Abstract

Electro-optical target acquisition models predict the probability that a human observer recognizes or identifies a target. To accurately model targeting performance, the impact of imager blur and noise on human vision must be quantified. In the most widely used target acquisition models, human vision is treated as a “black box” that is characterized by its signal transfer response and detection thresholds. This paper describes an engineering model of observer vision. Characteristics of the observer model are compared to psychophysical data. This paper also describes how to integrate the observer model into both reflected light and thermal sensor models.

© 2009 OSA

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References

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2008 (2)

2007 (1)

2004 (2)

P. G. J. Barten, “Formula for the contrast sensitivity of the human eye,” Proc. SPIE 5294, 231–238 (2004) (Paper available on the Web at http://www.SPIE.org).
[CrossRef]

R. H. Vollmerhausen, E. Jacobs, and R. Driggers, “New metric for predicting target acquisition performance,” Opt. Eng. 43(11), 2806–2818 (2004).
[CrossRef]

2001 (4)

R. Driggers, R. Vollmerhausen, and K. Krapels, “Target Identification Performance as a Function of Temporal and Fixed Pattern Noise,” Opt. Eng. 40(3), 443–447 (2001).
[CrossRef]

N. M. Devitt, R. G. Driggers, R. H. Vollmerhausen, S. K. Moyer, K. A. Krapels, and J. D. O’Connor, “Target recognition performance as a function of sampling,” Proc. SPIE 4372, 74–84 (2001).
[CrossRef]

J. A. Ratches, R. Vollmerhausen, and R. Driggers, “Target Acquisition Performance Modeling of Infrared Imaging Systems: Past, Present, and Future,” IEEE Sens. J. 1(1), 31–40 (2001).
[CrossRef]

Z.-L. Lu and B. A. Dosher, “Characterizing the spatial-frequency sensitivity of perceptual templates,” J. Opt. Soc. Am. 18(9), 2041–2053 (2001).
[CrossRef]

1999 (1)

1998 (1)

J. Rovamo, H. Kukkonen, and J. Mustonen, “Foveal optical modulation transfer function of the human eye at various pupil sizes,” J. Opt. Soc. Am. 15(9), 2504 (1998).
[CrossRef]

1995 (1)

R. Vollmerhausen, “Incorporating Display Limitations into Night Vision Performance Models,” IRIS Passive Sensors 2, 11–31 (1995).

1994 (1)

P. Artal and R. Navarro, “Monochromatic modulation transfer function of the human eye for different pupil diameters: an analytic expression,” J. Opt. Soc. Am. 11(1), 246–249 (1994).
[CrossRef]

1988 (1)

1987 (1)

G. E. Legge, D. Kersten, and A. E. Burgess, “Contrast discrimination in noise,” J. Opt. Soc. Am. 4(2), 391–404 (1987).
[CrossRef]

1982 (1)

C. R. Carlson, “Sine-wave threshold contrast-sensitivity function: dependence on display size,” RCA Review 43, 675–683 (1982).

1979 (1)

V. Virsu and J. Rovamo, “Visual resolution, contrast sensitivity, and the cortical magnification factor,” Exp. Brain Res. 37(3), 475–494 (1979).
[CrossRef] [PubMed]

1974 (1)

A. van Meeteren, “Calculations of the optical modulation transfer function of the human eye for white light,” Opt. Acta (Lond.) 21, 395–412 (1974).
[CrossRef]

1972 (2)

A. van Meeteren and J. J. Vos, “Resolution and contrast sensitivity at low luminances,” Vision Res. 12(5), 825–833 (1972).
[CrossRef] [PubMed]

C. F. Stromeyer and B. Julesz, “Spatial-frequency masking in vision: critical bands and spread of masking,” J. Opt. Soc. Am. 62(10), 1221–1232 (1972).
[CrossRef] [PubMed]

1968 (2)

A. Watanabe, T. Mori, S. Nagata, and K. Hiwatashi, “Spatial sine-wave responses of the human visual system,” Vision Res. 8(9), 1245–1263 (1968).
[CrossRef] [PubMed]

F. W. Campbell and J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197(3), 551–566 (1968).
[PubMed]

1967 (1)

1966 (2)

1964 (1)

1962 (1)

Artal, P.

