A Flow Measurement Orientation
  The Flow Pioneers
  Flow Sensor Selection
  Accuracy vs. Repeatability

Differential Pressure Flowmeters
  Primary Element Options
  Pitot Tubes
  Variable Area Flowmeters

Mechanical Flowmeters
  Positive Displacement   Flowmeters
  Turbine Flowmeters
  Other Rotary Flowmeters

Electronic Flowmeters
  Magnetic Flowmeters
  Vortex Flowmeters
  Ultrasonic Flowmeters

Mass Flowmeters
  Coriolis Mass Flowmeters
  Thermal Mass Flowmeters
  Hot-Wire Anemometers

A Level Measurement Orientation
  Level Sensor Selection
  Boiling & Cryogenic Fluids
  Sludge, Foam, & Molten   Metals

Pressure/Density Level Instrumentation
  Dry & Wet Leg Designs
  Bubbler Tubes
  Floats & Displacers

RF/Capacitance Level Instrumentation
  Theory of Operation
  Probe Designs
  Installation Considerations

Radiation-Based Level Instrumentation
  Radar & Microwave
  Ultrasonic Level Gages
  Nuclear Level Gages

Specialty Level Switches
  Thermal Switches
  Vibrating Switches
  Optical Switches

  About OMEGA
  Information Resources

  Radiation-Based Level Gages

An entire class of level instrumentation devices is based on a material's tendency to reflect or absorb radiation. For continuous level gages, the most common types of radiation used are radar/microwave, ultrasonic, and nuclear. Optical electromagnetic radiation also can be used, but this has found its way primarily into the

Figure 9-1: Click on figure to enlarge.

point-switch applications discussed in the next chapter.

The main advantage of a radiation-based level gage is the absence of moving parts and the ability to detect level without making physical contact with the process fluid. Because they can in effect "see" through solid tank walls, nuclear radiation gages are perhaps the ultimate in non-contact sensing. Because they require a gamma radiation source and are relatively expensive, however, nuclear gages are often considered the level gage of last resort.

Radar & Microwave

In 1925, A. Hoyt Taylor and Leo Young of the U.S. Navy used radar (RAdio Detection And Ranging) to measure the height of the earth's ionosphere. By 1934, they were developing radar for Navy ships. In 1935, Robert Watson-Watt of England used radar to detect aircraft. The first radar level sensors were introduced in 1976, but they did not become economically competitive until a decade later.

Both radar signals and microwaves travel at the speed of light, but are distinguished by their frequencies (FM radio broadcast frequency is from 88 to 108 MHz, while microwaves range from 1-300 GHz) and by their power levels (radar is around 0.01 mW/cm2, while microwaves range from 0.1-5 mW/cm2). Because microwaves operate at a higher energy level, they can withstand more coating than can radar-type sensors.

Radar sensors consist of a transmitter, an antenna, a receiver with signal processor, and an operator interface. The transmitter is mounted on top of the vessel. Its solid-state oscillator sends out an electromagnetic wave (using a selected carrier frequency and waveform) aimed downward at the surface of the process fluid in the tank. The frequency used is typically 10 GHz.

The signal is radiated by a parabolic dish or horn-type antenna (Figure 9-1A) toward the surface of the process liquid (Figure 1B). A portion is reflected back to the antenna, where it is collected and routed to the receiver. Here, a microprocessor calculates the time of flight and calculates the level. Time of flight is the period between the transmission of the radar pulse and the reception of the return echo. It is determined by the radar detector, which is simultaneously exposed to both the sent and the reflected signal. The detector output is based on the difference. The frequency-modulated (FM) signal varies from 0 to 200 Hz as the distance to the process fluid surface varies between 0 and 200 ft. Because this measurement takes place in the frequency domain, it is reasonably free of noise interference.

The depth of the vapor space (the distance between the datum point and the level in the tank, identified as "d" in Figure 9-1B) is calculated from the time of flight (t) and the speed of light (c = 186,000 miles/sec):

The level (L in Figure 9-1B) is calculated by figuring the difference between the total tank height (E) and the vapor space depth (d):

Knowing the signal velocity (c) and the dielectric constant (dc) of the vapor (that is, the relative ability of the vapor to oppose and reflect electromagnetic waves), the velocity of the radar wave transmission (V) can be calculated:

Antenna Designs and Mounting

The two commonly used antennas are the horn and the parabolic dish antenna. When the radar level gage sends out its signal, the microwaves spread out. The larger the antenna diameter, the smaller the divergence angle and the greater the signal strength (Figure 9-1A). The disadvantages of smaller antennas include higher beam spreading and the correspondingly increased possibility of reflection from obstacles within the tank. On the positive side, there is a greater chance that the emitted beam will be reflected back to the detector. Therefore, alignment of the sensor is not as critical.

