Radiation, which refers to emissions of light or particles, is a type of energy transfer. Radiation takes place at any given moment in the environment or the body. Among sources of radiation to which humans are exposed daily are sun rays, radio waves coming from devices such as mobile phones and TV sets, appliances such as ovens or irons that emit heat, and medical machines such as ultrasounds. The radiation emitted from devices and machines do not cause ionization. Ionizing radiation is made up of high-energy wavelengths or particles, and this is the kind of radiation we get from x-ray, CT, and nuclear imaging. This is used to penetrate tissue to reveal the body’s internal organs and structures. Ionizing radiation can damage DNA, and when our cells cannot fully repair the damage, this may result in DNA mutations.[1] The radiation which poses real danger to humans and has the power to ionize is when radioactive—or unstable—atoms decay and emit alpha (α), beta (β), and gamma (γ) rays.

The earth, air, water, and all living things are more or less radioactive because radioactive atoms are everywhere. The average person is annually exposed to radiation levels of 2.6 – 10 mSv (millisievert), which is not that alarming. The maximum limit recommended for people exposed to radiation for occupational reasons is 100 mSv. The lungs of a person who smokes one pack of cigarettes a day are exposed to an annual radiation of 106 mSv.

How can we protect ourselves?

It is recommended by the World Health Organization that children younger than 16 should not use mobile phones; when they do, their calls should not exceed 10 minutes. When purchasing devices, you should also take into account its SAR (Specific Absorption Rate). Prefer devices with a SAR<1 W/kg. It is also recommended to unplug electrical devices when you are not using them, to keep electrical appliances as far away from your head as possible, use the hairdryer for short periods and in intervals, and to avoid using mobile phones for long conversations (or use headphones!).

It’s also worth reconsidering whether using radiation-emitting devices such as mammography, x-rays, or ultrasounds are absolutely necessary. In 2010, the British Department of Health and Social Care banned using tomography for screening purposes. Another study in the US found that one in ten people are exposed to high levels of radiation because of medical tests.

The average radiation rates (mSv) a person was exposed to during use of certain imaging devices is as follows:

Researchers also found that employees in nuclear power plants were exposed to amounts of radiation that far exceeded allowable amounts.

Beware of radon

The natural radiation humans are exposed to most is the gas radon. Some matter with radioactive atoms such as uranium and thorium – both present in the earth since its birth – emit radon, which seeps through the earth and into the walls of houses and through gaps in plumbing. It is recommended to air houses at least 15 minutes every 24 hours as the only way to be protected from radon.

The resistance of living things

Creatures have been created with different forms of resistance to the elements, including radiation. For example, dogs have a lower resistance than humans, while many other creatures such as rabbits, tortoises, and fruit flies have a higher resistance. And then there is the cockroach, which can survive even a nuclear attack. The lethal radiation dose for cockroaches is an incredible 670- 1000 Sv, whereas it is 6-8 Sv for humans.

Scorpions are also much more radiation-resistant than humans. They can withstand up to 1500 Sv, an amount that is 250 times the maximum dose humans can take. Studies have found a correlation between the strength of a scorpion’s venom and their resistance to radiation. The greater the amount of venom, the greater the resistance they have. The presence of the neural transmitter serotonin supports this view.

Are humans radioactive too?

Humans contain trace amounts of radioactive atoms, namely uranium (²³⁸U), potassium (⁴⁰K), and carbon (¹⁴C). An 80 kg human has natural radiation of 8000 becquerel every second, which is equal to 100Bq per kilogram. This amount is not high enough to cause any worry. The human body has 40 trillion cells on average, and every cell has about 100 trillion atoms. The proportion of the radiating atoms in the body is about 8000/4×10²¹.

Precision protection

The radioactive atoms in the body with the highest probability for carcinogenic effects are potassium (⁴⁰K) and carbon (¹⁴C) atoms. The decomposition that leads to cancer stems from mutations in genes, but the molecules that are the building blocks of genes do not have potassium atoms. The likelihood that a cell gets harmed is very low: it is necessary that the particles emitted from the radioactive potassium atom crash into the DNA molecule and harm it, which is as unlikely as threading a needle when blindfolded. The DNA is precisely protected inside the nucleus located at the center of the cell. If we consider the fact that the average diameter of a cell is about 10 microns (1 micron is one-thousandth of a millimeter), we can better appreciate how little space DNA occupies.

