Colour remote sensing of the impact of artificial light at night (II): Calibration of DSLR-based images from the International Space Station

Nighttime images taken with DSLR cameras from the International Space Station (ISS) can provide valuable information on the spatial and temporal variation of artificial nighttime lighting on Earth. In particular, this is the only source of historical and current visible multispectral data across the world (DMSP/OLS and SNPP/VIIRS-DNB data are panchromatic and multispectral in the infrared but not at visible wavelengths). The ISS images require substantial processing and proper calibration to exploit intensities and ratios from the RGB channels. Here we describe the different calibration steps, addressing in turn Decodification, Linearity correction (ISO dependent), Flat field/Vignetting, Spectral characterization of the channels, Astrometric calibration/georeferencing, Photometric calibration (stars)/Radiometric correction (settings correction - by exposure time, ISO, lens transmittance, etc) and Transmittance correction (window transmittance, atmospheric correction). We provide an example of the application of this processing method to an image of Spain.

Distortion effects, such Barrel, Pincushion, and Mustache can also be corrected. Step 6).

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Images of star fields from the ISS are not available for all combinations of 214 cameras and lenses that have been used to obtain images of the Earth. In order 215 to translate the light intensity measured using one lens to that which would 216 be measured using another the light transmission of the optical elements of the 217 latter needs to be considered. The f/ number can give a first order idea of 218 this in a standardised way. However, this is not sufficiently accurate for many 219 purposes, so instead the Transmission coefficient (T number) of the lens needs 220 to be measured. is taken using maximum apertures (explained in more detail in 2.5 Step 5c).

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On bright sources this can be considered a compromise between sharpness of 230 images, signal to noise ratios, and photometric accuracy. Fortunately, this has 231 been done for most of the images taken at night from the ISS. The astronauts do not only acquire images of cities at night. They also 234 acquire lots of other kinds of nocturnal images, including of auroras, sunsets, 235 and occasionally also star fields. The "Cities at Night" project has a NASA 236 archive selection of these images(Cities at night collaboration, 2015). They 237 can be used for several proposes, such as calculating lens distortion and lens 238 transmittance, or as we do in this case, for radiometric calibration.

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Once the characteristics of a camera and lens have been determined it is 240 necessary to use standard sources to calibrate the imagery of the Earth that 241 has been taken. The use for this purpose of starfield images taken from the ISS 242 has the great advantage that they were obtained with the equipment under the 243 same temperature, pressure and humidity conditions as the images of the Earth.

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They will also have been acquired through windows with the same reflection and 245 transmission characteristics; light transmission through the windows is very high 246 except for some Zvezda windows (we can assume that absorption in all bands 247 is less than 5% in the visible regime, although windows in the Destiny lab show 248 significant transmission reduction beyond the NIR), and special coatings have 249 been used to avoid reflections (see 2.9 Step 8).

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The first step in using starfield images as standard sources is astrometric 251 calibration, determining the coordinates of the stars in each image. This can be 252 done using standard astronomical methods. We use the software Astrometry.net 253 (Lang et al., 2010). This automatically spatially calibrates an image, so that 254 each pixel has corresponding celestial coordinates. Moreover, it extracts the 255 sources and identifies them using a catalog. Stars are the flux standard sources 256 that we will subsequently use.

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Astrometric calibration (also called the World Coordinate System) by As-258 trometry.net provides direction, orientation and plate scale (transformation be-259 tween the apparent angular separation and linear separation at the focal plane).

