Showing papers in "Journal of the Optical Society of America in 1989"

Temperature control apparatus

Abstract: Apparatus is disclosed for controlling the heating and cooling of a plurality of upright containers containing a mixture used for performing gene amplification. The apparatus includes a support rack comprising aluminum blocks which is partially submerged in a thermally conductive fluid such that at least the lower portions of the containers are submerged in the fluid with the upper portions engaging the aluminum blocks for efficient heat transfer. Heaters are disposed within the aluminum block for heating the block and a plurality of thermoelectric cooling cells are used to cool the block. A programmable microprocessor is used for controlling the heating and cooling cycles, thereby allowing repetitive heating and cooling of the mixture to produce the copies of the genetic material sought to be copied. A cam separates the support rack from the cooling cells during the heating portion of the process.

Reconstruction of two-dimensional signals from nonuniform samples or partial information

Abstract: The necessary and sufficient conditions for a set of nonuniform samples to determine a band-limited two-dimensional signal are discussed. The relationship between this set and the zero-crossing contours of any band-limited signal is elaborated. In general, the sampling set should not be a subset of the zero-crossing contours of functions of the same bandwidth. However, it is difficult to check whether nonuniform samples are a subset of zero-crossing contours, but some sufficient conditions and examples are discussed. Furthermore, these concepts are applied to the problem of reconstructing a two-dimensional signal from partial information.

A uniqueness characterization in terms of signed-magnitude for functions in the polydisc algebra

Abstract: In an excellent paper written in 1983 Van Hove et al. [ IEEE Trans. Acoust. Speech Signal Process.ASSP-31, 1286 ( 1983)] proved that a real polynomial P(z), free of zeros in |z| = 1, is determined uniquely by its magnitude A(θ) and the sign of its real part u(θ) for z = ejθ. Van Hove et al. also indicated a possible extension to real polynomials in more than one variable and suggested an iterative procedure for the recovery of P(z). The restriction to polynomials (or rational functions), real or otherwise, is not crucial. In fact, on due reflection, it is seen that the problem continues to make sense for functions H(z) = H(z1, z2, …, zn) in n variables that are holomorphic in the open polydisc Un = {z:|z1| < 1, |z2| < 1, …, |zn| < 1}, continuous in the closure Ūn = {z:|z1| ≤ 1, |z2| ≤ 1, …, |zn| ≤ 1}, and free of zeros on its distinguished boundary Tn = {z:|z1| = 1, |z2| = 1, …, |zn| = 1}. The collection A(Un) of functions holomorphic in Un and continuous in Ūn is Rudin’s polydisc algebra [ W. Rudin , Function Theory in Polydiscs ( Benjamin, NewYork, 1969)]. Our main result can be stated as follows. Let H(z) belong to A(Un) and be free of zeros in Tn. For real θ = (θ1, θ2, …, θn), write, in terms of real and imaginary parts, H(exp(jθ1), exp(jθ2), …, exp(jθn)) = H(ejθ) = u(θ) + jv(θ), and let A(θ) = |H(ejθ)|; then H(z) is determined uniquely by the functions A(θ) and sign u(θ), together with its value at one point z0 exp(jθ0) ∈ Tn for which u(θ0) ≠ 0. We also clarify the meaning and the scope of this theorem by the use of specific examples, but reconstruction techniques are not discussed.

Reconstruction of two-dimensional signals from nonuniform samples or partial information: reply to comment

Abstract: The comments of Brames and Fiddy on the paper by Marvasti [ J. Opt. Soc. Am. A6, 52 ( 1989)] are actually comments on the paper by Curtis et al. [ IEEE Trans. Acoust. Speech Signal Process.ASSP-35, 890 ( 1987)]. Nonetheless, some of the comments are either not related or erroneous.