Abstract

The background modulation method has been proposed as a useful test of early visual mechanisms [Biol. Cybern. 37, 77 (1980); Biol. Cybern. 47, 173 (1983)]. The task involves measuring detection thresholds for a luminous spot (increment) drifting over a spatially or temporally modulated background. The study explores the nature of the detecting mechanism in terms of spatial and temporal filters for both spatial and temporal background modulations. In both cases we find that thresholds can be explained by spatial contrast cues generated by the moving spot and that their spatiotemporal characteristics suggest detection by magnocellular processes.

© 2000 Optical Society of America

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References

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  1. J. L. Barbur, K. Ruddock, “Spatial characteristics of movement detection mechanisms in human vision. I. Achromatic vision,” Biol. Cybern. 37, 77–92 (1980).
    [CrossRef] [PubMed]
  2. I. E. Holliday, K. Ruddock, “Two spatial-temporal filters in human vision. 1. Temporal and spatial frequency response characteristics,” Biol. Cybern. 47, 173–190 (1983).
    [CrossRef]
  3. D. M. Coleston, E. Chronicle, K. H. Ruddock, C. Kennard, “Precortical dysfunction of spatial and temporal visual processing in migraine,” J. Neurol. Neurosurg. Psych. 57, 1208–1211 (1994).
    [CrossRef]
  4. A. R. Grounds, I. E. Holliday, K. Ruddock, “Two spatio-temporal filters in human vision. 2. Selective modification in amblyopia, albinism and hemianopia,” Biol. Cybern. 47, 191–201 (1983).
    [CrossRef]
  5. G. B. Wetherill, H. Levitt, “Sequential estimation of points on a psychometric function,” Br. J. Math. Stat. Psych. 18, 1–10 (1965).
    [CrossRef]
  6. C. Enroth-Cugell, J. G. Robson, “The contrast sensitivity of retinal ganglion cells of the cat,” J. Physiol. (London) 187, 517–552 (1966).
  7. A. R. Derrington, P. Lennie, “Spatial and temporal contrast sensitivities of neurones in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 219–140 (1984).
  8. D. H. Kelly, H. S. Magnuski, “Pattern detection and the two-dimensional Fourier transform: circular targets,” Vision Res. 15, 911–915 (1975).
    [CrossRef] [PubMed]
  9. F. L. van Nes, J. J. Koenderink, H. Nas, M. A. Bouman, “Spatiotemporal modulation transfer in the human eye,” J. Opt. Soc. Am. 57, 1082–1088 (1967).
    [CrossRef] [PubMed]
  10. G. E. Legge, “Sustained and transient mechanisms in human vision: temporal and spatial properties,” Vision Res. 18, 69–81 (1978).
    [CrossRef] [PubMed]
  11. D. C. Burr, “Temporal summation of moving images by the human visual system,” Proc. R. Soc. London Ser. B 211, 321–339 (1981).
    [CrossRef]
  12. R. J. Snowden, O. J. Braddick, “The temporal integration and resolution of velocity signals,” Vision Res. 31, 907–914 (1991).
    [CrossRef] [PubMed]
  13. J. J. Kulikowski, “Some stimulus parameters affecting spatial and temporal resolution of human vision,” Vision Res. 11, 83–93 (1971).
    [CrossRef] [PubMed]
  14. D. H. Kelly, “Frequency doubling in visual responses,” J. Opt. Soc. Am. 56, 1628–1633 (1966).
    [CrossRef]
  15. W. H. Merigan, “Chromatic and achromatic vision of Macaques: role of the P pathway,” J. Neurosci. 9, 776–783 (1989).
    [PubMed]
  16. W. H. Merigan, J. Maunsell, “Macaque vision after magnocellular lateral geniculate lesions,” Visual Neurosci. 5, 347–352 (1990).
    [CrossRef]
  17. R. S. Harwerth, D. M. Levi, “Reaction time as a measure of suprathreshold grating detection,” Vision Res. 18, 1579–1586 (1978).
    [CrossRef] [PubMed]
  18. D. J. Tolhurst, “Reaction times to the detection of gratings by human observers: a probabilistic mechanism,” Vision Res. 15, 1143–1149 (1975).
    [CrossRef] [PubMed]
  19. C. A. Burbeck, D. H. Kelly, “Contrast gain measurements and the transient/sustained dichotomy,” J. Opt. Soc. Am. 71, 1335–1342 (1981).
    [PubMed]
  20. H. A. Quigley, C. R. Dunkelberger, W. R. Green, “Chronic human glaucoma causing selectively greater loss of large optic nerve fibers,” Ophthalmology 95, 357–363 (1988).
    [CrossRef] [PubMed]
  21. M. Livingstone, G. D. Rosen, F. W. Drislane, A. M. Galaburda, “Physiological and anatomical evidence for a magnocellular defect in developmental dyslexia,” Proc. Natl. Acad. Sci. USA 88, 7943–7947 (1991).
    [CrossRef] [PubMed]

