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Antennas and Apertures in Earth Observation

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Understanding Earth Observation

Part of the book series: Remote Sensing and Digital Image Processing ((RDIP,volume 23))

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Abstract

Antennas [95, Chap. 3] and apertures [46] cover the dual role of receiving the wave carrying information on the observed target, as well as of acting as a source in case they are part of active systems.1 Passive instruments pick up either the solar radiation at ultraviolet, visible and near infrared wavelengths “reflected” in the sense seen in Sects. 9.3.1 and 10.2.1.1 by the observed portion of the Earth, or the thermal radiation which is spontaneously emitted by this latter in the infrared (Sect. 9.3.2) or at microwaves (Sect. 9.3.3). On their side, the active systems (Sect. 10.2.4) intercept a fraction of the power they have transmitted and that is carried back by the wave after interaction with the target.

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Notes

  1. 1.

    Earth observing active systems include lidars and radars in various forms, named after their peculiar function, such as: profiling, imaging, altimeter, scatterometer.

  2. 2.

    Reciprocity relations can be used in general, since they have been established for electromagnetic fields with arbitrary time dependence [22, 91].

  3. 3.

    The source current \(\boldsymbol{J}_{\!\mathrm{s}}\) denotes any source of electromagnetic radiation, independently of its origin (be it natural or man-made), wavelength (optical or microwave) and nature, i.e., physically present or virtual.

  4. 4.

    The line represents a radio-frequency guiding structure such as waveguide, strip-line, or coaxial cable.

  5. 5.

    The basically different features of incoherent-detection optical systems are outlined in Sect. 11.4.2.2.

  6. 6.

    Being arbitrary, here the “horizontal” direction is assumed parallel to the linear elements of Fig. 11.4.

  7. 7.

    “Internal” here denotes the space inside the system between the transmitter (or the receiver considered in Sect. 11.2) and A g.

  8. 8.

    For instance, in a microwave system, \(\boldsymbol{E}_{\ell\mathrm{T}}\) can be the field carried by the dominant mode of a waveguide.

  9. 9.

    In the microwave case to which Fig. 11.1 refers, η ℓ  ≡ η z, that is, it coincides with the wave impedance of the dominant mode in the guiding structure, while η ℓ  ≡ η 0, the intrinsic impedance of vacuum (4.35), for the free-space propagation inside the telescope optics of Fig. 11.2.

  10. 10.

    Alternatively, but less effectively in the present context, the currents could be those actually flowing on the physical structure, for instance those on the reflecting parabolic conducting surface of Fig. 11.1 or on the array elements of Fig. 11.4.

  11. 11.

    In practice, the accuracy of this serviceable assumption depends on the kind of system and on the band of operation.

  12. 12.

    Actually, the external field propagates perpendicularly to the equiphase plane in correspondence of A g; for simplicity, here the plane of A g is assumed equiphase.

  13. 13.

    The power radiated by the antenna coincides with the power delivered by the source when the structure is lossless.

  14. 14.

    The present radial coordinate r in the antenna reference system should not be confused with the distance from the antenna; similarly, the polar angle \(\vartheta\) must be kept distinct from the off-nadir angle.

  15. 15.

    Systems are frequently encountered that steer the beam (electronically or mechanically), i.e., vary the aperture boresight by tilting the equiphase surface of E 0T.

  16. 16.

    Linear polarization is assumed; complex \(\boldsymbol{\mathfrak{e}}_{0}\) are needed for circular or elliptical polarizations.

  17. 17.

    The neglected phase factor here is inessential.

  18. 18.

    It means that the direction of propagation of the arriving field must be reversed, making it to propagate back from the point where the receiver or the detector is located towards the external space, through any microwave component or optical element actually traversed by the incident field.

  19. 19.

    Once again, attention is called onto the normalizing effect of the denominator of (11.19), which makes the received power independent of the magnitude of the virtually transmitted field.

  20. 20.

    An exception is represented by the ionosphere at the lower microwave frequencies.

  21. 21.

    Airborne SARs have notoriously operated since several decades and systems are also in use on RPAPs.

