Abstract

It is usual to preprocess data before reduction, but it is not so common to study how this operation affects the final results. Determination of the centroid is a relevant task for many optical measurement devices, and the centroid is very often calculated over thresholded data. The influence of preprocessing thresholding algorithms on the statistical properties of intensity data affected by additive Gaussian noise is described as a different effective additive signal perturbation. Theoretical, simulated, and experimental analyses of the model of the effective noise were performed, and good agreement among the analyses was obtained. Direct extension of the analyses from the influence of preprocessing to centroid determination is also presented.

© 2001 Optical Society of America

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References

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  1. S. V. Plotnikov, “Comparison of the methods of signal processing in triangulation measurement systems,” J. Opt. Instrum. Data Proc. 6, 55–60 (1995).
  2. R. Irwan and R. G. Lane, “Analysis of optimal centroid estimation applied to SH sensing,” Appl. Opt. 38, 6737–6743 (1999).
    [CrossRef]
  3. G. Cao and X. Yu, “Accuracy analysis of HS wavefront sensor operated with a faint object,” Opt. Eng. 33, 2331–2335 (1994).
    [CrossRef]

1999 (1)

1995 (1)

S. V. Plotnikov, “Comparison of the methods of signal processing in triangulation measurement systems,” J. Opt. Instrum. Data Proc. 6, 55–60 (1995).

1994 (1)

G. Cao and X. Yu, “Accuracy analysis of HS wavefront sensor operated with a faint object,” Opt. Eng. 33, 2331–2335 (1994).
[CrossRef]

Cao, G.

G. Cao and X. Yu, “Accuracy analysis of HS wavefront sensor operated with a faint object,” Opt. Eng. 33, 2331–2335 (1994).
[CrossRef]

Irwan, R.

Lane, R. G.

Plotnikov, S. V.

S. V. Plotnikov, “Comparison of the methods of signal processing in triangulation measurement systems,” J. Opt. Instrum. Data Proc. 6, 55–60 (1995).

Yu, X.

G. Cao and X. Yu, “Accuracy analysis of HS wavefront sensor operated with a faint object,” Opt. Eng. 33, 2331–2335 (1994).
[CrossRef]

Appl. Opt. (1)

J. Opt. Instrum. Data Proc. (1)

S. V. Plotnikov, “Comparison of the methods of signal processing in triangulation measurement systems,” J. Opt. Instrum. Data Proc. 6, 55–60 (1995).

Opt. Eng. (1)

G. Cao and X. Yu, “Accuracy analysis of HS wavefront sensor operated with a faint object,” Opt. Eng. 33, 2331–2335 (1994).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

(a) Mean and (b) variance of the effective noise for different thresholding levels with simulated data.

Fig. 2
Fig. 2

(a) Mean and (b) variance of the effective noise for different thresholding levels with experimental data.

Fig. 3
Fig. 3

(a) Simulated intensity profiles. (b) Bias of the centroid estimation in the presence of thresholding for different intensity profiles. , symmetric; , asymmetric.

Equations (10)

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Ij=I0j+nj,Ij=I0j,
IUj=Ijif IjUj0if Ij<Uj,
IUj=I0j+Nj.
PNj=12πσnexp-Nj22σn2if Uj-I0jnjδN+I0j×-Uj-I0j12πσnexp-tj22σn2dtif Uj-I0j>nj0rest of the cases,
Nj=12πσnexp-Uj-I0j2σn2-I0j21+erfUj-I0j2σn,
σNj2=σn221-erfUj-I0j2σn+12πσnUj-I0j×exp-Uj-I0j22σn2-12πσn2exp-Uj-I0j22σn2+I0j21+erfUj-I0j2σn.
X=jxjIjjIj.
X=jxjI0jjI0j+nj+jxjnjjI0j+nj.
X=jxjI0jjI0j+nj+jxjnjjI0j+nj.
σX2=X2-X2.

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