Effect of elliptical manufacture error of an axicon on the diffraction-free beam patterns

Based on the generalized Huygens-Fresnel diffraction integral theory and the stationary-phase method, we analyze the influence on diffraction-free beam patterns of an elliptical manufacture error in an axicon. The numerical simulation is compared with the beam patterns photographed by using a CCD camera. Theoretical simulation and experimental results indicate that the intensity of the central spot decreases with increasing elliptical manufacture defect and propagation distance. Meanwhile, the bright rings around the central spot are gradually split into four or more symmetrical bright spots. The experimental results fit the theoretical simulation very well. (C) 2008 Society of Photo-Optical Instrumentation Engineers.

Algorithm of far-field centre estimation based on phase-only matched filter

Estimation of the far-field centre is carried out in beam auto-alignment. In this paper, the features of the far-field of a square beam are presented. Based on these features, a phase-only matched filter is designed, and the algorithm of centre estimation is developed. Using the simulated images with different kinds of noise and the 40 test images that are taken in sequence, the accuracy of this algorithm is estimated. Results show that the error is no more than one pixel for simulated noise images with a 99% probability, and the stability is restricted within one pixel for test images. Using the improved algorithm, the consumed time is reduced to 0.049 s.

A direct digital frequency synthesizer with fourth-order phase domain Delta Sigma noise shaper and 12-bit current-steering DAC

This paper presents a direct digital frequency synthesizer (DDFS) with a 16-bit accumulator, a fourth-order phase domain single-stage Delta Sigma interpolator, and a 300-MS/s 12-bit current-steering DAC based on the Q(2) Random Walk switching scheme. The Delta Sigma interpolator is used to reduce the phase truncation error and the ROM size. The implemented fourth-order single-stage Delta Sigma noise shaper reduces the effective phase bits by four and reduces the ROM size by 16 times. The DDFS prototype is fabricated in a 0.35-mu m CMOS technology with active area of 1.11 mm(2) including a 12-bit DAC. The measured DDFS spurious-free dynamic range (SFDR) is greater than 78 dB using a reduced ROM with 8-bit phase, 12-bit amplitude resolution and a size of 0.09 mm(2). The total power consumption of the DDFS is 200)mW with a 3.3-V power supply.

A direct digital frequency synthesizer with fourth-order phase domain Delta Sigma noise shaper and 12-bit current-steering DAC

This paper presents a direct digital frequency synthesizer (DDFS) with a 16-bit accumulator, a fourth-order phase domain single-stage Delta Sigma interpolator, and a 300-MS/s 12-bit current-steering DAC based on the Q(2) Random Walk switching scheme. The Delta Sigma interpolator is used to reduce the phase truncation error and the ROM size. The implemented fourth-order single-stage Delta Sigma noise shaper reduces the effective phase bits by four and reduces the ROM size by 16 times. The DDFS prototype is fabricated in a 0.35-mu m CMOS technology with active area of 1.11 mm(2) including a 12-bit DAC. The measured DDFS spurious-free dynamic range (SFDR) is greater than 78 dB using a reduced ROM with 8-bit phase, 12-bit amplitude resolution and a size of 0.09 mm(2). The total power consumption of the DDFS is 200)mW with a 3.3-V power supply.

Phase reconstruction from three interferograms based on integral of phase gradient

A novel algorithm of phase reconstruction based on the integral of phase gradient is presented. The algorithm directly derives two real-valued partial derivatives from three phase-shifted interferograms. Through integrating the phase derivatives, the desired phase is reconstructed. During the phase reconstruction process, there is no need for an extra rewrapping manipulation to ensure values of the phase derivatives lie in the interval [-pi, pi] as before, thus this algorithm can prevent error or distortion brought about by the phase unwrapping operation. Additionally, this algorithm is fast and easy to implement, and insensitive to the nonuniformity of the intensity distribution of the interferogram. The feasibility of the algorithm is demonstrated by both computer simulation and experiment.

New uniform algorithm to predict reversed phase retention values under different gradient conditions

A new numerical emulation algorithm was established to calculate retention parameters in RP-HPLC with several retention times under different linear or nonlinear binary gradient elution conditions and further predict the retention time under any other binary gradient conditions. A program was written according to this algorithm and nine solutes were used to test the program. The prediction results were excellent. The maximum relative error of predicted retention time was less than 0.45%. (C) 2002 Elsevier Science B.V. All rights reserved.

ESTIMATION OF THE ONE-PHASE STRUCTURE SEMINVARIANTS IN THE SINGLE ISOMORPHOUS REPLACEMENT CASE - AN APPLICATION OF HAUPTMANS DISTRIBUTION

A method for estimating the one-phase structure seminvariants (OPSSs) having values of 0 or pi has been proposed on the basis of the probabilistic theory of the three-phase structure invariants for a pair of isomorphous structures [Hauptman (1982). Acta Cryst. A38, 289-294]. The test calculations using error-free diffraction data of protein cytochrome c(550) and its PtCl42- derivative show that reliable estimates of a number of the OPSSs can be obtained. The reliability of the estimation increases with the increase of the differences between diffraction intensities of the native protein and its heavy-atom derivative. A means to estimate the parameters of the distribution from the diffraction ratio is suggested.

Dynamics of nonlinear error growth and season-dependent predictability of El Nino events in the Zebiak-Cane model

With the intermediate-complexity Zebiak-Cane model, we investigate the 'spring predictability barrier' (SPB) problem for El Nino events by tracing the evolution of conditional nonlinear optimal perturbation (CNOP), where CNOP is superimposed on the El Nino events and acts as the initial error with the biggest negative effect on the El Nino prediction. We show that the evolution of CNOP-type errors has obvious seasonal dependence and yields a significant SPB, with the most severe occurring in predictions made before the boreal spring in the growth phase of El Nino. The CNOP-type errors can be classified into two types: one possessing a sea-surface-temperature anomaly pattern with negative anomalies in the equatorial central-western Pacific, positive anomalies in the equatorial eastern Pacific, and a thermocline depth anomaly pattern with positive anomalies along the Equator, and another with patterns almost opposite to those of the former type. In predictions through the spring in the growth phase of El Nino, the initial error with the worst effect on the prediction tends to be the latter type of CNOP error, whereas in predictions through the spring in the decaying phase, the initial error with the biggest negative effect on the prediction is inclined to be the former type of CNOP error. Although the linear singular vector (LSV)-type errors also have patterns similar to the CNOP-type errors, they cover a more localized area than the CNOP-type errors and cause a much smaller prediction error, yielding a less significant SPB. Random errors in the initial conditions are also superimposed on El Nino events to investigate the SPB. We find that, whenever the predictions start, the random errors neither exhibit an obvious season-dependent evolution nor yield a large prediction error, and thus may not be responsible for the SPB phenomenon for El Nino events. These results suggest that the occurrence of the SPB is closely related to particular initial error patterns. The two kinds of CNOP-type error are most likely to cause a significant SPB. They have opposite signs and, consequently, opposite growth behaviours, a result which may demonstrate two dynamical mechanisms of error growth related to SPB: in one case, the errors grow in a manner similar to El Nino; in the other, the errors develop with a tendency opposite to El Nino. The two types of CNOP error may be most likely to provide the information regarding the 'sensitive area' of El Nino-Southern Oscillation (ENSO) predictions. If these types of initial error exist in realistic ENSO predictions and if a target method or a data assimilation approach can filter them, the ENSO forecast skill may be improved. Copyright (C) 2009 Royal Meteorological Society