Minimize FAST

FAST (Formation for Atmospheric Science and Technology Demonstration)

FAST is a Dutch-Chinese joint mission between the Delft University of Technology (TU Delft), The Netherlands, and Tsinghua University of Beijing, China (agreement signed in 2007). The goal is to jointly define, develop and operate the FAST mission using two microsatellites flying in formation to cover scientific objectives, technology demonstrations, and educational purposes alike.

The FAST mission has three equally important top level objectives, namely:

1) To characterize atmospheric aerosols, monitor variation of height profiles in the cryosphere, and correlate these data for improved science return.

2) To demonstrate autonomous formation flying (AFF) using various communication architectures with distributed propulsion systems and MEMS technology.

3) To teach a cutting-edge space technology curriculum by the university staff, to broaden the views of students through international contacts and the experience gained in joint ventures, and to boost the level of skills through the exchange of students and staff.

The science objectives comprise the synoptic evaluation of local, regional and global aerosol data and altitude profiles of the cryosphere with two cooperating microsatellites flying in formation. The complexity of the mission will require a concerted effort from national universities, knowledge and research institutes and industries in both countries. 1) 2) 3) 4) 5) 6)

An improved monitoring and prediction of the Earth's climate requires more and better in-situ measurements on a global scale. In particular, current uncertainties in climate forcings due to aerosols preclude meaningful climate model evaluations. The FAST mission will allow an unprecedented characterization of atmospheric aerosols and their forcings on the climate as well as a monitoring of the evolution of height profiles in the cryosphere. The mission will realize synergies between different data types from the scientific payloads on FAST for improved science return.


Space Segment:

The FAST space segment consists of two microsatellites: FAST-D which is being developed in Delft while the other spacecraft, FAST-T, is being developed at Tsinghua University in Beijing. Both spacecraft will fly a common payload referred to as Spectropolarimeter. FAST-T may carry an additional payload.

During the procedure of formation flying, i.e. the “scientific mode” as well as the “technology demonstration mode”, the two spacecraft will communicate with each other either through a direct ISL (Inter-Satellite Link) or through ground stations. The distributed computing and other technologies will be implemented via the ISL.

In total three scientific payloads will be flown by the FAST mission: the Dutch spectropolarimeter instrument is being flown on each spacecraft, FAST-D and FAST-T. The second payload on FAST-D is SILAT (Stereo Imaging Laser AlTimeter). FAST-T is flying one Chinese payload, namely DFMRM (Dual-Frequency Microwave RadioMeter) and the Dutch spectropolarimeter.


Figure 1: Overview of the FAST mission architecture (image credit: TU Delft)

Launch: A launch of the two microsatellites is planned for no earlier than 2011 as secondary payloads on a Chinese Long March launcher.

Orbit: Sun-synchronous orbit, altitude of 650 km, inclination = 98.7º, LTAN (Local Time on Ascending Node) of ~ 10:00 hours.

The LEOP (Launch and Early Operations) phase consists of the launch, orbit insertion, spacecraft detumbling, and checkout of the two satellites. During LEOP, which will take approximately one month, the two spacecraft will not fly in formation. In this period, the intersatellite distance will increase to 60 km, requiring a bang-bang formation initialization maneuver costing 0.2m/s to start the next mission phase.

Technology demonstration mode: The two satellites will demonstrate the ability to autonomously maintain an along-track separation of 1±0.1km by means of autonomous formation flying (AFF) using propellant optimized distributed propulsion. This capability requires a propulsion system on each spacecraft as well as an intersatellite communication link.

For solar maximum conditions, it will take the satellites slightly over one day to traverse the 200 m control window of this mission phase. To maintain the desired formation geometry, taking into account differential drag only, a ΔV of 2 mm/s is then required to bring the intersatellite distance back to the other extreme of the control window.

Although the orbital geometry is not optimized for it, some first science observations will be performed during this phase of the mission. Due to the relatively small inter-satellite distance, this phase also lends itself well to perform distributed computing experiments between the two spacecraft and to perform cross-calibration between the instruments on the different spacecraft. The AFF demonstration will be performed for several weeks and will be followed by a transition to the required relative geometry for science mode.


