A Practical Device for Measuring the Luminance Distribution
Thijs Kruisselbrink1,2,*, Myriam Aries= 1,3, Alexander Rosemann1,2
2Intelligent Lighting Institute, Eindhoven University of Techno= logy, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
3Department of Construction Engineering and Lighting Science, J= önköping University, P.O. Box 1026, 551 11, Jönköping, Sweden
Received
03 February 2017, Accepted 20 April 2017
Abstract
Various applications in building light=
ing
such as automated daylight systems, dynamic lighting control systems, light=
ing
simulations, and glare analyzes can be optimized using information on the
actual luminance distributions of the surroundings. Currently, commercially
available luminance distribution measurement devices are often not suitable=
for
these kind of applications or simply too expensive for broad application. T=
his
paper describes the development of a practical and autonomous luminance
distribution measurement device based on a credit card-sized single-board
computer and a camera system. The luminance distribution was determined by
capturing High Dynamic Range images and translating the RGB information to =
the
CIE XYZ color space. The High Dynamic Range technology was essential to
accurately capture the data needed to calculate the luminance distribution
because it allows to capture luminance ranges occurring in real scenarios. =
The
measurement results were represented in accordance with established methods=
in
the field of daylighting. Measurements showed that the accuracy of the
luminance distribution measurement device ranged from 5% to 20% (worst case)
which was deemed acceptable for practical measurements and broad applicatio=
ns
in the building realm.
Keywords: High Dynamic Range, Raspberry Pi, Measurement device, CIE XYZ, Luminance distribution, Single-board computer<= o:p>
1. Introduction
Lighting simulation is an efficient way for
designing comfortable and sustainable lighting conditions in the built
environment. However, the reliability of the simulation depends, among other
things, on the quality of the input model. An important aspect of daylight
simulations is the sky luminance distribution. Previous studies have shown =
that
representation of the sky luminance distribution continues to be a challeng=
e [1,2]. The International Commission on Illumination (=
CIE)
developed 15 generic sky models representing sky luminance distributions for
conditions varying from overcast to cloudless skies [3], based on long-term measurements using sky
scanners. The usability of the expensive sky scanners is limited: it takes a
few minutes to measure the hemisphere and it only allows measurements in low
resolution [4,5]. The generic CIE sky-models are very suitable f=
or
comparing design decisions under different sky conditions, but they do not
represent the actual luminance distribution of the sky for any location and=
the
models are not sensitive to transient luminance variations in different
sections of the hemisphere [6]. Due to their generic character these models cr=
eate
uncertainties in the lighting simulations.
More and more buildings are applied with automat=
ed
daylight systems like automated Venetian blinds and dynamic solar shading.
Relevant and actual luminance distributions can increase the performance of
daylight systems because both the influence of the neighboring environment =
and
the fast variations of the sky can be included in the input [7], resulting in optimized user comfort and energy
performance. Currently available luminance distribution measurement methods,
sky scanners and cameras with proprietary software, are not suitable for br=
oad
market penetration to support the control of automated daylight systems bec=
ause
of their extremely high price (cameras with proprietary software) or because
they cannot handle fast variations of the sky (sky scanners) [8].
Electrical lighting and daylight influence the
satisfaction and performance of the occupants. Especially daylight can cause
discomfort glare, which is often translated into the Daylight Glare Index
(DGI). The following factors are incorporated in the definition to the DGI =
[9]:
These quantities are not easily measured
simultaneously, with the currently available methods due to complex luminan=
ce
distributions [10]. A luminance distribution measurement device is
capable of measuring all required variables to calculate the DGI
simultaneously.
Previous research has shown that it is possible =
to
measure the luminance distribution with cheap commercial digital cameras us=
ing
the Red-Green-Blue (RGB) information captured using High Dynamic Range (HDR)
photography [2,11–13]. However, these methods require extensive
post-processing and knowledge and/or assume constant correlated color
temperature (CCT).
This paper describes a method for fast capturing=
the
luminance distributions, indoors and outdoors, based on a commercially
available camera. Capturing real-time luminance distributions will offer
possibilities to help optimize lighting simulations, to inform building
automation systems and by this, increasing the use of daylight in building
interiors and the dynamic control of the electric lighting indoors, as well=
as
to potentially carry out glare analyses on the run.
The aim of this research was to develop a practi=
cal
and autonomous camera-based luminance measurement device using an inexpensi=
ve
single-board computer equipped with a camera and a fisheye lens. In contras=
t to
other measurement devices for the luminance distribution, this method was t=
o be
cheap, quick, practical and completely automated. An accuracy in the range =
up
to ¡¾20% was targeted, a range which was deemed appropriate for a practical
measurement device [11,14]. Such a practical and autonomous device can be
placed at a certain location in the building realm and provide information =
on
the luminance distribution in real time.
2. Methods and Results
In order to build a stand-alone device a
single-board computer, Raspberry Pi 2 model B, was used to control the came=
ra,
carry out the computations and communicate the results using a Wi-Fi dongle=
(Fig. 1). The camera functionality was accounted for by=
the
Raspberry Pi Camera Board version 1.3 with a CMOS sensor (3.60 mm, f/2.9) w=
ith
a maximum resolution of 2592 x 1944 pixels, comparable to cameras in
smartphones. A miniature equisolid-angle fisheye lens, suitable for the
Raspberry Pi Camera Board, with a measured angle of view of 187¡Æ (3mm, f/0=
.4)
was used on top of the camera sensor to provide a hemispherical image. In
combination with the camera board, this lens system had a focal length of 1=
.26
mm and provided an equisolid-angle projection with a field of view of 84% of
the sky hemisphere. The code, used to automate the measurement procedure, w=
as
composed in Python 3, which is one of the programming languages supported by
the Raspberry Pi.
Fig. 1. The measurement
device, including a Raspberry Pi 2, Camera Board, fisheye lens, dongle, and
control panel (see section 2.4)
1.1.=
Image Projection
Fisheye lenses have an extremely short focal len=
gth.
