The first step in the raw data analysis was to match each time-tagged SHIMMER exposure to the corresponding time-tagged ephemeris information, which locates the measurements in latitude, longitude, and altitude. The ephemeris information is determined from the on-board GPS (Global Positioning System), the star tracker data, and two line element (TLE) sets.
 In section 5.1, we describe the calibration algorithm using one particular SHIMMER limb exposure, which was taken on 16 July 2007 at 104736Z at a tangent point latitude of 57.16°N, a longitude of 20.76°E (local time, 120435), a solar scattering angle of 98.31°, a solar zenith angle of 35.63°, and the nominal exposure time of 12 s. This particular measurement was chosen because it is part of an averaged spectrum that was previously published [Englert et al., 2008] and it contains the brightest PMC signature measured by SHIMMER on this particular day. Other than the presence of a PMC in this exposure, which only occurs in a small fraction of all SHIMMER observations and does not contaminate the OH retrieval, this is a typical example.
5.1. Interferogram Corrections
 The raw CCD data processing starts with the correction for the CCD readout bias, the detector nonlinearity, and the dark current. Information for the bias and dark current corrections is derived from dark measurements taken during the same orbit. At the nominal CCD operating temperature of −40°C and below, the dark current is very small compared to the bias value and the atmospheric signal. The nonlinearity correction is performed using a quadratic function. The parameters of the quadratic function were determined from prelaunch measurements using variable integration times and a constant UV signal level. Figure 4 shows CCD data that are bias, dark current, and nonlinearity corrected.
Figure 4. (a) CCD image after corrections for readout bias, dark current, and nonlinearity. (b) Selected rows of the image shown in Figure 4a. The rows are numbered from 0 to 31 from low to high tangent point altitudes on the limb, i.e., row 0 is the bottom row and row 31 is the top row in Figure 4a. Every row covers an altitude interval of about 2 km. For nominal pointing, the centers of row 0 and row 31 correspond to tangent altitudes of ∼34 and ∼96 km, respectively.
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 The next step in the calibration is the flat field correction, which accounts for the response variations between CCD pixels and nonuniformities throughout the entire SHIMMER optics, especially the gratings. The flat field correction is performed according to the “Unbalanced Arm Approach” [Englert and Harlander, 2006], using prelaunch laboratory measurements.
 Since the gratings are imaged on the focal plane array, any localized grating imperfection, like a scratch, will have a localized effect on the interferogram detected by the CCD. For SHIMMER, the CCD pixel-to-pixel sensitivity variations are small and generally slowly varying with pixel position. However, the effects from grating imperfections are in part large, mostly due to the grating scratches that resulted from the vibration test failure, discussed earlier in section 4.1.4. Thus, it is important to ensure that the grating image is properly registered to the CCD, since a small shift or rotation of the image on the CCD will cause the flat field to change, which means that the laboratory flat field measurements also have to be shifted or rotated to achieve the best possible flat field correction. Therefore, before the flat field correction is applied, the grating image on the CCD is registered to subpixel precision, for each exposure, using the grating imperfections as fiducials.
 The next step was to identify and correct for high-energy particle effects on the CCD. Even outside of the South Atlantic Anomaly, isolated high-energy particle hits are present in the CCD data, since no special precautions were taken in the camera design to shield the CCD. These sporadic, localized, very high signals are easily identified and are replaced using information from neighboring, unaffected rows.
 Subsequently, we performed a phase correction using a simple wavelength-dependent phase shift correction that is familiar from FTS interferograms and which can also be applied to SHS data [Englert et al., 2004]. This method uses a narrow interferogram region around the zero path difference (ZPD) location to determine a low-resolution, wavelength-dependent phase shift. To isolate this narrow region around ZPD, we use a Hann function with a total width of 61 interferogram samples. As expected from interferograms that are not sampled symmetrically around the ZPD location, the SHIMMER interferograms show a nearly linear phase shift versus wave number. Once the phase shift is determined, it is easily corrected in the interferogram domain by a convolution with the Fourier transform of the imaginary exponential of the phase shift [Brault, 1987].
 The final correction of the interferograms is made in regions of severe grating scratches, since these regions might also have degraded modulation efficiencies, which are not properly corrected by the unbalanced arm flat-fielding approach [Englert and Harlander, 2006]. These regions are identified in the SHIMMER prelaunch laboratory measurements and are replaced in the flight data, similar to the high-energy particle impact locations on the CCD.
