PHYS 2022: Observational Astronomy
Astronomical Spectroscopy
Learning Objectives

Spectroscopy:
- spectrum
- spectrograph or spectrometer

Spectral Lines:
- electron orbits and energy levels in atoms
- emission and absorption of photons
- energy levels and spectrum of hydrogen atoms and hydrogen-like ions
- naming spectral lines
- permitted and forbidden transitions
- other ways for atoms/molecules/ions to produce spectral lines

Continuum and Spectral Line Formation:
- Kirchoff’s laws
- absorption lines
- emission lines
- continuous emission
Learning Objectives

Spectrometers or Spectrographs:
- objective prism
- slit spectroscopy
- diffraction grating
- line grating
- blazed grating
- spectral resolution
- echelle grating
- multi-object spectrographs
- integral field spectrographs

Spectral Line Profiles and Shifts:
- natural broadening
- pressure broadening
- Doppler effect
- thermal or Doppler broadening
Learning Objectives

Slit Spectroscopy:
- setup and observations
- data reduction
- extracting spectrum
- wavelength calibration
- extinction correction
- flux calibration
- removing sky lines
Learning Objectives

Spectroscopy:
- spectrum
- spectrograph or spectrometer

Spectral Lines:
- electron orbits and energy levels in atoms
- emission and absorption of photons
- energy levels and spectrum of hydrogen atoms and hydrogen-like ions
- naming spectral lines
- permitted and forbidden transitions
- other ways for atoms/molecules/ions to produce spectral lines

Continuum and Spectral Line Formation:
- Kirchoff’s laws
- absorption lines
- emission lines
- continuous emission
Spectroscopy and Spectrum
Spectroscopy is the act of measuring the energy output rate (flux density) from a
(celestial) object as a function of wavelength or frequency so as to study its
spectral lines.

Plot of the flux density vs wavelength or frequency is the spectrum of the object.

What can we learn from measuring the spectra of celestial objects?
Flux Density (10-8 erg cm-2 s-1 Å-1)

Spectrograph or Spectrometer

Conversion between expressing flux density in wavelength and frequency
Fλ = (ν2/c) Fν

To measure spectra, we use a spectrograph or spectrometer to separate the
incoming radiation into its component wavelengths.

Common wavelength separator: prism, diffraction grating, grism (grating + prism).
Learning Objectives

Spectroscopy:
- spectrum
- spectrograph or spectrometer

Spectral Lines:
- electron orbits and energy levels in atoms
- emission and absorption of photons
- energy levels and spectrum of hydrogen atoms and hydrogen-like ions
- naming spectral lines
- permitted and forbidden transitions
- other ways for atoms/molecules/ions to produce spectral lines

Continuum and Spectral Line Formation:
- Kirchoff’s laws
- absorption lines
- emission lines
- continuous emission
Electron Orbits and Energy Levels

In atoms, electrons can only prescribe certain orbits around the atomic nucleus.
Electrons in different orbits can have the same or entirely different energies.

Each electronic orbit therefore defines an energy level of the atom. A given
energy level can be degenerate (i.e., comprising different orbital configurations.)
Electron Orbits and Energy Levels

Figure below shows the energy level diagram for the hydrogen atom. At n = ∞,
the electron has the highest potential energy (defined to be 0) but no kinetic
energy. At n < ∞, the energy of the electron is a sum of its potential and kinetic
energy.
Emission of Photons

An electron in an atom can make a transition from a higher to lower energy level,
emitting a photon with an energy equal to the energy difference between the two
energy levels. An emission line is produced.
Absorption of Photons

A photon with the appropriate energy can be absorbed by and therefore excite an
electron in an atom to make a transition from a lower to higher energy level. An
absorption line is produced.

A photon with a sufficiently high energy can excite an electron from a bound to
free state, thus ionizing an atom. What is the energy required to ionize the
hydrogen atom in the ground state?
Electron Transitions

Every atom, ion, and molecule has a unique spectroscopic signature which
depends on its electron orbital structure and possible electron transitions.

E.g., Some possible transitions of excited hydrogen.
Electron Transitions

Spectral lines of atomic hydrogen.
Electron Transitions

Spectral lines at optical wavelengths produced by selected atoms.
Energy Levels of Hydrogen Atom

Energy levels of the hydrogen atom:
where n = principle quantum number. (μ = reduced mass of the electron, e =
electronic charge, ħ = h/2π where h = Planck’s constant.)

Ground state: n = 1.

