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Abstract
The stratospheric wind field provides significant information on the dynamics, constituent, and energy transport in the Earth's atmosphere. The measurement of the atmospheric wind field on a global basis at these heights is still lacking because few wind imaging interferometers have been developed that can measure wind in this region. In this paper, we describe an advanced compact static wind imaging Michelson interferometer (SWIMI) developed to measure the stratospheric wind field using near-infrared airglow emissions. The instrument contains a field widened and thermal compensated interferometer with a segmented reflective mirror in one arm, which replace the moving mirror in a conventional Michelson interferometer, to provide interference phase steps. The field widened, achromatic, temperature compensated scheme has been designed and manufactured. The characterization, calibration, inversion software, and test of the instrument have been completed. The capacity of two-dimensional wind, temperature, and ozone measurement of the instrument has been verified in the lab experiment and model simulation. What we believe to be the novel principle, modeling, design, and experiment demonstrated in this paper will offer a significant reference to the static, simultaneous and real-time detection and inversion of the global wind field, temperature, and ozone.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The atmospheric wind field is an important atmospheric dynamic parameter, which reflects the local or global atmospheric fluctuation, the coupling process between the atmospheric layers, and the characteristics of material and energy transport in the global range [1,2]. The remote sensing of the global atmospheric wind field by optical interference technology is of great significance to human understanding for the mechanism and development of important climate phenomena such as atmospheric circulation, global climate change, and sudden stratospheric warmings.
Passive Doppler wind imaging interferometry measures the atmospheric wind field using the natural airglow emission in the atmosphere as the light source. The Wind Imaging Interferometer (WINDII) is the first use of field widening Doppler Michelson imaging in space. It was carried on the Upper Atmosphere Research Satellite (UARS) and launched in 1991 [3–5]. The precursor of WINDII is the wide-angle Michelson Doppler imaging interferometer (WAMDII) that was proposed by Shepherd et al. in 1985 [6]. The other instrument carried on UARS for wind measurement is the high-resolution Doppler imager (HRDI), which is based on the Fabry-Perot interferometer [7–10]. HRDI mainly observes the emission of ${\textrm{O}_2}{}^1\Sigma $ (A, B, and $\gamma $ bands), which contains the wind information of the stratosphere, mesosphere, and lower thermosphere. The thermosphere-ionosphere-mesosphere energetics and dynamics Doppler interferometer (TIDI) is a passive wind imaging interferometer based on Fabry-Perot interferometer, which has been launched in December 2001 [11–13]. It utilized the circle-to-line imaging optic and has a vertical spatial resolution of 2 km. The Michelson interferometer for global high-resolution thermospheric imaging (MIGHTI) is the instrument designed for the Ionospheric Connection Explorer (ICON), which was launched in October 2019. It is a field-widened, temperature compensated Doppler asymmetric spatial heterodyne (DASH) spectrometer, observing the Doppler shift of the atomic oxygen red and green lines at 630.0 nm and 557.7 nm wavelength [14–16].
The E-region wind interferometer (ERWIN) is a typical ground-based wind measurement instrument, which is operating at Polar Environment Atmospheric Research Laboratory (PEARL) [17–19]. ERWIN is based on the field widened Michelson interferometer that contains a moving mirror for interferogram fringes scan. Many other schemes for atmospheric wind passive measurement are in research, such as the polarizing atmospheric Michelson interferometer (PAMI) [20,21], the stratospheric wind interferometer for transport studies (SWIFT) [22–24], the Michelson interferometer for airglow dynamics imaging (MIADI) [25,26], the mesospheric imaging Michelson Interferometer (MIMI) [27], the dynamic atmosphere Mars observer (DYNAMO) [28], the waves Michelson interferometer (WaMI) [29,30] and the Birefringent Doppler wind imaging interferometer (BIDWIN) [31,32].
In this paper, we developed the static wind imaging Michelson interferometer (SWIMI) for the measurement of the stratospheric wind field. Based on the concept of four-sectored wind imaging interferometry proposed by Ward et al [29], we implemented the full scheme of SWIMI prototype. The field widened, achromatic, temperature compensated glass pairs, four-sectored phase step mirror, and the optical system have been designed and manufactured (a detailed discussion of these aspects of the design can be found in Rong et al [33], where a similar instrument is proposed for Mars observations). The characterization, calibration, and test of the instrument have been completed using the proposed method for it. To test the capacity of two-dimensional wind measurement of the instrument, we designed and manufactured the Doppler shift simulation system [26]. The capacity of two-dimensional wind, temperature, and ozone measurement of the novel instrument has been verified in the lab experiment and model simulation. The principle, modeling, design, and experimental demonstration in this paper will offer a significant reference to the static, simultaneous and real-time detection and inversion of the global wind field, temperature, and ozone.
