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

Alejandro Sánchez de Miguel<EMAIL_ADDRESS>Jaime Zamorano  Martin Aubé
Jonathan Bennie  Jesús Gallego  Francisco Ocaña  Donald R. Pettit  William L.
Stefanov  Kevin J. Gaston  Environment and Sustainability Institute,
University of Exeter, Penryn, Cornwall TR10 9FE, U.K.  Depto. Física de la
Tierra y Astrofísica. Instituto de Física de Partículas y del Cosmos
(IPARCOS), Universidad Complutense, Madrid, Spain  Physics dept., CEGEP de
Sherbrooke, Sherbrooke, J1E 4K1, Canada  Instituto de Astrofísica de
Andalucía, Glorieta de la Astronomía, s/n,C.P.18008 Granada, Spain  Centre for
Geography and Environmental Science, University of Exeter, Penryn, Cornwall
TR10 9FE, UK  Quasar SR for ESA, European Space Astronomy Centre, E-28691
Villanueva de la Cañada, Spain  Astronaut Office, Flight Operations
Directorate, NASA Lyndon B. Johnson Space Center, Houston, Texas, USA
Exploration Science Office, Astromaterials Research and Exploration Science
Division, Exploration Integration and Science Directorate, NASA Lyndon B.
Johnson Space Center, Houston, Texas, USA

###### Abstract

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.

###### keywords:

artificial lighting , light pollution , night , remote sensing , urban

††journal: Remote Sensing for Environment

##  1 Introduction

There is growing demand for colour imagery of the Earth at night. This has
particularly been driven by increasing recognition of the impacts of outdoor
artificial nighttime lighting (from streetlights and other sources) on the
natural environment, human health, and associated policy and public concerns
(e.g. Rich and Longcore [2013]; Hölker et al. [2010]; Falchi et al. [2011];
Gaston et al. [2012, 2015]; Gaston [2013, 2018]; Garcia-Saenz et al. [2018]).
These impacts are not only influenced by the spatial extent, the timing and
the intensity of that lighting, but also by its spectrum. This last
consideration limits the insights that can be obtained from the vast majority
of historical and current sources of geographic scale data on the occurrence
of such lighting, including data from the Defense Meteorological
Program/Operational Line-Scan System (DMSP/OLS; Elvidge et al. [1997]) and
from the Suomi-National Polar-Orbiting Partnership/Visible and Infrared
Imaging Radiometer Suite - Day/Night Band (SNPP/VIIRS-DNB; Elvidge et al.
[2013]).

By far the most important source of colour imagery of the Earth at night is
that obtained from the International Space Station (ISS) by the astronauts and
cosmonauts of the five space agencies that constitute the ISS consortium:
NASA, ESA, JAXA, CSA-ASC and ROSCOSMOS (Stefanov et al. [2017, 2019a]).
Between 2002 and 2018, more than 3 million images have been taken by the crew
of the ISS, of which 1.34 million were taken at night (sun elevation less than
0 degrees). The diurnal and nocturnal images from NASA, CSA-ASC and ESA are
stored in the NASA archive (http:/eol.jsc.nasa.gov; Stefanov et al. [2017,
2019a]). Some, but not all, of the images taken by JAXA and ROSCOSMOS are also
stored in the NASA archive. The scientific value of these images is immense,
as they constitute the only large public dataset with nighttime colour
information obtained from space over the last 17 years (Levin et al., 2020).
Due to the limitations of data from the VIIRS and DMSP satellites, this
dataset is key to determining change in visible artificial lighting over this
long period (Kyba et al. [2017]; Sánchez de Miguel et al. [2019]).

The camera bodies and lenses used by the astronauts to take images of the
Earth have mainly been from Nikon’s professional product line (see Table 1 for
those used for nocturnal photography). These have usually been unmodified,
with the exception of the Nikon D3S S/N:2007944 used on missions ISS030 and
ISS031 that had the infra-red filter removed. Most of the Nikon cameras used
have had a CMOS sensor, although the Kodak 760C and the Nikon D1 that were
used had CCD sensors (Waltham [2013]). All the cameras have a Bayer filter
that provides simultaneous images in three colours (two green, one red and one
blue).

The environmental conditions on the ISS are strictly controlled, with
temperature at 24ºC $\pm$ 2ºC, pressure around 745-721 mmHg, and relative
humidity around 60%. This means that the cameras have not only been operating
well within their nominal environmental ranges but effectively in constant
environmental conditions. Although cameras have been used during
extravehicular activity (EVA) or in external experiments, principally windows
in the cupola and elsewhere on the ISS enable astronauts to take images of the
Earth from a wide variety of angles. The ground track of the ISS covers nadir
latitudes from 51.6º N to 51.6º S, at an altitude of approximately 405 km,
although this can vary in the range of 330 to 435 km. Usually images have been
taken by astronauts using cameras that are handheld. Pettit [2009] developed a
prototype system that partially compensated for movement during image
acquisition and was used during mission ISS006. Later missions, like ISS030 to
ISS040, have employed a special tripod (Nightpod; Sabbatini [2014]). At least
for images held in the open NASA archive there is no information on their
acquisition beyond the metadata of the images themselves, thus it is not easy
and frequently impossible to attribute them to a specific window, tracking
device or operator. Only when an astronaut posts their own images, on Twitter
for example, can we have reasonable confidence in their authorship.

A growing number of science studies have attempted to use images taken from
the ISS in their raw or crudely enhanced forms [Venzke et al., 2009, Lockwood
and Hazlett, 2013, Anderson et al., 2010, Levin and Duke, 2012, Liu et al.,
2011, Metcalf, 2012, Kuechly et al., 2012, Mazor et al., 2013, Sánchez de
Miguel et al., 2014, Li et al., 2014, So, 2014, Kyba et al., 2014, Rybnikova
and Portnov, 2017, 2018, Xu et al., 2018, Levin et al., 2020]. Indeed, the
only research work we are aware of that made some attempt to address issues of
calibration is that of So [2014], which used a dark subtraction, and those in
which the current team has been involved [Zamorano et al., 2011, Sánchez de
Miguel, 2015, Garcia-Saenz et al., 2018, 2019, Hale and Arlettaz, 2019, Bará,
2020, Pauwels et al., 2019, Sánchez de Miguel et al., 2019, 2020]. The effects
of this lack of calibration can be very different from study to study and need
to be considered carefully. Unfortunately, in many cases calibration of images
taken by astronauts from the ISS will be necessary in order to provide
accurate representations of the colour composition of scenes, and this is not
a trivial task.