 Since the data on one side of the ZPD location (Figure 4a, left) is more severely impacted by the grating imperfections and also shows an unexpected feature that spans over many CCD rows, possibly due to an extended surface contamination of the grating, we have used only the other side of the interferogram for the ensuing radiometric calibration. To keep the format of a double-sided interferogram, the higher-quality side of the corrected interferograms is duplicated on the other side of the ZPD location. Using only one side of the interferogram effectively reduces the throughput of the instrument by a factor of 2 and, assuming shot noise limit, decreases the signal to noise in the interferogram by a factor of square root of 2. Finally, the interferograms are apodized using a Hann function with a total width of 511 interferogram samples. The resulting, corrected interferograms are shown in Figure 5 for the same exposure that is shown in Figure 4.
Figure 5. (a) CCD image after applying all corrections listed in Figure 5b. The color scale is chosen to enhance the interferogram features on either side of the zero path location. The large dynamic range of the data results in little color contrast for (top) high row numbers, where the signal decreases, and (left and right) high optical path differences, where the interferogram contrast decreases. (b) Selected rows of the image shown in Figure 5a. The scale of the ordinate is shifted down for rows 14, 19, and 23 as indicated, in order to separate the traces for clarity. Row definitions are the same as in Figure 4.
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5.2. Instrumental Line Shape Function
 The instrument's line shape function was investigated using a laboratory spectrum of a manganese neon (MnNe) hollow cathode lamp. For this measurement, a holographic diffuser was placed in front of the SHIMMER aperture to improve the homogeneity of the field illumination. The measured interferogram was corrected as discussed in the previous section, and two Ne+ lines were subsequently isolated in the spectrum with a Hann function and transformed back into the interferogram domain, yielding a virtually monochromatic fringe pattern. The phase of this fringe pattern was determined as discussed by Englert et al. , and the interferogram envelope was obtained by dividing the interferogram by the cosine of the phase and subsequent normalization. The Fourier transform of this envelope function is the instrumental line shape function, examples of which are shown for different wavelengths and different detector rows in Figure 6. As expected from self apodization and the Hann apodization of the interferogram, the full width half maximum (FWHM) of the line shape function is slightly wider than two spectral samples. No significant differences were found between the line shapes at the two wavelengths and the different rows. For all following data analysis steps, the line shape was parameterized as a Gaussian function, which is a good representation of the measured line shape (see Figure 6).
Figure 6. The solid lines are instrumental line shape functions measured in the laboratory using two Ne+ lines at 308.817 and 309.713 nm, which corresponds to about 118 and 189 fringes, respectively, across the detector. The laboratory measurement is analyzed similar to the on-orbit spectra, including the interferogram apodization with a Hann function. The differences in the width of the instrumental line shape functions for different signal wavelengths and detector rows are small. Crosses are the core region of normalized Gaussian functions, illustrating that the line shape function can be approximated and parameterized with a Gaussian function. Row definitions are the same as in Figure 4.
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 In the operational analysis of the on-orbit data, the Gaussian line shape width parameter was determined for each exposure, and it corresponds to a line shape FWHM of about 0.03 nm. The knowledge of the instrumental line shape is of critical importance for the separation of the OH signal from the highly structured Rayleigh scattered solar background, especially at low tangent altitudes, where the background is significantly brighter than the OH features. As discussed below, we find that for the middle and upper mesosphere (60–90 km), the assumption of a Gaussian line shape is adequate. Future work might include a more sophisticated treatment of the line shape function to improve the results at lower altitudes.
5.3. Radiometric Calibration
 The radiometric calibration of SHIMMER data can be divided into two fundamental parts: The laboratory calibration and the on-orbit corrections that we made to this calibration. All elements of these two parts of the calibration are discussed below, except for the measured on-orbit degradation of the SHIMMER sensitivity, which is discussed in section 7.1.
