CEE 610: Remote Sensing Fundamentals
1.
Angular measurements
1 EXAM 1
As reported in Science News in the Fall of 2002 (Science News, 162(9):141), an observation by a telescope equipped with adaptive optics (optics systems that compensate for atmospheric fluctuations that would otherwise blur the image), achieved an effective resolution of ~130 m when imaging the lunar surface. The image was collected at an oblique incidence angle on the moon, and if the surface had been perpendicular to the viewing direction the corresponding resolution limit would have been
100m. This corresponds to a pixel size of 50m. The same article reported that a single pixel of the digital camera viewed a square with angular dimensions of 0.027 arcsec (1.31 x 10
-7
rad) on a side.
(See: http://www.eso.org/outreach/press-rel/pr-2002/phot-19-02.html
.) a.
[1.0] Assuming that the surface imaged was on a surface of the moon that was perpendicular to the telescope viewing direction, what is the solid angle that would correspond to a pixel size of
50 m x 50 m area on the lunar surface? b.
[0.5] If a polar orbiting satellite flying at an altitude of 800 km had an imaging system that was capable of the same angular resolution, what would the spot size be on the earth immediately below the satellite (viewing at nadir, or a viewing angle of 0

). The earth-moon distance is d em
= 3.84 x 10
8
m.
2.
Radiometry
Given:
Earth-sun distance (Astronomical Unit)
Mars-sun distance
Radius of the sun
Radius of Earth
Radius of Mars
Solar constant
Stefan-Boltzmann's constant
A.U.
D mars
R sun
R e
R mars
E s

1.50E+11
2.28E+11
6.95E+08
6.37E+06
3.38E+06
1.37E+03
5.67E-08 m m m m m
W m
-2
W m
-2
K
-4 a.
[1] Use the Stefan-Boltzman Law to estimate the temperature of the sun assuming that the sun is a blackbody. (Hint: Find the area at the sun's surface corresponding to the solar constant for the earth. The solid angle subtended by a 1m
2
area on the earth's surface subtends a much smaller area on the sun's surface, but the same amount of energy flows through this area. The irradiance on this smaller area is the solar emittance. Knowing the solar emittance, compute the approximate temperature at the sun's surface. Check your answer against published values.) b.
[0.5] Using your estimate of the sun's temperature, compute a solar constant for Mars, E mars

CEE 610: Remote Sensing Fundamentals 2 EXAM 1
3.
Reflectance
The radiance measurements shown below have been made using the same instrument to observe both the target and the standard. You may assume that the dark current measurement remained constant during all measurements. L i
and L si
represent measurements made at time t i
. The standard used during this exercise was a Lambertian standard with a 50% reflectance at all wavelengths. a.
[1.5] In the data provided below, L dark
= dark current, L i
= radiance from a target, and Ls i
= radiance from a standard collected immediately after the target radiance. Correct the readings for dark current, compute the remote sensing reflectance, R
RS
, for each of the four targets and plot the results. Determine if the four targets are similar or different in terms of Remote Sensing reflectance. (Assume that the uncertainty in reflectance is ±1%.)
Source Data

L dark
L
1
Ls
1
L
2
Ls
2
L
3
Ls
3
L
4
Ls
4
(µm) counts counts counts counts counts counts counts counts counts
0.45 30 136 1065 145 444 80 547 118 340
0.55
0.65
20
10
278 2349 575 1650 248
452 3825 1133 3062 347
1417 404 1184
3444 829 2299
0.75
0.85
20
25
286 2250 915 1804 1371
163 1163 526 935 773
2250 832 1581
1163 535 935 b.
[1.0] If you had to choose only 2 of the 5 spectral bands to optimally discriminate among the 4 targets based on their reflectance spectra, which bands would you choose? Please justify your answer. c.
[0.5] Would the choice be the same if you were basing your choice on the radiance spectra?
4.
Scale issues a.
[1.0] Given an image taken by a camera with a focal length of f = 3" and a photo scale =
1:30,000, what was the altitude of aircraft if the average terrain elevation was 1,000 ft.? b.
[1.0] An image collected at a flying height of 12,000 ft. has a nominal scale of 1:18,000.
Determine the focal length in millimeters. c.
[1.0] A one mile long section of road (5,280 feet) appears on an image with a photo distance of
1.5". The photo was taken with a camera having a focal length = 6 inches. i.
What is the scale of the image? ii.
What was the altitude of the aircraft?
5.
Extra Credit
[1.0] When a color slide (positive transparency) is projected on a screen for display, is this an example of an additive or subtractive color process? Please explain your answer.