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Chapter: 6 -Problem: 1 >> The cross-section of a glass prism is an equilateral triangle. The refractive index of the glass is 1.601 at a free-space wavelength of 0.4 ?m and 1.569 at 0.7 ?m. Show that if white light is incident on the prism at an angle of 40? to the surface normal, the spectrum from 0.4 to 0.7 ?m will be dispersed over an angular width of 4.9?.
Answer Preview: We have and the total deviation of the ray is c 20. For n …

, Chapter: 3 -Problem: 10 >> Prove Equation 3.29.vvg = c2,
Answer Preview: Combining equations (3 83) …

, Chapter: 2 -Problem: 3 >> Show that Equation (2.31) can be approximated by Equation (2.33) at sufficiently low frequencies. exp(x) ? 1 + x when |x| << 1.
Answer Preview: Using the hint, we see tha…

, The Planck formula can be inverted to obtain the brightness temperature from the spectral radiance as follows: Show that, for observations at a wavelength of 10.7 ?m, K1 and K2 have values of 851 W m-2 sr-1 ?m-1 and 1347 K respectively. Hence calculate the brightness temperature of a body whose spectral radiance is 5.84 W m-2 sr-1 ?m-1 at a wavelength of 10.7 ?m.
Answer Preview: K1 = 851 W m-2 sr-1 ?m-1 K2 = 1347 K To calculate …

, Chapter: 10 -Problem: 5 >> The satellite Jason is in a circular orbit with a semimajor axis of 7714 km and an inclination of 66°. (i) Show that this orbit is suitable for altimetry. (ii) Comment on the suitability of the orbit for measuring ocean tides.
Answer Preview: (i) We can use equations (10 19) to (10 21) to calculate the velocity of the subsatellite point rela…

, Chapter: 9 -Problem: 4 >> ASAR operates at a frequencyof 5.3GHz. Its satellite platformis 775kmabove the Earth’s surface and has a speed relative to the surface of 6.73 kms-1. The swath width is 100 km and the incidence angle at the centre of the swath is 23°. The along-track resolution is 30m. Estimate (i) The coherence time of the radiation transmitted by the radar, and (ii) The difference in two-way travel time between
Answer Preview: First we consider a single component, with amplitude aand phase . Writing …

, Chapter: 3 -Problem: 7 >> Consider scattering form a surface with r.m.s. height variation of ?/2, where ? is the wavelength. Show that the stationary phase model can describe this scattering provided that the incident angle is less than about 60o and m < 0.60, whereas the scalar model requires m < 0.25, where m is the r.m.s surface slope variation.
Answer Preview: Write R = A cos 0 cos 1 for the BRDF, where A is a cons…

, Chapter: 3 -Problem: 11 >> According to the Minnaert model of surface scattering, the BRDF R is given by where A and a are constants; θ0 and θ1 are the angles between the incident and scattered rays, respectively, and the surface normal; and the BRDF has no azimuthal dependence. Show that the reflectivity r at angle θ0, and the diffuse albedo rd, are related through in this model.
Answer Preview: The absorption coefficient is given by equation (3 87) as a = n a where n is the number density of a…

, Chapter: 3 -Problem: 14 >> Show that Doppler broadening will dominate over pressure broadening of a spectral line for a gas at temperature T and pressure p provided that the wavelength of the spectral line is less than kT/p?, where sis the collision cross-section defined in Equation (3.84).
Answer Preview: Following the argument presented for cloud on page 96 we estimate the …

, Chapter: 10 -Problem: 2 >> Consider a satellite in orbit about a spherically symmetric planet. If the orbit is circular, the sub-satellite point travels uniformly along its circular track. If the orbit is not circular, however, the sub-satellite track is still circular, but the sub-satellite point moves along it at a variable rate. Show that the maximum along-track error in calculating the position of the sub-satellite poin
Answer Preview: Equation (10 10) shows that the lar…

