Understanding the MTF Graph and Its Key Parameters

Modulation Transfer Function (MTF) is a key benchmark for assessing the performance of optical systems. It determines how well an optical system can convey contrast at various spatial frequencies from an object to the image plane. So, a thorough understanding of the MTF graph and its parameters is crucial for assessing lens quality, sharpness, contrast, and the impact of optical aberrations.

In this blog, you’ll understand the components of MTF, the interpretation of its graph, and the significance of its key metrics.

What is the Modulation Transfer Function?

MTF assesses the performance of optical systems, from single lenses to complex multi-element assemblies. It is defined by two primary aspects: resolution and contrast. Resolution is the ability of optical systems to differentiate fine details, while contrast measures how accurately intensity differences between light and dark regions are transferred.

Resolution

Resolution helps imaging systems to distinguish object details and is expressed as line pairs per millimeter (lp/mm) or cycles per mm, also known as spatial frequency. It is typically analyzed using a USAF Bar target, which contains alternating black and white lines with different spacings. The performance of the lens is evaluated based on how many groups and elements it can resolve.

If the distance between alternate black and white lines is less (higher frequency), the resolution of the optical system decreases. If the distance is greater (lower frequency), the resolution increases.

Figure 1: USAF Resolution Test Chart

For instance, a lens system that can resolve finer details at higher spatial frequencies demonstrates better resolution capabilities, making it effective at distinguishing closely spaced patterns on a USAF Bar target.

Contrast

Resolution without contrast is meaningless. Contrast is defined as the accuracy with which an optical system transfers the intensity of alternate black and white lines from the object plane to the image plane. It indicates how well the system can reproduce intensity variations between light and dark regions, as shown in the below images.

Figure 2: Contrast Comparison in Optical Systems

Figure 3: Contrast Comparison in Optical Systems

The factors affecting contrast are:

• Illumination
• Optical quality
• Camera sensor capabilities

Lens contrast is typically expressed as a percentage, indicating how faithfully the object contrast is reproduced on the image side. As a standard, a minimum of 20% contrast is needed for an imaging system to transfer resolution effectively.

At higher spatial frequencies, contrast tends to decrease due to limitations in the optical system, making it a critical parameter for evaluating overall performance.

Understanding the MTF Graph

The MTF graph is a tool for evaluating the performance of optical systems by plotting contrast on the Y-axis and spatial frequency on the X-axis. It demonstrates how contrast varies with an increase in spatial frequency. As spatial frequency increases, contrast typically decreases, indicating the system’s ability to retain contrast at different resolutions.

Figure 4: Modulation Transfer Function (MTF) Graph

The above image clearly shows the contrast decreases at higher frequencies, and thus, MTF decreases with increases in frequency.

The MTF is also a tool for understanding the overall performance of the optical systems, which includes optics as well as sensors.

How to read the MTF

The MTF (Modulation Transfer Function) graph from Zemax represents the optical performance of a system by plotting the modulus of the Optical Transfer Function (OTF) against spatial frequency in cycles per millimeter.

Figure 5: MTF Graph – Contrast vs. Spatial Frequency

Graph description:

• X-Axis: Represents spatial frequency in cycles per mm (0 to 150 cycles/mm).
• Y-Axis: Modulus of the Optical Transfer Function (OTF) in percentage (0% to 100%).
The solid black line refers to the diffraction limit, indicating the theoretical best possible performance. It serves as a reference for comparing the actual lens performance.

As spatial frequency increases, MTF values decrease, which means contrast is reduced at higher frequencies. The colored lines correspond to different Tilted Spherical (TS) values representing varying levels of field curvature or defocus:

• TS 0.00mm (blue dashed line): On-axis performance
• TS 4.00mm (green dashed Line): Mid-field performance
• TS 5.50mm (red dashed line): Edge-field performance

The separation between curves illustrates off-axis aberrations such as field curvature or astigmatism. A wider gap between the curves suggests a higher degree of aberration.

What are the MTF50 and MTF20 Metrics?

• MTF50: Indicates the spatial frequency where MTF drops to 50% of its maximum value, representing the perceived sharpness of the optical system.
• MTF20: Reflects the spatial frequency where MTF drops to 20%, indicating resolution performance in lower-contrast conditions.

The higher values for MTF50 and MTF20 suggest better sharpness and detail retention.

Astigmatism in Optical Systems

Astigmatism occurs when light rays passing through a lens focus at different points based on their orientation, causing images to appear elongated. The light rays can be categorized into two main planes:

• Tangential plane (Meridional plane): Contains the chief ray and the optical axis
• Sagittal plane (Radial/equatorial plane): Perpendicular to the tangential plane and contains only the chief ray

When off-axis rays pass through a lens, their path lengths can differ, leading to astigmatism. Instead of forming a sharp point, the image of a specimen appears as a line or an ellipse. The orientation of this elongated image depends on the angle at which the off-axis rays enter the lens:

Since the light rays in these two planes refract differently, they focus at different points, creating two separate focal planes:

• Tangential focal plane (Line image)
• Sagittal focal plane (Line image)

Figure 6: Astigmatism in Optical Systems – Tangential and Sagittal Planes

Figure 7: Representation of Sagittal and Meridional Planes in Optical Systems

Between these two planes lies a region called the circle of least confusion, where the image appears closest to a perfect circle. This is crucial in understanding and correcting optical aberrations.

Ultimately, the MTF analysis provides key insights into lens performance, including sharpness, contrast, and off-axis aberrations. When evaluating optical systems, parameters such as MTF50, MTF20, field curvature, and astigmatism must be considered to ensure optimal image quality across the entire field of view (FOV).

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