Figure 2: FAST-D and FAST-T in technology demonstration mode, illustrating the overlapping field-of-views of the spectropolarimeter (image credit: TU Delft)

Science Mode: In this mission mode, the along-track separation between the satellites will be 1225 ± 5.7 km (Figure ). Since natural drift of the formation will require approximately 100 days before this geometry is achieved, preference is given to a controlled maneuver requiring a total ΔV of 2 m/s and taking a bit more than two days. For one year of formation maintenance, taking only differential drag into account, approximately 1.2 m/s of ΔV is required and a maneuver needs to be executed every nine days.

The orbital geometry of this mission phase lends itself extremely well to perform synoptic and synergetic observations with the altimeters and especially the spectropolarimeter instruments on both spacecraft. The orbital geometry combined with the nine Earth-looking FOVs (Fields-Of-Views) of the spectropolarimeter results in many simultaneous intersections of the spectropolarimeter FOVs and in several overlapping the spectropolarimeter FOVs at the Earth’s surface. This allows retrieval of aerosol characteristics at specific altitudes at a single moment in time and it permits making more observations of geolocations from various angles during a single pass (especially near the equator), which is highly desired for aerosol characterization. The ±5.7 km accuracy in the intersatellite range is driven by the pixel size of the spectropolarimeter at 650 km altitude, which is approximately 11.4 km.


Figure 3: Artist's view of the science mode configuration (image credit: TU Delft)


FAST-D microsatellite:

The FAST-D microsatellite employs a stackable tray design to accommodate the various subsystems and payloads. The square trays are made of aluminum alloy; honeycomb material is being used for the panels. The spacecraft is designed to ensure a balanced thermal environment in all operating modes, including eclipse and safe modes. Due to the utilization of the cold gas generator, the local heating for the propellant tank is not necessary anymore.

Thermal control is achieved primarily by simple passive approaches. For instance, on external surfaces a mixture of first surface tape and second surface tape is utilized, and plain black carbon radiating surfaces are used to control the heat flow by balancing absorption and emissive characteristics. Another example is internal equipment whose radiating energies are controlled by applying appropriate surface finishes.

The spacecraft is 3-axis stabilized. Of the payload, the LAT device of SILAT (Stereo Imaging Laser Altimeter) requires a pointing stability of 25 µrad on a timescale of 5 ms which corresponds to the time-of-flight (TOF) of the laser altimeter photons. 7)

The FAST-D microsatellite has a launch mass of ~50 kg and dimensions of 50 cm x 50 cm x 70 cm. It is being developed by Dutch academia and industries.


Figure 4: Illustration of the FAST-D spacecraft (image credit: TU Delft)

The AOCS (Attitude and Orbit Control Subsystem) plays a key role for the FAST-D spacecraft. Due to the requirements from the payloads, FAST-D’s AOCS shall be able to provide attitude information with at least 30 arcseconds accuracy around the various body axes using fine attitude sensors, and shall allow the control of attitude with a minimum pointing accuracy of 300 arcseconds.

Attitude determination is achieved with the use of two redundant 3-axis magnetometers and two micro sun sensors for coarse information. For precise determination two miniaturized CMOS star trackers and a 3-axis gyro are being used.

Actuation: Attitude control is performed with reaction wheels and with magnetorquers for momentum dumping and coarse control. The four micro reaction wheels are mounted in a pyramid configuration maximizing control effectiveness, and the three magnetorquer rods are mounted in an XYZ configuration.

A double-loop NDI (Nonlinear Dynamic Inversion) technique will be adopted, which allows flexible control of a nonlinear system in different flying modes. The double-loop NDI technique avoids strong nonlinear feedback which causes unnecessary actuator saturations, and provides flexibility for multiple operational modes by separating rate and angular control.

A GNSS (Global Navigation Satellite System) receiver will function as absolute navigation sensor for onboard orbit determination. It is further enhanced through uploading precise GNSS ephemerides from ground. The relative position and attitude information will be obtained by exchanging navigation and attitude data via intersatellite communication. Orbit control will be implemented by means of a cold gas thruster.

EPS (Electrical Power Subsystem): Power to the satellite is provided by three body-mounted solar arrays; a central panel is body-mounted to the zenith face of the microsatellite. Each panel houses triple junction InGaP/GaAs/Ge solar cells with an average efficiency of 26.8%. An orbit average power of 45 W is provided. The electrical power is conditioned, then distributed along a 28 V regulated bus. The excess solar power generated is stored in a set of lithium-ion batteries with a total capacity of 133 Wh.

