were members of clusters counting a minimum number of activated pixels (typically 6) (

). In a second step, the cross-correlation coefficient of " " [START_REF] Forman | Improved assessment of significant activation in functional magnetic resonance imaging (fMRI): use of cluster-size threshold[END_REF] the average signal intensity within each cluster was determined. We kept only the clusters with an average cross-correlation coefficient above a second threshold (typically 0.5). The functional maps were obtained by superimposing the activated pixel clusters onto the " "

anatomical images derived from the 3D PC MR scan. The functional areas were identified in each subject on the basis of the Talairach atlas ( ). [START_REF] Talairach | Co-planar stereotaxic atlas of the human brain[END_REF] For the sake of presentation, the functional maps (corresponding to individual slices) were also combined into a single functional projection map. This projection map was obtained by superimposing the maximum intensity projections of the activation clusters onto averaged intensity projections of the corresponding anatomical images. The projections were performed perpendicularly to the individual image planes (projection maps thus were also oriented transversally). Following radiological practice, the left and right hemispheres are displayed on the right and left, respectively.

Results

A typical pattern of activation obtained with Experiment 1 is shown in (Subject S9). The four functional maps centered Figure 2 within this figure are from the central four slices (slices 2 5) of the volume explored. Positioning of this volume with respect to the calcarine sulcus is shown on the left, on a medio-sagittal scout MR image. For the sake of clarity, the calcarine sulcus has been manually darkened on this image. Relative positioning of the transverse images with respect to the antero-posterior direction may be appreciated by means of the reference levels drawn on the scout image and on the functional maps (dotted lines). The image on the right represents the functional projection map obtained from the four functional maps. We interpret the activation in and around the calcarine sulcus as representing areas V1 V2 and that located far laterally as corresponding to area V5, as documented in previous publications ( -

Goebel et al.

). A third cluster of activation has been detected in the GOm (Gyrus Occipitalis medius, i.e. Brodmann areas 18/19). This cluster was 1998 found within the slices 2 to 4 (positioned symetrically with respect to the AC-PC plane). It was centered approximately 20 mm posteriorly and medially to V5. Thus the cluster detected within GOm included part of area KO, Kinetic Occipital (

) and van Oostende et al. 1997 region LOS, Lateral Occipital Sulcus, (

). Henceforth, we identify this region as LOS/KO ( ). [START_REF] Sunaert | Motion-responsive regions of the human brain[END_REF][START_REF] Sunaert | Motion-responsive regions of the human brain[END_REF] The individual results obtained on subjects S1 S11 in response to the moving illusory contour perception are summarized in .

-Table 1 The number of pixels are presented which were found activated in the areas of interest, namely V1/V2, V5 and LOS/KO. Also, the mean cross-correlation coefficients in those areas are indicated. Functional responses were detected in V1/V2 and LOS/KO for all subjects, and in V5 in all but two subjects. The volume of the activated areas was on average 0.3 0.2 cm in V1/V2, 0.6 0.5 cm in LOS/KO and 0.2

± 3 ± 3 0.2 cm in V5. ± 3
The inter-individual variability in the functional responses from V1/V2 can be appreciated in which presents the activation in Figure 3 that region for six subjects (S4, S5, S7, S8, S10, and S11). The mean cross-correlation thresholds applied for producing these figures have been increased compared to those used for pixel counting ( ), so that only the strongest activations are shown. As with , Table 1 Figure 2 positioning of the transverse images with respect to the calcarine sulcus is indicated by a reference level in the antero-posterior direction.

In the two experiments performed on control subjects C1 and C2, we wanted to verify the location of the activations with respect to areas V1, V2 and V5 and to determine whether moving illusory contours activate the same regions as static illusory contours. Figure 4 shows the maps obtained for one of the two subjects (C1). The upper part of the figure (  ) shows the activities recorded in Figs. 4a c response to the static illusory contour ( ), to stimulation of the vertical meridian ( ) and to the moving illusory contour ( Fig. 4a Fig. 4b Fig. 4c ). The border between areas V1 is found in response to stimulation of the vertical meridian. On the basis of the activations displayed in , we thus have delineated V1 and the border areas V1 V2 in . The activations in clearly demonstrate, with Fig. 4b -Figs. 4a and4c Fig. 4c this subject, that the moving illusory contours activate cortical regions inside area V1. Although less strong, the activation during the perception of the static illusory contour is also present in area V1, near the border with V2 ( ). Similar results were obtained with Fig. 4a subject C2.

