# [argyllcms] Re: A better way to measure paper white?

• From: Gerhard Fuernkranz <nospam456@xxxxxx>
• To: argyllcms@xxxxxxxxxxxxx
• Date: Sat, 31 Oct 2009 20:35:53 +0100

```Omari Stephens wrote:
> Err... four strobes?  That seems like serious overkill.  How far is
> the target from your lens, and what focal length and exposure settings
> are you using?  I would expect a single strobe shooting directly at
> the target to be able to illuminate it properly and without any
> noticeable fall-off — unless you're using a giant target, the flash's
> hotspot should be able to cover it easily.

Well, in order to achieve a good illuminance uniformity, I would also
recommend a symmetric setup with (at least) two equal light sources. A
single light source is IMO only sufficient if

* the target can be illuminated under a steep angle
[ optimally orthogonal to the surface - but this is rather not an
option due to specular reflections ]

* or otherwise (using a flatter angle) only if the distance between
target and light source is VERY LARGE

[ For instance, a distance of about 150(!) times the width of the
target is necessary to achieve 1% illuminance uniformity, when
using a single point source and 45° illumination angle:

# note: 1/sqrt(2) = sin(45°) = cos(45°)
octave:6> x = z = 150/sqrt(2); ((x-0.5)^2+z^2)/((x+0.5)^2+z^2)
ans = 0.99062 (==> 1% between brighter and darker edge)

The sun as a single light source would certainly meet this
criterion :-)
Clouds or reflections from nearby other object may still disturb
uniformity though, so one still needs to be careful when
photographing a target under sun light ]

* and the target is perfectly flat
[ multiple light sources also reduce (compensate) the impacts of a
non-flat, slightly curved surface ]

In order to get a feeling for the impact of the illumination setup on
the uniformity, please find below a simple illustration of the spatiall
illuminance distribution across a target,

* a) for a single light source (coming only from left) and
* b) for two symmetric light sources (coming from left and right),
* for different distances between target and light source(s)
1 x width of the target ... 10 x width of the target
* assuming a 45° illumination angle,
* making the simplified assumption that the light sources are point
sources (thus having the property that the illuminance is
proportional to 1/d^2, where d is the distance from the light source),
* and assuming that the whole setup is located in a dark room with
infinite size, so that the result is not affected by any
reflections in the room.

[ Light sources with a larger diameter (say diameter > 0.1 * distance -
e.g. flash or lamp with large diffuser) will likely result in better
uniformity than point sources. Reflections in a real-world room can
improve or deteriorate the uniformity - however the effect will be hard
to predict. ]

Example result picked from below:
In order to obtain a uniformity of better than 1%, with a 45° two-lamp
setup, a distance between each lamp and the center of the target of >= 7
x width of the target is required. On the other hand, with a single lamp
and the same angle and distance, only a uniformity of ~20% is achieved.