Excited states: n = 2, 3, …

n = ∞ and continuum states correspond
ionized (free) states.

Transition of an electron from the mth
to nth energy level will require a photon
of wavelength:
to
-1.51 eV
-3.4 eV
æ1
1ö
= RH ç 2 - 2 ÷, m < n
èm n ø
l
1
where RH = Rydberg constant =
1.10x107 m-1.
-13.6 eV
Energy Levels of Hydrogen Atom

Energy levels of the hydrogen atom:
where n = principle quantum number. (μ = reduced mass of the electron, e =
electronic charge, ħ = h/2π where h = Planck’s constant.)

Ground state: n = 1.

Excited states: n = 2, 3, …

n = ∞ and continuum states correspond
ionized (free) states.

Transition of an electron from the nth to
mth energy level will result in a photon
of wavelength:
to
-1.51 eV
-3.4 eV
æ1
1ö
= RH ç 2 - 2 ÷, m < n
èm n ø
l
1
where RH = Rydberg constant =
1.10x107 m-1.
-13.6 eV
Spectral Lines of Hydrogen Atom

Emission lines are produced when
electrons make transitions from higher
to lower energy levels and emit photons.
(A given transition by a single electron
results in the emission of a single
photon having an energy equal to the
energy difference between the energy
levels.)

Absorption lines are produced when
electrons absorb photons to make
transitions from lower to higher energy
levels. (A given transition by a single
electron requires a single photon having
an energy equal to the energy difference
between the energy levels.)
Spectral Lines of Hydrogen Atom

Lyman series correspond to transitions from or to the ground (n = 1) state,
requiring or emitting UV photons.

Balmer series correspond to transitions from the first excited (n = 2) to a higher
state, or from a higher to the first excited state, requiring or emitting optical
photons.
Spectral Lines of Hydrogen Atom

Paschen series correspond to transitions from the second excited (n = 3) to a
higher state, or from a higher to the second excited state, requiring or emitting
near-infrared photons.

Followed by the Brackett, Pfund, and Humphreys series in the near-infrared to
mid-infrared.
Naming Spectral Lines of Hydrogen

Individual spectral lines of hydrogen are identified by the series to which they
belong.
Naming Spectral Lines of Hydrogen

Wavelengths of Lyman series lines. Lyman limit corresponds to n = 1 → ∞.
Naming Spectral Lines of Hydrogen

Wavelengths of Lyman series lines. Lyman limit corresponds to n = 1 → ∞.
Naming Spectral Lines of Hydrogen

Wavelengths of Balmer series lines. Balmer limit corresponds to n = 2 → ∞.
Naming Spectral Lines of Hydrogen

Recall from the last chapter that the sharp drop-off at the Balmer limit can be used
to estimate the redshifts of galaxies.
(Notice the shift in
wavelength of the
Balmer limit with
increasing
redshifts.)
Energy Levels of Hydrogen-like Ions

Atoms which are ionized to the stage where they only have one electron
remaining – hydrogen-like or hydrogenic ions – have an energy-level pattern
similar to that of hydrogen (but the energy levels do not have the same energies as
those of hydrogen).
Singly-ionized Helium
Hydrogen
Naming Spectral Lines of Hydrogen-like Ions

Atoms which are ionized to the stage where they only have one electron
remaining – hydrogen-like or hydrogenic ions – have an energy-level pattern
similar to that of hydrogen (but the energy levels do not have the same energies as
those of hydrogen).

Hydrogen-like ions therefore exhibit spectra that have a pattern similar to
hydrogen (except that the lines are not at the same wavelengths as hydrogen).

The individual spectral lines of hydrogen-like ions are identified by the series to
which they belong just like for hydrogen.

E.g., Ly-α line of singly-ionized helium at a wavelength of 304 Å.
Naming Spectral Lines of other Atoms/Ions

For all other emission lines, they are identified by the species and its wavelength.

E.g., neutral oxygen (O) is O I, singly-ionized oxygen (O+) is O II, doubly-ionized
oxygen (O2+) is O III, etc.

E.g., a particular line of OI at 5577Å is referred to as O I λ 5577Å.

Furthermore, transitions between different energy levels have different
probabilities of occurring. E.g., for hydrogen, a transition between n = 3 → 1 has
a factor of nearly 8 times higher probability than between n = 3→ 2.

Transitions that have a high probability of
occurring are known as permitted transitions;
i.e., electrons spend relatively little time at the
higher energy level before transitioning to the
lower energy level.
Naming Spectral Lines of other Atoms/Ions

For all other emission lines, they are identified by the species and its wavelength.

