1. Using Scanning MethodsScanning utilizes the linear system theory, in which an image captured by the test lens (with a known input) is studied to derive MTF parameters. Determining the spatial frequency of the image captured by the test lens will give the spatial profile, which in turn will help calculate the spread function. Executing Fourier transform of this derived function will help determine the quality of the optical system under test.

The fact that such MTF test stations can be operated by anyone without a high level of optical training is an added advantage. The tool can be plugged into any in-progress system for quick testing, which can then command a course correction if required.

A corollary to this advantage is that MTF also allows modeling concatenated systems i.e., systems that use two or more optical or optics-related equipment. The product of MTF measurement of each of those systems can be correlated with that of the system as one. This is beneficial for testing complex systems that are made of different types of optical test devices such as collimators and integrating spheres.

For instance, an MTF chart can be used to derive the Bokeh effect, which is used to measure the quality of the out-of-focus areas of an image that a lens produces. The Bokeh effect is influenced primarily by the quality of the lens materials and the number of aperture blades. According to various studies on lenses and their quality, more blades promise a higher Bokeh.

While there are a handful of methods available to measure the performance of optical systems, some are better and offer more actionable metrics than others. This is partly influenced by the equipment and technology used in the testing.

Spherical aberration refers to rays focusing at different distances depending on where they interact with the lens and is a function of aperture size. To describe spherical aberration, the incident angle of light must be known. This angle occurs where light rays strike the curved surface of a lens and is the angle between the ray and the surface. The steeper the incident angle, the more the light will be refracted (Figure 1). Figure 1 shows that as the parallel rays in object space collide with the lens, the incident angle increases the farther up they hit on the lens’s surface. Image quality from lenses with large apertures (small f/#s) are more likely to suffer from spherical aberration, because of this larger angle of incidence. Lenses that suffer from spherical aberration can be improved by increasing the f/# by closing the iris, but there is a limit to how much this improves image quality. Closing the iris too much causes diffraction to limit performance sooner (see diffraction limit in The Airy Disk and Diffraction Limit). Optical designs that include high index glass or additional elements are used to correct spherical aberration in a fast (small f/#) lens; these designs reduce the amount of refraction at each surface and, with it, the amount of spherical aberration. However, this increases the size, weight, and cost of the lens assembly.

3. Lens MTF measurement is possible in real-timeAnother advantage of using the MTF testing standard is that it can be applied directly in an application environment. The MTF testing environment can be customized according to the nature of the equipment and setup of the entire system. This allows in-process optics testing regardless of the type of optical system that needs testing.

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MTF measurement also acts as a universal testing method for optical systems. Using the MTF system prevents the influence of any kind of human error or other external forces in the designs or their testing. Lastly, MTF measurement offers additional parameters of image characterization for engineers to work on. Field curvature is just one such element that can be gauged using an MTF test system.

A type of chromatic aberration, chromatic focal shift describes how different wavelengths focus along different longitudinal positions (along the optical axis). The goal of most imaging lens designs is to have all desired wavelengths focus on the same plane (where the sensor is located). It is physically impossible to get a singular focus plane over a wide spectral range. However, it is possible to come close. If the wavelengths are focused closer to the same plane, fewer issues will be observed in the image.

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3. Using Frequency GenerationFrequency generation is the simplest method in this list as it deals with a single spatial frequency. Manual measurement of contrast of the captured image is noted and plotted in a graph over a range of spatial frequencies. The variance in image contrast and source frequencies gives the required MTF information to ascertain the quality of the lens under test.

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It’s the most cost-effective yet time-consuming way of measuring optical systems. The OptiShop by CI Systems is capable of testing using the scanning methods.

1. MTF is a quantitative measure of image qualityThe best way to test out an optical system is to measure the quality of the image it records. It can be anything from as common as contact lenses used by individuals to imagers used in automotive industries. Out of all the technical parameters of such an optical system, its ability to transfer various levels of detail from an object to a recorded image within an expected range of resolution is considered the foremost. This ability is measured in terms of modulation, or in the context of images, contrast.

Shown at the same scale as Figure 6, Figure 7 shows an apochromatic lens. An apochromatic lens is designed to focus three wavelengths on the same plane. While this is a far more complicated design, it allows for superior balancing across the wavelength spectrum. As shown, all three LED colors can be brought to focus on the same sensor plane allowing for superior image quality. Apochromatic lens designs have high performance, but low versatility and work well over a smaller range of magnifications and WDs. Additionally, these are often high-cost designs due to additional elements made of expensive materials. Many high-end, high-magnification objectives (such as microscope objectives) are apochromatic.