, Chapter: 5 -Problem: 3 >> A vertical aerial photograph reveals a tall building. The foot of one corner of the building has (x, y) coordinates (30.5, 62.0) (both measured in mm from the lower left-hand corner of the negative), and the top of the same edge appears at (19.0, 58.0). The corresponding coordinates for an adjacent edge of the building are (30.5, 73.0) and (19.0, 71.5). Given that the camera’s focal length was 88
Answer Preview: A diagram is helpful! (i) The principal point P is where the projections of the lines BA and DC meet…

, Chapter: 9 -Problem: 3 >> Show that the amplitude of fully developed speckle has a Rayleigh distribution. Assume that the signal is composed of a very large number of components, each of which has the same amplitude but a phase randomly selected from the range 0 to 2?.
Answer Preview: (i) If the along-track resolution is r a , and the distance from the antenna to the ground is R, the …

, Chapter: 11 -Problem: 1 >> How many uniformly spaced geostationary satellites would be needed to ensure that all points on the Earth’s surface with latitudes less than 66.5° can be seen at an elevation angle of at least 10°?
Answer Preview: Putting = 10 and h = 35800 km into equation (11 1) gives = …

, Chapter: 3 -Problem: 6 >> A rough surface has a BRDF proportional to cos(?0)cos(?1), where ?0 and ?1 are respectively the angles of the incident and scattered radiation measured from the surface normal. The BRDF has no azimuthal dependence. Show that, if the albedo for normally incident radiation is 1, the diffuse albedo of the surface is 2/3.
Answer Preview: In section 3 3 2 it is shown that the diffuse albedo is given by whe…

, Chapter: 2 -Problem: 1 >> The electric field of an electromagnetic wave in free space is given byEx = 0Ey = Ecos(?t - kx)Ez = 2Esin(?t - kx)where E = 1 kVm-1. Find (i) the direction of propagation,(ii) the polarisation,(iii) the magnetic field and(iv) the flux density of the radiation.
Answer Preview: (i) The direction of propagation is along the positive x-axis (this can be se…

, Chapter: 7 -Problem: 4 >> A passive microwave radiometer operating at 37 GHz has an effective area of 0.3 m2, and can detect a change of 0.9 K in its antenna temperature. It is operated from an altitude of 800 km to observe a single ice floe (whose brightness temperature is 253 K) surrounded by water (brightness temperature 119 K). Calculate the area of the smallest detectable floe.
Answer Preview: If the fraction of the footprint occupied by ice i…

, Chapter: 8 -Problem: 6 >> For microwave radiation propagating vertically through the Earth€™s atmosphere, the delay to a pulse as a result of the dry component of the atmosphere, expressed as an equivalent distance, is 2.33 meters irrespective of frequency. The corresponding figure for the water vapour component of the atmosphere is 7.10 meters per meter of precipitable water, again irrespective of frequency. (i) Explain w
Answer Preview: (i) The propagation delay in each case is proportional to the column-integral of the density of the …

, Chapter: 6 -Problem: 6 >> A surface shows daily temperature fluctuations with amplitude 23 K, lagging 2.3 hours behind the fluctuations in incoming solar radiation. Use the model of thermal inertia developed in this chapter to estimate (i) The value of ?cK, (ii) The amplitude of the variations in the incoming solar flux, if the value of ? is taken as 5.5 W m–2 K–1. By differentiating Stefan’s law with respect to temperat
Answer Preview: Substitute the expression for (h) into equation (6 30): Now make the s…

, Chapter: 3 -Problem: 13 >> The absorption cross-section at 20 GHz of a water droplet with a radius of 48 ?m is about 2 × 10-11 m2. Hence calculate the absorption coefficient of a cloud consisting of droplets of radius 48 ?m with a number density of 2 million droplets per cubic metre. Would you expect this cloud to be opaque?
Answer Preview: The two-stream model is represented by equations (3 98 1) and (3 98 2) and we are looking fo…