E.g., neutral oxygen (O) is O I, singly-ionized oxygen (O+) is O II, doubly-ionized
oxygen (O2+) is O III, etc.

E.g., a particular line of OI at 5577Å is referred to as O I λ 5577Å.

Furthermore, transitions between different energy levels have different
probabilities of occurring. E.g., for hydrogen, a transition between n = 3 → 1 has
a factor of nearly 8 times higher probability than between n = 3→ 2.

Transitions that have a low probability of
occurring are known as forbidden transitions;
i.e., electrons spend a relatively long time at the
higher energy level before transitioning to the
lower energy level. Lines corresponding to
forbidden transitions are denoted by []; e.g.,
[O III] λ 5007Å. Lines from forbidden
transitions are not seen from gases on the Earth
but seen from gases in interstellar space. Why?
Naming Spectral Lines of other Atoms/Ions

Examples of permitted and forbidden lines in the spectrum of the Orion nebula.
Other Ways to Produce Spectral Lines

Transitions between different orbitals of an electron are not the only way to
produce spectral lines.

E.g., the 21-cm line of atomic hydrogen is produced by transitions between
different spin alignments of the electron and proton in the ground state of
hydrogen.
Other Ways to Produce Spectral Lines

Transitions between different orbitals of an electron are not the only way to
produce spectral lines.

Molecules can rotate at certain prescribed rotational frequencies, and vibrate at
certain prescribed vibrational frequencies. Transitions between different rotation
states at the same vibrational states are known as rotational transitions, and
between the same or different rotational states at different vibrational states are
known as rotational-vibrational transitions.
Learning Objectives

Spectroscopy:
- spectrum
- spectrograph or spectrometer

Spectral Lines:
- electron orbits and energy levels in atoms
- emission and absorption of photons
- energy levels and spectrum of hydrogen atoms and hydrogen-like ions
- naming spectral lines
- permitted and forbidden transitions
- other ways for atoms/molecules/ions to produce spectral lines

Continuum and Spectral Line Formation:
- Kirchoff’s laws
- absorption lines
- emission lines
- continuous emission
Kirchoff’s Laws

In the mid-19th century, based on experiments Kirchoff summarized his three
empirical laws under which spectral lines were produced:
Kirchoff’s Laws

To understand the physical basis of
Kirchoff’s laws, know that an
atom/ion/molecule can be excited
either by the absorption of photons
or collisions with another particle
(which absorbs a part or all of
kinetic energy of the colliding
particle).

Similarly, an atom/ion/molecule can
be de-excited either by the emission
of photons or collisions with another
particle (which excites the colliding
particle or adds to its kinetic energy).
Absorption Lines

What is the physical explanation for the following Kirchoff’s law?
Photospheric Absorption Lines

Spectral lines from stellar photospheres are seen in absorption. Why?
Photospheric Absorption Lines

Spectral lines from stellar photospheres are seen in absorption. Why?
Emission Lines

What is the physical explanation for the following Kirchoff’s law?
Emission Lines

What is the physical explanation for the following Kirchoff’s law?
Emission Lines
Continuous Emission

What is the physical explanation for the following Kirchoff’s law.
Forbidden Lines

Forbidden lines are are not seen from gases on the Earth, but seen from gases in
interstellar space. Forbidden lines can be just as bright if not brighter than
permitted lines.

Recall that forbidden lines have low transition probabilities; i.e., electrons spend a
relatively long time at the higher energy level before transitioning to the lower
energy level. Why are forbidden transitions not seen from gases on the Earth but
seen from gases in interstellar space?
Continuous Emission

In astronomy, continuous emission at optical wavelengths usually produced by:
- thermal motions of atoms (e.g., stellar photospheres)
Continuous Emission

In astronomy, continuous emission at optical wavelengths usually produced by:
- thermal motions of atoms (e.g., stellar photospheres)
- recombination (electrons recombining with ions) in ionized gas
Learning Objectives

Spectrometers or Spectrographs:
- objective prism
- slit spectroscopy
- diffraction grating
- line grating
- blazed grating
- spectral resolution
- echelle grating
- multi-object spectrographs
- integral field spectrographs

Spectral Line Profiles and Shifts:
- natural broadening
- pressure broadening
- Doppler effect
- thermal or Doppler broadening
Measuring Spectra

There are a number of ways in which the spectra of celestial objects can be
measured.

One way is to place a prism just in front of the the telescope objective, known as
an objective prism.
Measuring Spectra

An example of objective prism spectra of the Hyades open star cluster.