Large antennas generate a more focused signal, helping to eliminate noise interference from flat and horizontal metal surfaces. On the other hand, they are more prone to errors caused by unwanted reflections from turbulent or sloping surfaces. A fully isolated antenna mounted outside the tank (Figures 9-2 and 9-4) provides both sealing and thermal isolation. If the antenna is positioned below the process seal, it is exposed to the process vapors, but gains the advantages of stronger signal amplitudes and suitability for higher operating pressures.

Contact & Non-Contact Radar

Non-contact radar gages either use pulsed radar waves or frequency-modulated continuous waves (FMCW). In the first, short-duration radar pulses are transmitted and the target distance is calculated using the transit time. The FMCW sensor sends out continuous frequency-modulated signals, usually in successive (linear) ramps. The frequency

Figure 9-2: Click on figure to enlarge.

difference caused by the time delay between transmittal and reception indicates the distance.

Radar beams can penetrate plastic and fiberglass; therefore, non-contact radar gages can be isolated from the process vapors by a seal. The seal can be above the parabolic disc (Figure 9-1A) or can totally isolate the sensor (Figure 9-2A). The beam's low power allows for safe installation in both metallic and non-metallic vessels. Radar sensors can be used when the process materials are flammable or dirty and when the composition or temperature of the vapor space varies.

Contact radar gages send a pulse down a wire to the vapor-liquid interface. There, a sudden change in the dielectric constant causes the signal to be partially reflected. The time-of-flight is then measured (Figure 9-2B). The unreflected portion travels on to the end of the probe and provides a zero-level reference signal. Contact radar technology can be used on liquids and on small-grained bulk solids with up to 20-mm grain size.

Reflection-type microwave switches measure the change in amplitude of a reflected signal (Figure 9-3A). Air and vapors return a small percentage of the signal because of their low dielectric constants, while high dielectric materials such as water return almost all the signal. More sensitive switches can distinguish liquid-liquid or liquid-solid interfaces having as little as 0.1 difference in dielectric constant. Low dielectric materials like plastic pellets (dielectric 1.1) can be measured if the particle diameter is less than 0.1 in (larger than that, excessive beam scattering occurs).

The beam-breaker switch sends a microwave beam from a transmitter to a receiver located on the opposite side of the tank. When the beam is blocked, the signal is weakened (Figure 9-3B). Beam-breaker alignment is not critical, and separation distance can be up to 100 ft.

Both reflection and beam-breaker microwave switches are typically used in applications where it is desirable not to penetrate the tank. These non-intrusive sensors send electromagnetic radio waves through plastic, ceramic or glass windows, or through fiberglass or plastic tank walls.

Advantages & Limitations

The reflective properties of the process material affect the returned radar signal strength. Whereas liquids have good reflectivity characteristics, solids do not. Radar can detect the liquid level under a layer of light dust or airy foam, but if the dust particle size increases, or if the foam or dust gets thick, it will no longer detect the liquid level. Instead, the level of the foam or dust will be measured.

Internal piping, deposits on the antenna, multiple reflections, or reflections from the wall can all interfere with the proper operation of a radar sensor. Other sources of interference are rat-holing and bridging of solids, as well as angled process

Figure 9-3: Click on figure to enlarge.

material surfaces that can reflect the radar beam away from the receiver.

In comparison to other radiation reflection sensors, radar has some advantages. For example, ultrasonic sensors are affected by the composition of the vapor space. On the other hand, ultrasonic sensors perform better in dirty applications, or with solids when the grain size is larger than 20 mm.

Ultrasonic Level Gages

The origin of ultrasonic level instrumentation goes back to the echometers used in measuring the depth of wells by firing a blank shell and timing the return of the echo. SONAR detectors used in naval navigation also predate industrial applications of this principle.

The frequency range of audible sound is 9-10 kHz, slightly below the 20-45 kHz range used by industrial level gages. The velocity of an ultrasonic pulse varies with both the substance through which it travels and with the temperature of that substance. This means that if the speed of sound is to be used in measuring a level (distance or position), the substance through which it travels must be well known and its temperature variations must be measured and compensated for.

