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### 2.4.3 Level 1b products and algorithms

2.4.3.1 Algorithms

The goal of the level 1b processing is to transform the interferograms generated at the end of the level 1a processing into calibrated and corrected spectral radiance spectra. The overall processing , divided in high level functions, will be processed in the following order:

The following flowchart shows how the Level 1b ground processing is organised:

During the Level 1b processing there are also some auxiliary functions, applied to both the scene and the calibration data, that are part of several of the above high level functions. These auxiliary functions are:

All these algorithms are described in more details in the "Algorithm Technical Baseline Document for MIPAS Level 1b Processing Ref. [1.6 ] ".

2.4.3.1.1 Calculate Offset Calibration function

Level: 1b

Main objectives:

The main objective of the Calculate Offset Calibration function is to deliver offset calibration measurement data in a form suitable for radiometric calibration of the spectra by the Calculate Radiance function.
Specific objectives:
Specific objectives of the function are:
• Perform spikes detection
• Sort offset data according to the direction of interferometer sweep.
• Coadd six interferograms in each band.
• Detect and correct fringe count errors in spectral bands C and D.
• Gain spectral interpolation
• Calculate coarse spectra
• Calculate calibrated spectra
• Responsivity scaling
• Correct for detector non-linearity.
• Equalize and combine interferograms in band A.
• Assess NESR performance.
• Accumulate statistics from deep space readings to obtain the NESR of the instrument
• Check the validity of incoming readings
Organigram:
 Figure 2.6
Input: Output:
Detailed description:
The radiometric offset is an estimate of the instrument contribution, due to its elf-emission, to the total measurement. This estimate of the instrument contribution is made by simply pointing the instrument to deep space and performing a measurement cycle as in the nominal case. For practical reasons, the deep space measurement is taken at a tangential height of around 150 km. Also, due to the potential difference in phase between different sweep directions of the instrument, a measurement is taken in each of the forward and reverse directions of the interferometer. In the ground segment, the closest in time offset measurement (in the correct sweep direction) is simply subtracted from each interferogram during processing. Click here for details on the offset measurement 1.1.3.4.1. .

The signals detected during offset measurements arise mainly from noise sources in detectors/ amplifiers and from thermal emission of the optical components within the interferometer. Even if the spectrum will be weak, it is believed that fringe count errors can be effectively determined. The scheme applied to scene and calibration measurements will most probably detect the occurrence of fringe errors, and the use of all interferograms (including offsets) maximizes the chance of detecting and correcting the errors as soon as possible after their occurrence.

The zero offset measurements will be subtracted from the relevant individual interferograms. Logically, these measurements should be made at the same spectral resolution as the scene measurements themselves, in order that the vectors are directly comparable. However, it is not expected that any high resolution features will be present in the offset spectra, which means that the measurements may be made at low resolution, with an interpolation on the ground segment. This has the advantage of reducing the duration of the offset measurement.

Offset calibration is performed such that the closest in time available valid offset measurement is used until a new valid offset measurement becomes available. If no offset data are found at the beginning of the Level 0 product input data set, then the first available offset found leading to valid measurement shall be used for all initial scenes. If one or more invalid offset measurements are detected in the middle of the input stream, then a “closest in time strategy shall be applied, which means that complete scans shall be calibrated with the closest valid offset. If no valid offset at all is found in the input data, then the offset calibration data contained in the offset validation file shall be used.