The projection lines that do not pass through the center of the image are
strongly bent, resulting in an angle of view up to 180¡Æ but with a lower
resolution and large distortions at the lens¡¯ periphery [15]. Tohsing et al. suggested a straightforward met=
hod
to describe the projection image of a fisheye lens by relating the elevation
angle to the image radius by curve fitting [13]. The relation is described in the following
equation with ri as the image radius of the pixel, c as focal
length, and ¥åi as the polar angle, being the opposite of the
elevation angle.
This equation relates every pixel to the elevati=
on
as well as to the azimuth angle. With a coefficient of determination (R
Two identical lenses were compared to determine =
the
deviation percentage. There was no significant difference between the
projection equations of two lenses of the same type. The two similar lenses
displayed a relative difference of 0.18%.
To provide input for building simulations and
automated operation it is not necessary to get luminance information for ev=
ery
individual pixel due to the overly great spatial resolution and sheer amoun=
t of
data. Therefore, a subdivision was used as suggested by Tregenza ADDIN CSL_CITATION { "citationItems" : [ { "id&q=
uot;
: "ITEM-1", "itemData" : { "DOI" :
"10.1177/096032718701900103", "ISSN" :
"1477-1535", "abstract" : "A scanning pattern for =
sky
photometry is described, in which the hemisphere is divided into 151 zones =
in
bands parallel with the horizon.", "author" : [ {
"dropping-particle" : "", "family" :
"Tregenza", "given" : "P.R.",
"non-dropping-particle" : "", "parse-names" :
false, "suffix" : "" } ], "container-title" :
"Lighting Research and Technology", "id" :
"ITEM-1", "issued" : { "date-parts" : [ [
"1987", "1", "1" ] ] }, "page" :
"13-14", "title" : "Subdivision of the sky hemisph=
ere
for luminance measurements", "type" :
"article-journal", "volume" : "19" },
"uris" : [
"http://www.mendeley.com/documents/?uuid=3Ddb44e571-edf1-4dde-b20f-392=
80208f6db"
] } ], "mendeley" : { "formattedCitation" :
"[16]", "plainTextFormattedCitation" : "[16]",
"previouslyFormattedCitation" : "[16]" },
"properties" : { "noteIndex" : 0 }, "schema" :
"https://github.com/citation-style-language/schema/raw/master/csl-cita=
tion.json"
}[16], as shown in =
Fig.
2. Tregenza¡¯s subdivision provides the luminance
distribution of a hemisphere in a limited amount of samples (145) while
ensuring enough resolution to prevent major information losses for daylight
applications. The single-board computer ran a script developed to map the
Tregenza subdivision on the image sensor using the projection equation (1).
This mapping algorithm had an inaccuracy of 0.1%. Subsequently, the computer
determined the average luminance of each Tregenza sample by considering all
pixels within it. The camera system was bound to an aspect ratio of 4:3 sin=
ce
the focal length was not customizable, resulting in an 84% field of view (<=
/span>Fig. 2).
Fig. 2. Tregenza¡¯s
subdivision placed over an image taken with the Raspberry Pi camera system.=
Due
to the fixed focal length, only 84% of the hemispherical view was captured.=
The applied image resolution was chosen based on=
the
optimum between the resulting file size, the processing time, and the accur=
acy
of the Tregenza sample mapping. The optimization between file size and accu=
racy
of the Tregenza samples led to a resolution of 901 pixels horizontally and =
676
pixels vertically, instead of 2592 and 1944 pixels respectively. With this
resolution, 95% of each Tregenza sample was represented by whole pixels As a
result, the projection equation (1) was scaled to this resolution.
1.2.=
Input settings
Determining the luminance based on a photograph
requires High Dynamic Range (HDR) imaging technology. The luminance
distribution occurring in the real world can consist of luminance values in=
a
range of 8 orders of magnitude (typically from 10-3 to 105<=
/sup>
cd/m2) [17]. Standard 8-bit images only capture a dynamic r=
ange
of 1.6 orders of magnitude [18]. The most common method to achieve a high dynam=
ic
range is the sequential exposure change technique [19]. With this technique, simple digital cameras are
used to take Low Dynamic Range (LDR) photographs with sequential exposure
settings to cover the desired dynamic range. In order to keep the optical
properties constant, it is recommended to only change the shutter speed [19].
A measurement setup was designed, providing cons=
tant
conditions, to determine which set of exposures efficiently covered the dyn=
amic
range of the real world conditions (Fig. 3). A diffuse reflecting target (Kodak Gray Card)=
was
illuminated with a lamp in an otherwise completely dark lab room with black
interior surface. The lamp (Halogen, 220V, 650W) was dimmed by applying AC
voltages in steps of 20V (within the range from 100V to 260V). In addition,=
the
lamp was placed at multiple positions in order to achieve multiple luminance
values at the target. The luminance of the target was measured with a Hagner
Universal Photometer S2 and simultaneously photographed by the Raspberry Pi
with shutter speeds ranging from 17,000-1 s to 2 s (f/2.9, ISO-1=
00).
Based on the under/over-saturation empirical equations, representing the
minimum, mean, and maximum luminance, were determined describing which
luminance range the different shutter speeds were able to capture. These
equations allowed to generate a nine-step exposure sequence to capture High
Dynamic Range images. It has previously been shown that the quality of an H=
DR
image does not significantly increase with a higher number of exposures [19].
Fig. 3. Measurement setup=
to
relate luminance to shutter speed. Images and luminance measurements were t=
aken
for the target in a black room only illuminated by a light source that was
dimmed and placed at multiple positions while baffles were applied to preve=
nt
direct light entering the camera. The influence of the monitor light is
negligible since only a full-screen window with a black background (termina=
l)
was opened during the measurements.
Based on the relation between the shutter speed =
and
the luminance range, as shown in =
Fig.
