Computation Method for the Real-Time Control Problems in Differential-Algebraic Systems

In this paper, a real-time computation method for the control problems in differential-algebraic systems is presented. The errors of the method are estimated, and the relation between the sampling stepsize and the controlled errors is analyzed. The stability analysis is done for a model problem, and the stability region is ploted which gives the range of the sampling stepsizes with which the stability of control process is guaranteed.

Study of weighted space deconvolution algorithm in computer controlled optical surfacing formation

Theoretical and experimental research on the deconvolution algorithm of dwell time in the technology of computer controlled optical surfacing （CCOS） formation is made to get an ultra-smooth surface of space optical element. Based on the Preston equation, the convolution model of CCOS is deduced. Considering the morbidity problem of deconvolution algorithm and the actual situation of CCOS technology, the weighting spatial deconvolution algorithm is presented based on the non-periodic matrix model, which avoids solving morbidity resulting from the noise induced by measurement error. The discrete convolution equation is solved using conjugate gradient iterative method and the workload of iterative calculation in spatial domain is reduced effectively. Considering the edge effect of convolution algorithm, the method adopts a marginal factor to control the edge precision and attains a good effect. The simulated processing test shows that the convergence ratio of processed surface shape error reaches 80%. This algorithm is further verified through an experiment on a numerical control bonnet polishing machine, and an ultra- smooth glass surface with the root-mean-square （RMS） error of 0.0088 tim is achieved. The simulation and experimental results indicate that this algorithm is steady, convergent, and precise, and it can satisfy the solving requirement of actual dwell time.

Calibration of optical tweezers based on acousto-optic deflector and field programmable gate array

Accurate calibrations of stiffness and position are crucial to the quantitative measurement with optical tweezers. In this paper, we present a new calibration scheme for optical tweezers including stiffness and position calibrations. In our system, acousto-optic deflectors （AODs） are used as laser beam manipulating component. The AODs are controlled by a field programmable gate array （FPGA） connected to a computer using universal serial bus （USB） communication mode. Our results agree well with the present theory and other experimental results.

Coherent addition of gratings for chirped-pulse-amplified lasers based on near-field and far-field measurements

The development of phased-array grating compressor is a crucial issue for high-energy, ultra-short pulse petawatt-class lasers. Almost all systems have adopted a tiled-grating approach to meet the size requirements for the compression gratings. We present a computer-control test system utilizing near-field interference and far-field focusing capable of monitoring and fast correcting tiled errors of the grating compressor. In this system, the tilt/tip errors between the two gratings are determined by the Fourier transform （FT） of the individual interference fringe, and the piston errors are determined by the ratio of the two primary peaks formed in the far-field pattern as a function of the piston difference. Monochromatic grating phasing is achieved experimentally and pulse compression is demonstrated with a tiled grating system.