In a previous paper [Sánchez de Miguel et al., 2019], we described the use of
colour-colour diagrams to analyse images taken by astronauts on the ISS and to
estimate spatial and temporal variation in the spectrum of artificial lighting
emissions. In this paper we provide a methodology for calibrating such images.
The approach that we describe is also relevant to the calibration of images
taken with standard DSLR cameras for other purposes, including meteor science
(meteor photometry - Borovička et al. [2014]; meteor video photometry -
Madiedo et al. [2019]; meteor spectroscopy - Cheng and Cheng [2011]),
measurement of skyglow [Hänel et al., 2018], and more generally scientific
photography using DSLR cameras with antiblooming. In order to use well
characterized standard emitters, we use stars as calibration sources, as the
variability and stability of their spectra is well known. Indeed, laboratory
calibration sources typically have a precision of 0.2% [Wolfe, 1998], whilst
calibration by stars can attain precisions of 0.001% [Poddanỳ et al., 2010].
This technique also allows us to use multiple calibrations from onboard the
ISS that are stable in time and that account for the window through which
images were obtained. A similar technique has also been proposed for
calibration of data from the SNPP/VIIRS-DNB [Fulbright and Xiong, 2015] and
was suggested first by Zamorano et al. [2011].

Calibration of images of the earth acquired from the ISS requires a number of
steps that we will address in turn (Fig. 1): 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). The steps marked with an
asterisk may not be required for some specific science cases (e.g.
differential evolution time - Meier [2018], Bará et al. [2019]; edge detection
- Kotarba and Aleksandrowicz [2016]). Neglecting any particular correction
should always explicitly be justified.

In this paper, we will focus primarily on calibration of images taken with the
Nikon D3S (for calibration equipment see Supplementary Information) because
this is the best studied case and the camera that has been used most
intensively for nocturnal photography at the ISS over the two last decades
(from mission ISS026 until mission ISS045). However, in general, with small
adjustments, the procedures described can be applied to any other digital
camera, and we will consider all of the cameras used at the ISS (Table 1) and
highlight the differences between them when it is relevant. The Nikon D3S has
a 12.1 megapixel sensor equivalent to a full frame (35mm) and was announced by
Nikon Corporation on 14 October 2009. It has interchangeable lenses using the
F-mount, an ISO range from 200 to 12800, and 14-bit A/D conversion.

##  2 Calibration steps

###  2.1 Step 1: Decodification

A DSLR camera obtains information as photons of light that produce electrons,
and these electrons are effectively stored in pixels of the CCD/CMOS chip. The
electrons are trapped by the nearest potential well (one per pixel) and
digitalized by an analogue conversion (DA Converter) sensor that measures the
electrical potential on the wells of the chip. Whilst in some professional
cameras a non-destructive read out is possible [Nakamura et al., 1995], most
CCD/CMOS chips are read by measuring the current when it passes though the DA
converter [Fowler and El Gamal, 1995, Fossum et al., 2000]. This information
is pre-processed and saved as a data file. This file is usually coded in a
proprietary format, and in the case of Nikon cameras, this is called NEF. This
is what is called a RAW file. The first step in the calibration process is the
decodification of this file, taking the data coded in the proprietary format
and transforming it into a readable open format, such as TIFF [Desk, 1992] or
FITS [Hanisch et al., 2001], without losing crucial information or changing
the physical meaning.

Even so-called RAW files from a DSLR tend to have undergone some pre-
processing. A pure ideal CCD/CMOS RAW file coming from an ideal sensor will
have three components: (i) the signal itself, (ii) an artificial signal (bias)
included on the sensor to avoid negative values in the process of
digitalization, and (iii) Gaussian noise plus an additive constant (dark
current) arising from the sensor’s sensitivity to heat. On our reference
camera, the Nikon D3s, and all subsequent versions except the Nikon D5, a
complex hardware treatment is applied to the signal [Koyama and Jiang, 2011,
Sánchez de Miguel, 2015]. This treatment means that we do not need to do any
bias or dark correction in these cases, but noise effects need to be
controlled. DSLR sensors are capable of a 16-bit dynamic range. However, in
practice on commercial models it is 14 or 12 bits, because saving 16-bit
information takes too much time. This means that some detailed information is
lost in the digitalization process with a loss of dynamic range.

The current most widely used software to undertake decodification is DCRAW
[Coffin, 2008] and the most conservative decodification options are: -6 that
means 16 bit extraction, -o 0 that means no color balance, -H 1 that means
nothing excluded, and -v to show any error in the decodification process.

###  2.2 Step 2: Linearity correction

While most scientific camera sensors force linearity between numbers of
incident photons and pixel signal strength as a key characteristic, commercial
DSLR cameras have sensors with an anti-blooming function. By using an overflow
channel, this system ensures that when a well of the chip is saturated then
excess electrons do not contaminate adjacent wells (as can happen with regular
CCD or CMOS sensors)[Sakai et al., 2009]. This produces a roughly linear
response in the pixel signal when high gain is used. Unfortunately, there are
no details available of the specific technology used for the Nikon DX sensors.
Currently, we have not detected differential absorption by chip substrate,
although this could be investigated further in future versions of the
processing pipeline.

Typically, the gain of the camera operates to an ISO standard [ISO 12232:2006
(2006), E]. Fig. 2 shows the effect of anti-blooming when a camera is exposed
to a stable light source across all of the different exposure times that the
camera is able to produce. This effect can be compensated by characterization
of this response for a particular ISO. Even if a camera is in principle
calibrated to the ISO standard, this still allows a 20% error, and there can
be differences on the different channels. Indeed, without corrections, bad
colour information (aka. band ratios, see Sánchez de Miguel et al. [2019]) can
be produced. As Metcalf [2012] found, radiance values can be underestimated,
and radiance ratios can appear variable even if they are stable.

