Abstract

A detailed theory of the detection of sinusoidal gratings displayed with suprathreshold luminous fluctuations is developed by employing a previous model of the visual and decision-making systems. An important feature of the model is the organization of the photoreceptors and decision-making system into a set of parallel, independent photoreceptive field (PRF)-decision center channels that function like a set of parallel spatial-frequency filters, each associated with an independent threshold detector. A technique is proposed for determining the modulation sensitivity functions (MSFs) of single detection channels by obtaining threshold modulation (MTN) data at a fixed sinusoidal grating frequency (ν) while varying the center frequency (νc) of narrow-band luminous fluctuations caused by video noise (VN). The theory predicts that the ratio, at a given ν, of MTN obtained as a function of νc to the MTN obtained without VN is proportional to the MSF of the particular channel for which the widths of the excitatory and inhibitory regions of the PRF equal a half-period of ν. Good agreement between theoretical curves and experimental data appearing in the literature provides strong corroboration of the theory.

© 1976 Optical Society of America

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References

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  1. A. D. Schnitzler, J. Opt. Soc. Am. 66, 608 (1976).
    [Crossref] [PubMed]
  2. E. W. H. Selwyn and J. L. Tearle, Proc. Phys. Soc. Lond. 58, 33 (1946).
    [Crossref]
  3. See Perception of Displayed Information, edited by L. M. Biberman (Plenum, New York, 1973), p. 4.
  4. A. D. Schnitzler, J. Opt. Soc. Am. 63, 1357 (1973).
    [Crossref] [PubMed]
  5. D. H. Kelly, Vision Res. 12, 89 (1972).
    [Crossref] [PubMed]
  6. O. H. Schade, J. Opt. Soc. Am. 46, 721 (1956).
    [Crossref] [PubMed]
  7. F. W. Campbell and J. G. Robson, J. Physiol. (Lond.) 197, 551 (1968).
  8. C. Enroth-Cugell and J. G. Robson, J. Physiol. (Lond.) 187, 517 (1966).
  9. D. H. Kelly and R. E. Savoie, Perception and Psychophysics 14, 313 (1973).
    [Crossref]
  10. C. Blakemore and F. W. Campbell, J. Physiol. (Lond.) 203, 237 (1969).
  11. H. Pollehn and H. Roehrig, J. Opt. Soc. Am. 60, 842 (1970).
    [Crossref] [PubMed]
  12. The small signal transconductance in Eq. (9) depends on the bias votlage. The nonlinear relationship between beam current IB and bias voltage VG can be represented by IB=gm′VGγ, where gm′ is independent of VG and γ is typically 2.5–3.0. In terms of gm′ and γ the small signal current-voltage relationship is ΔIB=γgm′VGγ-1ΔVG. Thus by comparing with Eq. (9), gm=γgm′VGγ-1. Note, by Eqs. (9) and (10), that gm cancels informing the signal-to-noise ratio.
  13. F. W. Campbell and R. W. Gubisch, J. Physiol. (Lond.) 186, 558 (1966).

1976 (1)

1973 (2)

A. D. Schnitzler, J. Opt. Soc. Am. 63, 1357 (1973).
[Crossref] [PubMed]

D. H. Kelly and R. E. Savoie, Perception and Psychophysics 14, 313 (1973).
[Crossref]

1972 (1)

D. H. Kelly, Vision Res. 12, 89 (1972).
[Crossref] [PubMed]

1970 (1)

1969 (1)

C. Blakemore and F. W. Campbell, J. Physiol. (Lond.) 203, 237 (1969).

1968 (1)

F. W. Campbell and J. G. Robson, J. Physiol. (Lond.) 197, 551 (1968).

1966 (2)

C. Enroth-Cugell and J. G. Robson, J. Physiol. (Lond.) 187, 517 (1966).

F. W. Campbell and R. W. Gubisch, J. Physiol. (Lond.) 186, 558 (1966).

1956 (1)

1946 (1)

E. W. H. Selwyn and J. L. Tearle, Proc. Phys. Soc. Lond. 58, 33 (1946).
[Crossref]

Blakemore, C.

C. Blakemore and F. W. Campbell, J. Physiol. (Lond.) 203, 237 (1969).

Campbell, F. W.

C. Blakemore and F. W. Campbell, J. Physiol. (Lond.) 203, 237 (1969).

F. W. Campbell and J. G. Robson, J. Physiol. (Lond.) 197, 551 (1968).

F. W. Campbell and R. W. Gubisch, J. Physiol. (Lond.) 186, 558 (1966).

Enroth-Cugell, C.

C. Enroth-Cugell and J. G. Robson, J. Physiol. (Lond.) 187, 517 (1966).

Gubisch, R. W.

F. W. Campbell and R. W. Gubisch, J. Physiol. (Lond.) 186, 558 (1966).

Kelly, D. H.

D. H. Kelly and R. E. Savoie, Perception and Psychophysics 14, 313 (1973).
[Crossref]

D. H. Kelly, Vision Res. 12, 89 (1972).
[Crossref] [PubMed]

Pollehn, H.

