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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 9 — Apr. 23, 2012
  • pp: 9535–9544
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Flat-fields in DASH interferometry

Kenneth D. Marr, Chrisoph R. Englert, and John M. Harlander  »View Author Affiliations


Optics Express, Vol. 20, Issue 9, pp. 9535-9544 (2012)
http://dx.doi.org/10.1364/OE.20.009535


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Abstract

When analyzing the fringe pattern of an interferogram to determine atmospheric wind velocities, inhomogeneities in the optical components and illumination can introduce uncertainty into the results. These variations in the image, which are generally characteristics of the measurement device, are commonly referred to as the “flat-field” of the system. In this work we discuss the effect of this flat-field on measurements made with a Doppler Asymmetric Spatial Heterodyne (DASH) spectrometer. It is found that the flat-field can have a significant effect on any single calculation of the fringe phase, but because the flat-field affects all measurements made with the same system, the uncertainty in the derived wind velocity, which is determined through a comparison of two interferogram fringe phases, typically remains small. Nonetheless, it is recommended to account for the flat-field when analyzing DASH data, if possible. To this end we discuss a method for determining the flat-field using only temperature variations of the system, which is particularly suitable for space-based instruments.

© 2012 OSA

1. Introduction

There is a widely recognized need for global-scale observations of thermospheric winds in order to advance our understanding of thermospheric and ionospheric processes and to improve specification and forecasting of the uppermost part of the atmosphere [1

1. Heliophysics Roadmap Team, “Heliophysics: The solar and space physics of a new era,” NASA Advisory Council, Washington DC, (2009).

, 2

2. J. D. Huba, S. L. Ossakow, G. Joyce, J. Krall, and S. L. England, “Three-dimensional equatorial spread F modeling: zonal neutral wind effects,” Geophys. Res. Lett. 36, L19106 (2009). [CrossRef]

]. Thermospheric winds can be observed by measuring the Doppler shift of naturally occurring atomic oxygen airglow emission lines at 557.7 nm and 630.0 nm or of molecular oxygen emission at 762 nm. To date, two systems have been used to make this type of measurement from a low Earth orbit satellite: the Fabry-Perot Interferometer [3

3. P. B. Hays, V. J. Abreu, M. E. Dobbs, and D. A. Gell, “The high-resolution Doppler imager on the Upper Atmosphere Research Satellite,” J. Geophys. Res. 98, 10713–10723 (1993). [CrossRef]

, 4

4. T. L. Killeen, Q. Wu, S. C. Solomon, D. A. Ortland, W. R. Skinner, R. J. Niciejewski, and D. A. Gell, “TIMED Doppler interferometer: overview and recent results,” J. Geophys. Res. 111, A10S01 (2006). [CrossRef]

], which is also widely used for ground based observations [5

5. J. W Meriwether, “Studies of thermospheric dynamics with a Fabry-Perot interferometer network: a review,” J. Astro. Sol. Terr. Phys. 68, 1576–1589 (2006). [CrossRef]

, 6

6. P. A. Greet, M. G. Conde, P. L. Dyson, J. L. Innis, A. M. Breed, and D. J. Murphy, “Thermospheric wind field over Mawson and Davis, Antarctica; simultaneous observations by two Fabry-Perot spectrometers of 630 nm emission,” J. Astro. Sol. Terr. Phys. 61, 1025–1045 (1999). [CrossRef]

] and the stepped Michelson interferometer [7

7. G. G. Shepherd, G. Thuillier, W. A. Gault, B. H. Solheim, C. Hersom, J. M. Alunni, J. F. Brun, S. Brune, P. Charlot, L. 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, 10725–10750 (1993). [CrossRef]

, 8

8. G. G. Shepherd, R. G. Roble, C. McLandress, and W. E. Ward, “WINDII observations of the 558 nm emission in the lower thermosphere: the influence of dynamics on composition,” J. Astro. Sol. Terr. Phys. 59, 655–667 (1997). [CrossRef]

].