What are the advantages and disadvantages of objective prism surveys?
- spectra of all objects can be measured in a single exposure
- spectra of different objects can overlap

In this course, we consider spectrographs using diffraction gratings.
Spectrograph

Basic components of a spectrograph are:
- entrance aperture, which can be a slit or circular apertures (optical fibers)
- collimator, which is an optical element to make light parallel and hence have
the same angle of incidence over the surface of the dispersing element
- dispersing element (e.g., prism), which separates light to different wavelengths
- spectrum imager, which focuses the spectrum onto a detector
- detector, which in modern times is a CCD
Spectrograph
Slit Spectroscopy

If you are measuring the spectrum of one object that is unresolved or in its entirety,
it would not matter what shape aperture you use so long as the aperture only lets
through light from that object.
Slit Spectroscopy
What if you want to measure the spectrum as a function of position in an extended
object? One way is to use a slit, which of course restricts the spectrum to just
locations along the slit.
slit orientation
position

λ
Diffraction Gratings

A diffraction grating is a collection of equally spaced transmitting or reflecting
elements (grooves) separated by a distance comparable to the wavelength of light.

A simple diffraction grating consists of lines (opaque to light) scratched onto a
glass surface, so that only the smooth surface transmits (transmission grating) or
reflects (reflection grating) light.
Line Gratings

A simple transmission (line-diffraction) grating. Only 2 grating apertures are
shown in this example; in practice, there can be many thousands of grating
apertures.

Maxima occur when the path difference between adjacent rays, d sin θ, is an
integer multiple of the wavelength, λ, of light.
m=2
m=1
m=0
m = -1
m = -2
m
λ
(m – ½ ) λ
Line Gratings

m is known as the order of the maxima in the diffracted pattern. E.g., m = 0 is the
zeroth order, |m| = 1 is the first order, etc.

Disadvantage of this type of grating is that much of the light falls at the zeroth
order where no spectrum is produced, and the light intensity drops quickly
towards higher orders. Note also that higher order maxima are more closely
separated, so that high order maxima can overlap.
m=2
m=1
m=0
m = -1
m = -2
m
λ
(m – ½ ) λ
Line Gratings

m is known as the order of the maxima in the diffracted pattern. E.g., m = 0 is the
zeroth order, |m| = 1 is the first order, etc.

Disadvantage of this type of grating is that much of the light falls at the zeroth
order where no spectrum is produced, and the light intensity drops quickly
towards higher orders. Note also that higher order maxima are more closely
separated, so that high order maxima can overlap.
m=3
m=2
m=1
m=0
m = -1
m = -2
m = -3
Line Gratings

A simple reflection (line-diffraction) grating.

Sign convention: angles on the side of the incident ray relative to the grating
normal are defined to be positive, whereas angles on the side of the reflected ray
relative to the grating normal are defined to be negative.

Maxima occur when the path difference between adjacent rays, (d sin θi + d sin
θm), is an integer multiple of the wavelength, λ, of light; i.e., d sin θi + d sin θm =
mλ.
d
Line Gratings

Is the any advantage of this design over a transmission grating? Hint: law of
reflection states that -θm = θi (recall sign convention); at which order is most of the
light concentrated?
d
Blazed Gratings

In modern diffraction gratings, grooves are cut into the surface to give a regular
geometrical shape. Such gratings are called blazed gratings, and have the
advantage of causing most of the diffracted light energy to be concentrated in a
certain direction away from the zeroth order.
Blazed Gratings

Definition of groove spacing and angles in a blazed diffraction grating. Note that
most of light is now reflected not to m = 0 but instead to a higher m order.
Blazed Gratings

Ray 2 has to travel an extra distance d sin θi compared to ray 1 to reach their
respective grooves.

On reflection, ray 2 travels a lesser distance d sin (θr) compared to ray 1.

Path difference between rays 2 and 1 is
d sin θi + d sin (θr) = mλ for
constructive interference. (Recall that
θr is negative by the sign convention.)
θi
θr
Blazed Gratings

d sin θi + d sin (θr) = mλ = 0 when θr = -θi . This is the zeroth order where no
spectrum is produced. In a blazed grating, relatively little light is diffracted into
the zeroth order.

Illuminate grating such that the angle
of incidence θi and the blaze angle
together gives rise to the highest light
intensity at the desired order m.
θi
θr
Blazed Gratings

At progressively higher orders m, angular separation between adjacent orders
decreases so that maxima at different wavelengths can overlap.