, Chapter: 3 -Problem: 9 >> A typical pack of freshly fallen snow has a density of 100 kg m-3 and consists of ice crystals which can be modelled as spheres of radius 0.5 mm. Show that if the snow pack is sufficiently deep it would be expected to have a visible-band albedo close to 1, and estimate the depth necessary for this to occur. The absorption coefficient for light in ice can be taken as 0.01 m-1, and the density of pu
Answer Preview: First we consider the stationary phase model. Condition (3 …

, Chapter: 6 -Problem: 5 >> Assume that the atmospheric absorption coefficient γ varies with height h as and use the simple model of limb-sounding geometry derived in Section 6.7.4 to show that the reduction in intensity I is given by where h0 is the height at which the radiation path passes closest to the Earth€™s surface. For atmospheric aerosols under clear-sky conditions, 1/β ‰ˆ 3 km and 1/γ0 ‰ˆ 14 km for visible ra
Answer Preview: The phase angle between the incoming solar flux and the surface temperature fluctuations is g…

, Chapter: 3 -Problem: 4 >> Randomly polarised radiation at a wavelength of 3 cm is incident on a plane water surface at an angle of 83o to the normal. Calculate the Stokes vector, and hence polarisation state, of the reflected radiation. The dielectric constant of water at 3 cm is 63.1 – 32.1i.
Answer Preview: We can write the dielectric constant of (3 24) as and so t…

, Chapter: 4 -Problem: 1 >> Assuming that the temperature T of the troposphere is given by the expression T = 288 - 0.0065z, where T is measured in kelvin and z is the altitude in meters, and that the pressure p in kPa is given by p = 101(T/288)5.25, calculate the density of the troposphere at an altitude of 10 km.
Answer Preview: At z = 10000 m the temperat…

, Chapter: 9 -Problem: 1 >> A radar transmits a power of 4 kW at a wavelength of 5 cm and over a range of 800 km. If the radar can detect a received signal of 10 - 16 W, calculate the required gain of the antenna, and hence estimate the area of the antenna, if it is to be able to detect values of ?0 down to –25 dB from an area of 103 m2. Assume that the antenna has unit efficiency.
Answer Preview: We can rearrange equation (9 4) to …

, Chapter: 6 -Problem: 2 >> Sunlight is incident on a rough surface at an angle of 450 to the normal. Calculate the brightness temperature of the surface at wavelengths of 4 ?m and 10 ?m, assuming that the surface is a perfect Lambertian scatterer (i.e. one for which the diffuse albedo is 1) at both wavelengths. Ignore atmospheric propagation effects.
Answer Preview: From equation (2 24), the spectral irradiance at the surface ca…

, Chapter: 3 -Problem: 8 >> Verify the solution given in the text for the two-stream scattering model.
Answer Preview: The reflectivity is given by This can e…

, Chapter: 3 -Problem: 12 >> If scattering is insignificant, show that the radiative transfer equation may be written as and if hf = kT this can be rewritten as By comparing these two equations, show that Explain its significance. Transcribed Image Text: 2hf3 c2(ehf ]kt – 1) dLf dz -- L; = Ya ??? %3 7a(? — ??). dz
Answer Preview: The first result follows very straightforwardly from substituti…

, Chapter: 8 -Problem: 1 >> A laser profiler is operated at a wavelength of 1?m from an altitude of 10000 m, and views at 45° to the nadir. Estimate the range corrections needed to account for the dry atmosphere and the water vapour component if the atmosphere contains 50 mm of precipitable water. The atmospheric pressure at 10000 m altitude can be taken as 0.26 atmospheres.
Answer Preview: Figure 8 7 shows a dry-atmosphere zenith correction of about 2 35 m for …

, Chapter: 4 -Problem: 4 >> Use Equation (4.12) to show that, at low microwave frequencies, the absorption coefficient of a cloud of water droplets is given approximately by (i.e. independent of the droplet size), where ris the mass of water in kg per m3 of cloud. Assume that, for water at microwave frequencies, εp = 75.9, εˆž = 4.5 and Transcribe
Answer Preview: Assume that the water droplets are spherical with radius a. The absorption cross-section of each dro…

