SUMMARY
An approximate expression for the Strehl ratio that is easily
evaluated for any turbulence distribution was derived. It applies
for various anisoplanatic effects. This expression was shown to
give much better agreement with the exact answer than the extended
Marechal approximation. The zenith dependence is included in the
formula. This approximation was applied to parallel path
displacements, angular offsets, time-delay induced offsets, and
offsets owing to refractive effects that vary with wavelength.
Examples for each type of anisoplanatism at various zenith angles
were evaluated.
The Strehl ratio in the presence of several effects was examined.
It was shown that, depending on the direction of the relative
displacements, one can get a cancellation or an enhancement of the
effect of the displacements. Therefore it is possible for there
to be little reduction in the Strehl ratio if there is little net
path displacement. If the displacements are in the same
direction, the Strehl ratio is less than the product of the Strehl
ratios of the individual terms.
This research was sponsored by the Strategic
Defense Initiative Organization through the U.S. Department of the
Air Force.
#references380#
<#1278#>Figure<#1278#>:
<#1279#> Comparison of the Maréchal and the two- to six-term
approximations with the exact value of the Strell ratio, for an
anisoplanatic displacement, for D/r0 equal to 1.<#1279#>
| #figure414# |
<#1283#>Figure<#1283#>:
<#1284#> Comparison of the Maréchal and the two- to six-term
approximations with the exact value of the Strell ratio, for an
anisoplanatic displacement, for D/r0 equal to 5. <#1284#>
| #figure418# |
<#1288#>Figure<#1288#>:
<#1289#> Comparison of the Maréchal and the two- to six-term
approximations with the exact value of the Strell ratio, for an
anisoplanatic displacement, for D/r0 equal to 10. <#1289#>
| #figure422# |
<#1293#>Figure<#1293#>:
<#1294#>Strehl ratio for angular anisoplanatic error at zenith,
for various turbulence models, versus separation angle for a 0.6-m
system. Upper-altitude turbulence has a strong effect on the
Strehl ratio.<#1294#>
| #figure426# |
<#1296#>Figure<#1296#>:
<#1297#> Strehl ratio for angular anisoplanatism at #math107#30o
for a 0.6-m system.<#1297#>
| #figure430# |
<#1301#>Figure<#1301#>:
<#1302#> Strehl ratio versus time delay at zenith for a 0.6-m
system.<#1302#>
| #figure434# |
<#1304#>Figure<#1304#>:
<#1305#> Strehl ratio versus time delay for a 0.6-m system at
#math109#30o zenith angle. Strehl ratio at #math110#30o for a
0.6-m system. <#1305#>
| #figure438# |
<#1311#>Figure<#1311#>:
<#1312#> Difference (#math113#×106) in refractive index between
#math114#0.5 μm and other wavelengths.<#1312#>
| #figure443# |
Table:
Values of T2 and T5/3 to Solve for the Chromatic
Displacement for Various Turbulence Models for a Wavelength of 0.5
μm
| Model |
T2The units of T2 are m1/3. |
T5/3T5/3 is dimensionless. |
| SLC-Day |
#math117#2.71 × 10-6 |
#math118#2.00 × 10-7 |
| HV-21 |
#math119#6.16 × 10-6 |
#math120#3.60 × 10-7 |
| HV-54 |
#math121#3.40 × 10-5 |
#math122#1.87 × 10-6 |
| HV-72 |
#math123#5.95 × 10-5 |
#math124#3.25 × 10-6 |