Spectral Filters Based Approach
Spectral filters based hyperspectral sensors are less popular and appear more recently. For this type of hyperspectral sensors, one or more spectral filters, such as an absorption or interference filter, are used to transmit the selected spectral bands of interest. As the beam passes through a filter, some of its spectral components are blocked through an absorption or interference process, while the desired spectral components are transmitted. Various interference filters, from the ultraviolet through the far-infrared region, in various dimensions, are available as commercial-off-the-shelf (COTS) products. Electronically tunable filter (ETF) is another kind of filters that transmit desired spectral bands by controlling voltage, or acoustic signal, etc. (Gat 2000).
The basic principle of a spectral filter based hyperspectral sensor is similar to that of a dispersive element based sensor. However, the main difference is that the radiation light from a telescope, instead of being collimated and then dispersed by a grating or a prism in a traditional spectrometer, is directly focused on a 2D filter. The filter has the same size as the 2D detector array and is assembled in front and close to the detector’s sensitive surface. It distributes spectral content of the ground samples in the spectral dimension (Qian 2013). Figure 1.4 shows a block diagram of the composition of a filter-based hyperspectral sensor. It is essentially composed of three parts: a telescope, a filter, and a detector array. A traditional bulky spectrometer is omitted and replaced by a tiny optical filter.
Figure 1.5 shows an example of how the volume and mass of a spectral filter based hyperspectral sensor are reduced in comparison to a conventional grating-based hyperspectral sensor (Mouroulis et al. 2008). In this case, a linear variable filter (LVF) based hyperspectral sensor is chosen. Both designs use the same front-end optical elements. The elimination of the spectrometer results in a much more compact instrument. In the figure, an optical filter based imaging spectrometer replaces the traditional spectrometer assembly with a simple optical filter mounted in front of the detector array at the focal plane (Qian et al. 2013). A filter-based hyperspectral sensor can yield a much more compact design when compared to the conventional approaches using Dyson (1959) or Offner (1973) type spectrometers. However, this simplified optical design comes with several limitations.
Linear Variable Filters
FIGURE 1.5 An example of how the volume and mass of a filter-based hyperspectral sensor is reduced compared to a traditional dispersive element based approach.
spectral position of the peak of the transmission curve varies linearly along one physical dimension of the filter. The slope of that curve is called the LVF's spectral gradient (upper right in Figure 1.6).
At a given position on the LVF. the transmittance has a certain shape. That shape shifts with the position. Figure 1.7 shows the transmittance curves of a typical LVF for a few positions along the spectral direction of the filter. Because the change is gradual, a LVF in the visible region exhibits a gradual rainbow pattern when seen in transmittance, as shown in the photo in the lower part in Figure 1.6. The shape of the transmittance curve also varies along the spectral dimension of the LVF. For example. Figure 1.7 shows the full width at half maximum (FWHM) of a typical LVF at different positions. Typical LVFs have spectral gradient between 10 nm/mm and 200 nm/mm.
The LVF exists in the spectral range from visible to the thermal infrared region, typically within the visible and near-infrared (VNIR) regions (e.g.. 450-900 nm). The spectral bandwidth of an optical filter varies as a function of wavelength. The longer the wavelength, the wider is the spectral bandwidth.
FIGURE 1.7 Transmittance curves of a typical linear variable filter.
The spectral bandwidth is limited by its coating thickness, glass index, quality of the coatings, the f/# of the optics, and the wavelength of the light. A typical band-pass (i.e., FWHM) ranges from ~7 nm at 450 nm to ~12 nm at 900 nm. Typical LVFs have a FWHM variation 1-2% of the center wavelength or more. The LVF transmission degrades as the FWHM is narrowed. The throughput ranges from -40% to -66% over the spectral range.
Figure 1.8 illustrates the concept of a LVF-based hyperspectral sensor. A simple spectrometer can be built by placing a LVF in front of a 2D detector array after the telescope collects the input light of a ground scene. A pushbroom hyperspectral sensor can then be built based on this type of a spectrometer. The 2D detector array of the instrument “sees” the complete scene at once. As described in Section 1.2.1, a dispersive element based hyperspectral sensor working in the
FIGURE 1.9 Two field of views of a linear variable filter based hyperspectral sensor passing over a ground track when a satellite flies at the moment T= 0 and T=t.
pushbroom mode acquires an entire cross-track line on the ground at a moment (see Figure 1.2), whereas a dispersive element based hyperspectral sensor working in the whiskbroom mode acquires a single sampling cell in a cross-track line at a moment (see Figure 1.3). Unlike a dispersive element based hyperspectral sensor, a LVF-based hyperspectral sensor acquires simultaneously all the cross-track lines in the FOV, this is because the FOV of a LVF-based hyperspectral sensor is not limited by a slit to only one cross-track line in the along-track direction. Each row' of the detector array images a corresponding cross-track line of the scene but in a different w'aveband than the neighboring lines. Hence, every moment of time a detector frame is imaged, a complete 2D scene is acquired. Each line of the scene is acquired at a different wavelength. Figure 1.9 illustrates the two FOVs of a LVF-based hyperspectral sensor passing over a ground track when a satellite flight at the moment T = 0 and T=t. As the satellite flies over the scene, each filter row passes over the scene. Once the complete FOV has passed over the scene, each different filter row has sensed all cross-track lines of ground sampling cells in the scene and acquired all spectral components. A spectrum of each ground sampling cell can be reconstructed by reorganizing these images acquired at different moments.
Like a grating- or prism-based spectrometer, the throughput of an optical filter based spectrometer is a complex function that includes a principle wavelength as well as a variety of cross-talk wavelengths. For a single detector row, there is a principle wavelength, and up to 15% of the total throughput corresponds to cross-talk from other wavelengths. Removal of the spectral cross-talk needs to be carefully done as part of the image post-processing. Trying to correct too many crosstalk wavelengths, for example, will introduce excess noise and degrade the resulting product SNR. The optimal approach is to correct only the key cross-talk wavelengths.
At the time of this book being written, there were two spaceborne hyperspectral imagers based on a LVF. The Hyperspectral Imager (HySI) onboard Indian Mini Satellite-1 (IMS-1) launched in April 2018 used a LVF, w'hich covers a wavelength range from 400 nm to 900 nm w'ith a bandw'idth of 10 nm dispersed over 512 spectral elements. This hyperspectral satellite is described in Section 2.12. Another LVF-based spaceborne hyperspectral imager is hyperspectral nanosatellite HyperScout.
FIGURE 1.10 The principle of a Fabry-Perot filter.
It is a 3U CubeSat with the hyperspectral imager being 1U (10 cm x 10 cm x 10 cm). The LVF covers a wavelength range from 450 nm to 900 nm with a spectral resolution of 10 nm (Conticello et al. 2016). This spaceborne hyperspectral imager is described in Section 2.20.