A space-based tempo-spatially modulated polarization atmosphere Michelson interferometer (TSMPAMI) is described. It uses the relative movement between the TSMPAMI and the measured target to change optical path difference. The acquisition method of interferogram is presented. The atmospheric temperatures and horizontal winds can be derived from the optical observations. The measurement errors of the winds and temperatures are discussed through simulations. In the presence of small-scale structures of the atmospheric fields, the errors are found to be significantly influenced by the mismatch of the scenes observed by the adjacent CCD sub-areas aligned along the orbiter’s track during successive measurements due to the orbital velocity and the exposure time. For most realistic conditions of the orbit and atmosphere, however, the instrument is proven suitable for measuring the atmospheric parameters.
© 2011 OSA
Classically, a temporally modulated wind imaging interferometer (TMWINDII) is used to measure the atmosphere. The TMWINDII is based on a scanning Michelson interferometer, e.g. WINDII (the Wind Imaging Interferometer) on UARS (Upper Atmosphere Research Satellite) and PAMI (the Polarizing Michelson interferometer for measuring thermospheric winds) [1–3]. The scanning system changes the optical path difference (e.g. four times) to get different interference intensities, from which the information of atmospheric wind velocity and temperature can be derived. The scanning system requires high precise mechanism and high stable design, implying high cost and substantial bulk [2, 4, 5].
Because of these drawbacks, static systems are encouraged to be developed, e.g. MIMI (the Mesospheric Imaging Michelson Interferometer) for MODE mission  and SPAMI (static polarizing atmosphere Michelson interferometer) . These devices are called spatially modulated wind imaging interferometers (SMWINDII). SMWINDII uses a divided mirror or a divided polarizer instead of scanning system in TMWINDII to change optical path difference [8, 9]. But the divided mirror technology needs a pyramid to divide the light from the same source into four parts. This implies a very complex optical system.
Another method, discussed here, is a system called tempo-spatially modulated polarizing atmosphere Michelson imaging interferometer (TSMPAMI). In this device, four sub-areas on the CCD detector are aligned along the moving direction of an orbiter; each has an optical phase change of quarter wavelength with respect to the adjacent one. A given target area of the atmosphere can be imaged successively onto the sub-areas of the CCD during the orbiter motion. Thus, the TSMPAMI does not require a scanning system or a divided mirror system. It uses the relative movement between the TSMPAMI and the measured target to change optical path difference. Because TSMPAMI has no moving part, it is more robust than TMWINDII. And because TSMPAMI does not need divided mirror system, its optical system is more simpler than that of SMWINDII. So it is valuable for the atmosphere measurement, resource investigation and environment observation, etc.
On the other hand, for TSMPAMI, the interference intensities of the same target are not acquired at the same time, and the same target may not be imaged exactly onto each of the CCD sub-areas if the orbiter’s motion and the sampling time do not match perfectly. This time-space mismatch will introduce some measurement errors in the presence of fluctuation of atmospheric field. Since the exposure time is very short (about 28 sec in our discussion) and the half field view is small (about 3 degree), the effect due to the time-mismatch and the phase change could be neglected for the atmospheric motions with periods generally greater than a few minutes. In this paper, the errors due to the space-mismatch are discussed through computer simulations.
An optical setup of the TSMPAMI is shown in Fig. 1 . TSMPAMI is based on a modified PAMI. The system consists of one telescope lens system, one polarizer, one polarizing beam splitter (PBS), two different component glasses, three quarter wave plates (QWP), two mirrors, one imaging lens system and one polarizing array. The polarizer in the incident beam lies in a parallel to mirror 2 and has its axis at 45 degree to the vertical. Each quarter wave plate has its axis parallel to the input polarizer axis or its projection in the beam splitter. The light collected by the telescope is polarized by the input polarizer to two components, parallel and perpendicular to the plane of the beam splitter, respectively. The beams parallel p and perpendicular s to the plane of incidence are, respectively, transmitted and reflected by the polarizing beam splitter. Then the two beams are transmitted by the compensatory glass used for field-widening and achromatic purpose. In both arms, the quarter wave plates are at 45 degree to the polarization. Since, in both arms, the quarter wave plates are traversed twice, they act as half wave plate and rotate the direction of polarization in the returned beams by 90 degree with respect to the input beams. The s-wave light in arm 1 is converted to p-wave light, which is transmitted by the polarizing beam splitter. The p-wave light in arm2 is converted to s-wave light, which is reflected by the polarizing beam splitter. The s-wave and p-wave lights traversed the quarter wave plate are transmitted by the polarizer array. The polarizer array is coated on the CCD detector and splits the CCD detector to four sub-areas. The axis of the polarizer arrays are at 0 degree, 45 degree, 90 degree and 135 degree to the fast axis of the quarter wave plate respectively. Then the s-wave and p-wave are imaged in interference on the CCD detector.
