User:Mysticdan/sandbox

Radar cross-section (RCS) is a measure of how detectable an object is with a radar. A larger RCS indicates that an object is more easily detected.

An object illuminated by a radar transmitter reflects a limited amount of radar energy back to the source. Several factors can influence the amount of reflected energy: the material of which the object is made; the absolute and relative size (compared to the wavelength of the illuminating radar) of the object; the incident angle (angle at which the radar beam hits a particular portion of target); and the polarization of transmitted and the received radiation with respect to the orientation of the target. For example, a stealth aircraft, which is designed to have low detectability, will have design features that give it a low RCS such as absorbent paint, flat surfaces, surfaces specifically angled to reflect signal somewhere other than towards the source. A passenger airliner that will have a high RCS due to bare metal, rounded surfaces, exposed engines, and antennas which can all increase the amount of signal that will be reflected back to the source. The strength of the radar emitter and distance between emitter and object are not factors that affect the calculation of the object's RCS. RCS is integral to the development of radar stealth technology, particularly in applications involving aircraft and ballistic missiles. RCS data for current military aircraft is most highly classified.

In some cases, it is of interest to look at an area on the ground that includes many objects. In those situations, it is useful to use a related quantity called the differential scattering coefficient (also called the normalized radar cross-section or backscatter coefficient) &sigma;0 ("sigma naught"), which is the average radar cross-section of a set of objects per unit area.

Definition
Informally, the RCS of an object is the cross-sectional area of a perfectly reflecting sphere that would produce the same strength reflection as would the object in question. (Bigger sizes of this imaginary sphere would produce stronger reflections.) Thus, RCS is an abstraction: The radar cross-sectional area of an object does not necessarily bear a direct relationship with the physical cross-sectional area of that object but depends upon other factors.

Somewhat less informally, the RCS of a radar target is an effective area that intercepts the transmitted radar power and then scatters that power isotropically back to the radar receiver.

More precisely, the RCS of a radar target is the hypothetical area required to intercept the transmitted power density at the target such that if the total intercepted power were re-radiated isotropically, the power density actually observed at the receiver is produced. This is a complex statement that can be understood by examining the monostatic (radar transmitter and receiver co-located) radar equation one term at a time:


 * $$P_r = {{P_t G_t}\over{4 \pi r^2}} \sigma {{1}\over{4 \pi r^2}} A_\mathrm{eff}$$

where
 * $$P_t$$ = power transmitted by the radar (watts)
 * $$G_t$$ = gain of the radar transmit antenna (dimensionless)
 * $$r$$ = distance from the radar to the target (meters)
 * $$\sigma$$ = radar cross-section of the target (meters squared)
 * $$A_\mathrm{eff}$$ = effective area of the radar receiving antenna (meters squared)
 * $$P_r$$ = power received back from the target by the radar (watts)

The $${{P_t G_t}\over{4 \pi r^2}}$$ term in the radar equation represents the power density (watts per meter squared) that the radar transmitter produces at the target. This power density is intercepted by the target with radar cross-section $$\sigma$$, which has units of area (meters squared). Thus, the product $${{P_t G_t}\over{4 \pi r^2}} \sigma$$ has the dimensions of power (watts), and represents a hypothetical total power intercepted by the radar target. The second $${{1}\over{4 \pi r^2}}$$ term represents isotropic spreading of this intercepted power from the target back to the radar receiver. Thus, the product $${{P_t G_t}\over{4 \pi r^2}} \sigma {{1}\over{4 \pi r^2}}$$ represents the reflected power density at the radar receiver (again watts per meter squared). The receiver antenna then collects this power density with effective area $$A_\mathrm{eff}$$, yielding the power received by the radar (watts) as given by the radar equation above.

The scattering of incident radar power by a radar target is never isotropic (even for a spherical target), and the RCS is a hypothetical area. In this light, RCS can be viewed simply as a correction factor that makes the radar equation "work out right" for the experimentally observed ratio of $$P_r/P_t$$. However, RCS is an extremely valuable concept because it is a property of the target alone and may be measured or calculated. Thus, RCS allows the performance of a radar system with a given target to be analysed independent of the radar and engagement parameters. In general, RCS is a strong function of the orientation of the radar and target, or, for the bistatic (radar transmitter and receiver not co-located), a function of the transmitter-target and receiver-target orientations. A target's RCS depends on its size, reflectivity of its surface, and the directivity of the radar reflection caused by the target's geometric shape.

Radar ground return is described by the normalized radar cross-section &sigma;0 (also called the differential scattering coefficient or backscatter coefficient):
 * $$\sigma^0 = \left\langle {{RCS_i}\over{A_i}} \right\rangle $$

where: The total radar cross section of a patch of ground depends on the area of that patch and the contributions of each scattering element within the patch. Using a differential scattering coefficient implies that the area has a large number of contributors with independent phases.
 * RCSi is the radar cross-section of a particular object, and
 * Ai is the area on the ground associated with that object.