8.8 SPATIAL RESPONSE
8.8.1 Lambertian “Cosine” Response
Lambertian Response is in reference to a particular
angular response which is proportional to the cosine of the
incident angle. In other words, for the angle normal to the
face of the detector (0 degrees), the magnitude is the cosine
of 0 degrees, or 1.0 (100%). As the angle goes off axis and
becomes parallel to the face of the detector, the reading goes
to zero, since the cosine of 90 degrees is zero. At 45
degrees, the cosine is 0.707, which means that the detector
should read the rays with 70.7% of the value produce by the
same rays entering normal to the input device.
The reason this spatial response is necessary for
accurate measurements is that it matches the spatial response
of a perfect absorbing surface. Since Irradiance and
Illuminance are measurements of light falling on a surface,
the cosine is compatible with these measurements. An
analogy of the perfect absorber might be considered as being
a small hole in a piece of sheet metal placed over a well. All
the light that goes in that hole will be absorbed by the deep
well hole underneath. None will get reflected back up out of
the same hole. If we analyze the effect of a change of angle,
such as the sun moving from high noon to sunset, we will
see that less light can make it into the hole at sunset,
because the effective area of the hole is smaller as you view
it from an oblique angle. This reduction in area is directly
proportional to the cosine of the angle normal to this
surface. On polar plotting paper, the cosine makes a circle,
which is convenient when comparing the ideal response with
that of an actual plot.
8.8.2 Field Baffling
There are times when you should restrict the field of view to
delete oblique angles. In a lab environment, you may be
working with a light source on an optical bench. The only
light of interest is from that source, yet light bounces off the
people in the room and back to the detector, creating errors
in the readings. This means that you are better off to
restrict the field of view if you know there are no sources to
be measured at the oblique angles. This can be done with
external baffles or with our accessory hood
(H). Baffles can be made from sheet metal cut to form a
sharp edged hole in the middle. A square hole is actually
better than a round hole, since it is less likely to create
reflections in a multi-baffle array. Also, black velvet is
excellent for dividing off test areas from the rest of the room
lighting. If it is necessary to have light travel down a tube,
you can thread the inside of the tube to reduce the wall
reflections. When making Luminance or Radiance
measurements, it is absolutely necessary to restrict the field
of view to one that ‘sees’ only an intended test area of a
reflecting or rear-lit surface. Baffles can be used to
implement this kind of measurement without resorting to
expensive optics.
8.8.3 Narrow Angle (Luminance / Radiance)
As just mentioned, there is a requirement for a narrow
field of view when making Luminance and Radiance
measurements. This can be accomplished by lenses as in our
Radiance barrel “R” accessory. In some applications it is
accomplished by using a telescope where the light is picked
up from a small spot in the image plane. This is very nice
for measuring the brightness of an illuminated segment of an
alphanumeric display, or for measuring the dot brightness on
the face of a CRT. Unfortunately, these systems are very
expensive. Another alternative is to use simple lenses to
image a small portion of a test field onto an aperture which
has a detector behind it. This is very effective, especially if
the source is a repetitive configuration in a production
situation. A custom setup can be made to specifically
measure that on a small emitting surface. Our “R” barrel has
a 1.5 degree field of view, with the objective lens being
about one inch in diameter. This is effective as long as the
target is larger than one inch. The target requirement is
calculated by multiplying the distance
(measured from the target surface to the front lens of the R
Barrel, in inches) times 2*tan(2.5/2), plus the 1 inch (25.4
mm) diameter of the input aperture and some margin for
error. If you were 12 inches away, the detector ‘sees’ a
circular target approximately 1.5 inches in diameter. Since
the target should generally be much larger than the field of
view of the detector, the target should be at least 2 inches in
diameter when you are 12 inches away.
8.8.4 Uniform Linear Translation Response
The best type of detector setup for uniform receiver
sensitivity is the input port of an integrating sphere, since
any off axis beam will still be captured in the chamber. For
flux measurements, it is necessary to have this uniformity so
that small errors in centering the beam do not contribute to
any error in the measured reading. Our narrow beam
adapter (H/N/K15) attachment is designed to accept a few
millimeters of axial misalignment without appreciable
changes in the reading. This is necessary to allow for
non-critical positioning in laser beam measurements.
The SEL100/FQ/K15 allows the greatest margin of
error in axial misalignments. The large, 100 square
millimeter silicon cell is fitted with a 15 millimeter
diameter conical aiming aperture with an attenuated “flat”
response filter. The user is simply required to aim his
laser beam inside the aperture for guaranteed linear
continuity. Of course, if centering errors are compounded
by an angular offset, the laser beam may not directly
strike the silicon cell, causing significant errors in the
readings. Centering and normalizing the detector to the
incoming beam is a simple procedure and should not
cause any problems
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