The region activated by the moving illusory contour nearby V5 is shown in , and may be compared with the activation Figure 4f resulting from expanding rings (

). This comparison demonstrates that moving illusory contours activate a region corresponding to Fig. 4e area V5 as well as some neighbouring areas. In addition, proper registration of the activities evoked by the moving illusory contours and the expanding rings within and around V5 was also tested and found in two other subjects (S3 and S4) among the 11 subjects having performed Experiment 1 only.

The results obtained for the 2 control subjects in response to moving (Experiment 1) and to static illusory contours (Experiment 2) are summarized in . Again, the number of pixels are presented which were found activated within the areas of interest namely V1/V2, Table 2 LOS/KO and V5, together with the mean cross-correlation coefficients in those areas. Activation was also found in the Cuneus, the Lingual Gyrus, the superior parietal gyrus and the Cerebellum. Note that the number of pixels and the cross correlation coefficients are larger for moving than for static illusory contours in areas V1/V2 as is also apparent in . The volume of the activated areas was on Figure 4 average 1.4 0.4 cm in V1/V2 and 0.4 0.2 cm in V5 for the moving illusory contours and 0.5 0.05 cm in V1/V2 for the static

± 3 ± 3 ± 3 illusory contours.

Discussion

The Experiment 1 performed on the eleven subjects S1 S11 has yielded functional responses to moving illusory contours within -V1/V2 (undifferentiated). The Experiment 2 performed on control subjects C1 and C2 has allowed us to refine the localization of these responses. The involvement of the primary visual area was clearly demonstrated. In addition, activations were found in a region containing area V5 and its satellites. Other activations were found in a region corresponding to LOS/KO ( ), probably included in [START_REF] Sunaert | Motion-responsive regions of the human brain[END_REF] the large area V3A as defined in (

). The region LOS/KO has been reported to respond to moving stimuli and kinetic [START_REF] Tootell | Functional analysis of V3A and related areas in human visual cortex[END_REF] contours ( ; ; , ). [START_REF] Orban | A motion area in human visual cortex[END_REF][START_REF] Reppas | Representation of motion boundaries in retinotopic human visual cortical areas[END_REF][START_REF] Van Oostende | The kinetic occipital (KO) region in man: an fMRI study[END_REF][START_REF] Sunaert | Motion-responsive regions of the human brain[END_REF] In Experiment 1, the stimuli presented during the reference and the stimulation epochs differed in the 45 tilt of the pacmen.

" " " " °A
, part of the activations detected could be ascribed to this mere difference. The continuous rotation of the pacmen in reference and priori

"

" "

stimulation epochs lowers the perception of this difference, however. Moreover, in the two experiments on the control subjects, pacmen " were tilted by only 10 and similar results were obtained. Since most cortical neurons respond similarly to orientations differing by 10 °degrees,

we therefore assume that the activations observed in Experiment 1 are not to be ascribed to a greater sensitivity to vertical and horizontal elements than to oblique ones.

Because the fixation task was the same during the reference and the stimulation epochs, it is also unlikely that the activations

" " " "
reported here result from differences in spatial attention. Artefactual activations due to eye movements appear unlikely since the subjects were instructed to report the dimming of the fixation spot, a task which is difficult to perform without precise fixation of the spot. From monkey studies, this task is known to provide an efficient means to stabilize the eye position ( ). There is motion [START_REF] Wurtz | Visual receptive fields of strate cortex neurons in awake monkeys[END_REF] correspondence between pacmen in the the stimulation epochs which is not perfectly matched in the reference epochs. Therefore, a " " " "

contribution from this effect to the activations detected may not be ruled out completely.

For all these reasons, we consider that the activations observed are due without ambiguity to the perception of moving illusory contours. The inter-subject variability observed ( ) may furthermore reflect functional and anatomic differences in visual areas Table 1 between subjects (

) and/or differences in the ability of the brain to perform perceptual grouping [START_REF] Hasnain | Intersubject variability of functional areas in the human visual cortex[END_REF] McCourt and Paulson, ). The volumes activated with the control subjects (

) were found larger than with the eleven subjects having performed only 1994

Table 2 Experiment 1 ( ). This may be ascribed partly to the larger cerebral volume explored with the control subjects and partly to the Table 1 difference in MR acquisition techniques used in these two series of experiments.