4, Exposure Values (EV) ranging from 5 to 19.4 EV=
in
steps of 1.8 EV have been determined for the use by the camera system. The
upper limit of 19.4 EV represents the maximum shutter speed of the camera. =
The
exact exposure values slightly differ due to the inaccuracy of the camera
device as displayed in =
Table
1. This sequence guaranteed that, except for the
extreme values, each possible luminance value was captured by at least two
exposures, with a theoretical maximum luminance of approximately 70,000 cd/=
m2.
Table 1. Exposure sequence
with nine exposures values that were conducted by the Raspberry Pi camera
system to make an accurate High Dynamic Range image for each possible
condition. (EV =3D exposure value)
|
Exposu=
re |
Shutter
Speed [¥ìs] |
EV |
|
1 |
250,000 |
5.07 |
|
2 |
76,923 |
6.77 |
|
3 |
21,739 |
8.60 |
|
4 |
6,211 |
10.40 |
|
5 |
1,779 |
12.21 |
|
6 |
507 |
14.02 |
|
7 |
130 |
15.98 |
|
8 |
36 |
17.83 |
|
9 |
12 |
19.42 |
<=
span
lang=3DEN-US style=3D'mso-no-proof:yes'>
Fig. 4. The relation betw=
een
luminance and shutter speed. In a measurement, the shutter speed of the
Raspberry Pi camera system was related to the luminance based on the satura=
tion
of the images (o). The luminance range captured by the camera system was
approximated with curve fitted equations for the minimum luminance (dashed
line), median luminance (solid line) and maximum luminance (dash-dot line).=
Tests with the exposure sequence showed that a
number of exposures were always under- or over-saturated. For high luminance
values, exposures 1 and 2 turned out to be always completely over-saturated,
while for low luminance values, exposures 8 and 9 were always completely
under-saturated. Therefore, the exposure sequence was further optimized by
leaving out the first or last two exposures depending on the conditions. Th=
is
way, the quality of the HDR images increased and the influence of transient
processes was limited. The most applicable sequence was determined by
conducting a base of the exposure sequence (exposure 3-7) and subsequently
assessing the 7th exposure on the level of saturation. When an area of expo=
sure
7 was (almost) saturated exposure 8 and 9 were conducted instead of exposur=
e 1
and 2 (=
Fig.
5).
Photographs taken according to the determined
exposure sequence were transformed into a single HDR image by the command-l=
ine
HDR builder for the Raspberry Pi (HDRgen), originally developed by Ward [20]. This process uses the OpenEXR (.exr) format wi=
th
RGB encoding and a depth of 96 bits, providing a sufficient dynamic range (=
76
orders of magnitude). The resulting files were smaller than for other
established formats (e.g., HDR and TIFF), it had a relative step size, the
relative difference between adjacent values, of 0.1% and was easy to read u=
sing
the OpenCV library (Version 2) for Python [18,21]. The HDR builder was able to approximate the
specific camera response curve using radiometric self-calibration ADDIN CSL_CITATION { "citationItems" : [ { "id&q=
uot;
: "ITEM-1", "itemData" : { "DOI" :
"10.1191/1365782806li164oa", "ISSN" : "14771535&qu=
ot;,
"abstract" : "In this paper, the potential, limitations and
applicability of the High Dynamic Range (HDR) photography technique are
evaluated as a luminance mapping tool. Multiple exposure photographs of sta=
tic
scenes were taken with a commercially available digital camera to capture t=
he
wide luminance variation within the scenes. The camera response function was
computationally derived by using Photosphere software, and was used to fuse=
the
multiple photographs into an HDR image. The vignetting effects and point sp=
read
function of the camera and lens system were determined. Laboratory and field
studies showed that the pixel values in the HDR photographs correspond to t=
he
physical quantity of luminance with reasonable precision and
repeatability.", "author" : [ { "dropping-particle"=
; :
"", "family" : "Inanici", "given" :
"M.N.", "non-dropping-particle" : "",
"parse-names" : false, "suffix" : "" } ],
"container-title" : "Lighting Research and Technology",
"id" : "ITEM-1", "issue" : "2",
"issued" : { "date-parts" : [ [ "2006", "=
;6",
"1" ] ] }, "note" : "Sage Journals\nSearch Term:
Luminance, Pattern\n\n\nBelangrijk artikel", "page" :
"123-136", "title" : "Evaluation of high dynamic r=
ange
photography as a luminance data acquisition system", "type" :
"article-journal", "volume" : "38" },
"uris" : [
"http://www.mendeley.com/documents/?uuid=3D07eabadf-f4ab-4a90-8680-ca4=
eae217cda"
] }, { "id" : "ITEM-2", "itemData" : {
"DOI" : "10.1177/1477153516649229", "ISSN" :
"1477-1535", "author" : [ { "dropping-particle&quo=
t; :
"", "family" : "Mead", "given" :
"AR", "non-dropping-particle" : "",
"parse-names" : false, "suffix" : "" }, {
"dropping-particle" : "", "family" :
"Mosalam", "given" : "KM",
"non-dropping-particle" : "", "parse-names" :
false, "suffix" : "" } ], "container-title" :
"Lighting Research and Technology", "id" :
"ITEM-2", "issued" : { "date-parts" : [ [
"2016", "5", "13" ] ] }, "page" :
"1-18", "title" : "Ubiquitous luminance sensing us=
ing
the Raspberry Pi and Camera Module system", "type" :
"article-journal", "volume" : "0" },
"uris" : [
"http://www.mendeley.com/documents/?uuid=3D0dd42ec8-fdbf-4c76-bb2f-b96=
f4251555c"
] }, { "id" : "ITEM-3", "itemData" : {
"DOI" : "10.1109/CVPR.1999.786966", "ISBN" :
"0-7695-0149-4", "ISSN" : "1063-6919",
"abstract" : "A simple algorithm is described that computes =
the
radiometric response function of an imaging system, from images of an arbit=
rary
scene taken using different exposures. The exposure is varied by changing
either the aperture setting or the shutter speed. The algorithm does not
require precise estimates of the exposures used. Rough estimates of the rat=
ios
of the exposures (e.g. F-number settings on an inexpensive lens) are suffic=
ient
for accurate recovery of the response function as well as the actual exposu=
re
ratios. The computed response function is used to fuse the multiple images =
into
a single high dynamic range radiance image. Robustness is tested using a
variety of scenes and cameras as well as noisy synthetic images generated u=
sing
100 randomly selected response curves. Automatic rejection of image areas t=
hat
have large vignetting effects or temporal scene variations make the algorit=
hm
applicable to not just photographic but also video cameras",
"author" : [ { "dropping-particle" : "",
"family" : "Mitsunaga", "given" : "T.&qu=
ot;,
"non-dropping-particle" : "", "parse-names" :
false, "suffix" : "" }, { "dropping-particle"=
:
"", "family" : "Nayar", "given" :
"S.K.", "non-dropping-particle" : "",
"parse-names" : false, "suffix" : "" } ],
"container-title" : "IEEE Computer Society Conference on Com=
puter
Vision and Pattern Recognition", "id" : "ITEM-3",
"issued" : { "date-parts" : [ [ "1999" ] ] },
"note" : "via: Improving the quality of high dynamic range
images", "page" : "374-380", "publisher"=
:
"IEEE Comput. Soc", "publisher-place" : "Fort Coll=
ins,
USA", "title" : "Radiometric self calibration",
"title-short" : "Computer Vision and Pattern Recognition, 19=
99.