Robson, J. G.

F. W. Campbell and J. G. Robson, J. Physiol. (Lond.) 197, 551 (1968).

C. Enroth-Cugell and J. G. Robson, J. Physiol. (Lond.) 187, 517 (1966).

Roehrig, H.

Savoie, R. E.

D. H. Kelly and R. E. Savoie, Perception and Psychophysics 14, 313 (1973).
[Crossref]

Schade, O. H.

Schnitzler, A. D.

Selwyn, E. W. H.

E. W. H. Selwyn and J. L. Tearle, Proc. Phys. Soc. Lond. 58, 33 (1946).
[Crossref]

Tearle, J. L.

E. W. H. Selwyn and J. L. Tearle, Proc. Phys. Soc. Lond. 58, 33 (1946).
[Crossref]

J. Opt. Soc. Am. (4)

J. Physiol. (Lond.) (4)

C. Blakemore and F. W. Campbell, J. Physiol. (Lond.) 203, 237 (1969).

F. W. Campbell and R. W. Gubisch, J. Physiol. (Lond.) 186, 558 (1966).

F. W. Campbell and J. G. Robson, J. Physiol. (Lond.) 197, 551 (1968).

C. Enroth-Cugell and J. G. Robson, J. Physiol. (Lond.) 187, 517 (1966).

Perception and Psychophysics (1)

D. H. Kelly and R. E. Savoie, Perception and Psychophysics 14, 313 (1973).
[Crossref]

Proc. Phys. Soc. Lond. (1)

E. W. H. Selwyn and J. L. Tearle, Proc. Phys. Soc. Lond. 58, 33 (1946).
[Crossref]

Vision Res. (1)

D. H. Kelly, Vision Res. 12, 89 (1972).
[Crossref] [PubMed]

Other (2)

See Perception of Displayed Information, edited by L. M. Biberman (Plenum, New York, 1973), p. 4.

The small signal transconductance in Eq. (9) depends on the bias votlage. The nonlinear relationship between beam current IB and bias voltage VG can be represented by IB=gm′VGγ, where gm′ is independent of VG and γ is typically 2.5–3.0. In terms of gm′ and γ the small signal current-voltage relationship is ΔIB=γgm′VGγ-1ΔVG. Thus by comparing with Eq. (9), gm=γgm′VGγ-1. Note, by Eqs. (9) and (10), that gm cancels informing the signal-to-noise ratio.

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Figures (5)

FIG. 1
FIG. 1

Theoretical curves of relative modulation sensitivity versus log frequency ν. Dot, dash–dot, and dash curves represent single detection channels for which the widths, α of excitatory and inhibitory regions equal 2.25, 1.5, and 0.75 mrad, respectively. Solid curve, tangent to single channel curves at ν = 1/2α, represent overall system.

FIG. 2
FIG. 2

Experimental curves of threshold elevation due to narrow-band suprathreshold luminous fluctuations versus log center frequency of band (Ref. 11). Solid and dash curves correspond to grating frequency equal to 0.403 and 0.672 c/mrad, respectively.

FIG. 3
FIG. 3

Functional block diagram of composite CRT display-human visual system. Note lower part of figure represents one of a set of parallel independent detection channels.

FIG. 4
FIG. 4

Threshold elevation ratio versus log center frequency of narrow-band suprathreshold luminous fluctuations. Data points (Ref. 11), triangle, circle, and square, obtained at grating frequency equal to 0.0258, 0.403, and 0.672 c/mrad, respectively. Video noise voltage amplitude and bandwidth equal to 1v and 200 kHZ, respectively. Dot curve is graph of Eq. (37c). Solid and dash curves are graphs of Eq. (37a).

FIG. 5
FIG. 5

Log threshold modulation versus log grating frequency. Solid curves are theoretical. Dash curves are experimental (Ref. 11). Video noise voltage amplitude indicated on graphs, bandwidth equal to 5 MHz. Theoretical curve fitted to experimental curve at VN = 0 with one adjustable parameter. Theoretical curve at VN = 1v was predicted by previously determined parameters.

Equations (43)