Having characterised the response of the camera for a particular ISO, the
intensity values of an image that has been taken using this can be divided by
these corrected ones. Those over the range of the linear response will not
change (aka. under $\sim 17.000$ ADU) whilst those in the range of the non-
linear response will be linearized.

###  2.3 2.3 Step 3: Flat field

A wide range of lenses have been used with DSLRs on the ISS, from fish eyes to
telephotos. A few have been used for long periods, but others on just a single
mission. These lenses introduce various additional calibration issues. The
first of these is flat field/illumination/vignetting correction. This is a
very standard correction with DSLR imagery, although unfortunately not usually
addressed with imagery from the ISS (see [Burggraaff et al., 2019] for
standard corrections to consumer cameras). This correction consists of the
acquisition of shots from a uniform emitting source (aka. flat field), so that
any heterogeneity in the acquired image is the result of vignetting of the
lens and linearity effects. Distortion effects, such Barrel, Pincushion, and
Mustache can also be corrected. However, this should be avoided unless
absolutely necessary because of the challenges of combining such corrections
with those necessary due to the angular perspective at which many ISS images
are obtained as a consequence of the Earth’s curvature, and because performing
several successive distortions will amplify errors [Cardiel et al., 2002])
(see 2.7 Step 6).

Images of star fields from the ISS are not available for all combinations of
cameras and lenses that have been used to obtain images of the Earth. In order
to translate the light intensity measured using one lens to that which would
be measured using another the light transmission of the optical elements of
the latter needs to be considered. The f/ number can give a first order idea
of this in a standardised way. However, this is not sufficiently accurate for
many purposes, so instead the Transmission coefficient (T number) of the lens
needs to be measured. Table 2 provides these values, as well as the f/ number
for some of the most frequently used lenses on the ISS. Values in this table
have been calculated using the SaveStar Consulting S.L. lab by acquiring
images of a $4\pm 0.1$ lux illuminated lambertian surface. The light Source
was a tungsten filament.

Note that in general the apertures of lenses can be closed down to provide
sharper images. When this happens, the diaphragm rarely closes to exactly the
same position (except when fully open), so it is recommended that imagery is
taken using maximum apertures (explained in more detail in 2.5 Step 5c). On
bright sources this can be considered a compromise between sharpness of
images, signal to noise ratios, and photometric accuracy. Fortunately, this
has been done for most of the images taken at night from the ISS.

###  2.4 Step 4: Astrometric calibration

The astronauts do not only acquire images of cities at night. They also
acquire lots of other kinds of nocturnal images, including of auroras,
sunsets, and occasionally also star fields. The ”Cities at Night” project has
a NASA archive selection of these images[Cities at night collaboration, 2015].
They can be used for several proposes, such as calculating lens distortion and
lens transmittance, or as we do in this case, for radiometric calibration.

Once the characteristics of a camera and lens have been determined it is
necessary to use standard sources to calibrate the imagery of the Earth that
has been taken. The use for this purpose of starfield images taken from the
ISS has the great advantage that they were obtained with the equipment under
the same temperature, pressure and humidity conditions as the images of the
Earth. They will also have been acquired through windows with the same
reflection and transmission characteristics; light transmission through the
windows is very high except for some Zvezda windows (we can assume that
absorption in all bands is less than 5% in the visible regime, although
windows in the Destiny lab show significant transmission reduction beyond the
NIR), and special coatings have been used to avoid reflections (see 2.9 Step
8).

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

Astrometric calibration (also called the World Coordinate System) by
Astrometry.net provides direction, orientation and plate scale (transformation
between the apparent angular separation and linear separation at the focal
plane). The software does not require any additional input, and makes a blind
calibration using only the image. It is a powerful tool as there is no need to
know spacecraft attitude nor window orientation nor the direction in which an
astronaut was pointing the camera. It has also been used successfully in non-
stabilised high-altitude balloon observations where attitude is not controlled
[Ocaña, 2017, Ocaña et al., 2019].

###  2.5 Step 5a: Photometric calibration on board

To perform photometric calibration, we need a standard source. As there are no
electronic standard flux sources onboard of the ISS the most accurate method
of calibration is using the stars, as has been proposed for other satellites
[Fulbright and Xiong, 2015] and as is routinely done in astronomy.

We will focus on use of a selection of stars from Ducati [2002]. Even though
stars are very well characterized light sources, there are differences between
the filters that were used in making those measurements and those used in DSLR
cameras. To solve this problem we can use a statistical correction based on
the synthetic photometry technique [Straizys, 1996, Sánchez de Miguel et al.,
2017, 2019]:

$GN=V+0.1291(2)\times(B-V)-0.0051(2)$ (1)
$BN=GN+0.6123(7)\times(B-V)-0.0340(6)$ (2)
$RN=GN+0.0262(3)+0.5880(5)\times(R-V)$ (3)

where BN, RN and GN are the respective RGB bands of the DSLR image, and B, V
and R are Johnson bands (an astronomical standard); these relationships are
shown in Fig. 3. These corrections have been calculated for the spectral
response of the D3S although, as can been seen in Sánchez de Miguel et al.
[2019], all Nikon cameras have extremely similar spectral responses. Once
these corrections to the intensities of the stars are applied, the
transformation from data numbers to radiometry units is immediate by applying
a linear fit (see Fig. 4).

As the Ducati [2002] catalogue has few stars in the dim part of the
calibration and only 18 stars in total, for verification purposes we used the
Tycho catalogue [Hog et al., 2000], which contains many more stars.Fig. 5
shows the effect of the saturation of the brightest stars. Future analysis can
be done the new catalog Cardiel et al. [2021], specifically designed for DSLR
cameras.

By using these methods we get the correspondence between the radiance and the
data numbers in magnitudes. To convert this on the international system of
units we need to use:

$AB=-2.5\log_{10}(flux)-5\log_{10}(w)+2.401$ (4)

where AB is in $mag/arcsec^{2}$, flux in
$nW/cm^{2}/sr/$\mathrm{\SIUnitSymbolAngstrom}$$,and w is wavelength in
$\mathrm{\SIUnitSymbolAngstrom}$ [Sánchez de Miguel et al., 2017].

