Keywords: astro-30m-emir-time-estimator

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### Relation between and

By construction

- The number of submaps is the area of the map divided by the area of a submap

  | (25)

- The number of on per off is the number of independent resolution elements in each submap

  | (26)

- The number of independent resolution elements in the map is the product of number of submaps by the number of on per off

  | (27)

- The submap area is the product of the area velocity by the time to cover it

  | (28)

- The time to scan a submap is the sum of the independent on integration time

  | (29)

- The relations between times per coverage and times integrated over all the coverages are

  | (30)

- Using the last two points, it is easy to derive

  | (31)

- Finally, the total time spent on and off is given by

  | (32)

  Using Eqs. and , we derive

  | (33)

Both and are proportional to (cf. Eqs. and ). It is thus easy to derive that

| (34)

Using Eq. , we can replace and obtain

| (35)

Using Eqs. , and , we obtain

| (36)

The last equation in theory enables us to find the rms noise as a function of the elasped telescope time (sensitivity estimation) and vice-versa (time estimation). However, it is not fully straightforward because we must enforce that and have an integer value.

Next: Time/Sensitivity estimation Up: Position switched Previous: Two key points: 1) Contents