2. Configuration and system design
The optical layout of the SWIMI system is depicted in Fig. 1. SWIMI consists of a group of filters, fore optics, a beam splitter, two glass slabs, a fully reflective mirror, a sectored mirror, middle optics, pyramid prism, imaging optics, and a detector [33]. Passing through the filters, the selected emission lines enter the system. The fore optics and the middle optics are the combinations of telescope and collimator. The collimated light enters the static Michelson interferometer and is split into two beams by the beam splitter. One beam passes through Glass 1 and the air gap, then reflected by the sectored mirror, while the other beam passes through Glass 2 and is reflected by the fully reflective mirror. Both two beams return to the beam splitter, the beam from the sectored mirror is divided into four quadrants, each quadrant has specified phase retardation produced by the designed film coating of the sectored mirror. The path difference steps of the quadrants are $\lambda /4$ at a wavelength of 1.27 µm. Using the middle optics, the sectored mirror and the pyramid mirror are conjugated. Therefore, after passing through the middle optics, the collimated light beams are exactly split into four beams corresponding with the four sectors of the sectored mirror.
Simultaneously, the light reflected from the normal mirror is also split into four beams by the pyramid prism. The four beams interfere with the corresponding four beams reflected from the sectored mirror. Using the imaging optics, those light beams are focused on the detector and form four interferograms. The intensities of the four interferograms can be expressed as
The light source utilized for SWIMI is the O21Δ (0,0) emission band at 1.27 µm. The dayglow is mainly distributed in the vertical height range of 40∼100 km, with a peak intensity of 500MR for limb observation. We used the same six lines in the O21Δ (0,0) emission band as selected for WaMI [29,30]. The effective basic OPD of the interferometer is 10 cm, which ensures that the precision of wind measurement is < 5 m/s at SNR ∼150. The field widening, achromatic and thermal compensation scheme has been designed to get a high throughput and thermal stable Michelson interferometer. The principle for field widening, achromatic and thermal compensation is given by [3,33]
When selecting proper glass pairs for compensation, there are a few issues in practical engineering that need to be considered [33]. Besides the refractive indices, the temperature coefficient of refraction, and the coefficient of thermal expansion in the computer program, we should also check the internal transmittance, color, hardness, and water resistance of the glasses. The large difference in refractive index between the two glasses should also be avoided. The optimal glass combination was selected from more than 40 thousand glass pairs, based on the SCHOTT optical glass catalog and CDGM optical glass catalog [34,35]. Table 1 lists the optimal combinations for the three-layer structure scheme for SWIMI.
Table 1. The optimal combinations for the three-layer structure scheme for SWIMI.
The performance of the optimal glass combination has been tested by the instrument model in simulation, which is shown in Fig. 3. The half field of view can be larger than 4° with the OPD variation of less than $\lambda /10$. When the temperature change is less than ±2 K, the variation of the reference OPD is less than 0.3 nm.
The core component of the static Michelson interferometer to realize the simultaneous detection of the four interferogram intensities is the sectored mirror, which can modulate the phase retardation through the specially designed thin film. Because the detection wavelength band for SWIMI is relatively narrow (about 14 nm), we use the film coating with four thicknesses to get four 90° stepped reflective phase retardation.
We plated SiO2 monolayers with different physical thicknesses on the substrate to form the bottom layer of each zone. Then the same high reflective film was plated on the four quadrants, which is shown in Fig. 4. The thicknesses of the films of four zones were measured by a stylus-based surface profiler, which is 0 nm, 158 nm, 322 nm, and 484 nm, respectively. The stepped reflection phases at 1270 nm corresponding to those thicknesses are 0°, 89.57°, 182.55°, and 274.39°, respectively. In practice, the real reflection phases are also affected by the tilt and pitch of the sectored mirror, which should be calibrated before the instrument is put into use. The reflectivity of the sectored mirror was also tested. The overall reflectivity of the film coating is higher than 99.9% in the 1270 nm band for wind measurement.
