We have several imaging options, but can only afford to use one,so we must understand what will produce the best image ahead oftime. The options are described in detail in Table 1, and consistof:
A large, visible wavelength, CCD telescope on an island.
The same telescope but with photographic film instead of aCCD. Note that the peak wavelength response of the film is shorterthan the CCD. This is important because both the solar illuminationand the emitted radiation from the hotspot will be less at shorterwavelengths, as shown in Table 1. Assume the image is focused onto35 mm film with 1 micron grains.
A CCD telescope on an airplane. This telescope has a smalleraperture than the ground-based telescope, so we might expect it tohave poorer resolution, but note that there is less blurring fromatmospheric turbulence at high altitude (5 microradians) than atlow altitude (15 microradians).
A human observer with 8X binoculars.
We know that there will be multiple sources of blur that willlimit our resolution and thereby our image quality, and we willconsider several of them:
Motion blur
Diffraction blur, equal to 2.44*wavelength/aperture
Pixel size, or footprint, equal to IFOV
Atmospheric blur, which at low altitude = 15 microradians inangular diameter and at high altitude = 5 microradians in angulardiameter. We will model atmospheric blur as having the same effectas diffraction, but instead of the angular diameter of a pointobject being 2.44*wavelength/aperture, it is the constant 15 or 5microradian value, as described in lecture.
We would like to know which of these effects will be thelimiting factor in our resolution, and if any will make itimpossible to resolve the hotspot on the vehicle. In order toevaluate this, we will quantify our objectives by saying we havetwo imaging goals. First, we would like to make a nice resolvedimage of the glowing hotspot, which is 20 cm across. To get a niceimage, we’d like a resolution of 10 cm or better. This way, thediameter of the hot spot is at least twice our limiting resolution,ensuring that we can make some estimate of its size rather thanjust make an image of an unfocused-looking blurry spot. Second, ifwe can’t achieve the first goal we still want to at least image thevehicle itself. The vehicle length is 4 meters long, so we wouldlike a limiting resolution of less than 2 meters in order to get atleast 2 pixels along the length of the vehicle. The goal then is touse the various resolution equations from class to determine theresolution limit at the imaged object due to pixel size,diffraction (airy disk), atmospheric seeing, and motion blur. Wewon’t worry about adding them together, we just want eachindividually to be less than 10 cm if possible, or if not that, atleast less than 2 meters.
Also remember that we are comparing the diameter of the blurcircle at the imaged object, so use the range to the object toconvert between angular size and pixel footprint in order to do allcomparisons in the same space, either angular or length. We willalso need to take into account the signal to noise and contrast ofthe vehicle body and hotspot, and so will have to calculate thosequantities as well.
Problem 1 (20 points)
For the given 75 km range, what angular size, in microradians,do the 10 cm and 2 m resolution goals correspond to? What spatialfrequencies, in cycles/mrad, do these angular sizes correspond to,if we take the 10 cm and 2 m numbers to correspond to one half of acycle?
Problem 2 (20 points)
a. From the information given in Table 1, determine the focallength and f/# for the two CCD systems (the film system will be thesame as the ground-based CCD system, as they use the same opticaldesign).
b. How large is the field of view of each CCD system compared tothe size of the target? Is the 4 m target entirely within the FOVat the given range, assuming it is centered perfectly?
Problem 3 (20 points)
Assuming the vehicle is moving perpendicular to the line ofsight during imaging, what is the maximum integration time (orshutter time, the time during which the image is taken) we can usethat will avoid motion blur of more than 10 cm? How does this valuecompare to the typical consumer camera shutter speeds listed inlecture?
Problem 4 (20 points)
For each of the two CCD telescope systems described in Table 1,what is the pixel footprint, in meters at 50 km range, due to theifov, or sampling, of the CCD?
Problem 5 (20 points)
For each of the two CCD imaging systems, what are the limits onresolution from diffraction and from atmospheric seeing?
Problem 6 (20 points)
For the two CCD imaging systems, compare the differentapplicable resolution limits (pixel/grain size, diffraction,atmospheric seeing, visual acuity) to the 10 cm hotspot size and 2meter resolution goals described above. Note that you’ll need toget everything in the same units, either angular units(microradians, like problem 1) or pixel footprint units (meters),to be able to compare directly. What is the limiting resolutionfactor for each imaging option?
Problem 7 (20 points)
For each of the two CCD imaging options, what is the contrastbetween the hotspot and the main vehicle body in daylight (bothemitted and reflected light observed)? Both the vehicle’s main body(our “background” here) and the hotspot will have a totalbrightness that will be given by the amount of solar radiationreflected (the i(x,y)*r(x,y) we usually have) plus the amount ofemitted radiation due to their high temperatures (given in theradiant emittance columns), so the total intensity will be I =i(x,y)*r(x,y) + e(x,y) for each. The contrast is given by (Ihotspot– Ibody)/Ibody. In this case do not worry about contrastdegradation due to blur or MTF, just calculate the contrast at thebody itself (take the “I” in the contrast equation to be theintensity due to emitted plus reflected light at the body). Aswe’ve seen in the previous problems, blur is going to be a majorissue, so the final contrast at on the image will be different, butwe will ignore that for now.
Problem 8 (20 points)
For each CCD imaging option, how many photons will be focusedonto a single pixel of the hotspot during the integration timecalculated in problem 3?
Problem 9 (20 points)
If each of the CCD options has an average quantum efficiency of0.5 and the following noise sources:
Photon noise determined from the # of signal electronsproduced during the integration time
Dark current of 5,000 electrons per millisecond
Charge transfer inefficiency of 10-3. Assume # of transfers =number of pixels in one dimension
Readout noise of 500 electrons
What will be the SNR for each imager over the integration timeyou calculated in problem 4? Ignore reductions in SNR that wouldoccur due to some photons ending up in neighboring pixels due todiffraction or atmospheric blur.
- Nasa Has Contracted You To Setup The Imaging Plan For A Test Flight Of Their New High Altitude Ultrasonic Glide Vehicle 1 (129.56 KiB) Viewed 60 times