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Design of a monolithic Michelson interferometer for fringe imaging in a near-field, UV, direct-detection Doppler wind lidar.

01 Sep 2016-Applied Optics (Optical Society of America)-Vol. 55, Iss: 25, pp 6910-6929

TL;DR: A monolithic, tilted, field-widened, fringe-imaging Michelson interferometer (FWFIMI) combines the advantages of low angular sensitivity, high thermo-mechanical stability, independence of the specific atmospheric conditions, and potential for fast data evaluation.

AbstractThe low-biased, fast, airborne, short-range, and range-resolved determination of atmospheric wind speeds plays a key role in wake vortex and turbulence mitigation strategies and would improve flight safety, comfort, and economy. In this work, a concept for an airborne, UV, direct-detection Doppler wind lidar receiver is presented. A monolithic, tilted, field-widened, fringe-imaging Michelson interferometer (FWFIMI) combines the advantages of low angular sensitivity, high thermo-mechanical stability, independence of the specific atmospheric conditions, and potential for fast data evaluation. Design and integration of the FWFIMI into a lidar receiver concept are described. Simulations help to evaluate the receiver design and prospect sufficient performance under different atmospheric conditions.

Topics: Lidar (59%), Michelson interferometer (56%), Wind speed (53%)

Summary (4 min read)

1. INTRODUCTION

  • Wake vortices, gusts, and turbulence in clear air impose a major risk in commercial air transport because onboard weather radars cannot detect turbulence in clear air [1].
  • Further possibilities to reach this goal include a direct reaction to the forces of the wake vortex on the aircraft by new flight controller routines, examined by Looye et al. [6], or the remote sensing of the disturbances caused by wake vortices and turbulences.
  • Doppler wind lidars (DWL) measure frequency changes caused by the Doppler effect of molecules and aerosols moving with the ambient wind in order to derive wind speed components along the line-of-sight (LoS) of the laser beam.
  • Direct-detection DWLs may consist of filters, which transmit only a certain spectral bandwidth.
  • In particular the authors consider a FIMI for the following reasons: first, a FIMI with slanted mirrors produces linear fringes, which can be imaged on fast, linear detectors for range-resolved detection.

A. Atmospheric Backscattering Spectrum and Single-Scattering Lidar Equation

  • The atmospheric backscattering spectrum has contributions from light scattering by molecules (“Rayleigh–Brillouin” scattering, rotational and vibrational Raman scattering) [42] and from light scattering by aerosols/hydrometeors.
  • As the pressure increases and the temperature decreases, density fluctuations moving at acoustic speeds deform the lineshape (kinetic regime), until at the hydrodynamic limit, two acoustic side bands (Brillouin lines) appear.
  • The scattering properties of aerosols in the atmosphere, such as the lidar ratio and particle depolarization rato, are highly dependent on their type and shape, and there is large variability [46].
  • The total backscattering coefficient is β βRay βMie. σw ffiffiffiffiffiffiffi 4∕3 p ∕νLur:m:s is the broadening due to the r.m.s. wind speed ur:m:s at flight level.
  • ΑMie is the overall atmospheric extinction coefficient [1/m], where αRays 8π∕3βRay is the molecular extinction [1/m], αRaya is the molecular absorption [1/m], and αMie is the extinction and absorption by aerosols.

B. Theoretical Performance of a Fringe-Imaging

  • The principle of direct-detection DWLs based on the FIMI is summarized, and the FIMI’s optimized theoretical performance is compared with other directdetection DWL methods.
  • Assuming dispersion-free media in the interferometer arms, OPD0 is equal to c∕FSR, where FSR is the free spectral range.
  • A general way to find the optimal FSR setting of the FIMI for the measurement of wind speeds is to introduce a penalty factor κVLOS, comparing the interferometer with an ideal spectral analyzer (ISA).
  • The penalty factor κVLOS (by Cezard et al. for pure Rayleigh scattering) compares the Cramer–Rao bounds (CRBs) of the FIMI and the ISA.
  • If the FSR is too small, the fringe constrast is too small for an efficient determination of the fringe phase.

A. Lidar Geometry Requirements

  • Rangeresolved detection in the near-field requires a large FOV of the telescope for full overlap at all ranges in order to maximize the received signal.
  • The pointing stability and lateral shift of the illumination function in a free-beam setup have to be monitored, such that the bias on wind speed measurements can be corrected.
  • The marginal rays of each point source are traced, and the direction cosines are determined at a surface b behind the collimating lens.
  • In case of the FIFI, the fringe shape is strongly dependent on the angular distribution.
  • Accordingly, the field-widening compensation is necessary in the fiber-coupled case, as well.

D. Temperature Compensation

  • The FWFIMI can be more easily temperature stabilized at elevated operational temperatures.
  • The spacer material should be optimized for small temperature tuning.
  • To evaluate the rate for different values of the spacers’.
  • The temperature tuning rate is plotted in Fig. 5(a) as a function of the CTEs of the spacers for both TTCD and TTCP.

E. Fabrication Tolerances

  • For a realistic evaluation of the expected performance, fabrication tolerances and their influence on the instrumental contrast V , and therefore on the performance, have to be considered.
  • In the following, some of the important parameters of the FWFIMI are varied in order to visualize the significance of fabrication tolerances and their consequences.

1. Arm Lengths and Refractive Index Tolerances

  • At first, the influence of arm length tolerances on the instrumental contrast is considered.
  • The transmission functions for different σi are summed up to yield the global transmission function for the angular distribution.
  • The contrast of the global fringe pattern is determined for each configuration.
  • A reduction of the tilt of the FWFIMI decreases the sensitivity of field widening to the arm length tolerances.
  • Similar considerations can be done for the refractive index of the glass arm.