3. The measurement principle of the TSMPAMI
The principle of the TSMPAMI is shown in Fig. 2 . The viewing geometry is at the Earth’s limb and the viewing direction is at 90 degrees from the satellite velocity vector. Generally, the distance between the TSMPAMI and the target is large compared with the size of the target and the TSMPAMI. The target atmosphere can be split to small pieces. Each piece of the atmosphere is imaged on one sub-area of the CCD exactly. At first exposure time, the first target piece is imaged at the first sub-area of the CCD. At the second exposure time, the first target piece is imaged on the second sub-area of the CCD and the second target piece is imaged on the first sub-area of the CCD, and so on. When the TSMPAMI moves over whole target area, the image of each piece of the target atmosphere will be moved from first sub-area of the CCD to the fourth sub-area of the CCD. At the same time, the detector records four different interference intensities of each target piece. Each interference intensity is given by 10]
In which v is the velocity of the wind along the line of sight, c is the velocity of the light andis the wavelength of the emission line, U is the instrument visibility of the TSMPAMI, V is the visibility which is due to the finite width of the observed emission line. It is given by 
With, , , , four corresponding intensities , , , can be obtained from Eq. (1). Here is the optical path difference, it changes against incident angle. Because of the compensatory glass, the changes against incident angle very slowly .
The four intensities can be written as a linear equation .
Where J 1, J 2 and J 3 are the signal of the atmosphere, defined as
So Eq. (4) can be written as
The signal can be obtained from Eq. (6)
If the J’s are known, for one single-layer atmosphere, the Doppler shift and emission line visibility can be obtained 
4. Errors analysis and computer simulation
To get enough signal to noise ratio, a large array EMCCD with low read noise and dark current is used. The On-chip multiplication gain can reach to 1000x. The CCD size is 256×256. Each pixel is 32μm square. The quantum efficiency is more than 90% in the 500-700nm band. The total area is 8.2×8.2 mm2. The field view of the system is about 6 degree×6 degree. So the focal length is fixed at 7.83cm. Assume that, aperture of the system is 5×5cm2, the photon flux collected by a pixel is about 4.2×10−6cm2sr. If we introduce a system transmission of 0.3 and quantum efficiency of 0.9, we find that the responsivity is 0.09 electrons/sec/R. That is, for a 1-kR aurora, the rate is 90 electrons/sec. If the On-chip multiplication gain is set to 100, a possible number, 18k electrons are accumulated in the two minutes exposure time. This is a large signal. The optical path difference of TSMPAMI is set to 4.5 cm and the instrument visibility of TSMPAMI is 0.8, for atmosphere target with 100 m/s velocity and 1000k temperature, the I1, I2, I3 and I4 of Eq. (4) are 3.5799×104, 1.5317×104, 201.0451 and 2.0683×104 respectively, for 630nm line. So the J1, J2 and J3 are 1.8000×104, 1.7799×104 and 0.2683×104 got from Eq. (7), respectively. So the velocity is 100 m/s and the temperature is 1000k. So the intensity values collected by such a system are sufficient to ensure that the rest simulations are practicable.