Regards,
Gerhard

-------------------------------------------------------------------------------
Angle = 45.0
Distance lamp(s) <-> center of target = 1.0 x target width:
Spatial illuminace distribution across the target =>
(illuminace at the points of a 11x9 grid covering the target area)

I_one_lamp =

142.3  132.6  121.1  109.0   97.2   86.2   76.3   67.4   59.7   53.0
47.2
158.0  146.1  132.3  118.0  104.3   91.7   80.6   70.8   62.3   55.1
48.8
171.6  157.7  141.7  125.4  110.1   96.2   83.9   73.4   64.3   56.6
50.1
180.9  165.5  148.0  130.4  113.8   99.0   86.1   75.0   65.6   57.6
50.8
184.2  168.3  150.2  132.1  115.1  100.0   86.8   75.6   66.0   57.9
51.1
180.9  165.5  148.0  130.4  113.8   99.0   86.1   75.0   65.6   57.6
50.8
171.6  157.7  141.7  125.4  110.1   96.2   83.9   73.4   64.3   56.6
50.1
158.0  146.1  132.3  118.0  104.3   91.7   80.6   70.8   62.3   55.1
48.8
142.3  132.6  121.1  109.0   97.2   86.2   76.3   67.4   59.7   53.0
47.2

I_two_lamps =

94.8   92.8   90.4   88.2   86.7   86.2   86.7   88.2   90.4   92.8
94.8
103.4  100.6   97.3   94.4   92.4   91.7   92.4   94.4   97.3  100.6
103.4
110.8  107.1  103.0   99.4   97.0   96.2   97.0   99.4  103.0  107.1
110.8
115.9  111.5  106.8  102.7  100.0   99.0  100.0  102.7  106.8  111.5
115.9
117.6  113.1  108.1  103.8  101.0  100.0  101.0  103.8  108.1  113.1
117.6
115.9  111.5  106.8  102.7  100.0   99.0  100.0  102.7  106.8  111.5
115.9
110.8  107.1  103.0   99.4   97.0   96.2   97.0   99.4  103.0  107.1
110.8
103.4  100.6   97.3   94.4   92.4   91.7   92.4   94.4   97.3  100.6
103.4
94.8   92.8   90.4   88.2   86.7   86.2   86.7   88.2   90.4   92.8
94.8

Center      = 100 %
One-Lamp:
Darkest   = 47.23 %
Brightest = 184.20 %
Max - Min = 136.96 % (non-uniformity)
Two-Lamp:
Darkest   = 86.21 %
Brightest = 117.65 %
Max - Min = 31.44 % (non-uniformity)

-------------------------------------------------------------------------------
Angle = 45.0
Distance lamp(s) <-> center of target = 2.0 x target width:
Spatial illuminace distribution across the target =>
(illuminace at the points of a 11x9 grid covering the target area)

I_one_lamp =

133.5  125.4  117.6  110.1  102.9   96.2   89.8   83.9   78.5   73.4
68.7
136.7  128.3  120.1  112.2  104.8   97.8   91.3   85.2   79.5   74.3
69.5
139.1  130.4  121.9  113.8  106.2   99.0   92.3   86.1   80.3   75.0
70.1
140.6  131.6  123.0  114.8  107.0   99.8   93.0   86.7   80.8   75.5
70.5
141.1  132.1  123.4  115.1  107.3  100.0   93.2   86.8   81.0   75.6
70.6
140.6  131.6  123.0  114.8  107.0   99.8   93.0   86.7   80.8   75.5
70.5
139.1  130.4  121.9  113.8  106.2   99.0   92.3   86.1   80.3   75.0
70.1
136.7  128.3  120.1  112.2  104.8   97.8   91.3   85.2   79.5   74.3
69.5
133.5  125.4  117.6  110.1  102.9   96.2   89.8   83.9   78.5   73.4
68.7

I_two_lamps =

101.1   99.4   98.0   97.0   96.4   96.2   96.4   97.0   98.0   99.4
101.1
103.1  101.3   99.8   98.7   98.0   97.8   98.0   98.7   99.8  101.3
103.1
104.6  102.7  101.1  100.0   99.2   99.0   99.2  100.0  101.1  102.7
104.6