2. Coatings

  • The quality of the coatings applied to the interfaces of the FWFIMI determines the instrumental fringe contrast V and the efficiency of the FWFIMI as well.
  • The term splitting ratio refers to the ratio of the luminous light intensity transmitted (IT tI 0) and reflected (IR rI 0) by the beam splitter coating.
  • The reflectance for p-polarized light is low (3–8%).
  • A polarizing element before the FIMI should guarantee that the incident light is s-polarized in order to ensure a high instrumental contrast.
  • The instrumental contrast depends, as well, on the antireflection (AR) coatings applied to the surfaces of the beam splitter.

3. Mirror Inclination Angle

  • The net inclination angle between the mirrors (θ, Fig. 3) is specified with 17.8 1 μrad.
  • The corresponding number of imaged fringe periods (Np) is 1 0.06.

4. Net Surface Accuracy

  • The fringe shape is sensitive to deviations of the net contour from planarity.
  • The effect on the fringe shape is modeled with a non-sequential ray trace in ZEMAX.
  • The authors consider here surface errors SE of infinity, 20, and 10.
  • The y-axis is normalized to the intensity of the planar case.

1. Illumination Function

  • The above simulations were carried out with a quadratic cross section of the illuminating beam.
  • Less light traverses the FIMI at locations where the condition for maxima is fulfilled.
  • This effect is not observed with a quadratic beam cross section.
  • The resulting fringes are plotted for a round and a quadratic illumination shape in Figs. 8(a) and 8(b).
  • Furthermore, the illumination is not uniform (flat top) in reality, due to the laser profile (e.g., a deformed TEM00), due to the transmission through optical fibers or due to the obstruction by a telescope spider, for instance.

2. Fringe Localization

  • Until now, the authors only considered the etendue of the illumination in terms of field widening, but not for fringe-imaging simulations.
  • The actual fringe pattern is the incoherent superposition of these elementary “non-localized” fringe patterns.
  • The arm lengths and refractive index values are set to the ideal ones determined in Section 3.
  • Alternatively, the mirror inclinations of the FWFIMI and the mean incidence angle could be designed such that the localization plane is located at the detector plane.
  • Concepts for a possible receiver setup are proposed in the next section.

4. CONCEPT OF A RECEIVER SETUP

  • As pointed out in the sections above, the imaging Michelson interferometer for Doppler shift analysis may not be considered alone, but only by factoring in also the dedicated optics and detection systems.
  • A small fraction of the laser light is split off as a reference beam with a splitter (SP) and is coupled into a single- or multimode fiber (RF) using the lens Cl3.
  • The plano-convex cylindrical lens (Lc1) focuses the light in the direction parallel to the linear fringe on the linear detector, e.g., a linear photomultiplier tube array (LPMT1).
  • Furthermore, speckle patterns are generated due to the interference of multiple modes in the fibers.
  • Neglecting the pitch between the detector elements, the modulation factor V pix, due to the integration over the elements of a linear detector, has the tolerable value of sinc(1/P) (i.e., V pix 99% for P 12).

5. ESTIMATION OF PERFORMANCE

  • In the following, an end-to-end simulation for an estimation of the performance of the receiver system, using output 1 [Fig. 10(i)] only, is described.
  • The total speckle patterns for and are computed by the incoherent sum of MMie and MRay speckle patterns and Mf speckle patterns for every laser pulse.
  • The signal-to-noise ratio for every detector element is IL∕in, where IL is the photocurrent of the respective detector element.
  • The centroid method [77] and a Gaussian correlation algorithm (which maximizes the correlation function with a Gaussian) [78] produced large systematic errors, which increased linearly with the wind speed.
  • At high signal strengths, MULTIPLY and AWIATOR profit from higher SNR values for each pulse and a higher number of pulses for averaging during the measurement time (0.1 s), such that WALES is outperformed.

6. CONCLUSION

  • The authors have reviewed different direct DWL techniques and consider a fringe-imaging Michelson interferometer with inclined mirrors (FIMI) a good compromise between theoretical performance and complexity, for range-resolved measurements of LoS wind speeds in the near-field (50–300 m) in front of an aircraft.
  • The authors estimated the non-negligible bias (>0.4 m∕s per μrad) of the measured wind speed induced by a laser-telescope misalignment.
  • A net inclination angle between the mirrors of the FWFIMI provides linear fringes, which can be imaged on fast, linear detectors for range-resolved detection independent of the flight altitude and scattering ratio.
  • For every measurement, digital averaging is applied for a measurement duration of 0.1 s [ME(0.1 s)].
  • Only detector noise (DN), 2. DN and atmospheric speckle, and 3, also known as Three cases are considered.

