Download 157a_midterm_2016

EE/Ae 157a
MIDTERM/FINAL
Due Date: November 14, 2016
Instructions:
1. Open book, take home
2. No time limit, but it should not take you more than 4 hours to complete
3. No collaboration
Problem 1 (20 points)
A telescope is orbiting Mars at 300 km altitude. The telescope lens diameter is 40 cm,
the focal length is 120 cm, and the focal plane is 4 cm wide. The pixels in the detector
are 10 microns on a side. Calculate the swath width, size of the pixels on the ground, and
the number of pixels across the swath assuming a pushbroom design. Also, calculate the
maximum integration time per pixel, and the resulting data volume per day if we acquire
20 images that are 50 km long in the along-track direction.
The instrument is now changed into a spectrometer. The incoming light is dispersed
using a grating such that the different colors are separated spatially in a direction
orthogonal to the pushbroom line array. Assume that the wavelength region 0.4 microns
to 2.4 microns is dispersed over 1 mm in the focal plane. Now assume that we stack 100
line arrays next to each other to cover the dispersed spectrum. Calculate the bandpass of
each channel, the dwell time per spectral channel and the resulting data volume if we
acquire the same number of images as before.
Problem 2 (20 points)
Consider the case of a planet orbiting a star as shown in the figure below. The planet
orbits the star once every 2 earth days.
Planet appears
from behind star
Planet disappears
behind star
Sun-like star
Transit
starts
Transit
ends
The star has the following characteristics
Tstar  6000 K
Rstar  7  108 m
emissivity  0.8
The planet is tidally locked to the star, so that the side facing the star (day side) is hotter
than the side facing away from the star (night side). The planet has the following
characteristics:
Tday  1200 K
Tnight  900 K
Rp  89000 km
Orbit radius  47 108 m
emissivity  0.3
We are observing this system from a long distance, so we cannot resolve individual
details. Plot the relative intensity that we would observe as a function of time (i.e. as a
function of the planet position in its orbit) at a wavelength of 16 microns. Can we detect
the presence of the planet? Ignore the star light reflected from the planet. Hint: The
total intensity is the sum of the powers emitted by the sun and the planet. For part of the
time, the planet blocks out a portion of the star, which means we receive less starlight.
For a different portion of the time the planet is not visible while it is behind the sun, so
we only receive starlight. Assume that the planet orbit is in the same plane as the equator
of the star, and that we are observing in the plane of the equator of the star. Let us define
time = 0 when the planet is directly behind the star. Further assume that the temperature
of the planet varies linearly between 1200K at t = 0 to 900K at t = 24 hours, and then
back to 1200K at t= 48 hours.
By the way, this is a real-life problem of an actual star/planet combination that was
observed with the Spitzer space telescope.
Problem 3 (10 points)
We are imaging surfaces that could be one or more of the following materials: limestone,
montmorillonite, kaolinite, olivine basalt, and quartz monzonite. Our system images in
five bands as shown in the figure on the next page. Select a set of criteria that would
allow the discrimination and identification of these five materials.