When we calibrate a starfield image taken from the ISS, we do not need to
apply any atmospheric correction, as is usually done when this technique is
used with starfield images taken from the ground, because the ISS is at 400 km
above the Earth and the density of the atmosphere there is negligible and for
this purpose is considered to be a vacuum (at this elevation pressure is even
higher than that of the regular vacuum labs on Earth, from $10^{-6}$ to
$10^{-9}$ torr [Finckenor and de Groh, 2017], compared to the 760 torr of the
atmosphere at sea level).

####  2.5.1 Step 5b: Photometric calibration from the ground

As previously mentioned, some images of the Earth taken from the ISS have been
obtained using lenses for which starfield images are not available (for
example, because their focal lengths make it impossible to take sharp
starfield images given the speed of movement of the ISS). For those cases when
starfield calibration is not possible, the solution is to apply a standard
absolute photometry technique to achieve photometric calibration of the lens
from the ground.

For observations taken from the ground the light of the stars travels through
the atmosphere and suffers absorption, scattering, and dispersion depending on
the wavelength. The amount of extinction (the combined effect) depends on the
extinction coefficient of the atmosphere at this time and on the length of the
path of the light across the atmosphere. As a result, the flux density (in
units of $ergs/s/cm^{2}/$\mathrm{\SIUnitSymbolAngstrom}$$) measured on the
ground for a star is lower than the flux at the top of the atmosphere:

$F\mbox{(observed)}=F_{o}\cdot 10^{-0.4KX}$ (5)

where $F_{o}$ is the flux outside the atmosphere (which we know since we are
observing standard stars), K is the extinction coefficient for this
wavelength, and X the airmass calculated as X = sec z (this formula is only
usable for zenith angles up to about $60^{\circ}$ to $75^{\circ}$; for more
accurate version see 2.8 Step 7), z being the zenith angle (90 - elevation
above horizon). We call photometric nights those clear nights with constant
transparency (see definition of photometric night at
https://www.eso.org/sci/observing/phase2/ObsConditions.html). For these nights
the extinction coefficient is constant for the whole night. Observing several
standard stars through the night at different heights above the horizon we can
derive this coefficient and the zero point of the photometry for each
photometric band. The derived zero point of the photometric band is valid for
this observational setup (camera, lens, ISO, and f number) regardless of the
night of the observation, i.e. it depends only on the instrumentation. So, the
atmospheric effects only need to be considered on the particular night that
the calibration images are acquired.

####  2.5.2 Step 5c: Setting adjustments

It is not possible to have images calibrated for all of the possible cameras
and settings. So, we scale the adjustments to 50 mm f/1.4. It is well known
that the repeatability of mechanical iris-type lens diaphragms is limited,
having a noticeable tolerance. The blades move back and forth during each
image acquisition, limiting the entrance pupil to approximately the same
position but not exactly so [Chylinski, 2012], creating so-called ‘aperture
flickering’. We have created a model to estimate the potential effect of
closing the shutter but the current one is a general correction with the f/
number:

$L_{0}=2\times f/^{-2}\>\mbox{ or }\>Tn$ (6)

$\mbox{Correction factor}=1/(ISO/100)\times C_{0}/T/B_{N}\times C_{1}/L_{0}$
(7)

where, ISO is the ISO 12232:2006 standard for digital photography, $C_{0}$ is
a correction for the sensitivity of the camera model, T is the exposure time,
$B_{N}$ is the correction for the bit rate, and $C_{1}$ is the colour
correction between different camera models. $L_{0}$ is the correction for the
aperture expressed as the f number or the Tn true transmission of the lens
when the shutter is fully open (see Table 2). Some of these settings can have
up to 15% error according to the ISO 12232:2006 standard.

##  3 Step 6: Georeferencing

Images of the earth from the ISS need to be georeferenced to establish the
link between image pixels and actual points on the ground. The time of
acquisition of each image is known but, although the orbit of the ISS is
precisely defined, unfortunately this does not provide sufficient information.
The time stamp data are not precise enough to define a nadir location (errors
may be more than 1000 km), and an image may be taken in a direction that
departs substantially from the nadir. A major citizen science program, “Cities
at Night” (http://www.citiesatnight.org,[Sánchez de Miguel et al., 2014]), is
being used to automate the georeferencing of large numbers of ISS images by
identifying the urban areas that these represent. More generally, and where
sufficient control points cannot automatically be identified, georeferencing
can be done manually, for which purpose we have used QGIS [Team et al., 2015]
and Global Mapper [Geographics, 2011]. Several Python libraries have been used
in this process, like NumPy [Oliphant, 2006], AstroPy [Robitaille et al.,
2013] and GDAL [Warmerdam, 2008]. The preferred sampling method is bilinear
for the pixels and thin plate spline for the coordinates. The number of
recommended control points can depend a lot on the inclination of the image
and lens. For nadir and 400 mm, 20 control points can be enough to reach RMSE
2.5 pixels using polynomial third degree fitting. For tilted images taken with
a 24 mm, for example, more than 100 points would be needed and with 400 points
can be visually indistinguishable from a comparison layer (VIIRS); the only
transformations able to rectify deformations on tilted images are Thin Plane
Splines that provide unrealistic values of RMSE - a conservative estimation
can be RMSE $\sim 4$ pixels, but more research is needed to systematise this
analysis.

###  3.1 Step 7: Atmospheric correction

Whilst no atmospheric correction is required for starfield images taken from
the ISS, this needs to be done for images taken of the Earth. The procedure
selected depends on the concept of airmass. In astronomy, one airmass is
equivalent to the volume of atmosphere in the direction of the zenith of an
observer on the ground (that is equivalent to the same volume of mass to an
observer located in orbit looking to the nadir at the same geographical
coordinates). Using this approach it is straightforward to estimate the
equivalent volume of atmosphere at different zenith angles or the
corresponding nadir angles. The formula X = sec z, as above, can be used up to
80 degrees of zenith angle considering a plane parallel approximation of
atmosphere with about 3% error and for higher angles several models are
available (e.g. Pickering [2002]). Then, we can atmospherically correct each
image using:

$I/I_{0}=10^{X_{h}(h)\times K/-2.5}$ (8)

where $X_{h}$ is the airmass function of the height, h is the height (in
metres), I is the observed intensity, $I_{0}$ the intensity with atmospheric
effect, and K is the extinction coefficient (derived from Harwit [1973]). The
extinction coefficient for 1 air mass can be calculated as:

$K=A_{rag}+A_{aer}+A_{oz}$ (9)

where $A_{rag}$ is Raleigh scattering, $A_{aer}$ the absorption by aerosols,
and $A_{oz}$ the absorption by ozone. Using the definitions compiled in García
Gil et al. [2012]:

$A_{ray}=9.4977\times
10^{-3}\left(\frac{1}{\lambda}\right)^{4}c^{2}\times\mbox{exp}\left(-\frac{H_{obs}}{7.996}\right)$
(10)

$c=0.23465+\left(\frac{1.076\times
10^{2}}{146-(1/\lambda^{2})}\right)+\left(\frac{0.93161}{41-(1/\lambda^{2})}\right)$
(11)

where $H_{obs}$ is the height of the observer, $\lambda$ is the wavelength in
microns, and ”c” is the air’s refraction index.