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Design of a monolithic Michelson interferometer
for fringe imaging in a near-field, UV,
direct-detection Doppler wind lidar
JONAS HERBST* AND PATRICK VRANCKEN
Institut für Physik der Atmosphäre (IPA), German Aerospace Center (DLR), Oberpfaffenhofen, Münchener Str. 20, 82234 Weßling, Germany
*Corresponding author: jonas.herbst@dlr.de
Received 18 April 2016; revised 19 July 2016; accepted 29 July 2016; posted 1 August 2016 (Doc. ID 263498); published 25 August 2016
The low-biased, fast, airborne, short-range, and range-resolved determination of atmospheric wind speeds plays a
key role in wake vortex and turbulence mitigation strategies and would improve flight safety, comfort, and
economy. In this work, a concept for an airborne, UV, direct-detection Doppler wind lidar receiver is presented.
A monolithic, tilted, field-widened, fringe-imaging Michelson interferometer (FWFIMI) combines the advantages
of low angular sensitivity, high thermo-mechanical stability, indep endence of the specific atmospheric conditions,
and potential for fast data evaluation. Desig n and integration of the FWFIMI into a lidar receiver concept are
described. Simulations help to evaluate the receiver design and prospect sufficient performance under different
atmospheric conditions.
© 2016 Optical Society of America
OCIS codes: (280.3640) Lidar; (120.3180) Interferometry; (280.3340) Laser Doppler velocimetry; (280.7060) Turbulence.
http://dx.doi.org/10.1364/AO.55.006910
1. INTRODUCTION
Wake vortices, gusts, and turbulence in clear air impose a major
risk in commercial air transport because onboard weather radars
cannot detect turbulence in clear air [1]. Recent radars provide
some turbulence detection functionality in the presence of
clouds and precipitation [2]. If encountered by another aircraft,
turbulence can cause unexpected rolling moments or abrupt
changes of altitude, which may result in damage to the plane
or injuries to the passengers [3,4].
In particular, wake vortices are a well-studied phenomenon
since their discovery in the early 20th centur y. Two rotating,
long-life vortices are produced at the wing tips of any aircraft.
Todays traditional risk reducer is a standard minimum distance
of travel between any two planes, which is chosen according to
the aircrafts weights, such that the vortices have safely decayed
or subsided before the encounter. One way to meet the ongoing
trend of increasing passenger numbers is to increase the timing
frequency between any two planes without a reduction of
safety. Plate lines are a concept to increase the decay rate of
wake vortices that works only in ground proximity [5].
Further possibilities to reach this goal include a direct reaction
to the forces of the wake vortex on the aircraft by new flight
controller routines, examined by Looye et al. [6], or the remote
sensing of the disturbances caused by wake vortices and
turbulences.
Remote sensing is the only means for measuring wind
vectors in the near field (50300 m), ahead of the aircraft.
This would allow for a fast reaction of the flight controller
(autopilot) [7,8]. Ehlers et al. deem a full-scan update rate
of the wind field measurement of 510 Hz appropriate for
their concept of wake impact alleviation control to work rea-
sonably well at a range of 60 m [8,9]. The control conce pt
includes a wake identification algorithm, which allows one
to reconstruct the wake vortex disturbance, and alleviates
its impact by specific control commands to compensate for
the determined disturbance. After a computation time of
200 ms for the first identification of the wake vortex, the con-
trol system continuously (typical sampling time in the order of
20 ms [9]) countervails the disturbances on the basis of the
determined wake vortex model. Note that the disturbance
reconstruction step allows the anticipation of the disturbances
at locations where no measurement was made (or not yet),
leading to rather complex relationships between the sensor
measurements (location, orientation, and quality) and the dis-
turbance rejection capability [8]. Actuator time delays, which
are assumed to be 100 ms, are compensated by predicting the
wake vortex impact on the aircraft for a moment 100 ms in
the future [9]. This control concept can be applied in very
similar ways for the mitigation of wake vortices, gusts, and
turbulences [10].
However, currently, no reliable sensing system for onboard
measurements of wind speeds exists, which could guarantee
that the safety standards of the International Civil Aviation
Organization are met in such a future scenario.
6910
Vol. 55, No. 25 / September 1 2016 / Applied Optics
Research Artic le
1559-128X/16/256910-20 Journal © 2016 Optical Society of America

Amongst the remote sensing devices, lidar has the advantage
of speed and high local precision. Doppler wind lidars (DWL)
measure frequency changes caused by the Doppler effect of
molecules and aerosols moving with the ambient wind in
order to derive wind speed components along the line-of-sight
(LoS) of the laser beam. A distinction can be made between
coherent and incoherent (direct) DWLs.
Coherent DWLs often use IR laser light, which provides
sensitivity to backscatter from micron-sized aerosols [11,12].
Furthermore, IR laser technology is reliable and often asserted
eye-safe depending on the laser parameters, e.g., at low pulse
energies and low exposure durations [13]. The Doppler-shifted
signal scattered mainly from aerosols is superimposed coher-
ently with a frequency-shifted reference (local oscillator). The
Doppler shift is determined from the beat frequency by a fast
Fourier transform from the power density spectrum. Systems
with CO
2
-lasers, Tm:LuAG-lasers, and with Er-doped fiber