A recently developed technique, Doppler asymmetric spatial heterodyne (DASH) spectrometry, offers a combination of advantages from these conventional techniques and is therefore an attractive candidate for future flight instrumentation [9

9. C. R. Englert, D. D. Babcock, and J. M. Harlander, “Doppler asymmetric spatial heterodyne spectroscopy (DASH): concept and experimental demonstration,” Appl. Opt. 46, 7297–7307 (2007). [CrossRef] [PubMed]

]. The DASH system, which is derived from the concept of spatial heterodyne spectroscopy (SHS), is similar to a Michelson interferometer, which is commonly used to perform Fourier-transform spectroscopy (FTS), except that the mirrors that terminate the arms of the Michelson interferometer have been replaced with fixed, tilted diffraction gratings [10

10. J. M. Harlander, R. J. Reynolds, and F. L. Roesler, “Spatial heterodyne spectroscopy for the exploration of diffuse interstellar emission lines at far-ultraviolet wavelengths,” Astrophys. J. 396, 730–740 (1992). [CrossRef]

]. The gratings heterodyne the spatial fringe frequency around the Littrow wavenumber, σL, determined by the tilt and characteristics of the grating. Unlike an FTS interferometer, which sequentially scans the interferogram fringe pattern by changing the optical path length in one interferometer arm, the tilt to the gratings allow the SHS and DASH systems to image the entire interferogram simultaneously in a single exposure by using an array of detectors. The difference between the SHS and DASH concepts is that in the DASH setup an additional optical path difference is introduced in one interferometer arm in order to shift the measurement away from OPD = 0, which maximizes the information on the Doppler shift [9

9. C. R. Englert, D. D. Babcock, and J. M. Harlander, “Doppler asymmetric spatial heterodyne spectroscopy (DASH): concept and experimental demonstration,” Appl. Opt. 46, 7297–7307 (2007). [CrossRef] [PubMed]

].

Doppler shifts from thermospheric winds cause a wavelength change of only a few parts in 107, which corresponds to a similarly small change to the spatial fringe frequency of the associated DASH interferogram. Defining the “fringe phase” at a given OPD as the cumulative phase of the fringe pattern starting from the smallest OPD, we find that even for such small frequency changes the fringe phase of a Doppler shifted DASH interferogram will be measurably different from that of an unshifted, or zero-speed, interferogram. Furthermore, this difference increases with increasing path difference. Therefore, the sensitivity of the phase response to the Doppler shift increases with optical path difference. However, an emission line with non-zero thermal width will exhibit an envelope on the interferogram resulting in a decrease in fringe contrast with increasing OPD. Thus, there is an optimal OPD, 2Δd, which depends on the width of the emission line in question, that maximizes the signal to noise for the combined effect of the increasing fringe phase difference and the decreasing fringe contrast [9

9. C. R. Englert, D. D. Babcock, and J. M. Harlander, “Doppler asymmetric spatial heterodyne spectroscopy (DASH): concept and experimental demonstration,” Appl. Opt. 46, 7297–7307 (2007). [CrossRef] [PubMed]

]. The atmospheric velocity, v, is derived from this phase difference through the following relation,
δϕ=4πΔdσ(v/c),
(1)
where σ is the rest wavenumber of the Doppler-shifted emission. Due to this measurement’s sensitivity to small frequency changes, such as those from thermal variations within the instrument, an internal calibration source with a known and stable wavelength should be measured simultaneously. It has been found previously that the relative difference between the cumulative phases of the fringe patterns from the calibration line and from the atmospheric emission line is insensitive to instrument temperature drifts [11

11. J. M. Harlander, C. R. Englert, D. D. Babcock, and F. L. Roesler, “Design and laboratory tests of a Doppler asymmetric spatial heterodyne (DASH) interferometer for upper atmospheric wind and temperature observations,” Opt. Express 18, 26430–26440 (2010). [CrossRef] [PubMed]

, 12

12. C. R. Englert, J. M. Harlander, J. T. Emmert, D. D. Babcock, and F. L. Roesler, “Initial ground-based thermospheric wind measurements using Doppler asymmetric spatial heterodyne spectroscopy (DASH),” Opt. Express 18, 27416–27430 (2010). [CrossRef]

].

