Thursday, July 21, 2016

Key Parameters for Optical Designs

At Sensics, we completed many optical designs for VR over the years, and are busy these days with new ones to accommodate new displays and new sets of requirements. For those thinking about optics, here is a collection of some important parameters to consider, when focusing in optical systems for VR.

Field of View: typically measured in degrees, the field of view defines what is the horizontal, vertical and diagonal extent that can be viewed at any given point. This is often specified as a monocular (single eye) field of view, but it is also customary to specify the binocular field of view and thus the binocular overlap

Eye relief: typically measured in millimeters, the eye relief indicates the distance between the eye and the closest optical element as seen in the illustration below. 

Eye Relief
Illustration of eye relief

Regular eyeglasses have an eye relief of about 12mm. Advantages of larger eye relief:
  • If the optics are too close to the eye, they generate discomfort such as when the eyelashes touch the optics.
  • If the eye relief is large enough, the system might be able to accommodate people wearing glasses without the need to provide a focusing mechanism to compensate for not having glasses
Disadvantages of larger eye relief:
  • The total depth of the optical system (distance from eye to screen) becomes larger and the overall system potentially more cumbersome.
  • The minimal diameter first optical element is dictated by a combination of the desired field of view and eye relief. Larger eye relief requires the lens to be wider and thus likely heavier.
Eye box: often specified in millimeters, the eye box determines how much the eye can move up/down/left/right from the optimal position without significant degradation in the image quality. Some optical systems such as rifle scopes have very narrow eye box because they want to 'force' the eye to be in the optimal position. Other optical systems, such as HMDs used in soldier training, might desire larger eye boxes to allow the trainee to see a good image even as the HMD moves on the head while the trainee is running. The image quality at the optimal position is most always best, but if the eye box is too narrow, the user will not obtain a good image without tedious adjustments. For instance, the diagram below shows the simulation results of an optical design at the nominal eye position (left) and at 4 mm away from the optimal position:
Eye box simulation
Comparing optical quality at a distance away from the optimal eye position

Material and type of lensa lens is typically made from optical-grade plastic or from glass. There are hundreds of different optical-grade glass types but only about a dozen optical-grade plastic material. Different material provide different light bending properties (e.g. index of refraction) so it is quite common that multi-element optical systems are made with more than one material. Glass is typically heavier, more expensive to mold, but has greater variety, provides better surface quality and is often physically harder (e.g. more resistant to scratches). Plastic is cheaper and lighter. Additional lens types and non-linear optical elements such as Fresnel Lenses and polarizers are also available.

Distortion: optical distortion is one type of imperfection in an optical design. Distortion causes straight lines not being seen as straight lines when viewed through the optics. An example of this is shown below.

Optical distortion
Optical distortion
Distortion is reported in percentage units. If a pixel is placed at a distance of 100 pixels (or mm or degrees or inches or whichever unit you prefer) and appears as if it at a distance of 110, the distortion at that particular point is (110-100)/100 = 10%. During the process of optical design, distortion graphs are commonly viewed during the iterations of the design. For instance, consider the distortion graph below for a design with 96 degrees field of view (2 x 48): 

Sample Distortion Curve
Distortion graph

The graph shows, for instance, that at 30 degrees away from the center, distortion is still about 2-3%, but at 40 degrees away from the center it increases to about 8 percent. The effect of distortion is sometimes shown in a distortion grid shown below. If the optical design was perfect and had no distortion, each blue cross would line up perfectly at the grid intersection points. 

Distortion Grid
Distortion Grid
Sometimes, distortion is monotonic, meaning that it gradually increases as one moves towards the edge. Non-monotonic distortion can cause the appearance of a 'bubble' if not corrected. 

Chromatic aberration: Just like white light breaks into various colors when passing through a prism, an optical system might behave differently for different wavelengths/colors. This could cause color breakup. It is useful to explore how much the system is 'color corrected' so as to minimize this color breakup. The image below shows a nice picture at the center of the optical system but fairly significant color breakup at the edges. 

Color breakup
Color breakup
Relative illuminationthe ability of an optical system to collect light can change throughout the image. Consider a uniformly-lit surface that is viewed through an optical system. Often, the perceived brightness at the center of the optics is the highest and it drops is one moves towards the edges. This is numerically expressed as relative illumination such as the graph below. While the human eye has amazing dynamic range, non-monotonic illumination can cause the appearance of dark or bright 'rings' in the image. 

Relative Illumination
Relative Illumination

Spot size: imagine a screen with a pattern of tiny dots. In a perfect world, all dots would appear with the same size and no smear when looking through the optical system. In reality, the dot size typically increases as one moves away from the center. The numerical measurement of this is the spot size and diagrams indicating the spot size at different points through the optics often look something like this:

Spot size
Spot Size
Other characteristics: depending on the desired use case, there are often size, weight and cost limitations that need to be considered to narrow the range of acceptable solutions to the specifications. Just like it is easier to fit a higher-degree polynomial to a set of data points because more terms provide additional degrees of freedom, it is easier to achieve the a set of desired optical parameters with additional lenses (or more precisely with additional surfaces), but extra lenses often add cost, size and weight. 

Putting it all together: it is practically impossible to find a car that is inexpensive, has amazing fuel efficiency, offers fantastic acceleration, seats 7 people and is very pleasing to the eye. Similarly, it is difficult to design an optical system that has no distortion, provides wide field of view, large eye box, costs next to nothing and is very thin. When contracting the design of an optical system, it is useful to define all desired characteristics but specify which parameters are key and which parameters are less important.