Measuring Optical Scattering

No optical surface transmits or reflects light without scattering at least a little of it. The function that describes the results of measuring optical scattering is the BSDF (Bidirectional Scattering Distribution Function). The BSDF comes in two flavors, the BRDF for reflection and BTDF for transmission. To measure these functions, one needs a scatterometer, which is an instrument that measures the angular distribution of light reflected or transmitted by a surface.  There are several types of scatterometers: scanning, Imaging Sphere, conoscope and multiple lens. Let’s go over each of these in a bit more detail.

Scanning Scatterometers

A scanning scatterometer is an instrument that has a laser and a single pixel detector.  The sample is illuminated by a collimated laser beam and the detector is scanned over the sphere around the sample to generate a map of where the light goes.  Because the laser beam is highly collimated and the detector can be made arbitrarily small, this type of scatterometer is capable of resolving extremely fine detail.  Single pixel detectors are also known for their high dynamic range, which can approach six orders of magnitude (20 bits). Its optical simplicity is also beneficial for avoiding measurement defects caused by the instrument.  The downside of this type of scatterometer is the fact that the detector must be scanned; it can take hours to generate a high resolution measurement of any significant portion of a sphere.  If this type of instrument interests you, they are available from The Scatter Works and also Westboro Photonics.

Imaging Sphere

The Imaging Sphere is a patented device for measuring light distribution. The idea is that a gray hemisphere is placed over a light source, the source illuminates the hemisphere and a camera takes a picture of the inside of the hemisphere through a hole in it. The advantage of this arrangement versus a scanning scatterometer is that almost the entire hemisphere is measured in a single image, so the measurements happen in real time.  A disadvantage is that the obtainable resolution is lowered by the fact that there are only so many pixels on the camera used to capture the picture.  This is exacerbated by the fact that it is impossible to map a hemisphere onto a plane without distortion; any such mapping must decrease the available resolution.  If you would like to learn more about this type of scatterometer, please visit Radiant Vision Systems.

Conoscopic Scatterometers


Conoscope on a Precision Translation Stage

Our favorite type of scatterometer is based on a conoscope.  This type of instrument shares the speed advantage of the Imaging Sphere – up to almost a hemisphere can be captured in less than a second.  If measurement over a hemisphere is required, it shares the resolution disadvantage of the Imaging Sphere, but this can be overcome by trading off  how much of a hemisphere is viewed for resolution.  Assuming a 4-5 megapixel imager, you can get anywhere from 0.1° resolution with an 80° half angle to 0.005° resolution with a 4° half-angle.  If the conoscope lens is well designed, there is no distortion, so that resolution loss is completely avoided.  The primary disadvantage of a conoscopic scatterometer is that it has quite a few lenses, and each optical surface reflects roughly 0.25% of the incident light, so it is possible to get ghost images.  If an image is captured with a nearly black sample, this image can be subtracted from the sample measurements to eliminate most of the ghost images, but correction can never be perfect.  If you would like to learn more about how conoscopic scatterometers work, you may read about it on this page.  Or, if you agree that this is the type of scatterometer for you, please view our brochure for an overview. Visit our scatterometer product page for a more in depth examination. A couple of the conoscopes we have built can be seen on the Completed Projects page.

If a scatterometer is out of your price range…

Scatterometers typically cost from tens of thousands of dollars to a quarter of a million dollars. For some of us, that cost is prohibitive. Another way to estimate the amount of scattered light is to use a surface roughness gauge to measure the surface and estimate the Total Integrated Scatter based on this measurement. Please refer to our pages on Measuring Surface Roughness and Optical Scattering and Surface Roughness for more information on this technique.