Radiocarbon atoms (¹⁴C), on the other hand, might be present in DNA molecules, and they are more dangerous because the emitted particles are more likely to find the target despite having weaker radioactive properties than potassium. A radioactive carbon atom turns into a nitrogen (¹⁴N) atom and may thus cause a chemical change in the DNA. In other words, the carbon atom is possibly to blame for the unexpected development of cancer.

The likelihood of harmful radioactive particles hitting a person’s DNA is low, and the protective system provided for it lowers the likelihood of developing cancer even more. New DNA molecules that form during DNA coupling are repeatedly checked by inspector enzymes. If there is an error, it is detected and then corrected. The broken code is taken out to be replaced with the correct version. Meanwhile, all these steps are checked by other enzymes assigned to the task. More errors might be made in the newly produced DNA molecule because of external factors. Yet ribosomes in the cell start to produce repair enzymes, as per the instructions from the DNA.

When thinking about all the protective factors that have been coded into the DNA for our survival against the 8000 radioactive activities that occur in our body every second, one cannot help but feel awe for the infinite mercy and wisdom that operate in our lives.

References

• http://time.com/5069317/california-mobile-phone-radiation/
• https://www.health.harvard.edu/cancer/radiation-risk-from-medical-imaging
• Choppin, G. et al., Radiochemistry and Nuclear Chemistry, Oxford: Elsevier Science & Technology, 1995.
• www.physics.isu.edu/radinf/natural.htm

[1] https://www.health.harvard.edu/cancer/radiation-risk-from-medical-imaging

In today’s cellular communication systems, cellular phones operate in several frequency bands. European systems use the Global System for Mobile Communications (GSM) at around 900 MHz and 1800 MHz; American systems use 850 MHz and 1900 MHz, frequencies that fall between the operating frequency ranges of televisions and microwaves. This frequency range is called non-ionizing, for the wave’s energy does not release electrons from atoms in living tissue. For instance, an X-ray is an ionizing wave that, to a degree, damages exposed biological material. Therefore, most concerns deal with RF energy’s heating effect rather than with ionization.

Technical Motivation

The electromagnetic spectrum extends from DC (direct current) to ionizing radiation. Scientists divide this spectrum into subregions. Cellular phones fall into the ultra-high frequency (UHF) regime, specifically from 300 MHz to 3000 MHz. By itself, a continuous UHF wave carries no information and does not enhance communication. It only becomes useful when modulation, defined as means carrying the information on a high frequency carrier, like UHF, is applied. The most common modulation techniques are amplitude modulation (AM) and frequency modulation (FM).

The capacity of the spectrum’s given section to carry information is limited by the Shannon Theorem. According to this theorem, channel capacity can be increased by increasing the system’s signal-to-noise ratio. In wired communications, channel capacity can be increased by adding more parallel optical fibers. Channel capacity in wireless communications can be increased by transmitting weak signals that attenuate rapidly near the transmitter and thus provide a given portion of the electromagnetic spectrum to be utilized many times. How a given spectrum is allocated among users affects the channel capacity. Therefore, there are several coding techniques, the most common of which are Frequency Division Multiple Access (FDMA), Time Division Multiple Access (TDMA), and Code Division Multiple Access (CDMA).

Neglecting some small details, an electromagnetic (EM) wave’s energy is expressed in terms of power density (W/m2) across a surface. Power density measures an incident EM wave’s strength. Easily measured, it is a very preferable metric to UHF fields. For uncontrolled environments, the American National Standards Institute and the Institute of Electrical and Electronics Engineers (ANSI/IEEE C95.1) recommend a 2 to 20 W/m2 for an average external exposure to UHF. The International Commission on Non-Ionizing Radiation Protection (ICNIRP) has similar power density recommendations for limiting the general public’s exposure to RF energy so that people will not be overheated by RF energy. As a comparison, for example, summer sunshine peaks around 1000 W/m2.

However, as power density is not a good indicator inside a living organism, scientists have defined a Specific Absorption Rate: SAR (in W/kg). For uncontrolled environments, ANSI/IEEE limits the spatial-average SAR to 0.08 W/kg whole body and to 1.6 W/kg averaged over any 1 gram of tissue. Also, 1998 ICNIRP restrictions are similar to ANSI/IEEE’s. The SAR can be estimated in three ways.