At room temperature, the speed of sound in atmospheric air is 340 m/s or 762 mph. At that same temperature, an ultrasonic pulse travels through water at 1,496 m/s or 3,353 mph. If the air is heated to 100°C, the speed of sound rises to 386 m/s. Indeed, the speed of sound is proportional to the square root of temperature. At near ambient temperatures, the speed rises by 0.6 m/s per each 1°C increase, corresponding to an increase of 0.18%/°C.

Ultrasonic level switches (point sensors) operate by detecting either dampening of ultrasonic oscillation or by sensing the absorption or transmission of an ultrasonic pulse. Ultrasonic level transmitters measure actual distance by issuing an ultrasonic pulse and measuring the time required for the reflected echo to be received.

Ultrasonic Transducers

The transducer that generates the ultrasonic pulse is usually piezoelectric, although in the past electrostatic units also were used. An electrostatic transducer is constructed of a thin, flexible gold-plated plastic foil, stretched over an aluminum back-plate and held in place by a leaf spring. This design was used in early Polaroid auto-focus cameras and is still utilized in clean environments. Piezoelectric transducers utilize

Figure 9-4: Click on figure to enlarge.

ceramic or polymer crystals vibrated at their natural frequency. These units are much more rugged, can withstand wash-down pressures of 1,200 psig and can conform to NEMA-6P (IEC IP67) standards.

Figure 9-5: Click on figure to enlarge.

Generally, the larger the diameter of the transducer, the longer the range and the lower the frequency. This is because, after releasing an ultrasonic pulse, the transducer needs time for the vibration to settle. The oscillation frequency is inversely proportional to the element's diameter, so smaller diameter transducer elements generate higher frequencies. Standard transducers have a beam angle of about 8°, require a connection size between in and 2.5 in NPT, and are suited for operating temperatures in the range of -20 to 60°C (-30 to 140°F). Accuracy is typically within 0.25-0.5% of full range, up to about 30 ft. Output typically is 4-20 mA with a 12-amp relay output.

Level Transmitter Configurations

The ultrasonic level sensor assembly can consist of separate transmitter and receiver elements (Figure 9-4A). Most often, however, a single transducer is cycled on and off at regular intervals to listen for the reflected echo (Figure 9-4A). When mounted on the top of the tank, the sensor detects the depth of the vapor space. Accurate knowledge of the shape of the tank's cross-section is required in order to determine the volume of liquid.

If it is desired to measure the height of the liquid column directly, the transducer can be mounted in the bottom of the tank (Figure 9-4A). However, this configuration exposes the transducer to the process fluid and limits accessibility for maintenance. Alternately, the transducer can be mounted on the outside of the wall of the vessel bottom, but the ultrasonic pulse is likely to be substantially weakened by the absorbing and dispersing effects of the tank wall (Figure 9-4A).

Stagnant, unagitated liquids and solids consisting of large and hard particles are good reflectors, and therefore good candidates for ultrasonic level measurement. Fluff, foam, and loose dirt are poor reflectors, and dust, mist, or humidity in the vapor space tend to absorb the ultrasonic pulse. The ultrasonic signal also is attenuated by distance. If a 44-kHz sound wave is traveling in dry, clean ambient air, its sound power drops by 1-3 decibels (dB) for each meter of distance traveled. Therefore it is important, particularly when measuring greater depths, that the transducers generate a strong and well-focused ultrasonic pulse (Figure 9-4B).

It is also desirable that the surface be both flat and perpendicular to the sound wave. In liquid-level applications, the aiming angle must be within 2 degrees of the vertical. If the surface is agitated or sloping (as in the case of solids), the echo is likely to be dispersed. Therefore, the key to

Figure 9-6: Click on figure to enlarge.

successful ultrasonic level sensor installations is the careful analysis of the reflection, propagation, and absorption characteristics of the tank's contents.

When detecting the interface between two liquids, such as the hydrocarbon/brine interface in a salt dome storage well, the transducer is lowered down to the bottom of the well. The ultrasonic pulse is sent up through the heavy brine layer to the interface. The time it takes for the echo to return is an indication of the location of the interface (Figure 9-4C).

Special Features

Most modern ultrasonic instruments include temperature compensation, filters for data processing and response time, and some even provide self-calibration. Figure 9-5 illustrates a fixed target assembly that provides a point reference to automatically recalibrate the level sensor. Multiple calibration targets can be provided by calibration ridges in sounding pipes. This can guarantee measurement accuracy of within 5 mm over a distance of 30 meters.