The scientific objective of SWIMI is measuring the velocity of wind, the temperature, and the concentration of ozone of the atmosphere at altitudes of 25 km to 110 km, with a 2 km vertical spatial resolution. Based on the objective, we designed a limb view orbit for SWIMI at the altitude of 600 km, and all the parameters of the optical system have been determined, which is shown in Table 2.
Table 2. The designed parameters for the optical system of SWIMI.
It should be noted that the positions of the entrance pupil, the sectored mirror, and the pyramid prism are conjugate, which can avoid the aliasing of different parts of the off-axis beam in aperture division. SWIMI fits within an envelope of 616 mm × 550 mm × 122 mm and weighs 14.4 kg.
3. Installation, calibration, and experiment
The SWIMI prototype instrument was manufactured and installed at the Institute of Space Optics of Xi’an Jiaotong University. The appearance of the instrument is shown in Fig. 5.
To obtain the Doppler wind velocity, the parameters of the SWIMI prototype are calibrated. Unlike the moving mirror Michelson interferometer, the relative intensities and the instrument visibilities of SWIMI can vary among four quadrants, which correspond to the four phase steps [36,37]. If we assume the relative intensities and the instrument visibilities in various measurements are fixed, for a single point, the intensity $I_i^j$ of the ith step (frame) in the jth measurement can be modeled as
where $I_0^j$ is the mean intensity, ${V^j}$ is the line visibility. The parameters to be calibrated are the relative intensities ${A_i}$, instrument visibilities ${U_i}$, and phase steps ${\varphi _i}$ (i = 1, 2, 3, 4). The calibration can be done by scanning wavelength or scanning temperature. In the calibration experiment, we found that the wavelength of the 1268 nm diode laser varied with current, so the scan of wavelength was realized by adjusting the current of the diode laser.The intensities of the center points of four quadrants measured by wavelength scanning of SWIMI has been analyzed. The frequency of the cosine curve is changing in the scan, which means the variation of the wavelength with the current is not fully linear. Thus, the traditional curve fitting method does not work here for calibration. The LMS algorithm for the wind imaging interferometer with a moving mirror also works well here, but the solutions become more complex with more variables [38]. There is an alternative calibration method based on the Lissajous map. It offers a simple way to retrieve the ${A_i}$, ${U_i}$, and ${\varphi _i}$ simultaneously.
We draw the measured intensities of two quadrants in one plot and fit the formed ellipse. Using the parameters of the ellipse, the ${A_i}$, ${U_i}$, and ${\varphi _i}$ can be calculated. Applying the calibration to all the points in the field of view, we can get the maps of the calibrated ${A_i}$, ${U_i}$, and ${\varphi _i}$, which are shown in Fig. 6–8.
Two sets of wind measurements were conducted in the lab to verify the feasibility of the SWIMI system, which also were described in detail by Langille et al [26]. The first experiment we did is the single point wind measurement by observing one point on the wind wheel rotating at a series of velocities. This experiment tested the Doppler shift measuring capacities of SWIMI without imaging. The second experiment is the two-dimensional wind measurement by imaging an area of the wind wheel rotating at a certain velocity. Both experiments can be carried out using the verification system shown in Fig. 9.
The wind wheel system for producing the wind field is also shown in Fig. 9. We used a 1270 nm diode laser from Changchun New Industries Optoelectronics Tech. Co. Ltd., as the source. Behind the diffuser, the light beam passed through the beam splitter and illuminated on the wind wheel. The wind wheel was oriented at an angle of 45° to the optical axis and attached to a motor, the rotation rate of which can be accurately controlled by a digital controller. Light retro-reflected from the wind wheel was reflected by the beam splitter and collimated before being collected by the SWIMI system. Finally, the interferogram data was obtained and processed by the computer.
The wind field measurement experiment setup for SWIMI is shown in Fig. 10. In each measurement, the dark images of the system and the zero wind must be taken to correct the intensities and remove the background phase. Although the thermal compensation design for SWIMI is implemented in the prototype, the small thermal drift and wavelength drift of the laser could affect the precision of wind measurement. Therefore, we used the following measurement sequence for Doppler wind measurement.