  22. 22.

    The imaginary unit factor in (11.25), which refers to the absolute phase of the field, is also disregarded.

  23. 23.

    For the time being, receiving systems called diffraction-limited are considered; Sect. 11.4.2.2 looks at optical sensors with alternative properties.

  24. 24.

    This means that the incident waves arrive from a narrow angular range about the axis of the aperture.

  25. 25.

    Note that different conventions can be adopted.

  26. 26.

    As said, in case of optical sensors the result holds for diffraction-limited systems.

  27. 27.

    Also called antenna beam width .

  28. 28.

    The subscriptdl is suitable to distinguish the diffraction-limited angular resolution considered here from the optics-limited field of view outlined in Sect. 11.4.2.2.

  29. 29.

    As observed, identifying horizontal and vertical directions presupposes a target (e.g., Earth) reference.

  30. 30.

    Aperture field tapering entails η A < 1.

  31. 31.

    Different (and possibly inconsistent) terms are found denoting spatial resolution. Just as an example, [108] use “coarse resolution” for pixels larger than 100 m, “medium” for dimensions between 10 and 100 m, and “high” for a resolution equal to or finer than 10 m, while [43] introduce the following nomenclature for TIR pixel size: “ultra-fine” resolution for pixel sizes of less than 1 m, “very fine” fo sizes of 1–5 m, “fine” for 5–15 m, “medium” for 15–100 m, and “coarse resolution” for pixel sizes greater than 100 m.

  32. 32.

    Ground-Resolved Distance (GRD) is an alternative parameter frequently used.

  33. 33.

    The aperture axis is understood to coincide with the pointing direction of the beam.

  34. 34.

    To simplify the notations, average is not indicated, but it is implied when measuring solar radiation or the Earth’s thermal emission.

  35. 35.

    Reflection can be considered a particular (coherent) case of scattering.

  36. 36.

    It should be remembered that the emissivity depends on polarization according to the basic results throughout Chap. 8, and that usually T S is an equivalent temperature.

  37. 37.

    The reciprocity approach replaces receiving devices with virtually transmitting ones, keeping phase features.

  38. 38.

    In practice, the IFOV angle is generally determined by the field stops forming the instrument optics.

  39. 39.

    The effective area A e includes the spectral response for each instrument channel “centred” on \(\lambda _{\mathrm{c}}\).

  40. 40.

    As usual, the aperture boresight is assumed to be the system pointing direction.

  41. 41.

    The target is assumed to be in the direction of the antenna boresight.

  42. 42.

    Accurate analysis actually requires considering the point spreead function [12, 34] of the system.

  43. 43.

    Different angular discrimination criteria may be found.

  44. 44.

    The radar system scans the region of atmosphere to be monitored by changing the direction of the antenna boresight with time, either mechanically or electrically, in a known fashion.

  45. 45.

    Also aerosol particles in lidar observation.

  46. 46.

    Substantially analogous alternative definitions can be found.

  47. 47.

    The difference between ground range , that is along the reference earth surface, and slant range , i.e., along the satellite-to ground path, should be well kept in mind.

  48. 48.

    The limitation in spatial resolution set by the distance R in (11.43) is clearly mitigated when the observations are carried out from aerial platforms.

  49. 49.

    Practical reasons related to the processing time lead to a synthesis technique exploiting the Doppler frequency shift of the received scattered field.

  50. 50.

    Enhanced spatial resolution may require particular observing techniques, such as the spotlight mode.

  51. 51.

    The formalism is readily extended to airborne platforms.

  52. 52.

    Atmospheric extinction is neglected here.

  53. 53.

    The theoretical limit d a = a (Fig. 11.27) is overcome by suitable synthesis processing.

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  1. Dipartimento di Ingegneria Civile e Ingegneria Informatica, Tor Vergata University, Roma, Italy

    Domenico Solimini

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Solimini, D. (2016). Antennas and Apertures in Earth Observation. In: Understanding Earth Observation. Remote Sensing and Digital Image Processing, vol 23. Springer, Cham. https://doi.org/10.1007/978-3-319-25633-7_11

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