I.Definition
MTF (Modulation Transfer Function) is the modulus of the Optical Transfer Function (OTF), defined as the ratio of the output modulation of the system to the input modulation, describing the contrast transfer capability of an imaging system at different spatial frequencies.

Its calculation formula is: $$MTF(f)=\frac{M_{\text{out}}(f)}{M_{\text{in}}(f)}=|OTF(f)|$$

Modulation $M$ (also known as Michelson contrast) is calculated based on the maximum and minimum brightness of line pairs or sinusoidal patterns: $$M=\frac{I_{\max}-I_{\min}}{I_{\max}+I_{\min}}$$ where $I_{max}$ and $I_{min}$ are the maximum and minimum brightness of the pattern, respectively.

MTF values range from 0 to 1. The closer the value is to 1, the stronger the contrast transfer capability of the system at the corresponding spatial frequency.

Note: SFR (Spatial Frequency Response) describes the system’s response capability to spatial frequencies and is often used interchangeably with MTF in engineering testing. This entry uniformly uses MTF.

Terminology
Concepts often associated with MTF in image quality evaluation (at different levels) are discussed; understanding their relationship with MTF helps interpret the MTF curve more comprehensively.

Resolution: The smallest spatial detail that an imaging system can resolve, usually expressed as line pairs per millimeter (lp/mm). On the MTF curve, it is often characterized by the spatial frequency at which the MTF drops to a specified threshold, representing the system’s physical resolution limit.

Contrast: The degree of brightness difference between bright and dark areas in an image. Modulation $M$ is its quantitative form, and MTF describes the transfer efficiency of the system for input contrast at various frequencies—higher MTF values mean more output contrast is retained at that frequency.

Acutance: The steepness of edge transitions in an image; steep transitions result in clear, distinct boundaries, while gradual transitions lead to blurred edges with wide gray-scale transition zones. Edge acutance can be enhanced by sharpening, but sharpening only increases edge contrast and does not change the system’s limiting resolution. Some modern standards (e.g., IEEE CPIQ) extend the definition of acutance to a perceptual sharpness metric that combines the system’s MTF, the human eye’s contrast sensitivity function (CSF), and viewing conditions (e.g., distance, display size), making it more aligned with actual human visual experience.

Sharpness: A subjective perceptual quantity of the clarity of image details as perceived by the human eye, influenced by multiple factors such as resolution, edge acutance, contrast, and noise, and cannot be precisely defined by a single physical quantity. The MTF curve comprehensively reflects the system’s contrast transfer characteristics at different spatial frequencies and serves as the core objective basis for analyzing sharpness; perceptual sharpness metrics (e.g., Acutance/SQF) further incorporate the human eye’s contrast sensitivity function (CSF) and viewing conditions to predict subjective sharpness.

Resolution	Contrast	Acutance	Sharpness

II. MTF Curve

X-axis: Spatial frequency, from low to high frequencies. Common spatial frequency units: lp/mm (line pairs per millimeter), LW/PH (line widths per pixel height), cycles/pixel (cycles per pixel).

Y-axis: MTF value (the ratio of output modulation to input modulation), with a theoretical range of 0 to 1. MTF=1 indicates that the modulation at the corresponding frequency is fully transmitted, while MTF=0 indicates complete loss.

Trend: As the spatial frequency increases, the modulation (MTF) gradually attenuates.

Frequency Regions of the MTF Curve
The MTF curve is typically divided into three regions: low, medium, and high frequency, each corresponding to different imaging characteristics:

Low-frequency region: Corresponds to large-area, slowly varying components in the image, mainly reflecting the macroscopic contours and overall brightness tone of the scene. In this region, the MTF value is usually close to 1, indicating minimal contrast attenuation by the system.

Medium-frequency region: Corresponds to the transition of medium-scale spatial features in the image, reflecting the main shape and structure of the scene, and is the key frequency band affecting visual clarity.

High-frequency region: Corresponds to rapidly changing fine details in the image, such as complex textures and small features. In this region, the MTF value attenuates significantly; when it drops to the human eye's contrast sensitivity threshold (usually defined as MTF₁₀, i.e., 0.1), the system's limiting resolution is reached.

