DT = SL + DI_T + TS - 2TL - (NL-DI)    (Equation 1)

The right hand side of equation 1 is the signal (S) to noise (N) ratio (S/N) expressed on the decibel scale. Where:

SL + DI_T + TS - 2TL = 10 log(S)   (Equation 2, Signal on the dB scale)

and

- (NL-DI) = -10 log(N)  (Equation 3, 1 / Noise on the dB scale)

Thus, the definition of DT given by equation 1 may equivalently be expressed as:

DT = 10 log(S/N)

If the signal to noise level (in dB) measured by the receiving hydrophone exceeds DT then a target is registered as being present (DT < SL + DI_T + TS - 2TL - (NL-DI)). However, all the time  DT > SL + DI_T + TS - 2TL - (NL-DI) the system registers the target as absent. You will notice that the condition  DT = SL + DI_T + TS - 2TL - (NL-DI) defines the minimum signal to noise level required for successful detection. You will also remember from our discussions of transmission loss that this equality was used in order to define the maximum range of a given sonar system for a given set of environmental conditions. It is of great importance that the DT is set at an appropriate level. If it is set too low the system may be prone to false alarms. That is a target may be registered as being present when actually it is just noise! Conversely, if the DT is set too high the output from the receiving hydrophone may never detect a target even if there is one present! Therefore it is very important to adjust the system appropriately taking into consideration the environmental condition at the time of measurement as these will dictate the background noise levels.

Intuitively a minimum detection threshold would correspond to a S/N ratio of >1. That is the the signal must be greater than the noise before a target can be detected. This corresponds to a DT of zero, (10log(1)). However, certain signal conditioning methods may be employed to successfully detect targets for S/N values < 1. For example a band-pass filter may be implemented in order to remove all of the noise at frequencies above and below that of the signal pulse. In this way all of the signal is passed but some of the noise is removed.

Alternatively, a number of hydrophones can be used to detect the same signal pulse. When the output from each hydrophone is summed the coherent signal component constructively interferes and the incoherent noise component destructively interferes. The result is a reduction in the effective signal to noise ratio. Therefore do not be surprised if you see -ve detection thresholds quoted (S/N<1).