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Astronomical SNR Calculator

Author: Michael Newberry, Ph.D., Mirametrics, Inc.

This form calculates the Signal to Noise Ratio (SNR) for aperture photometry of a point source. The SNR is calculated for filtered or clear observations using the properties of the sensor (CCD), instrument (telescope and filter), and the observation. Use this calculator to plan observations by estimating the effect of exposure time and other parameters. You also can work backward to determine what combination of parameters gives a target SNR. Click [Save] to save parameters, click [Load] to fetch saved parameters. Use [Default] to load reasonable default parameters. Also see the Optimizer tool.   [Submit Comments]

Camera
 Pixel Size microns Binning Readout Noise electrons Gain e- / ADU Temp ° C T doubling ° C Tref ° C Dark Current pA / cm^2 @ Tref
Instrument
 Focal Length mm Diameter mm Secondary diameter, mm Efficiency percent
Bandpass
 Name Clear Johnson U Johnson B Johnson V Cousins R Cousins I Filter Factor percent (100%) QE percent Extinction mags @ zenith Airmass zenith = 1.0
Observations
 Object Mag  (bandpass) Exp Time seconds Seeing FWHM, arcsec Aperture radius, binned pix Sky Mag mag / arcsec^2

 All results are in units of binned pixels.
Results
 SNR Sigma(m) +/- mag

Calculations
 Dark Current e- / s / pix Base Noise e- / pix Image Scale arcsec / pix Object Flux ADU / s
 Sky Flux ADU / s / pix Total BG Flux ADU / s / pix Total BG SNR Sky / BG Noise Ratio
 Aperture diam (FWHM) Aperture diam (arcsec) Aperture Area arcsec^2 Ap Integral percent

#### Notes

Camera
 Pixel Size The fundamental width of the detector photo-site, assumed to be square. To calculate for a binned image, change the Binning field but do not change the fundamental Pixel Size. For example, suppose your CCD has a 9 micron pixel. To use a 2x2 binned image with effective 18 micron pixels, set Pixel Size=9 and Binning=2. All calculations are made for binned pixels. Binning The number of detector pixels per image pixel. This assumes the detector is binned n x n, where n = 1, 2, etc. See the Pixel Size parameter. Readnoise The detector readout noise is the intrinsic rms noise in a zero second exposure. Gain The number of electrons per ADU (Analog to Digital Unit) or DN (Digital Number) in the image. Temp The temperature of the detector. T doubling The doubling temperature for dark current approximated as a line in a log-log plot of dark current versus temperature. See the detector's data sheet. Tref The reference temperature for the detector Dark Current. See the detector's data sheet. Dark Current The rate of thermal electron production at a refernece temperature. See the detector's data sheet. The dark current is calculated using a simple doubling rule starting from a known reference dark current at a reference temperature. This is a very good approximation when the sensor temperature is not too far below the reference temperature, say within 5 or 6 doublings. However, getting even further below the reference temperature, the dark current can become so small that it has negligible effect on the calculated SNR.
Instrument
 Focal Length The telescope focal length in mm. Diameter The telescope primary diameter in mm. Secondary The telescope secondary obstruction in mm. Efficiency The percentage transmission of the optical system in the selected bandpass.
Bandpass
 Name The name corresponding to the filter set. This selects the photon flux for a star with the spectrum of Vega and magnitude 0 in the selected bandpass above the atmosphere. Filter Factor A response or transmission factor for the bandpass filter relative to the standard bandpass. This should usually be 100% unless using a low transmission filter. QE The quantum efficiency of the detector in the named bandpass. See the detector's data sheet. Extinction The atmospheric extinction coefficient per unit airmass in the named bandpass. This is site dependent. If set to 0.0, then nominal values will be entered into the field when [Calculate] is clicked. Airmass The airmass, or optical path length through the atmosphere. The shortest path is through the zenith, which has the minimal airmass value of 1.0. The airmass of an observation is approximated by sec(z), which is the secant of the zenith angle. If set to 0, the observation is considered above the atmosphere.
Observations
 Magnitude The magnitude of the target star through the bandpass filter. This magnitude must be adjusted to the bandpass, e.g., use a V magnitude for the V bandpass, B magnitude for the B bandpass, etc. Exp Time The exposure time in seconds. Seeing The FWHM of the point spread function which is a product of the atmospheric smearing and optical abberations. Sky Mag The sky brightness per square arcsecond in the named bandpass. Sample values for a very dark site are around 21.8 to 22 in B and 21.3 to 21.5 in the V bandpass.
Computed Values
 Aperture This is the value of the measuring aperture radius that you would specify in Mira. Some software packages specify the aperture in terms of diameter, not radius. Be sure you enter the appropriate value. Enter a value using binned pixels that you see in the image. For example, setting Aperture = 9 at Binning=1 gives the same arcsecond radius as Aperture = 4.5 at Binning=2. Aperture Integral The fraction of the star's light inside the photometry aperture, assuming a circular Gaussian profile and a circular aperture. Total BG Noise The total noise in the background underneath the star. This includes readout noise, digitization noise, dark noise, and photon noise from the sky. Sky / BG The ratio of sky photon noise to total background noise (which includes sky noise). If this field is 1.0, then the sky photon noise is the only source of noise in the background underneath the star. This result helps you address the question of whether an observation is "sky limited" or "sensor limited". Reference for equations and theory: Newberry, M. V. 1991, PASP 103, 122-130.
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