105.5  103.5  101.9  100.7  100.0   99.8  100.0  100.7  101.9  103.5
105.5
105.8  103.8  102.2  101.0  100.2  100.0  100.2  101.0  102.2  103.8
105.8
105.5  103.5  101.9  100.7  100.0   99.8  100.0  100.7  101.9  103.5
105.5
104.6  102.7  101.1  100.0   99.2   99.0   99.2  100.0  101.1  102.7
104.6
103.1  101.3   99.8   98.7   98.0   97.8   98.0   98.7   99.8  101.3
103.1
101.1   99.4   98.0   97.0   96.4   96.2   96.4   97.0   98.0   99.4
101.1

Center      = 100 %
One-Lamp:
Darkest   = 68.68 %
Brightest = 141.05 %
Max - Min = 72.38 % (non-uniformity)
Two-Lamp:
Darkest   = 96.15 %
Brightest = 105.84 %
Max - Min = 9.68 % (non-uniformity)

-------------------------------------------------------------------------------
Angle = 45.0
Distance lamp(s) <-> center of target = 3.0 x target width:
Spatial illuminace distribution across the target =>
(illuminace at the points of a 11x9 grid covering the target area)

I_one_lamp =

123.5  118.1  112.8  107.8  102.9   98.3   93.8   89.6   85.5   81.7
78.0
124.7  119.2  113.8  108.7  103.7   99.0   94.5   90.2   86.1   82.2
78.5
125.5  120.0  114.5  109.3  104.3   99.6   95.0   90.6   86.5   82.6
78.9
126.1  120.4  115.0  109.7  104.7   99.9   95.3   90.9   86.8   82.8
79.1
126.3  120.6  115.1  109.9  104.8  100.0   95.4   91.0   86.8   82.9
79.1
126.1  120.4  115.0  109.7  104.7   99.9   95.3   90.9   86.8   82.8
79.1
125.5  120.0  114.5  109.3  104.3   99.6   95.0   90.6   86.5   82.6
78.9
124.7  119.2  113.8  108.7  103.7   99.0   94.5   90.2   86.1   82.2
78.5
123.5  118.1  112.8  107.8  102.9   98.3   93.8   89.6   85.5   81.7
78.0

I_two_lamps =

100.8   99.9   99.2   98.7   98.4   98.3   98.4   98.7   99.2   99.9
100.8
101.6  100.7  100.0   99.4   99.1   99.0   99.1   99.4  100.0  100.7
101.6
102.2  101.3  100.5  100.0   99.7   99.6   99.7  100.0  100.5  101.3
102.2
102.6  101.6  100.9  100.3  100.0   99.9  100.0  100.3  100.9  101.6
102.6
102.7  101.7  101.0  100.4  100.1  100.0  100.1  100.4  101.0  101.7
102.7
102.6  101.6  100.9  100.3  100.0   99.9  100.0  100.3  100.9  101.6
102.6
102.2  101.3  100.5  100.0   99.7   99.6   99.7  100.0  100.5  101.3
102.2
101.6  100.7  100.0   99.4   99.1   99.0   99.1   99.4  100.0  100.7
101.6
100.8   99.9   99.2   98.7   98.4   98.3   98.4   98.7   99.2   99.9
100.8

Center      = 100 %
One-Lamp:
Darkest   = 78.05 %
Brightest = 126.25 %
Max - Min = 48.20 % (non-uniformity)
Two-Lamp:
Darkest   = 98.25 %
Brightest = 102.70 %
Max - Min = 4.45 % (non-uniformity)

-------------------------------------------------------------------------------
Angle = 45.0
Distance lamp(s) <-> center of target = 4.0 x target width:
Spatial illuminace distribution across the target =>
(illuminace at the points of a 11x9 grid covering the target area)

I_one_lamp =

117.8  113.8  109.9  106.2  102.5   99.0   95.6   92.3   89.2   86.1
83.2
118.4  114.4  110.5  106.7  103.0   99.4   96.0   92.7   89.5   86.4
83.5
118.9  114.8  110.9  107.0  103.3   99.8   96.3   93.0   89.8   86.7
83.7
119.1  115.0  111.1  107.2  103.5   99.9   96.5   93.1   89.9   86.8
83.8
