9 Sensitivity of the ampligram method

An interesting problem is the sensitivity of the method; i.e. what is the smallest amplitude of the deterministic component which may be detected when immersed in a pure Poisson-like background. A detailed study using different types of deterministic components was performed. The results will be published elsewhere, here only a short summary of relevant results will be given. The Poisson-like background was generated using the beta-decay event series. It is assumed in physics that the radioactive decay is a classical Poisson process. In the present study beta-decay pulses were counted in a series of 1 s bins. The radioactive source was collimated so that the average counting rate during the entire 1024 s sample was around 1 event/s. The deterministic component used in the present example was of the type shown in Fig. 16, with a period P bins and a maximum amplitude R counts/bin.

Figure 16: Deterministic component added to beta-decay series. In the present example P = 57 bins and R = 3 events/bin

The ampligram and time scale spectrum was calculated for the synthesized series. The time scale spectrum is shown in Fig. 17. A logarithmic scale is used on the horizontal axis of time scales. The white line on the diagram indicates the period of the deterministic component, P = 57 s.

Figure 17: Time scale spectrum of beta-decay data with a superimposed deterministic component shown in Fig. 16. The white vertical line indicates the period of the deterministic component

In the demonstrated case the deterministic component contains about 15% of photons in the background. It has been found that for average counting rate of 1 event/s a deterministic component containing 8% of background photons may still be detected on the time scale spectrum. The sensitivity of the method seems be dependent on the average counting rate. Transferring this result to continuous signals it would correspond to detection of a signal 22 dB below the background level.