Table 2
Computed data for plotting iso-magnification curves and transformation graphs.
| | 4.94 D | |
---|
| | | Left field | | b=20.0 cm | Right field |
---|
|
---|
Lane | | 16° | 12° | 8° | 4° | 2° | 1° | 0 | 1° | 2° | 4° | 8° | 12° | 16° |
---|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
---|
Distance from frontal plane for percent increase of longitudinal angles of O.D. mm | 0% | −14.79 | − 8.42 | − 3.77 | −0.95 | −0.24 | −0.06 | | −0.06 | −0.24 | −0.95 | − 3.77 | − 8.42 | −14.79 |
3% | −19.15 | −11.90 | − 6.20 | −2.20 | −0.87 | −0.38 | | 0.25 | 0.40 | 0.35 | − 1.28 | − 4.82 | −10.20 |
8% | −26.18 | −17.40 | −10.00 | −4.18 | −1.90 | −0.90 | | 0.80 | 1.48 | 2.40 | 2.80 | 1.25 | − 2.45 |
−3% | −10.05 | − 4.70 | − 1.20 | 0.35 | 0.40 | 0.25 | | −0.38 | −0.90 | −2.20 | − 6.26 | −12.00 | −19.25 |
−8% | − 1.30 | 2.10 | 3.40 | 2.62 | 1.48 | 0.75 | | −0.90 | −1.90 | −4.40 | −10.50 | −17.80 | −26.40 |
| | | | | 2.500 D | |
---|
| | | Left field | | b=40.4 cm | Right field |
---|
|
---|
Lane | | 16° | 12° | 8° | 4° | 2° | 1° | 0 | 1° | 2° | 4° | 8° | 12° | 16° |
---|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
---|
Distance from frontal plane for percent increase of longitudinal angles of O.D. mm | 0% | −30.5 | −17.36 | −7.78 | −1.95 | −0.49 | −0.12 | | −0.12 | −0.49 | −1.95 | −7.78 | −17.36 | −30.5 |
2% | | −26.8 | −14.3 | −5.4 | −2.20 | −0.99 | | 0.70 | 1.20 | 1.53 | −0.9 | −7.3 | −17.7 |
4% | | | −20.6 | −8.65 | −3.85 | −1.85 | | 1.60 | 2.98 | 5.0 | 6.1 | 3.0 | −4.6 |
−2% | −17.5 | −7.1 | −0.8 | 1.6 | 1.30 | 0.79 | | −1.00 | −2.22 | −5.4 | −14.5 | −26.9 | |
−4% | −3.4 | 3.9 | 6.6 | 5.3 | 3.17 | 1.68 | | −1.90 | −4.00 | −8.9 | −21.1 | | |
| | | | | 1.33 D | |
---|
| | | Left field | | b=75.6 cm | Right field |
---|
|
---|
Lane | | 16° | 12° | 8° | 4° | 2° | 1° | 0 | 1° | 2° | 4° | 8° | 12° | 16° |
---|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
---|
Distance from frontal plane for percent increase of longitudinal angles of O.D. mm | 0% | | −32.7 | −14.63 | −3.68 | −0.92 | −0.23 | | −0.23 | −0.92 | −3.68 | −14.63 | −32.7 | |
1% | | | −26.45 | −9.65 | −3.92 | −1.73 | | 1.22 | 2.20 | 2.45 | −2.45 | −15.2 | −35.8 |
2.5% | | | | −18.40 | −8.40 | −3.95 | | 3.51 | 6.82 | 11.65 | 16.00 | 12.5 | 0.4 |
−1% | −34.8 | −15.0 | −2.40 | 2.55 | 2.20 | 1.30 | | −1.70 | −3.99 | −9.80 | −26.40 | | |
−2.5% | 1.9 | 13.5 | 16.80 | 12.15 | 6.98 | 3.70 | | −4.05 | −8.62 | −18.90 | | | |
| | | 0.164 D | |
---|
| | Left field | b=6.1 m | Right field |
---|
|
---|
Lane | | 15° | 10° | 5° | 0 | 5° | 10° | 15° |
---|
|
|
|
|
|
|
|
|
|
---|
Distance from frontal plane for percent increase of longitudinal angles of O.D. cm | 0% | −40.9 | −18.4 | −4.7 | | −4.7 | −18.4 | −40.9 |
0.25% | −73.8 | −41.7 | −16.8 | | 8.0 | 6.9 | −3.5 |
0.50% | −103.0 | −63.1 | −28.5 | | 21.2 | 34.4 | 39.0 |
1.00% | −152.9 | −101.6 | −50.5 | | 49.4 | 97.7 | 145.1 |
−0.25% | −3.5 | 6.9 | 8.0 | | −16.8 | −41.7 | −73.8 |
−0.50% | 39.0 | 34.4 | 21.2 | | −28.5 | −63.1 | −103.0 |
−1.00% | 145.1 | 97.7 | 49.4 | | −50.5 | −101.6 | −152.9 |
Table 3
Apparent frontal plane (horopter) data for K.N.O. No refractive error. Fixation distance=404 mm (2.5 D). The number of settings for each lane is approximately 80.