119.2  115.1  111.2  107.3  103.6  100.0   96.5   93.2   90.0   86.8
83.9
119.1  115.0  111.1  107.2  103.5   99.9   96.5   93.1   89.9   86.8
83.8
118.9  114.8  110.9  107.0  103.3   99.8   96.3   93.0   89.8   86.7
83.7
118.4  114.4  110.5  106.7  103.0   99.4   96.0   92.7   89.5   86.4
83.5
117.8  113.8  109.9  106.2  102.5   99.0   95.6   92.3   89.2   86.1
83.2

I_two_lamps =

100.5  100.0   99.5   99.2   99.1   99.0   99.1   99.2   99.5  100.0
100.5
100.9  100.4  100.0   99.7   99.5   99.4   99.5   99.7  100.0  100.4
100.9
101.3  100.7  100.3  100.0   99.8   99.8   99.8  100.0  100.3  100.7
101.3
101.5  100.9  100.5  100.2  100.0   99.9  100.0  100.2  100.5  100.9
101.5
101.5  101.0  100.6  100.2  100.1  100.0  100.1  100.2  100.6  101.0
101.5
101.5  100.9  100.5  100.2  100.0   99.9  100.0  100.2  100.5  100.9
101.5
101.3  100.7  100.3  100.0   99.8   99.8   99.8  100.0  100.3  100.7
101.3
100.9  100.4  100.0   99.7   99.5   99.4   99.5   99.7  100.0  100.4
100.9
100.5  100.0   99.5   99.2   99.1   99.0   99.1   99.2   99.5  100.0
100.5

Center      = 100 %
One-Lamp:
Darkest   = 83.17 %
Brightest = 119.21 %
Max - Min = 36.04 % (non-uniformity)
Two-Lamp:
Darkest   = 99.01 %
Brightest = 101.54 %
Max - Min = 2.53 % (non-uniformity)

-------------------------------------------------------------------------------
Angle = 45.0
Distance lamp(s) <-> center of target = 5.0 x target width:
Spatial illuminace distribution across the target =>
(illuminace at the points of a 11x9 grid covering the target area)

I_one_lamp =

114.3  111.2  108.1  105.1  102.2   99.4   96.6   93.9   91.3   88.8
86.4
114.7  111.5  108.4  105.4  102.5   99.6   96.9   94.2   91.6   89.0
86.6
114.9  111.7  108.7  105.6  102.7   99.8   97.1   94.4   91.7   89.2
86.7
115.1  111.9  108.8  105.8  102.8  100.0   97.2   94.5   91.8   89.3
86.8
115.1  111.9  108.8  105.8  102.9  100.0   97.2   94.5   91.9   89.3
86.8
115.1  111.9  108.8  105.8  102.8  100.0   97.2   94.5   91.8   89.3
86.8
114.9  111.7  108.7  105.6  102.7   99.8   97.1   94.4   91.7   89.2
86.7
114.7  111.5  108.4  105.4  102.5   99.6   96.9   94.2   91.6   89.0
86.6
114.3  111.2  108.1  105.1  102.2   99.4   96.6   93.9   91.3   88.8
86.4

I_two_lamps =

100.3  100.0   99.7   99.5   99.4   99.4   99.4   99.5   99.7  100.0
100.3
100.6  100.3  100.0   99.8   99.7   99.6   99.7   99.8  100.0  100.3
100.6
100.8  100.5  100.2  100.0   99.9   99.8   99.9  100.0  100.2  100.5
100.8
100.9  100.6  100.3  100.1  100.0  100.0  100.0  100.1  100.3  100.6
100.9
101.0  100.6  100.4  100.2  100.0  100.0  100.0  100.2  100.4  100.6
101.0
100.9  100.6  100.3  100.1  100.0  100.0  100.0  100.1  100.3  100.6
100.9
100.8  100.5  100.2  100.0   99.9   99.8   99.9  100.0  100.2  100.5
100.8
100.6  100.3  100.0   99.8   99.7   99.6   99.7   99.8  100.0  100.3
100.6
100.3  100.0   99.7   99.5   99.4   99.4   99.4   99.5   99.7  100.0
100.3

Center      = 100 %
One-Lamp:
Darkest   = 86.37 %
Brightest = 115.13 %
Max - Min = 28.76 % (non-uniformity)
Two-Lamp:
Darkest   = 99.36 %
Brightest = 100.99 %
Max - Min = 1.63 % (non-uniformity)

