semi合集-English.pdf - 第7198页
SEMI ME1392-0305 © SEMI 2003, 2005 7 6.3.1 Absolute — An absolute normalization is made by moving th e receiver assembly onto the optical axis of the source with no sample in the sample holder. This method depends on ext…
SEMI ME1392-0305 © SEMI 2003, 2005 6
specular surfaces, since best angular resolution is needed near specular where BRDF has a steep slope. Best
sensitivity is needed at larger angles where BRDF might approach the NEBRDF.
5.5.3 It may be necessary to use an optical bandpass filter on the detector to minimize acceptance of background
light. This can also be accomplished by modulating the amplitude (with a mechanical chopper) of the source light,
and using a synchronized, phase sensitive (lock-in) amplifier with the detector.
5.5.4 Since depolarization can occur in scattering, complete characterization of scatter requires measurements with
a polarization analyzer at the receiver. The scatter reflux can be broken into perpendicular and parallel components
that are respectively perpendicular and parallel to the scatter plane (see Figure A1-2).
6 Calibration and Normalization
6.1 General — Instrument calibration is often confused with measurement of P
i
. Calibration of a BRDF instrument
involves systematic standardization and verification of its quantitative results. Incident power must be measured for
correct normalization of the scattered power. Absolute measurement of powers is not required as long as the P
s
/P
i
ratio is correctly measured. Alternatively, a reference sample can be used as a normalization reference.
6.2 Calibration — A leading cause of inaccuracy in BRDF measurement is a lack of instrument calibration. An
error analysis of the four quantities defining the BRDF (P
i
, P
s
,
,
s
) can help to accomplish a calibration.
7
Each of
these four independent variables is a function of system parameters. For example, P
s
depends on receiver linearity,
electrical noise and system alignment parameters. The total error is also a function of incidence angle and scatter
angle. It is reasonable to expect errors in the 3 to 10% range for measurements taken a few degrees from specular to
about
s
= 85°. System nonlinearity is a major contributor to error in this central region. At either end of this
central region errors rise dramatically. Near specular, this is caused by out of plane receiver position error, and near
the grazing angle the increase is due to uncertainty in
s
. Error is also a function of the type of sample being
measured. For example, larger errors are expected in the relatively steep BRDF associated with specular samples
than for the flatter response of a diffuse surface.
6.2.1 The receiver and preamplifier must be calibrated together over their useful operating range. The final result is
a calibration curve showing relative optical power versus voltage for each preamplifier gain setting. Operating
regimes are selected for each gain setting to avoid saturating the detector while remaining on a low gain setting. The
source monitor must also be calibrated in the same way.
6.2.2 There are several ways to vary the optical power and make this calibration curve. Optical filters with a known
attenuation can be used, but multiple reflections and coherent effects (interference between the two filter faces) can
change the attenuation. An excellent method of changing the optical power at the receiver is by moving away from
a diffuse source for 1/r
2
attenuation. Other methods include crossed polarizers or changing the duty cycle of a
chopper. The user must select an attenuation method with suitable reproducibility to perform the calibration.
6.2.3 The receiver and preamplifier each have a maximum output voltage to avoid saturation, but there is also a
minimum electronic noise level which should be kept in mind to avoid reporting noise as BRDF. When electronic
noise is expressed as NEBRDF, note that although the noise may be constant, NEBRDF depends on the receiver
solid angle, , the incident power, P
i
, and cos
s
. This means NEBRDF can be lowered by changing these system
parameters.
6.2.4 A full system calibration is not required on a daily basis, but the system should be checked daily. This check
can be accomplished by measuring the instrument signature and a stable reference sample that provides data over
several decades. Changes from past results are an indication of calibration problems and the cause of the change
must be determined. It is good operating practice to maintain a reference sample at the scatter facility for this
calibration check. Recalibration must be accomplished when components are changed, repaired, or realigned.
Include a data file number for the most recent reference sample measurement with every set of BRDF data as a
record of instrument response in case the data set is questioned at a later time.
6.3 Normalization — There are four acceptable methods for normalizing the scattered power to the incident power.
Each method is dependent on different measured parameters.
7 Cady, F. M., Bjork, D. R., Rifkin, J., and Stover, J.C., “BRDF Error Analysis,” Proceedings SPIE 1165, 154-164 (1989).
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.