**A New Hydrostatic Leveling System**

**Developed for the**

**Advanced Photon Source**[^1]

*Lassi A. Kivioja, Horst Friedsam, Merrick Penicka*

*Argonne National Laboratory, Argonne, Illinois, USA*

**1. INTRODUCTION**

![](media/image1.png)

All hydrostatic level systems (HLSs) use water or some other liquid to
provide an absolute elevation reference for measuring elevation changes.
Usually several measurement stations are inter­connected with tubes
providing a path for the liquid between individual vessels. Existing
HLSs differ mainly in the measurement concept used to detect changes in
the liquid level, which is equivalent to measuring the elevation change
of a particular vessel. Depending on the required accuracy, ultrasonic
sensors, touch probes, and capacitive sensors are used to record these
changes. In this paper a new method of measuring and recording the
changes of a liquid surface is proposed. In this case the free upper
surface of a liquid is used as an optical reflector (Fig. 1).

Common distilled water is used to provide an absolute reference system
for detecting elevation changes at each vessel location. In order to
measure these changes, a thin laser beam is sent into the water-filled
container through an optical window. After a total reflection from the
upper free liquid surface, the laser light produces a spot on a linear
optical position sensor (OPS) mounted at the bottom of the container.
When the liquid level changes, the reflected light beam moves to another
position on the sensor. Changes in liquid levels can be measured with an
accuracy better than 1 micron. Some prototypes using this schema were
built and tested at Argonne for the Advanced Photon Source (APS).

Usually two or more hydrostatic level vessels are interconnected by
water and air tubes. Once the system has been filled with liquid, the
water surface will come to an equilibrium parallel to the equipotential
surface of the local geoid in accordance with Archimedes' rule. In order
to eliminate the effects of trapped air in each vessel, all hydrostatic
level containers have been interconnected with air tubes providing the
same air pressure to all vessels. The distilled water is usually treated
with chemicals to prevent the growth of fungi and algae during the
operation of the system.

**2. HLS PROTOTYPES**

Development of this new type of hydrostatic leveling system started at
Argonne National Laboratories in May 1992. Working prototype units
became available for testing and calibration in April 1993.

**2.1 Liquid containers**

This system consists of liquid containers that are interconnected by
almost horizontal water tubes filled with distilled water such that the
water depth is almost the same in all vessels. For test purposes the
containers can be individually raised or lowered and leveled to achieve
this configuration (Fig. 2). In order to assure that the water surface
in each container is experiencing the same gas pressure, the gas volume
above the water in each container is interconnected to the adjacent
vessels using gas tubes. Under these conditions the center of the upper
free water surface in each container is a part of the same equipotential
surface, or surface of constant dynamic height, if the density of the
water is the same in all containers. Because the density of water
depends on its temperature, a thermocouple is placed into a horizontal
hole drilled from the edge of the bottom plate to the center just under
the bottom of water in each container (Fig. 3). Using this temperature
information, the water level in each container can be corrected as
necessary. It is well known that the thermal coefficient of expansion of
water is 0.0002 per 1° Celsius at 20° Celsius. This results in a change
of 2 µm per one 1° Celsius for a water column with a depth of 1 cm.
Similarly, the volume change of the container must also be considered
together with temperature changes for very accurate measurements.

![](media/image4.png){width="3.1847222222222222in"
height="4.4944444444444445in"}**2.2 Height measurement of the liquid
level**

The height of the upper free surface of water is measured in each
container by a light-sensitive optical position sensor (OPS). These
sensors are also available in versions that can function in high-UV
environments and nuclear power plants. A stable, parallel beam of light,
emanating, for instance, from a low power (1 to 2 mW) diode laser,
enters the water through a waterproof optical window and travels through
the water toward the water-air interface at a vertical angle of 40
degrees above the horizon (Fig. 2). The laser beam forms an angle of 50
degrees with the surface normal of the water. Because this angle is
greater than the critical angle of 48.8 degrees for the water-to-air
interface, a total reflection of the laser beam takes place. The laser
beam is reflected back through the water onto the OPS, where it produces
a voltage corresponding to the spot location. The OPS is covered with a
thin glass plate and, therefore, not all of the incident light is
absorbed. Instead, some of the laser light is reflected back into the
water and to the container walls. These multiple reflections are
undesirable for this application because multiple spots could be created
on the OPS, resulting in false readings of the actual elevation change.

