Design of a monolithic Michelson interferometer for fringe imaging in a near-field, UV, direct-detection Doppler wind lidar.
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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Citations
6 citations
Cites background or methods from "Design of a monolithic Michelson in..."
...Within this chapter content of Herbst and Vrancken (2016) is used....
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...Parts of this section are based on Herbst and Vrancken (2016)....
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...1 s, such that WALES is outperformed (Herbst and Vrancken, 2016)....
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...Inset: Global fringe patterns for different dz and raytracing layout of the FWFIMI (Herbst and Vrancken, 2016)....
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...The concept’s performance could optionally be enhanced by a factor of √ 2 by employing the FWFIMI in a 2◦-tilted configuration, and by imaging the back-reflected interference fringe (second channel) on a second linear detector (Herbst and Vrancken, 2016)....
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5 citations
Cites background or methods from "Design of a monolithic Michelson in..."
...…MZ interferometers in photometric or fringe imaging modes have already been proposed in HSRL systems for wind measurements or scattering analysis (Bruneau, 2001; BP03; Cézard et al., 2009; Liu et al., 2012; Bruneau et al., 2015; Cheng et al., 2015; Herbst and Vrancken, 2016; Tucker et al., 2018)....
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...It can also appear convenient to use the linear fringe’s interferometric pattern imaged on a CCD array, as its position depends linearly on the Doppler shift (Herbst and Vrancken, 2016)....
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5 citations
5 citations
Cites background from "Design of a monolithic Michelson in..."
...The interested reader is referred to [16, 17, 38] and the references therein for further information on the sensor technologies that could provide this capability....
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4 citations
References
27,271 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....
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669 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....
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...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....
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508 citations
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295 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]....
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Q2. What are the future works in "Design of a monolithic michelson interferometer for fringe imaging in a near-field, uv, direct-detection doppler wind lidar" ?
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.