E Ang
Moreover, the polarization and electric field are related through the dielectric constant by P s s0 E, so thatEq. 3.7.5 also gives the dielectric constant in terms of frequency. Maxwell's equations for a polarized medium lead to the wave equation For a plane wave travelling in the x-direction, and with the help of Eq. 3.7.5 , Eq. 3.7.6 reduces to 1 d 2E m s0 2 2 i d J d t2 The solution to this equation is given by Eq. 3.7.1 or 3.7.2 . Recognizing that the coefficient of the time-derivative term...
f n I Q
is the phase integral. By definition, the phase function, I 0 1 0 , is unity at zero phase angle. For the outer planets a measurement of the phase integral cannot be performed from Earth, and data from a space platform are required. Considering Eq. 8.6.9 , 8.6.10 , and 8.6.17 , the geometric albedo is p p a,0 sina cos a dadfi. 8.6.19 For the special case of a Lambert surface, where p is a constant, p can be evaluated analytically, However, real surfaces and atmospheres deviate from the...
Instrument effects
Interpretation of planetary measurements is a difficult task, even when emission and reflection spectra are precisely known. In reality, the task is even more complicated because physical parameters of planetary atmospheres and surfaces must be retrieved from data recorded by real instruments. Such devices do not faithfully reproduce planetary spectra, such as the full resolution spectra discussed in Chapter 4. Instead, instruments modify the true spectral radiances in several ways. The...
a Michelson interferometer
cadmium emission as a single, narrow line and confirmed the yellow sodium emission as a doublet. To perform the Fourier transformation Michelson amp Stratten 1898 constructed a mechanical Fourier analyser, and Michelson 1898 applied it to the investigation of magnetically broadened spectral lines. Although the principles of Fourier transform spectroscopy were clearly demonstrated, Michelson could not have used his interferometer as a spectrometer in the modern sense without the availability of...
The emerging radiation field
The last chapter dealt with the interaction of radiation with matter, mostly in the gaseous, but also in the liquid and solid phases. Absorption coefficients of infrared active gases, emission and scattering properties of surfaces, and single scattering albedos and phase functions of aerosols were considered. Applications of these concepts, along with the principles of radiative transfer discussed in Chapter 2, enable us to calculate the emerging radiation field of a planet or satellite. In...
b The solar radiation field
The solar flux crossing a horizontal plane depends on the Sun's elevation angle but is independent of azimuth. The infrared radiation field is always azimuthally symmetric. Therefore, because only fluxes contribute to heating rates, we are interested solely in azimuth-independent radiation fields in our analysis. By analogy with Eq. 2.5.10 , the appropriate equation for describing the transfer of radiation in the visible channel is a d v I tv, a - 2j2 amp IPi a PV I tv, aW - 4F amp IPi a Pi -ao...
Clouds and aerosols
The inference of cloud characteristics is based on much less sophisticated approaches than those for determining thermal structure and gas abundances. Clouds tend to be quite inhomogeneous compared with gaseous mixtures and require more parameters for adequate definition. Also, the appropriate equation of transfer Eq. 2.1.40 is considerably more complex than Eq. 8.2.1 , and not nearly as amenable to inversion techniques. Even so, direct techniques are sometimes capable of leading to rather...
Info Ebf
Fig. 6.3.2 Spectrum of Jupiter recorded with the Composite Infrared Spectrometer CIRS on Cassini. Fig. 6.3.2 Spectrum of Jupiter recorded with the Composite Infrared Spectrometer CIRS on Cassini. Fig. 6.3.3 Thermal emission spectra of Uranus and Neptune obtained with the Michelson interferometer IRIS carried on Voyager 2. The solid curves represent averages of 125 individual spectra from Uranus and 157 spectra from Neptune. For clarity the spectra have been offset from one another by 5 K. The...
Radiative equilibrium
The absorption of solar radiation leads to heating within the atmosphere, while cooling is achieved by the emission of infrared radiation. Thermal gradients are established, and the magnitudes and directions of these gradients, coupled with the forces of gravity and planetary rotation, give rise to imbalances in local pressure fields that lead to atmospheric motions. These internal motions are responsible for additional energy transport, and it is the balance of the dynamical and radiative...
Info Pdq
Fig. 5.4.3 Scanning function for a rectangular solid line and a circular dashed line field of view. sampling rate should, therefore, be at least 342 samples s-1. The lowest frequency to be reproduced is d.c. or zero hertz. Therefore, this type of radiometer is called a d.c. radiometer. However, detecting and amplifying d.c. levels is inconvenient. As a compromise, one may limit the low frequency end of the passband at 0.05 Hz, that is, well below that given by the rotation rate of 0.5 Hz in...
Thermistor Bolometer Mirror 1
Fig. 5.8.2 Michelson interferometer similar to the instrument flown on Nimbus 3 and 4 Hanel et al., 1970 . this is not the case. Integration between samples takes place in the electrical filter used to limit the frequency range before the sampling process. On the contrary, the stepping mode is slightly less efficient, because the time spent while moving the mirror between measurement points is lost. In the constant speed mode the detector signal is modulated sinusoidally at a frequency equal to...
Thermopile Detector 1
INTERFEROMETER MIRRORS AND BEAMSPLITTER ARE ROTATED 90 ABOUT AXIS INTERFEROMETER COLLECTOR 3.84 cm 01A Fig. 5.2.10 Optical layout of the infrared spectrometer on Voyager Hanel el al., 1980 . Fig. 5.2.11 Schematics of an off-axis Gregorian telescope, similar to one used on the Cosmic Background Explorer COBE Project, NASA . Fig. 5.2.11 Schematics of an off-axis Gregorian telescope, similar to one used on the Cosmic Background Explorer COBE Project, NASA . of the infrared photometer flown on the...
c Gas filter selective chopper and the pressure modulated radiometer
Besides solid substances infrared active gases may serve as filters. Many polyatomic gases have strong infrared absorption bands, each one consisting of numerous spectral lines. Absorption cells, charged with a suitable gas and hermetically sealed, are transparent, except at the narrow spectral intervals where the particular gas has absorption lines. Such filters are clearly not general purpose filters, but they are very useful for certain remote sensing tasks. The gas absorption cell differs...
b Chopped or ac radiometers
In the far infrared, where signals usually are weak and where detectors may show 1 f noise, operation at frequencies as low as a fraction of a hertz is often not possible for an explanation of 1 f noise see page 264. To raise the low frequency cut-off of such a radiometer is also undesirable. Inadequate reproduction of low frequencies affects mostly the overall signal level the absolute calibration , while inadequate response at high frequencies affects primarily spatial resolution and...
Detector Jkt
difference between internal and external reflections at the beamsplitter e.g., Born amp Wolf, 1959 . Suppose a collimated beam of monochromatic radiation strikes the interferometer while the movable mirror is set at the balanced position where both arms have equal length. In a nonabsorbing beamsplitter the phase difference between internal and external reflection is 180 . Consequently, both beams interfere destructively as seen from the detector the central fringe is dark. At the same time, the...
Info Apu
Fig. 5.3.1 Relative intensity of a point source impinging on a telescope with central obscuration s as a function of ka sin a see text . Fig. 5.3.1 Relative intensity of a point source impinging on a telescope with central obscuration s as a function of ka sin a see text . Since ka n D X and sin a a for small angles, which is the well-known equation for diffraction limited angular resolution. Because of the A-Omega invariance,