Stray Light, Scatter, and Black Coatings
This report is a tutorial on basic issues regarding stray light and scatter. A basic stray light problem is analyzed and a solution of using a black surface is given. The scatter metric of BRDF is explored and results of a BRDF model are shown. Other types of scatter metrics such as TIS and spectral reflectance are examined. Lastly, we compare different types of black coatings. The topics of this tutorial can be used by an opto-mechanical engineer to help identify stray light issues and provide a solution in the form of a specific black coating.
Stray light can be defined as light that does not contribute to the overall purpose of the design. It usually becomes a problem in the form of higher signal to noise ratio (SNR) or thermal loading. The suppression of stray light is often overlooked until later in the design process . Even if stray light reduction is budgeted for in the initial design, there are subtle complexities that are often unseen. A common solution to this problem is to just ‘make it black’. This involves specifying certain surfaces to have a black coating. This is an important tool to know, but there is usually more that needs to be done such as; scatter reduction, baffles, coating durability analysis, etc. In this report we focus more on just making preexisting surfaces black. Stray light is by nature an opto-mechanical issue because it involves the interaction of light with optical and mechanical parts. We did not specify anything about the surface properties of the lens barrel. The laser beam that the system was design for will probably never hit the lens barrel and will produce enough SNR (noise being the stray light) that it is not a problem. But if this lens assembly was used to view a field of somewhat constant irradiance (most imaging applications), light from outside of the sensor’s field of view could get to the detector. Light coming from some off-axis field angle (not the laser), that bounces off the lens barrel, then makes it to the detector.
Figure 1. Stray light from specular interior lens barrel surfaces
If the lens barrel were diffuse (rough surface), the light would scatter instead of being specular reflected. This particular field angle (ray bundle) may not have as much energy on the detector, but other field angles may produce more energy on the detector. Figure 2 (below) shows that case of a diffuse lens barrel. Note that only the rays that make it to the detector are shown. A diffuse surface will scatter and the light that reflected off the barrel goes everywhere. When the light scatters everywhere, it is distributed into the full hemisphere. Then the amount of energy depends on the solid angle from the scattering surface to the detector. The longer the ray path to the detector, the smaller the solid angle. Thus there will be less flux making it to the detector. Generally, a diffuse lens barrel has less stray light than the specular lens barrel.
Figure 2. Stray light from diffuse interior lens barrel surfaces
We can even further reduce stray light by making these diffuse surfaces black. In the case of the lens barrel, the surfaces being diffuse will scatter the incident light everywhere giving the light an equal chance of hitting the detector as is will to hit the lens barrel with the same solid angle. Now the more times the light hits the lens barrel the more energy it looses. The surfaces being black will not change the spatial distribution of the light, but will just reduce its overall energy. This is because most of the light energy incident on the black surface gets absorbed by the surface, converting that light energy into heat. There are other more complex solutions that involve changing the lens barrel design with types of baffles. Stray light reduction methods could be catagorized as specular vs. diffuse. Specular solutions of trapping the light into more bounces can be more effective and more resistant to contamination. However they can also be more complex, and have tighter tolerances. If the entire interior of the barrel were threaded, this would effectively increase the surface area and act as a series of light traps. Thus there would be more black area to absorb the light. A similar effect would be to include baffles. These baffles could be basic rings placed along the length of the barrel that trap light. However, this would require changing the initial design. The nice thing about using diffuse black surfaces is that we are not adding any parts; the drawing would still look the same except for the note about surface properties.
Scatter metric – BRDF
The most complete metric of scatter is the Bi-directional Reflectance Distribution Function (BRDF). The nomenclature can be credited to Nicodemus in 1977 . BRDF is the ratio of the scattered radiance (L~W/cm2 sr) to the incident irradiance (E~W/cm2). It can be thought of as reflectance per solid angle. It is a function of the incident angle and scatter angle. It is similar to intensity (W/sr) except the numerator is just reflectance, which is a unitless number from 0 to 1. For a specular mirror, the reflectance is near 1 at the specular angle and the beam has a very small solid angle (much less than 1). Thus, at the specular angle the BRDF can be very high (1e5-1e6). For the same surface, the BRDF at angles away from the specular angle can be very low (1e-3-1e-4). But for a diffuse surface the BRDF is somewhat constant over angle. A very diffuse surface, where there is no increase in power at the specular angle is known as a lambertian surface. Thus the scattered power falls off only as the cosine of the angle. This is because the apparent size of the beam footprint on the surface falls of as a cosine of the angle. The BRDF of a lambertian surface is constant at 1/π. This is shown in Appendix A. Although a perfect lambertian surface does not really exist, there are a few real surfaces that come close. White paper is actually pretty close, but an engineered surface that serves as a common standard is polytetrafluoroethylene. A sample of this material can be used to calibrate a scatterometer, which measures BRDF.
