Brian Schmidt

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Brian Schmidt

• Principles in Data Reduction

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Producing Good Data

• Essential to have a good working instrument
• Essential to take all of the relevant calibration
  data
• Correct data reduction procedures for the data
• Check constantly for errors
• All data is not alike. Do what is appropriate for
  your data.

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CCDs

• Linear
• Reasonable dynamic range (7 magnitudes)
• Superb Efficiency (90)
• Low noise ( 4 counts per pixel)
• Sensitivity X-ray to 1100nm
• No colour discrimination (except in X-ray)
• Can be run as fast as 100Hz (but typically has
  20-120 second down time between exposures)
• Largest Astro CCDs are currently 16 Million pixels

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CCDs are the detector of choice in most situations

• Exceptions are where fast readout times are
  needed (photocounting preferred)
• And where backgrounds are extremely low (sometime
  photocounting devices preferred)
• Very large Fields (CCDs very expensive) where
  Photography has been used.

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Noise in Astronomical Detectors

• Poisson Noise in most situations

Counts photons detected within aperture or
resolution element
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SNR of two detectors
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Glossary of CCD terms (from http//www.pha.jhu.edu
/cat/seminar.html) gate A thin layer of metal
or heavily doped polycrystalline attached to an
electrode forms the gate. A bias voltage may be
applied to the gate in order to change the shape
of the underlying potential. oxide layer The
0.1 micron thick oxide layer (usually SiO2)
beneath the gate functions as the dielectric of
the capacitor. The oxide is thickened to 0.5 -
1.5 microns above the channel stops to insulate
them from changes in the gate voltage. channel
stop The function of the channel stop regions is
to confine charge. They are made of heavily doped
p-type materials with an extra thickness of oxide
over top. This makes them relatively insensitive
to voltages applied to the gate and thus an
effective potential barrier. n-type buried
channel Most modern CCDs have buried channels. A
buried channel is created by the addition of a
n-type layer (1 micron thick) between the gate
and the oxide. A n-type (negative) semi-conductor
is one which has been doped with impurities of
higher atomic number yielding an excess of free
electrons in the conduction band. The effect of
the n-type layer is to move the potential minimum
back from the Si-SiO2 interface eliminating "fast
surface states" which cause problems with charge
transfer. The region where the signal charge
collects, termed a channel, is within the n-type
region. p-type substrate A p-type (positive)
semi-conductor is one which is doped with with
impurities of lower atomic number, resulting in
"holes" in the valence states. The substrate is
usually at least 15 microns thick. depletion
region In the depletion region, electrons from
the n-type region have combined with holes from
the p-type region. The result is the
establishment of a potential difference because
the n-type region becomes positively charged,
while the p-type region becomes negatively
charged. When photons are absorbed in the
depletion region they form electron-hole pairs.
The electrons are attracted to the the n-type
region. The holes diffuse away into the p-type
region.
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Traditionally, CCDs were illuminated on the
front side, meaning the side with the gates. Many
of the blue photons were absorbed by the
relatively thick (0.5 micron) gates. Today it is
possible to make back-side illuminated devices.
In these devices the silicon substrate is thinned
to 15 microns and the gate side is mounted
against a rigid surface. An enhancement layer is
also added which creates an electric field that
forces electrons toward the potential wells.
Back-side illuminated devices have higher QE
especially in the blue and UV portion of the
spectrum.                     
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Optical depth of 1 for 1 micron photons is
roughly 100 microns in Silicon (CCDs typically 15
microns thick) So red light travels straight
through CCDs. Plus, whole CCD acts as a
Fabry-Perot cavity and one gets fringing!
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High-resistivity Thick CCDs
The solution is to make the CCDs thicker than the
absorption depth of the silicon, incident photons
will then be absorbed on their first pass and
reflection from the rear surface will be greatly
reduced. Lincoln Labs and E2V have made 40
microns thick CCDs, LBL is experimenting with 100
micron thick CCDs. Standard silicon cannot be
used for this process since it cannot sustain the
high electric field throughout the full depth of
the device that is so important for good QE.
Instead a special grade of high-purity
high-resistivity silicon must be used.
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Reading out a CCD
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Serial Registers
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CCDs
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Charge Transfer Efficiency (CTE)

• Each transfer has the possibility of leaving some
  of the electrons behind.
• In a 2048x4096 pixel CCD, pixel 1,1 undergoes
  4096 parallel transfers and 2048 serial transfer.
  If the parallel transfers are 99.99 efficient
  then pixels in last row lose
• 1-(.9999)4096.334 of their charge relative to
  first row! Bad!

