مرکز منطقه ای اطلاع رساني علوم و فناوري - 6.4

Abstract :

An optical analog computer has been demonstrated which is capable of obtaining quantitative estimates of transfer functions of systems from finite records of input and response data and power spectra of the input and response. The input $x(t)$ and response $z(t)$ are recorded as amplitude-transmission variations on a photographic plate. To compute the power spectrum of $x(t)$ , the Fourier transform $X(\\omega )$ of $x(t)$ is formed by illuminating $x(t)$ with light from a He-Ne laser and focusing the resulting diffraction pattern with a lens to form $X(\\omega )$ . This diffraction pattern, when read out with a properly-shaped light-gathering probe connected to a photomultiplier, will yield an estimate of the power spectrum of $x(t)$ . In a similar manner, the power spectrum of $z(t)$ is estimated. To estimate the transfer function $H(\\omega )$ , a hologram of $X*(\\omega )$ is made. From the hologram, a transparency is made whose amplitude transmission is proportional to $1/ X*(\\omega )X(\\omega )$ . When the hologram is illuminated by $Z(\\omega )$ , the resulting diffraction pattern will contain $X*(\\omega )Z(\\omega ).X*(\\omega )Z(\\omega )$ is then imaged onto the transparency whose amplitude transmission is $1/X*(\\omega )X(\\omega )$ forming $H(\\omega ) = X*(\\omega )Z (\\omega )/ X*(\\omega )X(\\omega )$ . Experimental results are presented which indicate that good estimates of power spectra and transfer functions can be obtained by this method.