Lane | 16° | 12° | 8° | 4° | 2° | 1° | 0 | 1° | 2° | 4° | 8° | 12° | 16° |
---|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
---|
Readings mm | −5.45 | −3.20 | −1.35 | −0.19 | +0.26 | +0.11 | | −0.14 | −0.32 | −1.16 | −3.38 | −6.56 | −9.64 |
Mean deviation ± | 1.45 | 0.82 | 0.48 | 0.23 | 0.14 | 0.12 | | 0.11 | 0.21 | 0.31 | 0.59 | 0.89 | 1.62 |
Percent value from iso-mag. curves | −3.73% | −2.75% | −1.84% | −1.02% | −0.85% | −0.60% | | 0.00% | 0.20% | 0.47% | 1.29% | 2.15% | 3.25% |
Percent value of mean deviation ± | 0.20% | 0.16% | 0.14% | 0.13% | 0.16% | 0.34% | | 0.31% | 0.25% | 0.18% | 0.18% | 0.17% | 0.22% |
Table 4
Data for the apparent frontal plane of Helmholtz and the computed value of H for each fixation distance. a=34 mm.
Fixation distance b mm and diopters | 450 | 730 | 237 | 129 | 550 |
---|
2.22 D | 1.37 D | 4.22 D | 7.75 D | 1.82 D |
---|
Displacement of the central thread y−b | −10.5 mm | −6.0 mm | −4.2 mm | −8.1 mm | −2.0 mm |
Separation of the outer threads 2x | 256 mm | 256 mm | 117 mm | 117 mm | 120 mm |
Hering-Hillebrand deviation value H (Eq. 25) | 0.108 | 0.068 | 0.203 | 0.366 | 0.086 |
Table 5
Grid-nonius longitudinal horopter data of K.N.O. No refractive error. Fixation distance 404 mm (2.5 D). Eso-fixation disparity. P.D.=64 mm.
| Left field | Right field |
---|
|
---|
Lane | 16° | 12° | 8° | 4° | 2° | 1° | 0 | 1° | 2° | 4° | 8° | 12° | 16° |
---|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
---|
Mean of 15 sets of readings mm | — | −5.5 | −3.8 | −2.3 | −1.9 | −1.7 | | −1.4 | −2.1 | −2.7 | −4.1 | −8.1 | — |
Mean deviation of readings mm | — | ±2.8 | ±1.6 | ±0.9 | ±0.6 | ±0.4 | | ±0.4 | ±0.6 | ±0.9 | ±1.8 | ±4.0 | — |
Percent values from iso-mag. curves | — | −2.38 | −1.28 | +0.18 | +1.70 | +3.60 | | −2.85 | −1.83 | −0.45 | +1.07 | +1.88 | — |
Percent values of mean deviation | — | ±0.39 | ±0.47 | ±0.53 | ±0.68 | ±1.00 | | ±1.00 | ±0.68 | ±0.50 | ±0.52 | ±0.56 | — |
Computed percent values from theory | −3.25 | −2.20 | −1.05 | +0.56 | +2.50 | +5.80 | | −5.21 | −2.36 | −0.55 | +1.04 | +2.17 | +3.22 |
Table 6
Grid-nonius longitudinal horopter data of F.D.C. Small astigmatic correction. Fixation distance 756 mm (1.33 D). Exo-fixation disparity. P.D.=64 mm.