CDHS (Command and Data Handling Subsystem): The payloads and TT&C subsystems are interfaced to the on-board command and data bus using a SpaceWire interface. The microsatellite avionics interface with a lower speed CAN bus. The philosophy behind the CDHS is to develop a highly integrated avionics kernel that manages all the survival functions of the spacecraft. This architecture consists of computers, data storage, data buses, and the relevant software.

There are two ARM processors in the kernel, one for housekeeping and data processing, and the other for AOCS and formation flying. They are also hot redundant for each other in case of failure. The payload data are stored in a radiation tolerant solid state memory with the capacity of 8 GByte. The data buses are composed of a high speed bus for payload data transfer and a low speed bus for command/control. The onboard software performs three primary functions: system boot, housekeeping, and AOCS/FF processing.


Figure 5: Schematic view of the CDHS configuration (image credit: TU Delft)

Propulsion subsystem: The relatively large ΔV requirements and the volume limitation on the spacecraft prevent FAST-D from utilizing conventional chemical propulsion techniques. Alternatively, a cold gas generator is used on FAST-D to replace the cold gas tank.

The propulsion subsystem is composed of a cold gas generator (developed at TNO and Bradford Engineering), an electronics board, an orbit control thruster, and the associated valves and tubes. It provides for initial launcher injection corrections and formation maintenance. - The major advantage of the cold gas generator over the gas tank is that it stores the propellant in solid state. Hence, no large volume, high-pressured tank and associated valves are needed; no risks for leakage; and the mass and volume of the complete propulsion subsystem are both optimized.

For FAST-D, a nitrogen generator has been selected because of its relatively high gas output efficiency (each kg of solid propellant can output 260 liters of gas with the pressure range of 0.1-15 MPa) and its availability for space applications through its space qualification on ESA’s PROBA-2 satellite (launch on Nov. 2, 2009).


Figure 6: Schematic of the FAST-D propulsion subsystem (image credit: TU Delft)

RF communications: The onboard subsystem consists of two S-band transmitters, one low power transmitter, one high power transmitter. The low power transmitter is primarily used for telemetry, and the high power one is primarily for payload data downlink. However, for redundancy on the transmit chain, these two transmitters both can be used as the backup of the other one. The two command receivers share two patch antennas, which are mounted on the nadir and the zenith surfaces of the satellite, respectively. The low power transmitter feeds another two patch antennas. The high power transmitter is connected with a helical antenna.

The satellite uplink is performed by a set of 9.6 kbit/s redundant receivers. The downlink antennas will be operated at 7.5 W output at a frequency of 2.4 GHz (S-band). The downlink payload date rate is 6.5 Mbit/s.

ISL: FAST-D will be equipped with a RF (Radio-Frequency) intersatellite link, capable of transmitting data and measuring the distance to the FAST-T spacecraft. A GNSS receiver is to provide absolute position and velocity data.
The ICM (Intersatellite Communication Module) is composed of a transceiver and two patch antennas (Figure 7). During FF (Formation Flight), the satellites exchange state information, such as position and attitude, between each other through this link. As payload data are not intended to be exchanged, only a low power transceiver and low-gain antennas are being utilized.


Figure 7: Functional block diagram of the RF subsystem (image credit: TU Delft)


Sensor complement: (Spectropolarimeter, SILAT)


The spectropolarimeter is a small, innovative instrument currently under development in the Netherlands. The objective is to measure flux and polarization across a broad wavelength region (400-800 nm) with a spectral resolution of about 2 nm. To achieve this, it has only one detector and no moving parts. The instrument is compact enough to fit on a microsatellite, allowing low-cost and fast access to space.

As of 2008, SPEX, a candidate of the spectropolarimeter, is under development by a consortium of Dutch entities consisting of Dutch Space, TNO, SRON (Netherlands Institute for Space Research), the Netherlands Foundation for Research in Astronomy (ASTRON), and the Astronomy Department of the University of Utrecht. The instrument is primarily intended for a future planetary exploration (Mars mission). - A special version of of SPEX could be adapted for the FAST Earth observation mission.

