Theory

A square block function can be expressed as the infinite sum of sine functions:

This spatial light distribution will be influenced by the MTF performance of the VNS instrument (MTF_VNS(k)), which will result in a VNS response of

By taking the Fast Fourier Transform of the VNS response, the amplitude (A(k)) for the base frequency f and its (2k-1) multiples can be obtained

From these amplitudes the MTF performance for the embedded frequencies can be determined for each pixel

MTF measurements have been carried out using block patterns with 20 lines/mm (Nyquist) in both flight (along track) direction and across flight direction. Therefore the sinusoidal MTF response can be analysed concurrently for 20 (k=1), 60 (k=2), 100 (k=3), etc. lines/mm from one measurement, where the signal of each pixel is recorded during a scan of one period or more. In across flight direction MTF measurement have also been carried out with a 10 lines/mm block pattern (resulting in simultaneous analysis results for 10, 30, 50, etc lines/mm).

MTF tool

In order to determine the MTF for a pixel the block pattern has to be scanned over that pixel for one period or more. To achieve this a dedicated MTF tool has been designed and built, it consists of a scanning object platform which can hold different reticles, which are illuminated by a line shaped white light source. The illuminated reticle is imaged at infinity by a folding mirror M1 and a collimating mirror M2. The folding mirror reduces the straylight level at the MTF tool exit pupil position. The collimating mirror is split in two halves, to prevent light returning to the reticle that would affect the initial MTF value of the grating.

The reticle has several patterns of 5 x 110 mm in order to be able to measure different performance parameters of MSI. A block pattern of 1.8 lines/mm are used for MTF measurement in flight and across flight direction. Since the focal length of the MTF tool is about 11 times larger than the focal length of the MSI camera, the frequency of the imaged block pattern is 20 lines/mm. The object platform holding the reticle can be translated over a range of 10 mm in both flight and across flight direction independently with a resolution of 0.15 μm by means of stepper motors. The MTF measurements are performed with about 55 steps per period and using a scan length of at least 2 periods.

Figure 5.

Left: MTF tool with light source (A), scanning platform (B), folding mirror (C) and collimating mirror (D) Right: Reticle with different patterns

Results

The MTF performance has been measured with the VNS camera at operational conditions in a Thermal Vacuum setup. In this configuration the distance between the MTF tool and the VNS camera was about 1.3 m, which limited the MTF tool performance to an across flight field angle of about 1 degree. Therefore 25 measurements were performed to cover a total across flight field of view of 24 degrees. The presented results include predicted corrections for effects such as flight movement, spacecraft jitter, etc.

As can be seen the MTF performance of all the spectral channels (for the Nyquist frequency) is well above the required MTF performance of 0.25 (straight purple line in Figure 6) and confirms that the as build status of the VNS is in-line with the as designed status (and close to the nominal [without tolerances] expected performance).

Figure 6.

Measured MTF performance of the VIS (upper left), NIR (upper right), SWIR1 (lower left) and SWIR2 (lower right) camera in flight and across flight (swath) direction at several spatial frequencies. Note that the pink requirement line (@ 0.25) applies only to the Nyquist MTF.

Setup

Figure 3 shows the measurement setup with a tuneable laser (Ekspla NT242-SH) as light source. This laser provides nanosecond pulses with a 1 kHz repetition rate of which the wavelength can be tuned between 210 and 2600 nm. The laser beam was coupled via two mirrors into a 12 inch diameter integrating sphere in order to obtain an homogeneous illumination over the full field of view of the VNS camera. The VNS camera was installed close to the 4 inch main opening of the sphere. A pyroelectric detector with an organic black coating and a flat response between 0.1 and 20 μm wavelength was mounted on one of the smaller output ports. This detector was used as reference detector to correct for the wavelength dependent output of the laser, reflection of mirrors and scattering of the sphere. Since the pyroelectric detector needs a modulated signal of a few hertz, a chopper operating at 4 Hz was installed in the laser beam.

Figure 3.

Spectral response test setup with tuneable laser (A), ND filter wheel (B) chopper (C), steering mirrors (D), integrating sphere (E) with reference detector (F) and VNS camera (G).

The measurements were performed in steps of 1 nm within the spectral band of each channel and in steps of 2 nm outside the spectral bands of the VNS camera. For each wavelength one or multiple samples of 75 s were recorded. The signal amplitude at 4 Hz was determined by taking a Fast Fourier Transform of each sample. Dark current correction was performed using the recorded signal on the so called wing pixels. These pixels are at both ends of the multi -element detector in each channel and are not illuminated because they are outside the clear aperture of the detector cover. Next the data was corrected for the wavelength dependency of the test setup using the reference detector data and converted to photons. In wavelength regions with relative low output power of the tuneable laser, up to 16 samples were taken and results are averaged after analysis, in order to reduce the measurement uncertainty.