 The laboratory calibration assigns a wave number grid to the retrieved spectrum and provides a radiometric calibration of the spectral intensities based on prelaunch measurements. In order to determine the proper wavelength for each spectral sample, we analyzed the spectrum of a MnNe hollow cathode lamp. In particular, the two Mn lines at 307.963 and 308.133 nm and the two Ne+ lines at 308.816 and 309.713 nm were used to fit the Littrow wave number and the width of the spectral samples. The width of SHS spectral samples is generally equal in wave number units, but not in wavelength units. Even though this difference is small for a narrow band instrument like SHIMMER, the fit is performed using wave number units. The resulting wave number scale is ultimately converted into wavelength units. The resulting Littrow wavelength (in vacuum) and spectral sample width were 307.318 nm and 1.334 cm−1, respectively. These values are consistent with previously published data for the same interferometer [Harlander et al., 2003]. Small differences are due to thermal effects, and the fact that not the entire grating width is used for the SHIMMER data analysis.
 The radiometric calibration is ideally performed using one radiometrically calibrated source that covers the entire passband and fills the entire field of view of the instrument. For SHIMMER, the available calibrated source was the same large aperture integrating sphere that was used for the MAHRSI calibration [Conway et al., 1999]. The sphere was recalibrated by the National Institute of Standards prior to the SHIMMER calibration measurements. The absolute radiance was determined with an accuracy of ±0.4% and with a spectral resolution of 2 nm. The spatial source variation was found to be <1.5% across the area viewed by SHIMMER. However, within the SHIMMER passband, the quartz halogen lamps of the integrating sphere emit two aluminum lines on top of an otherwise slowly varying spectral shape. These lines are not resolved by the NIST measurement, so that for the radiometric calibration of SHIMMER the integrating sphere signal was only used in spectral regions that did not include these emission features. To compensate for this shortcoming, we also made measurements of a deuterium lamp spectrum, which is spectrally flat within the SHIMMER passband but for which only a relative spectral calibration was available.
 Figure 7a shows an example of SHIMMER's relative spectral response to the signal of the deuterium lamp, corrected for the small, known variation of the lamp brightness across the passband. By scaling the measured spectra to the correct radiance values, we obtained a single absolute calibration constant. This scaling was achieved by fitting the SHIMMER spectrum to the absolute NIST radiance data of the integrating sphere, in the spectral sample interval between 30 and 50, an area that is not affected by the aluminum lines and that is insensitive to thermal defocus effects (see below). Figure 7b shows such a calibrated spectrum of the integrating sphere. The fact that the calibrated integrating sphere spectrum falls on top of the NIST spectral radiance for spectral samples greater than 50 and away from the aluminum lines verifies the high quality of the relative response curve measured using the deuterium lamp.
Figure 7. (a) The solid line is the relative spectral response of row 19 versus spectral sample or fringe frequency, measured using a spectrally flat deuterium lamp and corrected for the small variation of brightness across the passband. The dashed line is the measured relative response smoothed with a 20 sample wide boxcar function. The dotted line is the imaginary part of the measured spectrum. The low values of the imaginary part are an indication of proper phase correction. Note that the spectral interval used for the SHIMMER data analysis (308.2–309.6 nm) corresponds roughly to the fringe frequencies between 57 and 167, which means that, within this interval, the response changes by less than a factor of 2. (b) The gray line is the calibrated integrating sphere spectrum. The dashed line is the linear interpolation of the NIST calibration measurement. The interpolated data exclude the areas that are influenced by the aluminum lines. The solid line is the spectral data used to fit the calibration constant, which scales the spectrum to the proper absolute radiance values.
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 To complete the SHIMMER calibration, we applied five on-orbit calibration corrections. They are (1) a shift in Littrow frequency, (2) an adjustment of the spectral sample width, (3) an adjustment of the instrumental line shape function width, (4) a spectral shift in the relative SHIMMER response, and (5) a wavelength-dependent adjustment of the relative spectral response. All these corrections were made simultaneously by fitting the spectra of suitable altitude rows of each exposure to the known spectral shape of the solar spectrum, the shape of the OH solar resonance fluorescence, and an offset term to account for the Ring effect. Sample fit results are presented in Figure 8, where calibrated spectra are shown in black and the sum of the fitted solar background and offset terms are shown in red. Figure 9 shows the residuals, which are equivalent to the OH resonance fluorescence signals within the measured spectra. Note that the spectra in Figures 8 and 9 are for a single 12 s exposure.
Figure 8. Examples of calibrated spectra from one 12 s exposure and different altitudes (black). The red lines show the solar background and offset contributions of the best fit to the spectra. Note that the dynamic range of the ordinate changes by a factor of 20 from row 4 to row 23. The altitudes corresponding to the row numbers are determined from the pointing data of this particular exposure.