An important modification of the spectropolarimeter compared to SPEX (Mars) is the change from seven planet-looking FOVs (Field of Views) and two limb-looking FOVs to nine planet-looking FOVs for the spectropolarimeter. The reason for this change is that the spectropolarimeter will focus on characterizing aerosols, leading to a preference for planet-looking FOVs over limb-looking FOVs.

Spectral range

400 - 800 nm

Spectral resolution

≤ 2 nm

Spectral sampling

2 detector pixels

Spatial resolution

19 km @ nadir from an orbital altitude of 650 km

Viewing directions

0º, ±18º, ±36º, ±54º, limb forward and backward view

FOV per viewing direction

7º x 1.7º (cross-track x along-track)

Instrument mass (excl. electronics, thermal)

~ 2 kg

Form factor spectropolarimeter subsystem

130 mm x 130 mm x 60 mm

Power requirement

CMOS detector: < 0.5 W

Operational constraints

Pointing knowledge and stability of platform < 360”

Data rate

16.6 Gbit/day (no compression)

Data storage

Spacecraft CDHS

Table 1: Key characteristics of the Spectropolarimeter instrument

The instrument baseline specification has seven downward viewing directions along the flight direction (at 0º, ±18º, ±36º, and ±54º with respect to the vertical direction, and two (forward and backward) limb viewing directions. The viewing angles are chosen such that the scattering angle dependence of the flux and polarization of the scattered sunlight is sufficiently sampled. The optimal sampling will be obtained for intermediate to large phase angles (Figure 8).


Figure 8: Illustration of the scattering angle (image credit: TU Delft)

The spectropolarimeter has a truly innovative method for doing polarimetry: the degree and direction of linear polarization of the scattered and observed sunlight is encoded as a sinusoidal modulation into the flux spectrum. Thus, from a single flux spectrum (measured in a specific viewing direction), the spectral dependence of the polarization and the flux itself can be retrieved. The spectral measurements in the various viewing directions are thus performed simultaneously.

The spectropolarimeter instrument will also be provided to Tsinghua University to fly on FAST-T.

SILAT (Stereo Imaging Laser Altimeter)

The SILAT design is based on an Europa mission heritage - and can be adapted for an Earth observation mission with an expected decrease in mass. SILAT is being developed at Cosine Research BV, Leiden, The Netherlands. The instrument is an example of a highly integrated payload where three different instruments are combined to create a new instrument with superior characteristics than all three instruments separately.

SILAT consists firstly of a miniature LAT (Laser Altimeter) that employs photon counting to measure height variations. Secondly, there is a HRC (High Resolution Camera) that can make detailed color pictures of the planet surface. Thirdly, together with a SCAM (Stereoscopic forward looking Camera), this allows the creation of accurate three dimensional maps of the planet's surface. 8)

The photon counting LAT is composed of two elements: the transmitting (LAT-TX) and the receiving (LAT-RX). A goal of the LAT concept is to provide a relatively low power laser altimeter using a microchip laser and a SPAD (Single Photon Avalanche Diode). The SPAD is a particular type of APD (Avalanche Photo Diode) that can trigger a very fast current switch with resolution times on the order of picoseconds with only the energy of a single photon as a trigger. This type of APD requires an active quenching circuit in order to halt the avalanche breakdown.

The idea of photon counting is to use lasers with high repetition rate (10 kHz or more) while the backscattered laser light is detected as efficiently as possible. The photon counting laser altimetry concept allows for laser power reduction by about an order of magnitude in comparison to previous methods. In SILAT, a miniaturized passively Q-switched, frequencyupconverted, diode-pumped Nd:YAG laser operating at 532 nm with as little as 10 – 25 µJ pulse energy is used. For operations, there is a choice of either one of two ND:YAG laser wavelengths available since the 1064 nm can be frequency doubled to 532 nm.

The LAT-TX is a removable system that consists of the Q-switched microchip laser and a series of collimating optics contained within a light baffle. The LAT-TX also contains electronics to record the exodus of outgoing laser pulses, in order to correlate their return the receiver with the time of flight.


Figure 9: Illustration of the SILAT instrument (image credit: TU Delft)

Legend to Figure 9: The laser emitter (LAT-TX) is located next to the combined HRC and the laser receiver (LAT-RX) TMA (Three Mirror Anastigmatic) optics. Both HRC and SCAM use miniaturized front-end electronics and a CMOS/APS (Active Pixel Sensor). The laser light detector, SPAD (Single Photon Avalanche Diode), is integrated in the HRC focal plane. The main electronics unit including the data processing unit and the power supplies is not shown.