Results

From the measurements the following output is extracted:

The spectral response for the central pixel in each channel is shown in Figure 4. The response is normalised in order to check if the response is within the required boundaries, which are represented by the red lines in Figure 4.

Figure 4.

In-band spectral response requirement (red) and measured results (blue) for the central pixel of the VIS, NIR and SWIR channels of the VNS camera.

Figure 5 shows the normalised spectral response of the VIS and SWIR2 channel over the full wavelength range for which the detector in the corresponding channel is sensitive. This figure also shows the measurement uncertainty, which is generally well below 0.5%. Especially above 2200 nm the output of the tuneable laser is very low, leading to an increased measurement uncertainty of up to 2%. With the given light source further reduction of the measurement uncertainty in this wavelength region would lead to very long measurement times of over 1 month.

Figure 5.

Spectral response of the VIS and SWIR2 channel (blue) and measurement uncertainty (red) over the full detector sensitive wavelength range of the corresponding channel.

The central wavelength of the spectral response for a certain pixel is determined by the symmetry of the spectral response. Shift of the central wavelength over the VNS field of view should be minimised but may occur due to the performance of applied optical coatings. Figure 6 shows the two channels with the best (NIR) and worst (VIS) performance on central wavelength stability over the VNS field of view. Characterisation data for the change of central wavelength across the swath allows algorithms in the ground processor to reduce its effect in the processed imagery.

Figure 6.

Measured central wavelength over VNS field of view for the VIS (left) and NIR (right) channel.

The out-of-band rejection (OOB) is defined as:

where R(λ) is the instrument spectral response and L(λ) is the spectral radiance of a source which simulates the solar spectral energy distribution (5820 K).

The total integrated energy has been measured between 0.3 and 2.6 μm since none of the VNS detectors is sensitive to radiation above 2.6 μm. The measured out-of-band rejection was found to be mostly below 1% and always below 3%. Figure 7 shows the out-of-band rejection for the VIS and NIR channel.

Figure 7.

Out-of-band rejection of the VIS (left) and NIR (right) channel.

Based on the measured spectral performances it was concluded that the VNS instrument fulfilled the specified requirements.

Setup

The straylight measurements are performed with the MTF tool described in section 3.1. In this case the scanning object platform holds a black coated mask to generate the step function scene with a bright illuminated and dark area, see Figure 7. Measurements were performed for both along track and across track directions. For along track measurements the mask is orientated such that the step function scene is in along track direction (see Figure 7). During these measurements the step function scene is moving along track with respect to the line of sight of the VNS camera; either towards the bright area (edge up) or away from the bright area (edge down). For across track measurements the mask is rotated 90 degrees rotated, resulting in the bright area being either left or right with respect to the track (flight) direction. During these measurements the step function scene is moving across track. The raw data obtained from the straylight measurements was dark level corrected and normalised on the maximum signal level; obtained when the pixel was fully illuminated by the bright area of the step function scene.

Figure 7.

Straylight test setup with MTF tool (A), theodolite base (B) and entrance port of TV facility (C) with the VNS camera inside. At the right the object plane of the MTF tool with a black coated mask to generate the step function scene with a bright and a dark area along track.

Results

Figure 8 shows the detector response for pixel 195 of the SWIR1 channel during along track scans. The orange line is plotted where the normalised signal is 0.5, representing the condition where the border between dark and bright area is at the line-of-sight of the pixel. The straylight requirement is defined for the condition where the step function to the bright area is at a distance of 2.5 pixels at detector level. This condition is represented by the green line when the bright area is moving towards the pixel line-of-sight (MSI flying into bright area) and a blue line when the bright area is moving away from the pixel line-of-sight (MSI flying away from a bright area). In this case the amount of straylight is respectively 0.66% and 1.45%. Figure 9 shows these straylight results for 23 pixels distributed over the total field of view of the SWIR1 channel of the VNS camera.

Figure 8.

Detector response of pixel 195 of the SWIR1 channel (on log scale) when scanning towards a bright area (left) and away from a bright area (right). See text for explanation of the green, orange and blue lines.

Figure 9.

Measured straylight level for 23 pixels distributed over the field of view of the NIR channel, when MSI is flying towards a bright area (upper left), away from a bright area (upper right) or with a bright area left or right from the pixel line-of-sight (below).

