Archive for August 10, 2017

Collimation, Etendue, Nits (Background for Understanding Brightness)


I’m getting ready to write a much requested set of articles on the pro’s and con’s of various types of microdisplays (LCOS, DLP, and OLED in particular with some discussion of other display types). I feel as a prerequisites, I should give some key information on the character of light as it pertains to what people generally refer too as “brightness”.  For some of my readers, this discussion will be very elementary/crude/imprecise, but it is important to have a least a rudimentary understanding of nits, collimation, and etendue to understand some of the key characteristics of the various types of displays.

Light Measures – Lumens versus Nits

The figure on the left from an Autodesk Workshop Page illustrates some key light measurements. Lumens are a measure of the total light emitted. Candelas (Cd) are a measurement of the light emitted over a solid angle. Lux measures the light per square meter that hits a surface. Nits (Cd/m2) measure light at a solid angle. Key for a near eye display, we only care about the light in the direction that makes it to the eye’s pupil.

We could get more nits by cranking up the light source’s brightness but that would mean wasting a lot of light. More efficiently, we could use optics to try and somehow steer a higher percentage of total light (lumens) to the eye. In this example, we could put lenses and reflectors to aim the light to the surface and we could make the surface more reflective and more directional (known as the “gain” of a screen). Very simply put, lumens is a measure of the total light output from a light source, nits is a measure of light in a specific direction.


The casual observer might think, just put a lens in front of or a mirror behind and around the light source (like a car’s headlight) and concentrate the light. And yes this will help but only within limits. The absolute limit is set down by a physics law that can’t be violated known as “etendue.”

There are more detailed definitions, but one of the simplest (and for our purpose practical) principles is given in a presentation by Gaggione on collimating LED light stating that “the beam diameter multiplied by the beam angle is a constant value” [for an ideal element]. In simpler terms, if we put an optical element that concentrates/focuses the light, the angles of the light will increase. This has profound implications in terms of collimating light. Another good presentation, but a bit more technical, on etendue and collimation is given by LPI.

Another law of physics is that etendue can only be increased. This means that the light once generated, the light rays can only becomes more random. Every optical element will hurt/increase etendue. Etendue is analogous to the second law of thermodynamics which states that entropy can only increase.

Lambertian Emitters (Typical of LEDs/OLEDs)

LEDs and OLEDs used in displays tend to be “Lambertian Emitters” where the nits are proportional to the cosine of the angle. The figure on the right shows this for a single emitting point on the surface. A real LED/OLED will will not be a single point, but an area so one can imagine a large set of these emitting points spread two dimensionally.

Square Law and Concentrating Light

It is very important to note that the diagram above shows only a side view. The light rays are spreading as sphere and nits are a measure of light per unit area on the surface a sphere. If the linear spread by is reduced by X, the nits will then increase by X-squared.

Since for a near eye display, the only light that “counts” is that which makes it into a person’s eye, there is a big potential gain in brightness that comes not from making the light source brighter but by reducing the angles of the light rays in the form of collimation.

Collimating Light

Collimation is the process of getting light rays to be a parallel to each other as possible (within the laws of etendue). Collimation of light is required for projecting light (as with projector), making for very high luminance (nits) near eye displays, and for getting light work properly with a waveguide (waveguides require highly collimated light to work at all)

Show below is the classic issue with collimating light. A light source with the center point “2” and the two extreme points point at the left “1” and right “3” edge of a Lambertian emitter are shown. There is a lens (in blue) trying to collimate the light that is located at a distances equal to the focal length of the lens. There is also shown a reflector in dashed blue that is often used to capture and redirect the outermost rays that would bypass the lens.

The “B” figure shows happens when 3 light rays (1a, 2a, and 3a) from the 3 points enter the lens at roughly the same place (indicated by the green circle). The lens can only perfectly collimate the center 2a ray to become 2a’ (dashed line) which exits along with all other rays from the point 2 perfectly parallel/collimated. While rays 1a and 3a have their angle reduced (consistent with the laws of etendue, the output area is larger than the source light area) to 1a’ and 3a’ but are not perfectly parallel to ray 2a’ or each other.

If the size of the light source were larger such that 1 and 3 are farther apart, the angles of rays 3a’ and 1a’ would be more severe and less collimated. Or if the light source were smaller, then the light would be more highly collimated. This illustrates how the emitting area can be traded for angular diversity by the laws of etendue.

Illuminating a Microdisplay (DLP or LCOS) Versus Self Emitting Display (OLED)

Very simply put, what we get conceptually by collimating a small light source (such as set of small RGB LEDs) is a bundle of individual highly collimated light sources to illuminate each pixel of a reflective microdisplay like DLP or LCOS. The DLP or LCOS device pixel mirrors then simply reflect light with the same characteristics with some losses and scattering due to imperfections in the mirror.

The big advantage in terms of intensity/nits for reflective mirodisplays is that they separate the illumination process from the light modulation. They can take a very bright and small LEDs and then highly collimate the light to further increase the nits. It is possible to get many tens of thousands of nits illuminating a reflective microdisplay.

An OLED microdisplay is self emitting and the light is Lambertian which as show above is somewhat-diffuse. Typically OLED microdisplay can emit only about 200 to at most 400 nits for long periods of time (some lab prototypes have claimed up to 5,000 nits, but this is unlikely for long periods of time). Going brighter for long periods of time will cause the OLED materials to degenerate/burn-up.

With the OLED you are somewhat stuck with the type of light, Lambertian, as well as the amount of light. The optics have to preserve the image quality of the individual pixels. If you want to say collimate the Lambertian light, it would have to be done on the individual pixels with miniature optics directly on top of the pixel  (say a microlens like array) to have a small spot size (pixel) to collimate. I have heard several people theorize this might be possible but I have not seen it done.

Next Time Optical Flow

Next time I plan to build on these concepts to lay out the “optical flow” for a see-through (AR) microdisplay headset. I will also discuss some of the issues/requirements.