The additional control experiments demonstrate that moving illusory contours, in contrast to kinetic boundaries, activate area V5 and its satellites. Involvement of area V5 has been confirmed by the co-registration of the activity evoked by the moving illusory contours ( ) and that generated by an expanding set of concentric rings ( ), a stimulus known to activate area V5 and its surrounding Figure 4e Figure 4f areas ( ). Activation of that region is not surprising, given the strong perception of movement generated by the stimulus Tootell et al., 1995b and the fact that the V5 area has repeatedly been shown to be activated by real ( ; ; [START_REF] Zeki | A direct demonstration of functional specialization in human visual cortex[END_REF][START_REF] Watson | Area V5 of the human brain: evidence from a combined study using PET and MRI[END_REF]Tootell et al., 1995a ), by illusory ( ; ) and by apparent ( ) moving stimuli. Surprising in our results is that [START_REF] Zeki | Going beyond the information given: the relation of illusory visual motion to brain activity[END_REF]Tootell et al., 1995b[START_REF] Goebel | The constructive nature of vision: direct evidence from functional magnetic resonance imaging studies of apparent motion and motion imagery[END_REF] the activity in area V5 is often weaker (in terms of cross correlation coefficients) than in areas V1/V2 ( and ) and that it was Table 1 Table 2 not observed for all subjects ( ). Table 1 Activation in low level areas has been reported with static illusory contours (Kanizsa type) in two earlier studies, one using PET ( ) and one using fMRI (

). In their recent fMRI studies, do not rule out these [START_REF] Ffytche | Brain activity related to the perception of illusory contours[END_REF][START_REF] Hirsch | Illusory contours activate specific regions in human visual cortex: evidence from functional magnetic resonance imaging[END_REF][START_REF] Mendola | The representation of illusory and real contours in human cortical visual areas revealed by functional magnetic resonance imaging[END_REF] findings but they insist on the predominant activations obtained in high level cortical regions, including V3A, V4v, V7 and V8. The activation patterns obtained in our study show that moving as well as static illusory contours activate low-order retinotopically organized visual areas, especially V1. Involvement of area V1 during the perception of moving illusory contours is clearly shown in and Figures 2 3

where activations are located along the calcarine sulcus, the location of area V1 ( ; ). The activation of area [START_REF] Holmes | Disturbances of vision by cerebral lesions[END_REF][START_REF] Tootell | Functional analysis of primary visual cortex (V1) in humans[END_REF] V1 has furthermore been confirmed by the co-registration, for the two control subjects, of the activities evoked by a static illusory contour ( ), by the moving illusory contour ( ) and by the hourglass-shaped stimulus centered on the vertical meridian ( ), Figure 4a Figure 4c Figure 4b a stimulus known to activate neurons located at the frontier between areas V1 and V2 ( , ). Tootell et al. 1995a[START_REF] Engel | Retinotopic organisation in human visual cortex and the spatial precision of fMRI[END_REF] The patterns of activity obtained here differ from those reported by and by for static [START_REF] Hirsch | Illusory contours activate specific regions in human visual cortex: evidence from functional magnetic resonance imaging[END_REF] Ffytche and [START_REF] Ffytche | Brain activity related to the perception of illusory contours[END_REF] illusory contours. In these studies, the activations which were assigned to V2 ( ; ) and possibly to Hirsch et al., 1995 Ffytche andZeki, 1996 V3 ( ) were located more laterally than in our study. It could be argued that the area labeled LOS/KO in our data [START_REF] Ffytche | Brain activity related to the perception of illusory contours[END_REF] corresponds to the cortex assigned to V2 and/or V3 in these earlier reports. In contrast, the active area labeled V1/V2 in our results is located more medially and overlaps the calcarine sulcus in most instances ( , and ), thus including area V1. Figures 2 3 4

