Author: Michael Newberry, Ph.D., Mirametrics, Inc.
This form calculates and graphs Signal to Noise Ratio (SNR) and Magnitude Error as a function of radius for doing aperture photometry of a point source. Use it for estimating the optimal aperture or the loss of precision for a non-optimal aperture size. Click [Save] to save parameters, click [Load] to fetch them. [Submit Comments]
Notes on Input and Output Quantities
This is the basic pixel size of the sensor. To use a binned image, change the Binning field but keep Pixel Size the same. For example, suppose your CCD has a 9 micron pixel. To use a 2x2 binned image, keep Pixel Size=9 and set Binning=2. Be sure to set the Aperture field according to the binning, since the photometry is done on binned pixels.
Aperture (radius, binned pix):
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 size as setting Aperture = 4.5 at Binning=2.
This is the total (multiplicative) throughput over all reflective and refractive optical surfaces in the telescope. For example: Consider a two mirror telescope where each mirror reflects 95% in the V band. Then Efficiency = 0.95 x 0.95 = 0.9 = 90% (enter 90 into the box).
This is the percentage transmission of the filter relative to the standard bandpass of the Filter you selected. For example, if you use a V filter made according to the standard "Johnson" (or Bessell) recipe, enter 100. If your filter transmits only 90% as much light as the standard Jonson V filter, enter 90, and so on. In general, you may need to set different values for different Filter choices.
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.
This is the average quantum efficiency of the sensor in the bandpass of the selected Filter.
This is the fraction of the star's light inside the photometry aperture, assuming a circular Gaussian profile and a circular aperture.
Filters other than V:
The calculator assumes the sky has the same spectrum as Vega. Since the sky may have a wide range of color index according to airglow, moon phase, and light pollution, this is a reasonable approximation.
Total BG Noise:
This field lists 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:
This field lists 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.