# Image Sensitivity

Image sensitivity is the RMS thermal noise (ΔI_{m}) expected in a single-polarization image. Image sensitivities for the 10-station VLBA, for typical observing parameters, are listed in column [7] of the "Receiver Frequency Ranges & Performance" table.

Alternatively, the image sensitivity for a homogeneous array with natural weighting can be calculated using the following formula (Wrobel 1995; Wrobel & Walker 1999).

[display]\Delta I_m = {\rm SEFD} / [\eta_s \cdot ( N \cdot (N-1) \cdot \Delta \nu \cdot t_{\rm int} ) ^{1/2} ] \; \rm{Jy\; beam^{-1}}[/display]

Parameters SEFD, [inline]\eta_s[/inline], and [inline]\Delta\nu[/inline] are the same as those used in computing baseline sensitivity, [inline] N [/inline] is the number of observing stations, and [inline]t_{\rm int}[/inline] is the total integration time on source in seconds.

The expression for image noise becomes rather more complicated for a heterogeneous array such as the HSA, and may depend quite strongly on the data weighting that is chosen in imaging. The EVN sensitivity calculator provides a convenient estimate. For example, the RMS noise at 22 GHz for the 10-station VLBA in a 1-hr integration is reduced by a factor between 4 and 5 by adding the GBT and the phased VLA.

If simultaneous dual polarization data are available with the above value of ΔI_{m} per polarization, then for an image of Stokes I, Q, U, or V,

[display]\Delta I = \Delta Q = \Delta U = \Delta V = \frac{\Delta I_m}{\sqrt{2}}[/display]

For a polarized intensity image of [inline]P = \sqrt{Q^2 + U^2}[/inline]

[display]\Delta P = 0.655 \times \Delta Q = 0.655 \times \Delta U[/display]

It is sometimes useful to express [inline]\Delta I_m[/inline] in terms of an RMS brightness temperature in Kelvins ([inline]\Delta T_B[/inline]) measured within the synthesized beam. An approximate formula for a single-polarization image is

[display]\Delta T_b \sim 320 \times \Delta I_m \times (B^{\rm km}_{\rm max})^2 \; {\rm K}[/display]

where [inline]B^{\rm km}_{\rm max}[/inline] is as in Table 5.