Photon Detectors, Spectrographs
PHY517 / AST443, Lecture 3
Outline
• Optical photon detectors: CCDs
–
–
–
–
principle of operation
properties
calibration
photometry and astrometry
• Spectrographs
–
–
–
–
principles of operation
properties
calibration
spectrophotometry
2
Context: Photographic Plates,
PMTs, CCDs
3
CCDs: Basic Concept
A charge-coupled
device (CCD) converts
photons to electrons
• works thanks to photoelectric effect
4
CCDs: Basic Concept
•
electron-hole pair generation
– 1 photon -> 1 electron
•
silicon (Si)
– band gap: Eg = 1.12 eV
• cut-off wavelength λoff = 1.11 µm
hc 1.24 µm
=
E g E g (eV)
– free-electron energy: 4 eV
"off =
• cut-on wavelength λon = 300 nm
!
5
CCDs: Basic Concept
•
electron-hole pair generation
– 1 photon -> 1 electron
•
silicon (Si)
– band gap: Eg = 1.12 eV
• cut-off wavelength λoff = 1.11 µm
hc 1.24 µm
=
E g E g (eV)
– free-electron energy: 4 eV
"off =
• cut-on wavelength λon = 300 nm
• !doping:
– n-type (electrons)
– p-type (holes)
– creates additional energy levels
within band gap
– increases conductivity
6
Basic Concept:
A P-N Photo Diode
•
depleted region
– has low conductivity
– can support an E field
•
•
•
net positive charge (higher charge density near top)
additional E-field applied
subsequently generated electrons get trapped in potential well near top
7
CCDs: Charge Trapping
8
CCDs: Charge Transfer
9
Buried Channel CCDs
• surface channel
– charge transfer via overlapping
gates
– but trapping can occur at gates due
to impurities
• low CTE (~99%)
• buried channels
– CTE > 99.9995%
– lower potential well
• allow low light illumination
• higher dynamic range and sensitivity
10
11
Front- vs. Back-Illumination
of CCDs
12
CCD Quantum Efficiency
13
QE Improvements
• UV coatings
14
QE Improvements
• UV coatings
• anti-reflection
(AR) coatings
n1
n2
d
n3
– n2 = sqrt(n1 * n3)
– n2*d = λ/4
15
Advanced CCD Technology
•
orthogonal transfer CCDs
–
–
–
–
•
30–100 Hz readout
tip/tilt wavefont correction
~30% improvement in “seeing”
large-format CCDs
low-light CCDs
– gain register clocked out with
higher voltage (40–60V vs.
~10V)
– 1–2% probability of generating
2nd electron at each gate
transfer
– total gain enhancement:
~1.01N = 145 for N=500
transfers
16
Analog-to-Digital Converters
• X electrons = 1 digital unit
(counts)
– X is “gain”: usually 1 to 10
• CCD saturation depends on
– well capacity
• ~300,000 photo-electrons for
“deep depletion” CCDs
– number of bits in ADC
• n = 16 bits: maximum is
216 – 1 = 65,535 counts
Howell (2006; Fig 3.9)
17
Charge Diffusion
•
•
due to substrate impurities
in front-illuminated CCDs, red
photons:
– are absorbed near back of CCD
– see shallower potential well
– can move into neighboring
pixels
•
problematic / uneven in thinned
CCDs
– HST ACS
• 0.5 mag loss at short
wavelengths
• alters shape of PSF
18
Read Noise
• electrons / pix / read
• sources
– A/D conversion not perfectly repeatable
• same pixel read out twice with identical charge will
produce a distribution of values
– spurious electrons from electronics (e.g., from
amplifier heating)
• alleviated through cooling
• nowadays: <3–10 electrons
19
Dark Current
• electrons / pixel / second
• source
– thermal noise at non-zero detector temperature
• higher at room temperature
• at cryogenic temperatures
– LN2, –100 C
– 0.1–20 e–/pix/s
20
Dark Current
21
Non-Linearity
• differential (digitization noise)
• integral
– examples of integral non-linearity in SDSS CCDs:
22
Large-Area CCD Mosaics:
The Sloan Digital Sky Survey (SDSS)
SDSS 2.5 m telescope at Apache Point, NM
Ritchey-Chretien design
(Cassegrain-like)
23
Large-Area CCD Mosaics:
The Sloan Digital Sky Survey (SDSS)
24
Large-Area CCD Mosaics:
The Sloan Digital Sky Survey (SDSS)
u
g
r
i
(ansgtroms)
z
25
Proxima Cen
26
Detector Calibration
• bias frames
– non-zero bias voltage
– 0 sec integrations
• dark frames
– equal exposure to science integrations
• flat field frames
– QE of detector pixels is non-uniform in 2-D
– QE is dependent on observing wavelength
• bad pixels
27
Raw Image vs. Reduced Image
raw
minus dark, bias
corrected for bad pixels
28
Centering of Point Sources
• centroid
– sub-pixel precision possible
– IDL Astronomy Library: cntrd.pro
• 2D profile fitting
!