lasers have successfully been applied to measure wind speed s
at the ground level and in the boundary layer [1416].
Turbulence detection in the troposphere at an altitude of
12 km with a cohere nt DWL has been demonstrated up to
9 km ahead of an aircraft with a range bin of 150 m [17]. At
these high altitudes, the concentration of aerosols is low and
the coherence of the received signal is reduced, which decreases
the signal-to-noise ratio (SNR) and the maximum range of
detection. As a consequence of the Fourier limit and the re-
quired coherence (small spectral bandwidth) properties of the
laser, the minimal pulse length and the spatial resolution are
limited [11], e.g., 170 ns and 30 m and a minimum detection
range of 150 m for the Halo Photonics 1.5-μm Streamline
pulsed coherent Doppler lidar [18].
Coherent DWLs have not yet been demonstrated to mea-
sure wind speeds reliably at high cruise flight altitudes (12 km)
or in clear air and with short range bins (1530 m) in the near
field (50300 m in front of an aircraft). Accurate range-resolved
LoS wind speed measurements with standard deviations of
approx. 1ms
1
with comparable lidar geometry parameters
would be required for reliable feed-forward control, as pointed
out in a lidar parameter study by Ehlers et al. [8].
Although coherent DWLs might still be an option, only
direct-detection DWLs are considered from now on, because
they can rely on pure molecular scattering, pure scattering from
aerosols or a combination , and because the range gate length
can be made smaller than 30 m. Direct-detection DWLs may
consist of filters, which transmit only a certain spectral band-
width. From the amount of light that is transmitted through
the filters, the Doppler frequency shift can be determined.
Iodine-vapor DWLs using abs orption bands of iodine as
filters are limited to a laser wavelength of 532 nm. In airborn
lidar, UV wavelengths (λ) are preferred, because UV systems
may be designed eye-safe beyond a certain, acceptable distance
(see, e.g., [19]) and because of the high efficiency of Rayleigh
scattering in the UV, which is roughly proportional to λ
4
(see Section 2.A).
The double-edge technique (DE) is based on two Fabry
Perot interferometers with different optical path lengths
that determine the frequency of maximum transmission.
The Doppler shift is determined by the ratio of transmission
through these filters [20]. The transmission through the filters
strongly depends on the shape of the light scattering spectra,
which is why this method requires the knowledge of the
altitude (backscatter ratio, temperature, pressure). In practice,
the required separation of the Rayleigh and Mie channels, e.g.,
used in ALADIN [21], can only be circumvented by the use
of multiple filters or the equivalent fringe-imaging technique
(FI). These FI techniques have the main advantage that mea-
surements can be performed without knowledge of the shape
of the backscattered signal spectrum.
The principle of fringe imaging relies on the imaging of the
interference pattern of an interferometer on a position-sensitive
detector. The frequency shift between an unshifted reference
and a Doppler-shifted signal can be determined from the dis-
location of the interference pattern. A distinction can be made
between multi-wave and two-wave interference. The most
common multi-wave interferometer is the FabryPerot inter-
ferometer (FPI). When properly illuminated with divergent
light, the produced interference fringes are rings. As the light
is Doppler shifted, the radii of the rings change. This principle
was applied in the AWIATOR (Aircraft Wing with Advanced
Technology Operation) project [22,23]. However, the evalu-
ation of the interference patterns is delicate, time consuming,
and prone to errors due to possible dislocations of the ring
centers on a two-dimensional CCD array [24]. Furthermore,
typical two-dimensional detectors, such as CCD, are too slow
for range-resolved detection.
Other interferometers are designed with an inclination of
one of their mirrors to produce a pattern of linear interference
fringes. The shift of the linear fringe can be determined with
fast, linear detectors.
A multi-wave type is the Fizeau interferometer. The com-
plex fringe shape of a deformed Airy can be accounted for
by the use of proper system parameters [25 ]. The fringe shape
depends strongly on the field angle of the incident light, but
the deformation and contrast loss impede us from being able
to use it with extended sources, as in the presently described
application (see Section 3.A).
For the purpose of collecting range-resolved backscattered
light in close range (50300 m) in front of the aircraft with
an equivalent region of total overlap, a telescope with a large
field of view (FOV) (about 4 mrad) is required. This large
FOV produces, independent of the setup design (free beam
or fiber coupled), an important angular distribution after col-
limation. The interferometer needs to be field widened in order
to accept a broad range of incident angles without a loss of
contrast.
The necessary field widening can be realized with two-wave
interferometers. Liu and Kobayashi proposed to use a Mach
Zehnder interferometer in a direct-detection DWL, using a
two-channel differential discrimination method (DMZ),
similar to the DE technique using the FPI [26]. Bruneau
considered a four-channel-based version (QMZ) [27] and an
equivalent field-widened fringe-imaging MachZehnder inter-
ferometer with inclined mirrors (FIMZ) [28], both optimized
for Rayleigh scattering. Bruneau and Pelon showed that the
concept can be used to measure wind speeds [29]. An applica-
tion of this principle is Ball Aerospace and Technologies Corp.s
Research Article
Vol. 55, No. 25 / Se ptember 1 2016 / Applied Optics 6911