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Figure 9. The residuals of the measured spectra and the background and offset terms shown in Figure 8 are given in black. The red lines correspond to the fitted OH resonance fluorescence component. For this single 12 s exposure, the noise dominates at low altitudes (e.g., row 4), where the background signal is high. The OH signal is clearly visible in rows 14 and 19. At higher altitudes (e.g., row 23), OH densities and signals are decreasing and thus the residual spectra are again dominated by noise.
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 The first correction, the shift in Littrow frequency, is mainly due to thermal effects and the fact that the interferometer is used in vacuum, as opposed to the ambient pressure environment in the laboratory. Thus, small corrections in the effect of the field-widening prisms and the gratings due to the slightly different index of refraction of the surrounding medium, the change in refractive index with temperature, and thermal expansion are expected. For our example exposure, the shift in Littrow wavelength is about +0.16 nm, which is consistent with expectations.
 The second correction, the small adjustment in spectral sample width, results from the thermal expansion of the grating and the thermal change in refractive index of the field-widening prisms. For our example exposure, this adjustment is less than 0.2%.
 The third correction, an adjustment to the width of the instrumental line shape function, is needed to account for potential on-orbit flat field variations, including a potential difference in the on-orbit illumination of the gratings compared to the laboratory MnNe measurements. A typical value for the on-orbit Gaussian line shape FWHM is 0.03 nm, which is slightly lower (better) than measured in the laboratory, indicating that the on-orbit illumination is more uniform than the illumination achieved by the MnNe lamp in the laboratory.
 Fourth, a shift in the relative spectral response is included in the fit to account for the effect of the wavelength change in vacuum and a thermal change in the filter transmittance. For the example exposure in Figures 8 and 9, the optimum response shift is about −0.1 nm.
 Finally, we determined the wavelength-dependent adjustment of the spectral response to account for the thermally induced defocus of the exit optics. This effect was observed before launch in the laboratory and can also be corrected for each exposure using the information within the exposure itself and a parameterization of the change in the spectral response. To parameterize this effect, we consider that it can be modeled by convolving the interferogram with a localized, narrow point spread function that is representative of the angular distribution of the signal that is imaged on the CCD pixels. The Fourier transform of this point spread function results in a function which can be approximated by a low-order Taylor expansion 1 − A × (x/256)2, where the parameter A depends on the point spread function and x is the spectral sample number, starting at x = 0 for the Littrow wave number. According to the convolution theorem, the spectrum will be multiplied by this simple quadratic function. As discussed below, by fitting the spectrum for the single parameter A, we can quantify this effect and thus correct for the thermal defocus of the exit optics. For the exposure shown in Figures 8 and 9, A is 0.216, which is equivalent to a response reduction of about 1% at 308 nm (x ≈ 55) and about 9% at 309.4 nm (x ≈ 165).
 In the operational calibration algorithm, the above on-orbit calibration corrections are performed in three steps.
 First, all five correction parameters, the magnitude of the background and OH spectra, and an offset are fitted to the data from tangent point altitudes above about 60 km that contain enough signal to support a meaningful fit. This is typically the altitude range between about 60 and 80 km for a measurement in the middle of the orbital day. CCD rows that correspond to altitudes below 60 km are avoided so that the defocus parameter determination is not contaminated by ozone absorption, which increases for decreasing altitudes and has a similar, wavelength-dependent effect on the observed spectrum. This step yields a single defocus parameter for each individual exposure. Second, all of the above parameters, except the defocus parameter, are fitted to all rows that contain enough signal to warrant a meaningful fit. This step yields all calibration correction results for these rows. Third, for the remaining rows, e.g., the ones above 80 km that are too dim to warrant a meaningful fit of seven parameters, the calibration uses the defocus parameter of this particular exposure and typical values for the other four on-orbit calibration parameters.
 After completing the calibration procedure described above, the calibration results, including the calibrated spectra, are inserted into the SHIMMER database. The fitted spectra shown in Figures 8 and 9 for individual frames are discarded. After the correction for the on-orbit degradation of SHIMMER described in section 7, the calibrated spectra are coaveraged in time and latitude and the resultant-averaged spectra are used to retrieve the OH radiances and density profiles presented here (see section 8).