Pulsed laser determination of surface electric charge distributions

2014 We propose a new method for high resolution determination of surface electric charge distributions on a dielectric plate. The method is based on the measurement of the variation of the charges induced on a probe when the charges to be measured are being displaced. This local perturbatidn is achieved by means of a laser pulse focused on a thin absorbing target adjacent to the dielectric. By sweeping the laser beam and the probe parallel to the dielectric surface, the distribution can be determined with a resolution better than 0.2 mm. This method could open new approaches in various fields, such as electrophotography, image processing or medical instrumentation. Tome 43 N" 19 ler OCTOBRE 1982 LE JOURNAL DE PHYSIQUE-LETTRES J. Physique LETTRES 43 (1982) L-687 .. L-693 ler OCTOBRE 1982, Classification Physics Abstracts 06. 70D 42.60 61.80C 87.60 In various fields such as electrophotography, non destructive testing or medical imaging, the information to be processed can be obtained or stored as a distribution of electric charges on the surface of a dielectric sheet or plate. The visualization of this distribution is generally achieved using solid or liquid toners. It is clear however, that an electrical measurement of the density of surface charges, with a high spatial resolution would present many advantages since it is non destructive and opens the way to analog or digital signal analysis. Several techniques have already been proposed in order to attain this goal [1~41. They all involve the measurement of the charges induced on a probe by the electric field created by the charges to be measured. This can be done in various ways which require some modulation. For instance the distance between the probe and the dielectric plate is modulated (vibrating capacitor). In another configuration a vibrating or rotating vane is periodically inserted between the probe and the plate. Whatever the technique used, the charges on the probe are induced by charges distributed on an area S of the plate larger than that of the probe, and which depends on geometrical parameters of the system. Such an effect is visible in figure la. In order to increase Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyslet:019820043019068700 L-688 JOURNAL DE PHYSIQUE LETTRES the resolution it is necessary to reduce not only the diameter of the probe, but also its distance to the dielectric plate, which creates new problems. First it makes it mechanically difficult to sweep the surface of the plate. Second, the irregularities of the surfaces produce in these conditions large relative variations of this distance, which strongly affects the measurement. In this paper we describe a new method which eliminates most of these problems and allows the determination of charge distributions with a higher resolution using a probe located at a larger distance from the plate. It is based on the fact that if a short duration perturbation is applied to a small area s of the plate, it produces a local displacement of the charges of the plate and consequently a variation of the induction charge on the probe. Although the total charge Q on the probe is induced by all the charges lying on S, the time dependent variation of Q is only related to the charges which have been displaced, as shown in figure lb. Fig. 1. a) The total charge Q on the probe is induced by charges distributed on an area S ; b) The variation AQ of the induction charge is related to the charges distributed on the small perturbed area s. In order to produce such a perturbation, various techniques can be considered, involving acoustical optical or electrical excitations of the local deformation. In the following, we describe an experiment using an optical excitation by a short duration laser pulse focused on a small area of the electrode opposite to the probe. The generation of short-rise-time pressure waves by pulsed laser irradiation of metal targets has been intensively studied in the last ten years [5]. In various recent publications [6-9], this technique was used to determine the electric field or charge distributions inside dielectric materials. As was shown in reference [10], these distributions can be derived, using a one dimensional model, from the time variations of the open-circuit voltage or short-circuit current during the propagation of the pressure wave through the dielectric. In the present paper, we use the impact of a short duration laser pulse focused on a metal target to produce a localized pressure wave which can be transmitted to the sample under investigation. 1. Theoretical We consider a dielectric plate of thickness e. One side is adjacent to an electrode; on the other side there is a non uniform distribution of surface charges a(x, y). We assume for simplicity that the dielectric plate has neither bulk space charges nor polarization. By focusing the laser beam at a point (xo, yo ) on the front electrode (Fig. 2), a local compressional wave is created and transmitted to the dielectric in which it travels at the sound velocity v. The related transit time is r = elv. The main effect of this wave is to decrease locally the thickness of the dielectric plate of an amount Ae, and to change the dielectric constant in the compressed region. L-689 LASER DETERMINATION OF SURFACE CHARGES Assuming that the pressure wave is uniform on an area s and null elsewhere, Ae can be expressed