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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 bandAccuracy 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. (1) DEFINE/CALCULATE RELEVANT INPUT PARAMETERS Nobj = photons/A (per arcsec^2 if extended) from object, calculated as above Nsky = photons/A/arcsec^2 from sky, calculated as above BAND = equivalent width of filter in A (integral T(l)dl where T(l) is transmission, l is wavelength) FWHM = object fwhm (intrinsic and due to seeing) in arcsec P = number of pixels over which integration carried out READ = CCD readout noise (e-) SLIT = slit width, or diameter of fibre or lenslet (arcsec) (2) CALCULATE SIGNAL-TO NOISE (2a) IMAGING AND SLIT SPECTROSCOPY: Imaging, point source: N is number of (detected) object photons S is number of (detected) sky photons per pixel N = Nobj * BAND S = Nsky * BAND * (arcsec/pixel)^2 P = pi * (FWHM/(arcsec/pixel))^2 (This assumption radius = FWHM is slightly pessimistic. Optimum S:N ratio is achieved for radius = 2/3 * FWHM, according to Naylor 1998, MNRAS 296 339.) Imaging, extended source: N is number of object photons/arcsec^2 S is number of sky photons per pixel N = Nobj * BAND * (arcsec/pixel)^2 S = Nsky * BAND * (arcsec/pixel)^2 P = 1 Spectroscopy, point source: N is number of object photons per pixel step in wavelength S is number of sky photons per pixel N = Nobj * A/pixel S = Nsky * SLIT (arcsec) * arcsec/pixel * A/pixel P = 2 * FWHM (arcsec) / arcsec/pixel Spectroscopy, extended source: N is number of object photons per pixel S is number of sky photons per pixel N = Nobj * SLIT (arcsec) * arcsec/pixel * A/pixel S = Nsky * SLIT (arcsec) * 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. (2b) INTEGRAL-FIELD OR FIBRE SPECTROSCOPY: Spectroscopy, point source: N is number of object photons per pixel step in wavelength S is number of sky photons per pixel step in wavelength (not per pixel) N = Nobj * A/pixel S = Nsky * 3.14159/4. * SLIT(arcsec)^2 * A/pixel P ~ 2 (depends on instrument) Signal-to-noise = N/sqrt(N+S+P*READ^2) Spectroscopy, extended source: Same calculation as for point source, except that object mag is integrated over circular aperture of diameter SLIT.The predicted counts are based on actual throughput measurements for all currently-offered instruments. The AF2 throughputs are for reflection mode. 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.
For more information on each detector, see the
ING detectors page .
Selecting INGRID or NAOMI/INGRID forces selection of the Rockwell detector.
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
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.
Information about converting SDSS u g r i z magnitudes to U B V R I
can be found on the
SDSS web pages.
If you want to specify to SIGNAL an
Oke
AB apparent magnitude, rather than a Vega magnitude,
add 100 and enter the total.
E.g. if mag(AB) = 24, enter 124.
If you want to specify the intensity in
Jy (10-26
W/Hz/m2), multiply by -1 and enter the result.
E.g. if S(Jy) = 0.01, enter -0.01.
For fibre or integral-field spectroscopy, the mag is assumed to be
per lenslet or per fibre.
SIGNAL converts Vega magnitudes
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).
These can be expressed as intensities in Jy for mag = 0 in each band:
Emission-line objects - imaging
For an extended object with known emission-line surface brightness S,
in W/m2/arcsec2, a
similar calculation can be carried out, to obtain surface brightness
in Jy/arcsec2, which can then be entered in SIGNAL to estimate S:N per
arcsec2.
Example: an object has a surface brightness of
10-15 erg/s/cm2/arcsec2
in the Hα emission line.
This corresponds to
10-18 W/m2/arcsec2.
Imaged through an Hα filter with a
50-A bandpass (i.e. bandpass 3.5 x 1012 Hz),
this corresponds to
2.9 x 10-31 W/m2/Hz/arcsec2,
or
2.9 x 10-5 Jy (r mag ~ 20) per arcsec2.
To predict the S:N for an 1800-sec ACAM imaging exposure of such an object
through an Hα filter in bright-of-moon, enter the appropriate
parameters in SIGNAL, i.e. 'apparent mag' = -0.00003, time = 1800 sec,
band = 'R', bandwidth = 50 A, object = 'extended' and
sky = 'b' (for bright).
SIGNAL should predict ~ 2100 photons/pixel from the object,
~ 10300 photons/pixel from sky and S:N ~ 19 (i.e. sky photon noise dominates).
[NB as a sanity check of the number of detected photons,
and given that the energy of an Hα photon is E = hc/λ =
2.9 x 10-19 J, one can convert the surface brightness
10-18 W/m2/arcsec2
into a photon arrival rate at the top of the atmosphere
~ 3.4 photons/s/m2/arcsec2.
For exposure time 1800 sec, WHT collecting area 12.5 m2,
assumed atmosphere/WHT/ACAM/CCD efficiency ~ 0.42, and pixel size
0.25 arcsec, this indeed corresponds to ~ 2000 photons/pixel,
as calculated by SIGNAL.]
Emission-line objects - spectroscopy
Exposure timeAny value of exposure time can be entered.In practice, the minimum useful exposure time is usually determined by the time taken for the shutter to open and close (~ 0.1 sec).
Most of the observing time is expended on exposures shorter than
half an hour.
Longer exposures (1) will suffer a large number of cosmic-ray hits,
and (2) incur a larger risk of lost time in the event of a technical failure.
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 setting D is for typical dark-of-moon conditions. For sky brightness typical of grey- or bright-of-moon, select G or B respectively. For the darkest sky seen on La Palma, i.e. median at dark-of-moon, solar minimum, at high galactic and ecliptic latitude and in the absence of twilight and moonlight, select 0.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 3.3Note 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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