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A light-addressable potentiometric sensor (LAPS) can measure the concentration of one or several analytes at the sensor surface simultaneously in a spatially resolved manner. A modulated light pointer stimulates the semiconductor structure at the area of interest and a responding photocurrent can be read out. By simultaneous stimulation of several areas with light pointers of different modulation frequencies, the read out can be performed at the same time. With the new proposed controller electronic based on a field-programmable gate array (FPGA), it is possible to control the modulation frequencies, phase shifts, and light brightness of multiple light pointers independently and simultaneously. Thus, it is possible to investigate the frequency response of the sensor, and to examine the analyte concentration by the determination of the surface potential with the help of current/voltage curves and phase/voltage curves. Additionally, the ability to individually change the light intensities of each light pointer is used to perform signal correction.
Chemical imaging systems allow the visualisation of the distribution of chemical species on the sensor surface. This work represents a new flexible approach to read out light-addressable potentiometric sensors (LAPS) with the help of a digital light processing (DLP) set-up. The DLP, known well for video projectors, consists of a mirror-array MEMS device, which allows fast and flexible generation of light patterns. With the help of these light patterns, the sensor surface of the LAPS device can be addressed. The DLP approach has several advantages compared to conventional LAPS set-ups, e.g., the spot size and the shape of the light pointer can be changed easily and no mechanical movement is necessary, which reduces the size of the set-up and increases the stability and speed of the measurement. In addition, the modulation frequency and intensity of the light beam are important parameters of the LAPS set-up. Within this work, the authors will discuss two different ways of light modulation by the DLP set-up, investigate the influence of different modulation frequencies and different light intensities as well as demonstrate the scanning capabilities of the new set-up by pH mapping on the sensor surface.
Upper and lower bound theorems of limit analyses have been presented in part I of the paper. Part II starts with the finite element discretization of these theorems and demonstrates how both can be combined in a primal–dual optimization problem. This recently proposed numerical method is used to guide the development of a new class of closed-form limit loads for circumferential defects, which show that only large defects contribute to plastic collapse with a rapid loss of strength with increasing crack sizes. The formulae are compared with primal–dual FEM limit analyses and with burst tests. Even closer predictions are obtained with iterative limit load solutions for the von Mises yield function and for the Tresca yield function. Pressure loading of the faces of interior cracks in thick pipes reduces the collapse load of circumferential defects more than for axial flaws. Axial defects have been treated in part I of the paper.