Error dependence of quantized kinoform reconstruction on the position of the desired image

Two-dimensional Fourier transform kinoforms can be calculated by use of a discrete Fourier transform. It is well known that the off-axis reconstruction has lower reconstruction error than the on-axis one. Here we make what to our knowledge is a new analysis on the effect of phase quantization in the Fourier domain. We find that the kinoform reconstruction error changes periodically according to the position of the desired image when a large dummy area is added. The error dependence of quantized kinoform reconstruction is simulated on the position of the desired image by use of the iterative dummy area method and the iterative interlacing technique.     

Interlacing technique approach for the synthesis of kinoforms

An interlacing technique algorithm is proposed for the synthesis of kinoforms. The conventional iterative methods are quite powerful for optimizing kinoforms, but there is still a large reconstruction error for a quantized kinoform. We suggest the use of a number of subkinoforms interlaced together to synthesize a multikinoform for reconstructing the desired image. The idea of our interlacing technique is to increase the size of a kinoform to reduce the reconstruction error. The first subkinoform is generated from the desired image. Other subkinoforms are generated from the error images between the desired image and the image reconstructed from the previous subkinoforms. A theoretical analysis shows that the reconstruction error will be reduced as the number of subkinoforms is increased. Simulation results show that our interlacing method can reduce the reconstruction error more than do the conventional iterative methods and that the reconstructed image can be improved.     

Error in determination of the number of parts by means of computing scales

Measurement errors using computing weighing scales in the number of parts due to nonhomogeneity of the parts according to the weight are analyzed. The procedure is illustrated by means of data of a specific statistical experiment. Translated from Izmeritel'naya Tekhnika, No. 3, pp. 15–18, March, 1998.     

Optimization of kinoform lenses with the Monte Carlo method

For the optimization of non-Fourier-type computer-generated phase holograms (kinoform lenses), a method based on the Monte Carlo procedure is suggested. This method can be regarded as analogous to the iterative Fourier transform algorithm method that is widely used for the optimization of Fourier-type computer-generated phase holograms (kinoforms).     

Error reduction in the measurement of reflection coefficients by an SF-18 spectrophotometer

Translated from Izmeritel'naya Tekhnika, No. 12, pp. 27–29, December, 1991.     

Direct inclusion of the proximity effect in the calculation of kinoforms

Within the direct inclusion method the proximity effect is already taken care of when one calculates the kinoform relief, whereas conventionally the proximity effect is compensated for after one has calculated the relief. In particular, when proximity effects are considerable, that is, for small structures, the direct inclusion method is shown to give significantly better results than the conventional two-step method. Provided that the proximity effect is correctly modeled, it is shown that for an 8 × 8 array illuminator nearly perfect uniformity can be achieved even for a kinoform with very small structures.     

Decreasing of the initial shear modulus with increasing axial strain explained by means of a plastic-hypoelastic model

Summary The purpose of this work is to examine in detail the possibility to explain the decreasing of the initial shear modulus with increasing axial strain, observed first by Feigen, by means of the plastic-hypoelastic stress-strain relation suggested by Lehmann and by the author of the present paper.Notations _ij components of the infinitesimal strain tensor dilatation - strain deviator - _ij components of the stress tensor - spherical part of the stress tensor - stress deviator - ²= _{ij ij} second invariant of the stress deviator - = ₃₃ axial strain - e= ₁₃ shear component of the strain tensor - =2 ₁₃ shear strain - = ₃₃ axial stress - s= ₁₃ shear stress - T _ij components of Cauchy's stress tensor - F _ij components of the deformation gradient - L _ij components of the velocity gradient (Eulerian coordinates) - components of the rate of deformation tensor - components of the spin tensor - components of the rate of deformations deviator - components of Cauchy's stress deviator - T=T ₃₃ axial Cauchy's stress With 7 Figures     

Solution of a multidimensional inverse radiation problem by means of mode reduction

The Karhunen–Loève Galerkin procedure is employed to solve an inverse radiation problem of determining the time‐varying strength of a heat source, which mimics flames in a furnace, from temperature measurements in three‐dimensional participating media where radiation and conduction occur simultaneously. The inverse radiation problem is solved through the minimization of a performance function, which is expressed by the sum of square residuals between calculated and observed temperature, using a conjugate gradient method. Through the Karhunen–Loève Galerkin procedure, one can represent the system dynamics with a minimum degree of freedom, and consequently the amount of computation required in the solution of the inverse problem is reduced drastically when the present technique is adopted. Copyright © 2004 John Wiley & Sons, Ltd.     

Recursive solution of inverse natural convection problems by means of mode reduction

 A recursive method based on the Kalman filtering is developed to solve inverse natural convection problems of estimating the unsteady nonuniform wall heat flux from temperature measurements in the flow. By employing the Karhunen–Loève Galerkin procedure that reduces the Boussinesq equation to a small set of ordinary differential equations, the computational difficulties associated with the Kalman filtering for the partial differential equations are overcome. The present method is assessed through several numerical experiments, and is found to yield satisfactory results. Received 20 January 2001 / Accepted 31 May 2001     

Spectrum leveling by an iterative algorithm with a dummy area for synthesizing the kinoform

This paper describes a new iterative algorithm for synthesizing the kinoform so that the Fourier spectrum of an object is leveled by adjusting the information of a dummy area introduced into the object's domain, spatially isolated from the signal area. Theoretical consideration of the effect of the dummy area derives the required size of the dummy area, and computer simulations prove it to be valid, although restricted to an object composed of binary numbers. Also, it is shown that highly efficient use of the incident light is possible to achieve. Experimental results verify the proposed scheme.     

Characterization by means of temperature programmed reduction and desorption of propylene metathesis catalyst

Temperature programmed desorption runs were performed on a 14% Re₂0₇/Al₂0₃ catalyst, prepared by using commercial amorphous alumina as support. By changing the adsorption temperature, some conclusions have been drawn about the adsorptive properties of this catalyst towards propylene, and subsequentely these properties have been compared with those towards ethylene and 2-trans- and 2-cis-butene.Finally, temperature programmed reduction runs allowed us to relate these features to the redox properties of the catalyst.