IEE", "type" : "paper-conference", "volume&qu=
ot;
: "1" }, "uris" : [
"http://www.mendeley.com/documents/?uuid=3D1b7c1228-90dd-49d8-bdb4-3d7=
9d99dde95"
] } ], "mendeley" : { "formattedCitation" :
"[9,11,22]", "plainTextFormattedCitation" :
"[9,11,22]", "previouslyFormattedCitation" :
"[9,11,22]" }, "properties" : { "noteIndex" :=
0
}, "schema" :
"https://github.com/citation-style-language/schema/raw/master/csl-cita=
tion.json"
}[9,11,22]. The camera-specific response curve was
approximated in accordance with the method described by Reinhard et al. [18], by determining the camera response curve for t=
hree
scenes and averaging the results into one final response curve that was used
for all luminance measurements. The response curve is camera-specific.
Measurements with another Raspberry Pi camera board showed that the differe=
nces
between response curves of two similar camera boards were limited to a maxi=
mum
absolute difference of 2% and a maximum relative difference, for very low
exposures, of 60%, and an average relative difference of 12%. The larger
differences were mainly present in the darkest 30%.
Fig. 5. Formation of High
Dynamic Range image. Two aspects were needed to form an HDR image: An image
sequence and a camera response curve. The image sequence consisted of two
parts: The base, this was always captured; and depending on the light inten=
sity
images 1 and 2 or images 8 and 9 were also captured.
1.3.=
Luminance Calculation
The luminance was determined based on the floati=
ng
point RGB values of an HDR image. In order to determine the luminance, the =
RGB
color space was converted to the XYZ color space. An important property of =
the
CIE XYZ color space is that the color matching function ȳ(¥ë) is equal=
to V(¥ë),
the sensitivity curve of the human eye for photopic vision, meaning that th=
e Y
channel indicates the incident radiation weighted by the sensitivity curve =
of
the human eye [5], or, in other words, the luminance. The transla=
tion
of RGB values to the Y tristimulus value was done according to the protocol=
as
described by Inanici [11]. By applying a conversion matrix depending on t=
he
primaries and the white point, the RGB tristimulus values could be turned i=
nto
equivalent XYZ tristimulus values. The primaries are stored in the EXIF dat=
a,
while the white point, depending on the CCT¡©, can be extracted from tables=
[18], or calculated according to three equations as
described by Schanda [23].
All variables of the conversion matrix except the
CCT were constant. The exact CCT for each condition was not determined sinc=
e it
is an extensive process. Most studies developing a luminance distribution
measurement device assumed a constant CCT [5,11,13,24], mostly illuminant D65, to determine the white
point. Such an approach results typically in significant luminance errors, =
as
the assumption of a constant CCT (i.e., constant white point) can cause
deviations up to 17.9% in the conversion matrix for CCTs far from 6,504 K, =
the
CCT of illuminant D65. This methodological error comes on top of uncertaint=
ies caused
by noise etc. Alternatively, the luminance distribution measurement device =
can
do the measurements in accordance with three reference CCTs, each with its =
own
conversion matrix, to limit this methodological error (Fig. 6). Next to CIE standard illuminant D65, CCT
references of 3,000 K and 14,000 K were used, reducing the maximum
methodological error from 17.9% to 5.4%. The CCT of 3,000 K was suitable for
luminance measurements indoors (warm white), illuminant D65 for overcast sk=
ies
(daylight white), and the CCT of 14,000 K for clear blue skies. The switchi=
ng
point between 3,000 K and D65 was at a CCT of 6,000 K and the switching poi=
nt
between D65 and 14,000 K was at a CCT of 8,600 K. When taking measurements,=
the
most suitable reference CCT was selected by the user (see section 2.4).
<=
span
lang=3DEN-US style=3D'mso-no-proof:yes'>
Fig.
.
Deviation from luminance caused by constant CCTs. The conversion matrix to
calculate the XYZ color space is dependent on the CCT, the figure illustrat=
es
the deviation that occurs when a reference CCT is used. CCT =3D3,000K (¡à),=
CCT =3D
D65 (¡Ô), CCT =3D 14,000K (o) and the three refere=
nce
CCT combined (black) with switching points 6,014 K and 8,571 K.
The primaries, obtained from the HDR files¡¯ EXIF
data, and the calculated white points, led to the color space conversion
matrices as displayed in =
Table
2. The luminance was calculated by extracting the=
CIE
Y tristimulus value, leading to a simple equation (L), with calibration fac=
tor
k and primaries R, G, and B.