– Micro-antenna: Small antennas can determine a tissue’s electric field as well as its SAR. But it is difficult to place the antenna, and the tissue’s properties may not be known.

– Miniature thermal probes: Since RF energy heats the tissue, this technique detects the heat and the SAR in the neighborhood of the temperature cell, which then can be computed accordingly. However, this method also seems very difficult technologically.

– Numerical modeling: The numerical modeling of macroscopic bodies enables a numerical simulation, known as the Finite Difference Time Domain (FDTD), that can estimate the SAR. However, this process can be time-consuming and expensive.

Possible Health Issues

An EM wave can effect a biological change in living tissue in two ways: Depositing enough energy while passing through the biological material to alter some structures, or depositing packets of energy larger than the bond energy. Yet neither way seems to be possible, for the photon energy within the UHF zone is far less than the bond energy or the energy required to alter a living tissue’s structures. Therefore, many scientists now argue that UHF radiation at subthermal power levels can cause some biological damage.

Due to relatively low exposure levels, relatively small populations, and a lack of reliable dose estimates, proving or disproving the existence of RF exposure’s biological hazards remains an issue for epidemiology (e.g., statistical analysis of health records and animal studies).

Epidemiological Studies

Epidemiological studies were conducted among people who worked in a high frequency environment, such as radar stations. Search criteria were not limited to cellular and personnel communication system (PCS) frequencies. Due to the nature of radar and other military equipment, broader frequency ranges were covered. The epidemiology of cancer and RF radiation includes studies of cancer mortality rates among those exposed to RF energy.

Throughout these studies, people’s records were searched to determine if their cancer was due to RF exposure. These studies were made in various institutions, including the Radar Laboratory of the Massachusetts Institute of Technology, the U.S. Navy and Air Force, and the Polish military. There was no conclusive evidence that RF exposure increases the risk of cancer. Also, due to the lack of comparisons with total cancer, it was suggested that RF exposure does not have a strong effect on cancer.

Since brain cancer takes a long time to develop and epidemiological studies tell nothing about future risks, these studies have not proved or disproved that RF exposure increases the risk of cancer.

Animal Studies

Animals are the other source of information that potentially may answer people’s concerns. Experiments have studied rats exposed to certain power levels of RF energy. However, these studies found no link between cell phones and cancer.

In 1999, a Motorola-funded research program concluded that exposing rats to pulse-modulated 837 MHz RF energy, very close to that radiated by a digital cell phone, does not cause or develop brain cancer. A study in April 2000 reported that this conclusion is valid for continuous-wave RF (analog cell phones). But a 1995 study at the University of Washington (Seattle) reported that exposing rats to RF radiation at an average whole-body exposure of 1 W/kg of body weight caused breaks in their brain cells’ DNA, which is an indication of cancer. No other study has confirmed this finding.

Other studies have focused on different aspects of RF radiation rather than brain cancer. They searched animals for certain diseases and noticed an increase in disease rate. However, despite such research findings, animal studies seem to be far removed from human health.

Conclusion

Epidemiological findings and animal studies have neither proved nor disproved the health hazards of mobile phones. A February 2000 essay by the U.S. Food and Drug Administration (FDA) stated that: There is currently insufficient scientific basis for concluding either that wireless communication technologies are safe or that they pose a health risk to millions of users. Research activity continues. For example, France’s International Agency for Research on Cancer has received a research project of 8 million euros from the European Commission for a 3-year, wide epidemiological study. Also, the FDA and the Cellular Telephone Industry Association have undertaken a $1 million research project to clarify the health risks of mobile phones.

Meanwhile, some researchers are trying to find the head’s SAR by using electromagnetic simulations (FDTD). So far, they have discovered that it is strongly affected by the cell phone’s position as well as the head’s shape and properties. Therefore phone-makers are trying to design handset designs to reduce the SAR. However, it seems that the debate will remain until scientific proof is confirmed and made available.

• References
• http://www.fda.gov/cdrh/ocd/mobilphone.html.
• IEEE Spectrum. Are Mobile Phones Safe? (August 2000): 23-28.
• Moulder et. al. Cell Phones and Cancer: What is the Evidence for a Connection? Radiation Research Society, 151 (1999): 513-31.