1994 (1)

D. M. Coleston, E. Chronicle, K. H. Ruddock, C. Kennard, “Precortical dysfunction of spatial and temporal visual processing in migraine,” J. Neurol. Neurosurg. Psych. 57, 1208–1211 (1994).
[CrossRef]

1991 (2)

R. J. Snowden, O. J. Braddick, “The temporal integration and resolution of velocity signals,” Vision Res. 31, 907–914 (1991).
[CrossRef] [PubMed]

M. Livingstone, G. D. Rosen, F. W. Drislane, A. M. Galaburda, “Physiological and anatomical evidence for a magnocellular defect in developmental dyslexia,” Proc. Natl. Acad. Sci. USA 88, 7943–7947 (1991).
[CrossRef] [PubMed]

1990 (1)

W. H. Merigan, J. Maunsell, “Macaque vision after magnocellular lateral geniculate lesions,” Visual Neurosci. 5, 347–352 (1990).
[CrossRef]

1989 (1)

W. H. Merigan, “Chromatic and achromatic vision of Macaques: role of the P pathway,” J. Neurosci. 9, 776–783 (1989).
[PubMed]

1988 (1)

H. A. Quigley, C. R. Dunkelberger, W. R. Green, “Chronic human glaucoma causing selectively greater loss of large optic nerve fibers,” Ophthalmology 95, 357–363 (1988).
[CrossRef] [PubMed]

1984 (1)

A. R. Derrington, P. Lennie, “Spatial and temporal contrast sensitivities of neurones in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 219–140 (1984).

1983 (2)

A. R. Grounds, I. E. Holliday, K. Ruddock, “Two spatio-temporal filters in human vision. 2. Selective modification in amblyopia, albinism and hemianopia,” Biol. Cybern. 47, 191–201 (1983).
[CrossRef]

I. E. Holliday, K. Ruddock, “Two spatial-temporal filters in human vision. 1. Temporal and spatial frequency response characteristics,” Biol. Cybern. 47, 173–190 (1983).
[CrossRef]

1981 (2)

C. A. Burbeck, D. H. Kelly, “Contrast gain measurements and the transient/sustained dichotomy,” J. Opt. Soc. Am. 71, 1335–1342 (1981).
[PubMed]

D. C. Burr, “Temporal summation of moving images by the human visual system,” Proc. R. Soc. London Ser. B 211, 321–339 (1981).
[CrossRef]

1980 (1)

J. L. Barbur, K. Ruddock, “Spatial characteristics of movement detection mechanisms in human vision. I. Achromatic vision,” Biol. Cybern. 37, 77–92 (1980).
[CrossRef] [PubMed]

1978 (2)

G. E. Legge, “Sustained and transient mechanisms in human vision: temporal and spatial properties,” Vision Res. 18, 69–81 (1978).
[CrossRef] [PubMed]

R. S. Harwerth, D. M. Levi, “Reaction time as a measure of suprathreshold grating detection,” Vision Res. 18, 1579–1586 (1978).
[CrossRef] [PubMed]

1975 (2)

D. J. Tolhurst, “Reaction times to the detection of gratings by human observers: a probabilistic mechanism,” Vision Res. 15, 1143–1149 (1975).
[CrossRef] [PubMed]

D. H. Kelly, H. S. Magnuski, “Pattern detection and the two-dimensional Fourier transform: circular targets,” Vision Res. 15, 911–915 (1975).
[CrossRef] [PubMed]

1971 (1)

J. J. Kulikowski, “Some stimulus parameters affecting spatial and temporal resolution of human vision,” Vision Res. 11, 83–93 (1971).
[CrossRef] [PubMed]

1967 (1)

1966 (2)

C. Enroth-Cugell, J. G. Robson, “The contrast sensitivity of retinal ganglion cells of the cat,” J. Physiol. (London) 187, 517–552 (1966).

