The amount of elapsed time required to map a certain field size, to a certain depth, at a given atmospheric transmission is described in the equations below. For users who simply want a quick time estimate we advise using the ITC gui which is explained here.

Contents

### Elapsed time

The elapsed telescope time (seconds) to map a given field size to a given 1-sigma depth (mJy) is described in the relations below.

Mapping Mode | Time elapsed 450 microns (s) | Time elapsed 850 microns (s) |
---|---|---|

Daisy | ||

900″ | ||

1800″ | ||

3600″ | ||

7200″ |

The 450 and 850 transmission factors (Τ_{450}, Τ_{850}) and the sampling factor (** f**) in the above equations are described below:

### Atmospheric transmission

For a given air mass (AM) and opacity (classically defined at 225GHz, τ_{225GHz}), the transmission can be calculated using the following relations:

The opacity (τ_{225GHz}) ranges for various weather Grades are given below:

- Grade 1: Less than 0.83mm PWV. (τ
_{225GHz}< 0.05) - Grade 2: 0.83 – 1.58 mm PWV. (0.05 < τ
_{225GHz}< 0.08) - Grade 3: 1.58 – 2.58 mm PWV. (0.08 < τ
_{225GHz}< 0.012) - Grade 4: 2.58 – 4.58 mm PWV. (0.12 < τ
_{225GHz}< 0.2) - Grade 5: More than 4.58 mm PWV. (τ
_{225GHz}> 0.2)

For a source at a given declination (δ, measured in degrees), a representative air mass near transit can be derived using:

### Sampling factor *f*

*f*

Elapsed times are derived using the basic reduction parameters in SMURF and use default map pixels of 2″ and 4″ at 450 and 850 microns, respectively. A change to this default pixel size is taken into account by the sampling factor (** f**) when estimating the elapsed time. The sampling factor f is simply defined as:

** f** = ( pixel size requested / default pixel size )

^{2}

At 450 and 850 this becomes:

*f*_{450} = ( pixel size requested / 2 )^{2 }and *f*_{850} = ( pixel size requested / 4 )^{2}

For Point-source detections the S/N can be dramatically improved by applying a matched-beam filter which utilizes the full flux in the beam rather than just the peak value at the position of a source. This will shorten required observing times to reach a certain S/N typically by factors of ** f =** 8 (450μm) and

**5 (850μm).**

*f*=### SCUBA-2 Confusion limit

The confusion limit depends on a number of factors including Galactic cirrus emission, the extra galactic background as well as the beam size. While dependent on assumptions and location the derived values are close to

- 850 microns = 0.7 mJy/beam
- 450 microns = 0.5 mJy/beam

The sensitivity of a SCUBA-2 blank field will be limited by a un-reduceable noise level of this order.

The implies that going below a detection limit of ~ 2 mJy in a blank field will give a high risk of false detections. See for instance Chen et.al Ap.J. 762, 81 (2011) “Faint Submillimeter Galaxy Counts at 450 micron”. The situation is better for detection of a source at a known position. The lower probability that a random peak coincide with your know source increases the chance it is a real detection. However, the confusion limit still needs to be taken into account when estimating the position and flux error.

### Overheads

The SCUBA-2 ITC currently takes into account the 90 seconds required for set ups and fast flats

If you are calculating an integration time for a proposal it should be noted that there is no need to provide an overhead estimate for calibrations (pointing, focus, flux). The time used for calibration is absorbed by the observatory.