2.4.3.1.2 Calculate Gain Calibration function

Level: 1b

Main objectives:

The main objective of the Calculate Gain Calibration function is to deliver a file representing the radiometric gain of the instrument, computed using gain calibration measurements, in a form suitable for radiometric calibration of the spectra by the Calculate Radiance function.
Specific objectives:
Specific objectives of the function are:
• Perform spikes detection
• Sort the gain calibration measurements according to types of measurement and sweep direction.
• Coadd interferograms to increase SNR.
• Detect and correct fringe count errors in spectral bands C and D.
• Gain spectral interpolation
• Calculate coarse spectra
• Gain shift correction
• Calculate calibrated spectra
• Responsivity scaling
• Correct DS and CBB measurements for non-linearity of each affected detector.
• Subtract offset due to contribution of the instrument.
• Equalize and combine interferograms in band A.
• Compute coarse spectra using a FFT algorithm applied on the zero-padded interferograms.
• Interpolate gain spectral vectors to provide the gain on a predefined spectral axis.
• Calculate expected blackbody radiance from temperature readings corresponding to blackbody measurements.
• Calculate the complex ratio of theoretical to calculated spectrum (gain computation).
• Check for radiometric accuracy of the incoming data.
Organigram:
 Figure 2.7
Input: Output:
• Calibration gains  [MIP_NL__1P: GAIN CALIBRATION ADS #1 ] 6.4.2.
• Spectral accuracy data for validation [MIP_NL__1P: GAIN CALIBRATION ADS #2 ] 6.4.2.
Detailed description:
The radiometric gain calibration requires all deep space and blackbody measurements of the gain calibration sequence. Since in this case the instrument is again contributing to the observed signal, it is also necessary to perform deep space measurements before the blackbody measurements in order to subtract the appropriate instrument offset. (In this instance, the term "Deep Space Radiometric Calibration" is used to distinguish the measurements from the regular Offset Calibration made with the scan sequences. The Deep Space (DS) Radiometric Calibrations are used only to correct the Calibration Blackbody (CBB) measurements and must be explicitly commanded. In fact, several measurements of each kind will be needed. This is because the signal to noise ratio of a single, offset-corrected, blackbody measurement is not high enough, particularly in band D, to achieve the required radiometric accuracy. Therefore a single gain calibration implies several successive measurements.
It is expected that there will be no high frequency features in either the CBB spectrum or in the instrument contribution (as assumed also for the offset calibration). These assumptions will be verified on the ground during instrument Assembly and Integration Test (AIT), but the assumption is reasonable. Therefore, each CBB or Deep Space sweep of the instrument will be made at low-spectral resolution, i.e. with a duration of 0.4 seconds. The baseline scenario uses 300 sweeps at low resolution in both forward and reverse directions for both CBB and DS measurements.
The gain data is processed by the Level 1b processor at the beginning before scene data. During processing, the gain file is not be modified by the processor.

2.4.3.1.3 Calculate Spectral Calibration function

Level: 1b

Main objectives:

The Calculate Spectral Calibration function performs the processing of some selected (radiometrically) calibrated scene measurements and generates the spectral calibration data.
Specific objectives:
Specific objectives of the function are:
• Compute a corrected spectral axis
Organigram:

 Figure 2.8

Input:

• Radiometrically and spectrally and locally calibrated (RSL) atmospheric spectra
• List of reference spectral lines

Output:

• Corrected spectral axis (spectral calibration data)

Detailed description:

