Doppler Asymmetric Spatial Heterodyne
The Doppler Asymmetric Spatial Heterodyne (DASH) technique is a spectroscopic method used to determine the velocity of emitting particles via the interferometric analysis of the Doppler shift of the emission. It is primarily used to measure the speed of oxygen in the upper atmosphere from both ground- and space-based platforms. The technique uses an interferometer with arms of different lengths terminated by tilted diffraction gratings to create a fringe pattern on a spatially extended detector array. Fringe patterns from particles in motion are compared to those generated by particles at rest to determine the Doppler shift of the emission and thus, the velocity of the emitting particle.
The path length differential between the arms of a DASH interferometer differentiates it from from Spatial Heterodyne Spectroscopy. Both techniques derive from the Michelson interferometer.
Configuration[edit]
The Doppler Asymmetric Spatial Heterodyne interferometer consists of a beamsplitter and two diffraction gratings. It can also include field-widening prisms which allow for the collection of more light (larger entrance aperture) without loss of coherence. Certain versions of the interferometer consist of a beamsplitter, only one field-widening prism, and only one grating. In this configuration two parallel light paths utilize half of each optical component. There is an on-axis optical path difference (OPD) inherent in the system that is chosen to maximize the information stored in the resulting interferogram.
During operation, light from an emitting source enters through an aperture into the beamsplitter (typically a double prism) and is evenly distributed between two paths. The light then travels through field-widening prisms and impinges upon the gratings. The gratings are tilted away from normal to the Littrow angle, which is the angle at which a certain wavelength of light is diffracted back along the path from which it came. Often this tilt angle is chosen to reflect one of the higher orders of the incident light (e.g. n=7 for the 630.038 nm emission line of oxygen) which eases the requirements on the number of lines per inch of the gratings and allows multiple wavelength ranges to be imaged simultaneously (e.g. also the n=8 order of 557.7 nm emission line of oxygen). This tilt essentially transforms the gratings into a series of mirrors each of which has a different optical path distance from the beamsplitter. Thus, the system samples many optical path differences simultaneously, rather than sequentially like a conventional Michelson interferometer. As the light recombines in the beamsplitter and exits towards a detector array, the different optical path lengths cause either constructive or destructive interference, which manifests as a fringe pattern characteristic of the difference between the Littrow wavelength and the wavelength of the incident light.
Analysis[edit]
One method for analyzing interferograms obtained from a DASH interferometer is as follows:
With DASH interferometers, the Doppler shift of measured emission cannot be determined from a single interferogram, or fringe pattern from an interferometer. It is a relative measurement and requires a baseline, or zero velocity, interferogram with which to compare subsequent measurements.[1] A change in velocity of the emitting source will cause a change in frequency of the measured fringe pattern. For expected wind speeds in the atmosphere, this frequency shift is so small as compared with the total frequency that, at the optical path differences considered, it appears simply as a change in phase in the fringe pattern.
Once an interferogram is obtained, the first step is to apply a Hann function to apodize the signal in order to reduce edge effects from non-periodic boundary conditions. Next, a Fourier transform is applied to change to frequency space. For an image with multiple wavelengths, there will be several components in the transform, including one near zero frequency representing the DC offset of the fringe pattern. Each line of interest will have a positive and a negative component in the frequency spectrum. To focus on only one line of interest, an isolating function is applied to the spectrum which suppresses all other lines but the positive component of that line.
Now the inverse transform is applied to the isolated component, which results in a signal with real and an imaginary parts and half the intensity of the original signal once the Hann function is removed. The phase of the original signal can be determined by taking the inverse tangent of the ratio of the imaginary part to the real part. This method has the benefit of removing any envelope function which may be affecting the interferogram. In atmospheric studies, this envelope may be a function of the temperature of the emitting oxygen, reducing fringe contrast with increasing optical path difference.
The resulting phase vs OPD is mod 2π and the absolute phase at the lowest OPD measured is unknown (as long as OPD = 0 is not measured). The cumulative phase from the lowest OPD measured can be calculated by adding 2π at every phase discontinuity. This cumulative phase can be compared to that obtained from the zero velocity measurement (or from any other measurement for a relative velocity) to determine the Doppler shift and thus the velocity of the emitting particles. The measurements can be compared point by point or, because the resulting phase is nearly linear, either by slope or by an average cumulative phase. The benefit to using the average is that it is simple to calculate (compared to fitting a line) and incorporates all the values from all the detectors in the array, resulting in a much smaller uncertainty for larger arrays.
DASH interferometers[edit]
REDDI The Red-line DASH Interferometer, is a monolithic (all pieces cemented together into a single piece) interferometer used for ground based detection.[2]
MIGHTI The Michelson Interferometer for Global High-resolution Thermospheric Imaging is an experiment on the Ionospheric Connection Explorer (ICON) mission;[3], chosen by NASA for launch in 2018. The MIGHTI system consists of two interferometers, one which looks ahead of the spacecraft and one which looks behind, both at roughly 45° to North.[4]
See Also[edit]
References[edit]
- ↑ Englert, Christoph R.; Babcock, David D.; Harlander, John M. (10 October 2007). "Doppler Asymmetric Spatial Heterodyne spectroscopy (DASH): Concept and experimental demonstration". Applied Optics. 46 (29): 7297–7307. doi:10.1364/AO.46.007297.
- ↑ Englert, Christoph R.; Harlander, John M.; Emmert, John T.; Babcock, David D.; Roesler, Frederick L. (14 December 2010). "Initial ground-based thermospheric wind measurements using Doppler asymmetric spatial heterodyne spectroscopy (DASH)". Optics Express. 18 (26): 27416–30. doi:10.1364/OE.18.027416. PMID 21197018.
- ↑ "ICON Mission". Ionospheric Connection Explorer. UC Berkeley. Retrieved 7 September 2018.
- ↑ Englert, Christoph R.; Harlander, John M.; Brown, Charles M.; Marr, Kenneth D.; et al. (October 2017). "Michelson Interferometer for Global High-resolution Thermospheric Imaging (MIGHTI): Instrument Design and Calibration". Space Science Reviews. 212 (1–2): 553–584. doi:10.1007/s11214-017-0358-4. ISSN 1572-9672. PMC 6042234. PMID 30008488.
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