Dear, friends
Sharing our experience as optical engineers specializing in augmented reality, me and my partners in JOYA Team want to create a common language, a database that can be shared and used by anyone who wishes to learn and understand the specifics of augmented &virtual reality systems – our optical terms library. If there is a term you want to learn about - leave a comment and we promise to give our interpretation of this term.
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What is MTF (Modulation Transfer Function)
MTF is commonly used term, as an image quality measure in optical design, but mostly this term is not fully understood. MTF (Modulation Transfer Function) is a measure of element or system which describes the system response to an input sine image. That meaning: if sine wave intensity profile is your input, what would be the system output relatively to this input. MTF is given in percent [%]. It’s not uncommon to see requirements in a general way, namely asking for best physically possible design without any aberrations:
MTF: diffraction limit
The MTF term is used historically mainly because it was more convenient to calculate using formulas. MTF was the relevant term for systems using CRT displays, but when considering AR/ VR/ MR display systems or camera systems, this term can be replaced by a more appropriate and easy-to-understand term – CTF (Contrast Transfer Function).
What is CTF (Contrast Transfer Function)
So, what is CTF? When you have a pixelated display or sensor, considering a sine intensity profile is not very realistic and helpful. The display image or the sensor output have discrete square wave intensity profile nature, so CTF represents the system response to a square wave intensity profile of a certain frequency. The highest system frequency, or the Nyquist Frequency, is when the square wave is produced by creating 1 pixel “on” - 1 pixel “off” sequence. The system CTF describes what would be the system output relatively to this input, or what would be the resulting Contrast between the “on” pixels and the “off” pixels, which is also given in percent [%]. Considering this contrast as a measure of the system image quality, it’s easy to project the CTF numbers on how the projected image quality will be seen and perceived by the user.
CTF / MTF Specification
Our addition to the CTF / MTF specifications:
For AR / VR / MR systems design we propose to define the CTF as a more adequate measure of image quality for pixelated image source.
System CTF, considering Image Source Contrast, electronics and other system components, shall be defined on a system level. Often the Image Source (micro-display) Contrast is not taken into account at all, while some micro-display technologies have CTF well below 100%, thus may have significant impact on the system CTF.
Optical System (relay lens) CTF shall be derived and defined separately. Separate CTF for the optics standalone is a must requirement for the optical imaging design. Although CTF is the parameter used for the design and the final system testing, many lens manufacturers still provide only MTF measurements, due to their equipment capabilities, thus often both terms are used.
CTF shall be defined for a specific spatial frequency, which is also connected to the Image Source Resolution. CTF can be defined for Nyquist Frequency and/or for 1/N Nyquist Frequency, where “N” is a number of pixels creating a typical line width for specific system use cases.
Nyquist Frequency expression for 1 pixel “on”– 1 pixel “off” pattern
CTF shall be defined for a given measurement pupil size, which correlates to the user’s eye pupil size and depends on outside lighting conditions (more on this will be detailed in a separate post dedicated to System Pupil).
CTF requirements shall be defined separately for different FOV areas, where applicable.
CTF requirements can also be defined for different spectrum, different pupil positions, different exit pupil distances.
CTF requirements shall be defined as minimum between the vertical and horizontal periodic lines patterns (tangential and sagittal), for real, as built optical system. There is no real value in nominal system characteristics.
Things to Consider in CTF Requirements
The CTF is the main optical system image quality measure and the CTF Requirements strongly depend on the system’s intended use. On the other hand, overkill CTF requirements have high impact on optical system complexity, size, weight and cost. The more detailed and accurate the CTF requirements are, considering the actual system intended use, the better optimization can be done in the optical design to minimize the high quality “cost”. Here are several different cases when system CTF should be tailored to the use-case scenarios in order to create an optimal design:
In all AR/ VR/ MR system types, it’s very important to consider the human vision characteristics in order to produce the requirements just-right for the mission or the use case. A significantly higher CTF will just slightly improve the user experience of image quality and sharpness and in many cases is not justified and results in the optical system being not optimal.
The distinction of CTF requirements for different FOV areas – Primary / Secondary / Peripheral FOV areas – is one of the tools for system customization to human vision. In addition, in systems with differentiated Resolution for different FOV areas, the CTF requirements shall match the different Resolution settings.
In case of an augmented reality system, when the projected image contains symbols or text, typically these elements’ line width is several pixels, and the CTF requirements for the Nyquist Frequency image resolution does not bring high added value and basically is overkill requirement.
The image quality and sharpness perception of symbolic or text image is different from that of a full video image. Thus, in case of a virtual reality system, when a full video image is projected, the image quality of a Nyquist Frequency micro-display spatial resolution is important.
In case of a mixed reality system, when the projected synthetic image is combined with a direct viewing camera / night vision image, the two images’ CTF shall be close so that there is no resonance that can be perceived by the user as a combination of a sharper and a more blurred image. In addition, one should keep in mind that when the direct viewing image is projected to the user’s eye by the projection system optics, the resulting CTF will be the multiplication of direct viewing system CTF with the projection system CTF.
CTF Requirements Example
Our definition of CTF (example):
CTF Measurement pupil: Diameter 4mm
CTF System pupil: 10mm vertical X 14mm horizontal (elliptical shape)
CTF spectrum: 0.525μm: weight 1; 0.505μm: weight 0.5; 0.545μm: weight 0.5
Provide CTF requirements Table (see example):