In digital imaging systems, the transmission of high frequencies is not infinitely extended and is also limited by the physical spacing of the sensor pixels. This limit is defined by the Nyquist frequency (fₙ = 1/(2×PixelPitch)), which is the theoretical boundary of digital sampling and represents the highest theoretical spatial frequency that the system can reproduce. When the frequency of scene details exceeds this limit, the MTF not only drops to an extremely low level but also triggers aliasing, resulting in false colors or moiré patterns.

MTF Evaluation Characteristic Frequencies:

• MTF50: Refers to the spatial frequency at which the MTF value drops to 0.5. It is strongly correlated with human visual perception of sharpness and is widely used as a core indicator for evaluating overall sharpness.
• MTF50P: Refers to the spatial frequency at which the MTF drops to 50% of the curve's peak value. For images processed with digital sharpening, the MTF peak may exceed 1.
• MTF10: Refers to the spatial frequency at which the MTF value drops to 0.1. It is close to the threshold for the human eye to distinguish fine details and is commonly used as a reference for the effective limiting resolution in engineering.

Directional Analysis: Tangential and Sagittal

Meridional direction (Tangential, denoted as T): The intersection of the meridional plane (containing the optical axis and the image point) with the image plane is radial. Sampling in the meridional (T) direction moves along the radius, used to measure tangential lines. It is sensitive to astigmatism and field curvature, with the MTF curve attenuating more rapidly.

Sagittal direction (Sagittal, denoted as S): The sagittal plane (perpendicular to the meridional plane) corresponds to the tangential direction. Sampling in the sagittal (S) direction moves along the circumference, used to measure radial lines. The MTF curve is more gradual, better reflecting the system’s fundamental resolution.

Interpretation of T/S Curve Diagram:

• X - axis: Represents the image plane position (from the center 0 mm to the edge 20 mm), reflecting the imaging performance at different fields of view.
• Y - axis: Represents the MTF value (contrast transfer capability), with a range of 0–1. The higher the value, the clearer the imaging.

The MTF curve, measured in both meridional (T) and sagittal (S) directions, intuitively reflects the magnitude of astigmatism and the contrast transfer characteristics of the entire field of view: The higher the coincidence of T/S curves, the smaller the astigmatism; High - frequency contrast transfer is weaker than low - frequency, and contrast gradually decreases from the central field of view to the edge field of view, with the T curve attenuating faster and the S curve being more gradual; Dual - direction testing can comprehensively evaluate imaging quality and accurately diagnose directional aberrations.

III. Causes of Imaging Blur
Image blur in digital cameras is caused by multiple factors, which can be mainly divided into three categories:
3.1 Geometric aberrations and diffraction of the lens
(1) Geometric Aberrations and Diffraction of the Lens

Geometric schematic diagrams of third-order monochromatic aberrations. (a) No aberration (b) Spherical aberration © Coma (d) Astigmatism (e) Field curvature (f) Distortion

Among them, spherical aberration, coma, and astigmatism all prevent point objects from converging into ideal point images, resulting in image blur. In addition, since optical media have different refractive indices for light of different frequencies, the imaging positions of different colors of light will differ. This type of aberration is called chromatic aberration, which also leads to unclear imaging. Some aberrations can be corrected by using lenses with complex surface shapes, lenses made of special materials, lens groups composed of multiple lenses, and more reasonable aperture stop positions. However, at the present stage, aberrations cannot be completely eliminated.

Diagram of diffraction causes and phenomena

As shown in Figure (a), when a plane wave passes through the aperture of an imaging system (such as the lens aperture), each point within the aperture can be regarded as a secondary wave source. When these secondary waves propagate to the image plane, they interfere and superimpose, and cannot converge into an ideal geometric point. Under far - field (Fraunhofer) conditions, this interference forms the one - dimensional intensity distribution in Figure (b) and the Airy disk (circular aperture diffraction pattern) in Figure ©. The Airy disk causes the image of a point target to disperse, and the light energy spreads to the geometric shadow area, ultimately producing imaging blur limited by diffraction.