P. Artal and R. Navarro, “Monochromatic modulation transfer function of the human eye for different pupil diameters: an analytic expression,” J. Opt. Soc. Am. 11(1), 246–249 (1994).
[CrossRef]

Barten, P. G. J.

P. G. J. Barten, “Formula for the contrast sensitivity of the human eye,” Proc. SPIE 5294, 231–238 (2004) (Paper available on the Web at http://www.SPIE.org).
[CrossRef]

Bouman, M. A.

Burgess, A. E.

G. E. Legge, D. Kersten, and A. E. Burgess, “Contrast discrimination in noise,” J. Opt. Soc. Am. 4(2), 391–404 (1987).
[CrossRef]

Campbell, F. W.

F. W. Campbell and J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197(3), 551–566 (1968).
[PubMed]

F. W. Campbell and R. W. Gubisch, “Optical quality of the human eye,” J. Physiol. 186(3), 558–578 (1966).
[PubMed]

Carlson, C. R.

C. R. Carlson, “Sine-wave threshold contrast-sensitivity function: dependence on display size,” RCA Review 43, 675–683 (1982).

DePalma, J. J.

Devitt, N. M.

N. M. Devitt, R. G. Driggers, R. H. Vollmerhausen, S. K. Moyer, K. A. Krapels, and J. D. O’Connor, “Target recognition performance as a function of sampling,” Proc. SPIE 4372, 74–84 (2001).
[CrossRef]

Dosher, B. A.

Z.-L. Lu and B. A. Dosher, “Characterizing the spatial-frequency sensitivity of perceptual templates,” J. Opt. Soc. Am. 18(9), 2041–2053 (2001).
[CrossRef]

Driggers, R.

R. H. Vollmerhausen, E. Jacobs, and R. Driggers, “New metric for predicting target acquisition performance,” Opt. Eng. 43(11), 2806–2818 (2004).
[CrossRef]

R. Driggers, R. Vollmerhausen, and K. Krapels, “Target Identification Performance as a Function of Temporal and Fixed Pattern Noise,” Opt. Eng. 40(3), 443–447 (2001).
[CrossRef]

J. A. Ratches, R. Vollmerhausen, and R. Driggers, “Target Acquisition Performance Modeling of Infrared Imaging Systems: Past, Present, and Future,” IEEE Sens. J. 1(1), 31–40 (2001).
[CrossRef]

Driggers, R. G.

Farell, B.

Gubisch, R. W.

F. W. Campbell and R. W. Gubisch, “Optical quality of the human eye,” J. Physiol. 186(3), 558–578 (1966).
[PubMed]

Hiwatashi, K.

A. Watanabe, T. Mori, S. Nagata, and K. Hiwatashi, “Spatial sine-wave responses of the human visual system,” Vision Res. 8(9), 1245–1263 (1968).
[CrossRef] [PubMed]

Hixson, J. G.

Jacobs, E.

R. H. Vollmerhausen, E. Jacobs, and R. Driggers, “New metric for predicting target acquisition performance,” Opt. Eng. 43(11), 2806–2818 (2004).
[CrossRef]

Julesz, B.

Kersten, D.

G. E. Legge, D. Kersten, and A. E. Burgess, “Contrast discrimination in noise,” J. Opt. Soc. Am. 4(2), 391–404 (1987).
[CrossRef]

Krapels, K.

R. H. Vollmerhausen, S. Moyer, K. Krapels, R. G. Driggers, J. G. Hixson, and A. L. Robinson, “Predicting the probability of facial identification using a specific object model,” Appl. Opt. 47(6), 751–759 (2008).
[CrossRef] [PubMed]

R. Driggers, R. Vollmerhausen, and K. Krapels, “Target Identification Performance as a Function of Temporal and Fixed Pattern Noise,” Opt. Eng. 40(3), 443–447 (2001).
[CrossRef]

Krapels, K. A.