Table SEQ Table \* ARABIC 2. Variables of
conversion matrices to translate RGB to XYZ for reference CCTs 3,000 K, 6,5=
04
(D65) and 14,000 K. In contrast to the primaries the white points were
dependent on the CCTs, resulting in three conversion matrices.
|
Refere=
nce
CCT |
3,000 K |
6,504 K (D65) |
14,000=
K |
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
|
|
|
|
|
|
|
For the three ranges of CCT used in this study t=
he
luminance is calculated according to equations (3-5).
Determining the CIE Y tristimulus value accurate=
ly
for all pixels requires accounting for the vignetting effect. The vignetting
effect of a lens refers to light fall-off at the periphery of the lens [2,5,25]. Especially fisheye lenses exhibit noticeable l=
ight
fall-off, visible by the gradual darkening towards the corners of the image=
. In
literature, it is noted that some fisheye lenses can exhibit 73% light fall=
-off
at the periphery of the lens [26]. The vignetting effect is a non-linear radial
effect along the image radius of the lens and is often approximated by a
polynomial function. It has a radial symmetric character, whereby the
polynomial function can be used to determine the vignetting effect for all
pixels of an image [26–28]. Even with the limiting aspect ratio, the used
fisheye lens was considered radial symmetric, despite the fact that the
complete projection was not captured by the sensor. Therefore, the vignetti=
ng
correction, the reciprocal of the vignetting effect, was approximated by an
empirical equation along the image radius.=
The vignetting effect was determined in an
Ulbricht¡¯s sphere (¨ª 700 mm). According to theory, such integrating spher=
es
create a uniform luminance distribution over its inner surface (¡¾1%) [29]. The vignetting effect was determined for every
tenth pixel along the image diameter by dividing the luminance, determined =
with
the Raspberry Pi, with the maximum luminance, which was the luminance close=
to
the zenith. The vignetting correction was measured along the diameter of the
image. The radial symmetry of the lens allowed to determine a function along
the image radius. This process was repeated multiple times to limit measure=
ment
uncertainties and achieve accurate results, since the vignetting effect
displayed differences up to 20% under ¡®constant¡¯ conditions. In contrast =
to
previous research [11,26,30], the vignetting filter was not described by a
polynomial function. Curve fitting to an exponential function showed the be=
st
match. Robust fitting to a second-degree exponential function resulted in t=
he
function as described in =
Fig.
7, with R2 =3D 0.9093. In order to ext=
ract
an applicable function outliers were neglected: The outliers at a distance =
of
240 pixels from the image center were caused by an irregularity of the sphe=
re.
Some outliers were exhibited at a distance of 450 pixels, the very last pix=
el
of the image, due to darkening caused by the image border. =
Fig.
7 shows that the luminance at the lens¡¯ peripher=
y was
56% (1/1.8) of the luminance in the lens¡¯ center in the case no vignetting
filter was applied. Application of the approximated function accounting for
this vignetting effect limited the maximum vignetting effect to 14% and the
average vignetting to 2.5%. The vignetting effect could not be eliminated
completely. Nevertheless, the reduction of the vignetting effect increased =
the
measurement accuracy close to the periphery significantly. With this equati=
on as
derived from =
Fig.
7, a post-process correction filter was defined,
containing a vignetting correction factor for each individual pixel.
In a last step, a photometric calibration was
required to accurately extract the luminance from the HDR image. This linear
calibration factor k related the CIE Y tristimulus to the real photometric
quantity luminance and brought the luminance to the correct order of magnit=
ude.
The calibration factor was determined for a gray (
1.4.=
Processing
The entire process was automated using a Python
script. The code is structured as shown in =
Fig.
8. =
The
process used an infinite loop, which guaranteed continuous measurements unt=
il
interrupted by the user. The code only asks for interaction regarding the C=
CT,
but choses the default setting of CIE standard illuminant D65 if there is no
user input. The user is able to switch between the reference CCTs at any ti=
me.
The luminance measurement is started by capturing the most suitable image
sequence. For scenes with too high luminance values, resulting in over-satu=
rated
exposures, the process is aborted and will retry after a time delay. If the
exposure sequence is captured successfully, it is formed to an HDR image. B=
ased
on the reference CCT the tristimulus value Y is extracted from the HDR imag=
e.
Consequently, the calibration factor and the vignetting correction are appl=
ied.
Once completed, the luminance of each individual pixel is known. The results
are represented in a more useful manner by averaging over Tregenza¡¯s
subdivision. Finally, the results are uploaded to a server, allowing access=
to
the measurement results from an external computer. The results are presente=
d as
a list with the average luminance for each Tregenza sample and a tone mapped
HDR image.
The process from taking the pictures to uploading
the results takes approximately 35 s. The duration of each individual task =
is
shown in =
Table
3. The loop is restarted every 5 minutes, indicat=
ing
that the process is roughly 4.5 minutes on hold. The measurement frequency =
can
be increased by changing the delay parameter but cannot be shorter that the
total processing time.
Table SEQ Table \* ARABIC 3. Processing time, =
in
seconds, of separate processes in the Python script, to calculate the
luminance, executed on a Raspberry Pi 2.
|
=
Process |
=
Processing
Time [s] |
|
|
|
|
|
8.2/8.0 |
|
|
|
|
|
2.1 |
|
|
|
|
|
33.7/33.5 |
|
|
|
|
|
300.0 |
* Suitable im=
age
sequence for dark or bright conditions.
** Including
vignetting correction and calibration.
*** Uploading
results and uploading and formation of a t=
one-mapped
HDR image.
1.5.=
Accuracy
The accuracy of the measurement device was measu=
red
according to the method described by Inanici [11]. Two gray Kodak cards were used next to an
uncalibrated gray scale and an uncalibrated color scale. Except for one gray
card, all color scales were placed in the center of the image. The remaining
gray card was placed close to the periphery of the image to address the
potential gradient in accuracy along the radius due to the vignetting effect
(see =
Fig.