CTE loss of charge
0.9999 0.336
0.99999 0.040
0.999999 0.004
0.9999999 0.0004
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QE of Modern CCDs
http//www.ing.iac.es/PR/newsletter/news5/simon2.g
if
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Gain, Bias, Readnoise, Dark Current

• At the end of the Serial Register, the
  transferred electrons need to amplified to create
  a voltage which can be measured by our
  electronics (and which are converted typically by
  a 16 bit 0-65536 Analog to Digital converter)
• Gain How many counts does each electron get
  (typically 1-8 e/ADU). Match so 65536-gtis where
  the CCD saturates (is not longer linear)
• Bias When there is no charge, how many counts do
  we read.
• Readnoise How many electrons of noise does the
  CCD amplifier add. (good CCDs now 4e-s, best are
  1e-))
• Dark Current If CCDs are cold (lt180K), they
  usually produce only a few electrons per hour per
  pixel. Warmer, they produce more.

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Measuring the Gain

• Fe55 source Fe-55 produces a 5.9 KeV soft X-ray.
  When this interacts with the CCD, 1620 electrons
  are generated in a volume much smaller than a
  pixel. Measure how many counts there are in each
  interaction, that tells us the of ADUs per 1620
  electrons. Very accurate at one input level, but
  not easy for the astronomer
• Take two images of the dome with lots of counts
  in them (30000 or so), subtract these, use the
  poisson noise to tell you how many electrons per
  ADU.

CountsADU - BIAS
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Measuring the Read Noise

• Take two BIAS images (0 second exposures) only
  need one if the bias has no structure in it like
  any decent modern CCD system should provide!
• Readnoise is just measured from the std deviation
  of the BIAS image (or their difference) adjusted
  by the gain.

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Measuring the Linearity

• In the lab, use a diode, and take different
  length exposures to see brightness of diode.
• or
• Under take gain test with several pairs of images
  at different light levels. Does the gain remain
  the same.
• or
• Take an image of a field of stars as twilight
  ascends/descends. Measure the aperture magnitude
  of the stars in increasing background light. Do
  the stars magnitude change as background
  increases.

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Measuring the Charge Transfer Efficiency.

• Fe55 source Fe-55 produces a 5.9 KeV soft X-ray.
  When this interacts with the CCD, 1620 electrons
  are generated in a volume much smaller than a
  pixel. Measure how many counts there are in each
  interaction as a function of position. that tells
  us the of ADUs per 1620 electrons. Comparison
  in the Y direction tells you charge loss in
  parallel registers, Comparison in X direction
  tells you charge loss in serial registers. Again,
  for the technition.
• Look at Cosmic Rays or defects in your images, do
  they bleed in either the X, or Y direction.
• In a dense field on a photometric night, image a
  set of stars in the 4 corners of the chip and
  compare their photometry.

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Atmospheric Refraction

• As stellar light passes through the atmosphere,
  it is refracted just as through a lens. Blue
  light is refracted more than red light. Like
  extinction, the amount of atmospheric refraction
  depends on the amount of air mass that light has
  to traverse.
• r is increased altitude due to refractionz is
  the zenith anglek is a constant which depends on
  wavelength, pressure (altitude), temperature, and
  humidity.

