**8. References**

120 Advances in Wavelet Theory and Their Applications in Engineering, Physics and Technology

periodicities (knife marks) greater than 50 marks per inch can be grouped together and used

By monitoring the amplitudes of the bins of interest (less than 50 marks per inch) and setting an amplitude threshold then a frequency bin that would have, for example, 25 percent of the amplitude values over the amplitude threshold would be considered slightly periodic AND slightly stationary. If 50 percent of the data points in a frequency bin exceeded the threshold value then the signal would be considered slightly periodic and moderately stationary. If the amplitudes exceeded a secondary threshold value then the surface would be considered moderately periodic. An example of the action of the controller is if 5% of data points, at a given frequency, exceed the threshold then the defect was considered a **peak** (representing a localized defect). If 25% of the points at a given frequency exceed the threshold value then the defect is considered a **slight ridge**. If 50% of the points exceed the threshold then the defect is considered a **medium ridge**. This continues for a **long ridge** and a **complete ridge**. A problem can arise when the surface descriptors get close to the threshold but do not exceed it. An example would be when only slightly less than 25 percent of the amplitude values exceeded the threshold value, which, based on traditional techniques, would be considered non-stationary. The interpretation of the 3-dimensional plots of the results from the time-frequency analysis, while being somewhat easy by a human, is difficult when attempting to have a computer automatically make decisions on the state of the manufacturing process. The approach that was evaluated here was to use fuzzy logic to decide where in three-space the specimen or workpiece of interest belonged. A detailed discussion of using fuzzy logic for surface quality evaluation can be found in Lemaster (2004). Two applications of fuzzy logic were evaluated. The first was to use the standard surface descriptors to determine if a primary surface defect present on a specimen was periodic or not and then the second was to use the results of the HWT to determine if the

The overall goal of the research was to be able to detect an unacceptable surface produced during a machining operation and then attempt to provide additional information to the machine operator regarding the type of defect, the degree of the defect, and the possible source of the defect. In manufacturing, a defect that extends above the surface such as a ridge along the surface is usually much easier to deal with (repair) than a defect that extends below the surface such as a gouge or fiber tear-out. It is also desirable to determine if a surface defect is periodic, random-like, or localized in nature. In addition, it is also desirable to determine if the defect is stationary or non-stationary **as referenced to the surface of one specimen** (it has been shown that a wood machining operation in which tool wear occurs is

As discussed previously an example of a periodic surface are the knife marks from a planer or moulder. An example of a random-like surface would be fuzzy grain. An example of a localized surface defect would be a dent or a ridge caused by a chip in the cutting tool. The difference between a stationary or a non-stationary defect is that a stationary defect would extend along the entire length of the workpiece whereas a non-stationary defect would

technically a non-stationary process when considering multiple specimens).

to monitor overall roughness.

periodic surface defect was stationary or non-stationary.

occur only along a portion of the workpiece.

**6. Conclusion** 


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**7** 

*Algeria* 

**Multi-Scale Deconvolution** 

*1Electrical Engineer Department,* 

 *2Electronics Department,* 

**of Mass Spectrometry Signals** 

M'hamed Boulakroune1 and Djamel Benatia2

*Faculty of Sciences and Technology, Kasdi Merbah Ouargla University, Ouargla* 

It has become more important to measure accurate depth profiles in developing more advanced devices. To this aim, Depth profiling in secondary ion mass spectrometry (SIMS) has been extensively used as an informative technique in the semiconductor and electronic devices fields due to its high sensitivity, quantification accuracy and depth resolution (Fujiyama et al, 2011; Seki et al, 2011). However, the depth resolution in SIMS analysis is still limited to provide reliable and precise information in very thin structures such as delta layers, abrupt interfaces, etc. By optimization of the experimental conditions, the depth resolution can be enhanced. In particular, lowering the primary energy seems to be a good solution, but this increases the measurement time and leads to other limitations, owing to the wrong focalization of primary ion beam, such as roughness in the crater bottom, not flat crater, etc. Therefore, the depth resolution remains so far to its perfect limit. It is only by numerical processing like deconvolution that the depth resolution can be improved beyond

For the past several years, different approaches of deconvolution have been proposed taking into account the different physical phenomena that limit depth resolution, such as collisional mixing, roughness, and segregation ( Makarov, 1999; Gautier et al, 1998; Fares et al, 2006; Dowsett et al, 1994; Mancina et al, 2000; Shao et al, 2004; Collins et al, 1992; Allen et al, 1993; Fearn et al, 2005). However, most problems encountered in these deconvolution methods are due to the noise content in the measured profiles. This instrumental phenomenon, which cannot be eliminated by the improvement of operating conditions, strongly influences the depth resolution and therefore the quality of the deconvoluted

The deconvolution of depth profiling data in SIMS analysis amounts to the solution of an appropriate ill-posed problem in that any random noise in data leads to no unique and no stable solution (oscillatory signal with negative components, which are physically not acceptable in SIMS analysis). Thus, the results must be regularized (Tikhonov, 1963; Barakat et al, 1997; Prost et al, 1984; Burdeau et al, 2000; Herzel et al, 1995; Iqbal, 2003; Varah, 1983;

**1. Introduction** 

its experimental limits.

profiles.

*Faculty of Engineer Sciences, Université Hadj-Lakhdar de Batna, Batna* 

Whitehouse, D. J., 2011. *Handbook of Surface and Nanometrology*, 2nd Edition, CRC Press, Taylor and Francis Group, Boca Raton, FL, U.S.A, ISBN: 1978-1-4200-8201-2, 976 pages.