The length of the sensitive surface of the OPS in this design is 30 mm.
If the water level increases by one millimeter in elevation, the
reflected spot on the sensor travels an additional 2.3835 mm. The depth
of the water over the sensor is approximately 18 mm when the light beam
strikes the center of the sensor. The water depth is approximately 12 mm
when the light beam strikes the near end of the sensor, and
approximately 24 mm when the light beam strikes the far end of the
sensor. Therefore, the maximum operating range in this design for
measuring the water level is approximately 12 mm. Other operating ranges
are possible by suitably choosing the angle of reflection, length of the
OPS, and the size of the container.

Depending on the chosen voltage range of the OPS, the 12-mm change in
the water level produces a measurable voltage range of 20 V or 15 V,
respectively, when the reflected light beam travels from one end of the
sensor to the other end. A good operational range for the water depth in
this design is between 21 and 15 millimeters, which corresponds to a
travel range of ±7.5 mm of the 30-mm sensor surface, starting at the
midpoint.

The manufacturer of these sensors claims that the sensors have a
submicron accuracy for sensing the position of the light spot where the
laser beam strikes the sensor. They also claim that should the light
beam intensity, wavelength, or the spot size vary, the normalized output
of the OPS will remain constant. This is a very important and
advantageous property of this OPS. It means that a constant water level
can be maintained even if the intensity, wavelength, or spot size of the
laser source shows slight variations.

Finally, it is important that the chosen 40-degree angle in this design
stays constant for each vessel. However, this angle may vary slightly
but cannot exceed 41.2 degrees because of the requirements for obtaining
total reflection. Small deviations from 40 degrees will cause a slightly
different calibration value for each leveling unit, which will be
determined during the calibration process.

**3. CALIBRATION**

Several methods for calibrating an HLS vessel have been developed and
tested for this system. The following sections describe some of these
methods in detail.

**3.1 Calibration using a micrometer probe**

A micrometer touch probe has been successfully used in other HLS designs
to measure the elevation of the water column in individual vessels.
Although this prototype design accommodated a micrometer probe, this
method was not used for calibration purposes. It could have provided
another check for the results of the other calibration methods.

**3.2. Calibration by a controlled elevation change of one vessel in a
system of two units**

The three leveling screws on the containers in this design are actually
standard micrometer screws (Fig. 1). One full turn of the micrometer
screw results in a change of elevation of 1.27 mm. These micrometers can
be used to level a vessel or to raise or lower a unit by an exact
amount.

For example, consider that two identical vessels, A and B, are properly
interconnected by water and air tubes. The laser beam in the prototype
units will produce a spot near the center of the sensor if the water
depth over the sensor is 18 mm for each unit. From this position, raise
or lower one of the units 1.27 mm using its three micrometer screws.
Raising unit A will cause some of the water to flow from A to the
stationary identical unit B until the water levels are equal in both
units. Theoretically the water depth will decrease by 0.635 mm in A
while it increases by the same amount in B. Water depths are then 17.365
mm in A and 18.635 mm in B. In unit A, the reflected spot of the laser
beam travels 1.514 mm in one direction from the center location while in
unit B the reflected laser spot travels the same distance in the
opposite direction. For the 30-mm-long 20-V sensor, this produces a
calculated voltage change over the 1.514-mm distance along the sensor of
1.009 V (1.514 \[mm\] x 20/30 \[V/mm\]). This same voltage change also
applies for the actual water level change of 0.635 mm, which gives 1.589
V/mm for the 0.635-mm water level change in units A and B. Similarly,
the 15-V sensor produces a voltage change of 1.192 V/mm in the water
level. If the angle at which the laser beam enters the liquid is not
exactly 40 degrees, these numbers will change.