Use filter to restrict input wavelength range and thus prevent order overlap.
Blazed Gratings

I will leave it as an exercise for you to show that the same mathematical
relationship applies to a transmission (blazed) grating.
Spectral Resolution

Irrespective of the exact design of the diffraction grating, the spectral resolution is
R = λ/Δλ = mN, where m is the order and N the number of grating apertures. (In
this course, we will not derive the relationship for spectral resolution.)

To get higher spectral resolutions, use more grating apertures (there is practical
limit) and higher order m (susceptible to order overlap; alternatively, restricted
wavelength range of spectrum).

Recall that d sin θi + d sin (θr) = mλ.
To use very high orders m, need very
large θi and θr (close to 90o).
Echelle Grating

An echelle grating is a particular type of blazed grating that has a very large blaze
angle to allow very large θi and θr to be used, and hence achieve large R.

Recall that large m is suspectible to order overlap. To separate out different orders,
a cross disperser (another grating) acts perpendicular to the echelle grating
dispersion direction.
Echelle Grating
Echelle Grating

Spectrum of the Sun produced by an echelle spectrum.
Multi-Object Spectrographs

In modern astronomy, we are often interested in taking spectra of hundreds to
thousands of objects (e.g., stars, galaxies) at the same time.

We use a multi-object spectrograph, which directs light from the focal plane of the
telescope using optical fibers (having circular apertures) to spectrographs.

E.g., the LAMOST multi-object spectrograph employs 4000 fibers at the focal
plane that can be individually moved, and a bank of sixteen spectrographs.
Integral Field Spectrographs

What if you want to measure the spectrum of an extended object at all positions at
the same time? Use an integral field spectrograph.

Several designs have been employed. A simple design is a matrix of optical fibers
analogous to a multi-object spectrograph.

E.g., PPAK on the 3.5-m telescope on Calar Alto has 331 target fibers surrounded
by 36 sky fibers.
Learning Objectives

Spectrometers or Spectrographs:
- prism
- diffraction grating
- line grating
- blazed grating
- spectral resolution
- echelle grating
- multi-object spectrographs
- integral field spectrographs

Spectral Line Profiles and Shifts:
- natural broadening
- pressure broadening
- Doppler effect
- thermal or Doppler broadening
Natural Broadening

The Heisenberg uncertainty principle dictates that we cannot know the position
and velocity of particles (objects) to arbitrarily high precision (foundation of
quantum physics).

Instead of orbits being at precise radii from the nucleus, orbits are “fuzzy;” i.e.,
decreasing probability of finding an electron away from the most probable radius.
Precise orbits
Fuzzy orbits
Natural Broadening

Transitions between the same two energy levels in different atoms can produce
photons with slightly different energies.
Natural Broadening

Transitions between the same two energy levels in different atoms can produce
photons with slightly different energies.

The resultant is that spectral lines are not infinitely sharp in wavelength or
frequency, but has a spread in wavelength/frequency described by a Lorentzian
profile.
Pressure Broadening

In describing atoms/ions/molecules so far, we have not considered electrostatic
forces between adjacent atoms/ions/molecules. Such forces perturb electron
orbits. The resulting broadening of spectral lines is known as pressure broadening.

Pressure broadening also
gives rise to a Lorentzian
profile.

Pressure broadening can be
important in stellar
atmospheres (e.g., mainsequence stars), but typically
not important in the
interstellar medium.
Doppler Effect

Doppler effect of sound due to an approaching or receding source can be
expressed in terms of: 1) the speed of the source relative to the wave-carrying
medium (air); and 2) the speed of the observer relative to the wave-carrying
medium.

Equation for Doppler effect of sound:
lobs
æ v + vs ö
= lsource ç
÷
where èν vis+thevospeed
ø of sound waves in air,
νs is the speed of the source relative to air (+ away from
observer), and
νo is the speed of the observer
relative to air (+ towards source).
Doppler Effect

The speed of light is a constant, c, for all observers. Doppler effect of light is
cased by a combination of: 1) geometrical effects (just like the Doppler effect of
sound); and 2) time dilation (an effect of special relativity).

Equation for Doppler effect of light:
1
lobs
æ1 + v / c ö 2
= lsource ç
÷
è1 - v / c ø
where ν is the speed of the source
relative to the observer (+ away from observer).