D. H. Kelly, “Frequency doubling in visual responses,” J. Opt. Soc. Am. 56, 1628–1633 (1966).
[CrossRef]

1965 (1)

G. B. Wetherill, H. Levitt, “Sequential estimation of points on a psychometric function,” Br. J. Math. Stat. Psych. 18, 1–10 (1965).
[CrossRef]

Barbur, J. L.

J. L. Barbur, K. Ruddock, “Spatial characteristics of movement detection mechanisms in human vision. I. Achromatic vision,” Biol. Cybern. 37, 77–92 (1980).
[CrossRef] [PubMed]

Bouman, M. A.

Braddick, O. J.

R. J. Snowden, O. J. Braddick, “The temporal integration and resolution of velocity signals,” Vision Res. 31, 907–914 (1991).
[CrossRef] [PubMed]

Burbeck, C. A.

Burr, D. C.

D. C. Burr, “Temporal summation of moving images by the human visual system,” Proc. R. Soc. London Ser. B 211, 321–339 (1981).
[CrossRef]

Chronicle, E.

D. M. Coleston, E. Chronicle, K. H. Ruddock, C. Kennard, “Precortical dysfunction of spatial and temporal visual processing in migraine,” J. Neurol. Neurosurg. Psych. 57, 1208–1211 (1994).
[CrossRef]

Coleston, D. M.

D. M. Coleston, E. Chronicle, K. H. Ruddock, C. Kennard, “Precortical dysfunction of spatial and temporal visual processing in migraine,” J. Neurol. Neurosurg. Psych. 57, 1208–1211 (1994).
[CrossRef]

Derrington, A. R.

A. R. Derrington, P. Lennie, “Spatial and temporal contrast sensitivities of neurones in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 219–140 (1984).

Drislane, F. W.

M. Livingstone, G. D. Rosen, F. W. Drislane, A. M. Galaburda, “Physiological and anatomical evidence for a magnocellular defect in developmental dyslexia,” Proc. Natl. Acad. Sci. USA 88, 7943–7947 (1991).
[CrossRef] [PubMed]

Dunkelberger, C. R.

H. A. Quigley, C. R. Dunkelberger, W. R. Green, “Chronic human glaucoma causing selectively greater loss of large optic nerve fibers,” Ophthalmology 95, 357–363 (1988).
[CrossRef] [PubMed]

Enroth-Cugell, C.

C. Enroth-Cugell, J. G. Robson, “The contrast sensitivity of retinal ganglion cells of the cat,” J. Physiol. (London) 187, 517–552 (1966).

Galaburda, A. M.

M. Livingstone, G. D. Rosen, F. W. Drislane, A. M. Galaburda, “Physiological and anatomical evidence for a magnocellular defect in developmental dyslexia,” Proc. Natl. Acad. Sci. USA 88, 7943–7947 (1991).
[CrossRef] [PubMed]

Green, W. R.

H. A. Quigley, C. R. Dunkelberger, W. R. Green, “Chronic human glaucoma causing selectively greater loss of large optic nerve fibers,” Ophthalmology 95, 357–363 (1988).
[CrossRef] [PubMed]

Grounds, A. R.

A. R. Grounds, I. E. Holliday, K. Ruddock, “Two spatio-temporal filters in human vision. 2. Selective modification in amblyopia, albinism and hemianopia,” Biol. Cybern. 47, 191–201 (1983).
[CrossRef]

Harwerth, R. S.

R. S. Harwerth, D. M. Levi, “Reaction time as a measure of suprathreshold grating detection,” Vision Res. 18, 1579–1586 (1978).
[CrossRef] [PubMed]

Holliday, I. E.

A. R. Grounds, I. E. Holliday, K. Ruddock, “Two spatio-temporal filters in human vision. 2. Selective modification in amblyopia, albinism and hemianopia,” Biol. Cybern. 47, 191–201 (1983).
[CrossRef]

I. E. Holliday, K. Ruddock, “Two spatial-temporal filters in human vision. 1. Temporal and spatial frequency response characteristics,” Biol. Cybern. 47, 173–190 (1983).
[CrossRef]

Kelly, D. H.