Initially, a dark image of the system was taken that was used to correct the images in the experiment. Then a measurement of the zero wind was taken with the wheel stationary. Next, we measured the rotating wheel to get the Doppler wind and then reduced the rotation rate of the wheel to zero. We repeated the process to get a relatively good background phase by averaging the two zero wind measurements for each Doppler wind measurement.
The velocity of the center point of the field of view was measured in the single-point experiment. The distance from the wheel center to the point is 37.5 mm. The tested rates of the wind wheel were 500 r/min to 8000 r/min, with a step of 500 r/min. By averaging 25 neighbor pixels, the SNR reached ∼200. The measured wind velocity is plotted versus the wind wheel velocity in Fig. 11. The straight blue line is the expected velocity, the red points are the average measured velocity of seven measurements and the error bars are the standard deviations. The average standard deviation of the sixteen points is 4.5 m/s, which confirms that the atmospheric Doppler wind measurements with a precision of 5 m/s are feasible using this technique.
Fig. 11. Measured wind velocity for single-point measurements is plotted versus the wind wheel velocity.
After the single-point measurement, the velocity of each bin in the field of view was measured by imaging the two-dimensional wind field. The wind field was produced by illuminating a circle area on the wind wheel. The position of each pixel relative to the center of the wind wheel was determined by imaging a grid-scale printed on a circle transparent plastic sheet that had the same size as the wind wheel. As is shown in Fig. 12, the center point of the field of view is 37.5 mm to the center of the wind wheel. The real size of the imaged area on the wind wheel is 25 mm × 25 mm. Seven measurement sets were taken using a rotation frequency of the wheel of 8000 r/min. The exposure time was adjusted to get an SNR of ∼200 by averaging the neighbor pixels. Because all bins in the wind field are measured simultaneously, there is no thermal or wavelength drift across the field of view. In the background removal process, the thermal drift calibration for one point can be applied to the whole field. The expected wind field is shown in Fig. 12(a) and the measured wind field is shown in Fig. 12(b). The velocity gradients of the two wind images are consistent.
Fig. 12. The expected and measured two-dimensional wind field across the wind wheel. (a) expected wind field; (b) measured wind field.
The difference between the expected and measured wind field is shown in Fig. 13. Most of the field of view has a small difference of less than 2 m/s. The errors in the edge regions are much larger because of the lower SNR. There are some other possible error sources such as the precision of the calibrated instrument parameters, the stability of the laser, the effects of the laser speckle, the residual errors of the thermal drift calibration and the presence of scattered laser light from the beam splitter, which will be undertaken in the future.
4. Inversion algorithm development
Besides wind measurement, SWIMI is also capable to measure the atmospheric temperature, pressure, and ozone number density of the stratosphere. We developed the inversion software for SWIMI. The inputs for the software are the observed interferograms produced by forward model, which is a full simulation of the atmospheric radiation and transmission process. The outputs are the information of wind, temperature, and ozone number density.
The radiation intensity (interferograms) I observed by the interferometer can be described by the Michelson equation [39,40]
where U is the instrumental visibility, $\varphi$ is the instrumental phase (phase steps for solving the Michelson equation), and ${I^{\prime}_b}$ denotes the sum of background radiation, dark current and random noise. The atmospheric apparent quantities ${J_1}$, ${J_2}$ and ${J_3}$ can be written asThe inversion algorithm has three steps as follow:
- 1) The atmospheric apparent quantities J1, J2, and J3 are retrieved from the detected interferogram, and the temperature, pressure, band volume emission rate, and oxygen number density are retrieved from J1. This step is called T-P-BVER-nO2 inversion [40].
- 2) After the T-P-BVER-nO2 inversion, ozone number density is obtained from photochemical equilibrium inversion, which is called ozone inversion.
- 3) The wind speed is retrieved from J2 and J3 through the “onion peeling” algorithm, which is called wind field inversion [41].
To verify the performance of the inversion software for SWIMI, a forward model was developed. The simulated interferograms of limb view were generated by the forward model and input into the inversion software. The inversion results of atmospheric parameters were obtained within a few iterations.
