SIGNAL calculates number of photons per A detected from a source of given
apparent magnitude (per arcsec^2 if extended), as:
10.^(-mag/2.5)
* photons/sec/A/m^2 giving mag = 0 at the top of the atmosphere
* transmission of atmosphere at given airmass
* exposure time in sec
* unobstructed area of main mirror in m^2
* measured throughput of telescope/instrument
* quantum efficiency of detector in the given band
Accuracy is typically +-20%.
Counts from the sky are calculated in a similar way.
For spectroscopic observations,
signal-to-noise is per pixel step in
wavelength for point sources, and per pixel for extended ones.
For imaging, the counts obtained above are multiplied by the
effective bandwidth of the filters in Angstrom, and the signal-to-noise
is calculated within a 2-FWHM-diameter aperture for a point
source and per pixel for extended sources.
The program can be used before observing to estimate the exposure time needed
for a particular experiment, and at the telescope to check that the expected
number of photons (counts * gain) is detected by the CCD.
Signal-to-noise is calculated as follows:
Nobj = photons/A (per arcsec^2 if extended) from object
Nsky = photons/A/arcsec^2 from sky
BAND = equivalent width of filter in A (integral T(l)dl
where T(l) is transmission, l is wavelength)
P = number of pixels over which integration carried out
READ = CCD readout noise (e-)
FWHM = object fwhm (intrinsic and due to seeing) in arcsec
Imaging, point or extended sources:
N = Nobj * BAND
S = Nsky * BAND*(arcsec/pixel)^2
P = pi*(FWHM/(arcsec/pixel))^2 for point source
(Using radius = FWHM is slightly pessimistic, optimum S:N
ratio is achieved for radius = 2/3 * FWHM, according to
Naylor 1998, MNRAS 296 339.)
P = 1 for an extended source
Spectroscopy, point source:
N = Nobj * A/pixel
S = Nsky * slit-width(A) * arcsec/pixel * A/pixel
P = 2 * FWHM (arcsec) / arcsec/pixel
Spectroscopy, extended source:
N = Nobj * slit-width(A) * arcsec/pixel * A/pixel
S = Nsky * slit-width(A) * arcsec/pixel * A/pixel
P = 1
Signal-to-noise = N/sqrt(N+P*(S+READ^2))
For point sources, the sky counts are those from a
2-FWHM-diameter circular aperture for imaging, and from
a 2-FWHM * slit-width rectangle for spectroscopy.
For extended sources, the calculations are per pixel.
For integral-field or fibre spectroscopy:
N = Nobj * A/pixel
S = Ssky * 3.14159/4.*slit-width(A)^2 * A/pixel
(photons/pixel-step-in-wavelength, not /pixel)
P ~ 2 (depends on instrument)
Signal-to-noise = N/sqrt(N+S+P*READ^2)
The predicted counts are based on actual
throughput measurements for
all currently-offered instruments except
the IDS 500-mm camera.
The WYFFOS throughputs are for reflection mode, and are
preliminary. They should be treated as lower limits.
For echelle mode, the throughputs for orders 3, 4, 5, 6,
7 are factors 1.0, 1.3, 1.3, 2.0, 3.2 lower respectively.
The program does not take into account losses due to
colour and ND filters or to polarisation
optics in spectrograph; to the lower
grating efficiency at large angles of incidence; or to
vignetting at large field radius.
Features added recently include:
- correction for vignetting by slit (or fibre) (2/02)
- approx calculator for NAOMI/OASIS/MIT-LL (2/02)
- option to specify sky as D, G or B (2/02)
- calculation of S:N (as well as object counts) for AF2 (2/02)
The original web interface to the program was written August 1998 by
Ashley James of UCL (ING summer student).
It was rewritten August 2003, in .php, by Robert Greimel.
Instruments and gratings
'N/A' in the menu indicates no longer available
as a common-user instrument (for coding reasons, this label also temporarily
appears against non-ING instruments).
For the latest news on available instruments, see the
ING astronomy
page under 'Overview'.