Radar, a contraction of the words radio detection and ranging, is an electronic device for detecting and locating objects. It operates by transmitting a particular waveform pattern and detects the nature of the echo (return) signal.1 Radar is used to extend the capability of the man’s senses, especially that of vision. We can think of radar as being a substitute for the eye, although it can do so much more: it can see objects through such impervious conditions as darkness, haze, fog, rain, and snow, for its wavelengths are much longer than those of visible or infrared light. The human eye works as a passive device, since the object is illuminated by sunlight or other light sources. However, radar produces its own illumination via electromagnetic waves, which means that it is an active device. 

APPLICATIONS OF RADAR AND RADAR IMAGING

Radar is used in civilian applications as air-traffic-control radar to guide aircraft to a safe landing, and in commercial aircraft as radar altimeters to determine height and weather avoidance, as well as wind-shear radars to navigate in severe weather conditions.

The military uses radar for surveillance and weapons control. Examples of such radars are DEW (Distant Early Warning) and AEW (Airborne Early Warning), which detect aircraft, long-range search radars, and guided missile radars.2

Research scientists use radar as a measurement tool. Radars have been placed on satellites, space modules, and shuttles to explore meteors, planets, and other objects in the solar system.

In the case of an imaging radar, the radar travels along an airplane’s or a space shuttle’s flight path. The area underneath is illuminated by the radar, and the radar architecture builds the image as it moves on the top of its footprint (Fig.1). The radar image’s finer resolution is achieved by using a very long antenna array to focus transmitted and received energy into a sharp beam.2 The beam’s sharpness defines the resolution. Similarly, such optical systems as telescopes require large apertures (mirrors or lenses that are analogous to the radar antenna) to obtain fine imaging resolution. Synthetic Aperture Radar (SAR) is a common and very popular technique in radar imaging that achieves a very fine resolution.3 In the following sections, we introduce and explain different types of SAR imaging techniques.

SYNTHETIC APERTURE RADAR (SAR)

SAR refers to a technique that synthesizes a very long antenna by combining echoes received by the radar when it travels.4.5 Typically, SAR is used to produce a two-dimensional (2-D) image. One dimension in the image is called range (or along track), and is a measure of the “line-of-sight” distance from the radar to the target (Fig.l). Range is determined by precisely measuring the time from a pulse’s transmission to receiving the echo from target. The range resolution is determined by the transmitted pulse’s width (i.e., narrow pulses yield fine range resolution).

The other dimension is called azimuth (or cross track), and is perpendicular to range. Usually, the length of the radar antenna determines azimuth resolution. However, a good azimuth resolution requires a radar antenna that is not practically carried by an airborne platform, for imaging radars are much lower in frequency (1 to 10 GHz) than optical systems (4,000 to 8,000 GHz). The length of the required antenna could be around several hundred meters, which obviously cannot be carried by an air vehicle.

However, SAR differs from other radars in that it collects data along the flight path when it travels, instead of using a large antenna. Therefore, a very small antenna is adequate for the job. After collecting the data, it processes this aperture data as if it came from a physically long antenna. The distance the aircraft flies in synthesizing the antenna is known as the synthetic aperture. A narrow synthetic beamwidth results from the relatively long synthetic aperture, which yields finer resolution than what is possible from a smaller physical antenna.

SARs are not as simple as described above. Transmitting short pulses to provide range resolution is generally not practical. Typically, longer pulses with wide-bandwidth modulation are transmitted, which complicates range processing but decreases peak power requirements on the transmitter. For even moderate azimuth resolutions, a target’s range to each location on the synthetic aperture changes along the synthetic aperture. The energy reflected from the target must be “mathematically focused” to compensate for the range dependence across the aperture prior to image formation. Additionally, for fine-resolution systems, range and azimuth processing is coupled (dependent on each other), which greatly increases computational processing. The trick in SAR processing is to correctly match the variation in frequency due to motion (moving target or moving radar) for each point in the image.

An example of SAR imaging is shown in Fig. 2. The colors in the image reflect the received signal intensity. The strongest signal level is red, whereas the weakest is black. The figure is a SAR image of San Francisco, California, obtained by the Spaceborne Imaging Radar-C/X-band Synthetic Aperture (SIR-C/X-SAR) imaging radar when it flew aboard the space shuttle Endeavour on October 3, 1994. The size of the image is about 26 miles by 36 miles. The center of the area is 37.83 degrees north latitude, 122.38 degrees east longitude.