DASH spectroscopy has several advantages over other techniques for observing thermospheric winds from space or from the ground. First, it benefits from relaxed tolerances for the optical components as compared to Fabry-Perot interferometers (FPI). Secondly, it can measure several emission lines simultaneously, including an on-board calibration source, which allows for constant, simultaneous calibration [9

9. C. R. Englert, D. D. Babcock, and J. M. Harlander, “Doppler asymmetric spatial heterodyne spectroscopy (DASH): concept and experimental demonstration,” Appl. Opt. 46, 7297–7307 (2007). [CrossRef] [PubMed]

]. However, the need for a detector array, rather than the single element detector that is often employed by FTS, raises concerns about the proper characterization of variations between detector elements and of spatial variations in the optics. These variations are typically grouped together in what is termed the flat-field associated with an optical system [13

13. C. R. Englert and J. M. Harlander, “Flatfielding in spatial heterodyne spectroscopy,” Appl. Opt. 45, 4583–4590 (2006). [CrossRef] [PubMed]

]. As in SHS, the DASH flat-field consists of two components which will modify the result of any fringe phase analysis: a mutiplicative factor on the measured interferogram (e.g. from variations of the grating performance across the field of view) and sample-to-sample variations in the fringe modulation (e.g. from CCD pixel sensitivities). Fortunately, the flat-field is typically nearly time-invariant for a given spectrometer, so that the same flat-field is applied to every measurement taken with that system. Moreover, the flat-field is expected to have a similar effect on the analysis of both the calibration line fringes and the fringes from the atmospheric signal, so that the total effect on the phase difference is expected to be much smaller than for the individual phases. Another way to picture this behavior is to consider the flat-field effect in the spectral domain. In the spectral domain, a multiplicative flat-field results in a modified instrumental line shape function, which is convolved equally with the calibration line and with the atmospheric line. Thus, though this modified instrumental line shape can result in an effective shift to any measured line position, a similar shift will be imposed on any calibration lines as well, resulting in derived velocities which have only a weak sensitivity to the flat-field.

In this work we study the effect of the flat-field correction and its importance during the analysis of DASH data. The following section addresses in the most general form, the process with which a phase is derived from the measured interferogram. We assess how the flat-field plays into this process and what effects can be predicted from these equations. Section 3 provides a study of the error associated with ignoring the flat-field when using a reference signal to derive atmospheric wind velocities with a DASH interferometer. As expected, we discover that even though a single measurement is corrupted by ignoring the flat-field during analysis, a comparison between two fringe phases is much less affected by the inclusion of a flat-field. Section 4 provides one method for accurately deriving the flat-field correction using three interferograms with different phases. These phase changes are induced through temperature variations of the optics. This method is particularly attractive for satellite instruments, since no additional hardware is required to obtain these measurements. Section 5 summarizes the results of this study and discusses their potential impact on future systems.

2. Theory

F(x)I(x)=F(x)S(1+E(x)cos(2πκx+δϕ))=F(x)S+F(x)SE(x)cos(2πκx+δϕ).
(3)