The peculiarity of scanning methods is in its choice of a tiny light source like a small pinhole. Any optical system will only capture a blur of this light source, helping engineers detect the variation in the image’s spatial profile.

MTF measurement can also be customized according to the type and size of the lens under test. For example, in 2010, a team of physicists developed a flexible MTF measurement system to measure micro lenses. The team used a “conventional optical microscope with an optimized approach for lens illumination”, after which the measurement data was correlated with that of a commercial MTF measurement system.

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2. MTF measurement can be tailored for specific applicationsWith MTF measurement, engineers can correlate the resulting information with the corresponding attributes of the end application. For example, if a photography system has a specific range of pixel resolution, MTF can allow testing within that range. This will ensure that the optical system is tested and rated according to its specifications. There is no need to use a standard one-size-fits-all measurement technique. Although, it should be noted that MTF is a system-agnostic measurement standard.

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Before getting down to the different methods of MTF measurement, here’s a quick consideration of MTF as a tool. With resolution and contrast as its two prime components, MTF offers an understanding of what happens when a lens or an optical system is unable to transfer the expected levels of details from an object to an image. In other words, the decrease or increase in MTF as a function of modulation or contrast versus resolution – which is called the MTF curve – is the critical takeaway here.

MTFtest

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Light of different wavelengths focuses at different points since the refractive index of glass varies based on the wavelength of light. Lenses using longer wavelengths of light have relatively longer focal lengths than lenses using shorter wavelengths. Because the dispersion of a glass determines the refractive power of the glass at different wavelengths, chromatic aberration can be removed by designing an imaging lens that contains both positive and negative lenses made using glasses with different dispersions. This is shown in Figure 5, which compares a singlet to an achromatic doublet lens. A downside to such a design is the increase in the number of lens elements used. To reduce the aberration, lower index lenses (having higher abbe numbers) must be used. As mentioned before, higher index lenses are needed to correct spherical and astigmatic aberrations; if corrections for spherical, astigmatic, and chromatic aberrations must be done, additional lens elements are needed. Additionally, the most desirable glasses for color correction often have properties that make them more expensive and difficult to manufacture. Minimizing chromatic aberration by using monochromatic light has considerable savings in cost and complexity.

MTF as a measurement system considers the spatial frequencies of an image structure and presents simple, direct information. This is akin to audio frequency response, which is why optical systems are often measured for their modulation.

OptiShop can also handle video capture more effectively as it is designed for a wide range of IR Imagers and other cameras. The video method is known to give much richer measurement data including additional parameters such as distortion and field curvature, which makes OptiShop a preferred test station for large organizations that handle different types of optical systems.

2. Using Video CaptureVideo capture MTF testing is the most thorough and versatile method of MTF measurement as it allows testing at higher throughput rates and can test a wide range of optical systems. It works on the linear system theory similar to the scanning methods with the exception that a solid-state array is placed at the focal plane of the lens under test instead of using a tiny light source.

MTF is also a great standard to use to measure two or more identical optical systems. Even though a manufacturer might guarantee identical composition in its systems, vendors and engineers can still use MTF charts to confirm whether the systems are indeed identical. This is widely used in ophthalmic measurements as that field of medicine requires high-precision systems.

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MTF measurement for lenses and other optical systems is an important testing method to gauge the quality of a system’s ability to record an image. The data given out by tools like the OptiShop is instrumental in ensuring quality control, especially for demanding systems where high accuracy and resolution are the norm. MTF measurement finds routine application in ophthalmology, advanced photography, and photo-lithography.

While applying one of these MTF measurement methods is essential to studying the performance of a lens, additional parameters can be recorded and analyzed to get more information on the quality.

MTF is also not restricted by wavelength ranges. There is no need for adjustments in measuring parameters either as MTF works as a one-size-fits-all testing device for any and all types of optical systems.

MTF

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This article explores some of these effective MTF measurement methods that can help engineers and manufacturers keep up with the demand for high standards in optical systems. It will also touch upon an MTF test station by CI Systems that can be used for effective testing of infrared (IR) elements.

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The numerical aperture (NA) is a number (mostly shown on the objective itself) describing the amount of light coming from the focus that the objective can ...

Modulation transfer function (MTF) is considered a standard of optical system characterization. Effective MTF measurement allows designers and optical metrology engineers to ensure electro-optical systems perform as expected with high accuracy and resolution.

There are four to five major methodologies of MTF measurement, namely frequency, slit scanning, video capture, and interferometry. Slanted-edge testing is the fifth method. The methods available today at the disposal of testing engineers are all variants of these techniques, thanks to advances in optical technologies. Here’s a quick look at these MTF measurement methodologies.

