Level-1B Algorithm Overview
The Level-1B algorithm enables generation of a Level-1B product from the precursor Level-1A product. The processing includes:
These steps are chained and can be activated as required for each band. Each algorithm step is described below. Radiometric CorrectionsThe SENTINEL-2/MSI radiometric model is given by equation 1: Equation 1: SENTINEL-2 Radiometric Model Where:
Two different functions are required for modelling ϒ (p,b,d,Y(p,l,b,d)):
For VNIR channels, the baseline is to consider a polynomial function of degree 3 to have a best fit of the detector response. For SWIR channel, the double linear is the baseline option that will be used.
Inversion of the On-board EqualizationThe bi-linear equalization is applied on-board to both channels (VNIR and SWIR) and per detection line before compression to reduce compression effect on detector photo-response non-uniformity. An inversion of the on-board equalization is performed to retrieve the original detectors response Xk(i,j) and further radiometric corrections are applied such as cross-talk correction and improved equalization processing. As output a reverse equalized image (output image is called X in the mathematical description) is obtained.
Equalization CorrectionThe objective of equalization is to achieve a uniform image when the observed landscape is uniform. It is performed by correcting the image of the relative response of the detectors (if equalization correction is activated).
Dark Signal CorrectionThe dark signal correction involves correcting an unequalized image by subtracting the dark signal (if equalization correction is activated). The dark signal DS(i,j) can be decomposed as shown in Equation 2: Equation 2: SENTINEL-2 Dark Signal
Dark Signal Non-UniformityVariability in the dark signal arises as a result of the different time required for integration by the individual bands. This signal varies as a function of the line number with a spatial frequency. Defining a cycle by the integration time for 60 m bands, there are:
For a given line 'i' in the image, the corresponding dark signal depends on the line number inside the area. The average of 'i' observations assumes that the same radiance is observed and allows noise reduction (Equation 3). Equation 3: SENTINEL-2 Dark Signal Uniformity where Nm is the number of lines being summed, and j is an index within the range [1,6] corresponding to the chronogram sub-cycle line numbe (j is within [1,6] range for 10 m bands, [1,3] for 20 m bands and [1,1] for 60 m bands). DS(p,j,b,d) is determined as an average of the dark signal along the columns and therefore is independent of the line variable. The values of DS are taken directly from the EQUALIZATION ONGROUND GIPP being calculated during the calibration activities and represent dark signal, break point, first slope and second slope.
Dark Signal OffsetThe offset variation of dark signal is due to voltage fluctuations. To compensate for this signal, an offset for each line is computed using blind pixels located at the extremity of each detector module. The number of blind pixels depends on the band (32 blind pixels for 10 m bands, and 16 blind pixels for 20 m and 60 m bands). For each band, each detector module and each line of the image, the offset is computed as the average value of the signal acquired by the valid blind pixels: Equation 4: SENTINEL-2 Dark Offset Computation where N is the number of valid blind pixels per detector module and l the blind pixel index and Inter_Image is the raw image corrected from the application of the Non-Uniformity Dark signal. The list of valid blind pixels is available in the corresponding GIPP. Blind Pixel RemovalFor each band and each detector module, blind pixels are removed from the image product. Cross-Talk CorrectionCross-talk correction involves correcting parasitic signal at pixel level from two distinct sources: electronic and optical cross-talk (if equalization correction is activated). In both cases, the parasitic signal of a pixel in a given band is modelled as a linear function of the signal in the other bands acquired at the same time and at the same position across track. The correction parameters are provided to the ground segment by a dedicated GIPP. Relative Response CorrectionRelative response correction involves correcting the image of the relative response of the detectors (if equalization correction is activated). The correction applies respectively a bilinear and a three degree polynomial function to the SWIR and VNIR channels. The coefficients of the polynomial function are made from sun diffuser observations during calibration mode; the BRDF of the diffuser being characterised before launch. An estimation of the coefficients for each instrument is performed at the same time as the estimation of the absolute radiometric calibration, i.e. every three repeat cycles (30 days). Assuming that the response of the instrument is a cubic function (e.g. VNIR channels) of the radiance, Eq. (1) can be written as: Equation 5: SENTINEL-2 Equalization Correction
In case of the SWIR band Equation (3) becomes: Equation 6: SENTINEL-2 Equalization Correction where: G3, G2, G1 and G0 are the parameters of the cubic model and A1, A2, Zc and Zs are the parameter of the bilinear model. Equalization processing is performed for each non-defective pixel or non-blind pixel. SWIR RearrangementPixels of the SWIR bands (band 10, band 11 and band 12) are rearranged. For the SWIR bands, each detector module is composed of three lines for band 10 and four lines for band 11 and band 12. To make optimal use of the pixels with the best SNR for the acquisition, one pixel over three lines for band 10 and two successive pixels over four lines for band 11 and band 12 is selected for each column. In the instrument, these bands work in Time Delay Integration (TDI) mode and are re-arranged along columns on the ground. This algorithmic procedure ensures the best registration between columns of SWIR images. For 20 m resolution bands (band 11, band 12), the shift to be applied is ± 1 pixel. For 60 m resolution band (band 10), the shift to be applied is ± 1/3 pixel and is performed using a one-dimensional filter.
