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SEMI ME1392-0305 © SEMI 2003, 2005 8 7 Procedure 7.1 Sam ple cleanliness can be a significant fa ctor in the scatter level. The user s hould adopt a procedure for cleaning samples prior to measurement and t his cleaning …

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SEMI ME1392-0305 © SEMI 2003, 2005 7
6.3.1 Absolute — An absolute normalization is made by moving the receiver assembly onto the optical axis of the
source with no sample in the sample holder. This method depends on extending receiver calibration to high power
levels. The entire incident beam must enter the receiver assembly and a voltage, V
di
, is recorded. If the unsaturated
detector response is R
(watts/volt):
RVP
dii
(2)
It is not necessary to know R
for the sample BRDF calculation if it remains constant. The source monitor voltage,
V
mi
, must also be recorded at this time.
6.3.2 Relative BRDF — A relative normalization is made by measuring a reference sample that has a known BRDF
level. This method depends on knowing the reference sample BRDF. This reference sample is usually a high
reflectance, diffuse surface. They are readily available for visible wavelengths and the BRDF is the same for a large
range of
i
and
s
. Ideally the reference sample has a known BRDF that is similar to the unknown sample to be
tested in both magnitude and incident/scatter directions, but this is rarely true. The reference sample should be
spatially uniform and isotropic to alleviate alignment concerns.
6.3.2.1 The reference sample is inserted in the sample holder and a detector voltage, V
di
, corresponding to the
scattered light for the known BRDF is recorded. The following can now be calculated:
s
di
i
RV
P
cosBRDF
(3)
It is not necessary to know or
s
for the sample BRDF calculation if they remain constant. The source monitor
voltage, V
mi
, must also be recorded at this time.
6.3.3 Relative Specular Reflectance — An alternative relative normalization can be made with a specular reference
sample having a known specular reflectance, R. This method depends on knowing R for the same collection solid
angle as used in the P
i
measurement.
6.3.3.1 Insert the specular reference sample in the sample holder and measure the detector voltage, V
di
, for the entire
specular beam into the receiver assembly. The following can now be calculated:
R
RV
P
di
i
(4)
It is not necessary to know R
for the sample BRDF calculation if it remains constant. The source monitor voltage,
V
mi
, must also be recorded at this time.
6.3.4 Relative Total Reflectance — The fourth method involves integration of relative BRDF over the hemisphere
and adjustment of constants to match the directional hemispherical reflectance,
(also referred to as total
hemispherical reflectance). Normalization can only be accomplished after sufficient scatter data are accumulated to
define the integral. This method depends on a separately measured directional hemispherical reflectance and
knowing relative scatter over the entire hemisphere. It is best suited to isotropic, diffuse samples.
6.3.4.1 When sufficient scatter data has been accumulated the following integral is performed.


2
0
2/
0
ddsincosBRDF
sssscalc
(5)
BRDF is obtained with constants, V
d
R
/P
i
, removed from the integral. These constants are adjusted to make
equal
to the externally measured
. The constants are then returned to Equation 7 for calculation of absolute BRDF.
6.3.4.2 A perfectly reflecting (
= 1) and diffuse sample has constant BRDF and integration of the above equation
shows that it is equal to 1/
. A diffuse sample depolarizes incident plane polarized light, therefore care must be
exercised so that the polarization state of the light is taken into account for both the scatter and directional
hemispherical reflectance measurements.
SEMI ME1392-0305 © SEMI 2003, 2005 8
7 Procedure
7.1 Sample cleanliness can be a significant factor in the scatter level. The user should adopt a procedure for
cleaning samples prior to measurement and this cleaning procedure should be reported with the BRDF results.
7.2 Correct alignment of the source, sample, and receiver are essential for accurate BRDF measurements. A typical
example of a subtle error that can be introduced by misalignment occurs when the receiver does not rotate in
s
about the sample face. As
s
increases, the receiver field-of-view “walks off” the illuminated area, A, and the
measured BRDF is then lower than actual BRDF. Although it is not necessary to perform a total system alignment
every day, alignment must be verified on a daily basis for movable components.
7.3 After cleaning the sample and verification of alignment, the sample is inserted in the sample holder. The
detector voltage, V
d
, and the source monitor voltage, V
m
, are recorded for each parameter set of interest. For
example, BRDF measured in the plane-of-incidence requires changing
s
while holding other parameters constant.
