SNR calculator

Signal to noise ratio for the detection of a point source.

Features

With the different sliders and buttons present in the left hand panel, the user can:

• adjust the telescope diameter, the Fried parameter \(r_0\) that characterizes the statistical properties of the atmospheric turbulence.
• switch from diffraction-limited (activating AO) to seeing-limited observations. The AO correction is perfect and leads to the ideal Airy pattern. When off, the structure of the PSF changes and is simulated by a Gaussian function, of characteristic size imposed by \(r_0\).
• pick a filter, which changes the scaling of the PSF, as well as the photometric zero-point.
• change the exposure time
• adjust the magnitude of the star as well as the brightness of the sky

On the right hand side panel, the user can visualize the instant PSF as it would appear on a detector in the absence of any treatment. A cyan circle isolates the area of the image where the core of the PSF is located. Below the images, three boxes keep track of: the total number of photons incoming from the target, the total number of photons landing within the area marked by the cyan circle, and the signal to noise ratio.

Caveats

• unfortunately, no actual optical design features a 100 % efficiency. It is not uncommon to see overall throughput of instruments quoted to 10 %. Clearly, this throughput should be taken into consideration when attempting to quantify the SNR of the application of your choosing.
• the noises associated to the detector readout and the dark current that depend on the specifics of the technology employed for the instrument are not implemented. If they were implemented, changes to the plate-scale parameter (required in order to visualize the PSF over the wide range of wavebands covered by the simulation) would also impact the SNR.