So each CCD sub-area has 256×64 pixels in the vertical and along the satellite track, respectively. So each pixel is made to correspond to a about 0.86 km×0.86 km atmosphere area along the satellite track and in the vertical, respectively for the satellite altitude assumed at about 700 km and its velocity of 7.9 km/s. If the exposure time is set to two seconds. Within one exposure time, the satellite moves about 15.8 km. That corresponds to 18.4 pixels. Because the movement of the satellite does not match the CCD divisions exactly, the atmosphere area imaging on the next sub-area of CCD in the next measurement does not correspond to the atmosphere area in the previous measurement exactly. There would be a distance shift. This distance shift is called as space-mismatch. The space-mismatch is determined by the orbital velocity and the exposure time. If the horizontal wind of interest is a constant, the space-mismatch does not influence the measurement. If the horizontal wind is not a constant and changes with the distance, the four-measurement targets are different. The space-mismatch will introduce some wind measurement errors.
In this paper, with the instrument errors neglected, the wind measurement errors introduced by the space-mismatch and the structures of the atmospheric fields are considered. The space-mismatch is set to its maximum of 1 km.
The horizontal wind is assumed to vary in the direction perpendicular to the viewing direction in the form of
The temperature is assumed to vary in the direction along the satellite track in the form of
The perturbation wavelengths in the upper atmosphere are from a few tens to several hundreds kilometers [12–14], the simulation is divided into two part for illustrative purpose. In the first part, the perturbation wavelengths are from 200 km to 600 km. In the second part, the perturbation wavelengths are from 16 km to 200 km.
Because the atmospheric wind velocity is as high as 150 m/s in the upper atmosphere , is set to 75 m/s and is set to 75 m/s. The range of the wind velocity is from 0 m/s to 150 m/s.
The average temperature in the thermosphere is about 1000 K. Generally, for small-scale atmospheric perturbations, such as gravity waves, 5 m/s wind fluctuation corresponds to 1% temperature change. is set to 1000 K and is set 150 K [15, 16]. The assumed amplitudes of wind and temperature perturbations likely represent the worst cases which produce the largest errors of interest to us.
For the perturbation wavelengths from 200 km to 600 km, some simulation results are shown in Fig. 3 , Fig. 4 , and Fig. 5 . The simulation is only about 0.86 km single layer atmosphere along the satellite track. So it is 1-D dimensional simulation.
Figure 3 shows the wind velocity and temperature measured by the TSMPAMI and SMWINDII. The wind velocity and temperature difference between measured by the TSMPAMI and SMWINDII are not distinct, implying the effect of space-mismatch is small, as expected.
Figure 4 shows the wind velocity and temperature errors measured by TSMPAMI and SMWINDII. The errors are defined as the difference between the measurement and the input model values. In Fig. 4, the measurement errors are seen to be influenced by the fluctuation of the atmospheric field, for both TSMPAMI and SMWINDII. When the perturbation wavelengths are larger than 400 km, the wind errors are less than 10 m/s, and the temperature errors are less than 20 K. When the perturbation wavelengths are from 200 km to 400 km, the wind errors are less than 18 m/s, and the temperature errors are less than 35 K. These errors increase when the wavelength decreases.
Figure 5 shows the errors introduced by the space-mismatch. The errors are defined as the difference between the simulation result with space-mismatch and without space-mismatch. In Fig. 5, Both wind and temperature errors measured by the TSMPAMI are influenced by the space-mismatch. The errors introduced by the space-mismatch decrease when the perturbation wavelength increases. When the perturbation wavelengths are larger than 200 km, the wind velocity errors are less than 2 m/s, and temperature errors are less than 2.5 K. They are smaller than the errors introduced by the fluctuation of atmospheric field. It means that measurement errors introduced by the space-mismatch are very small for large-scale structures of atmospheric field.
When the perturbation wavelengths are from 16 km to 200 km, some simulation results are shown in Fig. 6 , Fig. 7 and Fig. 8 . Figure 6 shows the wind velocity and temperature measured by TSMPAMI and SMWINDII respectively. Figure 7 show the wind velocity and temperature errors measured by TMSPAMI and SMWINDII respectively. In this condition, the measurement errors are larger than those of the perturbation wavelengths from 200 km to 600km. The wind velocity errors are less than 30 m/s and temperature errors are less than 50 K, when the perturbation wavelengths are larger than 110 km. When the perturbation wavelength decreases, the errors introduced by the fluctuation of atmospheric field increase. Our results are in consistency with those of Ungermann et al. ,who have simulated mesoscale gravity wave observations by the PREMIER Infrared Limb-Sounder and found that the measurement errors are the largest when the wavelengths of the atmospheric perturbations are less than 150 km.