N. M. Devitt, R. G. Driggers, R. H. Vollmerhausen, S. K. Moyer, K. A. Krapels, and J. D. O’Connor, “Target recognition performance as a function of sampling,” Proc. SPIE 4372, 74–84 (2001).
[CrossRef]

Kukkonen, H.

J. Rovamo, H. Kukkonen, and J. Mustonen, “Foveal optical modulation transfer function of the human eye at various pupil sizes,” J. Opt. Soc. Am. 15(9), 2504 (1998).
[CrossRef]

Legge, G. E.

G. E. Legge, D. Kersten, and A. E. Burgess, “Contrast discrimination in noise,” J. Opt. Soc. Am. 4(2), 391–404 (1987).
[CrossRef]

Lowry, E. M.

Lu, Z.-L.

Z.-L. Lu and B. A. Dosher, “Characterizing the spatial-frequency sensitivity of perceptual templates,” J. Opt. Soc. Am. 18(9), 2041–2053 (2001).
[CrossRef]

Mori, T.

A. Watanabe, T. Mori, S. Nagata, and K. Hiwatashi, “Spatial sine-wave responses of the human visual system,” Vision Res. 8(9), 1245–1263 (1968).
[CrossRef] [PubMed]

Moyer, S.

Moyer, S. K.

N. M. Devitt, R. G. Driggers, R. H. Vollmerhausen, S. K. Moyer, K. A. Krapels, and J. D. O’Connor, “Target recognition performance as a function of sampling,” Proc. SPIE 4372, 74–84 (2001).
[CrossRef]

Mustonen, J.

J. Rovamo, H. Kukkonen, and J. Mustonen, “Foveal optical modulation transfer function of the human eye at various pupil sizes,” J. Opt. Soc. Am. 15(9), 2504 (1998).
[CrossRef]

Nagaraja, N. S.

Nagata, S.

A. Watanabe, T. Mori, S. Nagata, and K. Hiwatashi, “Spatial sine-wave responses of the human visual system,” Vision Res. 8(9), 1245–1263 (1968).
[CrossRef] [PubMed]

Navarro, R.

P. Artal and R. Navarro, “Monochromatic modulation transfer function of the human eye for different pupil diameters: an analytic expression,” J. Opt. Soc. Am. 11(1), 246–249 (1994).
[CrossRef]

O’Connor, J. D.

N. M. Devitt, R. G. Driggers, R. H. Vollmerhausen, S. K. Moyer, K. A. Krapels, and J. D. O’Connor, “Target recognition performance as a function of sampling,” Proc. SPIE 4372, 74–84 (2001).
[CrossRef]

Patel, A. S.

Pelli, D. G.

Ratches, J. A.

J. A. Ratches, R. Vollmerhausen, and R. Driggers, “Target Acquisition Performance Modeling of Infrared Imaging Systems: Past, Present, and Future,” IEEE Sens. J. 1(1), 31–40 (2001).
[CrossRef]

Robinson, A. L.

Robson, J. G.

F. W. Campbell and J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197(3), 551–566 (1968).
[PubMed]

Rovamo, J.

J. Rovamo, H. Kukkonen, and J. Mustonen, “Foveal optical modulation transfer function of the human eye at various pupil sizes,” J. Opt. Soc. Am. 15(9), 2504 (1998).
[CrossRef]

V. Virsu and J. Rovamo, “Visual resolution, contrast sensitivity, and the cortical magnification factor,” Exp. Brain Res. 37(3), 475–494 (1979).
[CrossRef] [PubMed]

Stromeyer, C. F.

Valeton, J. M.

van Meeteren, A.

