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SEMI ME1392-0305 © SEMI 2003, 2005 6 specular surfaces, si nce best angular resolution is needed near specular where BRDF has a steep slope. Best sensitivity is needed at larger angles wh ere BRDF might approach the NEBR…
SEMI ME1392-0305 © SEMI 2003, 2005 5
5.2 Source Assembly — containing the source and associated optics to produce irradiance, E
e
, on the sample over a
specified spot area, A. If a broad band source is used, the wavelength selection technique should be specified.
Depending on the bandwidth and selection techniques, the detector assembly may affect the wavelength sensitivity.
If a laser source is used, it is usually sufficient to specify the center wavelength; however, it is sometimes necessary
to be more specific, such as providing the particular line in a CO
2
laser.
5.2.1 A source monitor is used to correct for fluctuations in the source intensity. If it is located at the source output
it only measures variations in the source power and is not sensitive to variations due to angular drift or downstream
transmission. The source monitor should monitor incident power as close to the sample as possible while
minimizing additional system scatter. Attention should be paid to possible laser mode hopping and consequent
wander of the beam on spatial filter pinholes and to fluctuations in source polarization.
5.2.2 Collimated or slightly converging source light can be used to measure BRDF. Most instruments use a
converging beam focused at the receiver. If the convergence angle is small, the uncertainty introduced by a non-
unique angle of incidence is usually negligible. The same considerations apply if a curved sample is measured. It is
the user's responsibility to assure that any spread in
i
does not compromise the results. Normal practice limits
convergence to f/20 or greater with a focus at the receiver to increase the angular resolution of measurements near
the specular beam or diffraction peaks.
5.2.3 Typically the source assembly is fixed in position and variations in
i
are made with the sample holder. Good
reduction of the instrument signature requires baffling around the source assembly and use of a spatial filter to limit
off-axis light. The final mirror (or lens) which directs light to the sample should have low scatter, since it
contributes directly to small angle scatter in the instrument signature.
5.2.4 A means should be provided for controlling the polarization state of the incident flux as this can impact the
measured BRDF. Orthogonal source polarization components (parallel, or p, and perpendicular, or s) are defined
relative to the plane defined by the source direction and the sample surface normal.
5.2.5 Absorbing samples may be heated by the incident flux and may change their scatter characteristics,
mechanically distort or burn. Special care must be taken with IR laser sources on absorbing samples.
5.3 Sample Holder — The sample holder should provide a secure mount for the sample that does not introduce any
warp. The rotation axes of the stages that achieve the (
i
,
i
,
s
s
) positioning must be relative to the sample front
surface; this can be accomplished by orienting the sample holder or the source, or both, and receiver assemblies.
Some sample mounts incorporate positioning stages for a raster scan of the sample surface at fixed incident and
scatter angles. The sample mount must be kept unobtrusive so that it does not contribute stray flux to the signature
or block large
s
scatter.
5.4 Beam Dump — It is important to trap any specular reflection from the sample so that it cannot contribute to the
scatter signal through lab/instrument reflections. Examples of beam dumps are black paper, a razor blade stack,
absorbing glass plates, or a tapered blackened glass tube.
5.5 Receiver Assembly — If the system design includes angular degrees of freedom at the receiver for achieving the
scatter direction, then the receiver assembly should normally have provisions for rotating about an axis on the front
face of the sample in order to vary
s
. If out of the PLIN measurements are required, the receiver assembly may also
rotate out of the PLIN. This capability may also be provided by pitch, yaw, and roll of the sample, but it becomes
more difficult to dump the specularly reflected beam.
5.5.1 The acceptance aperture for the receiver must be well defined, since the solid angle,
, subtended by the
receiver aperture stop from the sample, is used in the BRDF calculation and defines the angular resolution. The
field of view of the detector must include the entire irradiated area, A. There can be an exception to these
requirements if a relative BRDF or relative total reflectance normalization is used. In that case it is the user's
responsibility to ensure that the system parameters remain constant between measurements.
5.5.2 If the acceptance aperture is too small and a coherent source is used to irradiate the sample, speckle may
cause strong, unpredictable variations in the scatter. This is a common problem when measuring diffuse (that is,
rough) samples. It is sometimes desirable to spin a diffuse sample about its normal to average the effects of speckle
while making a measurement. It is the user’s responsibility to ensure that BRDF features are not due to speckle.
The user may wish to employ a variable aperture stop to trade sensitivity for angular resolution when measuring
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.