$A_{aer}(\lambda,h)=A_{o}\lambda^{-\Sigma}exp(-H_{obs}/H)$ (12)

where H is the density scale height for aerosols and $A_{o}$ is the total
optical thickness of atmospheric aerosols for $\lambda=1\mu m$, which depends
on the total content of particles and on their efficiency for scattering and
absorption and is taken to be 0.087 [Walker, 1988, Mohan et al., 1999].
$\Sigma$ is a parameter that depends on the size of the aerosol particles.

Each of these factors $(A_{rag},A_{aer},A_{oz})$ is wavelength dependent and
also depends on atmospheric conditions. By convention, by default we have
considered the aerosol content conditions of the AERONET [Holben et al., 1998]
Madrid station on the 29th March 2012 (AOD340 = 0.333, AOD380 = 0.305, AOD440
= 0.251, AOD500 = 0.208, AOD675 = 0.127, AOD870 = 0.084, AOD1020 = 0.066),
interpolated for the center of the Nikon bands. We use Rayleigh [1899] to
consider the Rayleigh scattering (equation 10), Stalin et al. [2008] to
consider the aerosols (equation 12) and Hayes and Latham [1975] to consider
the Ozone absorption ($A_{oz}$ factor). To correct for all of these effects
equation 8 should be applied to each pixel of the image. Currently, the
aerosol content correction is only accurate for a narrow field of view, for a
wide field of view different AODs would be needed per pixel. In the future,
these data could be obtained from VIIRs products [Huang et al., 2016].
Currently, no other nocturnal lights products provide multispectral aerosol
corrections and the only other nocturnal light product that provides some
correction of this nature is the dimensional panchromatic aerosol corrections
from VIIRS VNP46A2 [Román et al., 2018] that are still in the beta phase.

To determine the original location of the ISS we use a photogrammetric
technique. Considering a circle on geographical coordinates, we will obtain an
ellipse on the raw image coordinates. The axis of the ellipse is either
coincident with the direction of observation or perpendicular to the direction
of observation. Matching those two directions with the ISS ground track, we
obtain two potential solutions for the true nadir of the ISS. Most of the time
the minor axis indicates the direction of the true nadir, although, because of
lens aberrations and the curvature of the earth, when the ISS astronauts take
images very close to the nadir it can be the major axis that will align with
the true view direction (see Fig. 6). Most of the time, a visual inspection of
the image allows the identification of the true nadir, by looking at the
patterns of the streets and how the buildings block the light of the streets.

Once we know the true nadir, as the altitude of the ISS is also known, it is
straightforward to determine the tilt angle (we define the tilt angle as that
between the nadir and the view angle of the center of the image). Then, the
atmospheric extinction can be determined using the approach used in astronomy
because of the Helmholtz reciprocity law, the same extinction that an observer
has looking to the ISS from a location A is what an observer on the ISS has
looking to location A. As the lens used may have a very wide field of view,
the distance from the ISS to the ground can be significantly different from
one part of an image to another, so we calculate this extinction for each
pixel of the image.

In some ISS images of the Earth at night, high thin clouds, fog, etc are
apparent. These are challenging to address in the generic pipeline described
here, and may require more of a case-by-case approach, employing available
tools. So, currently, we recommend discarding any areas where the Point Spread
Function (PSF) of the emission sources is not homogeneous.

###  3.2 Step 8: Intercalibration

For a variety of reasons, there may be some systematic differences in the
extrapolation of the calibration with stars. One of the main unknowns in
analysing an image taken from the ISS is which window was used. Sometimes this
can be determined because of the date on which the image was obtained or
because the image was taken using the Nightpod, which is always used at the
main Cupola window. The most popular windows are the Cupola, Window
Observational Research Facility (WORF), and Window 7 of the Zvezda module. The
Cupola and WORF window have very similar transmission characteristics and so,
in principle, should not create differences in colour, although some ESA
contacts have reported lower transmission of the WORF. This effect is
explained mainly because of the Cupola scratch pane, that is not always in
place as it is removable. Window 7 of the Zvezda module is comparable although
it is even more transparent in principle as it is also UV and IR transparent
Pettit [2006]; more information about the transmission can be found in ESA
[2011] and Stefanov et al. [2017, 2019b]. Transmittance can also vary greatly
with the angle to the window at which an image was taken. It is typically
impossible to know what this angle was, although the geometry of the Cupola,
WORF, and Zvezda do not allow acquisitions with very shallow angles.

Apart from the different windows used, another reason why there may be
systematic differences between the extrapolation of the calibration with stars
with different lenses is the use of shutters that are not fully open.

For these reasons, and possibly others, we might want to intercalibrate
different images or calibrate them against another source, such as data from
SNPP/VIIRS-DNB. In a future paper we will focus on these techniques.

