The smile effect is caused by optical aberration and results in a variable curvature of the slit image across the spectral range6. It can be estimated by comparing, for a given column, the CWL of any pixel along this column w.r.t. to the CWL measured on the middle of the FOV at R=400, which can be expressed as:
Smile shift correction(R, C) = CWL(R, C) − CWL(400, C) (3) R and C indicate the position of a given physical pixel in the FOV in terms of row (spatial index range from 1 to 800) and column (spectral index range from 1 to 1016), respectively (see Fig. 1). Some spectral signatures used for the absolute calibration could not be used for the smile correction due to the low magnitude of the smile corrections (< 1 nominal spectel) and the low SNR precluding an accurate characterization along the FOV. The VISNIR channel smile was characterized using monochromator scan, atmospheric, sample, and ICU data (Table III). Because of the high ambient thermal background 31 occurring during the ground measurements, the IR channel smile was described using atmospheric signatures near 2660 nm only.

Still, thanks to the polystyrene signatures in the ICU acquisitions, the smile analysis was extended at around 3370 nm.
For all of the measurements except for the ICU and atmospheric measurements, three FOV positions were available.
The methodology used to derive the CWL along the FOV is the same as the one used for deriving the absolute spectral calibration (IV.A). The estimation of the spectral shift using the monochromatic measurements for the VISNIR channel is summarized in Table IX. It must be noted that the lower accuracy of the monochromator measurements (about 1 nm) makes it challenging to assess more minor magnitude distortions reliably.
Table IX. Monochromator scan scans smile table summary. The values indicate the shift in nm w.r.t. the center of the FOV according to Eq (3) for three wavelength ranges

| Smile (nm) | 700-900 nm | 1400 nm | 1900-2100 nm |
| --- | --- | --- | --- |
| FOV Row 20 | 1.5 ± 1.00 nm | 1 ± 1.00 nm | -1 ± 1.00 nm |
| FOV Row 380 | -0.5 ± 1.00 nm | 1 ± 1.00 nm | 2 ± 1.00 nm |

In the series of acquisitions for which the FPA frames are not “windowed” to a certain part of the FOV, the smile can be consistently estimated across the entire FOV. This is achieved using the ICU and certain OP3 acquisitions (Fig. 18).
Such data set can be used to establish a 2D map of the smile correction by using a second-degree polynomial interpolation (this provides a smoother correction that is less sensitive to algorithmic noise), first in the spatial direction and, then, in the spectral direction. Due to the limited data from the IR channel, only a 1D correction was derived by using a seconddegree polynomial interpolation in the spatial direction and a constant value in the spectral direction based on the average of the two smile corrections provided by the ICU and atmospheric signatures (Fig. 19). The map correction of the VISNIR channel is almost line-symmetrical w.r.t. the diagonal of the FPA. It is maximal at the corners of the FPA and decreases towards the center “cross”. For both channels, along-FOV corrections mostly follow linear trends and not second-degree polynomial trends, unlike the “smile” analogy typically indicates.

[Figure: Fig. 18. Smile characterization of both channels for full FOV measurements. The smile characterization uses both channels' ICU and OP3 measurements.]

[Figure: Fig. 19. Mapping of the smile correction factor to be applied for removing spectral smile aberration. A physical pixel scale is considered.]

Panel A is for VISNIR and Panel B for IR. The shift correction of the smile is to be added to the reference CWL (that correspond to FOV position 200 = 400 physical) to derive the CWL of any physical pixel. The effect of this correction is showcased in Fig. 20.
An example of smile characterization and correction using atmospheric signatures is shown in Fig. 20.

[Figure: Fig. 20. Illustration of the smile shift correction being applied to an atmospheric (water) signature. (A) Example of the smile effect using atmospheric signatures. The three FOV positions spectra are superposed and show that the signatures are slightly shifted. (B) The three FOV position spectra are superposed after the automatic correction (using shift presented in Fig. 19) of the smile effect has been applied.]