Optical Terms Library for AR/VR/MR Systems
Measurements of AR/VR/MR Systems Parameters
The incentive behind this and other articles that discuss the measurement of different parameters of AR/VR/MR systems is essentially assuring the user experience that we want to achieve. This is a significant part of system engineering process, the basis of optical system development.
The center of AR/VR/MR systems is a user, and a specific task this system aids the user perform, or a use-case. In order to cover this purpose, the user experience has to drive the development process. This also includes the measurement of the parameters that are part of the user experience.
One of the most important users experience parameters that represents the image quality, the resolution and the crispness of the image fine details is CTF.
What is CTF (Contrast Transfer Function)
Let’s start with the definition.
In general, in Augmented / Virtual / Mixed Reality Systems, a Micro-display Image Source is projected using optical system to infinity or a finite distance.
The system CTF describes what would be the system Contrast for a certain spatial frequency produced by the Image Source. The highest Image Source frequency, or the Nyquist Frequency, which is produced by creating 1 pixel “on” - 1 pixel “off” periodic sequence represents the maximum resolution.
CTF units are percent [%].
CTF is a main measure of the system image quality, the center goal of the optical design. In user experience aspect, it is or the ability to resolve a certain spatial resolution, up-to the maximum resolution.
For detailed explanation and requirements considerations see our post about CTF.
CTF Spec Example
CTF Requirements depend mainly on the following factors:
Human vision, or the ability to resolve fine detail
The environmental settings that have impact on the vision equity
Applications requirements, mainly the typical image detail (resolution)
Here is an example of CTF requirements that include a distinction of different FOV Zones; Eye Relief range; several Spatial Frequencies.
Example – CTF Requirements Table
How to measure CTF
Keeping in mind that XR systems are creating an image for the human eye, visual evaluation could serve a d Go-No Go testing evaluation. This is subjective evaluation, but sometimes this covers the need.
When you want to actually measure the CTF or get an objective numerical evaluation of the image quality, there is a need in a measurement equipment. In order to measure an XR System CTF, which means that you measure the output image, a camera is the most viable solution. Since camera is not a measurement equipment, a substantial system engineering work is needed to turn it into a measurement equipment.
Several general points that should guide the measurement setup building process:
The CTF measurement, as most imaging system parameters, is highly dependent on the measurement setup, the measurement pupil position, or Eye Relief (read more about Eye Relief in our dedicated post)
The CTF measurement is also highly dependent on the measurement pupil size. So, an external aperture should be used to define the measurement pupil size. In most cases when using a camera, an aperture shall be placed on the camera lens and located at the Eye Relief distance from the measured system.
When using a camera as a measurement equipment, for CTF or any other measurement, the camera and lens mapping using external equipment is required. The camera lens CTF should be significantly higher than the measured system CTF values, otherwise the measurement error would impact the results.
Another thing to consider when using a camera to measure the CTF, is the selection of sensor and lens which should be done after system engineering calculations in order to comply with the CTF measurement accuracy and cover the FOV range. This task becomes more and more difficult as the measured systems FOV and resolution increase. Often the camera lens becomes the limiting factor for the CTF measurements at higher FOV areas.
When camera lens CTF at higher FOV is not sufficient, then a rotation jig can be used to rotate the camera so that the lens center part is used for different FOV points, rather than the lens edges. In this setup, the rotation axis must be located on the aperture plane, so that the measurement pupil doesn't move during the rotation.
Building Engineering Measurement Setup
These guidelines create a set of requirements for the measurement setup that is not so easy to realize. It takes a lot of experience, and several iterations might be required to build such a setup. Sometimes, we need to change to a different camera or lens due to mechanical restrictions. Finally, a dedicated fixtures, holders and other parts provide the most effective setup. We often start from 3D printed parts, iterate based on measurements and tests and optimize the setup to provide the required measurement abilities. This setup can later become more robust, if needed.
Several iterations based on off-the-shelf mechanics and specially designed printed parts.