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The software does not require any additional input, and makes a blind cal- where F o is the flux outside the atmosphere (which we know since we are ob-320 serving standard stars), K is the extinction coefficient for this wavelength, and 321 X the airmass calculated as X = sec z (this formula is only usable for zenith 322 angles up to about 60 • to 75 • ; for more accurate version see 2.8 Step 7), z be- the current one is a general correction with the f/ number: Correction factor = 1/(ISO/100) where, ISO is the ISO 12232:2006 standard for digital photography, C 0 is a 344 correction for the sensitivity of the camera model, T is the exposure time, B N 345 is the correction for the bit rate, and C 1 is the colour correction between different 346 camera models. L 0 is the correction for the aperture expressed as the f number 347 or the Tn true transmission of the lens when the shutter is fully open (see Table   348 2). Some of these settings can have up to 15% error according to the ISO  be RMSE ∼ 4 pixels, but more research is needed to systematise this analysis. for higher angles several models are available (e.g. Pickering (2002)). Then, we 387 can atmospherically correct each image using: where X h is the airmass function of the height, h is the height (in metres), I 389 is the observed intensity, I 0 the intensity with atmospheric effect, and K is the 390 extinction coefficient (derived from Harwit (1973)). The extinction coefficient 391 for 1 air mass can be calculated as: where A rag is Raleigh scattering, A aer the absorption by aerosols, and A oz the where H obs is the height of the observer, λ is the wavelength in microns, and "c" is the air's refraction index.
where H is the density scale height for aerosols and A o is the total optical   photograph, we use a wide angle image of Madrid and its environs (Fig. 7) (Fig. 9). These are not linear at the high values, so linearity correction is applied 485 (Fig. 10). Fig. 11 shows the flat field correction that needs to be applied given Photometric calibration was carried out for the colour images using the stars 491 ( Fig. 12), followed by georeferencing (Fig. 13). Once we have the transforma-492 tion between geographic location and pixel, we can generate a map of the view 493 angle of the camera with respect to the ground (Fig. 14), which gives the amount 494 of atmosphere that the light goes through before hitting the sensor. After this 495 correction we have a calibrated image that is internally radiometrically coher-496 ent and colour coherent (Fig. 15). This could now be compared with other ISS 497 images and intercalibrated with them using reference points or compared with 498 VIIRS images. 102 control points were used with an RSME of ∼ 4 pixels (due 499 to the large deformation of the image, the pixels closer to the nadir have higher 500 precision, and points close to the horizon less. Also, the ISS sampling is 3 times 501 higher than that of the reference from VIIRS, so it is natural that the image 502 cannot have higher accuracy than the pixel size of the reference layer). In order to examine the performance of the calibration of ISS imagery, we 520 selected four images of Madrid (see fig. 19). All were acquired before a major  The two first images were obtained a few seconds from each other, but with     As we have laid out, the correct calibration of nighttime images of the Earth 551 from the ISS requires processing through a number of steps (Fig. 1). Whilst    researchers have in the past used the blue path, using just decoded RAW images or even JPG images. We cannot recommend that procedure, as the images will not have internal photometric coherence or colour coherence, they will only have geometric coherence (the degree of incoherence will depend on the lens and dynamic range of the image).     This simple technique allows us to find the true nadir. In a practical case, once the image is georeferenced, we do not use any target to stabilize the deformation of the image, we can use the georeferentiation formulas to estimate one at the centre of the image of the size that we prefer. In our case, we define a circle of 0.1 km of radius at the centre of the rectified image and we use the deformation formulas to calculate the deformed circle (ellipse). looks to be saturated, although this is not actually the case. This is only one of the reasons not to use JPG images, although geometrically it is equivalent to the RAW image, colours, relative intensities, and other issues like gamma correction mean that this is not recommended. as mentioned in the Introduction. It is common for commercial software to use debayering algorithms that can produce artifacts and change the photometry, so we do not use that approach but calibrate each image separately.     correspondence between pixel location and geographical location. This is the same image ( Fig.   8), as before, but because the area of the pixels closer to the horizon is larger than for the pixels closer to the nadir, the centre of the image now is France, but this is just a perspective effect. The four extracted channels are now in values of nW · sr −1 cm −2 A −1 . This image has not been stretched, so shows a lot of noise from low intensities and cosmic rays.  13). These data, along with the altitude and the true nadir, are the basis of the atmospheric correction. Figure 15: Calibrated version of the exemplar image. Note that artefacts can appear at the edges because the flat field correction enhances noise in those areas. Also, the farther the pixels are from the nadir the blurrier they are. This is because pixels that are closer to the horizon correspond to larger areas than those closer to the nadir, so when the rectification takes place, there is less information in the first ones and errors propagate more than in the second ones. That is why, when several images are available of the same area, it is better to choose those that were acquired with longer focal lengths and closer to the nadir. Units in nW · sr −1 cm −2 . This image has been stretched, so does not show noise as clearly as in the other cases.     ship. Units log10(nW · sr −1 · cm −2 ·Å −1 ).