The blue, green, and red dots represent wavelengths associated with common 470nm, 520nm, and 630nm (blue, green, and red) LEDs. Notice the green dot focuses to the left of the sensor plane, while the red and blue dots focus to the right; this is the most balanced position of focus of the lens system if all the wavelengths or white light (which encompasses all wavelengths) are used. This design displays non-ideal image quality, as none of the wavelengths are truly in focus. If only one wavelength is used, the performance will improve since balancing effects used for the other wavelengths are eliminated. While this example demonstrates that red and blue can be balanced, this is not always true. Most lens designs are achromatic, but for very small pixels, this can be an issue.

While it is the simplest, the frequency generation method is highly prone to human errors. Another disadvantage is the need for simultaneous manipulation of sources and detectors to vary the frequencies and contrast, which may not be viable for large optical systems. Furthermore, calibration of the test equipment, including of instruments such as black bodies and other sources also poses a hurdle in this method. It is no longer used as a defining MTF measurement method and is always supported by iterations or cross-checking using other methods.

Here’s a quick questionnaire to further break down the use cases of OptiShop as an effective MTF measurement tool. Engineers can use this questionnaire to pinpoint the type of information they hope to capture using MTF testing.MTF Station - OptiShop by CI Systems

Figure 6 shows a chromatic focal shift curve. Since this is an example of an achromatic lens design, two wavelengths are focused on the same plane. The y-axis shows changing wavelength from short to long (blue to red in the visible spectrum). The vertical black line represents a plane that could be the sensor location, and the x-axis shows the distance away from that location. The blue curved line shows the relative location of the best focus as a function of wavelength. The curve verifies that this design is achromatic since even if moved slightly to the left or right, the black line intersects the blue curve at only two points/wavelengths.

4. Using InterferometryIn this lens MTF measurement method, the pupil function of the lens under test is auto-correlated or its point spread function is calculated by Fourier transforming the pupil wavefront. The advantage of this method is that it can be linearly tested with certain applications that operate in limited wavelengths. Unlike video capture, interferometry is not capable of handling systems with wide ranges.

5. Using Slanted-Edge MethodThis is a relatively newer model and is applicable to closed test environments due to its aversion to noise. The method analyzes the image of a slanted knife-edge target, which can be one-dimensional or multi-dimensional as per the requirements.

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MTF measurement gives an easy picture of how well an optical system was built and how accurate it will be in its applications. This is more important in fields of science where high precision is the bare minimum requirement.

Field curvature (Figure 4) is the aberration that describes the amount in which the image plane curves due to the curvature in the lens design. This aberration is caused by the sum of the focal lengths of the lens elements in the system (multiplied by the refractive indices) not equaling zero. If the sum is positive (typical for an imaging lens), the image plane will have a concave curvature. Since curving the image plane is almost never an option for a machine vision lens, the optical designer must insert negative powered corrective elements to reduce this sum. This makes lenses longer and forces a negative lens to be close to the image plane, reducing the lens’s back focal length.

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All of this makes the MTF measurement standard an indispensable part of any optical system management. Investing in methods or test stations that apply MTF measurement in real time can thus be considered a wise use of one’s capital, time, and efforts.

Modulation transfer function

The key to measuring MTF is to know that image quality is measured in terms of contrast. As a principle, MTF can only be applied to systems where an input results in an output or response. Camera sensors, IR imagers, and seismometers are a few examples of such a system.

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Astigmatism is a function of field angles. To summarize, astigmatic aberration occurs when a lens must perform over a wide field, but the performance in the direction of the field is reduced compared to the performance orthogonal to the field (either sagittal or tangential, respectfully). If one looks at a series of bars that are half horizontal (tangential) and half vertical (sagittal), the bars in one direction will be in focus, but the bars in the other direction will be out of focus (shown in Figure 2a and 2b). This is caused by the fact that rays that are away from the center of the object, do not pass through rotationally symmetric surfaces like the on-axis rays do (Figure 3). To correct this, two things must occur: lens designs must be symmetric about the aperture and field rays must have low incident angles. Keeping a design symmetric leads to forms that are like a double gauss lens. Note that symmetric designs prevent the use of telephoto or reverse telephoto designs, which can cause long focal length designs to be large and short focal length designs to have small back focal lengths. Reducing the angles of incidence, much like for spherical aberration, requires higher index glasses and additional elements, leading to an increase in lens size, weight, and cost. The simplified definition used here intentionally combines the effects of astigmatism and coma for ease of understanding.

MTF is a variant of optical transfer function (OTF) and is widely used as a benchmark test today to measure the performance of lenses and other electro-optical systems such as infrared (IR) imagers and virtual reality (VR) optics.