-------------------------------------------------------------------------------
Angle = 45.0
Distance lamp(s) <-> center of target = 6.0 x target width:
Spatial illuminace distribution across the target =>
(illuminace at the points of a 11x9 grid covering the target area)

I_one_lamp =

111.9  109.3  106.8  104.3  101.9   99.6   97.2   95.0   92.8   90.6
88.6
112.2  109.6  107.0  104.6  102.1   99.8   97.4   95.2   93.0   90.8
88.7
112.3  109.7  107.2  104.7  102.3   99.9   97.6   95.3   93.1   90.9
88.8
112.4  109.8  107.3  104.8  102.4  100.0   97.6   95.4   93.2   91.0
88.9
112.5  109.9  107.3  104.8  102.4  100.0   97.7   95.4   93.2   91.0
88.9
112.4  109.8  107.3  104.8  102.4  100.0   97.6   95.4   93.2   91.0
88.9
112.3  109.7  107.2  104.7  102.3   99.9   97.6   95.3   93.1   90.9
88.8
112.2  109.6  107.0  104.6  102.1   99.8   97.4   95.2   93.0   90.8
88.7
111.9  109.3  106.8  104.3  101.9   99.6   97.2   95.0   92.8   90.6
88.6

I_two_lamps =

100.2  100.0   99.8   99.7   99.6   99.6   99.6   99.7   99.8  100.0
100.2
100.4  100.2  100.0   99.9   99.8   99.8   99.8   99.9  100.0  100.2
100.4
100.6  100.3  100.1  100.0   99.9   99.9   99.9  100.0  100.1  100.3
100.6
100.7  100.4  100.2  100.1  100.0  100.0  100.0  100.1  100.2  100.4
100.7
100.7  100.4  100.2  100.1  100.0  100.0  100.0  100.1  100.2  100.4
100.7
100.7  100.4  100.2  100.1  100.0  100.0  100.0  100.1  100.2  100.4
100.7
100.6  100.3  100.1  100.0   99.9   99.9   99.9  100.0  100.1  100.3
100.6
100.4  100.2  100.0   99.9   99.8   99.8   99.8   99.9  100.0  100.2
100.4
100.2  100.0   99.8   99.7   99.6   99.6   99.6   99.7   99.8  100.0
100.2

Center      = 100 %
One-Lamp:
Darkest   = 88.56 %
Brightest = 112.47 %
Max - Min = 23.92 % (non-uniformity)
Two-Lamp:
Darkest   = 99.56 %
Brightest = 100.69 %
Max - Min = 1.13 % (non-uniformity)

-------------------------------------------------------------------------------
Angle = 45.0
Distance lamp(s) <-> center of target = 7.0 x target width:
Spatial illuminace distribution across the target =>
(illuminace at the points of a 11x9 grid covering the target area)

I_one_lamp =

110.2  108.0  105.9  103.8  101.7   99.7   97.7   95.7   93.8   92.0
90.1
110.4  108.2  106.0  103.9  101.8   99.8   97.8   95.9   94.0   92.1
90.3
110.5  108.3  106.2  104.0  102.0   99.9   97.9   96.0   94.1   92.2
90.3
110.6  108.4  106.2  104.1  102.0  100.0   98.0   96.0   94.1   92.2
90.4
110.6  108.4  106.2  104.1  102.0  100.0   98.0   96.0   94.1   92.2
90.4
110.6  108.4  106.2  104.1  102.0  100.0   98.0   96.0   94.1   92.2
90.4
110.5  108.3  106.2  104.0  102.0   99.9   97.9   96.0   94.1   92.2
90.3
110.4  108.2  106.0  103.9  101.8   99.8   97.8   95.9   94.0   92.1
90.3
110.2  108.0  105.9  103.8  101.7   99.7   97.7   95.7   93.8   92.0
90.1

I_two_lamps =

100.2  100.0   99.9   99.8   99.7   99.7   99.7   99.8   99.9  100.0
100.2
100.3  100.1  100.0   99.9   99.8   99.8   99.8   99.9  100.0  100.1
100.3
100.4  100.2  100.1  100.0   99.9   99.9   99.9  100.0  100.1  100.2
100.4