| Left field | Right field |
---|
|
---|
Lane | 16° | 12° | 8° | 4° | 2° | 1° | 0 | 1° | 2° | 4° | 8° | 12° | 16° |
---|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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Mean of 15 sets of readings | — | −7.4 | +0.5 | +6.1 | +5.8 | +6.2 | | +6.5 | +5.8 | +1.6 | −2.1 | −4.9 | — |
Mean deviation of readings mm | — | ±5.7 | ±6.6 | ±3.6 | ±1.0 | ±2.5 | | ±2.7 | ±4.0 | ±5.6 | ±5.1 | ±5.5 | — |
Percent values from iso-mag. curves | — | −1.4 | −1.2 | −1.6 | −2.2 | −4.1 | | +4.4 | +2.2 | +0.9 | +1.0 | +1.6 | — |
Percent values of mean deviation | — | ±0.3 | ±0.6 | ±0.5 | ±0.4 | ±1.6 | | ±1.7 | ±1.4 | ±0.8 | ±0.5 | ±0.3 | — |
Computed percent values from theory | −1.7 | −1.4 | −1.3 | −1.5 | −2.4 | −4.5 | | +4.9 | +2.5 | +1.5 | +1.3 | +1.4 | +1.7 |
Table 7
Multiple partition data. Fixation distance=400 mm—K.N.O. Haploscope apparatus. Standard space—first wire on left field.
Left field | Right field |
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|
---|
Subjective directional separation Unit=j | −3 | −2 | −1 | 0 | 1 | 2 | 3 |
Mm separation of threads from center, O.D. | −37.20 | −24.23 | −12.00 | | 11.26 | 22.70 | 33.96 |
w2=tanα2 | −0.0930 | −0.0606 | −0.0300 | | 0.0281 | 0.0567 | 0.0849 |
α2 |
|
|
| |
|
|
|
w2/j | 0.0310 | 0.0303 | 0.0300 | | 0.0282 | 0.0284 | 0.0283 |
|
|
|
|
|
|
|
|
Mm separation of threads from center, O.S. | −39.82 | −25.95 | −12.58 | | 12.00 | 24.10 | 36.44 |
Same corrected for 12.0 standard left field | −37.98 | −24.75 | −12.00 | | 11.45 | 22.99 | 24.76 |
w1=tan α1 | −0.0949 | −0.0619 | −0.0300 | | 0.2862 | 0.0575 | 0.0869 |
α1 |
|
|
| |
|
|
|
w1/j | 0.0316 | 0.0309 | 0.0300 | | 0.0286 | 0.0287 | 0.0289 |
Table 10
Data of K.N.O. for the spatial region of binocular single vision determined on the horopter apparatus at b=404 mm.
Outer limits |
---|
| Left field | Right field |
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|
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LANE | 12° | 8° | 4° | 2° | 1° | 0 | 1° | 2° | 4° | 8° | 12° |
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|
|
|
|
|
|
|
|
|
|
|
|
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Mean position outer limits mm | +7.5 | +5.5 | +2.4 | +2.7 | +2.5 | | +3.3 | +3.1 | +3.5 | +3.7 | +3.0 |
Mean dev. mm. | ±3.9 | ±2.5 | ±1.8 | ±0.9 | ±0.4 | | ±0.8 | ±1.2 | ±1.7 | ±3.2 | ±5.1 |
Percent value of mean position from iso-mag. curves | −4.9 | −3.9 | −2.5 | −3.6 | −5.6 | | +8.0 | +4.1 | +3.2 | +3.5 | +4.3 |
Percent mean dev. | ±0.7 | ±0.7 | ±1.1 | ±1.1 | ±0.9 | | ±1.8 | ±1.4 | ±1.0 | ±0.9 | ±1.0 |
|
Near limits |
|
Mean position near limits mm | −10.3 | −6.8 | −3.4 | −2.2 | −2.0 | | −2.1 | −2.6 | −4.6 | −9.2 | −15.3 |
Mean dev. mm | ±1.2 | ±1.1 | ±1.0 | ±0.5 | ±0.6 | | ±0.3 | ±0.4 | ±1.1 | ±1.7 | ±2.9 |
Percent value of mean position from iso-mag. curves | −1.6 | −0.4 | +0.7 | +2.0 | +4.5 | | −4.4 | −2.4 | −1.4 | −0.3 | +0.7 |
Percent mean dev. | ±0.2 | ±0.3 | ±0.6 | ±0.6 | ±1.4 | | ±0.7 | ±0.5 | ±0.7 | ±0.5 | ±0.6 |
Table 11
Angular longitudinal magnitudes of the fusional areas computed from Table 10 from Eq. (20) for K.N.O. at 2.5 D.
