# SIGNAL Help

### Calculation made by SIGNAL

SIGNAL calculates the number of photons per Å detected from a source of given apparent magnitude (per arcsec2 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 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

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.

```
The predicted counts are based on actual throughput measurements for all currently-offered instruments.

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

'N/A' in the menu indicates no longer available as a common-user instrument.

Imaging calculations ignore the grating selected.
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### Band and effective bandwidth

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 the LN CCD filters page . SIGNAL assumes sensible defaults for broad-band filters.

### 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.

### Apparent magnitude

Apparent magnitudes ('Vega' mags) 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). These can be expressed as intensities in Jy for mag = 0 in each band:
``` U     B     V     R     I     Z     J     H     K
1810  4260  3640  3080  2550  2200  1570  1020   640
```
(These are the values used in version 14.3 of SIGNAL, and they are unlikely to change much.)

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.

Emission-line objects - imaging
To estimate for an imaging observation the signal-to-noise with which a point emission-line object will be detected, divide the emission-line intensity S (in W/m2) by the effective bandwidth (see above) of the filter in Hz (e.g. a 50-A Halpha filter with a transmission of 100% would have an effective bandwidth of ~ 3.5x1012 Hz) to calculate the mean intensity across the filter bandpass, in W/m2/Hz, then divide by 1026 to convert to Jy. The intensity in Jy can then be entered as noted above.

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.
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### Exposure time

Any 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.
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### Object FWHM

The 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
```

### Airmass

Airmass = 1/sqrt[1 - 0.96×sin2(ZD)] approximately, i.e. approx sec(ZD).
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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 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. 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.

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.

### 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.).

### Fortran source code

For faster turnaround, copy across the the Fortran source code (save as source, not text) and edit out the html tags from start and end.

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 Contact:  Last modified: 26 February 2014 © of original Isaac Newton Group of Telescopes © of modifications for Helmos Observatory, National Observatory of Athens