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Optical observations of asteroids – and the same for space debris…
Dr. D. KoschnyEuropean Space AgencyChair of Astronautics, TU Munich
Stardust school Feb 2015, Belgrade
Image:
ESA
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Survey programmes
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Catalina Sky Survey• http://www.lpl.arizona.edu/css/
• Mount Bigelow, north of Tuscon, AZ – 68/76 cm f/1.9 Schmidt telescope
• Mt. Lemmon 1.5 m f/2 telescope
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Survey programmes - 2
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Panoramic Survey Telescope & Rapid Response System
http://pan-starrs.ifa.hawaii.edu/public/
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Survey programmes - 3
http://scully.cfa.harvard.edu/iau/SkyCoverage.html
TOTAS – Teide Observatory Tenerife Asteroid Survey
1 m aperture, 10 % obstruction
Focal length 4.4 m
Camera with 0.65” per pixel image scale, normally used in 2x2 binning mode
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Modelling the detection system
Sun
Asteroid
Telescope
CameraEmitted light - 1366 W/m2
Distance to Sun
Distance to Earth
- Effective Aperture in m2
- Throughput
- Quantum efficiency- Noise
Abstract modelwith parameters
=> Signal-to-Noise of a given asteroid
Albedo pPhase function f()
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Brightness of an asteroid
Apparent magnitude
• Let F be the flux density (energy per time per area) in W/m2, then
• m = ‘magnitude’, brightness class
• Vega (Alpha Lyrae) is the reference, F0 is defined as the flux density of magnitude 0
• Sun: Mv = -26.8 mag; MR = -27.1 mag and Fsun, Earth = (1366 W/m2)
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Johnson-Cousins Filter bands
Namepassband in nm average wavelength
in nm
U – ultraviolet 300 – 400 360
B – blue 360 – 550 440
V – visual 480 – 680 550
R – red 530 – 950 700
I – infrared 700 – 1200 880
Good to know
Flux density in W/m2 is energy per time and area
Energy of one photon:
Where h = 6.626.10-34 Js, c = 2.998.108 m/s
hc
EPhot
Good to know
Flux density in W/m2 is energy per time and area
Energy of one photon:
Where h = 6.626.10-34 Js, c = 2.998.108 m/s
Flux density can be seen as number of photons per time and area
hc
EPhot
Brightness of the asteroid - 2
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The flux density reduces with the square of the distance. The solar flux density at the asteroid can be computed with
Where rast the distance between asteroid and Sun in AU.
With the albedo p of the asteroid, surface area S, distance asteroid-Earth rast, Earth, the flux at the Earth can be computed with:
Assume a simple sphere, homogeneous (Lambertian) scatterer (real formula depends on surface properties, shape… More complicated!):
f () = ½ (1 + cos ())
(i.e.: at 90 deg, half of the object is illuminated)
Absolute magnitude versus size
Absolute magnitude = magnitude of the asteroid at 1 AU from the Sun, seen from a distance of 1 AU, at a phase angle (angle Sun – asteroid – observer) of 0 degrees
Assumption: Albedo is 0.05
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Abs. magnitude Size
14.0 9400 m
16.0 3700 m
18.0 1500 m
20.0 590 m
22.0 240 m
24.0 95 m
26.0 37 m
28.0 15 m
30.0 6 m
The telescope
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)( obstrinDetect AAFF
where FDetect the detected energy per time, Fin the incoming flux density from the object, A the surface area of the prime mirror, Aobstr the area of the obstruction, and the throughput.
Definition of the f-ratio:
Flux at detector:
Sketch of a telescope - incoming flux density F in W/m2, surface area A in m2.The sensor obstructs the main mirror with an area Aobstr.
Focal length
Diameter of lens
The detector
CCD = Charge Coupled Device
Converts photons into e-
Readout results in data matrix in computer containing Digital Numbers
Quantum efficiency QE• Percentage of photons which generate
an electron
Gain g• e- per Digital Number
Full well• Maximum no. of e- in a pixel
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100
50
300 nm 1000 nm
Qu
an
tum
Effi
cie
ncy in
%
The detector – 2Star image taken with CCD
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100
102
98 100
101
100
99 150
223
140
102
100
150
402
803
400
200
98
102
130
220
130
107
102
98 99 120
98 100
100
Digital Number DN
Noise:comes from different sources: photon noise, dark noise, readout noise, bias
Not all light goes to center pixel – the percentage is ppx
The detector - 3
Signal is a function of input flux and detector properties:
Assume an ‘average wavelength’:
Signal-to-Noise ratio:
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Skyreadoutdarkbiassignal
signal
DNDNDNDNDN
DNNoiseSignalSNR
/
Typical values for OGS
1 m aperture, f/4.4
CCD camera has one sensor with 4096 x 4096 px2
Pixel scale 1.3”/px when binning 2x2, field-of-view 0.7 deg x 0.7 deg
For survey: We use 30 sec exposure time
Reaches ~21.5 mag
‘Deepest’ surveys go to22.5 mag
Faintest NEO observedby us: 26.3 mag (withLarge Binocular Telescope)
Summary
We have modelled the complete observation chain
We can compute the brightness of an asteroid at a given geometry
We can compute the sensitivity of a telescope
Magnitude of an asteroid
(1) How bright will a 40 m diameter asteroid be when at 15 Mio km distance?
• Use simplifications wherever you can! Which parameters do you need to guess?
(2) Which exposure time would you need using ESA’s Optical Ground Station to get a Signal-to-Noise ratio of at least 5 for this object?
• Instead of turning equations around and having to solve a quadratic equation – compute the SNR for a 21 mag object for 10 s, 30 s, 60 s
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Parameters of the Optical Ground Station
The camera at ESA’s telescope on Tenerife is cooled by liquid nitrogen to temperatures such that the dark current and its noise contribution can be neglected. The readout is slow enough so that also its noise contribution can be neglected. The camera is operated with a bias of DNbias ~ 3000. The typical exposure time at which the camera is used is 60 s.
The telescope uses a custom-built CCD camera by Zeiss with the following properties: QE = 80 %; g = 0.9 e-/DN. Assume that all the photons coming from the object are read at a wavelength of 600 nm. Assume that the telescope transmits = 60 % of the photons to the CCD; ppx = 40 % of the photons fall on the center pixel. The telescope obstruction is 10 % of the area of the main mirror.
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Relevant formulae/constants
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1
212 log5.2
F
Fmm
hc
EPhot
f () = ½ (1 + cos ())
)( obstrinDetect AAFF
Skyreadoutdarkbiassignal
signal
DNDNDNDNDN
DNNoiseSignalSNR
/
h = 6.626.10-34 Js,c = 2.998.108 m/sFsun, Earth = 1366 W/m2
Msun = -27.1 mag
