What is a projector? The short answer is that a projector is an optical device that illuminates a surface patterned to a desired image and projects that onto a screen. But in this post, we’ll take a deeper dive into what a projector is, its history, and common design challenges in creating projectors.
A Brief History
The oldest projection of an image may be dated back to magic mirrors made in Asia thousands of years ago.
A projected image was created onto a screen by a pattern embossed on the back of a bronze mirror. Curiously, when the reflected surface is illuminated, the image of the pattern is projected onto a screen even though the pattern is invisible by direct visual inspection. It turns out that the image created on the screen is due to the deviations of rays by small undulations on the reflecting surface reproduced in low relief during the manufacturing process. Sir M. V. Berry showed that the intensity of the image is proportional to the Laplacian of these undulations. The Laplacian is a measure of the local curvature of a surface.
Fast forward a few thousand years, and the projectors we see today largely use Digital Light Processing (DLP) based on Digital Micromirror Devices (DMD) developed by Texas Instruments. In DMDs, electronically-addressable micromirrors create the desired pattern by selectively directing the received light rays to the projection lens system.
While the technology has changed, the underlying science behind projectors is the same as it was thousands of years ago.
Main Components
Now that we know what a projector is and its origin, we can consider how a projector is created. The main optical components of a projector include:
- Illumination to flood the patterned surface with photons emitted by the light source as efficiently as possible.
- Coupling which couples the light in and out of the patterned surface.
- Projection that projects the patterned surface onto the screen.
An example of these three components in action is pictured above.
Typically, photons from the light source are mapped onto the DMD using either Abbe Illumination or Köhler Illumination. In the former, the source is imaged directly onto the DMD, while the latter images the pupil onto the DMD, more suitable for non-uniform light sources.
The coupling system is commonly achieved using refractive (total internal reflection (TIR) prism) or reflective optics.
Projection lens system images the DMD onto the screen, creating the desired pattern on the screen. Typical projection lens systems feature optical zoom and keystone correction.
Design Challenges and Étendue
Except for certain specific applications, LEDs have emerged as the mainstream light source used in contemporary projectors. For illumination applications, the most challenging part of the projector design is to direct as many photons as possible from the LED to the DMD and, ultimately, to the screen. The fundamental limitation in the design of projector systems lies in the number of photons that can be possibly delivered to the screen, imposed by the conservation of étendue.
Étendue is a measure of the spatial and angular extent of light. For example, LEDs often have a very small spatial extent in the range of millimeters but a very large angular extent, often over 120 degrees. In comparison, DMDs admit a very small angular range (~24 degrees) but have a larger spatial extent (10’s of millimeters). The étendue mismatch is minimized in a suitably designed projector.
Hamiltonian and Phase Space
The concept of conservation of étendue can be best understood in the context of Hamiltonian optics, which pictures the spatial and angular extension of light simultaneously and intuitively in phase space [4]. Figure 6 presents a simple example of the free-space propagation of an idealized LED source in phase space, whose axes indicate the spatial (q) and angular (p) extent of light.
The idealized LED emits light uniformly in a certain angular range over an area. This is equivalent to a rectangle in phase space. However, as light propagates away from the LED, the light pattern spreads out while the angular range remains constant. This translates to a shear in phase space, as shown in Figure 6.
It is not difficult to see that the shape of the region occupied in phase space can be changed using optical components or mere propagation. However, in a lossless optical system, the area occupied by the region remains constant as the system evolves, very much like an incompressible fluid. This is the conservation of étendue that limits the spatial and angular extent of light.
In the design of a projector, in mapping light from the LED to the DMD, it is desirable to rotate the phase space of the LED so that light impinging on the DMD has a small angular range with a larger spatial extent. However, such a translation is bound by the law of the conservation of étendue.
Projectors: A Final Word
So that’s a brief overview of projectors, their history, and design considerations. Like any topic in the optical field, there’s always plenty more to learn and a lot we weren’t able to cover here.
Have more questions about designing projectors? At Optikos, we have designed, developed, and manufactured projectors for various applications ranging from mainstream entertainment/multi-media settings to more specialized applications in scanning, imaging, and microscopy. If there’s an issue, we’ve faced it, and we’re happy to help share our expertise in your next projector-based project.