Now we apply a Fouier Transform, 𝔉(x,σ), to transform from the interferogram domain (pixel space) to the spectral domain (frequency space).
f(σ)=𝔉[F(x)S+F(x)SE(x)cos(2πκx+δϕ)]=𝔉[F(x)S]+𝔉[F(x)SE(x)cos(2πκx+δϕ)].
(4)
In frequency space, the transform of a real signal will have both positive and negative components for every frequency represented in the signal. To continue with our phase derivation, we isolate only the positive frequency component of the complex spectrum by multiplying f(σ) with a high frequency isolation function, T(σ). This function could be, for example, a simple boxcar shape or a Hann function centered at κ0, where κ0 is the expected fringe frequency of the specific emission line to be analyzed. In practice, T(σ) should have a flat top and be just wide enough to have a negligible effect on the line of interest while effectively suppressing all other frequencies. Using this method, we can analyze the data from a single emission line even though the system may have collected signal from several isolated lines simultaneously.
T(σ)f(σ)=T(σ)𝔉[F(x)S]+T(σ)𝔉[F(x)SE(x)cos(2πκx+δϕ)].
(5)
Note that in general, Eq. (5) represents a complex function, including both real (ℜ) and imaginary (𝔌) parts. Taking the reverse transform, 𝔉−1(σ,x), of (5) we find
I(x)=𝔉1[T(σ)𝔉[F(x)S]]+𝔉1[T(σ)𝔉[F(x)SE(x)cos(2πκx+δϕ)]].
(6)

Let us assume for a moment that F(x) = 1 (i.e. no flat-field). Because S is constant we find the following:
T(σ)𝔉[S]=0
(7)
(𝔉1[T(σ)𝔉[SE(x)cos(2πκx+δϕ)]])=12(SE(x)cos(2πκx+δϕ))
(8)
𝔌(𝔉1[T(σ)𝔉[SE(x)cos(2πκx+δϕ)]])=12(SE(x)sin(2πκx+δϕ)).
(9)
Dividing Eq. (9) by Eq. (8) we find
𝔌(I(x))(I(x))=2SE(x)sin(2πκx+δϕ)2SE(x)cos(2πκx+δϕ)=tan(2πκx+δϕ),
(10)
where the division eliminates S as well as any envelope effects. Thus, we define the phase along the x-axis of the interferogram as
Φ(x)2πκx+δϕ=tan1(𝔌(I(x))(I(x)))
(11)
where 2πκx is the zero-motion cumulative phase and δϕ the additional phase induced by the Doppler shift. Expanding this definition to include an arbitrary flat-field we arrive at the general equation for the phase
Φ(x)=tan1[𝔌(𝔉1[T(σ)𝔉[F(x)S]]+𝔉1[T(σ)𝔉[F(x)SE(x)si(2πκx+δϕ)]])(𝔉1[T(σ)𝔉[F(x)S]]+𝔉1[T(σ)𝔉[F(x)SE(x)cos(2πκx+δϕ)]])].
(12)
We see that similar to Eq. (7), if the flat-field only contains low frequency components, the high frequency isolation function gives T(σ)𝔉[F(x)S] = 0. However, even with the isolation function, the flat-field still remains as a multiplicative factor on the oscillating term in the phase calculation.

3. Effect of ignoring flat-field

Fig. 1 The three models used to test the effect of the flat-field on fringe pattern analysis.

The results of the study are presented in Table 1. To simplify, we aggregate the fringe phase information into a single value by taking the mean of the fringe phase across the CCD [12

12. C. R. Englert, J. M. Harlander, J. T. Emmert, D. D. Babcock, and F. L. Roesler, “Initial ground-based thermospheric wind measurements using Doppler asymmetric spatial heterodyne spectroscopy (DASH),” Opt. Express 18, 27416–27430 (2010). [CrossRef]

]. Even though there may be significant distortion in the linearity of the cumulative phase to OPD relationship for any given interferogram, the desired information is not contained in any single fringe phase, but rather in the comparison between two phases. Furthermore, it has been found that nearly identical distortion is evidenced in any other measurements made with the same system. Thus the averaging process ultimately reduces any uncertainty from statistically independent pixel-to-pixel noise [12

12. C. R. Englert, J. M. Harlander, J. T. Emmert, D. D. Babcock, and F. L. Roesler, “Initial ground-based thermospheric wind measurements using Doppler asymmetric spatial heterodyne spectroscopy (DASH),” Opt. Express 18, 27416–27430 (2010). [CrossRef]

]. The average phases are given in the second column of Table 1. When the mean values of the cumulative phases from Tests I, II, and III are compared to their corresponding values from the Reference test (third column), we confirm that the flat-field has an effect on the absolute phase calculation. As it is practice to “calibrate” each atmospheric measurement against a known source, the phase differences between the atmospheric emission lines and the calibration line are given in the fourth column of Table 1 for each of the four scenarios.