– gaussian (gcntrd.pro)
– modified Lorentzian, Moffat
– PSF fit (revisit later)
29
Aperture Photometry
• object flux = total counts – sky counts
• estimation of background
– Npix, bkg > 3 Npix, src
– use rbkg >> FWHM, whenever possible
• enclosed energy P(r)
– “curve of growth”
30
Palomar
AO PSF
Hayward et al. (2001)
31
Optimal
Photometry
• SNR is not constant as a
function of aperture radius
• There is an optimum radius
r at which SNR is
maximum
• r depends on PSF, source,
and background brightness
Howell (2006; Fig 5.7)
32
Aperture Photometry
Cookbook
•
determine object centers
– option 1:
• approximately from ATV
• precisely with gcntrd.pro
– option 2:
• find automatically and center precisely: find.pro
•
determine curve of growth from brightest star
– aper.pro
– get aperture corrections
•
find aperture size for optimum SNR on objects of interest
– aper.pro
– apply appropriate aperture corrections
33
Absolute vs. Differential
Photometry
•
absolute photometry:
– requires aperture correction
– requires non-variable photometric standard stars
• similar time and location on sky as science targets (same airmass)
• ideally, with identical color (e.g., B–V) as science targets
– requires photometric weather conditions
– best attainable accuracy: ~1% from ground, ~0.01% from space
– example applications:
• color-magnitude diagrams
• supernova flux measurements
34
source: Kitt Peak National Observatory
35
Absolute vs. Differential
Photometry
•
absolute photometry:
–
–
requires aperture correction
requires non-variable photometric standard stars
•
•
–
–
–
requires photometric weather conditions
best attainable accuracy: ~1% from ground, ~0.01% from space
example applications:
•
•
•
similar time and location on sky as science targets (same airmass)
ideally, with identical color (e.g., B–V) as science targets
color-magnitude diagrams
supernova flux measurements
differential photometry:
–
usually, with respect to stars of known brightness in the same field
•
–
–
–
identical time and airmass
subject to variability of reference stars
best attainable accuracy ~0.05% (ground), ~0.001% (space)
example applications:
•
•
searches for transiting planets
measuring stellar oscillation
36
PSF-fitting Cookbook
•
•
DAOPHOT I, II, III (P. Stetson 1987, 1991, 1994)
Implemented in IDL:
– getpsf.pro
– rdpsf.pro
- step 1, determining the PSF
– pkfit.pro
- step 2, fitting the PSF to a single star
or
•
– group.pro
– nstar.pro
- step 2, simultaneous PSF fitting to
groups of stars
– substar.pro
- step 3, subtracting stars to check residuals
produces accurate positions, photometry
– especially in crowded fields
37
Astrometry: Limitations
• limiting precision
– δr ~ FWHM / SNR
– unattainable in practice
• systematic effects
– differential atmospheric refraction
– pixel sampling
– focal plane curvature, distortion
38
Recall: Differential
Atmospheric Refraction
n (3200 Å) = 1.0003049
n (5400 Å) = 1.0002929
n (10,000 Å) = 1.0002890
differential atmospheric
refraction D between
3200 Å and 5400 Å
39
Astrometry: Pixel Sampling
• r = FWHM / (pixel size)
• r < 1.5: under-sampled
• Nyquist sampling: r ~ 2 (r = 2.355, precisely)
– optimal SNR, error rejection, positional precision
• r > 2 desirable for best photometry, astrometry on
bright point sources
40
Hayward et al. (2001)
41
Distortion of the Wide Field Camera on
the HST Advanced Camera for Surveys
HST ACS Instrument Handbook
42
HST Focal Plane
• HST
focal
plane
HST ACS Instrument Handbook 43
Distortion of the Wide Field Camera on
the HST Advanced Camera for Surveys
HST ACS Instrument Handbook
44
Outline
• Optical photon detectors: CCDs
–
–
–
–
principle of operation
properties
calibration
photometry and astrometry
• Spectrographs
–
–
–
–
principles of operation
properties
calibration
spectrophotometry
45
Diffraction
• multiple orders
order overlap
46
Spectrographs without Slits
“To Meausre The Sky,” Chromey (2010)
47
Spectrometers without Slits
“To Meausre The Sky,” Chromey (2010)
credit: Ulrike Keiter (www.anst.uu.se/ulhei450)
48
A Simple Slit Spectrograph
49
“To Meausre The Sky,” Chromey (2010)
The DADOS Spectrograph
50
http://www.baader-planetarium.de/dados/dados.htm
Efficient Spectrographs
• Ebert Spectrograph
– flat grating
– combining collimator and focuser allows compact design
51
Efficient Spectrographs
• Wadsworth Spectrograph
– curved grating allows compact design
52
Blazing Angle: Efficient m > 0
Order Dispersion
53
Echelle Spectrographs:
High Dispersion
• need to cross-disperse to avoid order
overlap
54
Echelle Spectrographs:
High Dispersion
• high blaze angle
55
Example: a Long-Slit Spectrum
• a telluric calibrator (a white dwarf)
56
Example: a Long-Slit Spectrum
• a galaxy
57
Example: an Echelle Spectrum
• RU Lupi
• 1100–1700 Å
58
Example: an Echelle Spectrum
• Sun, 4000–7000 Å
59
Multi-Object Spectroscopy
• use multiple
slits
• one per
science target
60
Multi-Object Spectroscopy
• use multiple
slits
• one per
science target
61
An Extracted Spectrum, Summed
along the Spatial Direction
62
Spectroscopic Calibration
• wavelength (dispersion solution)
– use a standard “arc” lamp: hot, optically thin gas
• atmospheric (telluric) + instrumental transmission
– use a star with an a priori known spectral shape
(normalized Fλ)
• spectrophotometry
– use a star with an a priori flux-calibrated spectrum (Fλ)
63
Wavelength Calibration
• He, Ar, Ne standard arc lamps
• each line has a known wavelength
• solve for λ/pix scale
“dispersion”
• Ne: 6000–7500 A
64
Transmission, Spectrophotometric
Calibration
•
stars with known spectral
shapes, featureless continua
– B, A stars
– white dwarfs
•
after calibration
stars with well known Fλ
(spectral flux distributions)
– at each λ measure count rate
[counts s–1 Å–1]
– get λ-dependent conversion
factor [erg cm–2 count–1]
– need photometric conditions
before calibration
65