Intelligent units can perform automatic self-calibration or convert the level in spherical, irregular, or horizontal cylindrical tanks into actual volume. They can also be used in multi-tank or multi-silo installations, which, through multiplexing, can reduce the unit costs of obtaining level measurements.

Level Switches

When it is sufficient to detect the presence or absence of level at a particular elevation, dampened or absorption-type level switches can be considered. In the dampened design, a piezoelectric crystal vibrates the sensor face at its resonant frequency. The vibration is dampened when the probe face is submerged in process fluid. As shown in Figure 9-3A, these switches can be mounted outside or inside the tank, above or below the liquid level. The probe can be horizontal or vertical. These switches are limited to clean liquid installations because coating can dampen the vibration. Solids may not provide sufficient dampening effects to actuate the switch.

In the absorption-type level switch, one piezoelectric crystal serves as a transmitter and another as the receiver. When the gap between them is filled with liquid, the sonic wave passes from one crystal to the other. When vapors fill the gap, however, the ultrasonic pulse does not reach the

Figure 9-7: Click on figure to enlarge.

receiver. The crystals can be mounted on opposite sides of the tank, contained in the fingers of a fork-shaped sensor, or located on the two sides of one or more 0.5-in gaps in a horizontal or vertical probe. When the process fluid is a sludge or slurry, it is desirable to provide a large gap between the transmitter and receiver in order to make sure that sticky or coating fluids will drain completely from the gap when the level drops.

Typical accuracy of these switches is 1/2-in or better. Connection size is 3/4-in NPT. Operating temperature range is 40-90°C (100 to 195°F) (with special units capable of readings up to 400°C/750°F) and operating pressure to 1000 psig. Standard output is a 5 or 10 amp double-pole/double-throw (DPDT) relay, but voltage and current outputs are also used.

The presence or absence of an interface between clean liquids can be measured by inserting an absorption (gap) probe at a 10° angle below the horizontal. In this configuration, as long as the probe is immersed in the heavy or light liquid, the ultrasonic pulse will reach the receiver. When the interface moves into the gap, however, it is reflected away and does not reach the receiver.

When a sludge or slurry interface is to be detected or when the thickness of the light layer is of interest, an ultrasonic gap sensor can be attached to a float. As long as the absorption characteristics of the two layers differ, the sensor will signal if the layer is thicker or thinner than desired.

Nuclear Level Sensors

In 1898 Marie Curie discovered radium by observing that certain elements naturally emit energy. She named these emissions gamma rays. Gamma rays exhibited mysterious properties--they could pass through a seemingly solid, impenetrable mass of matter. In the passage, however, the gamma rays lost some of their intensity. The rays were predictably affected by the specific gravity and total thickness of the object, and by the distance between the gamma ray source and the detector.

For example, Figure 9-6 shows that, if radiation from Cesium 137 is passing through an 3-in thick steel object, 92% of the radiation energy will be absorbed and only 8% will be transmitted. Therefore, if the observer can hold all variables except thickness constant, the amount of gamma transmission can be used to measure the thickness of the object. Assuming that the distance between the source and detector does not change, one can make accurate measurements of either thickness (level), or, if thickness is fixed, then of the density of a process material.

Radiation Sources

The development of nuclear level sensors began when this technology moved from the lab to the industrial environment. This necessitated the design and manufacture of suitable detectors and the mass production of radioisotopes. Both occurred in the 1950s.

The penetrating power of nuclear radiation is identified by its photon energy, expressed in electron volts (eV) and related to wavelength (Figure 9-7). The most common isotope used for level measurement is Cesium 137, which has a photon energy level of 0.56 MeV. Another isotope that is occasionally used is Cobalt 60, which has an energy level of 1.33 MeV. While the greater penetrating power of this higher energy radiation appears attractive at first, the penalty is that it also has a shorter half-life. As any isotope decays, it loses strength--the time it takes to lose half of its strength is called its half-life.

The half-life of Cobalt 60 is 5.3 years. This means that, in 5.3 years, the activity of a 100 millicurie (mCi) Cobalt 60 source will be reduced to 50 mCi. (One mCi is defined as the rate of activity of one milligram of Radium 226.) When used for level measurement, the continuous loss of source strength requires not only continuous compensation, but, eventually (in the case of Cobalt 60, in about 5 years), the source must be replaced. This means not only the expense of purchasing a new source, but also the cost of disposing of the old one.

In contrast, the 33-year half-life of

Figure 9-8: Click on figure to enlarge.