In Fig. 4 and Fig. 7, it is easy to find that the wind and temperature errors introduced by the space-mismatch and small-scale structures of the atmospheric fields increase when the wind velocity increase. For a real atmosphere, the wind velocities are generally smaller than 150m/s. Therefore, the errors are smaller than those presented in this paper.
Because the atmospheric motions have periods generally greater than a few minutes and the perturbation wavelengths in the upper atmosphere are from a few tens to several hundreds kilometers [12–14], TSMPAMI’s measurement errors introduced by the space-mismatch and wind fluctuation of atmospheric field are small in most cases of relatively large wavelength.
Figure 8b shows the wind velocity and temperature errors introduced by space-mismatch. Same as Fig. 5, the errors are influenced by the space-mismatch and fluctuation of atmospheric field and change against the perturbation wavelength. When the perturbation wavelengths are larger than 100 km, the wind velocity errors are less than 5 m/s and temperature errors are less than 5 K. When the perturbation wavelength decreases, the errors increase. The errors are small compared with the errors introduced by the small-scale fluctuation of atmospheric field.
- 1. A space-based tempo-spatially modulated polarization atmosphere Michelson interferometer (TSMPAMI) is described. The acquisition method of interferogram is presented. The atmospheric temperatures and horizontal winds can be derived from the optical observations.
- 2. The measurement errors are discussed through simulations, and found to be significantly influenced by the space-mismatch, the mismatch between the scenes observed by the adjacent along-track CCD sub-areas during a series of successive measurements due to the orbital motion of the instrument and its exposure time, and small-scale structures of the atmospheric fields.
- 3. For most realistic conditions, the errors introduced by the space-mismatch are very small compare with the errors introduced by the small-scale structures of the atmospheric fields. The wind velocity errors introduced by the space-mismatch are less 2.5 m/s and the temperature errors introduced by the space-mismatch are less than 2.5 K when the perturbation wavelengths are larger than 200 km. The wind velocity errors introduced by small-scale structures of the atmospheric fields are less 18 m/s and the temperature errors introduced by the small-scale structures of the atmospheric fields are less than 35 K when the perturbation wavelengths are larger than 200 km. For the perturbation wavelengths less than 200 km, however, the measurement errors increase rapidly with the decreasing wavelengths, and the smaller the perturbation wavelengths are, the larger the errors are, in line with other instruments.
- 4. Since the TSMPAMI has no moving part and optical system is simpler than TMWIND and SMWINDII. The TSMPAMI is proven suitable for measuring the atmospheric parameters when perturbation wavelengths are larger than 200 km.
However the images of the target pieces will move up and down on different sub-area. This problem is also in WINDII. Because the four images are not archived at the same time in WINDII. This problem can be solved in data processing by height correction. This is not the key point at present and not discussed this in this paper.
The authors gratefully acknowledge the support of the State key Program of National Natural Science of China (Grant No. 40537031), National High Technology Research Development Special Fund (863 Project) of China (Grant No. 2006AA12Z152), National Defense Basal Scientific Research Foundation of China (Grant No. A1420080187), the National Natural Science Foundation of China (Grant No. 40875013, 40375010, 60278019).
References and links
1. W. Gault, G. Shepherd, G. Thuillier, and B. Solheim, “The Wind Imaging Interferometer (WINDII) on the Upper Atmosphere Research Satellite” Instrumentation for planetary and terrestrial atmospheric remote sensing; Proceedings of the Meeting, San Diego, CA, July 23, 24, 1992 (A93-27076 09-35), p. 54-60.