A. van Meeteren and J. M. Valeton, “Effects of pictorial noise interfering with visual detection,” J. Opt. Soc. Am. A 5(3), 438–444 (1988).
[CrossRef] [PubMed]

A. van Meeteren, “Calculations of the optical modulation transfer function of the human eye for white light,” Opt. Acta (Lond.) 21, 395–412 (1974).
[CrossRef]

A. van Meeteren and J. J. Vos, “Resolution and contrast sensitivity at low luminances,” Vision Res. 12(5), 825–833 (1972).
[CrossRef] [PubMed]

Van Nes, F. L.

Virsu, V.

V. Virsu and J. Rovamo, “Visual resolution, contrast sensitivity, and the cortical magnification factor,” Exp. Brain Res. 37(3), 475–494 (1979).
[CrossRef] [PubMed]

Vollmerhausen, R.

R. Vollmerhausen and A. L. Robinson, “Modeling target acquisition tasks associated with security and surveillance,” Appl. Opt. 46(20), 4209–4221 (2007).
[CrossRef] [PubMed]

J. A. Ratches, R. Vollmerhausen, and R. Driggers, “Target Acquisition Performance Modeling of Infrared Imaging Systems: Past, Present, and Future,” IEEE Sens. J. 1(1), 31–40 (2001).
[CrossRef]

R. Driggers, R. Vollmerhausen, and K. Krapels, “Target Identification Performance as a Function of Temporal and Fixed Pattern Noise,” Opt. Eng. 40(3), 443–447 (2001).
[CrossRef]

R. Vollmerhausen, “Incorporating Display Limitations into Night Vision Performance Models,” IRIS Passive Sensors 2, 11–31 (1995).

Vollmerhausen, R. H.

R. H. Vollmerhausen, S. Moyer, K. Krapels, R. G. Driggers, J. G. Hixson, and A. L. Robinson, “Predicting the probability of facial identification using a specific object model,” Appl. Opt. 47(6), 751–759 (2008).
[CrossRef] [PubMed]

R. H. Vollmerhausen, R. G. Driggers, and D. L. Wilson, “Predicting range performance of sampled imagers by treating aliased signal as target-dependent noise,” J. Opt. Soc. Am. A 25(8), 2055–2065 (2008).
[CrossRef]

R. H. Vollmerhausen, E. Jacobs, and R. Driggers, “New metric for predicting target acquisition performance,” Opt. Eng. 43(11), 2806–2818 (2004).
[CrossRef]

N. M. Devitt, R. G. Driggers, R. H. Vollmerhausen, S. K. Moyer, K. A. Krapels, and J. D. O’Connor, “Target recognition performance as a function of sampling,” Proc. SPIE 4372, 74–84 (2001).
[CrossRef]

R. H. Vollmerhausen, “Predicting the effect of gain, level, and sampling on minimum resolvable temperature measurements,” Opt. Eng. (to be published).

Vos, J. J.

A. van Meeteren and J. J. Vos, “Resolution and contrast sensitivity at low luminances,” Vision Res. 12(5), 825–833 (1972).
[CrossRef] [PubMed]

Watanabe, A.

A. Watanabe, T. Mori, S. Nagata, and K. Hiwatashi, “Spatial sine-wave responses of the human visual system,” Vision Res. 8(9), 1245–1263 (1968).
[CrossRef] [PubMed]

Wilson, D. L.

Appl. Opt. (2)

Exp. Brain Res. (1)

V. Virsu and J. Rovamo, “Visual resolution, contrast sensitivity, and the cortical magnification factor,” Exp. Brain Res. 37(3), 475–494 (1979).
[CrossRef] [PubMed]

IEEE Sens. J. (1)

J. A. Ratches, R. Vollmerhausen, and R. Driggers, “Target Acquisition Performance Modeling of Infrared Imaging Systems: Past, Present, and Future,” IEEE Sens. J. 1(1), 31–40 (2001).
[CrossRef]

IRIS Passive Sensors (1)

R. Vollmerhausen, “Incorporating Display Limitations into Night Vision Performance Models,” IRIS Passive Sensors 2, 11–31 (1995).