? k
3000Å 63.4
5000Å 60.6
1? 59.6
40? 59.3
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Differential Refraction

• At 1.5 airmasses, an image at 4000Å is displaced
  towards the zenith by 1.1 relative to the image
  at 6000Å. If you are trying to observe over this
  wavelength range using a 2 arcsec slit, you will
  suffer large amount of light-loss unless the slit
  happens to be aligned at the parallactic angle,
  i.e., the position angle on the sky that results
  in the slit being perpendicular to the horizon.
• Try to always observe at low airmasses.
• Rotate the spectrograph so that the slit is near
  the parallactic angle.
• Broad Blue filters are to be avoided when imaging
  (e.g. Gunn-g) at high airmass.
• Use Atmospheric Dispersion Compensator

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Atmospheric Extinction
Extinction per airmass depends on wavelength, on
altitude, and on thenight. Mauna kea, for
example as an average pressure which is 60 that
at Sea Level. So to go to Asiagos curve,
should multiple Mauna Keas by1.4.
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Atmospheric Dispersion Compensator (ADC)

• Many large telescopes are with a ADC typically
  a pair of Risley prisms", which rotate relative
  to each other and provide excellent atmospheric
  dispersion compensation. They can cause ghosting
  and scattered light, and chew up a lot of the
  light below 4000Å, but they do get rid of
  differential refraction.

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Sky Brightness
Days from New moon U B V R I
0 22 22.7 21.8 20.9 19.9
3 21.5 22.4 21.7 20.8 19.9
7 19.9 21.6 21.4 20.6 19.7
10 18.5 20.7 20.7 20.3 19.5
14 17 19.5 20 19.9 19.2
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Sky Brightness
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Sky transmission in Red

• Telluric Lines caused by molecules in atmosphere
  (O2, H20)
• Do not scale linearly as airmass
• Observe smooth spectrum standard to remove

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Telescopes

• Alt-Az
• Orientation of image changes as telescope tracks,
  corrected by an image rotator
• Choose rotator angle to orient image (N-E) or
  slit (parallactic or desired galaxy position) to
  desired angle
• Equatorial
• Orientation of image typically fixed, but should
  choose angle so slit is at parallactic angle or
  to minimise galaxy gradient.

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Telescope Optics

• Each mirror surface looses about 8 of the light
• Each coated transmissive surface looses about 4
  of the light
• Large glass correctors tend to remove UV (Fused
  Silica is the best)

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Slit Spectrographs

• Classic long slit spectrograph is very simple
• (But orders overlap, so tough to get more than a
  factor of two in wavelength coverage) And hard to
  optimise system from 320nm-1micron

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Double Beam Spectrograph

• Split light into two channels using a dichroic.
• Orders now do not overlap
• Can use Blue and Red optimised CCDs on either arm

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Echelle Spectrograph

• Echelle Spectrographs use a highly dispersive
  grating which output many order.
• Orders are separated out by an additional grating
  (Cross-disperser) which moves the light as a
  function of wavelength and position.

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Integral Field Spectrographs

• Image slicer (or fiber pod) creates a series of
  slit spectra covering a 2-d piece of sky

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Taking a Spectrum

• Object Bright center directly into slit
• Object Faint offset from bright star
• Always good to take more than one spectrum of
  each object to remove Cosmic Rays Even better-
  define two places on the slit, take two spectra
  of each object (standards as well). Subtract the
  two images to remove most of the sky lines for
  each object. (not so useful if not photometric)

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Taking a spectrum

• Choosing slit size. As you increase your slit
  size,
• you loose resolution,
• increase the fraction of light of object landing
  on detector
• Increase the background hitting the detector
• Typically we choose a slitsize about 1.5 FWHM of
  image seeing, unless we are trying to get
  absolute spectrophotometry (then need a larger
  slit)

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Nod and Shuffle

• a.    An observation is taken at a first position
  on the sky (position A), while guiding.
• b.    The shutter is closed, and charge is
  shuffled by Y pixels.
• c.     The telescope is moved to a second
  position (position B).
• d.    The shutter is opened at position B and the
  observation is continued.
• e.    The shutter is closed and charge shuffled
  by Y pixels.
• f.      The telescope is moved back to position
  A.
• g.    The procedure is iterated until the
  exposure is complete. The final exposure time is
  the product of the sub-integration time and the
  number of sub-integrations.
• Data taken at position A has sky spectrum taken
  at position B subtracted, removing very
  effectively, the sky lines.