100.5  100.3  100.2  100.1  100.0  100.0  100.0  100.1  100.2  100.3
100.5
100.5  100.3  100.2  100.1  100.0  100.0  100.0  100.1  100.2  100.3
100.5
100.5  100.3  100.2  100.1  100.0  100.0  100.0  100.1  100.2  100.3
100.5
100.4  100.2  100.1  100.0   99.9   99.9   99.9  100.0  100.1  100.2
100.4
100.3  100.1  100.0   99.9   99.8   99.8   99.8   99.9  100.0  100.1
100.3
100.2  100.0   99.9   99.8   99.7   99.7   99.7   99.8   99.9  100.0
100.2

Center      = 100 %
One-Lamp:
Darkest   = 90.14 %
Brightest = 110.61 %
Max - Min = 20.47 % (non-uniformity)
Two-Lamp:
Darkest   = 99.67 %
Brightest = 100.51 %
Max - Min = 0.83 % (non-uniformity)

-------------------------------------------------------------------------------
Angle = 45.0
Distance lamp(s) <-> center of target = 8.0 x target width:
Spatial illuminace distribution across the target =>
(illuminace at the points of a 11x9 grid covering the target area)

I_one_lamp =

108.9  107.0  105.2  103.3  101.5   99.8   98.0   96.3   94.6   93.0
91.3
109.1  107.2  105.3  103.4  101.6   99.9   98.1   96.4   94.7   93.1
91.4
109.2  107.2  105.4  103.5  101.7   99.9   98.2   96.5   94.8   93.1
91.5
109.2  107.3  105.4  103.6  101.8  100.0   98.2   96.5   94.8   93.2
91.5
109.2  107.3  105.4  103.6  101.8  100.0   98.2   96.5   94.8   93.2
91.6
109.2  107.3  105.4  103.6  101.8  100.0   98.2   96.5   94.8   93.2
91.5
109.2  107.2  105.4  103.5  101.7   99.9   98.2   96.5   94.8   93.1
91.5
109.1  107.2  105.3  103.4  101.6   99.9   98.1   96.4   94.7   93.1
91.4
108.9  107.0  105.2  103.3  101.5   99.8   98.0   96.3   94.6   93.0
91.3

I_two_lamps =

100.1  100.0   99.9   99.8   99.8   99.8   99.8   99.8   99.9  100.0
100.1
100.2  100.1  100.0   99.9   99.9   99.9   99.9   99.9  100.0  100.1
100.2
100.3  100.2  100.1  100.0  100.0   99.9  100.0  100.0  100.1  100.2
100.3
100.4  100.2  100.1  100.0  100.0  100.0  100.0  100.0  100.1  100.2
100.4
100.4  100.2  100.1  100.1  100.0  100.0  100.0  100.1  100.1  100.2
100.4
100.4  100.2  100.1  100.0  100.0  100.0  100.0  100.0  100.1  100.2
100.4
100.3  100.2  100.1  100.0  100.0   99.9  100.0  100.0  100.1  100.2
100.3
100.2  100.1  100.0   99.9   99.9   99.9   99.9   99.9  100.0  100.1
100.2
100.1  100.0   99.9   99.8   99.8   99.8   99.8   99.8   99.9  100.0
100.1

Center      = 100 %
One-Lamp:
Darkest   = 91.34 %
Brightest = 109.23 %
Max - Min = 17.89 % (non-uniformity)
Two-Lamp:
Darkest   = 99.75 %
Brightest = 100.39 %
Max - Min = 0.64 % (non-uniformity)

-------------------------------------------------------------------------------
Angle = 45.0
Distance lamp(s) <-> center of target = 9.0 x target width:
Spatial illuminace distribution across the target =>
(illuminace at the points of a 11x9 grid covering the target area)

I_one_lamp =

107.9  106.3  104.6  103.0  101.4   99.8   98.2   96.7   95.2   93.7
92.3
108.0  106.4  104.7  103.1  101.5   99.9   98.3   96.8   95.3   93.8
92.4
108.1  106.4  104.8  103.1  101.5  100.0   98.4   96.9   95.4   93.9
92.4
108.1  106.5  104.8  103.2  101.6  100.0   98.4   96.9   95.4   93.9
92.4