The measurement results consist of three columns of data for
s
, V
d
, and V
m
. The constant parameters,
i
and
s
, are
retained in the header information for this data set. Post processing is used to calculate BRDF and express the
results in the desired tabular or graphical format, but P
s
can be calculated at this time. In this calculation, the ratio of
source monitor voltages is included to correct for variation of source intensity:
m
mid
s
V
VRV
P
(6)
where V
mi
= source monitor voltage (see ¶6.3.1).
7.4 BRDF can exhibit strong sensitivity to azimuthal orientation, spot size and position changes on the sample face.
Good operating practice dictates checking for sensitivity to these and other system parameters.
8 Calculation
8.1 The BRDF of an unknown sample is calculated at each incident and scattered direction from the following
relationship:
][sr
coscos
BRDF
1
si
d
m
mi
si
s
P
RV
V
V
P
P
(7)
The value of P
i
is determined by the normalization method used. The correct angular variables may also be
calculated in post processing with BRDF. In all cases
i
and
s
are referenced to the sample normal.
8.2 Many facilities prefer to store only raw data and calculate BRDF and display variables as required to produce a
graph or data table. If data are sent to another facility, it is essential to convert to BRDF and the angular variables
defined in this practice. A suggested reporting format is given in Related Information 3.
9 Report
9.1 BRDF data is expressed in tabular or graphical format as a function of the variable parameter. It is necessary to
state the accuracy of angular measurements and the size of the receiver solid angle, . These latter parameters are
important for small angle scatter. It is usually meaningless to measure within 1° of specular or to measure very
narrow “diffraction spikes” when spans several degrees.
9.2 It is necessary to furnish the instrument signature with the sample BRDF data so that the user can make an
informed decision about the angle where the sample’s scatter becomes lost in the signature. Correct comparison of
the signature with BRDF data requires multiplying the signature by the sample's specular reflectance for that portion
of the signature due to instrument scattered stray light (usually the case for
s
near specular). The portion of the
signature due to electronic noise is not reduced by the sample reflectance.
9.3 It is necessary to furnish the normalization method with BRDF data. If a relative normalization is used the
source of the reference sample BRDF must be stated.
9.4 BRDF data can span many decades so it is usually expressed in base ten exponential form or plotted on a
logarithmic scale.
SEMI ME1392-0305 © SEMI 2003, 2005 9
9.5 Related Information 3 provides a reporting format suggested for use. This format is general in nature and
allows for variation of any sample or system parameters.
10 Precision and Bias
10.1 Precision — The precision of the procedure outlined in this guide is inconclusive based on the results of an
interlaboratory round robin conducted in 1988.
8
This round robin was conducted at a single wavelength (632.8 m),
angle of incidence (10°), polarization state (s incident) and with four specific sample surfaces. It was found that
precision depends on the BRDF level and scatter angle.
9
Additional information on precision was accumulated in a
10.6 m round robin conducted in 1989.
10
10.1.1 A white diffuse sample with mean BRDF = 0.27/sr gave a fractional deviation (standard deviation of the 18
measurement sets divided by the mean BRDF) close to 17% at scatter angles from 15 to 70°. A black diffuse
sample with mean BRDF = 0.01/sr gave fractional deviations from 24 to 39% depending on scatter angle. Specular
mirrors gave fractional deviations from 31 to 134% depending on scatter angle. Variations were larger at large
scatter angles where detector noise levels of some instruments and errors in
s
had a large effect. These variations
are much larger then expected from a typical error analysis.
10.2 Bias — There is no bias inherent in this practice. BRDF is a number derived from the ratio of physical
parameters that can be specified in absolute units. However, individual laboratories may have measurement errors
that lead to systematic offsets, such as an inaccurately measured solid angle. Other possible mechanisms are
discussed in the literature.
9
It is not possible at this time to separate these systematic errors from bias; however,
intralaboratory measurements on the same instrument typically repeat within 5%.
7
11 Keywords
bidirectional reflectance distribution function (BRDF); diffuse; irradiance; power spectrum; radiance; reflectance;
reflectance factor; roughness; scatter; specular; total integrated scatter
8 Leonard, Thomas A. and Pantoliano, Michael, “BRDF Round Robin,” Proceedings SPIE 967, 226 (1988).
9 Leonard, Thomas A., “The Art of Optical Scatter Measurement,” Proceedings, Laser Induced Damage in Optical Materials: 1988 Symposium,
Special Publication 775 (National Institute of Standards and Technology, Gaithersburg, MD, 1988), pp. 42–47.
10 Leonard, Thomas A., Pantoliano, Michael, and Reilly, James, “Results of a CO
2
BRDF Round Robin,” Proceedings SPIE 1165, 444-449
(1989).