No optical surface transmits or reflects light without scattering at least a little of it.
The function that describes how light scatters from a surface is the BSDF. Measuring it requires a scatterometer, but different scatterometer architectures, scanning goniometers, imaging spheres, and conoscopic systems, make fundamentally different trade-offs between resolution, dynamic range, speed, and angular coverage. This page explains how BSDF measurements work and compares the three main instrument types to help you select the right approach for your application.
BSDF stands for Bi-directional Scattering Distribution Function. Physically, it represents the amount of light scattered in a given output direction (i.e. the Distribution of output light) as a function of the input direction (2 directions, in & out, => Bi-directional). BSDF has two components: BRDF for reflected scatter and BTDF for transmitted. Applications of BSDF are as varied as making video games look realistic to calculating the amount of sunlight scattered by the structure of a spy telescope.
An everyday example is that BTDF could be used to measure how dirty the windshield of your car is. If you have a clean windshield, it scatters very little light, so the BTDF would be narrow, but if your windshield is covered by frost, almost all of the light is scattered and the BTDF would be quite broad.
BSDF is the standard way to specify surface scatter performance. Optical design software like Zemax, LightTools, and FRED import data from any scatterometer that produces a compatible file.
TIS (Total Integrated Scatter) and PSD (Power Spectral Density) are terms related to BSDF. TIS is a measure of the amount of light that is scattered, but that begs the question of how much angular deviation from the theoretical is required before light is considered “scattered”. In mathematical terms, PSD is the Fourier transform of the height distribution of a surface. Yes, that is as clear as mud for most of us. A full treatment of these terms is beyond the scope of this page, so we suggest you read John Stover’s excellent reference, “Optical Scattering: Measurement and Analysis“.
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, Keysight, and Westboro Photonics.
The Imaging Sphere is a patented device for measuring light distribution. The idea is that when 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. Unfortunately Radiant Vision Systems has discontinued their Imaging Sphere, but you can view the patent using the link above.
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.
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Each scatterometer architecture makes different trade-offs between angular resolution, dynamic range, measurement speed, and coverage. The right choice depends on your application requirements.
| Specification | Scanning Goniometer Single-detector, sequential scan | Imaging Sphere Hemisphere projection capture | Conoscopic Scatterometer Conoscope lens, parallel capture |
|---|---|---|---|
| Measurement Principle | Collimated laser illuminates sample; single-pixel detector scans angular positions sequentially | Source illuminates gray hemisphere; camera captures reflected distribution through aperture | Conoscope lens maps angular distribution onto 2D sensor in a single capture |
| Speed | ~45 s per angular profile; hours for full hemisphere mapping | Near real-time hemisphere capture (single image) | Near-hemisphere at 17 fps — full angular distribution per frame |
| Dynamic Range | 30 bits (10⁹:1) — resolves faint scatter far from specular | Limited by camera sensor; typically 8–10 bits | 8–12 bits (256:1 to 4,096:1) |
| Angular Resolution | ±0.01° on both illumination and detection axes | Limited by pixel count and hemisphere-to-plane mapping distortion | 0.1° at 80° half-angle; 0.005° at 4° half-angle (resolution trades off with coverage) |
| Angular Coverage | Illumination: 0°–180°; Detection: Θ, Φ ±90° | Near-full hemisphere per capture | Θ: 0°–80°; Φ: full 360° in every frame |
| Azimuthal (Φ) Data | Requires sequential Φ scanning — adds measurement time | Full Φ captured, but distortion reduces usable resolution | Full 360° Φ captured simultaneously with minimal distortion |
| Illumination Source | Collimated laser (typically HeNe or diode) | Broadband or LED | LEDs or monochromator — wavelength-flexible |
| Sample Size | Φ1 mm – Φ13 mm (flexible) | Varies by hemisphere diameter | Φ2 mm (fixed by conoscope design) |
| Polarization | Polarization-dependent BSDF measurement available | Not available | Not available |
| Spatial Uniformity Mapping | Requires repositioning sample — time-intensive | Limited | Maps scatter variation across sample surface |
| Instrument Size | 40 cm x 50 cm x 70 cm (WxDxH) | 50 cm x 40 cm x 50 cm (WxDxH) | 20 cm x 25 cm x 50 cm (WxDxH) |
| Primary Limitation | Slow — full hemisphere can take hours | Hemisphere-to-plane distortion reduces resolution Discontinued | Multiple lens surfaces can introduce ghost images (correctable via dark-frame subtraction) |
| Output Format | BSDF (BRDF/BTDF), ASTM-standard text files | Proprietary image-based formats | BSDF (BRDF/BTDF), ASTM-standard text files, PSD, TIS |
| Best Fit Applications | Low-scatter optics, coating qualification, R&D characterization, polarization-dependent studies | General light distribution measurement (no longer commercially available) | Display testing, AR/VR optics, production QC, diffuser characterization, high-throughput environments |
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.
The beamsplitter serves to reflect light from the light source in the direction of the sample. Given that the beam diameter
To turn a conoscope into a scatterometer, we add light sources for transmissive measurements …
Custom lenses for AR/VR test systems and remote sensing platforms are at the core of our work…