The LAT-RX houses the SPAD, as well as the biasing electronics and FPGA that controls the instrument. The LAT-RX uses the same mirrors as the HRC, but the detector is mounted on a separate, dedicated PCB (Printed Circuit Board) that is aligned with the HRC electronics assembly. This allows the HRC and LAT to share electronics, with only the SPAD mounted on a separate PCB. This integration provides power and mass savings, but results in a non-trivial assembly procedure for the HRC and LAT-RX units.

The resolution of the LAT is based not only on the SPAD hardware, but also the method used to interpret the incoming current. This software and electronics package, called the Correlation Range Receiver (CRR), provides the parameters that determine whether or not a true photon reception event occurred, determines the TOF (Time of Flight) of the photon, and stores the result within a user-controlled range gate, which is used to statistically determine the height of the terrain that the altimeter passed over during that time.


Figure 10: Alternate view of the SILAT instrument (image credit: Cosine Research)







SILAT overall

Total mass

7.77 kg

Instrument size

287 mm x 327 mm x 327 mm

Power consumption

11.92 W

Temperature range

263 -303 K

Platform pointing accuracy

24” (arcsec), required

Data rate

30.7 Mbit/s (no compression, 100% duty cycle)






Power consumption

10.34 W

Vertical resolution

0.15 m

PRF (Pulse Repetition Frequency)

10.000 kHz


532 nm

Emitter FOV

0.050 mrad

Receiver FOV

0.150 mrad

Detector type

Single photon avalanche diode

LAT-RX aperture size

65 mm





Power consumption

0.5 W


3.7º, 0.0018º (0.031 mrad)

Detector type

APS (Active Pixel Sensor)

Filter configuration

404 nm, 559 nm, 671 nm

Shutter time

2.5 ms





Power consumption

1.1 W

Off nadir pointing



4.7º, 0.0045º

Detector type

APS (Active Pixel Sensor)

Filter configuration

559 nm

Shutter time

6.3 ms

Focal length, aperture size

126 mm, 18 mm

Table 2: Key parameters of the SILAT instrument

The HRC (High Resolution Camera) is designed to provide multi-band, high resolution images of planetary surfaces (nadir view). The instrument uses a 2048 x 2048 pixel array, 10 µm pitch APS (Active Pixel Sensor) detector with a tri-band filter. The APS sensor is based on an IBIS 5 A 3000 sensor and is currently under development at ESA.

The HRC optics subsystem uses three SiC mirrors coated with protected silver. The mirrors are designed to optimize performance versus manufacturing; the primary requirement being ellipsoidal, the secondary hyperboloid and the tertiary ellipsoidal. The detector is controlled using a FPGA (Field Programmable Gate Array) mounted on the same board assembly as the detector. The front end electronics are shared with the LAT device. The electronics are connected to the spacecraft power and CDH (Command and Data Handling) systems, preferably via a SpaceWire interface.

The SCAM (Stereoscopic forward looking Camera) is designed to complement the mandatory inclusion of the HRC by providing simultaneous low resolution imaging in a single spectral camera. By utilizing the same detector type and filter bandwidth combination, the SCAM provides stereo imaging of the target at a reduced design overhead. The IBIS-based APS detector features the same pixel pitch (10 µm) as HRC, but with an array size of 1024 x 1024 pixels. The band chosen for the SCAM spectral channel is 559 nm ± 37.5 nm. As with the HRC, the SCAM is controlled using a local FPGA, connected to the bus power and CDH subsystems. - The SCAM instrument points at an angle of 27º off nadir to provide stereoscopic imagery.

FAST-T microsatellite:

FAST-T is a microsatellite under development at Tsinghua University, Beijing, China. The bus has almost a cubic size of 750 mm x 750 mm x 730 mm featuring two deployable panels. The spacecraft mass is < 130 kg. The FAST-T spacecraft design is of Tsinghua-2 heritage (Tsinghua-2 is under development as of 2008 at Tsinghua University).

The FAST-T spacecraft is 3-axis stabilized and nadir pointing with the control accuracy of ≤ 0.1º (3σ) and a stability of ≤ 0.01º/s (3σ). In case of any critical fault, the satellite will automatically switch into the safe mode, and then the opposite side of Y axis will point to the sun with the accuracy of ≤ 5º and a stability of ≤ 0.05º/s (3σ).