Table 1. Results of simulated flat-fields on perfect interferograms with respect to a reference calibration line. The values in the last two columns are calculated with respect to their associated bold value, which is the associated zero-wind measurement.

table-icon
View This Table

To determine the wind speed through the Doppler shift of the emission, the calibrated mean phase of any atmospheric emission (ϕV+,−ϕCal) must be compared to that of a calibrated zero-speed emission (ϕV0ϕCal). It is the phase difference between these two values that ultimately leads to the desired velocity. For reference, we have highlighted the calibrated zero-speed values in bold for each of the four tests. We find that these relative phase shifts are much less affected by the flat-field than are the absolute phases. This can be seen in the fifth column of Table 1 where we have converted this relative phase difference into a derived velocity by assuming an optimal path difference in the DASH spectrometer of 2ΔdOPT ≃ 4.2 cm for emission that comes from atmospheric oxygen (rest wavelength = 630.03 nm) at T = 1000K. As expected, we see in the final column that for all cases, we have less than 4% error between the expected velocity and the velocity derived from an interferogram with an associated flat-field.

4. Use of temperature to derive flat-field

As before, changes to the frequency of the measured emission line in a DASH interferometer are evidenced by a change in the fringe frequency of the interferogram recorded by the detector array. For very small changes in signal frequency, the slight change to the interferogram is most visible at large optical path differences and appears as a phase shift of the fringe pattern. Changes to the temperature of the system similarly affect the fringe frequency of the imaged interferogram and therefore also cause a change in phase for the fringe pattern in the OPD interval observed by the DASH spectrometer. Like the FPI, Michelson, and SHS systems before it, it is common for the DASH system to employ temperature controls to reduce thermal variations [11

11. J. M. Harlander, C. R. Englert, D. D. Babcock, and F. L. Roesler, “Design and laboratory tests of a Doppler asymmetric spatial heterodyne (DASH) interferometer for upper atmospheric wind and temperature observations,” Opt. Express 18, 26430–26440 (2010). [CrossRef] [PubMed]

, 12

12. C. R. Englert, J. M. Harlander, J. T. Emmert, D. D. Babcock, and F. L. Roesler, “Initial ground-based thermospheric wind measurements using Doppler asymmetric spatial heterodyne spectroscopy (DASH),” Opt. Express 18, 27416–27430 (2010). [CrossRef]

] and to measure a calibration line to account for stray thermal effects in the system [9

9. C. R. Englert, D. D. Babcock, and J. M. Harlander, “Doppler asymmetric spatial heterodyne spectroscopy (DASH): concept and experimental demonstration,” Appl. Opt. 46, 7297–7307 (2007). [CrossRef] [PubMed]

]. However, it is possible to use this thermal sensitivity to determine the flat-field of the system. By changing the temperature we can sweep the fringe phase across every sample in the interferogram. In this way, we characterize the individual response to the strength of the incident signal for each detector element in the array. In practice, we compare two distinct phase shifted measurements of the interferogram, which allows us to separate the signal into a modulated and a non modulated part. A third distinct phase shifted interferogram is used to supplement the locations where the first two interferograms intersect and the original comparison is invalid [13

13. C. R. Englert and J. M. Harlander, “Flatfielding in spatial heterodyne spectroscopy,” Appl. Opt. 45, 4583–4590 (2006). [CrossRef] [PubMed]

]. Knowledge of the absolute temperatures and phases is not necessary for this process as long as three well-separated phase patterns are obtained.

