Table 1
General Mirror Equations
| Surface Equation (in local coordinates) | Distance between Surfaces | Incident Ray Slope | Eq. |
---|
Hyperbolic mirror-1 |
|
a + c
|
| (7) |
Hyperbolic mirror-2 |
|
|
| (8) |
Parabolic mirror |
|
|
| (9) |
Table 2
Global Coordinate Equations of the Mirrors
| Coordinates (in global coordinate system) | Eq. |
---|
Hyperbolic mirror-1 |
|
| (10) |
Hyperbolic mirror-2 |
|
| (11) |
Parabolic mirror |
|
| (12) |
| | |
Table 3
Equations of the Slopes of the Rays Reflected from Each Surface
| Reflected Ray Slope | Eq. |
---|
Hyperbolic mirror-1 |
| (13) |
Hyperbolic mirror-2 |
| (14) |
Parabolic mirror |
| (15) |
Table 4
Parameters of the First Example Designed with the First Method
θ∥
| θ⊥
| α |
a (cm) |
b (cm) |
d (cm) |
e (cm) |
g (cm) |
w
f
(cm) |
---|
5° | 15° | 5° | 0.96 | 1.04 | 0.96 | 3.96 | 34.49 | 10 |
Table 5
Parameters of the Second Example Designed with the First Method
θ∥
| θ⊥
| α |
a (cm) |
b (cm) |
d (cm) |
e (cm) |
g (cm) |
w
f
(cm) |
---|
6° | 23° | 3° | 0.75 | 0.75 | 0.75 | 4.89 | 20.51 | 10 |
Table 6
General Mirror and Ray Equations
Surface Equation for All Mirrors (in local coordinates) → x
2 = 4gz
| (18) |
---|
| Incident Ray Slope | Distance between Surfaces | Reflected Ray Slope | Eq. |
---|
Mirror-1 |
|
|
| (19) |
Mirror-2 |
|
|
| (20) |
Mirror-3 |
|
|
| (21) |
Table 7
Global Coordinate Equations of the Mirrors
| Coordinates (in global coordinate system) | Eq. |
---|
Mirror-1 |
|
| (22) |
Mirror-2 |
|
| (23) |
Mirror-3 |
|
| (24) |
| | | |
Table 8
Parameters of the Example Designed with the Second Method
θ∥
| θ⊥
| α |
g
1 (cm) |
g
2 (cm) |
g
3 (cm) |
w
f
(cm) |
---|
6° | 23° | 5° | 2.42 | 9.36 | 95.41 | 10 |
Table 9
β Parameter Calculations of Each Studied Example Separately for Perpendicular and Parallel Transverse Directions
| Design Method I | Design Method II |
---|
10°–30° Beam | 12°–46° Beam | 12°–46° Beam |
---|
x-axis | y-axis | x-axis | y-axis | x-axis | y-axis |
---|
First mirror | | | | | | |
w
0 (cm) | 0.67 | 0.22 | 0.80 | 0.21 | 1.03 | 0.26 |
w
f
(cm) | 1.67 | 1.65 | 3.15 | 3.07 | 1.03 | 1.00 |
d (cm) | 3.75 | 3.75 | 5.54 | 5.54 | 7.08 | 7.37 |
β | 2.15 × 104
| 7.05 × 103
| 3.29 × 104
| 8.20 × 103
| 1.08 × 104
| 2.53 × 103
|
Second mirror | | | | | | |
w
0 (cm) | 1.67 | 1.65 | 3.15 | 3.07 | 1.03 | 1.00 |
w
f
(cm) | 10.00 | 9.94 | 10.36 | 10.10 | 10.34 | 10.12 |
d (cm) | 31.08 | 31.08 | 17.75 | 17.75 | 86.76 | 86.76 |
β | 3.88 × 104
| 3.81 × 104
| 1.33 × 105
| 1.25 × 105
| 8.86 × 103
| 8.42 × 103
|
Table 10
Analytical Calculations of the Input and Output Beam for Both 10°–30° and 12°–46° Beam Examples
| 10°–30° Beam | 12°–46° Beam |
---|
w
0∥
| 3.18 μm | 2.64 μm |
w
0⊥
| 1.06 μm | 0.69 μm |
z
0∥
| 36.32 μm | 25.30 μm |
z
0⊥
| 4.04 μm | 1.72 μm |
w
f
(∥,⊥)
| 10 cm | 10 cm |
z
0f
(∥,⊥)
| 36.11 km | 36.11 km |
θ
f
(∥,⊥)
| 2.77 μrad | 2.77 μrad |
Table 11
Output Beam Results of all Studied Design Examples
| 10°–30° Beam First Design Method | 12°–46° Beam First Design Method | 12°–46° Beam Second Design Method |
---|
w
f∥
| 9.94 cm | 10.10 cm | 10.12 cm |
w
f⊥
| 10 cm | 10.36 cm | 10.34 cm |
z
0f∥
| 35.70 km | 36.49 km | 38.56 km |
z
0f⊥
| 36.12 km | 37.46 km | 36.79 km |
θ
f∥
| 2.79 μrad | 2.74 μrad | 2.74 μrad |
θ
f⊥
| 2.77 μrad | 2.67 μrad | 2.68 μrad |