(2) Pixel aperture and optoelectronic crosstalk of the image sensor

Schematic diagram of image blur caused by the aperture of the photosensitive element in a solid - state imager

When the English character “W” is imaged on an 8×8 pixel array, each pixel can only output one brightness value. This results in spatial averaging of the light intensity information within its aperture area, causing the edges and details of the character to be smoothed, thus producing image blur.

Schematic diagram of the crosstalk generation mechanism in a solid - state imager

In CMOS imagers, both electrical crosstalk caused by carrier diffusion in the quasi - neutral region and optical crosstalk caused by photons incorrectly entering adjacent pixels can lead to image blur. Both optical and electrical crosstalk can be improved through physical methods. For example, using a back - illuminated design can improve optical crosstalk, and adding insulating trenches between pixels can reduce electrical crosstalk. However, the impact of the geometric characteristics of the photosensitive element aperture is always present.

3.2 Software Level of Image Processing

Blur caused by image processing is generally either intentional (such as blur resulting from beauty filters and background blurring for shallow depth of field effects) or a side effect of a certain processing step (such as blur caused by the loss of some image details while denoising).

3.3 Environmental Factors
When photographing distant targets, atmospheric turbulence and aerosols can cause atmospheric blur. Relative motion between the subject and the imager during exposure can introduce motion blur. Stray light (non - imaging light) from strong light sources within and outside the camera’s field of view, forming ghosting, glare, etc., will reduce brightness contrast and thus cause image blur.

IV. MTF Testing Methods
4.1 Using Sine Patterns
Input sinusoidal grating patterns with brightness varying sinusoidally (e.g., logarithmic frequency stripes or Siemens star targets) into the imaging system. In the spatial domain, extract peak and valley values at various frequencies from the linearized image, calculate modulation depth, and normalize by ratioing with the original contrast (or low-frequency baseline) at the input to fit a complete MTF curve.

Logarithmic frequency stripe target	Siemens star target

Advantages: The measurement principle most closely aligns with the physical definition of MTF; less affected by image sharpening and other post-processing; Siemens star patterns can measure MTF in all directions simultaneously, suitable for astigmatism diagnosis and full-angle resolution assessment. Additionally, aliasing phenomena such as “reverse contrast” or “pseudocolor” appearing in the central region of the star pattern can accurately detect the Nyquist frequency limit of the sensor.

Limitations:Low spatial utilization of targets; highly sensitive to focusing accuracy, light source uniformity, and image noise; slower calculation speed; typically requires noise reduction or multi-frame averaging algorithms to ensure accuracy.

Applications: Primarily used for laboratory-level optical reference calibration, lens image quality assessment, edge method result verification, and evaluating the real detail preservation capability of imaging systems after strong ISP algorithm processing.

4.2 Using Edge Spread Function
4.2.1 Slanted-Edge Method
According to the latest ISO 12233 standard, capture a straight edge with a slight tilt angle (typically 5°). The tilted edge creates different “phases” to form oversampled edge spread functions, counteracting uncertainties introduced by the spatial variation of the discrete pixel array on the sensor. Subsequently, the first derivative of the edge spread function is calculated to obtain the line spread function, which is then Fourier transformed and its magnitude taken to yield the MTF curve. The calculation process is shown in the figure below:
Advantages: Compliant with ISO 12233 standard; using recommended 4:1 low-contrast edges effectively suppresses MTF overestimation caused by post-processing sharpening; high spatial utilization, strong noise resistance, and high computational efficiency, suitable for mass production scenarios.

Limitations: Susceptible to lens distortion, which can cause edges to become curved or deviate from the set tilt angle, thereby reducing oversampling reconstruction accuracy.

Applications: Widely used for automated production line MTF testing and quality control of products such as smartphones, automotive imaging, and industrial cameras, as well as for evaluating resolution performance and algorithm verification of laboratory imaging systems.