Optical Autocovariance Wind Lidar [30], which was proposed
to measure wind speeds from the international space station
[31]. Recently, a modified DMZ using three wavelengths was
proposed for an Fe Doppler lidar for wind measurements from
ground to thermosphere [32].
Multiple filters can be created with a Michelson interferom-
eter as well. Cezard et al. considered a dual fringe-imaging
Michelson interferometer (FIMI) with inclined mirrors for
the measurement of the wind speed and other air parameters
(temperature, scattering ratio, density) [33].
The monolithic Michelson interferometer design we present
in this work is based on the same fringe-imaging principle.
In contrast to the cited test setup, our field-widened, fringe-
imaging Michelson interferometer (FWFIMI) design provides,
however, the thermo-mechanical stability and design features
necessary for fast, range-resolved, and airborne measurements
of wind speeds in the near field in front of an aircraft. The
advantages of a monolithic FIMI are detailed more closely
below.
There is a long tradition of the design and application of
monolithic, field-widened Michelson interferometers (FWMI)
or wide-angle Michelson interferometers (WAMI). The basic
idea of FWMI was developed in 1941 [34]. FWMIs can be built
temperature compensated as solid model, where the two inter-
ferometer arms consist of different glasses at a certain length
ratio, or as air-spaced models, where the air arm mirror is fixed
by spacers of the same or different materials as the glass arm
and may be positioned with a piezo feedback control. They have
been realized with cube [35] or hexagonal beam splitters [36]
and as a Doppler asymmetric spatial heterodyne version [37],
just to name a few.
For the presently considered application of measuring
LoS wind speeds that are range resolved in the near field, we
consider only two-wave interferometers to be adequate. In par-
ticular we consider a FIMI for the following reasons: first, a
FIMI with slanted mirrors produces linear fringes, which
can be imaged on fast, linear detectors for range-resolved
detection. Secondly, airborne interferometers call for stability
with respect to vibrations and temperature. An FIMI is more
easily built in a monolithic way than an FIMZ. Third, a mono-
lithic FIMI can be constructed to be both field widened
(FWFIMI) and temperature compensated. Finally, our design
of a monolithic FWFIMI can be arranged to be tilted to the
incident light, enabling a two-channel operation, in which case
the FIMI can reach the theoretical performance of the FIMZ
(see Section 2.B).
The proposed measurement concept is detailed more closely
in the following, considering certain assumptions: we consider
different lidar transmitters (lasers) used in WALES/DELICAT
(WAter vapor Lidar Experiment in Space project/
Demonstration of LIdar based Clear Air Turbulence project)
[38,39], AWIATOR [23], and MULTIPLY (ESA project). We
assume a moderately sized, airborne-compatible telescope of
about 15 cm diameter in a monostatic configura tion. Two
receiver concepts are presented: free beam and fiber coupled.
In a free-beam arrangement, the image of the fringes on the
detector is range dependent and changes with the misalignment
of the laser beam with respect to the telescope (see Section 3.A).
Even with a field-widened interferometer, a fiber-coupled
design may be preferred in the context of bias reduction [40]
in comparison to a free-beam setup (see Section 3.A). In a fiber-
coupled setup, the backscattered collimated light is coupled
into a large-core multimode fiber. The scrambling properties
of the fiber produce a constant far field of the out-coupl ed light
and a constant illumination of the interferometer, independent
of the position and the angular orientation of the light focused
on the multimod e fiber core during coupling (see Section 4).
The fiber-coupled concept is enhanced by the application of a
two-lens optical scrambler to increase the far-field scrambling
gain [41] and by mechanical vibrations for speckle reduction.
Because of the finite extension of the fiber core, the recolli-
mated light is expected to come by a centered range- and
misalignment-independent angular distribution. The FWFIMI
has a net inclination angle fixed such that one linear fringe
is imaged on a linear detector, which allows range-resolved
measurements in the near field in front of the aircraft.
To begin with, we summarize in Section 2 the fundamentals
of light scattering and of the FIMI as a direct-detection DWL,
and we compare the theoretical performances of different
direct-detection DWLs for the measurement of wind speeds.
In Section 3, the lidar geometry requirements and all aspects
of our design of a temperature-compensated FWFIMI are de-
scribed in detail. In Section 4, the integration of the FWFIMI
in a lidar receiver prototype for the measurement of wind
speeds in the near field is detailed. In Section 5, we evaluate
the proposed receiver concept in terms of expected perfor-
mance, using simulations, while taking into acco unt the detec-
tor and speckle noise during the data evaluation.
2. FUNDAMENTALS
A. Atmospheric Backscattering Spectrum and
Single-Scattering Lidar Equation
The atmospheric backscattering spectrum has contributions
from light scattering by molecules (RayleighBrillouin
scattering, rotational and vibrational Raman scattering) [42]
and from light scattering by aerosols/hydrometeors. The
RayleighMie-Laser spectrum (RMLS ) is introduced here to
model the spectral contributions from RayleighBrillouin
scattering by molecules, from scattering by spherical particles
[43] and from the lineshape of the laser as Gaussian-shaped
lines [24].
The quasi-elastic molecular (RayleighBrillouin) scatter-
ing spectrum (the so-called Cabannes line composed of the
LandauPlaczek line and the Brillouin doublet) is the result
of coherent scattering, which dominates molecular scattering,
and therefore, the scattered light is mostly polarized [44]. For
a DWL only, this central part is considered. The shape of the
Cabannes line depends on the density of the scatterers.
Accordingly, different regimes (hydrodynamic: e.g., gas-liquid
mixtures [45], kinetic: atmosphere, and Knudsen: thin gases)
can be discriminated. If the mean free path between the ther-
mally moving molecules is large, a Gaussian lineshape
(Knudsen) can be assumed. As the pressure increases and the
temperature decreases, density fluctuations moving at acoustic
speeds deform the lineshape (kinetic regime), until at the
6912 Vol. 55, No. 25 / September 1 2016 / Applied Optics
Research Article

