When filters of unequal optical density are placed in front of the two eyes, a target which is actually oscillating in a frontoparallel plane appears nearer than it really is for one direction of stroke and farther than it really is for the return stroke (Pulfrich stereophenomenon). Measurements of the near and far displacements of an oscillating black vertical rod are obtained as functions of (a) target thickness, (b) target velocity, and (c) condition of unequal binocular retinal illuminance.
The experimental data show that variation in target thickness has no effect on the magnitude of the apparent near and far displacements. Variations in target velocity and in condition of unequal binocular retinal illuminance produce characteristic effects which are shown to be in good quantitative agreement with geometrical predictions based on the theory of the Pulfrich stereophenomenon. Discrepancies in the magnitude of the displacements at low target velocities are noted and discussed.
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Depth displacements obtained under a given condition of unequal binocular retinal illuminance for six target thicknesses (diameters) and eight target velocities. The retinal illuminance of the left eye is 2.06 log trolands and that of the right eye is 3.13 log trolands. CN and CF refer, respectively, to the near and far displacements of a target oscillating at the specified linear velocities in a frontoparallel plane located 100 cm from the observer’s eyes. Each entry for the two observers (F.C. and M.M.) is based on the mean of 12 settings.
Target thickness
Target velocity (cm/sec)
Observer
0.031 in.
0.050 in.
0.080 in.
0.125 in.
0.230 in.
0.460 in.
CN (cm)
CF (cm)
CN (cm)
CF (cm)
CN (cm)
CF (cm)
CN (cm)
CF (cm)
CN (cm)
CF (cm)
CN (cm)
CF (cm)
2.59
F.C.
0.71
0.47
0.56
0.67
0.64
0.54
0.69
0.57
0.67
0.68
0.52
0.69
M.M.
0.73
0.68
0.75
0.58
0.72
0.72
0.80
0.76
0.74
0.82
0.74
0.89
5.90
F.C.
1.29
1.01
1.29
1.15
1.30
1.03
1.37
1.17
1.45
1.15
1.34
1.18
M.M.
1.27
1.22
1.35
1.23
1.26
1.31
1.42
1.49
1.36
1.42
1.49
1.60
8.16
F.C.
1.81
1.22
1.74
1.45
1.77
1.22
1.67
1.36
1.73
1.36
1.70
1.43
M.M.
1.78
1.66
1.81
1.69
1.64
1.65
1.71
1.67
1.80
1.88
1.76
2.01
10.28
F.C.
2.30
1.58
2.08
1.63
2.13
1.53
2.08
1.52
2.03
1.54
2.31
1.71
M.M.
2.09
2.01
2.12
1.73
2.12
1.94
2.06
2.01
2.36
2.07
2.31
2.43
13.76
F.C.
2.76
1.88
2.58
1.99
2.68
1.96
2.55
1.84
2.66
1.96
2.69
2.26
M.M.
3.02
2.49
2.71
2.18
2.46
2.38
2.46
2.37
2.79
2.76
2.88
2.98
19.96
F.C.
4.05
2.40
3.79
2.54
3.74
2.34
3.48
2.55
3.73
2.46
3.47
2.55
M.M.
3.99
3.59
3.69
3.15
3.49
3.46
3.25
3.03
3.35
3.24
3.81
4.16
35.56
F.C.
6.46
3.37
5.98
4.01
5.79
3.74
5.43
3.68
5.45
3.55
5.70
3.65
M.M.
5.17
5.32
5.37
6.17
5.07
6.07
4.62
5.35
4.65
6.13
5.07
5.93
68.17
F.C.
11.26
3.67
9.57
6.72
10.21
7.40
9.19
6.29
8.99
6.62
9.42
6.27
M.M.
6.45
9.08
6.65
11.21
6.50
12.19
5.93
10.09
5.43
12.38
5.75
12.39
Table II
Depth displacements obtained under three conditions of unequal binocular retinal illuminance, log(ER/EL), for two target thicknesses (diam) and eight target velocities. The retinal illuminance of the left eye, logEL, is kept constant at 2.06 log trolands. CN and CF refer, respectively, to the near and far displacements of a target oscillating in a frontoparallel plane located 100 cm from the observer’s eyes. Each entry is based on the mean of 12 settings obtained from observer M.M.
The negative sign is used to indicate that the localized near position of the oscillating target lies farther from the observer than does the actual plane of oscillation.
Table III
Average latency difference 〈Δt〉 as a function of target thickness (diam) and target velocity. Each entry represents the average of the near and far latency differences (ΔtN and ΔtF) computed from Eq. (4) for each set of values of the near and far displacements (CN and CF) obtained from observer M.M. The retinal illuminance of the left eye, logEL, is kept constant at 2.06 log trolands. The latency differences are given in msec.