, Chapter: 11 -Problem: 2 >> (i) Estimate appropriate values, corresponding to those in Table 11.1, for printed paper as a data storage medium. (ii) Estimate the potential data storage requirements from a 5-year spaceborne remote sensing mission. Table 11.1 Transcribed Image Text: Medium/device Storage capacity (GB) Volume nee
Answer Preview: A printed page of A4 paper might contain up to around 1000 Engl…

, Chapter: 9 -Problem: 5 >> A SAR operates at a wavelength of 6 cm and is used for interferometric SAR observations. In position M, the radar has (x, y) coordinates (-400000, +800000) m, while in position S its coordinates are (-400100, +800000) m. A scatterer A located near the origin has coordinates (x, y).(i) Show that the range from M to A is given approximately by 0.4472136x - 0.8944272y plus a constant, and that the di
Answer Preview: (i) The range from M to A is where (x M , y M ) are the coordinates of M. Thus Setting x M = - 40000…

, Chapter: 8 -Problem: 5 >> Prove Equation (8.16). Equation 8.16 Transcribed Image Text: dP, P,(t+2(h – H)/c)f(h)dh dt 0-
Answer Preview: Suppose the radar is located a height H above the mean surface, and cons…

, Chapter: 11 -Problem: 3 >> Identify the nature of the spatial filters whose kernels are given below: (i)                     (ii)                     (iii)1 3 1              1 3 1             –1 –3 –1 3 –8 3            3 6 3             –3 16 –3 1 3 1             1 3 1             –1 –3 –1
Answer Preview: The satellite data given in the box on pages 353-4 show that, in band 6 1, a digital nu…

, Chapter: 8 -Problem: 4 >> A radar altimeter emits a pulse whose variation of power with time is Gaussian with a length of 3.00 ns between 1/e points. The pulse is reflected from a surface whose height distribution is Gaussian with a range of 1.00 m between the 1/e points. Calculate the time for the reflected pulse to rise from 8% to 92% of its final value, neglecting coherence effects.  Distribution
Answer Preview: From equation (8 16), the time-differential of the return pulse is the convolution of the transm…

, Chapter: 3 -Problem: 1 >> Show that the real and imaginary parts of the refractive index of a non-magnetic material are given by Transcribed Image Text: 22+e"2+£,2 2'2+e"2-e' m? ? K' %3D
Answer Preview: Rearrange (3 12 2) to make the subject, substitute for into (…

, Chapter: 8 -Problem: 2 >> An airborne scanning laser profiler transmits pulses at a frequency f0. Its field of view is scanned in a direction perpendicular to the aircraft€™s velocity through an angle ±Î¸ either side of the nadir direction, at a scanning frequency fs. The aircraft€™s speed is v and its flying height is H over level ground. The spatial arrangement of samples on the surface is shown schematically in Figure 8
Answer Preview: The time taken for one complete back-and-forward scan of the mirror is 1/f s , during which the airc…

, Chapter: 11 -Problem: 6 >> The relationship between spectral radiance Lλand brightness temperature T in a thermal infrared band of a satellite sensor can be expressed as For band 6 of the Landsat-7 ETM + instrument, the constants have values K1 = 666.1 Wm-2 sr-1 mm-1 and K2 = 1282.7 K. Use the satellite metadata given in Section 11.2.1.1 to find the at-satellite brightness temperature corresponding to a digital number of
Answer Preview: The image histogram is approximately where A is a constant. The total number of pixels in …

, Chapter: 7 -Problem: 5 >> If the atmospheric microwave absorption coefficient γ varies with height z as γ = τ βexp (-βz), τ being the optical thickness of the entire atmosphere, show that the brightness temperature measured by a passive microwave radiometer looking vertically down through the atmosphere is given by where the weighting function a(z) is given by Show that a(z) takes its maximum value at (ln τ)/β, a
Answer Preview: First, plot the points W, M and F corresponding to water, first-year and multi-year ice and connect …