##  4 Spain/Madrid: a worked application

Artificial nighttime lighting has been more extensively studied across Spain
than almost any other country [Sánchezde Miguel et al., 2014, Kyba et al.,
2014, Estrada-García et al., 2016, Oriol et al., 2017, Ges et al., 2018, Tong
et al., 2020]. To provide a worked example of the calibration of an astronaut
photograph, we use a wide angle image of Madrid and its environs (Fig. 7)
taken from the ISS (ISS053-E-249189) on 19/11/2017 at 21:51:38 GMT (note: that
the database time is incorrect by 1 h in this exceptional case. This is known
because the nadir location that corresponds with the RAW EXIF information is
in the Pacific Ocean [lat -49.2, -126.2], which is clearly not possible. The 1
h corrected location is just $\sim 200$ km [lat 38.4,lon -6.4]) from the true
nadir [lat 37.49,lon -7.77]) and downloaded on 21/05/2020 from NASA’s Gateway
to Astronaut Photography of Earth (https://eol.jsc.nasa.gov/). Fig. 8 shows
the RAW image. This is extracted and separated into four different colour
images (Fig. 9). These are not linear at the high values, so linearity
correction is applied (Fig. 10). Fig. 11 shows the flat field correction that
needs to be applied given that the original image was taken with a 24mm lens.
The parameters of equation 7 are, according to the image metadata and camera
model reference Nikon D3s, T=1/10, C0=1, C1=1 for the Green channel, 1.12 for
the Red Channel and 0.95 for the Blue Channel, ISO=5000, BN=4, and Tn=1.050.

Photometric calibration was carried out for the colour images using the stars
(Fig. 12), followed by georeferencing (Fig. 13). Once we have the
transformation between geographic location and pixel, we can generate a map of
the view angle of the camera with respect to the ground (Fig. 14), which gives
the amount of atmosphere that the light goes through before hitting the
sensor. After this correction we have a calibrated image that is internally
radiometrically coherent and colour coherent (Fig. 15). This could now be
compared with other ISS images and intercalibrated with them using reference
points or compared with VIIRS images. 102 control points were used with an
RSME of $\sim 4$ pixels (due to the large deformation of the image, the pixels
closer to the nadir have higher precision, and points close to the horizon
less. Also, the ISS sampling is 3 times higher than that of the reference from
VIIRS, so it is natural that the image cannot have higher accuracy than the
pixel size of the reference layer).

Fig 16 and Fig 17 show how this calibrated ISS image compares to a VIIRS
image. The comparison is not simple as the sensors used have different
spectral sensitivity, different flyby times and were obtained at different
angles, and there are not sufficient calibrated ISS images yet fully to
determine any systematic differences between the emissions detected in ISS and
VIIRS data. fig.18 shows that in comparing the calibrated ISS image of Madrid
and VIIRS data the main differences are due to small georeferencing/resolution
issues, and light sources that are visible on one image but not the other
because of the time of acquisition or the tilt. Nonetheless, despite in the
present example there being a 1 month difference in the timing of acquisition
of the data, 4 h difference in the flyby time, spectral sensitivity
difference, and difference in spatial resolution, there is predominantly a
linear relationship between the emissions detected by the two images, and they
compare very well. There is an absolute offset between the two of a factor
1.92. This could be explained by several factors, including dimming of the
streetlights of Madrid after midnight.

##  5 Madrid: ISS-ISS intercalibration

In order to examine the performance of the calibration of ISS imagery, we
selected four images of Madrid (see fig. 19). All were acquired before a major
street lighting change took place in the city in 2014 [Robles et al., 2021].

File | Tilt | Exp T. | f/ | ISO | Lens | Cam | Time
---|---|---|---|---|---|---|---
iss030e292893 | 7.0 | 1/50 | 2.8 | 10000 | 180mm f/2.8 D | D3S | 2012:02:08 21:09:16.87
iss030e292895 | 4.0 | 1/50 | 2.8 | 10000 | 180mm f/2.8 D | D3S | 2012:02:08 21:09:02.37
iss031e095634 | 7.0 | 1/50 | 1.4 | 3200 | 85mm f/1.4 D | D3S | 2012:06:04 22:26:49
iss035e023371 | 29.0 | 1/40 | 3.2 | 51200 | 400mm f/2.8 | D3S | 2013:04:18 22:10:09.73
Table 1: Specifications of the images used for comparison.

The two first images were obtained a few seconds from each other, but with
small changes of view angle and exactly the same camera settings, so they are
probably as similar as images taken from the ISS are likely to be. The third
image, was obtained with a different lens, ISO and aperture settings, and was
acquired 1 h and 30 min later, but with a similar view angle. The fourth image
was again obtained with a different lens, ISO, aperture and view angle, still
in the same daily time frame, but more than one year apart. A 5 pixel Gaussian
blur was applied to each image to minimize effects of errors in
georeferencing.

R2 values for the pixel by pixel comparison of light intensities determined
from the four images varied between 0.88 and 0.98 (Table 2), with the majority
of data points lying close to the 1:1 line (Figure 20). The differences in
intensities between images increase with variation in how those images were
acquired. Given the challenges of nocturnal remote sensing that result from
the nature of the light sources [Tong et al., 2020], we conclude that these
are satisfactory results and comparable to findings for panchromatic data from
satellite sensors [Coesfeld et al., 2018].

Ref Pro | iss030e292893 | iss030e292895 | iss031e095634 | iss035e023371
---|---|---|---|---
iss030e292893 | 1 | 0.98 | 0.95 | 0.88
iss030e292895 | 0.98 | 1 | 0.96 | 0.88
iss031e095634 | 0.95 | 0.96 | 1 | 0.88
iss035e023371 | 0.88 | 0.88 | 0.88 | 1
Table 2:  $R^{2}$ values corresponding to the plots fig 20.

##  6 Conclusion

Calibration of nighttime images of the Earth taken by astronauts aboard the
ISS is not, in general, an easy task. These images were never designed to
provide remote sensing data. However, if handled properly, they can provide
multispectral information on the distribution and change in nighttime lighting
that is not available from any other source, and at spatial resolutions that
are comparable or better than those obtained by the DMSP-OLS and SNPP/VIIRS-
DNB platforms. Reflection correction is not needed and we did not apply it
because most studies of light pollution are concerned with the total light
received. Also, in urban areas the vast majority of the surfaces are asphalt
and concrete, and such grey materials do not change significantly the spectral
characteristics of the light.

As we have laid out, the correct calibration of nighttime images of the Earth
from the ISS requires processing through a number of steps (Fig. 1). Whilst
some of these undoubtedly have more significant effects on the final image
than others, we recommend that all are carried out, as their influences on
different images can vary greatly.

