Downconverting Signals & Continuum

9008-071

9008-071a

Graph 9008-072 shows how the noise in the Planckian continuum, absorption and emission lines are downconverted to the intermediate frequency. Illustration (a) shows the Planck starlight continuum superimposed on the optical carrier. Because the bandwidth is small, the Planckian noise can be considered as "white", i.e., as having uniform spectral density (N_pl) over the observation bandwidth. Illustration (b) shows the spectrum of the I.F. signal within the bandwidth B_I.F.. Because of the double-sided nature of the Planckian starlight continuum, its spectral energy density (W/m².Hz) at the I.F. output of the receiver is doubled.

This spectral energy density doubling effect is easier to understand if we note that the Planckian spectral energy N_pl in a 1 Hz optical bandwidth at frequencies, say 1 kHz above and below the optical carrier (signal) frequency and 1 kHz above and below the local oscillator beam frequency, are both downconverted to frequencies ±1 kHz about the heterodyned beat frequency. Since the noise in the continuum is uncorrelated, noise powers add, and the electrical output noise spectral density is doubled to 2N_pl. Thus, there is twice the amount of Planckian noise in every Hz of electrical output bandwidth.

9008-071b

When calculating signal-to-noise ratio (SNR) at the output of the optical heterodyne receiver, the doubled Planckian spectral energy density should be used. For determining the amount of signal integration required to detect an alien planet the 2N_pl figure should be used. In this case the Planckian "noise" is now the Planckian "signal".

The discrete absorption and emission lines that are not symmetrically placed about the optical carrier frequency as shown in (c), are reproduced at the same relative energy density about the radio frequency carrier when downconverted, as shown in (d). Notice that the linewidth of the radio frequency (I.F.) carrier is greater than the received optical carrier because of the finite linewidth of the local oscillator.