hydrodynamic limit, two acoustic side bands (Brillouin lines)
appear.
The scattering properties of aerosols in the atmosphere, such
as the lidar ratio and particle depolarization rato, are highly
dependent on their type and shape, and there is large variability
[46]. Here, the simplifying assumption of spherical particles is
made (the Mie theory is valid only for spherical particles [43]).
This allows us to describe the backscattering from aerosols as
purely elastic and without depolarization.
In our simulations in Section 5, we consider an approxima-
tion of the (kinetic) S6 model [47]. It describes the kinetic re-
gime by the sum of three Gaussian functions (henceforth called
the G3 model) [48]. Here, for a simple analytical description of
the theoretical performance of the FIMI, the Knudsen model
(neglecting the Brillouin doublet) is presented in the following
to produce the RMLS. The neglected Brillouin contribution
does not affect the spectrums central frequency and has
therefore no effect on the performance of the wind speed mea-
surements [33]. Furthermore, there is no effect on the contrast
factor G in the vicinity of the optimal FSR determined in
Section 5.B.
The RMLS consists of the weighted sum of the Gaussian
molecular scattering peak and the Gaussian aerosol scattering
peak, convolved with the Gaussian laser lineshape,
I
RMLS
ν
1
R
b
1
ffiffiffiffiffi
2π
p
σ
G
exp
ν ν
c
ffiffi
2
p
σ
G
2
1
1
R
b
1
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2πσ
2
L
σ
2
w
p
exp
ν ν
c
ffiffi
2
p
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
σ
2
L
σ
2
w
p
2
:
(1)
Here, R
b
is the particle scattering ratio given by R
b
1 β
Mie
β
Ray
with the Mie and Rayleigh backscattering
coefficients [m
1
sr
1
] β
Mie
and β
Ray
. Values of β
Ray
for differ-
ent altitudes H can be obtained by β
Ray
pH
R
air
T Hm
air
× 550λ
L
nm
4
× 5.45 × 10
32
after Collis
and Russell [49], where pH and T H are altitude-depen-
dent pressures and absolute temperatures obtained from an
atmospheric model. Here, R
air
287.058 JkgK is the gas
constant of air, and m
air
4.811 × 10
26
kg is the mass of an
air molecule. A more complete model provided by Bucholtz
[50] includes the dispersion of the refractive index of air,
the anisotropy of air molecules, and the dispersion of the
depolarization factor of air. The differential scattering cross
section and backscattering coefficients calculated with the
simplified model stated above are 4.5% smaller than those cal-
culated by Bucholtz. This approximation has, however, a neg-
ligible influence on the absolute values of the signal-to-noise
ratios calculated in Section 5 (deviation: 2.3%). The values
of β
Mie
are scaled from values determined by Vaughan at
10.6 μm[51], using β
Mie
are scaled from values determined by
Vaughan at 10.6 μm[51], using β
Mie
β
Mie
10.6 μm×
10.6λ
L
μm×0.104×lnβ
Mie
10.6 μm 0.62. The total
backscattering coefficient is β β
Ray
β
Mie
. The Doppler
shift [Hz] is defined as Δν ν
c
ν
L
2ν
L
u
r
c, where ν
L
is the frequency of the laser, ν
c
is the Doppler-shifted central
frequency, and u
r
is the LoS wind speed. σ
L
Δν
L
ffiffiffiffiffiffiffiffiffiffiffi
8ln2
p
is the standard deviation [Hz] of the Gaussian laser line
shape, where Δν
L
is the laser linewidth (FWHM) [Hz].
σ
G
σ
2
Ray
σ
2
L
12
is the standard deviation in Hz of the
RayleighLaser spectrum, whereby σ
Ray
2λ
L
k
B
TN
A
m
air
12
is the standard deviation in Hz of the Rayleigh spec-
trum, where k
B
is the Boltzmann constant, N
A
is the Avogadro
constant, and T is the air temperature in the scattering volume.
λ
L
is the wavelength of the laser. σ
w
ffiffiffiffiffiffiffi
43
p
ν
L
u
r:m:s
is the
broadening due to the r.m.s. wind speed u
r:m:s
at flight level.
Typical, conservative values of u
r:m:s
and σ
w
at H
3040; 000 ft are 1.7 m/s [52] and 5.5 MHz for moderate
turbulence, which is about 3% as broad as the WALES trans-
mitter lineshape.
The amount of backscattered light received by the lidar is
calculated with the single-scattering lidar equation [53]ina
monochromatic approximation. The amount of time-resolved
EM wave power detected, imagined here as number of photons
per range gate n
p
(no assumptions on the nature of light) [54]is
given by
n
p
ν
L
;RE
L
ΔR
hν
L
A
R
2
ξrη
R
η
T
β exp
2
Z
R
0
αdr
: (2)
Here, R is the distance [m] of the light scattering volume in
front of the telescope. ΔR is the length [m] of the range gate.
E
L
is the transmitted energy of one laser pulse with pulse
duration τ
p
. h 6.62610
34
Js is Plancks constant. A is
the receiver telescope area [m
2
]. ξr is the range-dependent
overlap function. η
R
and η
T
are the receiver and transmitter
loss factors. α α
Ray
s
α
Ray
a
α
Mie
is the overall atmos-
pheric extinction coefficient [1/m], where α
Ray
s
8π3β
Ray
is the molecular extinction [1/m], α
Ray
a
is the molecular absorp-
tion [1/m], and α
Mie
is the extinction and absorption by
aerosols. For monodispersed spherical particles, the aerosol
extinction is α
Mie
k
0
β
Mie
[55]. Here, a constant extinction-
to-backscatter ratio of k
0
50 sr is assumed.
B. Theoretical Performance of a Fringe-Imaging
Michelson Interferometer
In this section, the princ iple of direct-detection DWLs
based on the FIMI is summarized, and the FIMIs optimized
theoretical performance is compared with other direct-
detection DWL methods.
The monochromatic transmission function (TF) of a
Michelson interferometer with inclined mirrors is cosine shaped
and varies in space along the x-axis. It can be written as
Ix;y;νFI
0
1 V cosϕ: (3)
Here, the linear interference fringes are aligned perpendicular to
the x-axis and parallel to the y-axis. V is the instrumental inter-
ference contrast; its contributions are described in Section 3.E
and F. ϕ 2πνcOPD
0
2θx is the fringe phase. OPD
0
is the fixed optical path length difference between the arms.
Assuming dispersion-free media in the interferometer arms,
OPD
0
is equal to cFSR, where FSR is the free spectral range.
The FSR is the width of one fringe period in [Hz]. θ is the angle
of inclination in the x-direction rotated along the y-direction.
θ creates a linear variation of OPD
0
within the illuminated area
of width d
w
. It determines the amount of periods N
p
of the TF.
To image exactly N
p
fringe periods, θ equals N
p
λ
L
2d
w
.The
prefactor F 0.5 accounts for the reflection losses of a
Research Article
Vol. 55, No. 25 / Se ptember 1 2016 / Applied Optics 6913