The values listed in these columns for target thicknesses 0.031 and 0.460 were computed from the data given in Table II of this report; the values reported for target thickness 0.125 were computed from the data given in Table I of a previous report.4
All values listed in this column were computed from the data given in Table I of this report.
Tables (3)
Table I
Depth displacements obtained under a given condition of unequal binocular retinal illuminance for six target thicknesses (diameters) and eight target velocities. The retinal illuminance of the left eye is 2.06 log trolands and that of the right eye is 3.13 log trolands. CN and CF refer, respectively, to the near and far displacements of a target oscillating at the specified linear velocities in a frontoparallel plane located 100 cm from the observer’s eyes. Each entry for the two observers (F.C. and M.M.) is based on the mean of 12 settings.
Target thickness
Target velocity (cm/sec)
Observer
0.031 in.
0.050 in.
0.080 in.
0.125 in.
0.230 in.
0.460 in.
CN (cm)
CF (cm)
CN (cm)
CF (cm)
CN (cm)
CF (cm)
CN (cm)
CF (cm)
CN (cm)
CF (cm)
CN (cm)
CF (cm)
2.59
F.C.
0.71
0.47
0.56
0.67
0.64
0.54
0.69
0.57
0.67
0.68
0.52
0.69
M.M.
0.73
0.68
0.75
0.58
0.72
0.72
0.80
0.76
0.74
0.82
0.74
0.89
5.90
F.C.
1.29
1.01
1.29
1.15
1.30
1.03
1.37
1.17
1.45
1.15
1.34
1.18
M.M.
1.27
1.22
1.35
1.23
1.26
1.31
1.42
1.49
1.36
1.42
1.49
1.60
8.16
F.C.
1.81
1.22
1.74
1.45
1.77
1.22
1.67
1.36
1.73
1.36
1.70
1.43
M.M.
1.78
1.66
1.81
1.69
1.64
1.65
1.71
1.67
1.80
1.88
1.76
2.01
10.28
F.C.
2.30
1.58
2.08
1.63
2.13
1.53
2.08
1.52
2.03
1.54
2.31
1.71
M.M.
2.09
2.01
2.12
1.73
2.12
1.94
2.06
2.01
2.36
2.07
2.31
2.43
13.76
F.C.
2.76
1.88
2.58
1.99
2.68
1.96
2.55
1.84
2.66
1.96
2.69
2.26
M.M.
3.02
2.49
2.71
2.18
2.46
2.38
2.46
2.37
2.79
2.76
2.88
2.98
19.96
F.C.
4.05
2.40
3.79
2.54
3.74
2.34
3.48
2.55
3.73
2.46
3.47
2.55
M.M.
3.99
3.59
3.69
3.15
3.49
3.46
3.25
3.03
3.35
3.24
3.81
4.16
35.56
F.C.
6.46
3.37
5.98
4.01
5.79
3.74
5.43
3.68
5.45
3.55
5.70
3.65
M.M.
5.17
5.32
5.37
6.17
5.07
6.07
4.62
5.35
4.65
6.13
5.07
5.93
68.17
F.C.
11.26
3.67
9.57
6.72
10.21
7.40
9.19
6.29
8.99
6.62
9.42
6.27
M.M.
6.45
9.08
6.65
11.21
6.50
12.19
5.93
10.09
5.43
12.38
5.75
12.39
Table II
Depth displacements obtained under three conditions of unequal binocular retinal illuminance, log(ER/EL), for two target thicknesses (diam) and eight target velocities. The retinal illuminance of the left eye, logEL, is kept constant at 2.06 log trolands. CN and CF refer, respectively, to the near and far displacements of a target oscillating in a frontoparallel plane located 100 cm from the observer’s eyes. Each entry is based on the mean of 12 settings obtained from observer M.M.
The negative sign is used to indicate that the localized near position of the oscillating target lies farther from the observer than does the actual plane of oscillation.
Table III
Average latency difference 〈Δt〉 as a function of target thickness (diam) and target velocity. Each entry represents the average of the near and far latency differences (ΔtN and ΔtF) computed from Eq. (4) for each set of values of the near and far displacements (CN and CF) obtained from observer M.M. The retinal illuminance of the left eye, logEL, is kept constant at 2.06 log trolands. The latency differences are given in msec.
The values listed in these columns for target thicknesses 0.031 and 0.460 were computed from the data given in Table II of this report; the values reported for target thickness 0.125 were computed from the data given in Table I of a previous report.4
All values listed in this column were computed from the data given in Table I of this report.