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SIGNAL Help
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.
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.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. 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.
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.
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
ING filter effective bandwidths.
SIGNAL assumes sensible defaults for broad-band filters.
The approximate wavelengths used for spectroscopy are given in Å
in the menu.
For FOS, U,B are for second order, V,R,I are first order.
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.
Values exceeding 50 are assumed to be 100 +
Oke
AB apparent magnitude.
Negative values are assumed to be in Jy (10-26
W/Hz/m2)
For fibre or integral-field spectroscopy, the mag is assumed to be
per lenslet or per fibre.
Object FWHMThe image FWHM (seeing convolved with object size) is 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.
Slit widthThe 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 the specified diameter.
For imaging calculations, this parameter is ignored.
AirmassAirmass = 1/sqrt[1 - 0.96×sin2(ZD)] approximately, i.e. approx sec(ZD).Top of the page ExtinctionThe default values are taken from La Palma Technical Note 45 and the WHIRCAM Users Manual. Visit the online ING technical notes and manuals for more information, and the site quality web pages for more information about dust on La Palma.Top of the page Sky brightnessSIGNAL'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. 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, ~2007. 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 brightness of the sky. 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:
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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