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Calibration Data-Spectra

• Arc at the position of each object
• A smooth spectrum standard
• A spectral flux standard star
• Biases 10 or so are usually sufficient
• Internal flats (quartz) Make sure that you have
  lots of counts in the blue You might need to
  take two exposure times one where you saturate
  the red part of the spectrum
• Skyflat Not that important, but useful if you
  are planning to use more than one position on the
  slit.

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Smooth Spectral Standards

• Smooth spectrum stars have basically no features
  (EG 131 is a flux standard and has no features)
  a unique star in the sky

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Flux Standards
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Spectral Reductions

• Cadillac treatment requires
• Bias frames
• Dark Frames
• Quartz Flats (removes high frequency CCD
  variations) at each object if fringing
• Sky Flat (removes variations across slit)
• Flux standard stars at several airmasses
• Smooth spectrum standard stars at several
  airmasses
• ARCs at each position of each object and standard
  star

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Minimum observing Set to get good Spectral data

• Bias (Dark if required)
• ARC at each position
• Observe object a parallactic angle
• Smooth flux spectrum standard star at close to
  same airmass as your program object. (parallactic
  angle)
• Or smooth spectrumflux standard
• Quartz at position if fringing and flexture

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Imagers

• Imagers typically give a focal plane a the
  desired scale (arcseconds per pixel) and with
  some field size.
• The key to a good imager is no scattered light
  (telescope baffled), high throughput (little
  glass), well characterised filters, and good
  CCDs. Many imagers are parts of spectrographs
  (FORS), and while convenient, it ultimately
  hampers their performance compared to a dedicated
  instrument.

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Taking an Image

• Point to object
• Do you need to guide (short exposure maybe not)
• How many counts do you need? SNR gt 200 is a waste
  as photometry of SN is always dominated by other
  errors. But make sure you have several comparison
  stars with this type of SNR as well.
• Multiple exposure on different places on the chip
  are preferred over single long exposure
  exception is U band if you are read noise
  limited.

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Basic Calibration Data imaging

• Bias images (10)
• Standard stars (Landolt are easiest at present)
• Covering colour range of your objects
• Airmass range if photometric
• Twilight flats (gt3 in each filter gt 10000 counts
  in each)
• (Dome flats are sometime useful)
• Dark images (gt3 of 1/2 hour each)
• Random data taken with instrument of pieces of
  uninteresting sky.

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BASIC CCD reduction

• Most people find IRAF a good package to undertake
  their Basic CCD reduction. However, do not be
  scared to do it yourself!
• Iraf imred.ccdred.ccdproc
• A good tutorial is available at
• iraf.noao.edu/iraf/web/tutorials/tutorials.html
• But do not necessarily believe this is the bible
  of data reduction

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Data Reduction -BIAS

• Always take 10 BIAS frames every night to assess
  the state of your instrument
• Determine trim area (area which has data you
  want)
• Determine position of Overscan
• Median 10 Bias frames together, subtract
  overscan from image (either a constant value for
  the whole image, or a fit value (as a function of
  y) as necessary.
• Look at the ZERO frame. Is just noise with Zero
  level? If so, you DO NOT need to apply it
  (instead simply subtract off the overscan from
  each image). If it has structure, then you will
  need to subtract this from every frame along with
  the overscan.

Data
overscan
Data
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DATA Reduction - Flatfield

• Each pixel has a slightly difference response
  from each other intrinsic to the CCD (and due to
  the telescope instrument), and this depends on
  colour, and somewhat on time.
• Typically one takes images of the twilight sky
  (pictures off the dome are also) need
  5000-40000 counts per image.
• U, B, Z, V, I, R is the best order to take your
  flats in in the evening (reverse order in
  morning). Depending on readout time of CCD, you
  may only be able to do a subset.
• Remove overscan/BIAS of all images. For each
  colour, measure the median value in a region near
  the centre of each image, and then scale each of
  the set so this middle region has a value of 1.
  Then Take median of each the set of sky flat
  images to create a flatfield for this colour.
• All data then first is trimmed, overscan
  subtracted, bias subtracted as necessary, and
  then is divided through by the flatfield. This is
  generally your reduced data
• For spectra, need to use a lamp inside the
  spectrograph to get flatfield. But must remove
  the wavelength shape of the lamp before dividing.

