Typical S/N Estimation

By typical S/N estimation we mean that the signal-to-noise ratio is calculated using typical input parameters and for pointlike sources. The basic formulae for S/N adopted here is expressed as

Where:

total star counts ( electrons )

total sky counts per fiber ( electrons )

  CCD read noise per pixel ( electrons )

  CCD dark counts per pixel ( electrons )

number of fibers for sky observation per spectrograph

number of BIAS frames used in data reduction

number of DARK frames used in data reduction

number of pixels used in spectra extraction per resolution element

The Input

On the input GUI of our S/N calculator, options are provided for the following instrument and observation parameters:

Instrument:  

telescope aperture:  4 / 2 meters ( 2-meter for “Small System”)

LRS:  low resolution spectrograph

With/Without Slit:  0.25 / 0.5 nm in spectral resolution

Band:  the Johnson U B V wavebands

FWHM:  Full-Width-Half-Magnitude of star images on the focal plane, mainly depending upon the site seeing condition. ( choices from 1 to 5 arcsecs)

Fiber Deviation:  the amount of deviation of the fiber center off the star image center. ( choices from 0.0 to 1.5 arcsecs )

Other typical quantities used in S/N calculation are ( given for V band ):

integration time: 1.5 hours

angular diameter of fiber: 3.3 arcsec

atmospheric extinction: Kv = 0.25

telescope efficiency: 0.88 x 0.88 x 0.80

fiber transmission: 0.80

spectrograph efficiency: 0.36

CCD quantum efficiency: 0.85

CCD read noise: 4 electrons/pixel

CCD dark current: 4.5 electrons/pix/1.5hour

The Output

On the output page of our S/N calculator, the input parameters selected are listed first. S/N results are tabled according to different sky and star brightness.

** NOTE ** :  More detailed information is to be reported.