2. J. Bird, F. Liang, B. Solheim, and G. Shepherd, “A polarizing Michelson interferometer for measuring thermospheric winds,” Meas. Sci. Technol. 6(9), 1368–1378 (1995). [CrossRef]
3. A. Title, “Improvement of birefringent filters,” Sol. Phys. 33, 521–523 (1973).
4. G. Shepherd, G. Thuillier, W. Gault, B. Solheim, C. Hersom, J. Alunni, J. Brun, S. Brune, P. Charlot, L. Cogger, D.-L. Desaulniers, W. F. J. Evans, R. L. Gattinger, F. Girod, D. Harvie, R. H. Hum, D. J. W. Kendall, E. J. Llewellyn, R. P. Lowe, J. Ohrt, F. Pasternak, O. Peillet, I. Powell, Y. Rochon, W. E. Ward, R. H. Wiens, and J. Wimperis, “WINDII, the wind imaging interferometer on the Upper Atmosphere Research Satellite,” J. Geophys. Res. 98(D6), 10725–10750 (1993). [CrossRef]
6. W. E. Ward, “The middle atmosphere ozone, dynamics and energetics experiment (MODE).” in Phase A report submitted to the Canadian Space Agency, D. W. Tarasick, ed. (1998).
7. J. Wang, C. Zhang, B. Zhao, and N. Liu, “Study the rule of light transmission through the four-side pyramid prism in the static polarization wind imaging interferometer,” Acta Phys. Sin . 59 (2010).
8. W. Gault, S. Sargoytchev, and G. Shepherd, “Divided-mirror scanning technique for a small Michelson interferometer,” Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research II, P.B. Hays and J. Wang, Eds: Proc SPIE, 2830, 15–18, 1996.
9. W. Gault, S. Sargoytchev, and S. Brown, “Divided mirror technique for measuring Doppler shifts with a Michelson interferometer,” Proc. SPIE 4306, 266–272 (2001). [CrossRef]
10. G. G. Shepherd, W. A. Gault, D. W. Miller, Z. Pasturczyk, S. F. Johnston, P. R. Kosteniuk, J. W. Haslett, D. J. Kendall, and J. R. Wimperis, “WAMDII: wide-angle Michelson Doppler imaging interferometer for Spacelab,” Appl. Opt. 24(11), 1571–1584 (1985). [CrossRef] [PubMed]
11. Y. Rochon, “The retrieval of winds, Doppler temperatures, and emission rates for the WINDII experiment,” Ph.D. Thesis, York University (2000).
12. G. Liu and G. Shepherd, “Perturbed profiles of oxygen nightglow emissions as observed by WINDII on UARS,” J. Atmos. Sol. Terr. Phys. 68(9), 1018–1028 (2006). [CrossRef]
13. D. Wang, C. McLandress, E. Fleming, W. Ward, B. Solheim, and G. Shepherd, “Empirical model of 90-120 km horizontal winds from wind-imaging interferometer green line measurements in 1992-1993,” J. Geophys. Res. 102(D6), 6729–6745 (1997). [CrossRef]
14. G. Liu, G. Shepherd, and R. Roble, “Seasonal variations of the nighttime O (1S) and OH airglow emission rates at mid-to-high latitudes in the context of the large-scale circulation,” J. Geophys. Res. 113(A6), A06302 (2008). [CrossRef]
15. D. Wang, W. Ward, Y. Rochon, and G. Shepherd, “Airglow intensity variations induced by gravity waves. Part 1: generalization of the Hines-Tarasick's theory,” J. Atmos. Sol. Terr. Phys. 63(1), 35–46 (2001). [CrossRef]
16. D. Wang, Y. Rochon, S. Zhang, W. Ward, R. Wiens, D. Liang, W. Gault, B. Solheim, and G. Shepherd, “Airglow intensity variations induced by gravity waves. Part 2: comparisons with observations,” J. Atmos. Sol. Terr. Phys. 63(1), 47–60 (2001). [CrossRef]
17. J. Ungermann, L. Hoffmann, P. Preusse, M. Kaufmann, and M. Riese, “Tomographic retrieval approach for mesoscale gravity wave observations by the PREMIER Infrared Limb-Sounder,” Atmos. Meas. Tech. 3, 339-354 (2010). [CrossRef]