Spatial filtering in tone reproduction and vision

This thesis is concerned with spatial filtering. What is its utility in tone reproduction? Does it exist in vision, and if so, what constraints does it impose on the nervous system?

Tone reproduction is just the art and science of taking a picture and then displaying it. The sensors available to capture an image have a greater dynamic range than the media that may be used to display it. Conventionally, spatial filtering is used to boost contrast; it ameliorates the loss of contrast that results when the sensor signal range is scaled down to fit the display range. In this thesis, a type of nonlinear spatial filtering is discussed that results in direct range reduction without range scaling. This filtering process is instantiated in a real-time image processor built using analog CMOS VLSI.

Spatial filtering must be applied with care in both artificial and natural vision systems. It is argued that the nervous system does not simply filter linearly across an image. Rather, the way that we see things implies that the nervous system filters nonlinearly. Further, many models for color vision include a high-pass filtering step in which the DC information is lost. A real-time study of filtering in color space leads to the conclusion that the nervous system is not that simple, and that it maintains DC information by referencing to white.

Filtering N.M.R. spectra

Methods of filtering an n.m.r. spectrum which can improve the resolution by as much as a factor of ten are examined. They include linear filters based upon an information theory approach and non-linear filters based upon a statistical approach. The appropriate filter is determined by the nature of the problem. Once programmed on a digital computer they are both simple to use.

These filters are applied to some examples from ¹³C and ¹⁵N n.m.r. spectra.

Gas laser discharge noise and its effect on the laser output

A large portion of the noise in the light output of a laser oscillator is associated with the noise in the laser discharge. The effect of the discharge noise on the laser output has been studied. The discharge noise has been explained through an ac equivalent circuit of the laser discharge tube.

The discharge noise corresponds to time-varying spatial fluctuations in the electron density, the inverted population density and the dielectric permittivity of the laser medium from their equilibrium values. These fluctuations cause a shift in the resonant frequencies of the laser cavity. When the fluctuation in the dielectric permittivity of the laser medium is a longitudinally traveling wave (corresponding to the case in which moving striations exist in the positive column of the laser discharge), the laser output is frequency modulated.

The discharge noise has been analyzed by representing the laser discharge by an equivalent circuit. An appropriate ac equivalent circuit of a laser discharge tube has been obtained by considering the frequency spectrum of the current response of the discharge tube to an ac voltage modulation. It consist of a series ρLC circuit, which represents the discharge region, in parallel with a capacitance C', which comes mainly from the stray wiring. The equivalent inductance and capacitance of the discharge region have been calculated from the values of the resonant frequencies measured on discharge currents, gas pressures and lengths of the positive column. The experimental data provide for a set of typical values and dependencies on the discharge parameters for the equivalent inductance and capacitance of a discharge under laser operating conditions. It has been concluded from the experimental data that the equivalent inductance originates mainly from the positive column while the equivalent capacitance is due to the discharge region other than the positive column.

The ac equivalent circuit of the laser discharge has been shown analytically and experimentally to be applicable to analyzing the internal discharge noise. Experimental measurements have been made on the frequency of moving striations in a laser discharge. Its experimental dependence on the discharge current agrees very well with the expected dependence obtained from an analysis of the circuit and the experimental data on the equivalent circuit elements. The agreement confirms the validity of representing a laser discharge tube by its ac equivalent circuit in analyzing the striation phenomenon and other low frequency noises. Data have also been obtained for the variation of the striation frequency with an externally-applied longitudinal magnetic field and the increase in frequency has been attributed to a decrease in the equivalent inductance of the laser discharge.