In reflection mode, WYFFOS is normally used with ISIS
diffraction gratings. It can also be used with IDS gratings
(but SIGNAL doesn't cater for this option).
Imaging calculations ignore the grating selected.
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Detectors
For the latest news on available detectors, see the
ING detectors page .
As of August 2003, EEV is the default detector on WHT ISIS blue arm,
and for WHT PF and INT PF imaging;
Marconi on ISIS red arm;
TEK on WHT aux-port and WYFFOS;
MIT on WHT OASIS.
The detector for the IR camera WHIRCAM was a 256*256 InSb array, those
for INGRID and CIRSI are 1k*1k Rockwell arrays.
Selecting INGRID or NAOMI/INGRID forces selection of the Rockwell detector.
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Band and effective bandwidth
For imaging, the bandwidths used correspond to the 50-mm
CuSO4/UG1 or liq-CuSO4 U filters, the Harris B,V,R,I set,
the RGO glass Z filter and the WHIRCAM J, H and Kshort
filters. Note that the 125-mm glass U filter
has a factor 3 lower throughput than the 50-mm U.
Note also that the throughputs of the Harris B filters are
up to 25% less than that of the KPNO B filters.
The effective bandwidth of a filter is taken to be the integral over
T(l)dl, where T(l) is the transmission of the filter and l is the
wavelength, i.e. the area under the filter transmission curve,
measured in A, see
table.
SIGNAL assumes sensible defaults for broad-band filters.
The approximate wavelengths used for spectroscopy are given in A
in the menu.
For FOS, U,B are for second order, V,R,I are first order.
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Object type
The calculations can be carried out for point sources, with specified
FWHM and apparent magnitude; or for extended sources, with
specified apparent mag per square arcsec.
For fibre and integral-field spectroscopy, point sources are assumed,
i.e. SIGNAL assumes that the given mag is for
one fibre or lenslet.
For observations of an extended object, just give the mag per
fibre or lenslet.
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Apparent magnitude
Apparent magnitudes are converted to SI units using the calibrations
given by Bessell (1979, PASP, 91, 589) and Bessell and Brett
(1988, PASP, 100, 1134), which are similar to those given by
Johnson (1966, Ann Rev Astr Astrophys, 4, 193).
Values exceeding 50 are assumed to be 100 +
Oke
AB apparent magnitude.
Negative values are assumed to be in Jy (10
-26
W/Hz/m
2)
For fibre or integral-field spectroscopy, the mag is assumed to be
per lenslet or per fibre.
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Exposure time
For CCDs, the minimum exposure time is typically determined by the
time taken for the shutter to open and close (~ 0.1 sec).
The maximum (~ half an hour) is
typically determined by the rate of cosmic-ray
events on the CCD.
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Object FWHM
The image FWHM (seeing convolved with object size)
is now used to determine both vignetting by the slit and the number of
pixels over which to integrate for point-source observations:
pi * (FWHM / arcsec/pixel)**2 for imaging
2 * FWHM / arcsec/pixel for spectroscopy
For NAOMI/INGRID, SIGNAL uses the appropriate throughput and
pixel scale, but doesn't attempt to model the AO-corrected PSF
- the user is left to set an appropriate FWHM.
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Slit width
The slit-width is now used both to determine the intensity of the signal
from (uniformly) extended objects, including the sky, and to calculate
vignetting (for point sources).
For fibre or integral-field spectroscopy (e.g. WYFFOS, OASIS),
the fibre or lenslet is assumed to be circular with a diameter
equal to the value provided for this parameter.
For imaging calculations, this parameter is ignored.
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Airmass
Airmass = 1/sqrt[1 - 0.96*sin
2(ZD)] approximately, i.e.
approx sec(ZD).
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Extinction
The default values are taken from La Palma Technical Note 45 and
the WHIRCAM Users Manual. Click
here
for access to online ING technical notes and manuals.
For more information about dust on La Palma, click
here .
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Sky brightness
SIGNAL's default optical sky-brightness settings are median for
dark-of-moon, solar minimum, at high galactic and ecliptic
latitude and in the absence of twilight and moonlight
(enter D, G or B for typical dark (brighter than default),
grey and bright of moon).