Calibration of nighttime images of the Earth taken from the ISS opens up
enormous possibilities for studying the spatial occurrence of artificial
lighting and how this is changing with time (nightly, through the year, and
across years). Determining how the spatial and temporal variation covaries and
determining the influences on other factors (e.g. human health and
environmental impacts) is of great interest. As we have previously shown, by
using colour-colour diagrams, inferences can also be drawn as to how
differences and changes in the lighting technologies being used give rise to
these spatio-temporal dynamics [Sánchez de Miguel et al., 2019].

##  7 Acknowledgements

We thank R. Moore of the Image Science and Analysis Group, NASA Johnson Space
Center for information on ISS cameras and window properties. We thank Lucía
García for her help with improving some figures. We also thank the anonymous
reviewers for their constructive feedback. This work was supported by the
EMISSI@N project (NERC grant NE/P01156X/1), Fonds de Recherche du Québec :
Nature et Technologies (FRQNT), COST (European Cooperation in Science and
Technology) Action ES1204 LoNNe (Loss of the Night Network), the ORISON
project (H2020-INFRASUPP-2015-2), the Cities at Night project, FPU grant from
the Ministerio de Ciencia y Tecnologia and F. Sánchez de Miguel.

Cameras were tested at Laboratorio de Investigaciónn Científica Avanzada
(LICA), a facility of UCM-UPM funded by the Spanish program of International
Campus of Excellence Moncloa (CEI). We acknowledge the support of the Spanish
Network for Light Pollution Studies (MINECO AYA2011-15808-E) and also from
STARS4ALL, a project funded by the European Union H2020-ICT-2015-688135. This
work has been partially funded by the Spanish MICINN,
(AyA2018-RTI-096188-B-I00), and by the Madrid Regional Government through the
TEC2SPACE-CM Project (P2018/NMT-4291).

The ISS images are courtesy of the Earth Science and Remote Sensing Unit, NASA
Johnson Space Center. Thanks to S. Doran for helping us to locate the missing
image that we use as an example. We are very grateful to all members of the
crews of the ISS from all agencies, NASA, ESA, JAXA, CSA-ASC and ROSCOSMOS,
for their images.

## Description of author’s responsibilities

A.S.M., J.Z., J.G., M.A., D.R.P., J.B. and K.J.G. conceived the study, A.S.M.,
M.A. and J. Z. conducted the calibration procedures, A.S.M., F.O. and J.Z.
analyzed the results, D.R.P. acquired very many of the images used, and
designed and developed the basic techniques for the acquisition of images and
documented the ISS specifications, W.L.S. led the Earth Science and Remote
Sensing Unit, NASA Johnson Space Center and provided key technical
information, and A.S.M., K.J.G. and J.Z. wrote the original manuscript, A.S.M,
J.Z., J.G., W.L.S., J.B. and K.J.G. conducted the funding requests. All
authors reviewed the manuscript.

## Declaration of interest

A.S.M., J.Z. and K.J.G. are members of environmental organizations, including
Bird Life, Celfosc and the International Dark-Sky Association. A.S.M.
occasionally provides consultancy advice for the Instituto de Astrofisica de
Andalucia - CSIC and the company SaveStars Consulting S.L.

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Model | Kodak DCS760 | Nikon D1 | Nikon D2Xs | Nikon D3 | Nikon D3S | Nikon D4 | Nikon D5 | Sony Alpha a7S II
---|---|---|---|---|---|---|---|---
Agencies | All | All | All | All | All | All | All | JAXA
Model launch | 22/03/2001 | 15/06/1999 | 01/06/2006 | 23/08/2007 | 4/10/2009 | 06/01/2012 | 05/01/2016 | 11/09/2015
In use at ISS | 2002–2007 | 2004–2006 | 2008–2014 | 2009–2012 | 2010-2015 | 2015–2017 | 2017- | 2018-
Megapixels | 6 | 3 | 13 | 13 | 13 | 17 | 21 | 12
Sensor format | APS-H | APS-C | APS-C | Full Frame | Full Frame | Full Frame | Full Frame | Full Frame
Sensor type | CCD | CCD | CMOS | CMOS | CMOS | CMOS | CMOS | CMOS
ISO Range | 80 - 400 | 200 – 1600 | 100 – 800 | 200 -6400 | 200 – 12800 | 100 – 12800 | 100 – 102400 | 100 – 102400
Image format | RAW | RAW | RAW | RAW | RAW + TIFF | RAW | RAW | RAW
Fitting | Nikon F | Nikon F | Nikon F | Nikon F | Nikon F | Nikon F | Nikon F | Sony E
Amplification | 1.3x | 1.5x | 1.5x | 1x | 1x | 1x | 1x | 1x
Live view | No | No | No | Yes | Yes | Yes | Yes | Yes
Video resolution |  |  |  |  | 1280 x 720 | 1920 x 1080 | 3840 x 2160 | 4K
Storage | PCM CIA | CF | CF | CF | CF | CF,XQD | Dual CF,XQD | SD/SDH/C/SDXC
Table 3: Main characteristics of the most popular cameras used for nighttime photography and video at the ISS. Other cameras have been used but rarely or never for this purpose or only for specific experiments (like Nikon D800E and Nikon D850). More info at: https://eol.jsc.nasa.gov/FAQ. Source: https://www.dpreview.com/. Table 4: Transmission coefficients for the most popular lenses used at the ISS or in light pollution research, relative to that of the 50mm f/1.4 lens. The values correspond to the ratio between the signal of surface brightness of lambertian reference source illuminated at 4 lux with a tungsten lamp, at 1/60 s and ISO 200 with a Nikon D5, for different lenses. This number is equivalent to the transmission stop (T-stop), but on a linear scale. Source: This work. Lens | Transmission coefficient |
---|---|---
Nikon 180mm f/2.8 | 0.297 |
Nikon 85mm f/1.4 | 1.070 |
Nikon 85mm f/1.8 | 0.765 |
Nikon 50mm f/1.8 | 0.750 |
Nikon 50mm f/1.4 | 1 |
Nikon 10.5mm f/2.8 | 0.295 |
Nikon 24mm f/1.4 | 1.050 |
Nikon 400mm f/2.8 | 0.215 |
Sigma 8mm f/3.5 | 0.187 |
Nikon 200mm f/4 | 0.136 |
Nikon 28mm f/1.4 | 1.630 |
Nikon 28mm f/2.8 | 0.326 |
Nikon 28-70mm f/2.8 | 0.324 |
Nikon 14-24mm f/2.8 | 0.307 |
Figure 1: Schema of the potential calibration paths. The red path requires the
calibration of the camera using stars. This calibration provides colour
coherence and absolute calibration based on stars. The black path indicates
what can be done if we do not have an absolute calibrated image with stars, we
can alternatively calibrate against the VIIRS-DNB. Some 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). Figure 2: Response of camera to a uniformly lit screen with
stabilized source across all ISOs and times of exposure (T) in seconds. The
dispersion of the dots is compatible with the errors of the stabilization
(0.5%). Response values expressed in dimensionless units (aka ADU). Data
calculated with a D5, although compatible with previously calculated data for
D3S. Source: this work.

