Optics: measuring and testing – Lamp beam direction or pattern
Reexamination Certificate
2000-05-26
2002-12-17
Font, Frank G. (Department: 2877)
Optics: measuring and testing
Lamp beam direction or pattern
C073S147000
Reexamination Certificate
active
06496252
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention is in the field of atmospheric turbulence, and in particular, relates to an optical apparatus designed to provide in-situ estimates of the Rytov parameter for the propagation of light through atmospheric optical turbulence.
2. Description of the Prior Art
The term “Rytov parameter” refers to the theoretical log-amplitude variance predicted by Rytov theory. The Rytov parameter for spherical-wave propagation is given as a weighted integral of the random index-of-refraction structure constant C
n
2
as follows:
σ
x
2
≡
0.5631
(
2
π
λ
)
7
/
6
∫
0
L
ⅆ
z
C
n
2
(
z
)
[
z
(
1
-
z
/
L
)
]
5
/
6
(
1
)
where &lgr; is the wavelength, L is the propagation distance, and z is a position along the propagation path. Though strictly a theoretical quantity, the Rytov parameter is a useful metric of the optical effects for extended-turbulence propagation and is a leading indicator of the performance limitations of adaptive-optical compensation devices not related to the transverse coherence diameter (Fried parameter) (D. L. Fried, “Optical resolution through a randomly inhomogeneous medium for very long and very short exposures,”
J. Opt. Soc. Am.
56, pp. 1372-1379, October 1966). This instrument bases the estimate of the Rytov parameter on an appropriate difference of variances for the differential image motion (average wave-front gradient, wave-front tilt) between two receiving apertures. The use of differential tilts for determining the Rytov parameter is a primary novel aspect of this invention, for these quantities are not conventionally recognized to be indicative of the Rytov parameter. When interpreted properly, differential-tilt measurements are a reliable and predictable indicator of the Rytov parameter. It is important to clarify that the differential-tilt Rytov parameter monitor is used to estimate the value of the integral expression for &sgr;
&khgr;
2
given in Eq. (1), not the observed log-amplitude variance for point-source propagation.
The Rytov approximation is the predominant theoretical construct used to derive a solution to the scalar wave equation for propagation through a medium with random index-of-refraction fluctuations. Analysis of turbulence effects using the Rytov approximation is often referred to as “Rytov theory.” The variance of the log-amplitude computed using Rytov theory is called the “Rytov parameter.” This quantity is designated &sgr;
&khgr;
2
is related to point source propagation parameters as indicated in Eq. (1). While Eq. (1) indicates that &sgr;
&khgr;
2
should increase proportionately with any constant multiplier of C
n
2
, experimental and simulation-based studies have concluded that this trend does not hold for full-wave propagation. Instead, the irradiance variance (scintillation) increases monotonically from 0 to a maximum value greater than 1, then decreases as C
n
2
increases. This behavior is referred to as the “saturation” of scintillation. Saturation imposes a limit on the utility of irradiance-based instrumentation (scintillometers) to adz accurately determine turbulence strength parameters using Rytov theory. In many experiments, the Rytov parameter cannot be measured directly, but rather must be inferred from measurable quantities making key assumptions about the turbulence profile that are not generally valid.
The Rytov parameter is often used to quantify the severity of turbulence effects in propagation, especially in studies of scintillation. Moreover, the Rytov parameter is a critical metric in determining the utility of adaptive-optical systems for compensation of extended-turbulence effects. Recently, it has been recognized that the Rytov parameter is related to a rotational component of the turbulence-induced phase due to phase dislocations (branch points) which limit the ability of conventional wave-front reconstruction procedures (D. L. Fried, “Branch point problem in adaptive optics,”
J. Opt. Soc. Am. A
15, pp. 2759-2768, October 1998). The Rytov parameter addresses additional adaptive optics performance degradation not quantified by considering only the transverse atmospheric coherence length r
0
or Fried parameter. Thus, it is desirable to accurately estimate the Rytov parameter in field experiments where little or nothing is known about C
n
2
(z). For simulation studies, the Rytov parameter may be computed directly from the input parameters. An accurate estimate of the Rytov parameter in practical experiments therefore facilitates comparison with simulation-based studies.
In current laser propagation and adaptive-optical compensation field tests, at least two types of atmospheric characterization measurements are typically made. The first type of measurement relates to the variation of the received irradiance or scintillation. This measurement is made with a device called a scintillometer, which measures the random fluctuation of received light in a collection aperture. Devices of this type have been patented by Hill and Ochs (U.S. Pat. No. 5,150,171, Thierman (U.S. Pat. No. 5,303,024), and Wang (U.S. Pat. No. 5,796,105). For conventional scintillometers, the irradiance variance is computed from the data and analysis is performed to yield an estimate of C
n
2
. Since these measurements are typically made over nearly horizontal paths, it is assumed that C
n
2
varies little over the path. The observed irradiance variance may be interpreted using Rytov theory in the weak-fluctuations regime, or a comparison with wave-optics simulation results may be made in the saturated or asymptotic regimes. From the estimate of C
n
2
obtained with the scintillometer, the Rytov parameter may then be computed using Eq. (1).
The second type of atmospheric characterization measurement often made in field tests relates to the strength of the turbulence-induced phase, quantified by the transverse coherence length r
0
which is related to point-source propagation parameters as follows:
r
0
≡
(
[
2.91
6.88
(
2
π
λ
)
2
∫
0
L
ⅆ
z
C
n
2
(
z
)
(
1
-
z
/
L
)
5
/
3
]
)
-
3
/
5
(
2
)
A mathematical comparison between Eq. (1) for &sgr;
&khgr;
2
and Eq. (2) for r
0
indicates that while the bulk of the contribution to &sgr;
&khgr;
2
comes from the middle of the propagation path, r
0
is affected primarily by turbulence near the receive aperture. Thus, &sgr;
&khgr;
2
and r
0
are indicative of disparate optical effects arising from different regions of the propagation path. For an optical system with diameter D, atmospheric effects on resolution are determined by the quantity (D/r
0
)
5/3
. A device for measuring r
0
has been patented by Wilkins (U.S. Pat. No. 5,343,287) that employs beam-spread and angle-of-arrival variance. However, work dating back more than 20 years (D. L. Fried, “Differential angle of arrival: Theory, evaluation, and measurement feasibility,”
Radio Science
10, pp. 71-76, January 1975; F. D. Eaton, et al., “Comparison of two techniques for determining atmospheric seeing,” in
Proc. SPIE: Optical, Infrared, and Millimeter Wave Propagation Engineering,
vol. 926, pp. 319-334, 1988; and F. D. Eaton, et al., “Phase structure function measurements with multiple apertures,” in
Proc. SPIE: Propagation Engineering,
vol. 1115, pp. 218-223, 1989) demonstrates the superiority of techniques employing differential angle-of-arrival measurements of two spatially-separated receive apertures for estimating r
0
.
In cases where C
n
2
may reasonably be assumed constant over the entire propagation path, either irradiance variance measurements from a scintillometer or r
0
measurements from a suitable device could be used to compute C
n
2
from Rytov theory or simulation, and the Rytov parameter could then be computed using Eq. (1). In practice, however
Callahan Kenneth E.
Font Frank G.
Lauchman Layla
Skorich James M.
The United States of America as represented by the Secretary of
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