The BVR values are accurate to +- 0.1 mag and are similar to
those measured at other dark sites (Chile, Hawaii etc.).
U and I are accurate to 0.5 mag. R and I sky brightnesses
vary randomly by several tenths of a mag with variations in
the OH airglow. The V and R sky brightness include a
contribution of about 0.1 mag due to NaD light pollution.
Light pollution is negligible in other bands, and it is
decreasing.
The sky brightness values used by SIGNAL refer to low spectral
resolution. Between the OH lines in the red, the sky is
1 - 2 mag darker.
The sky is markedly brighter (several tenths of a mag) under
very dusty conditions (> 0.3 mag extinction).
The sky is 0.4 mag brighter at solar maximum. Recent minima
were in 1986.8, 1996.5.
Last maximum was 2000.4.
Variation is approximately
sinusoidal with time.
The sky is 0.4 mag brighter on the ecliptic than at the
poles, varying as sine(b) approximately.
The airglow contribution (typically about 70% of the total
in V) brightens approximately as airmass. The sky is 0.3 mag
brighter at airmass 1.5.
Stars fainter than apparent magnitude
20 contribute negligibly to the total.
Starlight scattered by interstellar dust contributes about
5% of the total, rising to about 30% on the galactic plane.
The extragalactic contribution is negligible (< 1%).
The brightness of the sky does not vary with time after
astronomical twilight.
For further details of the calculations of moonless sky
brightness, see La Palma technical note 115
(Benn & Ellison 1998).
SKY BRIGHTNESS WITH MOON UP:
When the moon is 60 deg from zenith, with extinction 0.15 mag,
the zenith sky will brighten roughly by M as tabulated below:
New Crescent Quarter Gibbous Full
Phase angle (deg) 180 135 90 45 0
Approx day: 1 4 8 12 15
D, G or B: D G G B B
Illum. frac. % 0 25 50 75 100
M (U, B, V) 0 0.5 2.0 3.1 4.3
M (R) 0 0.3 1.3 2.4 3.5
M (I) 0 0.2 1.1 2.2 3.3
Note that the quarter moon (i.e. half disc illuminated)
is a factor of 10 (not 2) fainter than full, due to the
opposition effect (also responsible for gegenschein on the
ecliptic and dry heiligenschein on earth).
Sky brightness for other values of lunar phase, lunar zenith
angle, sky position and extinction, can be estimated with
SIGNAL's sky-brightness calculator (see the interface above).
The contribution of moonlight in V has been calculated
according to the scattering formula of Krisciunas & Schaefer
(1991, PASP, 103, 1033), normalised (multiplied by a factor
of 2.4) to agree with measurements of sky brightness made at
the JKT on a dust-free night in 7/98.
The moonlight contribution in the other bands is calculated
according to the U-B, B-V, V-R, R-I colours of moonlight
measured on the same night in 7/98.
These values agree +-40% with measurements made by DHPJ in
9/89, but the contribution of moonlight probably depends
strongly on local conditions (e.g. dust, telescope baffling),
and with current data, the contribution by moonlight on
La Palma can probably only be predicted within a factor ~2.
Ian Steele (LJMU) has found that the background brightness
at the JKT rises dramatically (factor >~5 brighter than
the above numbers) if moonlight falls on the telescope
structure (scattering within the telescope).
For further information on optical sky brightness, see the
ING site quality web page .
The J, H and K sky brightnesses are taken from bright-of-moon
INGRID commissioning observations (Mar 2000). They probably
depend little on lunar phase (particularly in K, in which band
observing can often continue until after sunrise).
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Output format
The default format is a text listing of input parameters and results.
'Graph' format gives the text listing plus a choice of graphs e.g. S:N vs
exposure time, S:N vs magnitude, optionally for different sky brightness,
airmasses etc (for parameters other than sky brightness, specify
the required values in the boxes 'curve 1' etc.).
This facility was added by Robert Greimel Aug 2003.