Figure 14 shows the inversion results of temperature (T). For temperature inversion, the average absolute error of the last iteration result relative to the “real” temperature (T) is 3.445 K, and the average relative error is 1.475%. Figure 15 shows the inversion results of ozone number density (nO3) based on the last iteration results of T-P-BVER-nO2 inversion. The atmospheric ozone abundances may be deduced from the measured volume emission rates using a simple photochemical model based on that described by Evans et al [42]. The “real” state setting is the same as that in T-P-BVER-nO2 inversion. As can be seen from Fig. 15, within the whole inversion height range, the inversion profile is in good agreement with the “real” ozone number density profile, with an average relative error of 2.832%.
Fig. 14. The inversion result of temperature (T), in which the black dotted line is the real height profile, and the red solid line is the height profile obtained in final iteration of the inversion. The absolute error (middle) and relative error (right figure) of the inversion profile are calculated.
Fig. 15. The inversion results of ozone (nO3), in which the black dotted line is the real height profile, and the red solid line is the inversion height profile. The absolute error (middle) and relative error (right figure) of the inversion profile are calculated.
Figure 16 shows the results of wind speed inversion in the line-of-sight direction. It can be seen that the average absolute error of wind speed in the whole inversion height range is 4.02 m/s. The inversion assumes that all parameters are described in the inertial coordinate system. In fact, interferograms are recorded in the spacecraft coordinate system. Therefore, the estimated spacecraft velocity needs to be removed from the retrieved Doppler frequency shift. After obtaining the line-of-sight wind in the inertial coordinate system, it is converted to the earth fixed coordinate system by eliminating the contribution of earth rotation at each height.
Fig. 16. The wind speed inversion results along the line of sight, in which the red solid line is the inversion profile and the black dotted line is the “real” profile, in which the absolute error of the inversion profile (right figure) is calculated relative to the red solid line.
5. Discussion
In view of many challenging problems in the theory, technology, experiment, and engineering of passive detection of the atmospheric wind field in the world, we implemented the SWIMI for the measurement of the stratospheric wind field. Although the instrument verification was completed in the lab using laser and rotational wheel, the results are still valuable and the capacity of the instrument for airglow observation can be predicted according to the relationship between wind precision and SNR of the interferogram. The expressions for the uncertainty in the wind measurement for the Michelson were originally developed by Ward and Rochon and general expressions for the sensitivity of Doppler wind measurements are presented by Kristoffersen et al [19,23]. In the ideal case, where four samples are obtained with 90-degree phase steps, the expression for the standard deviation of the wind measurement is
To calculate the needed SNR for a wind precision of ∼ 5 m/s, we substitute the instrument parameters into Eq. (10). The designed effective optical path difference ${\Delta _0}$ is 10 cm and the averaging wavelength of the airglow emission lines is 1270 nm. UV is 0.6 in the calibration of SWIMI. Thus, the wind precision of < 5 m/s is achievable with an SNR of ∼ 160.The O21Δ (0,0) emission has an expected limb intensity of 2000 kR, the expression for the signal S at the detector is given by
The etendue $A\Omega $ for SWIMI is 0.198 cm2sr, the quantum efficiency $\eta $ is 0.9, and $\tau $ is 0.1 when accounting for the transmittance of the filter and lens system. If the spatial resolution is 43*43, we can get an SNR of ∼160 with an integration time of 0.02 seconds. This calculation combines the SNR of ∼160, the precision of 5 m/s, the expected atmospheric emission rates, and realistic instrument parameters.6. Conclusion
In conclusion, we implemented the concept of static four-sectored wind interferometry and constructed a prototype, the SWIMI, to measure Stratospheric wind fields, temperature, and ozone concentration using near-infrared airglow emissions. The instrument contains a field widened and thermally compensated interferometer with a segmented reflective mirror in one arm, which replaced the moving mirror in a conventional Michelson interferometer. The field widened, achromatic, temperature compensated scheme has been designed and manufactured. The characterization, calibration, inversion software, and test of the instrument have been completed. The capacity of two-dimensional wind, temperature, and ozone measurement of the instrument has been firstly verified in the lab experiment and model simulation. The novel principle, modeling, design, and experiment demonstrated in this paper will offer a significant reference to the static, simultaneous and real-time detection and inversion of the global wind field, temperature, and ozone.
Funding
Major International (Regional) Joint Research Project of National Natural Science Foundation of China (42020104008, 41530422); Shaanxi Fundamental Science Research Project for Mathematics and Physics (22JSZ007); Sichuan Province Science and Technology Support Program (2023NSFSC0747); National High-tech Research and Development Program 863 Program (2012AA121101).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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