In general, MTF graphs with high values indicate good contrast and resolution, meaning that the optical system is capable of reproducing fine details in the image. On the other hand, a low MTF value at a specific spatial frequency indicates a loss of contrast and resolution at a specific level of detail.

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Figure 1 – Left: Cross-sectional CAD drawing of the Optical Tube Assembly (OTA). Right: Optical model of the OTA. The Field Selector Mechanism (FSM) is located between the two lenses (L1 = Ø30 mm and L2 = Ø380 mm) of a Galilean beam expander.

In reality, the smaller the spacing of the stripes, the harder it becomes for optical systems (like lenses and cameras) to express them—as shown in the illustration below. Lenses capture these line patterns and project them onto a sensor, and as the line spacing decreases, it becomes increasingly challenging to accurately reproduce them. Consequently, as the line spacing becomes tighter, the contrast of the black and white lines represented through the lens decreases. The MTF (Modulation Transfer Function) graph visually represents this phenomenon, helping us understand how well a lens can reproduce fine details in terms of contrast.

Multiple lines plotted in different colors represent different points along the curvature of the lens (i.e., 0.0000 mm is image center while 5.5000 mm is 5.5 mm from the image center)

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Contrast Performance: MTF graphs show contrast levels at various spatial frequencies. High contrast is crucial for image clarity, and MTF graphs help you to evaluate a lens's contrast performance under different conditions.

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Line pairs per millimeter (lp/mm), a unit of measurement that refers to pairs of alternating dark and white lines (line pairs) that can be distinguished in one millimeter of an image.

Absolute accuracy is achieved with two differential inductive sensor pairs. Friction in the spindle drive is overcome by creating a local velocity control loop between the spindle drives and the shaft encoders. Accuracy is achieved by using a cascaded low bandwidth control loop with feedback from the inductive sensors.

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Note that the absolute accuracy requirement contains dynamic requirements on the pointing jitter of the mirror, as well as on the absolute pointing knowledge with respect to a fixed reference. Furthermore, although the required stroke and step is not equal in tip and tilt direction, the FSM is designed symmetrical such that the largest stroke can be attained in both directions.

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In general, similar sagittal and tangential characteristics create a more uniform image. This means that if the sagittal and tangential lines are closer to each other on an MTF graph, the images produced by the lens will have more uniform image performance on both the X-axis (horizontal) and Y-axis (vertical). On the other hand, if the sagittal and tangential lines diverge across an image, it indicates an uneven image with aberrations—meaning the lens is astigmatic. Ideally you want the curves to be closer to each other for more uniform image performance.

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The X-axis (horizonal) refers to the Spatial frequency in cycles per mm by indicating the number of line pairs (i.e., one black and one white line) per millimeter (lp/mm)

MTF information is plotted onto MTF graphs for easy visualization when assessing the resolution of a lens, and it can be presented in different ways. Generally, MTF graphs are broadly categorized into two main types. The first type (MTF Graph by Frequency) presents the X-axis in terms of lp/mm (line pairs per millimeter). However, this type of graph has the drawback of not accurately depicting a lens's MTF performance across the entire sensor. To address this, the second type of graph (MTF Graph by Image Circle) has been introduced. In this graph, the X-axis represents the position (beginning at the center of the sensor and moving toward its edges), allowing for a more precise assessment of the lens's performance across the entire sensor. However, it has the limitation of only examining specific lp/mm values. For this reason, in most cases, these graphs display representative lp/mm values simultaneously.

By comparing MTF graphs of different lenses, you can make informed decisions based on the optical characteristics that matter most for your specific needs. In a real application, there may also be additional factors, such as sensor image size, magnification, and F/# sensor specifications to be considered.

For industrial lens users, it is highly recommended to utilize the MTF (Modulation Transfer Function) graph more proactively for a better assessment of the lens's resolution, contrast performance, and consistent image quality. In this article, we will to go into more detail about MTF graphs and share how you can use them for better lens comparisons.

It is often a challenge to pick the right lens, since a lens's performance is not easily determined by specific measurements like camera or computer specifications. For this reason, lens manufacturers created standard methods of measuring lens performance under a controlled environment and offer the testing results as MTF information for their products.

