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Cosine Effect
You may have noticed in the images above that the center of the image is brighter than the edges. This
is an optical property that's present in nearly all imaging systems. It's known as the "cosine effect", and it
makes images appear brighter near their centers than at the edges. This happens because a light
emitter, such as a diffuse backlight, is brighter on-axis than off-axis. Since the edges of a flat light source
are captured more off-axis than the center, they appear darker. Compounding the effect is the fact that,
behind the lens, light striking the sensor at the edges comes in at a more oblique angle than light striking
the center. This effect becomes more pronounced as the imaging lens's focal length decreases (i.e.
becomes more wide-angle).
Here's a scan of just the backlight, without anything in front of it. Even though the backlight itself is very
evenly illuminated, it appears to have a cosine-shaped brightness contour when imaged with the camera.
Different ways of dealing with this effect are discussed later in the section "Image Analysis and
Measurment".
Note: This also illustrates the importance of keeping everything clean. Do you see that little divot in
the trace, about two-thirds of the way across? It was caused by a tiny lint fiber clinging to the sensor
chip. If you see something like this, unscrew the lens housing from the board, and use dry
compressed air, or a soft cloth to remove whatever is causing the problem.
Binary Image Acquisition
The AVR firmware that you uploaded to the MoBoStamp-pe enables a wealth of image acquisition
options, particularly in the conversion of grayscale pixel values to binary light/dark values suitable for
image analysis. Binary pixels are acquired using
binary pixels from the 128 grayscale pixels output from the TSL1401R. The firmware accomplishes sub-
pixel resolution during image acquisition time by interpolating a virtual pixel between every pair of actual
pixels, as shown below:
© Bueno Systems, Inc. • TSL1401-DB (2009.10.01)
Image from Backlight Only, Showing the Cosine Effect
sub-pixel resolution
. This enables the acquisition of 255
Page 16 of 52
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