In a preliminary calibration performed in June 1993, unit A was raised
in eight successive 0.635-mm increments for a total of 5.08 mm, then
lowered by four 1.270-mm increments to return to the starting level.
Then the unit was lowered by eight successive 0.635-mm increments and
finally raised by four 1.270-mm increments to arrive at its original
elevation. The corresponding voltages of the optical position sensors
for units A and B were read after each incremental change. Unit A was
thus moved up and down over a total range of 10.16 mm, and its water
level changed over a total range of 5.08 mm, first down by 2.54 mm and
then finally up by 2.54 mm. When the water level went down in A, it went
up in B by the same amount, and vice versa. Once the readings had
stabilized after each incremental change in elevation of unit A, the
voltmeters were read and recorded. In more elaborate calibrations, and
also in actual usage, vibrations of the ground and the support system
affected the water level. Therefore, an average of a few hundred voltage
readings over a period of time should be used to represent the best
reading.

The entire procedure of calibrating these two units took about 34
minutes. The calibration values of the voltmeter Fluke 97 were not
known. Unit A was found to produce 1.17 ± 0.02 mV/µm for the water level
changes, and unit B 1.32 ± 0.02 mV/µm. As mentioned earlier, the angle
at which the laser light enters the liquid may not have been exactly 40
degrees and could be the cause for the difference in the scale values
for the two units.

More than two units can be calibrated by this method of raising and
lowering one unit by a known amount s. If there are n units and one of
the units is raised by a distance s, its water level goes down by
s(n-l)/n while the water level in each of the other units rises by s/n.
There are other somewhat similar calibration methods. For instance, one
unit could be raised and another unit could be lowered by the same
amount. In this case, the remaining units should display their same
original elevations when the water level has stabilized after this
disturbance.

**3.3 Calibration using an auxiliary water reservoir**

Another calibration method for a large number of vessels is the use of a
reservoir with a known volume containing the same liquid as the HLS and
connected to the closed system via a valve. This reservoir is placed on
a platform that can be leveled, raised, and lowered so that its free
upper water surface is at the same elevation as the water level in all
the leveling units. This reservoir could be installed outside of the
accelerator housing, providing easy access for monitoring and
calibration purposes even during machine operation times.

The size of the reservoir to serve, for example, 200 of the described
prototype units with water containers 8 cm in diameter should be such
that 10 liters of water can flow out of or back into the reservoir. This
volume of reservoir would be more than enough to calibrate all leveling
units over ± 10 mm water depth changes starting from the center position
of the laser beam on the OPS of each leveling unit. Recording the
voltage output of all sensors in the system will produce data that can
be used to calibrate all leveling units at once.

**3.4 Calibration by adding a known amount of water**

As previously mentioned, the diameter of each prototype container is 8
cm. Adding one cubic centimeter of water to a single container raises
the water level by 0.1989 mm. Adding one cubic centimeter of water to
two interconnected vessels raises the water level by 0.0995 mm in both
containers. For example, if the system contains 200 units, adding one
cubic centimeter of water raises the water level in each vessel by 0.995
µm. Consequently, a 10-liter reservoir provides a water level elevation
changes of 9.95 mm per unit. This method provides the means to calibrate
all vessels at once, given that the volume of the reservoir can be
controlled and that all vessels are stable during the calibration
process.

**4. CONCLUSION**

As a result of the calibration tests performed with the first prototype
units using the new measurement principle, we believe that the described
leveling method is stable and accurate to the micron level with a
sufficiently large range for the expected elevation changes of the
support girders used in the APS storage ring. Although long-term studies
with this system have not been conducted, we believe that after
installation this system requires little or no servicing for long
periods of time. The methods described in this paper cover only the
elevation changes of individual vessels. However, changes in the tilt of
a girder must also be known. Therefore, a combination of tiltmeters in
conjunction with this HLS would be most suitable for measuring the tilt
and elevation changes of the APS girders.

[^1]: ^^ Work supported by U.S. DOE, Office of Basic Energy Sciences
    under Contract No. W-31-109-ENG-38.