J. Opt. Soc. Am. (9)

N. S. Nagaraja, “Effect of Luminance Noise on Contrast Thresholds,” J. Opt. Soc. Am. 54(7), 950–955 (1964).
[CrossRef]

G. E. Legge, D. Kersten, and A. E. Burgess, “Contrast discrimination in noise,” J. Opt. Soc. Am. 4(2), 391–404 (1987).
[CrossRef]

J. Rovamo, H. Kukkonen, and J. Mustonen, “Foveal optical modulation transfer function of the human eye at various pupil sizes,” J. Opt. Soc. Am. 15(9), 2504 (1998).
[CrossRef]

F. L. Van Nes and M. A. Bouman, “Spatial modulation transfer in the human eye,” J. Opt. Soc. Am. 57(3), 401–406 (1967).
[CrossRef]

A. S. Patel, “Spatial resolution by the human visual system. The effect of mean retinal illuminance,” J. Opt. Soc. Am. 56(5), 689–694 (1966).
[CrossRef] [PubMed]

J. J. DePalma and E. M. Lowry, “Sine wave response of the visual system. II. Sine wave and square wave contrast sensitivity,” J. Opt. Soc. Am. 52(3), 328–335 (1962).
[CrossRef]

P. Artal and R. Navarro, “Monochromatic modulation transfer function of the human eye for different pupil diameters: an analytic expression,” J. Opt. Soc. Am. 11(1), 246–249 (1994).
[CrossRef]

C. F. Stromeyer and B. Julesz, “Spatial-frequency masking in vision: critical bands and spread of masking,” J. Opt. Soc. Am. 62(10), 1221–1232 (1972).
[CrossRef] [PubMed]

Z.-L. Lu and B. A. Dosher, “Characterizing the spatial-frequency sensitivity of perceptual templates,” J. Opt. Soc. Am. 18(9), 2041–2053 (2001).
[CrossRef]

J. Opt. Soc. Am. A (3)

J. Physiol. (2)

F. W. Campbell and J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197(3), 551–566 (1968).
[PubMed]

F. W. Campbell and R. W. Gubisch, “Optical quality of the human eye,” J. Physiol. 186(3), 558–578 (1966).
[PubMed]

Opt. Acta (Lond.) (1)

A. van Meeteren, “Calculations of the optical modulation transfer function of the human eye for white light,” Opt. Acta (Lond.) 21, 395–412 (1974).
[CrossRef]

Opt. Eng. (3)

R. H. Vollmerhausen, E. Jacobs, and R. Driggers, “New metric for predicting target acquisition performance,” Opt. Eng. 43(11), 2806–2818 (2004).
[CrossRef]

R. Driggers, R. Vollmerhausen, and K. Krapels, “Target Identification Performance as a Function of Temporal and Fixed Pattern Noise,” Opt. Eng. 40(3), 443–447 (2001).
[CrossRef]

R. H. Vollmerhausen, “Predicting the effect of gain, level, and sampling on minimum resolvable temperature measurements,” Opt. Eng. (to be published).

Proc. SPIE (2)

N. M. Devitt, R. G. Driggers, R. H. Vollmerhausen, S. K. Moyer, K. A. Krapels, and J. D. O’Connor, “Target recognition performance as a function of sampling,” Proc. SPIE 4372, 74–84 (2001).
[CrossRef]

P. G. J. Barten, “Formula for the contrast sensitivity of the human eye,” Proc. SPIE 5294, 231–238 (2004) (Paper available on the Web at http://www.SPIE.org).
[CrossRef]

RCA Review (1)

C. R. Carlson, “Sine-wave threshold contrast-sensitivity function: dependence on display size,” RCA Review 43, 675–683 (1982).