9 on the far right). The luminance was measured w=
ith
the Hagner Universal Photometer S2 as well as determined by the Raspberry P=
i.
Based on a CCT measurement taken with the Konica Minolta illuminance
spectrometer CL-500A, the most suitable reference CCT was determined and us=
ed.
The accuracy was indicated by relating the physical measurement to the
measurement results of the Raspberry Pi. This process was repeated for mult=
iple
scenes under different indoor and outdoor conditions.
Fig. 8. Flowchart
representing the automated luminance distribution measurement. The straight
arrows represent the flow, the blocks the processes, the diamond decisions,=
and
the curved arrows represent user input that is acquired at the start of the
process and used later in the measurement process.
Fig. 9. Setup for the
accuracy measurements. Gray and colored targets were placed in the center of
the image and one gray target was placed at the border. The accuracy was
determined by comparing luminance measurements with the calculated luminanc=
e,
this was repeated for multiple conditions.
A selection of the accuracy results is shown in =
=
Fig.
10 and 11. Other accuracy measurements showed simi=
lar
results for different luminance ranges. The measurements had an average err=
or
of 10.1% for a range of 3 to 18,000 cd/m2. The average errors for
the gray and colored targets were 8.0% and 12.5% respectively. The accuracy
measurements also showed that the device did not work accurately enough for
very high luminance values (e.g. sun or reflections of the sun) due to satu=
ration
of the shortest exposure, leading to errors in the HDR assembly and,
subsequently, to false results. The exact luminance that saturated the shor=
test
exposure could not be determined but was assumed to be in the range between
18,000 and 70,000 cd/m2. The lower end of this range represents =
the
highest luminance measured during the tests; its maximum the greatest
calculated luminance for the shortest exposure (device limitation).
Fig. 10. The measured accu=
racy
for an indoor condition with a CCT of 6,370K. The black bars represent the
luminance measured with the Hagner Universal Photometer while the gray bars
represent the luminance determined by the Raspberry Pi. (M =3D middle, B =3D
border)
Fig.
.
The measured accuracy for an outdoor condition with a CCT of 6,170K. The bl=
ack
bars represent the luminance measured with the Hagner Universal Photometer
while the gray bars represent the luminance determined by the Raspberry Pi.=
(M
=3D middle, B =3D border)
It was expected that close to the periphery of t=
he
sensor the error would increase because the vignetting correction could not
completely account for the vignetting effect. The results supported this
hypothesis (=
Fig.
10 and 11), the errors close to the border (Kodak =
B)
of the sensor were significantly higher than at the center of the image (Ko=
dak
M); for the Kodak gray cards, it displayed an average inaccuracy of 27%
compared to 8% in the center. It is assumed that this error applies to the =
last
75 pixels along the radius because in this region the impact of the vignett=
ing
effect became significant. For the other pixels, the vignetting effect was =
much
smaller and therefore had a lower impact on the overall measurement accurac=
y.
The established exposure sequence had two variat=
ions
to minimize the number of saturated exposures. It was developed in such a w=
ay
that the entire range of possible luminance values was captured. The accura=
cy
of the HDR image, and hence the accuracy of the luminance measurement devic=
e,
can be improved by basing the exposure sequence on the current lighting
situation. Moreover, it turned out that the shortest exposure possible was =
not
able to capture the luminance of the sun and its direct reflections. The
luminance of the sun was several orders of magnitude greater than the maxim=
um
luminance that could be captured with this exposure sequence. The maximum
measurable luminance is currently limited to 18,000 cd/m2 becaus=
e no
higher luminance had been measured during the accuracy measurements. The ac=
tual
maximum luminance might be higher. With the chosen measurement setup it was=
not
possible to reach higher luminance values on the targets (color scales). Th=
ese
targets were required to assure that the same luminance was measured by the
Hagner Universal Photometer and the Raspberry Pi. The exposure sequence was
translated into an HDR image using the HDR-builder developed by Ward [20]. The settings were assumed constant for all
situations, which means that for some conditions the settings were not opti=
mal.
The camera response curve was approximated with =
the
HDR-builder, and therefore it was not the exact camera response curve. The
maximum relative difference between the camera response curves of two
comparable cameras was 60% with an average relative difference of 12%.
Therefore, the applied camera response curve cannot be applied for other
Raspberry Pi camera boards without consideration.
Additionally, two identical camera lenses were
compared. The maximum relative difference was 0.18%, therefore the lenses w=
ere
found to be equal. The developed code can be used to measure the luminance
distribution, with an acceptable accuracy, using another lens of the same t=
ype.
The luminance calculation was based on the
similarity between the tristimulus value Y and the sensitivity curve of the
human eye for photopic vision (V(¥ë)). Therefore, the measurement device can
only be applied to situations where photopic vision occurs, thus for lumina=
nce
values greater than 3 cd/m2 [31].
To calculate the luminance from an RGB HDR image=
the
CCT is required. A default CCT of 6500 K (D65) is a good solution when the =
main
light source is daylight. However, for CCTs far from 6500 K (i.e., blue sky)
this might lead to methodological errors up to 18%. In this study, three
reference CCT¡¯s were applied to limit this error to approximately 5%. A
downside of this is the required user intervention. This intervention will
result in some uncertainties, possibly increasing the inaccuracy. However, =
the
maximum methodological error will never exceed 18%.
It seems that in some other studies the vignetti=
ng
filter was based on a single measurement, resulting in extremely good fits =
[11,26]. This research showed that the vignetting
correction needs to be based on multiple measurements because the vignetting
effect displayed differences up to 20% under ¡®constant¡¯ conditions. The
vignetting effect close to the periphery was only limited to 14% by fitting=
to
data achieved by multiple measurements. The accuracy of most of the image w=
as
improved by slightly compromising the accuracy close to its periphery. This=
is
motivated by the fact that most information is extracted from the center pa=
rt
of the image, and not from its boundaries. Apparently, the conditions were =
not
entirely constant during these measurements, but due to the application of =
an
optimized vignetting filter the usability of the camera-lens system with
limited capabilities was improved. Nevertheless, it is still reasonable to
perform multiple measurements in all cases of vignetting effect measurement=
s to
achieve an optimal overall vignetting correction.
