Reflectance changes in white
reflectance standards measured in
different instruments with 0/d
geometry
Joaquín Campos, Alicia Pons and Jorge Martín
Instituto de Física Aplicada. CSIC. Spain
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Outline
Introduction
Instruments used
Measurements
Results
Summary
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Introduction
• Spectrophotometric errors in measurement of reflectance
0/d widely studied.
• Calibration standard (white standard) is assumed to be
constant.
• 0/d reflectance measurement are done with an integrating
sphere. Sphere error corrections
• Procedure developed at NPL: correction factors for the
correct inclusion and exclusion of the specular component
of reflectance.
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Specular beam exclusion error (gloss trap error)
A gloss trap which does not completely eliminate light
specularly reflected can lead to an error that depends on the
specific instrument.
Measuring the reflectance of a mirror in the specular
excluded geometry
m reading with the mirror
4  m ( )
K 2 ( ) 
Rt ( )
M ( )  t ( )
t reading with the standard
M mirror’s reflectance
Rt standard’s reflectance
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Specular beam weighting error
In many integrating spheres, light specularly reflected may not
be evaluated with the same efficiency as light diffusely
reflected. An error will be present in total reflectance
measurements.
Measuring the reflectance of a mirror in the specular included
geometry
 Rt ( )  m ( ) 
K 3 ( )  4 
 1
 M ( )  t ( )

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m reading with the mirror
t reading with the standard
M mirror’s reflectance
Rt standard’s reflectance
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To test the goodness of this procedure by
measuring the reflectance of several types of
white reflectance standards in different high
quality spectrophotometers and compare the
values obtained for every standard with every
instrument, once the corrections have been
applied.
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Measurements
Samples
–
–
–
–
–
Glossy white ceramic tiles
Matt white ceramic tiles
Spectralon type white standards
BCR matt white standards
BCR glossy white standards
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Measurements
Spectrophotometers
PE Lambda 900
PE Lambda 9
– Internal diameter:
150 mm
– Paint covering:
Spectralon
– Incidence angle:
7º for exclusion
and inclusion
– Internal diameter:
60 mm
– Paint covering:
Spectralon
– Incidence angle:
7º for exclusion
and inclusion
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Cary 17
– Internal diameter:
60 mm
– Paint covering:
barium sulphate
– Incidence angle: 0º
when excluding and
7,5º when including
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Specular beam exclusion error
0,20
Lambda 900
Lambda 9
Cary 17
Correction Factor K2
0,18
0,16
0,14
0,12
0,10
0,08
0,06
0,04
0,02
0,00
350
400
450
500
550
600
650
700
750
800
Wavelength (nm)
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Specular beam weighting error
Lambda 900
Lambda 9
Cary 17
0,8
Correction Factor K3
0,6
0,4
0,2
0,0
350
-0,2
400
450
500
550
600
650
700
750
800
-0,4
-0,6
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Wavelength (nm)
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Measurements
• Reflectance of every sample was measured
(including and excluding the specular component)
in the three instruments taking one of the matt
standards as a reference, the same for all
instruments
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Measurements
Corrected reflectance:
R ( ) 
  ( )

 s ( )
Rt ( )  K i ( )  s
  
 t ( )
  t ( )

s
t
Rt
Ki
instrument’s reading when sample is measured
instrument’s reading when reference is measured
reference standard’s reflectance (in practice not used)
correction coefficient for exclusion (i=2) or inclusion (i=3) of specular
component
 and  coefficients related to sample and standard, 1 for glossy specimens
and zero for matt ones.
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Differences from the mean (%)
Lambda 900
Lambda 9
Cary 17
1,00
0,75
0,50
0,25
0,00
400
500
600
700
800
-0,25
-0,50
-0,75
-1,00
Wavelength (nm) (glossy to matt)
Differences from the mean (%)
Differences from the mean (%)
Specular included geometry
Lambda 900
Lambda 9
Cary 17
1,00
0,75
Lambda 900
Lambda 9
Cary 17
1,00
0,75
0,50
0,25
0,00
400
500
600
700
800
-0,25
-0,50
-0,75
-1,00
Wavelength (nm) (matt to matt)
• Differences < uncertainties
0,50
0,25
0,00
400
500
600
700
-0,25
-0,50
800
• Procedure correct specular beam
weighting error
-0,75
-1,00
Wavelength (nm) (glossy to glossy)
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Differences from the mean (%)
Lambda 900
Lambda 9
Cary 17
1,00
0,75
0,50
0,25
0,00
400
500
600
700
800
-0,25
-0,50
-0,75
-1,00
Wavelength (nm) (glossy to matt)
Lambda 900
Lambda 9
Cary 17
1,00
0,75
0,50
0,00
400
500
600
700
-0,50
-0,75
-1,00
Wavelength (nm) (glossy to glossy)
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Lambda 900
Lambda 9
Cary 17
1,00
0,75
0,50
0,25
0,00
400
500
600
700
800
-0,25
-0,50
-0,75
-1,00
Wavelength (nm) (matt to matt)
• Differences > uncertainties (shorter
wavelengths)
0,25
-0,25
Differences from the mean (%)
Differences from the mean (%)
Specular excluded geometry
800
• Angles of incidence and sphere
diameters
• Different, function of , angular
distribution of reflectance
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Summary
• In specular included geometry, the adopted procedure allows
to correct for the possible specular beam weighting error.
• In specular excluded geometry, significant differences can be
observed not only for different angles of incidence, but also for
different spehere diameters.
• In the example glossy to matt, the differences seem to indicate
that the adopted procedure does not correct adequately for the
possible specular beam exclusion error; but this assumption
cannot be used to explain the differences in the matt to matt
example.
• A more exhaustive research is necessary. BRDF.
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