Figure 11: Illustration of the FAST-T spacecraft (image credit: Tsinghua University)


Sensor complement: (Spectropolarimeter, DFMRM)

The spectropolarimeter instrument is described under the sensor complement of the FAST-D mission.

DFMRM (Dual-Frequency Microwave RadioMeter):

DFMRM is a microwave radiometer at K-band (23.8 GHz) and at Ku-band (37 GHz). The objective is to measure the atmospheric brightness temperature in the respective bands for the deduction of the global luminosity and temperature profiles.

After data processing, the physical parameters related to water present in both liquid and vapor forms in clouds can be obtained. These parameters can then be used to construct more accurate precipitation prediction models, and also to aid the in-depth analysis of the effect of aerosols on precipitation.

The DFMRM radiometer is being developed GESSA/CAS (General Establishment of Space Science and Application / Chinese Academy of Sciences). The instrument has dimensions of 330 mm x 270 mm x 200 mm, a mass of ≤ 15 kg, and an average power consumption of < 20 W (peak power < 25 W). There are two observation channels on DFMRM: the primary one is nadir-oriented, and the secondary one points to cold space (off sunlight) for calibration purposes.

1) E. Gill, D. Maessen, E. Laan, S. Kraft, G. T. Zheng, “Atmospheric Aerosol Characterization with the Dutch-Chinese FAST Formation Flying Mission;” Proceedings of the 59th IAC (International Astronautical Congress), Glasgow, Scotland, UK, Sept. 29 to Oct. 3, 2008, IAC-08.B1.I.1

2) D. C. Maessen, E. Gill, C. J. M. Verhoeven, G. T. Zheng, “Preliminary Design of the Dutch-Chinese FAST Microsatellite Mission;” Proceedings of the IAA Symposium on Small Satellite Systems and Services (4S), Rhodes, Greece, May 26-30, 2008

3) D. C. Maessen, B. C. Gunter, C. J. M. Verhoeven, E. Gill, “Increasing System Performance and Flexibility: Distributed Computing and Routing of Data within the FAST Formation Flying Mission,” Proceedings of the 59th IAC (International Astronautical Congress), Glasgow, Scotland, UK, Sept. 29 to Oct. 3, 2008, IAC-08-D1.4.6

4) D. Maessen, J. Guo, E. Gill, E. Laan, S. Moon, G. T. Zheng, “Mission Design of the Dutch-Chinese FAST Micro-Satellite Mission,” Proceedings of the 7th IAA Symposium on Small Satellites for Earth Observation, Berlin, Germany, May 4-7, 2009, IAA-B7-0220P

5) J. Guo, D. C. Maessen, E. Gill, S. G. Moon, G. Zheng, “Status of the FAST Mission: Microsatellite Formation Flying for Technology, Science and Education,” Proceedings of the 60th IAC (International Astronautical Congress), Daejeon, Korea, Oct. 12-16, 2009, IAC-09.B4.2.5

6) Jian Guo, “FAST Microsatellite Formation Flying Mission for Technology, Science and Education,” Feb. 5, 2009, URL:

7) D. Maessen, J. Guo, E. Gill, B. Gunter, Q. P. Chu, G. Bakker, E. Laan, S. Moon, M. Kruijff, G. T. Zheng, “Conceptual Design of the FAST-D Formation Flying Spacecraft,” Proceedings of the 7th IAA Symposium on Small Satellites for Earth Observation, Berlin, Germany, May 4-7, 2009, IAA-B7-0805P

8) S. G. Moon , S. Hannemann, M. S. Bentley, S. Kraft, K. Wielinga, E. Kroesbergen, J. Rotteveel, E. Gill, “A Miniaturized Laser Altimeter and Stereo Camera for a Microsatellite Formation Mission,” Proceedings of the IAA Symposium on Small Satellite Systems and Services (4S), Rhodes, Greece, May 26-30, 2008, ESA SP-660, August 2008

The information compiled and edited in this article was provided by Herbert J. Kramer from his documentation of: "Observation of the Earth and Its Environment: Survey of Missions and Sensors" (Springer Verlag) as well as many other sources after the publication of the 4th edition in 2002. - Comments and corrections to this article are always welcome for further updates.