The calibration factor was determined for white =
and
gray targets to further increase the overall measurement accuracy. The expo=
sure
sequences both had their own calibration factor because different exposure
sequences of the exact same scene showed that the absolute Y tristimulus va=
lues
differed.
The time needed to perform the entire process was
33.7 s, meaning that it is possible to perform nearly 2 measurements within=
a
minute. For this study, measurements were performed every 5 min. The actual
time necessary to take the LDR images was the time that the device was
vulnerable to transient conditions. This was approximately 8 s, compared to=
3
min required for a sky scanner [32–34], and 1-2 min for HDR camera system measurement =
[8].
The accuracy was determined with the Hagner Univ=
ersal
Photometer S2, which itself has an accuracy of ¡¾5%. This means that the ac=
tual
accuracy of the luminance distribution measurement device could deviate ¡¾5=
%. By
taking the inaccuracy of the Hagner Universal Photometer into account the
average accuracy of the developed device was in the range of: 5.1% - 15.1%,=
3%
- 13.0% and 7.5% - 17.5% for respectively all targets, gray targets, and
colored targets. Even in the worst case scenario, this falls within the ran=
ge
of accuracies, ¡¾5% to ¡¾20%, found in other similar studies using more
sophisticated devices [11,14]. Thereby, this device performs along a similar
trend, higher accuracy for gray targets compared to colored targets, as fou=
nd
by Inanici [11].
3.
Conclusions
And Recommendations
3.1.=
Conclusions
The luminance distribution was determined based =
on
the similarity of the CIE color matching function ȳ(¥ë) and the sensit=
ivity
curve of the human eye, including some corrections. The CIE Y tristimulus v=
alue
channel was achieved by translating the RGB information of the High Dynamic
Range (HDR) image to the CIE XYZ color space. This was done using three
conversion matrices each representing an illuminant with a particular CCT. =
The
High Dynamic Range technology was essential to accurately capture the lumin=
ance
distribution because it is, in contrast to standard 8-bit images, able to c=
apture
the entire dynamic range that occurs in real scenarios. Finally, the lumina=
nce
distribution was represented according to Tregenza¡¯s subdivision.
The process of determining the luminance
distribution was conducted using a Raspberry Pi (with camera board) as a
single-board computer, which was able to perform all calculations
automatically. The device can operate autonomously. The best performance was acquired =
when
the user selected the suitable reference CCT at the start of the measurement
and changing this when the conditions had changed. The results were
automatically digitalized and uploaded to a server. The accuracy of the dev=
ice
falls within an acceptable range with an average accuracy ranging from 5.1%=
to
15.1% and an average accuracy range of 3.0% to 13.0% and 7.5% to 17.5% for
respectively gray and colored targets. All of this was achieved with low co=
sts
components.
The device in its current form is tested within a
limited performance range. Reliable results could only be guaranteed within=
a
luminance range from 3 to 18,000 cd/m2. Measurements showed that=
for
luminance values somewhere over 18,000 cd/m2 the results became
unreliable due to saturation of the shortest exposure. Therefore, the
measurement range was limited to 3-18,000 cd/m2, the actual maxi=
mum
luminance limit might be higher.
3.2.=
Recommendations
The device can potentially be further optimized =
by
applying some additional improvements that are subject to further research.=
In this study, two different exposure sequences =
were
used, being the optimal sequence for a limited set of conditions. To improve
the quality of the HDR image it is recommended to determine the exposure
sequence specifically for each condition. This prevents saturated images,
meaning that all nine exposures are evenly distributed within the occurring
luminance range.
The current device was limited to a maximum
luminance of 18,000 cd/mF. This was because high luminance values
lead to application of saturation of the shortest exposure time. The shutter
speed cannot be further shortened but a neutral density filter is a possibi=
lity
[30]. This way the current dynamic range can be shif=
ted
towards longer exposures and the shorter exposures can be used to capture
higher luminance values. Disadvantages are that for darker conditions the
exposure time becomes significantly higher, whereby the influence of transi=
ent
processes increases. This can potentially be accounted for by adding an ext=
ra
camera to the measurement device.
The fixed focal length limited the capture of a =
full
hemispherical view. There are two methods available to overcome this. A cam=
era
with an adjustable focal length can be used to fit the entire hemispherical
view on the image sensor. However, in the case of the Raspberry Pi, this me=
ans
that the fisheye lens cannot be placed in front of the camera as was done h=
ere.
Another option could be using two cameras which are rotated 90¡Æ compared to
each other. This way the entire hemispherical view is captured and fisheye
lenses can still be applied. It is recommended to test both suggestions, and
compare it with the original set-up.
The usability of the measurement device can be
expanded via the connection to networks, i.e., communication and interaction
using an SSH protocol. An automated start-up of the luminance distribution
calculation could be incorporated in the code. The next step in providing a
useful representation could be a false color representation instead of
Tregenza¡¯s subdivision. A false color representation can provide an intuit=
ive
and quick understanding of the measurement results.
Acknowledgements
The author(s) received no financial support for =
the
research, authorship, and/or publication of this article
References
[1] Spasojević, B., & Mahdavi, A. (2=
005,
August). Sky luminance mapping for computational daylight modeling. In
Proceedings of the 9th international Building Performance Simulation
Association Conference, Montreal–Canada (Vol. 1163).
[2] Inanici, M. (2010). Evalution of high dyn=
amic
range image-based sky models in lighting simulation. Leukos, 7(2), 69-84.
[3] CIE. (2014). CIE Standard General Sky Gui=
de.
Vienna, Austria.
[4] Kobav, M. B., & Dumortier, D. (2007).=
Use
of a digital camera as a sky luminance scanner. 26th Session of the CIE.
[5] Wüller, D., & Gabele, H. (2007, =
January).