Vision Res. (2)

A. van Meeteren and J. J. Vos, “Resolution and contrast sensitivity at low luminances,” Vision Res. 12(5), 825–833 (1972).
[CrossRef] [PubMed]

A. Watanabe, T. Mori, S. Nagata, and K. Hiwatashi, “Spatial sine-wave responses of the human visual system,” Vision Res. 8(9), 1245–1263 (1968).
[CrossRef] [PubMed]

Other (13)

R. J. Beaton, and W. W. Farley, “Comparative study of the MTFA, ICS, and SQRI image quality metrics for visual display systems,” Armstrong Lab., Air Force Systems Command, Wright-Patterson AFB, OH, Report AL-TR-1992–0001, DTIC ADA252116, (1991).

J. Raymond, Stefanik, Performance modeling for image intensifier systems, Report NV-93–14, Night Vision and Electronic-Sensors Directorate, U.S. Army Research, Development, and Engineering Command, Fort Belvoir, VA, (1993).

Ian Overington, Vision and Acquisition, (Crane, Russak & Company, 1976), Chapters 1,2,4.

G. J. Peter, Barten, Contrast Sensitivity of the Human Eye and Its Effect on Image Quality, (SPIE Press, Bellingham, WA, 1999).

R. A. Moses and W. M. Hart, “The temporal responsiveness of vision,’ in Adler’s Physiology of the Eye: Clinical Application, (Mosby 1987).

H. Davson, Physiology of the Eye, 5th ed., 221 & 271, (Macmillan Academic and Professional Ltd., 1990).

Kenneth R. Boss and Janet E. Lincoln, Engineering Data Compendium: Human Perception and Performance, Vol. 1, Harry G. Armstrong Medical Research Laboratory, Wright-Patterson Air Force Base, Ohio, (1988).

R. H. Vollmerhausen, E. Jacobs, J. Hixson, and M. Friedman, “The Targeting Task Performance (TTP) Metric; A New Model for Predicting Target Acquisition Performance,” Technical Report AMSEL-NV-TR-230, U.S. Army CERDEC, Fort Belvoir, VA 22060, (2005).

U. S. Army, RDECOM, NVESD target acquisition models (1 June 2009), https://www.sensiac.org

H. Richard, Vollmerhausen, “Modeling the Performance of Imaging Sensors,” In Electro-Optical Imaging: System Performance and Modeling, Lucien Biberman Ed., (SPIE Press, 2000), Chapter 12.

Harry L. Synder, “Image quality: measure and visual performance,” in Flat-Panel Display and CRTs, Lawrence E. Tannas, Jr., Ed., (Van Nostrand Reinhold, 1985), Chapter 4.

M. Raghavan, “Sources of visual noise,” Ph.D. dissertation (Syracuse Univ., Syracuse, New York, 1989).

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Figures (17)

Fig. 1
Fig. 1

Experimental setup for measuring CTF/CSF. Top right shows variation in contrast. Bottom right shows variation in spatial frequency.

Fig. 2
Fig. 2

Engineering model of eye showing the spatial filters and noise sources acting on the display signal and noise.

Fig. 3
Fig. 3

Numerical CSF compared to the data of van Meeteren and Vos [27].

Fig. 5
Fig. 5

Numerical CSF compared to the data of DePalma and Lowry [28].

Fig. 6
Fig. 6

Numerical CSF compared to the data of Van Nes and Bouman [30].

Fig. 4
Fig. 4

Numerical CSF compared to the data of Watanabe, Mori, Nagata, and Hiwatashi [29].

Fig. 7
Fig. 7

The figure shows relative improvement in CSF as the number of sine wave cycles presented to the observer increases. There is little improvement after about 10 cycles.

Fig. 8
Fig. 8

CSF data at 10 degree and 2 degree FOV. The dashed lines show numerical CSF predictions. Note that the numerical fit does not predict CSF equal at and above 0.25 mrad−1. The solid line (cycle fit) show the 10 degree CSF data degraded by the amount indicated in Fig. 7.