, Chapter: 3 -Problem: 5 >> Show that the diffuse albedo for specular reflection of perpendicularly polarised radiation and confirm that this expression has the correct limiting forms as the refractive index n tends to 1 and to infinity. Transcribed Image Text: ??? — 2?—1 3(?+1)?
Answer Preview: The following Octave code calculates the values of rpar and rperp, the perpendicular and parallel am…

, Chapter: 7 -Problem: 1 >> Use the data of Table 7.1 to show that the effective area of a rectangular or circular paraboloidal antenna is roughly equal to its geometrical area. Table 7.1 Transcribed Image Text: HPBW (degrees) D (dB) Antenna type Sidelobes (dB) Notes Monopole Short dipole Half-wave dipole Six-element Yagi (is
Answer Preview: We can calculate the effective areas from the directiv…

, Chapter: 5 -Problem: 1 >> Estimate the illuminance at the Earth€™s surface due to solar illumination when the Sun is 450above the horizon. Use Equation (5.1), but approximate the function V(λ) shown in Figure 5.1 by a function that is 1 for λ  between 0.51 μm and 0.61 μm, and zero everywhere else. Compare your answer with Figure 5.18.Figure 5.1
Answer Preview: The mean exoatmospheric irradiance due to the Sun at the Earth is (page 34) 1 37 kW m -2 , and t…

, Chapter: 4 -Problem: 3 >> The meteorological visibility in fog is defined as the distance that gives an optical thickness of 4. If a typical fog has a mass density of 10-3 kg water per cubic metre and gives a visibility of 100 m, estimate the size of the water droplets.
Answer Preview: If we assume that the water droplets are all spherical with radius a and scattering cross-section …

, Chapter: 8 -Problem: 3 >> Explain how it is possible for the horizontal resolution of a radar altimeter to exceed the limit set by diffraction at the antenna, provided that the pulse duration tpis short enough, and derive the result that the resolution is given by 2(cHtp)1/2, where c is the speed of light and H is the range to the surface. (Ignore any effects arising from the Earth€™s curvature.) Hence show that the vertic
Answer Preview: The answer to the first part of the question follo…

, Chapter: 3 -Problem: 2 >> A commonly used approximation to the absorption length is where λ0 is the free-space wavelength. Show that this approximation is accurate to within 1% if ε"/ε' < 0.28. Transcribed Image Text: .??? la = 2??"
Answer Preview: Substitute the result for from problem 1 into equation (3 15). Introd…

, Chapter: 5 -Problem: 2 >> A typical 35-mm camera with a standard lens and normal outdoor film can be assumed to have the following parameters: focal length f = 50 mm; spatial resolution l = 40 lp/mm; film format w = 25 x 35 mm. Estimate the performance of this system when used to obtain vertical aerial photographs from an altitude of 5000 m.
Answer Preview: Scale of negative: 1/100000 (equation 5 6). Spatial co…

, Chapter: 10 -Problem: 1 >> Prove Equations (10.2) to (10.5). Equation 10.2 Equation 10.3 Equation 10.4 Equation 10.5 Transcribed Image Text: Av = 2GM RE R GM Av
Answer Preview: Since we require only to calculate the velocity increments, without consideration of how these are a…

, Chapter: 3 -Problem: 3 >> Sea water has an electrical conductivity ? of typically about 4 S m-1. The real part of its dielectric constant at radio frequencies of 100 MHz and below is 88.2. By assuming that the imaginary part is given by Equation (3.21.2), find the absorption length of electromagnetic waves at 100 MHz and 100 kHz.
Answer Preview: Using the data given in the problem, the dielectric constant of sea water is 88 2 719i at 100 MHz. …

, Chapter: 4 -Problem: 5 >> Use the data of Table 4.3 to estimate the effective raindrop radius, number density and sedimentation rate for rain rates of 1 and 100 mm/hr, assuming that all the drops are spherical and have the same radius.
Answer Preview: For spherical raindrops of radius a, number density n, scat…