Cesium 137 is long enough that the source may well outlive the process. Another likelihood is that technological advances will increase the sensitivity of the detector faster than the rate at which the source is decaying. This provides users the option of replacing or upgrading the detector while keeping the source in place for the future.

Radiation Safety

The Nuclear Regulatory Commission (NRC) limits radiation intensity to a maximum of 5 milliroentgens per hour (mr/hr) at a distance of 12 in from the nuclear gage. If it is more, the area requires Radiation Area posting. The distance of 12 in is critical, because radiation intensity decreases by the inverse square of distance. Nuclear level gages are sized to provide radiation intensity at the detector that exceeds the minimum required, but is under the 5 mr/hr maximum. For ion chamber detectors, the minimum is 1 mr/hr. For Geiger-Mueller switches, it is 0.5 mr/hr. And for scintillation detectors, it is 0.1-0.2 mr/hr. Because the nuclear gage is basically measuring the vapor space above the liquid, as the level rises in the tank, the intensity at the detector drops. When the tank is full, radiation intensity is practically zero.

When used as a tank level sensor, radiation must pass through several layers of material before reaching the detector. At the detector, the maximum radiation must be less than some safety limit (such as 5 mr/hr) to avoid the need for "posting." Other criteria can be used, such as keeping a yearly dosage under 5 rems (roentgen + equivalent + man). If somebody is exposed to radiation throughout the year, such a dosage will result from exposure to radiation at an intensity of 0.57 mr/hr, while if an operator is exposed for only 40 hrs/wk, 5 rem/yr will correspond to what that person would receive if exposed to 2.4 mr/hr in the work area. As it is the total lifetime dosage of radiation exposure that really matters (maximum of 250 rems), the acceptability of the 5 rem/yr, or any other limit, is also a function of age (Figure 9-8). On the other hand, the radiation at the detector must still be sufficient to produce a usable change in detector output when the level changes.

This can be illustrated by an example:

Source Sizing

A point source of 10 mCi Cesium 137 (source constant for Cesium 137 is K=0.6) is installed on a high-pressure water tank having 1/2-in steel walls (Figure 9-9). Usually, two criteria need to be satisfied: First, the radiation intensity at the detector must drop by at least 50% as the level rises from 0-100%. The second and more important criterion is that the maximum radiation dose at the detector (when the tank is empty) must not exceed the safety limit (say, 2.4 mr/hr). It must exceed 1.0 mr/hr, however, in order to actuate the intended ion chamber detector.

First the in air intensity (Da in mr/hr) is calculated at the detector, for the condition when there is no tank between the source and receiver. Assume distance (d) is 48 in:

Because the source is shielded in all directions except towards the tank, the operator who is working near the detector will receive the maximum dosage when the tank is empty. The two 1/2-in steel walls will reduce Da (% transmission of 1-in steel in Figure 1 is 49%) to 0.49 x 2.6 = 1.27 mr/hr. This is below the allowable maximum but above the minimum needed by the detector.

When the tank is full, the presence of 30 in of water in the radiation path will reduce this maximum intensity to 0.045 mr/hr (0.035 x 1.9 = 0.045). This reduction in intensity well exceeds the required 50% drop needed for sensitive measurement. Note that the source size could have been cut in half if a Geiger-Mueller detector were used. A scintillation detector would reduce source size 5- to 10-fold.

The source size can also be reduced by locating the source in the tip of a probe inside the tank and moving it relatively close to the wall. When large level ranges are to be measured, a strip source can be used instead of a point source. The accuracy of most nuclear level gages is around 1% of range. If accounting accuracy is desired, the source and the detector can both be attached to motor driven tapes and positioned at the level (or at the interface level, if the tank contains two liquids).

Fortunately, today's computers can easily crunch the numbers and formulas of any combination of geometry and design criteria. The biggest challenge is not the calculation, but the obtaining of accurate inputs for the calculations. Therefore, it is very important that your vessel's wall materials, thicknesses, other tank components such as baffles, agitator blades or jackets, and all distances be accurately determined. In short, the performance of a nuclear gage installation is very much a function of the accurate knowledge of the installation details.