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Imaging Illumination Correction/Fringes

• After flatfielding your data, it is often found
  that their remains a residual in the data. This
  is because the twilight and night sky are a bit
  different.
• Create superflat Take all of your data that has
  been reduced to flatfield stage. Measure median
  value within a patch in the centre, and scale
  each image to a common value (e.g. divide the
  average value for all images by each images
  value). For each pixel, take median value over
  all images (removing some fraction of the top
  values to avoid print through). This requires gt50
  images to really work.
• Alternatively mask all objects out of each
  image, and only median the left over pixels in
  the stack of image.
• A well constructed Superflat image will have no
  stellar print through, and should reveal any
  imperfections in the twilight flat (illumination
  correction) and fringes.

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Illumination Correction

• Hopefully created superflat is essentially
  featureless. If it is not (and does not have
  fringes), then you can either divide all the data
  by this frame (if sufficient signal), or smooth
  the superflat by, for example, a 10 pixel
  gaussian, and divide through by this.
• NOTE If you are observing in dense stellar
  fields, this isnt going to work, it is
  impossible to get a superflat. If you are
  observing large galaxies, DO NOT put them in the
  same part of CCD each time, or you will not be
  able to make superflat.
• For spectra. Take an spectrum of the twilight
  sky. This should be uniform across the slit (but
  note the twilight sky is the spectrum of the sun,
  so need to look at each spectra line and fit the
  slit profile as a function of position on the
  CCD).

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Fringe Correction- Imaging

• If you are observing in Z, I, and possibly R (or
  other filters beyond 700nm) the superflat may
  show fringing. Fringing is additive (imaging
  data) because it is caused by the narrow night
  sky lines the transparency of the CCD at
  gt700nm.
• Best is to fit a low order surface to the
  superflat and assume this is the illumination
  correction. You will divide this through each
  image. What remains is the fringe frame.
• Fringe frame needs to be scaled and subtracted
  from each image. Scaling to first order is
  exposure time, but improvement can be done by
  tweaking the scaling to minimize residuals in the
  image.
• Fringing depends on the night sky, and this is
  often not stable even across a night.
• Thick deep depletion devices have much less
  fringing than thin devices, and fringing gets
  worse as one moves to the red.

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Fringing - Spectra

• Fringing is caused by the monochromatic light
  dispersed by the spectrograph to undergo
  interference within the CCD.
• Since everything is affected, works more as a
  multiplication effect.
• For spectra -
• - divide through by a smooth star, and ensure
  that you place the standard at the same place as
  your program objects. Challenging if spectrograph
  has lots of flexture.- if lots of flexture, take
  a internal flat after each program object and use
  this to flatfield each image or ask for new
  spectrograph!

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Shutter Correction - Imaging

• Shutter correction Short exposures often have a
  different illumination than long exposures due to
  the shutter.
• median 20x1 second exposure of dome/sky (scale to
  same mean)
• Median 3x20s dome/sky (scale to same mean).
• Scale short and long image to same mean
• Shutter corr image long/short
• Image correction to be multiplied through is
• Shutterimage /(exptime), assuming long image is
  perfect

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Absolute Photometry

• Astronomers have developed a peculiar system of
  magnitudes as their reference system.

Vega systems have !approximately! Kx defined such
that Vega has a magnitude of 0.03 in each band.
AB magnitudes use F? in units of ergs/cm2/s/Hz
with Kx !approximately! Defined as -48.6. In
reality, all systems are defined as the observed
magnitudes of a set of standards. Landolt,
Cousins, Gunn, etc, which themselves are
attempted to be tied to a fundamental standard
such as Vega, serious, or BD13.
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Absolute Photometry at the Telescope

• Typically need a photometric night (unless you
  have standard stars on your CCD frame)
• Observe Standards over the relevant range of
  Airmasses, and range of Colours of your program
  stars.
• Find constants of the transformation of the form

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Absolute Photometry at the Telescope (2)

• For example, for V, the form of the
  transformation is, neglecting 2nd order terms.

