Table 1
Part A: Evaluation of constants a aM, bM, xP, h, k, aR, bR
Step | Find Quantity | As equal to | Value found for this example |
---|
(1) | rCM: |
| 1158.09 |
(2) | yCM: |
| −509.05 |
(3) | xCM: | −yCMεM2 tan δC | 2653.63 |
(4) | aM2: | xCM2 + εM2yCM2 | 8078275. |
(5) | xP: | xCM − jC cos γC | 2303.00 |
(6) | yP: | yCM − (xCM − xP) tanγC | −603.00 |
(7) | rCR: |
| 1158.09 |
(8) | (yCR − k): |
| 509.05 |
(9) | k: |
| −313.10 |
(10) | bR2: | (yCR − k)2(εR2 tan2ωC + 1) | 2015969. |
(11) | h: | xCM + (yCR − yCM) cotϕC − εR[bR2 − (yCR − k)2)1/2 | 0.00 |
Table 2
Part B: Determination of S and D values at Edge of Field (where γd = 0° and γe = +30°)
Step | Find quantity | As equal to | Value found when |
---|
γd = 0° | γe = +30° |
---|
(1) | s: | yP−xP tan γ | −603.00 | −1932.64 |
(2) | xM: |
| 2573.67 | 2760.14 |
(3) | γM: |
| −603.00 | −399.06 |
(4) | δ: | tan−1[(−xM)/(εM2yM)] | 46.°857 | 63.°832 |
(5) | ϕ: | 2δ − γ | 93.°715 | 97.°663 |
(6) | t: | xM − h − (yM − k) cotϕ | 2554.85 | 2756.65 |
(7) | (yR − k): |
| 665.17 | 449.77 |
(8) | ω: |
| −43.°350 | −56.°286 |
(9) | α: | 180°+2ω − ϕ | −0.°415 | −30.°234 |
(10) | fR: |
| 516.30 | 231.41 |
(11) | fM: |
| 495.47 | 250.58 |
(12) | 1/u: |
| 0.002166 | 0.004358 |
(13) | S: | 100 · (1/fR − 1/u) | −0.25 | −0.03 |
(14) | D: |
| +2.8% | −1.5% |
Table I
Values of the Astigmatism S and the distortion D when Various Values of the Elliptical Eccentricities εM and εR are Used
| | γ = 0° | γ = +30° |
---|
εM | εR | S | D | S | D |
---|
2.00 | 2.00 | −0.25D | +2.8% | −0.03D | −1.5% |
1.30 | 2.00 | −0.33 | −5.2 | −0.25 | −0.2 |
1.00 | 2.00 | +0.20 | −11.8 | −0.07 | +0.9 |
1.30 | 1.70 | +0.08 | −4.2 | −0.53 | −3.8 |
Table II
Values of S and D Obtained when Fourth Order Curves are used for the Mirrors of Example 1
| Curve coefficients | γd = 0° | γe = + 30° |
---|
b | c × 10−6 | d × 10−8 | t | u × 10−6 | υ × 10−8 | S | D | S | D |
---|
0.0019 | −2.979 | 0.2645 | 0.0019 | −2.979 | 0.2645 | +1.07D | −6.3% | −4.80D | −13.5% |
0.0019 | −2.836 | 0.2554 | 0.0019 | −2.979 | 0.2645 | +0.86 | −6.6 | −1.29 | −8.9 |
0.0017 | −2.168 | 0.1888 | 0.00165 | −1.993 | 0.1715 | +0.55 | −3.5 | +0.02 | −4.6 |
Table III
Values of S and D when the Pupil Is Located at Various Positions (xP,yP)
| | γd = 0° | γe = +30° |
---|
xP | yP | S | D | S | D |
---|
2303.0 | −603.0 | −0.25D | +2.8% | −0.03D | −1.5% |
2303.0 | −635.5 | −0.26 | −0.1 | −0.17 | −0.2 |
2303.0 | −570.5 | −0.21 | +5.7 | +0.25 | −0.4 |
2303.0 | −686.3 | −0.22 | −6.3 | +0.06 | −3.8 |
2303.0 | −545.1 | −0.16 | +8.2 | +0.54 | +3.4 |
2366.5 | −603.0 | −0.28 | +2.8 | −0.18 | −0.1 |
2214.1 | −603.0 | −0.25 | +2.8 | +0.46 | −2.5 |
2214.1 | −545.1 | −0.16 | +9.9 | +1.14 | +31.8 |
2366.5 | −545.1 | −0.16 | +7.5 | +0.14 | −1.4 |
2366.5 | −686.3 | −0.16 | −10.1 | +0.63 | +2.1 |
Table IV
Binocular Convergence Values for Various Field Angles in the Design of Example 1
Field Angle γ | Convergence (αPL − αPR) |
---|
0.0° | +0.78° |
2.5 | +0.65 |
5.0 | +0.50 |
7.5 | +0.35 |
10.0 | +0.21 |
12.5 | +0.07 |
15.0 | −0.04 |
17.5 | −0.12 |
20.0 | −0.16 |
22.5 | −0.15 |
25.0 | −0.11 |
27.5 | −0.05 |
30.0 | −0.01 |
Table V
S and D Values Obtained for Various Field Angles In the Design of Example 2
Field angle γ | Degrees above horizon | S | D |
---|
−3.5° | 4.0° | −0.48D | +1.4% |
−2.5 | 5.0 | −0.40 | +1.1 |
0.0 | 7.5 | −0.20 | +0.5 |
+2.5 | 10.0 | 0.00 | 0.0 |
+5.0 | 12.5 | −0.18 | −0.3 |
+7.5 | 15.0 | +0.34 | −0.5 |
+10.0 | 17.5 | +0.47 | −0.5 |
+12.5 | 20.0 | +0.54 | −0.4 |
+15.0 | 22.5 | +0.55 | −0.2 |
+17.5 | 25.0 | +0.48 | −0.1 |
+20.0 | 27.5 | +0.32 | +0.1 |
+22.5 | 30.0 | +0.06 | 0.0 |
+25.5 | 33.0 | −0.37 | −0.4 |
+26.5 | 34.0 | −0.54 | −0.7 |