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g ( t ) = ( 1 / τ ) exp ( - t / τ ) ,
G ( f t ) = ( 1 - i 2 π f t τ ) / ( 1 + 4 π 2 f t 2 τ 2 ) ,
g ( x , y ) = 1 , - w / 2 x w / 2 , g ( x , y ) = - 0.5 , - 3 w / 2 x - w / 2 , w / 2 x 3 w / 2 ,
G ( f x , f y ) = 2 [ sin 3 ( π f x w ) sin ( π f y h ) ] / π 2 f x f y ,
M T N ( ν , α ) = ( 3 / π ) m F / T 0 ( ν ) G ( ν , α ) ,
m = π k T / D ( π R L ¯ τ ) 1 / 2 ,
G ( ν , α ) = 2 F [ sin 3 ( π ν α ) ] / π ν .
M T N ( ν ) = 3 m ν / 2 T 0 ( ν ) ,             1 / 2 α F ν ,
M T N ( ν ) = 3 m ν / 2 T 0 ( ν ) sin 3 ( π ν α F ) ,             ν 1 / 2 α F ,
I ( f t ) = g m V s ( f t ) ,
ϕ I ( f t ) = g m 2 ϕ N ( f t ) ,
q I ( f x ) = T B ( f x ) I ( f t ) / v ,
ϕ Q ( f x ) = ( 1 / v ) T B ( f x ) 2 ϕ I ( f t ) .
q L ( f x ) = K ξ T P ( f x ) q I ( f x ) ,
ϕ L ( f x ) = K 2 ξ 2 T P ( f x ) 2 ϕ Q ( f x ) ,
q E ( f x ) = ( ζ / m ) T 0 ( f x ) q L ( f x ) ,
ϕ E ( f x ) = ( ζ 2 / m ) T 0 ( f x ) 2 ϕ L ( f x ) ,
q i ( f x ) = R q E ( f x ) ,
ϕ i ( f x ) = R 2 ϕ E ( f x ) ,
q 0 ( f x ) = G ( f x , w ) q i ( f x ) ,
ϕ 0 ( f x ) = G ( f x , w ) 2 ϕ i ( f x ) ,
s 0 k ( f x , t ) = q 0 ( f x ) g ( t ) ,
n 0 k ( t ) = δ q 0 k g ( t ) ,
S 0 ( f x ) = j = 0 N F k = 0 N P q 0 ( f x ) g ( j t f ) ,
N 0 = j = 0 N F k = 0 N P δ q 0 k g ( j t f ) ,
S 0 ( f x ) = N P q 0 ( f x ) / τ [ 1 - exp ( - t f / τ ) ] ,
σ 0 2 = N P σ 01 2 / τ 2 [ 1 - exp ( - 2 t f / τ ) ] ,
σ 01 2 = - ϕ 0 ( f x ) d f x ,
k 0 ( ν , α ) = ( e v e H α τ / Ω D ) 1 / 2 × ( T D ( ν ) T 0 ( ν ) G ( ν , α ) 2 V N 2 ν 2 ν 1 T D ( ν ) T 0 ( ν ) G ( ν , α ) 2 ϕ N ( f t ) d ν ) 1 / 2 k V ,
M T ( ν ) = β T D ( ν ) V s ( f t ) ,
M T N ( ν , α ) = ( m V / π ) [ 2 ϑ ( α ) / α T 0 ( ν ) G ( ν , α ) 2 ] 1 / 2 ,
m V = ( π / 2 ) k T β V N ( Ω D / e v e H τ Δ f n ) 1 / 2 ,
ϑ ( α ) = ν 1 ν 2 T D ( ν ) T 0 ( ν ) G ( ν , α ) 2 [ ϕ N ( f t ) / ϕ ¯ N ] d ν .
[ ϑ ( α ) ] T D ( ν c ) T 0 ( ν c ) G ( ν c , α ) 2 Δ ν N .
M T N ( ν c , ν ) = ( m v / π ) ( 4 ν Δ ν N ) 1 / 2 T D ( ν c ) T 0 ( ν c ) × G ( ν c , ν ) / T 0 ( ν ) G ( ν ) ,
M T N ( ν c , ν , α F ) = ( m v / π ) ( 2 Δ ν N / α F ) 1 / 2 T D ( ν c ) T 0 ( ν c ) × G ( ν c , α F ) / T 0 ( ν ) G ( ν , α F ) ,
G ( ν c , ν ) = ( 3 / π ) m F M T N - 1 ( ν c , ν ) / T 0 ( ν c ) ,
M T N ( ν ) = ( 3 / π ) m F / T 0 ( ν ) G ( ν ) .
ρ ( ν c , ν ) = ( m ν / π ) ( 4 ν Δ ν N ) 1 / 2 T D ( ν c ) M T N - 1 ( ν c , ν ) .
ρ ( ν c , ν ) = ( 2 m v / 3 m ) ( Δ ν N / ν ) 1 / 2 T D ( ν c ) T 0 ( ν c ) × [ sin 3 ( π ν c / 2 ν ) ] / ( π ν c / 2 ν ) ,             1 / 2 α F ν ,
ρ ( ν c , ν ) = ( 2 m v / 3 m ) ( Δ ν N / ν ) 1 / 2 sin 3 ( π ν α F ) T D ( ν c ) T 0 ( ν c ) × [ sin 3 ( π ν c / 2 ν ) ] / ( π ν c / 2 ν ) ,             1 / 2 α F ν 1 / 2 α F ,
ρ ( ν c , ν ) = ( 2 m v / 3 m ) ( 2 α F Δ ν N ) 1 / 2 sin 3 ( π ν α F ) sin 3 ( π ν α F ) T D ( ν c ) T 0 ( ν c ) × [ sin 3 ( π ν c α F ) ] / ( π ν c α F ) ,             ν 1 / 2 α F .
T D ( ν ) = exp [ - ( ν / 1.74 ) 2 ] .