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Polarization spectroscopy in (4)He around 1083 nm is observed and optimized with a distributed feedback fiber laser and is applied for frequency stabilization. In order to improve the accuracy and long-term stability of the frequency-locking performance, a power stabilization module is added, and the dependences of the peak-to-peak amplitude and frequency difference (width) of the polarization spectroscopy signal on various pump and probe powers are investigated.

Two kinds of optical heterodyne saturation spectroscopies, namely, frequency modulation spectroscopy (FMS) and modulation transfer spectroscopy (MTS), are demonstrated for locking a fiber laser to the transition lines of metastable (4)He atoms around 1083 nm. The servo-loop error signals of FMS and MTS for stabilizing laser frequency are optimized by studying the dependence of the peak-to-peak amplitude and slope on the optical power of pump and probe beams. A comparison of the stabilization performances of FMS/MTS and polarization spectroscopy (PS) is presented, which shows that MTS exhibits relatively superior performance with the least laser frequency fluctuation due to its flat-background dispersive signal, originated from the four-wave mixing process. The Allan deviation of the stabilized laser frequency is 5.4 × 10(-12)@100 s with MTS for data acquired in 1000 s, which is sufficiently applicable for fields like laser cooling, optical pumping, and optical magnetometry.

ABSACDecomposing morphological structure element into Minkowski sum of several small ones is very useful for fast implementation of morphological operations and important for multiscale system. This paper wifi present some theoretical results on decomposition of digital structure element ,such as geontrica1 constraints ,sirigularity ,compatibility ,and decomposability ,etc. which is very different from that in continuous space. Based on them,methodology for decomposition will be proposed ,inc1iiing approximate decomposition ,eorreetion of singularity ,and so on. These results will be used in decomposition into 4 and 8 neighborhood configurations and series decomposition of multiscale structure sequen in the paper. IN'rRODUCTLoNMathematical morphology has been used widely in image processing ,pattern recognition ,and computer vision because of its explicit geometrical meaning and potential high parallel realizability"2. It is well known that mOrphOlOgical structure element(MSE) oxupies the mct important and the most fundamental position in mathematical morphology because it determines not only the aim and the effect of operation but also the efficiency of implementation. Thus ,whether to sttiy or to use morphology ,choosing a proper MSE has been a key step13.To implement morphological transforms efficiently is an essential requirement in real applications because very often we must perform a lot of morphological operations to constitute a practical processing3. For commonly u1 parallel computers such as Cellular logic nchines4 'only transforn by small sized MSE can be realized efficiently. So how to implennt transforms by large MSE's has been an attractive problem. In previous works ,son kinds of shift paths have been suggested for doing this on mesh connected arrays with a time cost proportional to the area of MSE56 ,but this time consumption seems to be still too large in practice. In fact , by natures of morphology ,a faster implementation is possible. That is, to decompose MSE B into following form. B=B13B3... ®B,Certainly , It has been nntioned by many researchers that decomposition of MSE can improve computing efficiency greatly7'°'19. Decomposition of MSE is necary not only for those stated here ,but also for son good characteristks of multiscale morphological systern'2 for a very efficient sequential algOrithm of morphological transfornis'.Decomposition of MSE has been discu.sed previously , but this problem i far away from a satisfactory solution. Zhuang and Haralick'° , for instance ,has designed a tree-search algorithm to do it,but it can be seen that their method encounters at least two problems which can not be dealt with by itself. One is its potential exponential time cost ,the other is the most digital MSE essentially n not be decomposed into the given form so that the algorithm will find nothing in most cases. The latter problem is very intrinsic in digital spaor ,which will be shown in this paper. This results from that decomposition in digital space is very different from that in continuous spac...

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