Kennard, C.

D. M. Coleston, E. Chronicle, K. H. Ruddock, C. Kennard, “Precortical dysfunction of spatial and temporal visual processing in migraine,” J. Neurol. Neurosurg. Psych. 57, 1208–1211 (1994).
[CrossRef]

Koenderink, J. J.

Kulikowski, J. J.

J. J. Kulikowski, “Some stimulus parameters affecting spatial and temporal resolution of human vision,” Vision Res. 11, 83–93 (1971).
[CrossRef] [PubMed]

Legge, G. E.

G. E. Legge, “Sustained and transient mechanisms in human vision: temporal and spatial properties,” Vision Res. 18, 69–81 (1978).
[CrossRef] [PubMed]

Lennie, P.

A. R. Derrington, P. Lennie, “Spatial and temporal contrast sensitivities of neurones in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 219–140 (1984).

Levi, D. M.

R. S. Harwerth, D. M. Levi, “Reaction time as a measure of suprathreshold grating detection,” Vision Res. 18, 1579–1586 (1978).
[CrossRef] [PubMed]

Levitt, H.

G. B. Wetherill, H. Levitt, “Sequential estimation of points on a psychometric function,” Br. J. Math. Stat. Psych. 18, 1–10 (1965).
[CrossRef]

Livingstone, M.

M. Livingstone, G. D. Rosen, F. W. Drislane, A. M. Galaburda, “Physiological and anatomical evidence for a magnocellular defect in developmental dyslexia,” Proc. Natl. Acad. Sci. USA 88, 7943–7947 (1991).
[CrossRef] [PubMed]

Magnuski, H. S.

D. H. Kelly, H. S. Magnuski, “Pattern detection and the two-dimensional Fourier transform: circular targets,” Vision Res. 15, 911–915 (1975).
[CrossRef] [PubMed]

Maunsell, J.

W. H. Merigan, J. Maunsell, “Macaque vision after magnocellular lateral geniculate lesions,” Visual Neurosci. 5, 347–352 (1990).
[CrossRef]

Merigan, W. H.

W. H. Merigan, J. Maunsell, “Macaque vision after magnocellular lateral geniculate lesions,” Visual Neurosci. 5, 347–352 (1990).
[CrossRef]

W. H. Merigan, “Chromatic and achromatic vision of Macaques: role of the P pathway,” J. Neurosci. 9, 776–783 (1989).
[PubMed]

Nas, H.

Quigley, H. A.

H. A. Quigley, C. R. Dunkelberger, W. R. Green, “Chronic human glaucoma causing selectively greater loss of large optic nerve fibers,” Ophthalmology 95, 357–363 (1988).
[CrossRef] [PubMed]

Robson, J. G.

C. Enroth-Cugell, J. G. Robson, “The contrast sensitivity of retinal ganglion cells of the cat,” J. Physiol. (London) 187, 517–552 (1966).

Rosen, G. D.

M. Livingstone, G. D. Rosen, F. W. Drislane, A. M. Galaburda, “Physiological and anatomical evidence for a magnocellular defect in developmental dyslexia,” Proc. Natl. Acad. Sci. USA 88, 7943–7947 (1991).
[CrossRef] [PubMed]

Ruddock, K.

A. R. Grounds, I. E. Holliday, K. Ruddock, “Two spatio-temporal filters in human vision. 2. Selective modification in amblyopia, albinism and hemianopia,” Biol. Cybern. 47, 191–201 (1983).
[CrossRef]

I. E. Holliday, K. Ruddock, “Two spatial-temporal filters in human vision. 1. Temporal and spatial frequency response characteristics,” Biol. Cybern. 47, 173–190 (1983).
[CrossRef]

J. L. Barbur, K. Ruddock, “Spatial characteristics of movement detection mechanisms in human vision. I. Achromatic vision,” Biol. Cybern. 37, 77–92 (1980).
[CrossRef] [PubMed]

Ruddock, K. H.