To demonstrate the efficacy of this method, we prepared a laboratory setup of a DASH interferometer with uncoupled optical components, thermal probes, and a nearby heat source. The system temperature was raised roughly one degree over the course of an hour and a half. Every five minutes, the camera recorded a 20 s exposure of the fringe pattern from a neon lamp of the type that might be used as a calibration source to track thermal drifts. As the system temperature slowly increased, the phase of the neon line changed. Figure 2a shows a sample interferogram, including an associated flat-field factor. Figure 2b displays a close up of a small feature of this interferogram caused by the flat-field, with the two additional phase-shifted interferograms shown in red and blue. These three interferograms were taken roughly eleven minutes apart.

Fig. 2 (a) The original interferogram with flat-field effects. (b) The three phase shifted interferograms used to determine the flat-field.

Using the determined phase, Φi, and signal intensity, Ii, from each interferogram, i, j = 1, 2, 3, Englert and Harlander derive in [13

13. C. R. Englert and J. M. Harlander, “Flatfielding in spatial heterodyne spectroscopy,” Appl. Opt. 45, 4583–4590 (2006). [CrossRef] [PubMed]

] the following equations for the modulated, Mi(x,κ0), and non-modulated, Ni(x,κ0), parts of an interferogram, where κ0 is the frequency of the emission source:
Mi(x,κ0)=Ii(x)Ij(x)cosΦi(x)cosΦj(x),ij,
(13)
Ni(x,κ0)=Ii(x)M(x,κ0)cosΦi(x),
(14)

Figure 3 shows the results of using the measured neon phases and intensities seen in Fig. 2 in these equations. For comparison, we include the flat-field as derived by the method of blocking light in each arm of the interferometer. Note that approximately 30 pixels at each end of the plot should be ignored due to the edge effects of the Fast Fourier Transform. Finally, Fig. 4 displays the original interferogram with the flat-field now removed. Notice that the feature seen earlier has been completely removed.

Fig. 3 The modulated and non-modulated parts of the interferogram. For comparison the flat-field as derived by blocking each arm of the interferometer is also shown.
Fig. 4 (a) The original interferogram now with the flat-field corrected (removed). (b) The close up view emphasizes that the feature near 685 pixels has been eliminated.

5. Summary

References and links

1.

Heliophysics Roadmap Team, “Heliophysics: The solar and space physics of a new era,” NASA Advisory Council, Washington DC, (2009).

2.

J. D. Huba, S. L. Ossakow, G. Joyce, J. Krall, and S. L. England, “Three-dimensional equatorial spread F modeling: zonal neutral wind effects,” Geophys. Res. Lett. 36, L19106 (2009). [CrossRef]

3.

P. B. Hays, V. J. Abreu, M. E. Dobbs, and D. A. Gell, “The high-resolution Doppler imager on the Upper Atmosphere Research Satellite,” J. Geophys. Res. 98, 10713–10723 (1993). [CrossRef]

4.

T. L. Killeen, Q. Wu, S. C. Solomon, D. A. Ortland, W. R. Skinner, R. J. Niciejewski, and D. A. Gell, “TIMED Doppler interferometer: overview and recent results,” J. Geophys. Res. 111, A10S01 (2006). [CrossRef]

5.

J. W Meriwether, “Studies of thermospheric dynamics with a Fabry-Perot interferometer network: a review,” J. Astro. Sol. Terr. Phys. 68, 1576–1589 (2006). [CrossRef]

6.

P. A. Greet, M. G. Conde, P. L. Dyson, J. L. Innis, A. M. Breed, and D. J. Murphy, “Thermospheric wind field over Mawson and Davis, Antarctica; simultaneous observations by two Fabry-Perot spectrometers of 630 nm emission,” J. Astro. Sol. Terr. Phys. 61, 1025–1045 (1999). [CrossRef]

7.

G. G. Shepherd, G. Thuillier, W. A. Gault, B. H. Solheim, C. Hersom, J. M. Alunni, J. F. Brun, S. Brune, P. Charlot, L. 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, 10725–10750 (1993). [CrossRef]

8.