Figure 3. Ideal surfaces
Figure 4. Actual surfaces
When you measure reflectance of a specular surface, the size of the detector does not matter as long as the detector in under-filled by the reflected beam. However, when you measure the reflectance of a diffuse surface, the scatter goes everywhere. Thus the size of the detector, hence solid angle matters. When you put a detector near a scattering surface the amount of energy hitting the detector is proportional to the area of the detector. So a larger detector will have a greater signal than a small detector for a given distance and angle. Real surfaces don’t scatter uniformly so it is a function of the 3-dimensional angle where the scatter was measured. This is why the solid angle must be reported with the reflectance.
Figure 5. BRDF geometry
BRDF data can be fit with various models. The Harvey-Shack model and the ABg model are probably the two most popular. The models give different formulas used to fit the data. One magical property about these models is that once the constants of the model have been fit to data from one particular angle of incidence (AOI), the model can be used to accurately predict BRDF for any AOI. This is known as shift invariance. For a specular surface, the peak BRDF (at the specular angle) does not change with various angles of incidence. However the scatter distribution does change. With increasing angle of incidence there will be more forward scatter than back scatter. This is shown in the following graph. The ABg model is explored for a sample mirror of average quality. The ABg model and notes are given for the quantity BSDF, which is the generalized S-scatter to account for transmissive and bulk scatter .
Note the following properties of the ABg BSDF model:
a. B must be greater than zero unless g is zero.
b. If g is zero, it becomes a Lambertian BSDF with value A/(B+1), and total inte-grated scatter equal to A/(B+1).
c. If g is less than zero, the BSDF increases with lB-Bol. Some surfaces displaythis behavior.
Figure 6. ABg Model giving BRDF as a function of angle of incidence (mirror)
This shift invariance property of BRDF models really only applies for mirrors. In general, the reflectance of a surface increases with angle of incidence. But for a mirror, the reflectance is already very high when the AOI = 0 deg. It can’t increase much more. This is why the peak BRDF doesn’t change with AOI. However, the reflectance of a black surface increases with AOI, no matter how black the surface. There are some caveats to this generalization when it comes to surfaces with engineered microstructure. Below is a graph of BRDF displaying this AOI effect for Black Hardlub at 10 microns. Although the surface may be more diffuse in the visible, the surface is specular in the IR over a wide range of incident angles. Substrate is stock aluminum. Note the increasing peak BRDF with increasing AOI.
Figure 7. BRDF as a function of angle of incidence (black surface) 
Other Scatter Metrics
Another common metric of scatter is Total Integrated Scatter (TIS). This is basically the ratio of the total scattered power (over all angles) to the specular power. The bad thing about TIS is that you loose the angle function, so it doesn’t tell you how the scattered power was distributed into the hemisphere. The good thing about this metric is that it is easier to actually measure and there is a simple formula that relates TIS to the RMS surface roughness (σ). Finely polish glass can typically have an RMS surface roughness of 2 nm = 20 angstroms.
To complete the story there is another metric that relates BRDF to TIS. This is the Hemispherical Reflectance RH. Hemispherical reflectance is the ratio of total scattered power to the incident power. It is equal to the integral of BRDF over the solid angle of the entire hemisphere.
If it looks black by eye, that doesn’t mean it is black in the infrared. The reflectance or BRDF should be tested at the wavelengths where it will be used. Spectral reflectance is just the measure of RH over a specific wavelength range. This is an important property not to overlook. This can be measured with a Monochromator. The opto-mechanical engineer should obtain data to verify the spectral reflectance. Another common metric which is used more in thermal design is to measure RH over a broad wavelength range all at once with a blackbody source. This metric is often called the hemispheric-directional reflectance, which is a misnomer because the reflectance is not measured at a particular direction, it is measured over the entire hemisphere. Emissivity, also known as emittance (ε), is defined as the efficiency for a surface to release thermal radiation. Coincidentally this is equal to the absorption (α) at a particular wavelength. For many black surfaces we are interested in how much the surface absorbs in the visible but emits in the infrared. Although the emittance and absorption are the same at a certain wavelength they can be different in the visible than in the infrared. Thus the metric α(λ=VIS)/ε(λ=IR). Below is data of α/ε for many types of black surfaces . It also serves as a good list of different black coatings to be aware of.