D. M. Coleston, E. Chronicle, K. H. Ruddock, C. Kennard, “Precortical dysfunction of spatial and temporal visual processing in migraine,” J. Neurol. Neurosurg. Psych. 57, 1208–1211 (1994).
[CrossRef]

Snowden, R. J.

R. J. Snowden, O. J. Braddick, “The temporal integration and resolution of velocity signals,” Vision Res. 31, 907–914 (1991).
[CrossRef] [PubMed]

Tolhurst, D. J.

D. J. Tolhurst, “Reaction times to the detection of gratings by human observers: a probabilistic mechanism,” Vision Res. 15, 1143–1149 (1975).
[CrossRef] [PubMed]

van Nes, F. L.

Wetherill, G. B.

G. B. Wetherill, H. Levitt, “Sequential estimation of points on a psychometric function,” Br. J. Math. Stat. Psych. 18, 1–10 (1965).
[CrossRef]

Biol. Cybern. (3)

A. R. Grounds, I. E. Holliday, K. Ruddock, “Two spatio-temporal filters in human vision. 2. Selective modification in amblyopia, albinism and hemianopia,” Biol. Cybern. 47, 191–201 (1983).
[CrossRef]

J. L. Barbur, K. Ruddock, “Spatial characteristics of movement detection mechanisms in human vision. I. Achromatic vision,” Biol. Cybern. 37, 77–92 (1980).
[CrossRef] [PubMed]

I. E. Holliday, K. Ruddock, “Two spatial-temporal filters in human vision. 1. Temporal and spatial frequency response characteristics,” Biol. Cybern. 47, 173–190 (1983).
[CrossRef]

Br. J. Math. Stat. Psych. (1)

G. B. Wetherill, H. Levitt, “Sequential estimation of points on a psychometric function,” Br. J. Math. Stat. Psych. 18, 1–10 (1965).
[CrossRef]

J. Neurol. Neurosurg. Psych. (1)

D. M. Coleston, E. Chronicle, K. H. Ruddock, C. Kennard, “Precortical dysfunction of spatial and temporal visual processing in migraine,” J. Neurol. Neurosurg. Psych. 57, 1208–1211 (1994).
[CrossRef]

J. Neurosci. (1)

W. H. Merigan, “Chromatic and achromatic vision of Macaques: role of the P pathway,” J. Neurosci. 9, 776–783 (1989).
[PubMed]

J. Opt. Soc. Am. (3)

J. Physiol. (London) (2)

C. Enroth-Cugell, J. G. Robson, “The contrast sensitivity of retinal ganglion cells of the cat,” J. Physiol. (London) 187, 517–552 (1966).

A. R. Derrington, P. Lennie, “Spatial and temporal contrast sensitivities of neurones in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 219–140 (1984).

Ophthalmology (1)

H. A. Quigley, C. R. Dunkelberger, W. R. Green, “Chronic human glaucoma causing selectively greater loss of large optic nerve fibers,” Ophthalmology 95, 357–363 (1988).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. USA (1)

M. Livingstone, G. D. Rosen, F. W. Drislane, A. M. Galaburda, “Physiological and anatomical evidence for a magnocellular defect in developmental dyslexia,” Proc. Natl. Acad. Sci. USA 88, 7943–7947 (1991).
[CrossRef] [PubMed]

Proc. R. Soc. London Ser. B (1)

D. C. Burr, “Temporal summation of moving images by the human visual system,” Proc. R. Soc. London Ser. B 211, 321–339 (1981).
[CrossRef]

Vision Res. (6)

R. J. Snowden, O. J. Braddick, “The temporal integration and resolution of velocity signals,” Vision Res. 31, 907–914 (1991).
[CrossRef] [PubMed]

J. J. Kulikowski, “Some stimulus parameters affecting spatial and temporal resolution of human vision,” Vision Res. 11, 83–93 (1971).
[CrossRef] [PubMed]

R. S. Harwerth, D. M. Levi, “Reaction time as a measure of suprathreshold grating detection,” Vision Res. 18, 1579–1586 (1978).
[CrossRef] [PubMed]

D. J. Tolhurst, “Reaction times to the detection of gratings by human observers: a probabilistic mechanism,” Vision Res. 15, 1143–1149 (1975).
[CrossRef] [PubMed]

D. H. Kelly, H. S. Magnuski, “Pattern detection and the two-dimensional Fourier transform: circular targets,” Vision Res. 15, 911–915 (1975).
[CrossRef] [PubMed]