G. G. Shepherd, R. G. Roble, C. McLandress, and W. E. Ward, “WINDII observations of the 558 nm emission in the lower thermosphere: the influence of dynamics on composition,” J. Astro. Sol. Terr. Phys. 59, 655–667 (1997). [CrossRef]

9.

C. R. Englert, D. D. Babcock, and J. M. Harlander, “Doppler asymmetric spatial heterodyne spectroscopy (DASH): concept and experimental demonstration,” Appl. Opt. 46, 7297–7307 (2007). [CrossRef] [PubMed]

10.

J. M. Harlander, R. J. Reynolds, and F. L. Roesler, “Spatial heterodyne spectroscopy for the exploration of diffuse interstellar emission lines at far-ultraviolet wavelengths,” Astrophys. J. 396, 730–740 (1992). [CrossRef]

11.

J. M. Harlander, C. R. Englert, D. D. Babcock, and F. L. Roesler, “Design and laboratory tests of a Doppler asymmetric spatial heterodyne (DASH) interferometer for upper atmospheric wind and temperature observations,” Opt. Express 18, 26430–26440 (2010). [CrossRef] [PubMed]

12.

C. R. Englert, J. M. Harlander, J. T. Emmert, D. D. Babcock, and F. L. Roesler, “Initial ground-based thermospheric wind measurements using Doppler asymmetric spatial heterodyne spectroscopy (DASH),” Opt. Express 18, 27416–27430 (2010). [CrossRef]

13.

C. R. Englert and J. M. Harlander, “Flatfielding in spatial heterodyne spectroscopy,” Appl. Opt. 45, 4583–4590 (2006). [CrossRef] [PubMed]

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(100.2650) Image processing : Fringe analysis
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(110.2650) Imaging systems : Fringe analysis

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: January 23, 2012
Revised Manuscript: March 14, 2012
Manuscript Accepted: March 15, 2012
Published: April 11, 2012

Citation
Kenneth D. Marr, Chrisoph R. Englert, and John M. Harlander, "Flat-fields in DASH interferometry," Opt. Express 20, 9535-9544 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-9-9535


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References

  1. Heliophysics Roadmap Team, “Heliophysics: The solar and space physics of a new era,” NASA Advisory Council, Washington DC, (2009).
  2. J. D. Huba, S. L. Ossakow, G. Joyce, J. Krall, and S. L. England, “Three-dimensional equatorial spread F modeling: zonal neutral wind effects,” Geophys. Res. Lett.36, L19106 (2009). [CrossRef]
  3. P. B. Hays, V. J. Abreu, M. E. Dobbs, and D. A. Gell, “The high-resolution Doppler imager on the Upper Atmosphere Research Satellite,” J. Geophys. Res.98, 10713–10723 (1993). [CrossRef]
  4. T. L. Killeen, Q. Wu, S. C. Solomon, D. A. Ortland, W. R. Skinner, R. J. Niciejewski, and D. A. Gell, “TIMED Doppler interferometer: overview and recent results,” J. Geophys. Res.111, A10S01 (2006). [CrossRef]
  5. J. W Meriwether, “Studies of thermospheric dynamics with a Fabry-Perot interferometer network: a review,” J. Astro. Sol. Terr. Phys.68, 1576–1589 (2006). [CrossRef]
  6. P. A. Greet, M. G. Conde, P. L. Dyson, J. L. Innis, A. M. Breed, and D. J. Murphy, “Thermospheric wind field over Mawson and Davis, Antarctica; simultaneous observations by two Fabry-Perot spectrometers of 630 nm emission,” J. Astro. Sol. Terr. Phys.61, 1025–1045 (1999). [CrossRef]
  7. G. G. Shepherd, G. Thuillier, W. A. Gault, B. H. Solheim, C. Hersom, J. M. Alunni, J. F. Brun, S. Brune, P. Charlot, L. 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, 10725–10750 (1993). [CrossRef]
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