In their report on the regions activated by apparent motion of illusory contours, Goebel and his collaborators ( ) [START_REF] Goebel | The constructive nature of vision: direct evidence from functional magnetic resonance imaging studies of apparent motion and motion imagery[END_REF] observed a weak activation in V1, contrasting with a robust activity in V5. The discrepancy with our results is likely due to differences in the stimuli used. In their study the two illusory contours were positioned 9 apart, symetrically with respect to the vertical meridian, thus ° stimulating alternatively each hemisphere. We used a distance of 1.7 to separate the four positions of the illusory contours which °straddled the vertical meridian. The motion with our stimulus was less saccadic and it involved activation of regions representing the vertical meridian. In the study of Goebel and collaborators, apparent motion must involve neurons located in both hemispheres along the representation of the horizontal meridian. A difference in stimulus velocity, 3 /s in our study and 17 /s in Goebel s study, could also have °°' contributed to the stronger activation of V1 in our study. This interpretation is consistent with the findings of a recent fMRI study showing that the V1 activation decreases linearly as speed increases during the perception of real motion ( ). In preliminary [START_REF] Chawla | Speed-dependent motion sensitive responses in V5: an FMRI study[END_REF] measurements, we have also observed that the activation within V1 is stronger with 3 /s than with 10 /s. °°With static illusory contours, V1 activation was not observed with PET (

), but was not entirely dismissed with Ffytche and Zeki, 1996 fMRI ( ;). Our results (see ) on the two subjects tested with the static illusory contours [START_REF] Hirsch | Illusory contours activate specific regions in human visual cortex: evidence from functional magnetic resonance imaging[END_REF][START_REF] Mendola | The representation of illusory and real contours in human cortical visual areas revealed by functional magnetic resonance imaging[END_REF] Table 2 confirm that area V1 is activated by these stimuli but suggest that the activation by moving illusory contours is stronger than with static illusory stimuli. Thus, animation such as 4Hz flickering (

), reversal of contrast polarity ( ) or [START_REF] Hirsch | Illusory contours activate specific regions in human visual cortex: evidence from functional magnetic resonance imaging[END_REF][START_REF] Mendola | The representation of illusory and real contours in human cortical visual areas revealed by functional magnetic resonance imaging[END_REF] movement seems to enhance activation in V1.

The detection of activations in low order visual areas for static as well as for moving illusory contours suggests that perceptual grouping involves neural processing in these areas. This is consistent with the results of animal studies showing activations in areas V1 and V2 by illusory contours ( ; ; ; ; ; von der [START_REF] Der Heydt | Illusory contours and cortical neuron responses[END_REF][START_REF] Redies | Neuronal responses to borders with and without luminance gradients in cat visual cortex[END_REF][START_REF] Grosof | Macaque V1 neurons can signal illusory contours[END_REF]Shapley 1994Sheth, et al., 1996 Baumann et ; ). Moreover, activation of the primary visual cortex with Kanisza-type illusory contours is in keeping with al., 1997 [START_REF] Leventhal | Neural correlates of boundary perception[END_REF] results from psychophysical studies that argue for local mechanisms in the perception of such figures ( ; [START_REF] Dresp | Psychophysical evidence for low-level processing of illusory contours and surfaces in the Kanizsa square[END_REF] ) and with a recent report of perception of illusory contours in patients with spatial neglect ( Bonnet, 1993 [START_REF] Davis | Parallel detection of Kanizsa subjective figures in the human visual system[END_REF] ). [START_REF] Vuilleumier | Illusory contours and spatial neglect[END_REF] The observation of activity in area V1 due to illusory stimuli is of particular interest in the context of the debate concerning the cortical regions activated by mental images, with several reports claiming that only areas outside area V1 are activated ( ; Roland and Gulyas, 1994 ; ; ), while others report evidence that area V1 is involved in visual imagery ( D [START_REF] Esposito | A functional MRI study of mental image generation[END_REF] ' [START_REF] Mellet | Cortical anatomy of mental imagery of concrete nouns based on their dictionary definition[END_REF][START_REF] Braun | Dissociated pattern of activity in visual cortices and their projections during human rapid eye movement sleep[END_REF] ; , ). Although perception related to illusory contours differs from [START_REF] Kosslyn | Visual mental imagery activates topographically organized visual cortex: PET investigations[END_REF][START_REF] Bihan | Activation of human primary visual cortex during visual recall: a magnetic resonance imaging study[END_REF][START_REF] Kosslyn | Topographical representations of mental images in primary visual cortex[END_REF][START_REF] Chen | Human primary visual cortex and lateral geniculate nucleus activation during visual imagery[END_REF] mental imagery, the strong activation of area V1 by moving illusory contours in our results is in keeping with the idea that low-order visual areas are activated by high-order processes such as visual imagery or illusory perception. These results suggest that V1 is a distributing center, rather than simply a spatially transformed replication of the retina (