This particular SAR image is a good illustration of how SAR distinguishes urban areas from nearby relatively less populated areas. Such densely populated regions as downtown San Francisco (center) and the city of Oakland (at the right across the San Francisco Bay) show up as red images due to the alignment of streets and buildings vis A vis the incoming radar beam. The bridges in the area are easily detected by the imaging radar, including the Golden Gate Bridge (left center) at the opening of San Francisco Bay, the Bay Bridge (right center), and the San Mateo Bridge (bottom center). All dark regions on the image represent smooth water. Radar also easily detects the major faults in the area: those bounding the San Francisco-Oakland urban areas and the San Andreas Fault (at the lower left), As seen from the image, faults are shown as dark straight lines in the SAR image.

INCERSE SAR (ISAR)

While SAR images a region of the Earth from an airplane or an air shuttle, Inverse SAR (ISAR) images a flying object, such as airplane or an asteroid, from land-based radar. ISAR is very popular, and also very critical in military applications.6 It is commonly used for identification purposes. In a possible war scenario where there are too many aircraft in the sky, it is almost impossible to guess which one is friendly or hostile. In that case, ISAR imaging technique is used to identify the approaching aircraft and classify it from a collection of possible targets.

In theory, ISAR is an imaging technique that maps the locations of dominant scattering points of a target based on the multi-frequency, multi-aspect, backscattered data.7 In this data, the signal’s amplitude reflects the magnitude information of the scattering points on the target, while the backscattered signal’s phase is related to the location information of the scattering point off the target. After collecting this 2-D raw data, several signal-processing tools extract from this data the amplitude and location information of the scattering centers. Then, a 2-D image of the target is constructed by using a convenient image processing technique.

An example of ISAR imagery is shown in Fig. 3. The model of the test airplane (C-29 model) is shown at the lower portion, while a 2-D ISAR image of the airplane is constructed at the upper portion of Fig.3. The measurement is taken at the center frequency of 10 GHz, where the frequency bandwidth is 16 GHz. The data is collected from 0.10 steps to cover the entire 3600 azimuth. At the end, a 2048 by 2048 2-D grid is constructed by using the ISAR algorithm. By comparing both, it is seen that ISAR imaging provides accurate target information. By looking at this image, it is very easy to identify and classify the aircraft.

ISAR is an active operation of the radar at the target’s far field. Both receiving and transmitting antennas must be far away from the target. Recently, new ISAR imaging techniques that allow passive radar operation have been discovered. Antenna SAR (ASAR) and Antenna Coupling (ACSAR) imaging techniques use direct radiation from an antenna mounted on the near field of an airplane or a ship to image the dominant radiation points off these platforms. In these cases, the radar functions only as a receiver, for the target’s own antenna provides illumination to the target. These techniques are mainly used to determine the dominant radiation points off the target to explore ways to cancel or mitigate undesired extra radiation from the target’s platform.

The development of fast computers during the 1980s allowed researchers to apply intensive computational electromagnetic (CEM) tools that ultimately led them to develop new SAR/ISAR algorithms. One of the most appreciated and widely used tool is Interferometric Synthetic Aperture Radar (INSAR) imaging, which allows the extraction of height information that can be used to render 3-D topographic views of a SAR scene.

INTERFEROMETRIC SAR (INSAR)

Radar interferometry involves coherently combining radar measurements made by two or more radar antennas displaced by a relatively small distance.8 Depending on the relative geometry of the two antennas, the combined measurements can be turned into measurements of surface topography, topographic change, or displacement over time. Mapping precision of around 2m in three dimensions over a wide area is now possible from airborne interferometric radars.

Here is how an INSAR works: A radar system launches electromagnetic energy to scan the ground terrain to be imaged. Two radar antennas collect the backscattered wave to obtain two different snapshots of SAR image. To avoid phase ambiguity, these antennas must be close enough to each other. Since the waves travel different distances from a particular scatterer to each antenna, the resultant phases of each SAR image is different. In the next step, an image called interferogram is formed by multiplying one SAR image by the complex conjugate of the other SAR image. The phase of the interferogram represents the differences in range to the scattering centers of each pixel in the image. These differences are caused by the terrain’s topography. Then, a signal-processing algorithm converts this phase information to extract the terrain’s topographic features. Finally, a 3-D INSAR image of the region is formed by combining the SAR images with the height information.