The usage of digital cameras as luminance meters. In Proc. SPIE (Vol. 6502, p. 65020U).
[6] Spas=
ojević,
B., & Mahdavi, A. (2007). Calibrated sky luminance m=
aps
for advanced daylight simulation applications. In Proceedings of the 10th
International Building Performance Simulation Association Conference and
Exhibition (BS2007), Beijing, China (pp. 1205-1210).
[7] Arie=
s, M.
B. C., & Zonneveldt, L. (2011). Daylight variations in a
moderate climate as input for lighting controls.
[8] Chiou, Y. S., & Huang, P. C. (2015). =
An
HDRi-based data acquisition system for the exterior luminous environment in=
the
daylight simulation model. Solar Energy, 111, 104-117.
[9] Mead, A. R., & Mosalam, K. M. (2016).
Ubiquitous luminance sensing using the Raspberry Pi and Camera Module syste=
m.
Lighting Research & Technology, 1477153516649229.
[10] Bellia, L., Cesarano, A., Iuliano, G. F., &=
amp;
Spada, G. (2009, May). HDR luminance mapping analysis system for visual com=
fort
evaluation. In Instrumentation and Measurement Technology Conference, 2009.
I2MTC'09. IEEE (pp. 957-961). IEEE.
[11] Inanici, M. N. (2006). Evaluation of high
dynamic range photography as a luminance data acquisition system. Lighting
Research & Technology, 38(2), 123-134.
[12]Sarkar,
A., & Mistrick, R. G. (2006). A novel lighting control system integrati=
ng
high dynamic range imaging and DALI. Leuko=
s,
2(4), 307-322.
[13] Tohsing, K., Schrempf, M., Riechelmann, S.,
Schilke, H., & Seckmeyer, G. (2013). Measuring
high-resolution sky luminance distributions with a CCD camera. Applied opti=
cs,
52(8), 1564-1573.
[14] Moeck, M. (2007). Accuracy of luminance maps
obtained from high dynamic range images. Leukos, 4(2), 99-112.
[15] Schneider, D., Schwalbe, E., & Maas, H.=
G.
(2009). Validation of geometric models for fisheye lenses. ISPRS Journal of
Photogrammetry and Remote Sensing, 64(3), 259-266.
[16] Tregenza, P. R. (1987). Subdivision of the =
sky
hemisphere for luminance measurements. Lighting Research & Technology,
19(1), 13-14.
[17] Moeck, M., & Anaokar, S. (2006).
Illuminance analysis from high dynamic range images. Leukos, 2(3), 211-228.=
[18] Reinhard, E., Heidrich, W., Debevec, P.,
Pattanaik, S., Ward, G., & Myszkowski, K. (2010). High dynamic range
imaging: acquisition, display, and image-based lighting. Morgan Kaufmann.
[19] Cai, H., & Chung, T. M. (2011). Improvi=
ng
the quality of high dynamic range images. Lighting Research and Technology,
43(1), 87-102.
[20] Ward, G. (2005). Photosphere, Anyhere Softw=
are.
[21] Holzer, B. (2006). High dynamic range image
formats. Institute for Computer Graphics and Algorithms, TU Wien.
[22] Mitsunaga, T., & Nayar, S. K. (1999).
Radiometric self calibration. In Computer Vision and Pattern Recognition, 1=
999.
IEEE Computer Society Conference on. (Vol. 1, pp. 374-380). IEEE.
[23] Schanda, J. (Ed.). (2007). Colorimetry:
understanding the CIE system. John Wiley & Sons.
[24] Roy, G. G., Hayman, S., & Julian, W.
(1998). Sky modeling from digital imagery. ARC Project A, 89530177.
[25] Cai, H. (2013). High dynamic range
photogrammetry for synchronous luminance and geometry measurement. Lighting
Research & Technology, 45(2), 230-257.
[26] Cauwerts, C., PhD, M. B., & Deneyer, A.
(2012). Comparison of the vignetting effects of two identical fisheye lense=
s.
LEUKOS, 8(3), 181-203.
[27]
Inanici, M.N., & Viswanathan, K. (2013). Hdrscope : High Dynamic =
Range
Image Processing Toolkit for Per-Pixel Lighting Analysis and Hdrscope =
;: Lighting
Analysis. 13th Conference of International Building Performance Simulation
Association, Chambéry, France, 3400-3407.
[28] Moore, T., Graves, H., Perry, M. J., &
Carter, D. J. (2000). Approximate field measurement of surface luminance us=
ing
a digital camera. International Journal of Lighting Research and Technology,
32(1), 1-11.
[29]
Ulbricht, R. (1920). Das Kugelphotometer. Berlin Und Munchen: Verlag Oldenb=
urg.
[30] Stumpfel, J., Tchou, C., Jones, A., Hawkins,
T., Wenger, A., & Debevec, P. (2004, November). Direct HDR capture of t=
he
sun and sky. In Proceedings of the 3rd international conference on Computer
graphics, virtual reality, visualisation and interaction in Africa (pp.
145-149). ACM.
[31]
Baer, R., Seifert, D., & Barfu©¬, M. (2016). Beleuchtungstechnik. (4th
editio). Berlin: HUSS-MEDIEN GmbH.
[32]
Coutelier, B., & Dumortier, D. (2002).Luminance calibration of the Nikon
Coolpix 990 digital camera. Application to glare evaluation. AIVC and EPIC
Conference, Lyon, France.
[33] Kobav, M. B., Bizjak, G., & Dumortier, =
D.
(2013). Characterization of sky scanner measurements based on CIE and ISO
standard CIE S 011/2003. Lighting Research & Technology, 45(4), 504-512=
.
[34] Ineichen, P., & Molineaux, B. (1993,
August). Characterisation and comparison of two sky scanners: PRC Krochmann=
and
EKO instruments. In First draft, IEA Task XVII expert meeting.
T. Kruisselbrink =
et
al. /International Journal of Sustainable Lighting 20 (2017) 75-90