G. E. Legge, “Sustained and transient mechanisms in human vision: temporal and spatial properties,” Vision Res. 18, 69–81 (1978).
[CrossRef] [PubMed]

Visual Neurosci. (1)

W. H. Merigan, J. Maunsell, “Macaque vision after magnocellular lateral geniculate lesions,” Visual Neurosci. 5, 347–352 (1990).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Comparison between our results and those reported by Coleston3 for the spatial background modulation task. Normalized luminance increment thresholds for subjects AM (circles), AT (squares), and JK (triangles) are shown along with normalized average data from the control group of Coleston3 (solid curve).

Fig. 2
Fig. 2

Contrast decrement detection thresholds of a spot drifting over a sinusoidal background grating (open symbols). Solid symbols show the pattern contrast cue (ΔC) present for the spatial background modulation thresholds measured in experiment 1. Data are expressed as the mean ± standard error of the mean for the three observers.

Fig. 3
Fig. 3

Comparison of spot detection thresholds with (open symbols) and without (solid symbols) a pattern contrast cue. Data are expressed as the mean of the three subjects ± standard error of the mean.

Fig. 4
Fig. 4

A, Method used to determine the change at threshold induced by the target spot of the spatial background modulation stimulus. A.1, Spatial background modulation stimulus for a background of spatial frequency S c/deg; A.2, schematic of the thresholds measured with stimulus A1, where the asterisk denotes the threshold for S c/deg; A.3, 2DFFT of the stimulus shown in A.1 for a background of 4 c/deg. The inner circles represent the contribution of the circular border of the target (centered on a spatial frequency of 0, 0) and the dots on the vertical meridian represent the contribution of the oriented background grating. The profiles at the right and lower edge of the figure represent the one-dimensional FFT along the vertical and the horizontal midline, respectively; A.4, see figure. B, Method used to determine an individual’s 2D contrast sensitivity profile. B.1, Radial cosine stimulus used to measure contrast thresholds (3.5° diameter, drifting at 15 °/s over a uniform background); B.2, schematic of the contrast-detection thresholds measured with the stimulus in B.1; B.3, schematic of the best-fit contrast function [Eq. (8)] for the maximum amplitude of the Fourier transform of the radial cosine at threshold; B.4, three-dimensional contrast threshold surface for one subject (AM). C, See Fig. 6.

Fig. 5
Fig. 5

Contrast-detection thresholds for a 3.5° radial cosine, drifting at 15 °/s over a uniform background for three subjects, along with comparative data from Kelly and Magnuski8 (curve). Data are expressed as the mean ± standard error of the mean for subjects AM (circles), AT (squares), and JK (triangles).

Fig. 6
Fig. 6

(a) Difference between the power spectrum of Fig. 4.A.4 and the contrast threshold surface of Fig. 4.B.4. for subject AM. Contrast threshold is attained only at low spatial frequencies (less than 0.5 c/deg), as represented by the peak of positive power in the center of the figure. (b) Cross section of surface along the plane where x=0 to show the 2D power for all subjects.

Fig. 7
Fig. 7

Comparison of the mean temporal response for subjects AM, TF, and JA (solid circles) and those reported for the control group of Coleston3 (open circles), and those from Fig. 2(a) of Holliday and Ruddock2 (open squares). All data have been normalized to permit comparison.

Fig. 8
Fig. 8

Contrast detection thresholds for a temporally modulated 3.5° radial cosine. Data are expressed as the mean ± standard error of the mean.

Fig. 9
Fig. 9

Integration time [as determined with Eq. (10)] for the spatial contrast cue to reach contrast threshold.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

C=Lmax-LminLmax+Lmin,
C=Lmax-LminLmax+Lmin+2ΔL.
C=Lmean×CLmean+ΔL,
a=Lmean×C.
C=aLmean+ΔL.
ΔC=C-C,
L(x, y)=exp-x22σx2+y22σy2×cos2πf×x2+y2×C100,
f(x)=C1 exp-(x-T1)22S12-C2 exp-(x-T2)22S22.
Lb=Lmean(1+a sin(ft+ϕ),
0t ΔLΔL+2(Lmean(1+a sin(bt+ϕ).

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