Because of the expansion of the Universe, distant galaxies are receding away from
us. The recession velocity of galaxy is expressed in terms of redshift, z:
ælobs - lsource ö
zºç
÷
è lsource ø
=
1+ v/c
-1
1- v/c
Thermal or Doppler Broadening

Motion of particles due to their thermal energy result in collisions that produce a
particular distribution of speeds. More particles are traveling at lower than higher
speeds. Furthermore, roughly equal number of particles are traveling towards as
away from us.
Thermal or Doppler Broadening

The distribution of speeds along the line of sight is a Gaussian (or normal)
distribution, giving rise to a spectrum with a Gaussian profile.

Full-width half-maximum (FWHM) of thermal or Doppler broadening:
Thermal or Doppler Broadening

The addition of a Lorentzian to a Gaussian profile is a Voigt profile.

In general, spectral lines have Voigt profiles.
Learning Objectives

Slit Spectroscopy:
- setup and observations
- data reduction
- extracting spectrum
- wavelength calibration
- extinction correction
- flux calibration
- removing sky lines
Slit Spectroscopy

Steps for doing slit spectroscopy using a CCD:
1.
Center the object within slit and take spectrum.
2.
Reduce CCD frames with bias, dark, and flat (previously covered)
3.
Extract spectrum of object
4.
Take a spectrum of the standard lamp for wavelength calibration
5.
Correct for Earth’s atmospheric extinction and interstellar extinction
(previously covered)
6.
Flux density calibration with standard stars
7.
Remove sky lines.
Setup and Exposure
1. Center the object within slit and take spectrum.

For a point source (e.g., a star), a slit of width smaller than the FWHM of the
seeing is chosen (i.e., the narrower the better).

What is the disadvantage of using such a narrow slit?
Setup and Exposure
1. Center the object within slit and take spectrum.

For a point source (e.g., a star), a slit of width smaller than the FWHM of the
seeing is chosen (i.e., the narrower the better).

What is the advantage of using such a narrow slit?
Setup and Exposure
1. Also take spectrum of standard lamp for wavelength calibration.

In optical astronomy, arc lamps containing gas of one or more elements (e.g., Hg,
C, Zn, ThAR) are usually used for wavelength calibration. The gas is ionized by
an electrical arc, and produces a rich spectrum.
Setup and Exposure
1. Also take spectrum of standard lamp for wavelength calibration.

In optical astronomy, arc lamps containing gas of one or more elements (e.g., Hg,
C, Zn, ThAR) are usually used for wavelength calibration. The gas is ionized by
an electrical arc, and produces a rich spectrum.
Setup and Exposure
1. Also take spectrum of standard lamp for wavelength calibration.

Of course, the wavelength of each line from the standard lamp has previously
been measured in the laboratory to high precision.
Setup and Exposure
1. Finally, also observe spectrophotometric standard star for flux density calibration.

Spectrophotometric standards are bright stars with accurate measurements of their
spectra: flux density as a function of wavelength
HR 9087
Spectral Extraction
3. Extract spectrum of object.

The spectrum of a point source recorded on CCD is a strip extending along the
dispersion/spectral direction. Ideally the strip should be a rectangle aligned with
the CCD rows/columns, but in practice the strip is curved depending on optics.

Obtain spectrum of the object by
integrating few pixels near source along
the spatial direction (over gwidth) and
subtracting background.
Need to correct for “missing light”
arising from integrating only a finite
width (similar to aperture correction in
photometry).
Spatial direction

CCD frame
Dispersion/Spectral direction
Wavelength Calibration
4. Use standard lamp spectrum for wavelength calibration.

After extracting a spectrum, we need to put the data on a wavelength scale.

From the standard lamp spectrum, create a mapping of the spectral direction pixel
number and wavelength.

A good diffraction grating will generate an almost linear mapping.
Arc
lamp
frame
Target
frame
Flux Density Calibration
6. Flux density calibration.

At this point, spectrum is in units of photon-counts sec-1 Å-1.

Compare with photon-counts sec-1 Å-1 from spectrophotometric standard to
convert to ergs-1 sec-1 cm2 Å-1.
Standard
star frame
Target
frame
Sky Lines
7. Remove sky lines (including lines from artificial man-made source).

Apart from spectral lines from target star in the slit, spectral lines produced by
Earth’s atmosphere, or scattered by the Earth’s atmosphere from man-made light
sources, also are imprinted on the spectrum of the source.

Flux density of sky lines generally vary in position and with time.

Removed by fitting a profile to the sky lines in the background spectrum and
subtracting from the target spectrum, or as a final resort blanking out affected
parts of the target spectrum.
From artificial
light source