Table 1 gives an overview of the measured straylight results for the different VNS channels at different conditions. These results include diffraction effects present in the measurement setup. Most straylight levels are around 1% which was the goal excluding diffraction effects, except for the SWIR2 channel. With the achieved straylight measurement results it was demonstrated that the VNS instrument is capable of fulfilling its overall performance requirements.

Table 1.

Straylight levels for different channels in the VNS camera and for different conditions (see text).

Theory

In Figure 10 a schematic representation of the MSI-VNS instrument is depicted. In the figure all relevant conversions that take place between receiving the TOA radiance and generating the instrument RAW data are described.

Figure 10.

Schematic representation of the MSI-VNS optical unit including SSTL FEE. Above the detector and FEE box the settings of the unit that can be modified in flight are indicated. Below each box the parameters that influence the conversion are indicated.

For the data processor to reverse the conversions present in the VNS instrument (in order to go from Level-0 to Level-1B data), the conversion factor(s) needs to be determined during the radiometric characterisation.

The detail with which the conversion factors are determined can be (to a certain extent) freely chosen. The options here can be roughly divided in three approaches:

For MSI-VNS it was decided (together with the customer chain) to follow the single conversion factor approach. For MSI-VNS the lower flexibility was deemed acceptable because the in-orbit sun calibration system could be used to determine/measure in-orbit a correction factor in case the instrument settings required an update.

Note that the characterisation of the in-orbit sun calibration system is outside of the scope of this paper.

Setup

In order to determine the radiometric CKD a measurement setup needed to be developed that is capable of illuminating the instrument with a known (to within a few percent) radiance level. Additionally the radiance levels between the different spectral bands of the instrument required a 1% relative accuracy.

As the instrument, and especially detector temperature, have a significant influence on the radiometric responsivity of the system, it was required that the instrument was located in a thermal vacuum chamber and controlled to operational temperatures.

Figure 11.

Setup for Radiometric Characterisation

The setup that was used consisted of a Finite Element Lamp (FEL; calibrated by the National Institute of Standards and Technology [NIST]) and a Spectralon diffuser. Although this setup seems quite simple the pain, is as usual in the details. The FEL lamp for example has a calibrated (to several tenths %) irradiance level that is only valid at 500mm distance. Any deviation from this distance directly results in additional errors; a 1mm alignment error results in an unacceptable error of 0.4%. So, during the characterization execution the distance between the FEL lamp and the diffuser was aligned to within 50μm. Due to the same effect only a small part of the surface of the flat spectralon diffuser could be used for accurate calibration purposes (the edges of the diffuser are further away from the lamp than the center).

Aside from all the apparent critical alignment error contributions in the setup, also the BRDF of the Spectralon diffuser needed to be known accurately (both absolute and relative between the four VNS channels) in order to execute a conversion from lamp irradiance levels to radiance levels. Based on a market research (in 2011) into the achievable calibration accuracies for this diffuser it was found that, especially for the SWIR (short wave infrared), the accuracy was lacking. The highest accuracy that could be found at institutes worldwide was ~1.2%. Although this accuracy was just acceptable for the absolute calibration of the instrument, it was insufficient for the 1% relative accuracy between the different instrument bands. In order to remedy this lacking accuracy a measurement was setup to use the VNS to calibrate the Spectralon diffuser.

The dedicated Spectralon diffuser calibration procedure consisted of two steps:

In Figure 14 a picture of the used setup is visible.

Figure 12.

Direct sphere measurement setup

Figure 13.

Sphere over diffuser measurement setup

Figure 14.

Photo of sphere over diffuser setup. On the left in the picture the VNS Optical unit is visible through the mounting frame of the Spectralon diffuser, on the right the integrating sphere is visible.

By combining the result of equation 5 and 6 the BSDF of the diffuser can be extracted

Using this approach, the BSDF of the spectralon diffuser could be determined with a 1.9% absolute accuracy and a 0.65% relative accuracy, resulting in an overall slight reduction of absolute accuracy but a significant gain in relative accuracy. By implementing this approach the overall instrument requirements for radiometric accuracy, could be achieved.

Results

Using the described setup the radiometric conversion factor (or CKD) for each pixel of the four VNS channels was determined. The results of these measurements are depicted in Figure 15.

Figure 15.

Determined Radiometric Response CKD values for each pixel and each VNS channel.

Based on these results 2 specific items can be pointed out:

The achieved characterisation error for these measurements is 1.98% absolute and ~0.95% relative between each VNS channel. With these accuracies the overall VNS instrument performance is guaranteed and the instrument requirements are achieved.