Limiting Magnitudes

# Limiting Magnitudes

Table 1.1 shows the seconds to reach the indicated magnitude at 5σ with 0.8″ seeing.

Table 1.2 shows the seconds to reach precision photometry at the indicated magnitude (S/N = 100, 0.6″ seeing).

## Signal to Noise Ratio Calculations

The theory behind the signal to noise behavior of aperture photometry from IR imaging cameras can be found here.

The situation can be simplified under the following assumptions:

• Background limited – The Poisson noise from the sky is much greater than the readnoise of the detector
• Low Dark current – The counts from the sky are much greater than the counts from the detector dark current
• Aperture size – The sky aperture is much larger than the object aperture

In addition, you should note that the signal to noise ratio is inversely proportional to the square root of your object aperture area.

### Faint Objects

When the object is much fainter than the sky, the achieved signal to noise ratio is proportional to the square root of integration time,  proportional to the flux of the object, and inversely proportional to the square root of the sky flux.

### Bright Objects

When the object is much brighter than the sky, the achieved signal to noise ratio is proportional to the square root of integration time and proportional to the square root of the flux from the object.