A holographic system for large time-bandwidth product multichannel spectral analysis.

The design parameters of a multichannel coherent optical sys­ tem for power spectral density (PSD) measurements have been presented and its performance described in earlier papers.Ultimate channel capacity is determined by input film size, spot size of the beam used to record the time-varying signals on film, and by aperture constraints. Frequency resolution, expressed as a time-bandwidth product, is determined by the ratio of aperture size to recording spot diameter. Time-bandwidth products of the order of 1000 are representative of existing multi­ channel systems. Thomas has recently described a single chan­ nel optical analyzer with an extremely large ( 10) t ime-band­ width product. The system considered herein represents an improvement of the multichannel optical analyzer, providing greater t ime-band­ width product capability. The aim is to obtain significant t imebandwidth product improvement without sacrificing multichannel processing capability. Briefly stated, the modification involves holographic storage to record Fourier spectra of sequential (mul­ tichannel) inputs and compensates for phase changes produced through advancing the input film record. Functional components of the system are shown in Figs. 1 and 2 of Ref. 2. A cylinder lens follows the transform lens to permit multichannel processing. For simplicity, this discussion illustrates single channel operation; the extension to a multi­ channel operation is readily made. The quantities x,y,t,v,Lξ, V,Λ,FT have the same meaning as in Ref. 2. A time varying signal, V(t) is recorded as a transmittance variation, T(x), on the input film. For the n th segment or frame of the input film record, χ and t are related as x = v(t tn-1) — L/2, where tn-1 ≤ t ≤ tn. The quantities tn-1,tn correspond to the values of t at the beginning and end, respectively, of the n th frame. If r denotes the time interval corresponding to the entrance aperture width, then ντ = L and tn = nτ. The film trans­ mittance is assumed to vary linearly with the input signal; i.e., for the nth frame, Tn(x) = A + BVn(x/v), where A and B are constants. The light amplitude distribution in the back focal plane of the transform lens, Fn(v), is proportional to the Fourier integral transform of the recorded function, Tn(x), within the aperture. This distribution is given by