Michelson interferometer. The instrument function is the con-
volution of the laser lineshape with the TF. The received instru-
ment function (I
F
) is the convolution of the RMLS [Eq. (1)]
with the TF [Eq. (3)]:
I
F
x;y;νFI
0
1 W T;α cosϕ Δϕ: (4)
The resulting interference pattern is shifted in phase by
Δϕ 4πFSRλ
L
u
r
and has a reduced global fringe contrast
W T;αV × GFSR,where
GFSRexp
2
πΔν
L
FSR
2
×
1
R
b
exp2πσ
Ray
FSR
2

1
1
R
b

: (5)
The LoS wind speed u
r
is determined by measuring the phase
shift Δϕ between a reference instrument function and a Doppler
frequency-shifted received instrument function, which are
both imaged sequentially on a position-sensitive detector.
In the above description, the FIMI is a multichannel spectral
analyzer. A general way to find the optimal FSR setting of the
FIMI for the measurement of wind speeds is to introduce a
penalty factor κ
VLOS
, comparing the interferometer with an
ideal spectral analyzer (ISA). An ISA performs the perfect spec-
tral analysis because it is composed of an infinite number of
sampling channels, which sample the spectrum with Dirac-type
transmission functions. In an ISA, there is no loss of informa-
tion, energy, or spectral content. An interferometer (like the
FIMI) mixes the photons spatially and spectrally and therefore
underperforms compared to the ISA.
Bruneau and Cezard et al. derived expressions for the
optimal fixed optical path difference of the fringe-imaging
MachZehnder interferometer (OPD
FIMZ
3cmat 250 K)
[28] and the fringe-imaging Michelson interferometer
(OPD
FIMI
2.8 cm at R
b
1, T 273 K)[33], respectively.
The penalty factor κ
VLOS
(by Cezard et al. for pure Rayleigh
scattering) compares the CramerRao bounds (CRBs) of
the FIMI and the ISA. The CRBs are the respective lowest-
achievable standard deviations of an unbiased estimator.
Cezard et al. used a maximum-likelihood estimator approach
(which asymptotically reaches the CRB) for inversion and
obtained the CRBs of the wind speed as diagonal elements of
the inverse Fischer matrices of the FIMI and the ISA. The
underlying assumptions are that the signal is shot-noise limited,
obeys a Poisson statistic, and that the different channels are
statistically independent. κ
VLOS
can be written as a function
of the FSR,
κ
VLOS
ε
FIMI
ε
ISA
d
c
FSR
ffiffi
2
p
c
1
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 V
2
exp
8
c
d
c
FSR
2
s
12
: (6)
Here, ε
FIMI
and ε
ISA
are the CRBs for the FIMI and the ISA.
d
c
2cπσ
Ray
ffiffiffi
T
p
is the coherence length of the Rayleigh
signal. If the FSR is too large, the fringe phase sensitivity
S 4πFSRλ
L
in rad/(m/s) with respect to the Doppler
shift is small. If the FSR is too small, the fringe constrast is
too small for an efficient determination of the fringe phase.
The FSR is optimized for the worst condition, where no aero-
sols contribute to backscattering (R
b
1). Here, the contrast
factor G is equal to 66%. In Fig. 1, κ
VLOS
is plotted as a func-
tion of the FSR at 273 K for R
b
1. The plot includes contrast
factors GFSR for R
b
1 (green) and R
b
2 (magenta) and
the phase sensitivity SFSR (black).
Cezard et al. showed that when R
b
increases, the global con-
trast increases, thus producing lower penalty factors, and that a
decrease of the temperature by 40 K decreases κ
VLOS
by 10%
[33]. The best measurement performance is thus expected at
low temperatures and high scattering ratios. The optimal
FSR value of 10.7 GHz 6.8 × σ
Ray
(at R
b
1, T 273 K)
is found at the minimum: κ
VLOS
4.4 (dotted line).
Table 1 lists the penalty factors of other DWL techniques
obtained in similar ways for comparison.
The two filter-based techniques, the double-edge Fabry
Perot (DFP) and the DMZ, have good theoretical performance,
but they are sensitive to the RayleighMie backscattering scat-
tering ratio and require inversion of the lidar signal to correct
this [27]. The fringe-imaging FabryPerot technique (FIFP) is
complicated by the evaluation of circular fringe patterns or
the complexi ties of circle-to-line converters [59]. The fringe-
imaging Fizeau interferometer (FIFI) provides linear fringes.
However, the fringe shape is very sensitive to the incident an-
gular distribution (see Section 3.A) and does require collimated
light, which complicates range-dependent measurements in the
near field (50300 m). This is not the case with field-widened
Michelson and MachZehnder interferometers. The QMZ and
FIMZ techniques have very low penalty factors and do not re-
quire knowledge of the scattering ratio. It can be seen that the
penalty factor for the FIMI is about two times the penalty
factor for the FIMZ. This is because half of the light is back
reflected [factor F, Eq. (3)].
A possible option to decrease the FIMI penalty factor by a
factor of two is to tilt the FIMI at a small angle with respect to
Table 1. Penalty Factors for Wind Speed Measurement
Technique κ
VLOS
Technique κ
VLOS
DFP 2.4 [56] DMZ 1.65 [27]
FIFP 3.1 [57], 24[58] QMZ 2.3 [27]
FIMI 4.4 [33] FIMZ 2.3 [28]
Fig. 1. Penalty factor of wind speed measurement κ
VLOS
(blue),
contrast factor G(FSR) (green: R
b
1, magenta: R
b
2), and phase
sensitivity S (black) as a function of FSR for 273 K, R
b
1 at a wave-
length of 355 nm.
6914 Vol. 55, No. 25 / September 1 2016 / Applied Optics
Research Article

Figures (10)
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Abstract: A high-performance airborne UV Rayleigh lidar system was developed within the European project DELICAT. With its forward-pointing architecture, it aims at demonstrating a novel detection scheme for clear air turbulence (CAT) for an aeronautics safety application. Due to its occurrence in clear and clean air at high altitudes (aviation cruise flight level), this type of turbulence evades microwave radar techniques and in most cases coherent Doppler lidar techniques. The present lidar detection technique relies on air density fluctuation measurement and is thus independent of backscatter from hydrometeors and aerosol particles. The subtle air density fluctuations caused by the turbulent air flow demand exceptionally high stability of the setup and in particular of the detection system. This paper describes an airborne test system for the purpose of demonstrating this technology and turbulence detection method: a high-power UV Rayleigh lidar system is installed on a research aircraft in a forward-looking configuration for use in cruise flight altitudes. Flight test measurements demonstrate this unique lidar system being able to resolve air density fluctuations occurring in light-to-moderate CAT at 5 km or moderate CAT at 10 km distance. A scaling of the determined stability and noise characteristics shows that such performance is adequate for an application in commercial air transport.