Detector Options

The simplest and oldest type of radiation detector is the Geiger-Muller tube. This instrument is most often identified with the Geiger counters that make a loud and dramatic clicking sound when exposed to radiation. The working component of this detector is a metal cylinder that acts as one of the electrodes and is filled with an inert gas. A thin wire down the center acts as the other electrode. Glass caps are

Figure 9-9: Click on figure to enlarge.

used as insulators, and a high voltage (700-1000 vdc) nearly sufficient to cause current flow between the electrodes is applied. When the tube is exposed to gamma radiation, the gas ionizes and the ionized particles carry the current from one electrode to the other. The more gamma radiation reaches the gas in the tube, the more pulses are generated. The resulting pulse rate is counted by the associated electronic circuitry, which makes measurements in pulses per second.

This detector can be used as a level switch if it is calibrated to engage or disengage a relay when radiation intensity indicates a high or low level condition. The G-M tube detector can only be used as a single point detection device. Its advantages include its relatively low cost, small size, and high reliability.

The ion chamber detector is a continuous level device. It is a 4 to 6-in diameter tube up to twenty feet long filled with inert gas pressurized to several atmospheres. A small bias voltage is applied to a large electrode inserted down the center of the ion chamber. As gamma energy strikes the chamber, a very small signal (measured in picoamperes) is detected as the inert gas is ionized. This current, which is proportional to the amount of gamma radiation received by the detector, is amplified and transmitted as the level measurement signal.

In level measurement applications, the ion chamber will receive the most radiation and, therefore, its output will be highest when the level is lowest. As the level rises and the greater quantity of measurand absorbs more gamma radiation, the output current of the detector decreases proportionally. The system is calibrated to read 0% level when the detector current output is its highest. 100% level is set to match the lowest value of the output current. Non-linearities in between can usually be corrected with the use of linearizing software. This software can correct for the effects of steam coils, agitator blades, baffles, stiffening rings, jackets and other components inside or outside the tank.

Scintillation counter detectors are five to ten times more sensitive than ion chambers. They also cost more, yet many users are willing to accept the added expense because it allows them either to use a smaller source size or to obtain a more sensitive gage. When gamma energy hits a scintillator material (a phosphor), it is converted into visible flashes comprised of light photons (particles of light).

These photons increase in number as the intensity of gamma radiation increases. The photons travel through the clear plastic scintillator medium to a photo multiplier tube, which converts the light photons into electrons. The output is directly proportional to the gamma energy that is striking the scintillator.

Scintillators are available in a multitude of shapes, sizes, and lengths. One of the latest is a fiber optic cable that allows one to increase detector sensitivity by installing more filaments in the bundle. Another advantage of the fiber optic cable is that it is manufactured in long lengths flexible enough to form-fit to the geometry of the vessel. This simplifies the measurement of levels in spherical, conical, or other oddly shaped vessels.

Nuclear Applications

Radiation gages typically are considered when nothing else will work, or when process penetrations required by a traditional level sensor present a risk to human life, to the environment, or could do major damage to property. The liquids and bulk solids measured by nuclear gages are among the most dangerous, highly pressurized, toxic, corrosive, explosive, and carcinogenic materials around. Because the nuclear gage "sees" through tank walls, it can be installed and modified while the process is running--without expensive down time or chance accidental release.

Because the installation of nuclear sensors requires a Nuclear Regulatory Commission (NRC) license, associated procedures are designed to guarantee that the installation will be safe. The best way to look at the safety aspects of radioactive gaging is to compare the well defined and understood risk represented by exposing the operators to radiation against the possibly larger risk of having an unreliable or inaccurate level reading on a dangerous process.

As detectors become more sensitive and are aided by computers, radiation source sizes and the resulting radiation levels continue to drop. Therefore, the safety of these instruments is likely to continue to improve with time.

References & Further Reading
OMEGA Complete Flow and Level Measurement Handbook and Encyclopedia®, OMEGA Press, 1995.
OMEGA Volume 29 Handbook & Encyclopedia, Purchasing Agents Edition, OMEGA Press, 1995.
Automated Process Control Electronics, John Harrington, Delmar Publishing Inc., 1989.
Fundamentals of Radar Techniques for Level Gauging, Detlef Brumbi, Krohne Metechnik GmbH & Co. KG, 1995.
Industrial Applications of Radar Technology for Continuous Level Measurement, W. L. Hendrick, Instrument Society of America, 1992.
Instrument Engineer's Handbook, Bela Liptak, Third Edition, CRC Press, 1995.
Process/Industrial Instruments and Controls Handbook, 4th Edition, Douglas M. Considine, McGraw-Hill, 1993.
Theoretical Nuclear Physics Volume I: Nuclear Structure, New York, A. deShalit, H. Feshback,: John Wiley & Sons, 1974.