A review and tutorial discussion of noise and signal-to-noise ratios in analytical spectrometry—II. Fundamental principles of signal-to-noise ratios

Boutilier, G. D.; Pollard, Bruce D.; Winefordner, J. D.; Chester, T. L.; Omenetto, N.

doi:10.1016/0584-8547(78)80050-0

Cited by 64 publications

(29 citation statements)

References 11 publications

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“…The prerequisites seem reasonable based on experimental evidence from a range of applications, especially for those in which the sample concentrations are near the detection limit. [1][2][3][4][5][6][7][8][9][10]17,21,[25][26][27] If the baseline noise can be modeled as the sum of an AR(1) and white noise random processes (Eqs. (3) and (4)), the uncertainty evaluation (Eq.…”

Section: Discussionmentioning

confidence: 99%

“…One is a general theory developed without any more assumptions than those required of a stationary process and the other is a specific theory based on a first order autoregressive (AR(1)) process plus white noise. Consequently, the former can cover the work by Alkemade et al [5][6][7] and the latter the FUMI theory, [8][9][10]21 respectively. This paper makes an attempt to lay the theoretical foundation for further development of measurement precision models under the generally acceptable assumption of the stationarity of the instrumental baseline noise.…”

Section: Introductionmentioning

confidence: 97%

“…[1][2][3][4][5][6][7][8][9][10] Within its domain of applicability, the theory can dispense with the repetitive measurement of real samples, thus helping to improve the global environment by saving energy and material. The time and human efforts that would be required by the repetition may also be reduced.…”

Section: Introductionmentioning

confidence: 99%

“…The time and human efforts that would be required by the repetition may also be reduced. Recently, some theories [5][6][7][8][9][10] for evaluating the instrumental uncertainty have been adopted as an ISO International Standard. 11 Background noise generally can be treated as random processes in probability theory and statistics.…”

Section: Introductionmentioning

confidence: 99%

“…[1][2][3][4][5][6][7][8][9][10]21 However, the value of stationary random processes has only been explicitly referred to in a few publications 5,22 despite its theoretical and practical importance as discussed above. Assuming stationarity, Alkemade et al [5][6][7] developed a useful theory for assessing the measurement SD from baseline noise, but its applicability is restricted to simple measurements usually carried out in spectroscopy (see below). The Function of Mutual Information (FUMI) theory [8][9][10]21 has wider applicability in stationary situations, but was derived based on a non-stationary process.…”

Section: Introductionmentioning

confidence: 99%

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Evaluation of Measurement Precision from Stationary Baseline Noise in Instrumental Analyses

Hayashi¹,

Zhang

2015

ANAL. SCI.

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This paper provides two approaches to estimate the standard deviation of measurements from baseline noise in instrumental output when (i) in theory, the noise can be approximated by a well-established random process in statistics and mathematics, referred to as a stationary process and (ii) in practice, the baseline noise is the predominant source of measurement error. For the first approach proposed, a general evaluation equation for measurement precision, when the baseline noise can be treated as a stationary process, is derived as a function of the process autocorrelations and process variance of the noise. In particular, for the second approach, when the baseline noise is a mixed random process of white noise and a first order autoregressive (AR(1)) process, the corresponding equation for the precision is also derived. The equations derived in the present paper include some results published elsewhere as special cases. For illustration, an example is presented.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Evaluation of Measurement Precision from Stationary Baseline Noise in Instrumental Analyses

Hayashi¹,

Zhang

2015

ANAL. SCI.

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Laser‐Induced Breakdown Spectroscopy

Cremers

Knight

2000

Encyclopedia of Analytical Chemistry

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Laser‐induced breakdown spectroscopy (LIBS) is a novel method of elemental analysis based on a laser‐generated plasma. Pulses from a laser are focused on a sample to atomize a small amount of material resulting in the formation of a microplasma. Because of the high plasma temperature, the resulting atoms are electronically excited to emit light. The plasma light is spectrallyresolved and detected to determine the elemental composition of the sample based on the unique emission spectrum of each element. Because of the simplicity of the method, it is suited for analyses that cannot be carried out using conventional methods of atomic emission spectroscopy (AES). This is particularly true for measurements that must be conducted outside of an analytical laboratory. A particular advantage of LIBS is the ability to analyze most types of samples without any preparation. This means that samples can be interrogated in situ, providing rapid measurement capability and permitting the method to be used in the analysis of gases, liquids, and solids in a variety of different sampling configurations. Although LIBS provides sensitive detection for many elements, it is not an ultrasensitive detection technique. In addition, under field conditions, the method typically does not provide the high accuracy and precision offered by laboratory‐based methods of AES.

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