Fig. 9
Fig. 9

MTF of eyeball ocular optics from various sources. Pupil size is 4 mm.MTF for a 4 mm pupil.

Fig. 10
Fig. 10

Optical, retinal, and tremor. Optical MTF data for a 4 mm pupil are also shown [37].

Fig. 11
Fig. 11

Comparison of Eq. (14) model to medium grain noise data from [11].

Fig. 12
Fig. 12

Comparison of Eq. (14) model to coarse grain noise data from [11] Fig. 13.

Fig. 13
Fig. 13

Comparison of Eq. (14) model to data for noise bands 1 and 3 in Table 3 [40].

Fig. 16
Fig. 16

Comparison of Eq. (14) model 4 in to data for noise band 5 in Table 3 [40].

Fig. 17
Fig. 17

Model versus data for low pass filters. The line represents a perfect fit between data on the ordinate and predictions on the abscissa.

Fig. 14
Fig. 14

Comparison of Eq. (14) model to data for noise band 2 in Table 3 [40].

Fig. 15
Fig. 15

Comparison of Eq. (14) model to data for noise band 4 in Table 3 [40].

Tables (3)

Tables Icon

Table 1 Pupil diameter in millimeters (mm) versus light level

Tables Icon

Table 2 Parameters for optics MTF.

Tables Icon

Table 3 Parameters for band pass filters [40]

Equations (25)

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

Θ=[δ(Ctgt(ξ,η,range)CTFsys(ξ,η))(Ctgt(ξ,η,range)CTFsys(ξ,η))ndξdηξrηrRng2]1/2
PID(Φ/Φ84)=erf(Φ/Φ84)=2π0Φ/Φ84et2dt
Φ=[δ(CTGTCTFsys(ξ))CTGTCTFsys(ξ)dξRngδ(CTGTCTFsys(η))CTGTCTFsys(η)dηRng]1/2
CTF(ξ,η)  CTF(ξ)  CTF(η)and thereforeCTFsys(ξ,η)CTFsys(ξ)CTFsys(η)
CTFsys2(ξ)=CTF2(ξ)(neye2(ξ)+σ2(ξ)neye2(ξ))
CTFsys2(ξ)=CTF2(ξ)(1+α2σ2(ξ)L2)
CTF(ξ)=[aξebξ1+0.06ebξ]1
a=540(1+0.2L)0.2/(1+12w2(1+5.8   ξ)2)
b=5.24(1+29.2L)0.15
MTFoptics=exp((ξ/f0)i0)
MTFretina=exp(0.375ξ1.21)
MTFtremer=exp(0.4441ξ2)
B(ξ')=exp{2.2[log(ξ'/ξ)]2}
CTFsys(ξ)=CTF(ξ/SMAG)Hsys(ξ)(1+α2σ2(ξ)   L2)1/2
σ2(ξ)=|B(ξ'/ξ)   D(ξ')Heye(ξ')|2|D(η)Heye(η)|2ρ2(ξ,η)dξ'dη
CTFsys2(ξ)=1H(ξ)(CTF2(ξ)+β2σ2(ξ)L2)
CTFsys(ξ)=CTF(ξ)(1+α2ρ2(ξ)   L2)1/2
CTFsys(ξ)=CTF(ξ)(1+κ2m2(ξ)teyeFR   teye2FR2L2)1/2
CTFsys(ξ)=CTF(ξ)(1+α2m2(ξ)/FR   L2)1/2
CTFsys(ξ)=CTF(ξ)(1+   κ2   (ξ)teyeEphototeye2Ephoto2)1/2
CTFsys(ξ)=CTF(ξ)(1+   α2   (ξ)EphotoEphoto2)1/2
noise to signal = Γdet/teyeS
noise to signal =       Ephoto/teyeEphoto
αthermal=α/teye
CTFsys(ξ)=CTF(ξ)(1+αthermal2(ξ)Γdet2S2)1/2

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