Table I
Coefficients of the Petzval Condition Equation
α0
=
F3D3 |
α1
=
F3(Pz
+ 1) +
FpF3(B(Pz
+ 1) + D3) +
F3D3B |
α2
= −
S0S1
−
FpS0S1
−
F3D3 |
β0
= −
F3D3
+
F2F3D3B |
β1
= −
S0S1B
+
F2F3(B(Pz
+ 1) + D3) |
β2
= −
S0S1
+
F2F3(Pz
+ 1) +
F3D3 |
γ0 =
[−
S0S1
+
F2F3(Pz
+ 1)] +
Fp[−
S0S1B
+
F2F3B(Pz
+ 1)] |
γ1 =
F3
+
FpF2F3
−
F3
+
F2F3B |
δ0
=
[−
S0S1
+
F2F3(Pz
+ 1) +
F3D3]
+
F2F3D3(Fp
− F2) |
δ1
=
Fp[−
S0S1
+
F2F3(Pz
+ 1)] +
F2F3D3 |
η0
= −
FpS0S1(Fp
+ B) |
η1
=
[F2(Pz
+ 1) + D3]
+
FpF2(B(Pz
+ 1) + D3) +
F2D3(B
− F2) |
Table II
Coefficients of the Third-Order Aberration Equations
A11 =
−2c13y14 |
A12 =
+2c23y24 |
A13 =
−2c33y34 |
A14 =
−S1i12
+
S2i22
−
S3i32
− SA3/γ |
A21 =
−2Q1c13y14 |
A22 =
+2Q2c23y24 |
A23 =
−2Q3c33y34 |
A24 =
−S1i1
+
S2i2
−
S3i3
−
CMA3/γ |
A31 =
−2Q12c13y14 |
A32 =
+2Q22c23y24 |
A33 =
−2Q32c33y34 |
A34 =
−S1
2 +
S2
2 −
S3
2 −
AST3/γ |
Table III
Variable Change Table
Fundamental design
parameter | System constructional
parameters |
---|
c1 | c2 | c3 | d1 | d2 | d3 |
---|
Fpri | X | X | | X | X | |
f2 | | X | X | X | X | X |
B | | X | | X | X | |
D3 | | | X | X | X | X |
Note: A change in
Fpri, for example,
will result in a change in
c1,
c2,
d1, and
d2, while
c3
and
d3 will not be affected.
Table IV
Design Alternatives Obtained from Solution of the Petzval Condition
Equation
Case | Fpri | F2 | B | D3 | σ |
---|
1 | 2.100 | 14.1388 | 6.800 | −4.5 | 2.715 – 03 |
2 | 2.100 | 467.861 | 6.800 | −4.5 | 1.258 – 01 |
3 | 2.16907 | 27.00 | 6.800 | −4.5 | 7.375 – 06 |
4 | 0.563 | 27.00 | 6.800 | −4.5 | 2.656 – 03 |
5 | 2.100 | 27.00 | 7.220 | −4.5 | 6.665 – 06 |
6 | 2.100 | 27.00 | 6.800 | −4.2173 | 7.785 – 06 |
Note: The 1-
σ spot radius is
plotted as a function of fractional field height for cases 3, 5, and 6
on
Fig. 2.
Table V
Design Prescriptions
Starting prescription
with B = 6.800 m |
Surface | Curvature | Conic constant | Separation |
0 | 0.0 | 0.0 | 1.000000 + 08 |
1 | −9.523810 – 02 | −1.13325 | −3.288372 |
2 | −2.053283 – 01 | −2.86345 | 5.588372 |
3 | −1.031746 – 01 | −6.49524 | −2.333333 |
4 | −1.383126 – 02 | 0.0 | 0.0 |
Figure of merit
σ = 3.097–05 m | |
Final prescription
with B = 7.220 m |
Surface | Curvature | Conic constant | Separation |
0 | 0.0 | 0.0 | 1.000000 + 08 |
1 | −9.523810 – 02 | −1.13378 | −3.220000 |
2 | −1.984127 – 01 | −2.84098 | 5.940000 |
3 | −1.031746 – 01 | −5.93792 | −2.333333 |
4 | 0.0 | 0.0 | 0.0 |
Figure of merit
σ = 6.665 – 06 m | |
Table VI
Parameters for the Design Optimization Experiment
Fundamental design
parameters |
Fpri | 1.50 | Angular field =
2.30° |
Y1 | 1.50 m | | |
F2 | 30.00 m | | |
F3 | 15.00 m | | |
B | 7.50 m | | |
D3 | −4.95 m | | |
Telescope design
prescription |
Surface | Curvature | Conic constant | Separation |
0 | 0.0 | 0.0 | 1.000000 + 08 |
1 | −1.111111 – 01 | −1.07961 | −2.934783 + 00 |
2 | −2.715278 – 01 | −2.19637 | 5.484783 + 00 |
3 | −1.010101 – 01 | −6.40165 | −2.475000 + 00 |
4 | −1.188131 – 01 | 0.00000 | 0.000000 |
Table VII
Performance of the Design Optimization Techniques
Figure of merit |
---|
Iteration | DLS | GSO | CG |
---|
0 | 0.3221 – 03 | 0.3221 – 03 | 0.3221 – 03 |
5 | 0.2106 – 03 | 0.8666 – 04 | 0.2459 – 05 |
10 | 0.1404 – 03 | 0.4115 – 04 | Converged |
15 | 0.9289 – 04 | Converged | |
20 | 0.6913 – 04 | | |
30 | 0.4564 – 04 | | |
40 | 0.3216 – 04 | | |
50 | 0.2737 – 04 | | |
60 | 0.2457 – 04 | | |
Note: In the DLS and GSO modes the system curvatures,
conic constants, and separations were allowed to vary. In the CG mode,
all four of the fundamental design parameters were varied. The test was
halted after sixty iterations in the DLS mode.
Table VIII
Design Prescription after OPD Based Optimization
Surface | Curvature | Conic constant | Separation |
0 | 0.0 | 0.0 | 1.000000 + 08 |
1 | −8.612228 –
02 | −1.12904 | −3.648252 + 00 |
2 | −1.869054 –
01 | −2.82780 | 6.198252 + 00 |
3 | −1.010101 –
01 | −5.08503 | −2.474981 + 00 |
4 | 0.0 | 0.0 | 0.0 |
Aspheric deformation
coefficients |
Surface | d | e | f | g |
| 0.0 | 3.2100319 – 09 | 2.7631462 – 11 | 7.3936803 – 10 |
2 | 6.1525915 – 08 | 8.7970424 – 07 | 6.7814425 – 06 | 0.0 |
3 | 0.0 | 0.0 | 0.0 | 0.0 |