4.2.2 Circular Edge Method
As described in 4.2.1, although the slanted straight-edge method is suitable for mass production testing, it has two core limitations: first, a single straight edge can only measure the one-dimensional SFR in the direction perpendicular to the edge, and cannot simultaneously obtain the imaging performance in the two key directions of tangential and sagittal; second, it is easily affected by the distortion of wide-angle cameras, leading to edge bending or angle deviation, which in turn invalidates oversampling and makes it difficult to accurately characterize the true resolution in distorted areas.
To address these issues, the circular edge MTF testing method provides an effective solution. This method replaces the straight-edge target with a circular edge target. First, an ROI containing a complete circle is selected in the image and pixel values are linearized. Then, the center of the circle is located and a sector area in the target direction is selected. Subsequently, the arc edge is extracted and fitted. An oversampled edge spread function is constructed by calculating the distance from pixels to the edge curve. After derivation and windowed smoothing, a discrete Fourier transform is performed on the obtained line spread function, and its modulus is taken and normalized to obtain the circular edge SFR in the specified direction. The calculation process is shown in the figure below:
Applications: Suitable for mass production of wide-angle/fisheye automotive cameras, full-field multi-directional MTF measurement, and upstream/downstream measurement benchmarking.

4.3 Using Random Patterns
The commonly used test target is the dead leaves chart, which has the characteristics of a known spectrum and full spatial frequency coverage. This target is composed of randomly overlapping circular “coins” whose radii, grayscale, and positions follow specific probability distributions, possessing a 1/f scale-invariant spectral characteristic. Its design typically adopts a 3:1 low contrast (compliant with standards such as CPIQ) to simulate the weak texture features of natural scenes and avoid signal saturation.

• Testing Principle: The imaging system photographs the “dead leaves chart” target with known spectral characteristics, and a Fourier transform is performed on the captured image to extract its actual power spectral density (PSD). By calculating the ratio of this actual spectrum to the predefined theoretical spectral model of the target, the modulation transfer function (MTF) of the imaging system at different spatial frequencies can be inversely derived.
• Advantages: A single shot can obtain the full-band MTF curve, resulting in high efficiency; the statistical characteristics of the low-contrast random texture are extremely close to natural scenes, which can effectively bypass the interference of edge sharpening algorithms, and the evaluation results are more aligned with the human eye's visual perception of true detail fidelity.
  
• Limitations: The spatial utilization of the target is lower than that of the slanted-edge method; the calculation highly relies on accurate noise power spectrum (PSD) subtraction and texture extraction algorithms; it is extremely sensitive to noise, requiring multi-frame averaging to ensure stability; and it is easily affected by target manufacturing accuracy and image plane uniformity, with absolute measurement accuracy slightly lower than the high-contrast slanted-edge method.
  
• Applications: The black-and-white version focuses on the basic resolution of the system's luminance channel; the color version is the core means for diagnosing the loss of color details caused by non-linear denoising algorithms and evaluating color texture fidelity.
  

V. From Laboratory to Production Line: Test Equipment Solutions
5.1 Testing Process:

1. Environment Setup: According to the testing requirements of the Device Under Test (DUT), configure a standard light source with continuously adjustable color temperature, illuminance, and optional spectral bands in a dark room. Set parameters according to testing needs (e.g., color temperature 6500K, chart center illuminance 800 lx) to simulate the target test scenario. Simultaneously, select standardized targets that comply with image quality testing specifications (such as the 4:1 contrast, 5° slanted-edge chart recommended by the ISO 12233 international standard) to provide an accurate theoretical reference for subsequent MTF calculations.
   
2. Image Acquisition: Securely mount the DUT using a dedicated fixture, connect supporting equipment, and turn on the power to bring it into normal working condition. Complete parameter configuration and locking according to the DUT output type to ensure stable and reproducible test conditions (e.g., RAW modules need to be switched to linear mode, hardware noise reduction, HDR, and other non-linear processing turned off, and key parameters such as exposure time and gain manually configured and locked; YUV modules need to complete 3A (Auto Exposure (AE), Auto Focus (AF), Auto White Balance (AWB)) convergence, then lock 3A core parameters and related settings such as sharpening and noise reduction).
   
3. Software Analysis: Use professional image quality analysis software (such as RIQA software) to process the captured target images, calculate, and generate the MTF curves corresponding to the selected targets.
   
4. Result Interpretation: Analyze the MTF curves and key metrics (such as MTF50, MTF10, etc.), compare them with preset standards and customer technical requirements, and determine whether the DUT's imaging resolution and sharpness meet the standards.
   

5.2 Testing Systems

See More
Spatial Frequency Response SFR Test, CMS Sharpness Test, CMS Depth of Field Test