108.2  106.5  104.8  103.2  101.6  100.0   98.4   96.9   95.4   93.9
92.5
108.1  106.5  104.8  103.2  101.6  100.0   98.4   96.9   95.4   93.9
92.4
108.1  106.4  104.8  103.1  101.5  100.0   98.4   96.9   95.4   93.9
92.4
108.0  106.4  104.7  103.1  101.5   99.9   98.3   96.8   95.3   93.8
92.4
107.9  106.3  104.6  103.0  101.4   99.8   98.2   96.7   95.2   93.7
92.3

I_two_lamps =

100.1  100.0   99.9   99.9   99.8   99.8   99.8   99.9   99.9  100.0
100.1
100.2  100.1  100.0   99.9   99.9   99.9   99.9   99.9  100.0  100.1
100.2
100.3  100.1  100.1  100.0  100.0  100.0  100.0  100.0  100.1  100.1
100.3
100.3  100.2  100.1  100.0  100.0  100.0  100.0  100.0  100.1  100.2
100.3
100.3  100.2  100.1  100.0  100.0  100.0  100.0  100.0  100.1  100.2
100.3
100.3  100.2  100.1  100.0  100.0  100.0  100.0  100.0  100.1  100.2
100.3
100.3  100.1  100.1  100.0  100.0  100.0  100.0  100.0  100.1  100.1
100.3
100.2  100.1  100.0   99.9   99.9   99.9   99.9   99.9  100.0  100.1
100.2
100.1  100.0   99.9   99.9   99.8   99.8   99.8   99.9   99.9  100.0
100.1

Center      = 100 %
One-Lamp:
Darkest   = 92.28 %
Brightest = 108.16 %
Max - Min = 15.88 % (non-uniformity)
Two-Lamp:
Darkest   = 99.80 %
Brightest = 100.31 %
Max - Min = 0.50 % (non-uniformity)

-------------------------------------------------------------------------------
Angle = 45.0
Distance lamp(s) <-> center of target = 10.0 x target width:
Spatial illuminace distribution across the target =>
(illuminace at the points of a 11x9 grid covering the target area)

I_one_lamp =

107.1  105.6  104.2  102.7  101.3   99.8   98.4   97.1   95.7   94.4
93.0
107.2  105.7  104.2  102.8  101.3   99.9   98.5   97.1   95.8   94.4
93.1
107.3  105.8  104.3  102.8  101.4  100.0   98.6   97.2   95.8   94.5
93.1
107.3  105.8  104.3  102.9  101.4  100.0   98.6   97.2   95.8   94.5
93.2
107.3  105.8  104.3  102.9  101.4  100.0   98.6   97.2   95.8   94.5
93.2
107.3  105.8  104.3  102.9  101.4  100.0   98.6   97.2   95.8   94.5
93.2
107.3  105.8  104.3  102.8  101.4  100.0   98.6   97.2   95.8   94.5
93.1
107.2  105.7  104.2  102.8  101.3   99.9   98.5   97.1   95.8   94.4
93.1
107.1  105.6  104.2  102.7  101.3   99.8   98.4   97.1   95.7   94.4
93.0

I_two_lamps =

100.1  100.0   99.9   99.9   99.9   99.8   99.9   99.9   99.9  100.0
100.1
100.2  100.1  100.0   99.9   99.9   99.9   99.9   99.9  100.0  100.1
100.2
100.2  100.1  100.0  100.0  100.0  100.0  100.0  100.0  100.0  100.1
100.2
100.2  100.1  100.1  100.0  100.0  100.0  100.0  100.0  100.1  100.1
100.2
100.2  100.2  100.1  100.0  100.0  100.0  100.0  100.0  100.1  100.2
100.2
100.2  100.1  100.1  100.0  100.0  100.0  100.0  100.0  100.1  100.1
100.2
100.2  100.1  100.0  100.0  100.0  100.0  100.0  100.0  100.0  100.1
100.2
100.2  100.1  100.0   99.9   99.9   99.9   99.9   99.9  100.0  100.1
100.2
100.1  100.0   99.9   99.9   99.9   99.8   99.9   99.9   99.9  100.0
100.1

Center      = 100 %
One-Lamp:
Darkest   = 93.04 %
Brightest = 107.32 %
Max - Min = 14.28 % (non-uniformity)
Two-Lamp:
Darkest   = 99.84 %
Brightest = 100.25 %
Max - Min = 0.41 % (non-uniformity)

```