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Performance across the Image Sensor: MTF graphs provide insights into a lens's performance across the entire image frame. This helps you select lenses that suit your requirement for consistent image quality from the center of the frame to the corners.

Resolution Assessment: MTF graphs provide a quantitative measure of a lens's ability to reproduce fine details. Higher MTF values indicate better resolution, helping you select lenses that suit your needs for sharpness.

Rijnveld, N., R. Henselmans, B. Nijland, “A tip/tilt mirror with large dynamic range for the ESO VLT Four Laser Guide Star Facility”, SPIE Optics & Photonics, 2011

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The Y-axis (vertical) represents the MTF on a scale from 0 to 100% or 1 and is marked by a scale of 10% or 0.1, respectively.

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How do you find the right lens for a camera? What roles do resolution, sensor size, image circle, focal length, and lens size play in creating optimal image quality?

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If you have 1 lp/mm, it means there's 1 pair of lines within a 1mm distance, with each line having a spacing of 0.5mm between them.

Laser beam viewers and sensor cards are used to safely locate optical beams that are invisible to the human eye.

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The MTF (Modulation Transfer Function) graph is useful not only for industrial users, but also for commercial users. The following illustration is an example of the MTF graph typically used by commercial customers, including those who engage in photography as a hobby or profession. These users typically utilize the MTF graph for a quick assessment of a lens's contrast and sharpness rather than for precise measurement.

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MTF (Modulation Transfer Function) is a measure of the ability of an optical system to transfer contrast from the object to the image. It describes the level of contrast a lens delivers at a specific resolution, e.g. Y % at X lp/mm.

A typical MTF graph includes both Tangential Lines (T) and Sagittal Lines (S). The Tangential Line (T)—also known as Meridional—is displayed as solid lines showing the tangential MTF measurements, while the dotted lines show Sagittal MTF. Sagittal means that the test pattern lines are parallel to a line running from the center of the image to the corner, while tangential lines are perpendicular to that diagonal. Usually, the MTF value of the solid line is higher because the lens is generally manufactured based on the tangential direction.

Two spindle drives actuate the mirror, using a stiffness-reduction transmission to increase resolution: when rotating the motor, the nut compresses a soft spring. The soft spring exerts a force against a high stiffness spring, which is connected to the mirror support. As the stiffness ratio between the soft and stiff spring is 1:22, motion of the nut results in a factor 22 smaller motion of the mirror. This principle increases the resolution dramatically, while compromising only slightly in the dynamic behavior of the FSM; the first eigenfrequency of the stiff spring is 135 Hz.

Now, with more understanding of MTF graphs, you will be able to perform quality assessment and comparison across different manufacturers' products or compare different models from the same manufacturer.

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These graphs are not different MTFs, they just present the information in different ways. MTF Graph by Frequency indicate how much of the object's contrast is captured in the image as a function of spatial frequency. MTF Graph by Image Circle shows the value changes from the center of the lens's image circle to the outside at a specific lp/mm. This can be extremely useful, especially when large fields of view are in play. Now, let’s have a closer look at both types of MTF graphs.

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To get a sharp image, you not only need the right camera, but also the right lens to go with it. Our beginner's guide to lens selection will help.

Figure 3 – 3D CAD cut-out of the VLT Field Selector Mechanism, showing left: the inside of the FSM and the custom acutator exerting force on the mirror support and right: the custom actuator singled out.

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The Field Selector Mechanism (FSM) design consists of a Zerodur mirror, bonded to an Invar 36 mirror support, which is constrained in four degrees of freedom (DOF) by a plate spring and a central strut. The former constrains the two in-plane translational DOF of the mirrorand rotation around the optical axisof the mirror, while the latter constrains the mirror in the optical direction, normal to the mirror surface. The remaining two DOF, the tip and tilt directions, are actuated by two actuators, which are located at the edge of the mirror support and are spaced 90° apart around the mirror normal.

In the context of resolution, higher values of lp/mm indicate a finer level of detail that the optical system can capture. Therefore, the number of lines that can be resolved becomes an important performance criterion for the optical system.