Figure 3: Relationship between emissions in the RVB Johnson bands and the RGB
Nikon bands. The 1:1 line is given in red, and the fit to the data in green.

Figure 4: Comparison of the radiance of stars in the Ducati II/237 catalogue
with the values determined from calibration images taken with the D3S.
Reference (X axis) brightness is in AB magnitudes. Instrumental magnitudes on
Y axis. The measurements are in green, the blue line is the fit to all of the
data, and the red line the fit excluding outliers using RANSAC.  Figure 5:
Comparison of the radiance of stars in the Tycho I/259 catalogue with the
values determined from calibration images taken with the D3S. Each colour
represents a different image, which was obtained using different camera
settings (exposure time, ISO). Longer exposure times and higher ISO lead to
detection of more stars, but also present more saturation problems for bright
stars, as exemplified by the image represented by the small red dots (more
details in Sánchez de Miguel [2015]). Figure 6: With an ideal nadir view, that
is typical of most observations from satellites, an imaginary circle seen from
the nadir (top right view), would always be a circle on the ground. But, from
a tilted observation, the circle would be transformed, approximately, into an
ellipse (top left view and bottom right view), where the minor axis would be
in the direction of observation and the major axis will point perpendicular to
it. If we intersect view direction with the ground track of the ISS, we can
find the true nadir point of observation (bottom left view). We have a first
guess of the nadir point of observation thanks to the clock of the camera, but
this can have an error as high as 500 km. The deformation is trivial to
calculate, for example at the centre of the image, once the image has been
georeferenced, using the reverse equations that give us the image coordinates
from the ground equations. 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). Figure 7: Original JPG image of Spain
used as an exemplar. Madrid (the spider-like lit area) 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. Figure 8: Detail of the center of Madrid on the
RAW image of Spain, with the Bayer matrix and the 4 channels merged in one
single image. The images do not appear clear because they have not been
stretched and the different bands are entangled on the Bayer matrix, 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. Figure 9:
Zoomed detail of Madrid from the exemplar image. The RAW image is extracted
and separated into four different images. From top left to bottom right, Red
(R1), Green (G2), Green (G3), and Blue (B4) channels. Figure 10: Zoomed detail
of the exemplar image, after linearity correction of the four separated
channels. Figure 11: Flat field correction for a 24 mm lens. The intensity at
the centre corresponds to 100%, the green lines 85%, 45% and 33%, from inside
to outside. Values presented correspond to percentage of the transmission
compared with peak.  Figure 12: Zoom in (not full picture) from fig 11 after
the flat field correction. Results of photometric calibration of the exemplar
image. The four extracted channels are now in values of $nW\cdot
sr^{-1}cm^{-2}$\mathrm{\SIUnitSymbolAngstrom}$^{-1}$. This image has not been
stretched, so shows a lot of noise from low intensities and cosmic rays.
Figure 13: Full picture rectified. The four channel images have to be
georeferenced to create 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 $nW\cdot
sr^{-1}cm^{-2}$\mathrm{\SIUnitSymbolAngstrom}$^{-1}$. This image has not been
stretched, so shows a lot of noise from low intensities and cosmic rays.
Figure 14: Angular distance to the horizon for the exemplar image. The X and Y
axis correspond to the coordinates of the image (see fig 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 $nW\cdot
sr^{-1}cm^{-2}$. This image has been stretched, so does not show noise as
clearly as in the other cases.  Figure 16: Zoom to Madrid region. Left is the
ISS Green band radiance calibrated with stars. Middle image is ISS green band
inter-calibrated with VIIRS. Right image is VIIRS comparison image. Units in
$nW\cdot sr^{-1}cm^{-2}$. The comparison is between the VIIRS October 2017
(November 2017 has a defect) image EOG average Elvidge et al. [2013] and ISS.

Figure 17: Left: Comparison between VIIRS and ISS Green band star calibrated.
Right: Comparison between ISS and VIIRS after background and slope offset. Red
line corresponds to 1:1 relationship. Black line, standard linear fit, blue
line RANSAC Pedregosa et al. [2011] linear fit. Slope Offset is calculated
ratio from $100nW\cdot sr^{-1}cm^{-2}$ ISS compared to corresponding VIIRS
equivalent intensity. Background offset corresponds to maximum density points.
Figure 18: Difference between the VIIRS and ISS image. The main differences
are due to time of acquisition of the images. In the ISS image the lights can
be seen of the main commercial centers of the Madrid area, the Sol square and
surroundings (center of image (a)), the commercial center Gran Plaza 2 (in the
west(b)), and the commercial center Plenilunio (in the East (c)) and Plaza
Norte (in the north (d)). Also, there is a small difference in the
georeferencing. The Santiago Bernabeu Stadium(e) does not appear on the ISS
image, probably because of the tilt effect (dark area in the center of the
image). Look-up table ”Roma” from Crameri [2021]. Figure 19:  From left to
right and top to bottom, the images iss030e292893, iss030e292895,
iss031e095634 and iss035e023371. Intensity scale in $nW\cdot
sr^{-1}cm^{-2}\mbox{\AA}^{-1}$. The grid represents latitude and longitude.
Figure 20:  Density plots of the comparison between the images iss030e292893,
iss030e292895, iss031e095634 and iss035e023371 on the Green band. The red
lines indicate the 1:1 relationship. Units log10($nW\cdot sr^{-1}\cdot
cm^{-2}\cdot\mbox{\AA}^{-1}$).