Which we solve for constants K1-K3, by
minimizing
Where I have assumed that the observational
uncertainty in each observation is the same
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Common Errors Photometry (1)

• Most people observe at at too large a range of
  colour, or too large a range of Airmass, and then
  apply linear corrections on their program stars
  at neutral colour and low airmass. Bracket your
  program stars Airmasses and colours. If you must
  observe at 2 airmasses, use 2nd order terms, and
  fit your equations for objects at high airmass
  only.

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Common Errors Photometry (2)

• Landolt observed his stars in 14 radii. People
  often use smaller apertures of each star. Since,
  especially in redder bands, there are often
  fainter stars, mags are systematically off
  because of these non-included interlopers. Either
  use apertures matched to the standard star
  (thereby incurring skynoise), or cull all stars
  with interlopers as standards.

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Aperture Photometry

• Aperture to maximise signal (r0.75xFWHM
  theoretical best), but then subject to variations
  of PSF shape!
• Background fit in annulus around each star
• Often this is largest source of error, especially
  if on complex galactic background
• Extend aperture to 8 by determining mag
  difference between small and large apertures for
  bright stars (only for absolute photometry)

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PSF photometry

• Model shape of a star, and fit this to each
  object. For each star fit (X,Y, height of PSF,
  background). Collectively across several stars
  fit shape.
• DAOPHOT (gaussian or other sub-pixel residual)
• DOPHOT (truncated power-series of a gaussian)
• For SN photometry applications, not so important
  to get PSF exactly right, so no disadvantage of
  purely analytic PSF. Extend PSF to 8 aperture
  by determining mag difference between PSF mag and
  large apertures for bright stars (only for
  absolute photometry)
• Beware of variable PSFs

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Image subtraction

• For SN photometry, subtract off a template, and
  perform photometry (aperture or PSF) with a
  clean background.
• Match PSF with Drew Phillips Fourier-based
  convolution (implemented in IRAF)
• Alard-Lupton least squares (sum of 3 gaussians)
• Gal Yams convolve each image with the other
  PSF.
• Getting subtractions to work perfectly in all
  situations is a bit of an art form.

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Intrapixel Sensitivity

• CCD pixels vary in sensitivity across the pixel
  by 20. If gt 2 pixel fwhm stars, then pixel is
  fully illuminated, and average holds.
• If undersampled image (fwhm lt 1.5 pixels), then
  brightness of stars depends on where they hit in
  pixel.
• Pixel to pixel, the nature of the sensitivity is
  very uniform.
• Do dithering with many exposures per field to
  mostly eliminate. To do better, model the shape
  of the pixel, and include it in the analysis.
• see Lauer, T 1999PASP..111.1434L

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Imaging Gotchas

• Is your CCD linear? test by observing stars in
  twilight
• Does your filter transform nicely to the standard
  system one photometric night, takes lots of
  standards stars and really see how the equations
  work
• Does your Imager deliver uniform photometry
  across the focal plane
• CTE problems (check CRs if really bad)
• Scattered light mascquerading as Flatfield

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Ultimate Check for Photometry

• Determining the uniformity of your photometry as
  a function of position is hard. The best way to
  do it is to do a stellar flat that is, check
  photometry of stars as a function of position.
• Take a series of exposures of a relatively dense
  field (e.g. R149 field is nice) doesnt need to
  be a standard field, doesnt need to be
  photometric. Offset each exposure so as to place
  your favourite set of stars into 16 different
  parts of the chip. After fully flatfield, biased,
  fringed, etc., photometer all bright stars on
  each image. Find average magnitude offset for
  each image to bring it into consistency with the
  first image, and calculate average relative mag
  for each star. Make a table of X,Y,m-mave for
  each star on each image. Plot X/Y versus m-mave
  and look for residuals.