Figure 8. α/ε data for various black surfaces 
a= solar absobtivity
ESH=equivalent Sun Hours
Coating thickness is usually critical
Black coating – Black anodizeAnodizing surfaces is mostly done for corrosion resistance, increased hardness, and/or reflectance properties. It is generally stronger and more adherent than paints or chromes but can’t be done on all materials. It is a process in which the part is submerged into an electrically charged acid bath. The acid alone will anodize the surfaces but the thickness of the oxide layer but can be increased by passing a current through the bath. The film thickness can range from under 5 micrometres on bright decorative work up to 150 microns . The oxide layer grows in roughly equal amounts into and out of the surfaces. Thus a 2 micron thick layer only increases your part dimensions by 1 micron. Typical acids used for the bath are; chromic acid, sulfuric acid, organic acid. Pure aluminum will naturally form this oxide layer very fast when exposed to our atmosphere. However, the more commonly used aluminum alloys don’t form this layer as effectively, thus requiring anodization. It cannot be done for just any material. The only materials anodizing is commonly applies to are; aluminum, titanium, zinc, magnesium, and niobium. Anodizing can also be used to prevent galling but beware of dimension change. Coming out of the acid bath the surface will have tiny pores. This is when a color dye can be added. The dye can be almost any color including black or white. The part is submerged in the dye. Finally, the pores are sealed by boiling the part in deionized water. So the important part of the process for stray light concerns is getting the dye to have the correct optical properties. The dye must have as low reflectance as you require at the correct wavelength. The spectral reflectance should be measured to ensure this. Martin Black is a type of anodized coating that is unique for its dye and surface microstructure. Use MIL-A-8625 for a standard way to specify it in a drawing or spec. Be sure to specify spectral reflectance and scattering properties; if specular specify surface roughness, if diffuse specify roughening method ex: sandblast, gritblast, etc.
Black coating – Black chromeChrome plating is similar to anodizing in that the part is placed in an acidic bath, usually having a current passing through it. Chrome plating is usually applied by an electrolytic deposition of chromium in a chromic acid bath. There is also an electro-less process of applying the chrome. The thickness can range from 10-1000 microns. Black chrome is created by altering the contents of the bath from a regular chrome bath. Black chrome surfaces are created by the process known as plating and can be electroplated or electroless plated. In this process chrome and your part are submerged into a solution of mostly chromium acid and small amounts of other ingredients that vary from vendor to vendor. Sometimes it involves electroplating nickel onto the object before plating the chrome. This can improve the smoothness and corrosion resistance. It is commonly applied to aluminum, steel, brass, beryllium, and copper. Black chrome can be very durable under salt-spray and high temperature environment.
Black coating – Black paint
Contamination and Environmental IssuesThe optical properties of black surfaces will change when exposed to changes in their environment or just time. The black surface itself can contribute to the contamination by outgassing. This is more so true for black paints and diffuse black surfaces. Many black surfaces are sensitive to degradation with time and accelerated degradation when exposed to contamination or other extreme environments. Some black parts may also need to bend, so the coating must be robust enough to handle strain. Below is data of stability of absorption with time. Also shown is outgassing data for various surfaces .
TABLE IV. Repeat measurements of 5-25 m, hemispheric-directionalreflectance to judge long term stability. Samples stored under room conditions.
Figure 9. Absorption stability (left) and Outgassing (right) data for various black surfaces 
Appendix ADerivation of BRDF for lambertian surface. Remember that a lambertian surface has constant radiance (L) with angle. We are actually integrating the ‘cosine corrected’ BRDF. RH=1 for a lossless surface (no absorption), but we replace RH with emissivity (ε) when we apply BRDF to a thermal emitting surface.
- Optical Systems Design by Fischer, 2000
- Geometrical Considerations and Nomenclature for Reflectance by F.E. Nicodemus, 1977
- Tracepro User’s Manual by Lambda Research Corporation, 2007
- Review of black surfaces for space-borne infrared systems by M. J. Persky, 1998