, Chapter: 7 -Problem: 6 >> The NASA Team algorithm for calculating sea-ice concentration from SSM/I data defines the polarisation ratio PR as and thegradient ratioGR as where, in both of these expressions,TfP represents the at-satellite brightness temperature of P-polarised radiation at a frequency of f GHz. It is known from experimental measurements that open water shows a PR of typically 0.22 and a GR of 0.08, while mul
Answer Preview: Since we are considering microwave radiation, we can assume the Rayleigh-Jeans approximation to be v…

, Chapter: 4 -Problem: 2 >> The attenuation coefficient of a typical tropospheric aerosol is 0.1 km-1 at sea level, and the total optical thickness of the aerosol for a vertical path through the atmosphere is 0.2. By assuming that the density, and hence the attenuation coefficient, of the aerosol obeys a negative exponential distribution with height (i.e. similar to Equation 4.5), calculate the scale height of the aerosol la
Answer Preview: We model the variation of the attenuation coefficient with …

, Chapter: 2 -Problem: 4 >> Calculate the ratio of the spectral radiances of black bodies at 300 K and 6000 K at (i) A wavelength of 0.1 ?m, (ii) A wavelength of 1 ?m, (iii) A frequency of 1000 GHz, (iv) A frequency of 1 GHz.
Answer Preview: The formula for the ratio is where T 1 = 6000 K and T 2 = 300 K. (i) A…

, Chapter: 9 -Problem: 2 >> A very simplified model of the radar back scattering coefficient of a sea surface is ?0 = A + Bcos 2? where ? is the angle between the wind direction and the radar look azimuth, and A and B are as follows for Ku band scattering at 40° incidence angle, HH-polarisation: A = 0.8v - 30, B = 3.5 - 01vv is the wind speed in ms-1 and ?0 is given by these expressions in dB. A scatterometer observation mea
Answer Preview: If the wind speed is v(metres per second) and its direction is measured from north to east, the data …

, Chapter: 2 -Problem: 5 >> Show that the Fourier transform of the Gaussian function is proportional to and interpret the result. Transcribed Image Text: - ?) f(1) = exp – 202 ioto o?o² exp 2
Answer Preview: From (2 18) we can write the Fourier transform as …

, Chapter: 7 -Problem: 2 >> A phased array is designed to operate at a wavelength of 6 cm. The antenna elements are spaced at intervals of 4 cm. (i) Show that if the beam is steered more than 30° away from the normal (? = 0) direction it will respond to radiation from two directions instead of just one. (ii) Show that this phenomenon of multiple responses can eliminated if the antenna elements are less than half a wavelength
Answer Preview: The discussion in section 7 1 3 shows that the phase shift between adjacent …

, Chapter: 6 -Problem: 3 >> Derive Equations (6.12) and (6.13). Equation 6.12 Equation 6.13 Transcribed Image Text: F = Fo cos(ot – zVoCp/2K) exp(-zVoCp/2K) Fo |T = cos(ot — zV???/2K — ?/4) ?xp(-?V??p/2K).
Answer Preview: Equation (6 6) shows that so Similarly equation (6 7) shows that so Thus which is eas…

, Chapter: 6 -Problem: 4 >> A two-look TIR radiometer views the same point on the Earth€™s surface at nadir and at 60 degrees from nadir. The brightness temperature of the detected radiation is T1and T2respectively. By assuming that the surface is a black body of temperature Tb, the atmosphere has a uniform temperature T1, and that the Rayleigh€“Jeans approximation is valid, show that and hence calculate Tb if T1 = 274.0 K,
Answer Preview: Differentiate equation (6 10) with respect to z and …

, Chapter: 6 -Problem: 7 >> The output of the band 6 sensor of the Landsat-7 ETM + instrument, as represented by an integer pixel value in an image, is the nearest integer to 16.03(L + 3.2) + 1, where L is the at-satellite spectral radiance measured in units (W m–2 sr–1 µm–1) as the graph. Band 6 is a TIR band, and the relationship between measured spectral radiance and brightness temperature can be assumed to be given by Eq
Answer Preview: If the band 6 output is 145, we know that 16 03 (L + 3 2) + 1 = 145 w…