Defective Pixel CorrectionDefective pixel correction involves allocating to a defective pixel, a radiometry corresponding to the (bi-linear or bi-cubic) interpolated radiometry of its neighbouring pixels (if they are valid, and their value is greater than a threshold). Defective pixels can arise as a result of:
As well as the pixel position and the type of defect, the interpolation filter is provided in a GIPP. The maximum number of allowed adjacent defective pixels is defined by a threshold provided in a GIPP as well. If the number of adjacent pixels is outside the threshold, the correction is not applied. Holes in the spectral filters can also affect the SENTINEL-2 images. The same correction as for defective pixels is applied.
RestorationRestoration processing combines two actions:
De-convolution processing compensates for blurring due to instrumental MTF. De-convolution is recommended when the MTF at Nyquist frequency is low, however, de-convolution processing increases the noise for high spatial frequencies, particularly over uniform areas. This phenomenon is limited by dedicated de-noising. De-convolution is performed by Fourier Transform (FT) and the de-noising process is based on a thresholding technique of wavelets coefficients. These restoration processes are implemented in the GPP. The processes are optional. The deconvolution step is not recommended for bands with a high MTF (i.e. 20 m and 60 m bands).
Binning for 60 m BandsFor bands B1, B9 and B10, the spatial resolution is approximately 60 m along track and approximately 20 m across track. To achieve a homogeneous resolution (i.e. 60 m) both along and across track, these bands are filtered and sub-sampled in the across track direction. The filter and the sampling rate (3, by default) are provided in a GIPP by the IQP.
No Data PixelsPixels with no data generally correspond to missing lines within the image product. These pixels are identified in a mask provided with the product. To correct for no data, and to insert a value, these pixels are interpolated using neighbouring valid lines. The interpolation filter is provided in a GIPP. A threshold for the maximum number of missing joined lines is defined. This threshold is provided in a GIPP. Beyond this threshold, no correction processing is applied.
Saturated PixelsSaturated pixels are identified in a mask associated to the product. No correction is applied.
Geometric Refining and RegistrationsAfter the radiometry step, and to improve the accuracy of geolocation performance, a geometric refinement can be carried out. This operation occurs before the orthorectification process for Level-1C products. It is performed on the full swath by the longest possible length in automatic mode. The algorithm is composed of two modules:
The reference segments are perfectly geo-referenced through a global spatio-triangulation in the IQP but they are not orthoimages. Each module is composed of the following steps:
For the refining module, images of the Level-1B (only radiometrically corrected) are correlated with reference images (i.e located on ground) and homologous points corresponding to GCPs are determined. For the registration module, images of VNIR focal plane corresponding to spectral bands B1 to B9 are correlated with images of the same Level-1B product from the SWIR focal plane. Homologous points in the images are tie-points. The processed images are then registered to improve absolute geo-location accuracy, spatial co-registration accuracy and multi-spectral co-registration. The execution of these operations requires the following inputs:
Quality control of the refining is performed with:
A multi-temporal registration performance indicator is computed, in metres, corresponding to the mean residual distance of the spatiotriangulation in pixels multiplied by the pixel size. A multi-spectral registration performance indicator that corresponds to a date provided by the GIPP is added. These results are appended in the product Level-1B. The two algorithmic modules, refining and registration, are optional.
Common GeometryThis step defines a new viewing model that is common to all detectors of one reference band in Level-1A. A new single virtual sensor is defined by modelling viewing directions. After this, the datation of the new viewing model is determined; the time of line sampling is equal to the mean value of the sampling time for all detectors. The first line datation, also called the "Earliest date", is the earliest datation of all lines in all detector. The last line datation, the "Latest date", is the latest datation of all lines in all detectors.
ResamplingThe resampling step computes the value of each individual pixel in an image via interpolation of the source image, and the combining of a re-sampling grid and integration of useful zones data. Useful zones are the areas of an image in which there is an overlap between neighbouring across track detectors. This is performed for each band and each detector. Having undergone resampling, the target image undergoes further refinement, using a filter. The range of this filter is defined in the GIPP. If the source image provides no data values, the pixels of the target image are filled with no data values. During this operation, each mask is also re-sampled.
Resampling in a Monolithic Geometry Matching ImagesThis operation identifies the areas of images that are overlapped. For example, if regions between the image of detector 1 and detector 2 overlap, a pair of these images is retained for the following correlation operation.
CorrelationThe goal of correlation is to define:
A correlation is performed to refine and register the target image with the reference image. The correlation is made for each pair retained in the matching images operation (Figure 1). There are three factors which improve the performance of correlation:
For each pixel, a radiometric resemblance criterion that uses the normalised co-variance (also called normalised cross-correlation) is computed to enable the degree of linear resemblance to be measured. The resultant values form a grid of resemblance and the best candidate points correspond to the maximum of the grids of resemblance. Poor homologous points are discarded by a model that filters aberrant pairs using polynomial models, and least square regression.
Figure 1: Image Correlation SpatiotriangulationThis operation corrects the attitude and orbital data which are estimated by a mean square regression. The viewing model is refined by spatiotriangulation using the GCPs derived earlier in the processing. It consists of:
The viewing vector (i.e. the line of sight) is computed at the time of pixel acquisition. The intersection between this viewing vector and the Earth model gives the geolocation (or direct location) of the pixel and is inverted to compute the position in the image of a point located on the ground. |
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