A statistical model of signal–noise in scanning electron microscopy

Timischl, Felix; Date, Munehiro; Nemoto, Shinji

doi:10.1002/sca.20282

Cited by 31 publications

(30 citation statements)

References 10 publications

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“…| µ 1 ‐ µ 2 | is given by the horizontal offset of the two signal peaks. Under the assumption that the central limit theorem holds, the signal peaks in Figure (c) can be approximated to have Gaussian distribution, and σ 1 and σ 2 can therefore be obtained by

F W H M = 2 \sqrt{2 \cdot \ln (2)} \cdot σ \approx 2.35 \cdot σ,

where FWHM is the full width at half signal height of each signal peak (Timischl, ).…”

Section: Resultsmentioning

confidence: 99%

“…Timischl, () showed how the SNR depends on the stage order in the signal transfer path of a SEM using a standard ET‐type secondary electron detector. The fact that CNR and SNR basically have the same information content suggests that both show a very similar if not equal dependence on stage order.…”

Section: Resultsmentioning

confidence: 99%

“…µ and σ are the expectation value and the standard deviation of each stage corresponding to the notation above. The analysis of Timischl, () gives for the SNR at the last stage, SNR tot(5)

S N R_{t o t (5)} = \frac{1}{(\frac{σ_{G U N}^{2}}{μ_{G U N}^{2}} + \frac{σ_{S E}^{2}}{μ_{G U N} μ_{S E}^{2}} + \frac{σ_{S c int}^{2}}{μ_{G U N} μ_{S E} μ_{S c int}^{2}} + \frac{σ_{P C}^{2}}{μ_{G U N} μ_{S E} μ_{S c int} μ_{P C}^{2}} + \frac{σ_{D y n}^{2}}{μ_{G U N} μ_{S E} μ_{S c int} μ_{P C} μ_{D y n}^{2}})^{\frac{1}{2}}}

where a uniform specimen (e.g. a polished specimen surface of uniform composition) is assumed.…”

Section: Resultsmentioning

confidence: 99%

“…Considering that the specimen used for CNR acquisition consists of two areas of different composition, we assume expectation values µ 1,SE and µ 2,SE , and standard deviations σ 1,SE and σ 2,SE for the secondary electron emission from area 1 and 2 of the standard specimen in Figure (a), respectively. Following the approach of Timischl, (), this gives for the total expectation values µ 1,tot(5) and µ 2,tot(5) and standard deviations σ 1,tot(5) and σ 2,tot(5) at the fifth stage of the signal transfer path

μ_{1, t o t (5)} = μ_{G U N} μ_{1, S E} μ_{S c int} μ_{P C} μ_{D y n},

{normalμ}_{2, t o t (5)} = {normalμ}_{G U N} {normalμ}_{2, S E} {normalμ}_{S c int} {normalμ}_{P C} {normalμ}_{D y n},

{normalσ}_{1, t o t (5)} = ({normalμ}_{G U N} {normalμ}_{1, S E} {normalμ}_{S c int} {normalμ}_{P C} {normalμ}_{D y n})^{2} \cdot ({normalσ}_{G U N}^{<...>}

…”

Section: Resultsmentioning

confidence: 99%

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The contrast‐to‐noise ratio for image quality evaluation in scanning electron microscopy

Timischl

2014

Scanning

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The contrast-to-noise ratio (CNR) is presented and characterized as a tool for quantitative noise measurement of scanning electron microscope (SEM) images. Analogies as well as differences between the CNR and the widely used signal-to-noise ratio (SNR) are analytically and experimentally investigated. With respect to practical SEM image evaluation using the contrast-to-noise ratio, a standard specimen and an evaluation program are presented.

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F W H M = 2 \sqrt{2 \cdot \ln (2)} \cdot σ \approx 2.35 \cdot σ,

where FWHM is the full width at half signal height of each signal peak (Timischl, ).…”

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

“…µ and σ are the expectation value and the standard deviation of each stage corresponding to the notation above. The analysis of Timischl, () gives for the SNR at the last stage, SNR tot(5)

S N R_{t o t (5)} = \frac{1}{(\frac{σ_{G U N}^{2}}{μ_{G U N}^{2}} + \frac{σ_{S E}^{2}}{μ_{G U N} μ_{S E}^{2}} + \frac{σ_{S c int}^{2}}{μ_{G U N} μ_{S E} μ_{S c int}^{2}} + \frac{σ_{P C}^{2}}{μ_{G U N} μ_{S E} μ_{S c int} μ_{P C}^{2}} + \frac{σ_{D y n}^{2}}{μ_{G U N} μ_{S E} μ_{S c int} μ_{P C} μ_{D y n}^{2}})^{\frac{1}{2}}}

where a uniform specimen (e.g. a polished specimen surface of uniform composition) is assumed.…”

Section: Resultsmentioning

confidence: 99%

μ_{1, t o t (5)} = μ_{G U N} μ_{1, S E} μ_{S c int} μ_{P C} μ_{D y n},

{normalμ}_{2, t o t (5)} = {normalμ}_{G U N} {normalμ}_{2, S E} {normalμ}_{S c int} {normalμ}_{P C} {normalμ}_{D y n},

{normalσ}_{1, t o t (5)} = ({normalμ}_{G U N} {normalμ}_{1, S E} {normalμ}_{S c int} {normalμ}_{P C} {normalμ}_{D y n})^{2} \cdot ({normalσ}_{G U N}^{<...>}

…”

Section: Resultsmentioning

confidence: 99%

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The contrast‐to‐noise ratio for image quality evaluation in scanning electron microscopy

Timischl

2014

Scanning

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“…Noise performances of detectors for standard SEM were analysed and measured by many authors, for example Wells (1974), Baumann and Reimer (1981), Comins and Thirwall (1981), Reimer (1985), Joy et al (1986), Agemura et al (2001), and Timischl et al (2012).…”

Section: Introductionmentioning

confidence: 99%

Noise coefficients of backscattered electron detectors for low voltage scanning electron microscopy

Hejna

2013

Journal of Microscopy

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SummaryNoise coefficients of backscattered electron (BSE) detectors for low voltage scanning electron microscopy were studied theoretically and experimentally. The conversion method of BSE detection, the scintillation detector with an acceleration of BSE and detectors with electron multipliers were considered. Formulae for noise coefficients were derived and noise coefficients of detectors were computed for different values of gains of detectors' components. Theoretical predictions of noise coefficients were compared with experimental results.

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A dynamic scanning method based on signal-statistics for scanning electron microscopy

Timischl

2013

Scanning

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A novel dynamic scanning method for noise reduction in scanning electron microscopy and related applications is presented. The scanning method dynamically adjusts the scanning speed of the electron beam depending on the statistical behavior of the detector signal and gives SEM images with uniform and predefined standard deviation, independent of the signal value itself. In the case of partially saturated images, the proposed method decreases image acquisition time without sacrificing image quality. The effectiveness of the proposed method is shown and compared to the conventional scanning method and median filtering using numerical simulations.

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A statistical model of signal–noise in scanning electron microscopy

Cited by 31 publications

References 10 publications

The contrast‐to‐noise ratio for image quality evaluation in scanning electron microscopy

The contrast‐to‐noise ratio for image quality evaluation in scanning electron microscopy

Noise coefficients of backscattered electron detectors for low voltage scanning electron microscopy

A dynamic scanning method based on signal-statistics for scanning electron microscopy

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