Left field | Right field |
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|
---|
Lane | 12° | 8° | 4° | 2° | 1° | 0 | 1° | 2° | 4° | 8° | 12° |
---|
|
|
|
|
|
|
|
|
|
|
|
|
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Minutes of arc | 12.5 | 8.6 | 3.8 | 3.4 | 3.0 | | 3.6 | 3.9 | 5.5 | 9.1 | 13.1 |
Table 12
Mean deviations for peripheral angle in percent P.
Fixation distance diopters | Data of K.N.O. Apparent frontal plane |
---|
|
|
|
|
|
|
|
|
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| 1° | 2° | 4° | 8° | 12° | 16° | Readings |
---|
0.164 (6.1 m) | — | 0.07% | 0.03% | 0.04% | 0.03% | — | 18 |
1.33 (75.6 cm) | 0.19% | 0.14% | 0.10% | 0.12% | 0.12% | 0.12% | 70 |
2.50 (40.4 cm) | 0.33% | 0.21% | 0.15% | 0.16% | 0.16% | 0.21% | 240 |
4.94 (20.0 cm) | — | 0.44% | 0.43% | 0.31% | 0.39% | 0.56% | 82 |
Fixation distance diopters | Data of F.D.C. Apparent frontal plane |
---|
|
|
|
|
|
|
|
|
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| 1° | 2° | 4° | 8° | 12° | 16° | Readings |
---|
0.164 (6.1 m) | 0.10% | 0.08% | 0.06% | 0.07% | 0.07% | — | 60 |
1.33 (75.6 cm) | 0.39% | 0.31% | 0.22% | 0.21% | 0.25% | 0.33% | 10 |
2.50 (40.4 cm) | 0.57% | 0.54% | 0.50% | 0.59% | 0.72% | — | 104 |
4.94 (20.0 cm) | — | 1.60% | 0.97% | 0.76% | 1.04% | 1.02% | 12 |
Fixation distance diopters | Data of K.N.O. Grid-nonius horopter |
---|
|
|
|
|
|
|
|
|
---|
| 1° | 2° | 4° | 8° | 12° | 16° | Readings |
---|
1.33 (75.6 cm) | 0.57% | 0.49% | 0.34% | 0.31% | 0.19% | — | 44 |
2.50 (40.4 cm) | 0.89% | 0.56% | 0.47% | 0.48% | 0.48% | — | 450 |
4.94 (20.0 cm) | — | 2.00% | 2.04% | 1.26% | 1.32% | 1.17% | 72 |
The greater increase in the errors at 4.94 diopters is due primarily to the fact that the magnitude of the personal errors approaches that of the errors of the apparatus.
Table 13
Values of dP/db for a=32.5 in percent P.
Fixation distance | Lane angle ϕ |
---|
| 1° | 2° | 4° | 8° | 12° | 16° |
---|
|
|
|
|
|
|
|
---|
756.8 mm | −0.0004 | −0.0008 | −0.0016 | −0.0031 | −0.0047 | −0.0063 |
404.3 mm | −0.0014 | −0.0028 | −0.0056 | −0.0113 | −0.0173 | −0.0236 |
199.8 mm | −0.0054 | −0.0107 | −0.0211 | −0.0416 | −0.0615 | −0.0811 |
Table 14
Values of dP/da for a=32.5 in percent P.
Fixation distance | Lane angle ϕ |
---|
| 1° | 2° | 4° | 8° | 12° | 16° |
---|
|
|
|
|
|
|
|
---|
756.8 mm | 0.0046 | 0.0091 | 0.0183 | 0.0365 | 0.0549 | 0.0735 |
404.3 mm | 0.0084 | 0.0169 | 0.0336 | 0.0669 | 0.0997 | 0.1330 |
199.8 mm | 0.0161 | 0.0319 | 0.0633 | 0.1244 | 0.1840 | 0.2427 |
Table 16
Error introduced in value of P for an average point in fixation frontal plane when head is displaced 1 mm to right.
Fixation distance | 20 cm | 40 cm | 75 cm | 606 cm |
---|
Error in percent difference in P | 0.33 | 0.08 | 0.02 | 0.0003 |