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TL;DR: A combined feedback and feedforward active load alleviation system and its associated design and tuning methodology that remains very easy to use and tune, thanks to a limited number of parameters that can easily be interpreted physically and that exhibit only very little and very predictable couplings.
Abstract: This paper presents a combined feedback and feedforward active load alleviation system and its associated design and tuning methodology The feedback part is strongly structured and its robust performance across the flight envelope is ensured by the use of a multi-model and multi-objective controller design approach The feedforward function is based on a Doppler LIDAR sensor and the processing of the measurements as well as their physical interpretation combines various ideas from the system identification, the signal processing, and the control design domains The proposed solution remains very easy to use and tune, thanks to a limited number of parameters that can easily be interpreted physically and that exhibit only very little and very predictable couplings The performance and behavior of the active load alleviation functions is shown extensively based on a representative flexible long range aircraft model (based on the Airbus XRF1 configuration)

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References
More filters

Journal ArticleDOI
TL;DR: A method is described for the minimization of a function of n variables, which depends on the comparison of function values at the (n 41) vertices of a general simplex, followed by the replacement of the vertex with the highest value by another point.
Abstract: A method is described for the minimization of a function of n variables, which depends on the comparison of function values at the (n 41) vertices of a general simplex, followed by the replacement of the vertex with the highest value by another point. The simplex adapts itself to the local landscape, and contracts on to the final minimum. The method is shown to be effective and computationally compact. A procedure is given for the estimation of the Hessian matrix in the neighbourhood of the minimum, needed in statistical estimation problems.

25,414 citations


"Design of a monolithic Michelson in..." refers methods in this paper

  • ...Here we use a “downhill simplex fit” (Nelder–Mead method [79]), which does not use derivatives and therefore converges very safely....

    [...]


Journal ArticleDOI
TL;DR: The dispersion of the depolarization factor is shown to affect the Rayleigh phase function slightly, by approximately 1% in the forward, backscattered, and 90° scattering-angle directions.
Abstract: Rayleigh-scattering cross sections and volume-scattering coefficients are computed for standard air; they incorporate the variation of the depolarization factor with wavelength. Rayleigh optical depths are then calculated for the 1962 U.S. Standard Atmosphere and for five supplementary models. Analytic formulas are derived for each of the parameters listed. The new optical depths can be 1.3% lower to 3% higher at midvisible wavelengths and up to 10% higher in the UV region compared with previous calculations, in which a constant or incorrect depolarization factor was used. The dispersion of the depolarization factor is also shown to affect the Rayleigh phase function slightly, by approximately 1% in the forward, backscattered, and 90° scattering-angle directions.

622 citations


"Design of a monolithic Michelson in..." refers methods in this paper

  • ...The differential scattering cross section and backscattering coefficients calculated with the simplified model stated above are 4.5% smaller than those calculated by Bucholtz....

    [...]

  • ...A more complete model provided by Bucholtz [50] includes the dispersion of the refractive index of air, the anisotropy of air molecules, and the dispersion of the depolarization factor of air....

    [...]


Journal ArticleDOI
Abstract: Rayleigh scattering is a powerful diagnostic tool for the study of gases and is particularly useful for aiding in the understanding of complex flow fields and combustion phenomena. Although the mechanism associated with the scattering, induced electric dipole radiation, is conceptually straightforward, the features of the scattering are complex because of the anisotropy of molecules, collective scattering from many molecules and inelastic scattering associated with rotational and vibrational transitions. These effects cause the scattered signal to be depolarized and to have spectral features that reflect the pressure, temperature and internal energy states of the gas. The very small scattering cross section makes molecular Rayleigh scattering particularly susceptible to background interference. Scattering from very small particles also falls into the Rayleigh range and may dominate the scattering from molecules if the particle density is high. This particle scattering can be used to enhance flow visualization and velocity measurements, or it may be removed by spectral filtering. New approaches to spectral filtering are now being applied to both Rayleigh molecular scattering and Rayleigh particle scattering to extract quantitative information about complex gas flow fields. This paper outlines the classical properties of Rayleigh scattering and reviews some of the new advances in flow field imaging that have been achieved using the new filter approaches.

461 citations


ReportDOI
01 Aug 1969
TL;DR: The primary purpose is to explain the concept and philosophy underlying MIL-F-8785B and to present some of the data and arguments upon which the requirements were based, and to define their significance and relationship to each other.
Abstract: : The document is published in support of Military Specification MIL-F-8785B, 'Flying Qualities of Piloted Airplanes.' It was compiled after an extensive literature review and many meetings and discussions with personnel from essentially all concerned civilian and governmental organizations. The primary purpose is to explain the concept and philosophy underlying MIL-F-8785B and to present some of the data and arguments upon which the requirements were based. A secondary purpose is to present what are believed to be the important governing variables in the field of flying qualities and to define their significance and relationship to each other. The significance of such mission- oriented factors as airplane class, flight phase, flight condition, loading and configuration is discussed, as is the treatment of failure states. The document should also, to a degree, serve as a summary of the state of the flying qualities art as determined from operational experience, flight test, experiment, analysis and theory.

350 citations


Journal ArticleDOI
Abstract: We analyze in detail, in the kinetic regime, the behavior of a model kinetic equation previously used by us for the description of the density fluctuation spectrum in molecular gases. We find that ...

277 citations


"Design of a monolithic Michelson in..." refers methods in this paper

  • ...In our simulations in Section 5, we consider an approximation of the (kinetic) S6 model [47]....

    [...]


Frequently Asked Questions (2)
Q1. What contributions have the authors mentioned in the paper "Design of a monolithic michelson interferometer for fringe imaging in a near-field, uv, direct-detection doppler wind lidar" ?

In this work, a concept for an airborne, UV, direct-detection Doppler wind lidar receiver is presented. A monolithic, tilted, field-widened, fringe-imaging Michelson interferometer ( FWFIMI ) combines the advantages of low angular sensitivity, high thermo-mechanical stability, independence of the specific atmospheric conditions, and potential for fast data evaluation. 

Future works are aimed at realizing a receiver prototype, including an FWFIMI for range-resolved LoS wind speed measurements. The authors sincerely acknowledge the technical support by I. Miller ( LightMachinery Inc., Canada ). The authors further thank N. Cézard ( Office national d ’ études et de recherches aérospatiales, France ), D. Bruneau ( Laboratoire Atmosphères, Milieux, Observations Spatiales, France ), V. Freudenthaler ( Ludwig-Maximilians-Universität, Germany ), G. Avila ( European Southern Observatory, Germany ), and J. Harlander ( St Cloud State University, U. S. A. ) for the fruitful discussions and correspondence.