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Soviet Journal of Quantum Electronics

Convolution and correlation of optical signals by nonlinearoptics techniques

R A Eremeeva, Vladimir A. Kudryashov, I. N. Matveev, T G Usacheva, A I Chekmenev

Published Dec 31, 1975• 7 citations
Publisher

Abstract

A method for real-time convolution and correlation of optical signals is based on the conversion of a spatial spectrum of a field due to its passage through a nonlinear medium. Examples are given of experimentally obtained convolution, auto-convolution, and correlation functions of objects representing two, three, and four luminous points.

DOI
10.1070/qe1975v005n12abeh012163

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A method for real-time convolution and correlation of optical signals is based on the conversion of a spatial spectrum of a field due to its passage through a nonlinear medium. Examples are given of experimentally obtained convolution, auto-convolution, and correlation functions of objects representing two, three, and four luminous points.
The interaction of light waves in crystals with a quadratic nonlinearity is considered. It is shown that when one of the interacting waves carries information on the image of an object, such information can be transferred to a different wavelength, providing the basis for a parametric image converter. The results are given of experimental measurements of the noise and sensitivity of parametric-conversion detectors. It is shown that when both interacting waves carry information on an object, the interaction in a nonlinear crystal allows us to obtain correlation functions of the initial images of the objects. Suitable systems make it possible to determine experimentally the correlation function of the images of simple objects. By way of example, a description is given of a system which makes it possible to remove phase distortions introduced by an optical system in the far-field zone.
The coherence-coupling effect in a space- and time-resolved, nonlinear-correlation measurement in a multiple-scattering medium was investigated. In this measurement, two laser beams are injected into the medium, and the total nonlinear optical signal is measured as a function of the relative time delay, spatial separation, and frequency and wave-vector differences between the two beams. Besides the general importance of the nonlinear-correlation measurement, the coherence-coupling effect is interesting because it could provide a novel method of investigating the fluctuations and the correlation effects inside the multiple-scattering medium. We examined the form factor of the coherence-coupling effect as a function of the frequency and wave-vector differences between the two beams.
The possibilities of obtaining information on the time dependence of the amplitude and phase of an optical signal by the spectral modulation method are analysed. Three variants of the signal analysis are considered: a direct analysis of the signal whose parameters are changing in time; studies of the time-dependent optical characteristics of an object or a medium under study by probing them with radiation of the known structure; and measurements of the parameters of radiation propagated through the object and simultaneous determination and analysis of time-dependent structures of the signal and transfer function describing the effect of the transfer medium, the object, or an optical system on the propagated signal.
Imaging is the estimation of the spatial distribution of a physical object by measuring the optical radiation it emits, or by making use of an optical wave that interacts with the object, via reflection or transmission, for example, before being measured by a detector. The resolution of an imaging system is limited by the inability to localize the optical field at points of the object. Under otherwise ideal conditions, resolution is limited by diffraction. The sensitivity of an imaging system is limited by the uncertainty in the measurement. Under ideal conditions, this is determined by photon noise, which depends on the statistical fluctuations of the light. In conventional imaging systems, an extended detector, such as a CCD camera or an array detector, measures the spatial distribution of the optical intensity, which is proportional to the photon flux density. In interferometric systems, the spatial distribution of the optical field is inferred from measurements of the optical intensity. With the emergence of coherence theory, imaging systems based on measurements of the second-order coherence function at pairs of points in the detection plane were developed. An example is the imaging of an incoherent object based on the van Cittert-Zernike theorem. Imaging systems based on measurement of intensity correlation, or the photon coincidence rate, at pairs of points, were developed in the 1960s. A classic example of the photon-correlation imaging of an object emitting thermal light is stellar imaging using a Hanbury-Brown-Twiss intensity-correlation interferometer. More recently, two-photon light, which may be generated via spontaneous parametric downconversion in a second-order nonlinear optical crystal, has been used for imaging. This type of two-photon (or biphoton) imaging, which has come to be called quantum imaging, is also based on the measurement of photon coincidence by the use of photon-counting array detectors or by scanning two photon-counting detectors at pairs of points. To compare the resolution and sensitivity of imaging systems based on the aforementioned types of measurements, it is necessary to derive expressions for the measured quantities in terms of the object distribution. The point-spread functions based on such expressions can be used to assess the resolution. One measure of the sensitivity of the imaging process is the signal-to-noise ratio (SNR) of the measured variables. The statistical nature of the light source must be known in order to determine the SNR. The purpose of this chapter is to compare the resolution and sensitivity of photon-correlation imaging systems that make use of thermal light and two-photon light. We will henceforth refer to these two imaging modalities as classical and quantum photon-correlation imaging, or simply classical and quantum imaging, respectively. Clearly, light in other quantum states can also be used for imaging.
We introduce and experimentally demonstrate a simple and reliable optical technique for matching between two periodic numerical sequences based on optical single-shot measurement of their broadband cross-correlation function in the frequency domain. Each sequence is optically encoded into the shape of the different broadband femtosecond pulse using pulse-shaping techniques. The two corresponding shaped pulses are mixed in a nonlinear medium together with an additional (amplitude-shaped) narrowband pulse. The spectrum of the resulting four-wave mixing signal is measured to provide the cross-correlation function of the two encoded sequences. For identical sequences it is the auto-correlation function that is being measured, allowing also the identification of the sequence period. The high contrast achieved here between cross-correlation and auto-correlation functions allows to determine with a very high reliability whether the two encoded sequences are identical or not. The demonstrated technique might be employed in an optical implementation of CDMA communication protocol.