CTF Measurement covering Eye Relief Range
When you need to cover an Eye Relief range (as in the requirements example above), or measure the CTF at various Eye Relief distances, the number of measurements becomes extensive. It generally makes sense to test CTF at various Eye Relief distances only once, as part of a POD process (Proof of Design). This should be done in combination with covering all the engineering stages, detailed below.
Optics Measurement vs System Measurement
All discussion above considers System CTF measurements, but sometimes only optics CTF or MTF measurement gives a more cost-effective testing strategy. Optics manufacturers usually have the equipment and setup to measure the optics MTF / CTF, without the Image Source (micro-display). This setup is completely different than what is used for System CTF measurements, using large Collimators and a Camera with a microscope lens.
There are also dedicated MTF / CTF measurement equipment for optics measurements. This type of equipment is very expensive, large and requires experienced operation personnel. They are used by large companies that produce optical lenses in high diversity of products and high volumes. Then it is required to have such a massive testing infrastructure.
Measurement accuracy
As a general rule, measurement accuracy must be ~5 times better than the value you’re trying to measure. Considering CTF measurement, this applies for the testing camera resolution, that has to be at least x5 higher than the highest tested frequency, and the camera CTF that has to be significantly higher (close to diffraction limit) for the highest tested frequency. Then image processing software can produce sufficient measurement accuracy.
Testing Strategy
CTF measurements are time consuming, and the measurement setup infrastructure is very expensive. This makes the testing strategy and planning a kind of optimization process, where the equipment and infrastructure are the NRE investment, and the in-line testing add to the unit production costs. This trade-off can be an important part of testing strategy.
So, one-time POD (proof of design), measurements can be more extensive, done in-part manually with more experienced engineers.
POD plan might include:
CTF measurement at several spatial frequency settings
CTF measurements through the entire FOV
CTF measurements at different Eye Relief positions
CTF measurements at different location in System Exit Pupil
Optionally CTF measurements for different spectra (when require)
In addition, in order to cover workmanship, calibration and other production issues, ATP (acceptance test procedure) is required, though it can be minimized to a shorter, more cost-effective list.
Another way to reduce the in-line testing expenses in the long run is by automation processes that lowers the requirement on the operator proficiency and also reduces test time-per unit.
ATP plan might include:
CTF measurement at one critical spatial frequency
CTF measurement at FOV Center Zone (more critical FOV area)
CTF measurement at nominal Eye relief and Exit pupil center location only
Supporting design processes are required in the engineering stages, so that they support the testing strategy and cover all the validation aspects.
Engineering tasks and processes include:
Detail Monte-Carlo tolerance analysis of performances evaluation for as-built system using optical design software that assures as-built system will meet the requirements tolerances
Assembly and calibration process plan that documents the production process and minimizes errors
Measurement process automation
When you consider in-process serial production testing, a careful planning and testing process design including introducing automation can assure the process is cost-effective and runs smoothly.
The automation process will require the following features:
Camera image and data capture software
Image processing using algorithms to calculate the CTF
Testing software dedicated to cover the whole process
Clear Pass/Fail criteria and results logging to map the failing units
Optional features could include more automation to reduce manual workload
PASS/FAIL Criteria
The Pass/Fail criteria commonly is based on the requirements, that’s why it’s very important to establish the requirements from the beginning. They will drive everything: the measurement strategy, the equipment, sampling and the Pass/Fail criteria and can also impact system calibration strategy and process.
Often, only when you reach the testing stages is when you realize how important setting the optimal requirements is. Do the requirements represent the user experience expectations, and how much you’re willing to pay to stick with those requirements. One of the final outputs of the entire process is the Yield factor. Often this factor would drive the process of requirements re-evaluation in order to save production costs and increase yield.
These questions sometimes take us back to re-evaluate the requirements and validate them based on actual user tests and feedback. So, we start the projects by asking these questions so the whole development process including the testing can be approach from a more cost-effective standpoint.
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