Spectral calibration is performed in MIPAS using standard limb measurements from the atmosphere already corrected for the Doppler effect by the Calculate Radiance function. Specific reference spectral lines will be retrieved in the observed spectra according to the extremities of specific microwindows listed in a reference lines database. From these microwindows will be performed the line position identification, with respect to a database containing the exact known theoretical position of the reference lines. In order to reduce noise, equivalent scenes are coadded, i.e., scenes with altitude included in the range of the processing parameter file. The computed known values of the reference lines positions will be used to establish the assignment of the calibrated wavenumber to the index of spectral data points. Following this operation, spectral calibration will be used for the wavenumber assignment of all subsequent measurements until a new spectral calibration is performed.
The Calculate Spectral Calibration will be performed when it is appropriate to update the spectral calibration, with a current baseline of twice per day.
Because it is related to the same parameters, the spectral shift can be considered as a part of the instrument line shape. The disadvantage is that it is then necessary to perform a deconvolution of the ILS from an observed spectrum to get the proper wavenumber assignment. Here we will assume that the spectral shift is included in the spectral calibration, i.e. it is calibrated out by the spectral calibration procedure without any ILS deconvolution.
It is also assumed that the spectral calibration will be the same throughout the spectral range. It is assumed that the definition of the optical axis is common to all four detectors on the output ports, for both output ports. It is also assumed that the residual misalignment between the two output ports is low enough so that the difference in wavenumber is negligible.
Two algorithms have been proposed to perform spectral calibration: the Peak Finding Method (PFM) and the Cross-Correlation Method (CCM). The feasibility of both these methods have been demonstrated, and both algorithms have demonstrated strengths and weaknesses. The PFM has shown to be a little simpler to implement and faster to execute, but the CCM presents the advantage of giving information related to the precision of a given fit. A switch between in the level 1b processor setup allows the selection of one of these two methods.

The PFM method uses an analytical model to describe the target line minimising the squared difference between the modelled and observed spectral lines within preselected spectral windows. The optimisation involves the simultaneous fit of four independent parameters using a simplex algorithm. The fitted parameters correspond to an additive offset, the line width, a line amplitude scaling factor and the line centre wavenumber.

For the  CCM method, the cross-correlation function of the measured spectral line and a modelled spectrum (within predefined spectral windows) is computed. The frequency shift in the observational data is obtained by computing the position of the peak in the cross-correlation function.

The precision of the peak identification algorithm is proportional to the number of equivalent scenes that are coadded, as the noise affecting the signal decreases when multiple readings are superposed. This number will probably vary between 1 and 5 (to attain stability and a precision equal or less than 0.001 cm“1), and will be defined in auxiliary data.

Spectral calibration is performed such that the latest available valid spectral measurement is used until a new valid spectral measurement becomes available. If in the middle of the input stream invalid spectral calibration are calculated, then a “previous closest in time strategy is applied, which means that complete scans shall be calibrated with the previous valid spectral calibration. If no valid spectral calibration at all is available, then the spectral calibration data contained in the current ILS and spectral calibration file is used. Spectral calibration data is written to auxiliary file simultaneously with ILS retrieved data. Otherwise the file is not be modified by the processor.

Level: 1b

Main objectives:

The Calculate Radiance function performs the processing of the scene measurements and generates a radiometrically calibrated spectrum. This function assumes that gain, offset and spectral calibrations are available as soon as they are produced, so that they can be used for the processing of all scene measurements following these calibrations. If this is not the case, then processing will proceed with the latest available calibration data.
Specific objectives:
Specific objectives of the function are:
• Perform spikes detection
• Detect fringe count errors in spectral bands C and D, and in the case of misalignment adjust the phase of the gain and offset according to the current fringe count.
• Gain spectral interpolation
• Calculate coarse spectra
• Calculate calibrated spectra
• Responsivity scaling
• Correct scene measurements for non-linearity of each affected detector.
• Equalize and combine interferograms in band A.
• Subtract offset due to contribution of the instrument.
• Compute spectra using a FFT algorithm applied on the zero-padded interferograms.
• Correct spectral axis for Doppler shift and perform spectral interpolation onto a predefined uniform spectral axis.
• Interpolates spectrum over a pre-determined user's grid
• Radiometric calibration by a complex multiplication of the actual scene spectrum with the actual gain.
• Perform scene measurement quality verification.
• Report of NESR

•
Organigram:

 Figure 2.9

Input:

Output:

•  Radiometrically and spectrally and locally calibrated spectral radiance of the scene

Detailed description:

Keywords: ESA European Space Agency - Agence spatiale europeenne, observation de la terre, earth observation, satellite remote sensing, teledetection, geophysique, altimetrie, radar, chimique atmospherique, geophysics, altimetry, radar, atmospheric chemistry

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