Analyses of the mesosphere and lower thermosphere suffer from a lack of global measurements. This is problematic because this region has a complex dynamic structure, with gravity waves playing an important role. A limb-sounding spatial heterodyne interferometer (SHI) was developed to obtain atmospheric temperature retrieved from the

In this paper a new processing method is investigated, which uses single-sided interferograms to gain horizontal across-LOS information about the observed temperature field. Hereby, the interferogram is split, and each side is mirrored at the centre of the horizontal axis. Each side can then be used to retrieve an individual 1-D temperature profile. The location of the two retrieved temperature profiles is analysed using prescribed horizontal temperature variations, as it is needed for deriving wave parameters. We show that it is feasible to derive two independent temperature profiles, which however will increase the requirements of an accurate calibration and processing.

The dynamical structure of the mesosphere and lower thermosphere (MLT) is mainly driven by atmospheric waves like planetary waves, tides, and gravity waves

Temperature in the MLT region can be derived by measuring the O

Simultaneously, a collaborative effort between the Jülich Research Center and the University of Wuppertal in Germany led to the development of a limb-sounding spatial heterodyne interferometer (SHI) for deriving temperature in the MLT from the oxygen A-band emission

The temperature is derived from the relative intensities of the O

The AtmoLITE instrument works as a camera where the atmospheric scene is mapped onto the detector. The SHI superimposes the spectral information of the O

To exploit some of the spatial information in the horizontal direction, we propose a new processing method which allows users to retrieve two 1-D temperature profiles from one image by using single-sided interferograms and mirroring them at the centre.

A thorough precision analysis is key to assess the limitations of this method. Therefore we detail the precision budget of the data product, in particular with regard to signal-to-noise limitations at the upper boundary of the measurement domain.

The paper is structured as follows. We introduce the instrument in Sect.

A spatial heterodyne interferometer (SHI) is similar to a Michelson interferometer, but the two mirrors are replaced by fixed tilted gratings. This measurement method was firstly developed by

Schematic of the SHI instrument.

An interferogram simulation is presented in Sect.

The mathematical derivation for an interferogram measured by an SHI is presented by

A line-by-line model is used to simulate spectra which are converted to interferograms. A 1-D interferogram with some horizontal variation is defined by

Summary of instrument specifications.

This section introduces shortly the simulation of the O

Panels

To calculate the

The first step in the data processing is to subtract the non-modulated part, which corresponds to the low frequencies in the spectrum. By subsequently applying a Fourier transformation along the x axis, the interferogram is converted into a spectrum. A two-dimensional radiative transfer model is used to simulate across-track temperature variations. Assuming that self-absorption is small, we can focus on the area close to the tangent layer, where most of the information comes from when integrating along the line of sight. Note that this holds true for tangent altitudes above 85 km for the

Since self-absorption is not considered in this study, a simplified forward model can be used to solve the inverse problem and retrieve temperature. Instead of calculating the full radiative transfer equation, it calculates the relative distribution of the oxygen A-band emission lines for a given temperature following

Apodization functions used for the assessment;

The ILS of a finite interferogram is defined by a sinc function whose resolution is determined by the length of the interferogram. To minimize the side lobes of the sinc function, apodization is commonly applied in Fourier spectrometry, resulting in a smoother spectral output. It increases the localization of the spectral information, which can also help to be more robust against instrumental errors. However, apodization decreases the spectral resolution, and it is therefore a trade-off between spectral resolution and a decrease of the side lobes.

Our simplified forward model relies on the temperature-dependent rotational distribution of the

Rotational distribution of the

In the following, we propagate the shot noise in the interferogram through the simplified temperature retrieval for different signal levels and constant temperatures. For each signal level and temperature, we perform a Monte Carlo simulation with

Results of the Monte Carlo simulations with

We then evaluate the interpolated temperature precision field presented in Fig.

Temperature precision calculated from the expected signal and input temperature presented in Fig.

In the next step, we assess the required number of binning rows to achieve a certain temperature precision. Hereby, we extract a contour line from the temperature precision field in Fig.

Required binning of rows to achieve a certain temperature precision

As explained in Sect.

Results of Monte Carlo simulations with

Performing the same analysis for multiple SNR and temperature levels gives the temperature precision of the right single-sided interferograms depicted in Fig.

To study the influence of horizontal temperature variation on the temperature retrieval, we look at a simple example first. A linear temperature gradient of 20 K over the horizontal field of view of 60 km, shown in Fig.

Results of Monte Carlo simulations with

It is important to acknowledge that the effectiveness of this method relies on accurate knowledge of the ZOPD location.

In this section we assess the sensitivity of the temperature retrieval to horizontal temperature variations. We define a function

The Jacobian matrix in Fig.

To evaluate this approximation, we use the simulated temperature variations from Sect.

Temperature error using derivative matrix from Fig.

Relative location of the retrieved temperatures within the temperature variation using single-sided interferograms

To get a comprehensive picture of the split interferogram processing method, we simulate interferograms according to temperature variations typically produced by gravity waves, split the interferogram, and retrieve temperature for each side. When observing temperature variations produced by an atmospheric wave, it is essential to localize that information in space to obtain proper wave characteristics from that data. A sinusoidal horizontal temperature variation can be modelled by

In this section we assess the influence of apodization on the retrieval of split interferograms. We evaluate this for horizontally linear temperature gradients with a spread of

Retrieved temperatures using a linear temperature gradient for multiple temperature levels and different strengths of apodization

Spatial heterodyne interferometers are often combined with a two-dimensional focal plane array and a telescope to obtain spatial and spectral information from a scene. This study deals with a limb-sounding SHI instrument, which delivers in its default configuration spatial information of the atmosphere in the vertical and spectral information in the horizontal direction across the LOS. However, it is possible to split the interferogram into half to obtain additional spatial information in the horizontal direction across the LOS, as well. This methodology is firstly applied to spatial heterodyne spectroscopy for atmospheric temperature, which then gives two horizontal temperature profiles (two temperature data points per tangent layer).

This paper first discussed the temperature sensitivity of the captured

Further, we show that the method of split interferograms reduces the temperature precision by a factor of

We can describe the noisy interferogram by

The shot noise can be propagated through the Fourier transformation, resulting in a noisy spectrum given by

In Fig.

The code applied for this study is available from the authors on request.

The simulated data generated throughout the study is available from the authors on request.

KN performed all simulations and wrote most of the text. JU initiated the analysis regarding the sensitivity to horizontal temperature variations. JU and MK supervised the study. All authors contributed to the discussion of the results, the manuscript review, and improvements.

At least one of the (co-)authors is a member of the editorial board of

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.

This project 19ENV07 MetEOC-4 has received funding from the EMPIR programme co-financed by the participating states and from the European Union's Horizon 2020 research and innovation programme.

This research has been supported by the European Metrology Programme for Innovation and Research (grant no. 19ENV07).The article processing charges for this open-access publication were covered by the Forschungszentrum Jülich.

This paper was edited by Robin Wing and reviewed by two anonymous referees.