An example of INSAR imaging is illustrated in Fig.4, which depicts the Long Valley of east central California. The images were taken by the Spaceborne Imaging Radar-C/X-band Synthetic Aperture Radar (SIR-C/X-SAR) aboard the space shuttle Endeavour during its two flights in April and October 1994. The four images show the steps necessary to produce 3-D data from radar interferometry. The image covers an area of 21 by 37 miles. The radar illumination is from the top of the image. The bright areas are hilly regions of big rocks and pine forest; the darker areas are the relatively smooth, sparsely vegetated valley floors. The curving ridge running across the image’s center from top to bottom is the northeast rim of the Long Valley caldera, a remnant crater from a massive volcanic eruption roughly 750,000 years ago.

The image in the upper right is an interferogram of the same region, constructed by combining data from the April and October flights. The different phases are shown as different color levels. These variations are caused by elevation differences in the area. The same color levels indicate that those regions have same altitudes. The image in the lower left shows a topographic map derived from the interferometric data. The black bold contour lines represent levels of elevation. In this particular image, elevation levels are spaced at 250-meter intervals. The last image is a 3-D view of the northeast rim of the caldera, looking toward the northwest. As can be seen from the image, it is possible to extract such geologic structural and landform features as elevation, vegetation, and soil type with the help of INSAR processing.

Another example of INSAR imaging is shown in Fig. 5, which depicts the Washington, DC, Mall area. A similar approach is used to form this 3-D image. The region starts from the Capitol building (top) to the Lincoln Memorial and the Arlington Memorial Bridge (toward the right bottom). The Washington Monument is very easy to observe at the center of the image. The bright areas (from white to yellow) represent higher elevation places; darker colors (from green to dark blue) represent the areas of lower elevation. The Potomac river (right bottom of the image) and the reflecting pool (from the Lincoln Memorial toward the Washington Monument) are all in dark blue because of the water and the lowest elevations. We can also clearly distinguish Constitution Avenue running from bottom to top. The green regions are intermediate elevation consisting mostly of vegetation. As seen from the image, the highest elevation is the top of the Washington Monument, the Library of Congress building, and the Capitol building.

CONCLUSION

In this paper, we presented a survey study of radar basics and radar imagery. It is obvious that radar has been a very important and useful tool throughout the 20th century, both in the military and industry. With developments in the computer era and new imaging algorithms, it looks like it will be a very critical tool in the 21st century as well. It is now possible to simulate very complex models and targets in a reasonable computation time in radar frequencies thanks to new developments in computational electromagnetics methods (CEM). Examples of those are Xpatch9 (a high frequency code that can predict the scattering from large, complex bodies) and FISC10 (a fast simulator of electromagnetic bodies at high frequencies). While computers continue to grow faster and faster, new electromagnetic simulators are also getting faster and more efficient. As a result, more compact, fancier, faster, and more accurate radar-imaging techniques are being developed.

REFERENCES

1. Morris, G. V. and Harkness, L. (1996) ‘Airborne Pulsed Doppler Radar’, Artech House.
2. Mensa, D. L. (1981) ‘High Resolution Radar Imaging’, pp. 185-189, Artech House.
3. Wehner, D. R. (1994) ‘High-Resolution Radar’. Artech House.
4. Carrara, W. C., Goodman, R. S. and Majewski, R. M. (1995) ‘Spotlight Synthetic Aperture Radar: Signal Processing Algorithms’, Artech House.
5. Franceschetti, G. and Lanari,. (1999) ‘Synthetic Aperture Radar Processing’, C. R. C. Press LLC.
6. Baltes, H. P. (1980) ‘Inverse Scatteiing Problems in Optics’, Springer-Verlag.
7. Chu, T. H. and Lin, D. B. (1991) ‘Microwave diversity imaging of perfectly conducting objects in the near-field region’, IEEE Trans. Antennas Propagat., vol. 39, pp. 480-487.
8. Askne, J., et al. (1997) ‘C-band repeat-pass inter ferometric SAR observations of forest, IEEE Trans. on Geoscience and Remote Sensing, vol.35, pp. 25-35.
9. Lee, S. W. (1992) ‘Test cases for XPATCH’, Electromagn. Lab. Tech. Rept., ARTI-92-4, Univ. of Illinois.
10. Ctr. Computat. Electromagn. (1997) ‘User’s Manual for FISC (Fast Illinois Solver Code)’, Univ. Illinois, Urbana-Champaign, and DEMACO. Inc.