**Example 2.1: Assuming that a leaf blade is divided into 2 thin layers, each of which has a reflectance of 0.4 and a transmittance of 0.3, calculate the total reflectance and transmittance of the blade.**

Answer: See textbook

**Example 2.2: Assuming that the other conditions for a particular conifer are the same as the default values in Table 2-2, the LIBERTY model is used to simulate the reflectance at 670 nm and 870 nm for values of chlorophyll content of 50, 100, 200 and 500 and to calculate the NDVI.**

Answer: In RAPID2 software, select Tools->Leaf Spectrum menu, tick the LIBERTY option to simulate. Input the specified parameters, you can get 400 to 2500nm simulation of the spectral curve, select the value of 670nm and 870nm, you can get the results, respectively, 0.054, 0.520, NDVI is 0.812.

**Example 2.3: A broadleaf, approximately 5.6 cm in length and width, 0.1 cm in thickness, and 50 per cent moisture content by weight, is available at room temperature 25°C. Calculate the dielectric constant and the scattering cross section (dB) at different angles.**

Answer: In RAPID2 software, select Tools->Leaf Spectrum menu, tick Dielect option to simulate the blade dielectric constant.Tick the RadarAngle option to simulate the backscattering coefficient at different angles. Input the specified parameters to get the simulation curve.

**Example 2.4: The scattering cross-section (dB) at different angles is calculated for an existing tree trunk, 15 cm in diameter, with a moisture content of 40 per cent by weight, at a room temperature of 25 degrees Celsius.**

Answer: In RAPID2 software, select Tools->Stem/Branch Spectrum menu, tick Dielect option to simulate the dielectric constant of the trunk and branches. Tick the RadarAngle option to simulate the backscattering coefficients at different angles. Input the specified parameters to get the simulation curve.

**Example 2.5: Set a soil roughness of 0.015 cm, an associated length of 18 cm, and a weight moisture content of 30 per cent, and calculate the soil scattering cross section (dB) at different angles at room temperature of 25 degrees Celsius.**

Answer: In RAPID2 software, select Tools->Soil Spectrum menu, tick Dielect option to simulate soil dielectric constant.Tick the RadarAngle option to simulate the backscattering coefficient at different angles. Input the specified parameters to get the simulation curve.

**Example 2.6: Please use the default values of the 5-Scale model (Table 2-4), modify the plant density to 1000 plants/ha, and then adjust the canopy radius to 0.1, 0.5, 1.0, 1.5, 2.0, and 2.5 m. Plot a line graph of the change in NDVI as a function of the canopy radius under vertical observation.**

Answer: In the five-scale GUI interface, click the menu Input parameters, input parameters, the lower left corner of the Crown radius (m) parameter is the crown radius.Modify it to 0.5, and then click OK, then click Run button on the toolbar, you can get the BRF curve in the main plane under 0.5m crown radius. Click the Switch view tool to see the reflectance table, record the NDVI of the point under the star. follow this method, continue to record the reflectance of other canopy radius, and then make a graph. See the textbook for details.

**Example 3.1: How to calculate canopy LAI when the porosity P is known for a given direction of observation (zenith angle theta).**

Answer: When the canopy is uniform and the leaves are ellipsoidically distributed, LAI = -2*cos(theta)*ln(P).When the canopy tends to have an aggregated distribution, the aggregation is usually described by the aggregation index C(0-1), LAI = -2/C*cos(theta)*ln(P)

**Example 3.2: Referring to Table 3.2, build a look-up table (LUT) for reflectance and chlorophyll and leaf area index for uniform vegetation based on the SAIL model and implement the inversion in code.**

Answer: See the textbook for the main steps.For specific algorithm code, please refer toMatlab code for LUT inversion

**Example 4.1: Write a Random Sampling Consistency ( RANSAC) algorithm for circle fitting for extracting chest diameters from a point cloud.**

Answers:Matlab Code Download

**Example 5.1: It is known that a SAR image has a pixel azimuth resolution (Azimuth Pixel Spacing) of 13.95m, a pixel distance resolution (Range Pixel Spacing) of 2.32m, and an Incidence Angle (Incidence Angle) of 39.27°, compute the ground-distance resolution and the number of views in order toperform multiview processing.**

Answer: Geopotential resolution = 2.32/sin(39.27°) = 3.67 m. A view number of 4 gives a geopotential resolution of 3.67m×4 = 14.68m.To get an approximate resolution of 14.68m, the azimuthal view number is 1, and the resolution after multiview is 13.95m.

**Example 6.1: Calculate the blackbody radiation at temperatures of 300 K, 800 K, 1400 K, 1900 K, and 2400 K at wavelengths from 0.4 to 4.0 um in steps of 0.05 um, plot the radiation curves, and verify Wien's displacement law.**

Answers:Matlab Code Download

**Example 7.1: Please use the PROSPECT model to simulate the spectral curves of leaves under different water content conditions, observe whether they are consistent with the textbook trends in reflectance, calculate the plant water spectral index, and analyse the relationship between the spectral index and water content by plotting a scatter plot.**

Answer: Fix the other variables in the PROSPCT code in Matlab, and use a for loop to change the EWT value to get the spectral curve of the leaf under different water content.Where water content FMC = EWT/DMC. see the textbook.