## 3 Space Segment
### Instrument
#### 3.1.2 Spectral and Radiometric Performance  
Detailed knowledge of the instrument performance based on a consolidated instrument model are already available for some key spectral and radiometric parameters of EnMAP. The spectral coverage and resolution of the two spectrometers is depicted in Figure 3. A typical top-of-atmosphere (TOA) radiance spectrum from a dry sand surface was simulated with the MODTRAN5 atmospheric radiative transfer code [49] at a spectral resolution of 0.5 nm and convolved with the EnMAP spectral response. The SSD is plotted as a function of wavelength in the lower panel. Mean SSD is about 6.5 nm in the VNIR and 10 nm in the SWIR. The spectral resolution is requested to be 1.2 larger than the SSD to avoid spectral artifacts due to signal undersampling. The variation of the SSD with wavelength, caused by the dispersion properties of the glasses, is characteristic for prism-based spectrometers [48]. The uniformity of an imaging spectrometer represents the degree of variability of the spectral and spatial responses in the two dimensions of the detector array [50]. In particular, the smile effect describes the variation of the center wavelength of a given spectral channel along the spatial (across-track) direction. The keystone effect is the counterpart of smile in the spatial domain. This is the variation of a pixel's spatial position with wavelength. Spectrally- and spatially-uniform datasets are required to fully exploit the information in hyperspectral measurements [4]. Even though EnMAP's optical design based on curved prisms is intended to minimize smile and keystone distortions, _a priori_ knowledge of the spectral and spatial uniformity of a spectrometer response is needed for proper data processing and interpretation. The expected magnitude of smile and keystone in the VNIR and SWIR spectrometers  
Figure 2: Schematic view of the main components of the EnMAP double-spectrometer instrument concept. as a function of spectral and spatial position in the VNIR and SWIR focal plane arrays is displayed in Figure 4. Characteristic spectral \"smile\" and \"frown\" (inverse smile) patterns can be observed along the across-track direction of the SWIR spectrometer at, e.g., 1000- and 2400-nm wavelength positions, respectively. Peak values of smile are about \(-\)0.5 nm (\(\sim\)5% of a spectral pixel) at the long wavelength edges of the two spectrometers, which is to be compared with the up to 4-nm variation in spectral channel position at 760 nm for Hyperion [51]. Keystone is generally below 3% of a spatial pixel for the EnMAP VNIR spectrometer and almost negligible in the SWIR spectrometer. These numbers for smile and keystone largely improve upon the \(<20\)% mission requirement (see Table 1). The radiometric sensitivity of EnMAP is defined by SNR specifications of 400:1 at 495 nm and 180:1 at 2200 nm for a given reference radiance level and by a 14-bit radiometric  
Figure 4: Expected spectral smile (**left**) and keystone (**right**) effects for the two EnMAP spectrometers as a function of spectral and spatial positions in the VNIR and SWIR focal plane arrays (**top** and **bottom**, respectively). The mission requirements of smile and keystone \(<\)20% are largely fulfilled thanks to the curved prism disperser approach adopted for the spectrometers’ optical system. Figure 3: Illustration of EnMAP spectral characteristics. (**Top**) Simulated top-of-atmosphere radiance spectrum for a dry sand surface convolved by the EnMAP spectral response. (**Bottom**) Spectral sampling distance (SSD) as a function of wavelength. The existing instrument model can be used to estimate the actual spectral SNR as a function of at-sensor radiance. Examples for four land cover types representing different application fields of EnMAP are displayed in Figure 5. For the sake of a simpler interpretation, the incoming at-sensor radiance used for the SNR simulation is expressed in terms of spectral surface reflectance at SZA = 45\({}^{\circ}\).