). [START_REF] Zeki | The functional logic of cortico-cortical connections[END_REF] In conclusion, these fMRI results provide additional ground to the hypothesis that low-level processes are involved in perceptual grouping and in illusory contour perception. This supports the idea that visual information processing is a cooperative task distributed over several interconnected brain modules (

). Whether such activity is generated through local computations involving [START_REF] Bullier | Parallel versus serial processing: new vistas on the distributed organization of the visual system[END_REF] horizontal connections or whether they require feedback input ( ) from higher order areas remains a subject for future Hup et al., 1998 é investigation. " "

The pacmen are titled with respect to the " stimulation epochs in order to avoid the perception of illusory edges. All the pacmen are animated with a rotational movement. A small white " circle at low contrast served as a fixation mark.

Figure 2

Typical functional map obtained in response to the moving illusory contours (subject S9).

. Scout image in the sagittal plane. The position Left of the volume (6 slices) acquired during the functional scans has been delineated. For the sake of clarity, the calcarine sulcus has been manually darkened.

r. Four functional maps corresponding to slices 2 to 5. The color code represents the cross-correlation value of the Cente voxels (red for 0.8 and 0.5 for green). The dashed line on the functional maps represents the intersection of the image planes with the coronal plane represented by the dashed line on the scout image.

. Projection map corresponding to the four functional maps shown in the center. Right

Figure 3

Functional projection maps obtained in response to the moving illusory contours for six subjects (S4, S5, S7, S8, S10 and S11). Top and . Scout images in the sagittal plane for each of the six subjects. The positioning of the volume acquired during the functional scans has bottom been delinated. For the sake of clarity, the calcarine sulcus has been manually darkened.

. The functional projection maps obtained for Center each subject. Those projection maps were obtained by projecting the functional maps corresponding to slices 2 to 5. The dashed line on the functional projection maps represents the intersection of these maps with the coronal plane represented by the dashed line on the corresponding scout image.

Figure 4

Functional projection maps for the control subject C1. The upper part of the figure (Fig. 4a c) shows the activations recorded in response to the static illusory contour (Fig. 4a), to the hourglass-shaped stimulus aimed at delineating the border between areas V1 and V2 (Fig. 4b) and to the moving illusory contours (Fig. 4c). These maps represent a projection of two coronal slices (4 5).

  was repeated 4 times (total measurement time about 9 min). Presentation time of the transition screen was about 15 sec. The functional scans applied a conventional gradient-recalled echo (GRE) MR sequence. The major parameters of this sequence were: TR 80 ms, TE 40 ms, acquisition matrix 45 64, FOV 154 220 mm , flip bandwidth per pixel 14 Hz, acquisition time per slice 2.45 sec, reconstruction matrix 128 128. For the experiments = °= = = × performed with the two control subjects (C1 and C2), a single shot EPI GRE MR sequence was used. The major parameters of this sequence were: TR 2s, TE 50 ms, acquisition matrix 64 64, FOV 192 192 mm , flip angle 80 , reconstruction matrix 64 64. The

Figure 1

 1 Figure 1 Figure 1-a. Stimuli presented during the stimulation epochs.

  shown. The arrow indicates the direction of the succession of the frames. The saccadic rotation of the pacmen provokes the illusion of a downward motion of the illusory rectangle. A small white circle at low contrast served as a fixation mark. Figure1-b. Stimuli presented during the reference epochs.

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  The position of the volume (8 slices) acquired during the functional scans has been delineated on the scout image in the sagittal plane (Fig.4d). For the sake of clarity, the calcarine sulcus has been manually darkened. The activations induced by the moving illusory contour near the V5 region are shown in Fig.4f. The activations induced by expanding rings is shown in Fig. 4e. Figs. 4e and 4f represent the projection maps obtained from three coronal slices (1 3) -

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Ackowledgements:

M. Seghier has a PhD grant from the French Ministry of Research and Technology. We are grateful to C. Icardo who participated to preliminary experiments. Financial support from the Groupement d Int r t Scientifique Sciences de la Cognition (1995) and from the