, Chapter: 5 -Problem: 4 >> An aerial photographic system is used for stereophotography. The film negative is a square of sides, the focal length is f, the baseline is band the photographs (which are acquired with the camera pointing vertically downwards) are obtained from a height H above sea level. The stereophotographs are used to determine the height h of topographic variations above sea level. It can be assumed that f «
Answer Preview: (i) The analysis on page 153 shows that the difference in the relief displacement between two vertic…

, Chapter: 8 -Problem: 7 >> A chirp signal, in which the angular frequency rises uniformly from ω0€“Δω/2 to ω0+ Δω/2 over a time T, can be written as exp(iφ(t)), where the phase φ(t) is given by for |t| ‰¤ T/2. This signal is then passed through a delay-line, whose effect on a component of angular frequency w can be represented as multiplication by the factor  Show that the signal that emerges from the delay-line i
Answer Preview: First, find the Fourier transform of the original chirp signal: The sig…

, Chapter: 10 -Problem: 3 >> A satellite is in a circular sun-synchronous orbit with an inclination of 98.2°. It makes exactly 233 orbits of the Earth in exactly 16 days, and crosses the equator southbound at 0930h local time. Calculate the local time at which it crosses latitude 52° north in the southbound direction.
Answer Preview: We are considering the descending (southbound) part of the satellite's orbit. For definiteness, let …

, Chapter: 11 -Problem: 5 >> (i) Show that if A, S and E are, respectively, isotropic smoothing (averaging), sharpening (high-boost) and edge-detection (high-pass) filters described in the spatial domain, and I is the identity operator, the following are possible relationships: (a) S = aI + (1 - a)A,(b) E = b(I - S). Discuss the range of values that a and b can take, and any further modification of (b) that may be needed in a
Answer Preview: (i) Consider the behaviour of each type of filter in the spatial frequency domain: q = 0 q large I 1 …

, Chapter: 11 -Problem: 4 >> A single band of an image has a histogram with a Gaussian distribution of standard deviations. Show that the theoretical limit to which the data can be compressed using Huffman coding is log2 Ïƒ + 2:05 Distribution The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual secur
Answer Preview: All the filters are isotropic, i e. they do not have any directionality. The change of sign in (a) s…

, Chapter: 2 -Problem: 2 >> When radiation having a Stokes vector S = [S0, S1, S2, S3] is incident on an antenna that receives only linearly x-polarised radiation, the detected power is proportional to S.P, where P = [1,1,0,0]. Show how the detected power varies with the polarisation state for radiation of a given flux density.
Answer Preview: For example, using the Stokes vectors given in section 2 2, …

, Chapter: 10 -Problem: 4 >> The nodal period of a satellite in a circular orbit of radius a and inclination i about the Earth is given by and the angular frequency of precession about the Earth€™s polar axis is given by where z = (a/ae) and ae is the Earth€™s equatorial radius, 6378.160 km. The coefficients in the equations areα = 5069.3sβ = 1.62395 x 10-3γ = 2.01280 x 10-6The orbit of the Envisat satellite is circular,
Answer Preview: (i) The angular frequency of precession is which is very close to the Earth's angular speed around t…

, Chapter: 7 -Problem: 3 >> At 10 GHz and a certain incidence angle, the apparent brightness temperatures of sea water, first-year ice and multi-year ice are 80 K, 252 K and 200 K respectively. At 37 GHz these figures become 119 K, 253 K and 168 K. If a microwave radiometer measures a brightness temperature of 180 K at both frequencies, what are the fractions of open water and multi-year ice present in the IFOV?
Answer Preview: The observed brightness temperature will be an area-weighted average of the different spec…

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12 Reviews for Physical Principles of Remote Sensing Textbook Questions And Answers