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.

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 illustrations of third-order monochromatic aberrations: (a) Ideal imaging without 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 illustrating the causes and manifestations of diffraction

As shown in Figure (a), when a plane wave passes through the aperture of an imaging system (such as a lens aperture), each point on the wavefront within the aperture acts as a secondary source. When these secondary waves propagate to the image plane, they undergo interference and superposition, failing to converge perfectly 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 object to disperse, with light energy spreading into the geometrical shadow, ultimately resulting in diffraction-induced image blur.

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

Schematic of Image Blur of Letter W Caused by Finite Pixel Apertures in Solid-State Imagers

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 Sinusoidal patterns
A sinusoidal grating is a periodic test pattern whose luminance varies continuously according to a sinusoidal function. Logarithmic frequency stripes and Siemens star targets are examples of such patterns. In the spatial domain, the peak and trough values at each frequency are extracted from the linearized image, the modulation depth is calculated, and the result is normalized by the input contrast or a low-frequency reference to obtain a complete MTF curve.

Logarithmic frequency stripe target	Siemens star target

Advantages: The measurement principle is closely aligned with the physical definition of MTF, and it is less affected by post-processing such as image sharpening. A Siemens star target can measure MTF in all directions in a single exposure, making it suitable for astigmatism diagnosis and full-angle resolution evaluation. In addition, aliasing phenomena such as reversed contrast or false color in the central region of the star target can be used to detect the sensor’s Nyquist-frequency limit.

Limitations:Obtaining a complete MTF curve requires coverage of multiple spatial frequencies. When multiple frequency patterns are integrated into a single target, different frequencies appear at different spatial positions, making it difficult to characterize the performance of a single field of view accurately. Acquiring each frequency separately is inefficient and requires high stability and registration accuracy. In addition, this method is sensitive to focus, illumination uniformity, and noise, and often requires multi-frame averaging to ensure accuracy.

Applications: This method is mainly used for laboratory optical calibration, lens image-quality evaluation, validation of slanted-edge results, and assessment of the true detail-preserving capability of imaging systems after strong ISP processing.

4.2 Using Edge Spread Function
4.2.1 Slanted-Edge Method
Per the latest ISO 12233 standard, a slanted edge (typically tilted at 5°) is captured. The slant introduces phase diversity, generating oversampled edge spread functions (ESFs) to mitigate uncertainties from the spatial variation of the sensor’s discrete pixel array. The first derivative of the ESF yields the line spread function (LSF), which is then Fourier transformed; the magnitude of this transform yields 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 Section 4.2.1, although the slanted-edge method is suitable for mass-production testing, it has two core limitations：

• First, a single straight edge provides the one-dimensional SFR only along the direction perpendicular to the edge, and it cannot simultaneously characterize the resolution performance in the tangential and sagittal directions.
• Second, the method is sensitive to wide-angle optical distortion, which can cause the detected edge to bend or its angle to shift; this makes the oversampling assumption invalid and makes it difficult to accurately characterize the actual resolution in distorted regions.

To address slanted - edge MTF limitations, the Circular - edge MTF method uses a circular edge target. First, define an ROI with a complete circle and linearize pixel values. Then, locate the circle center, select a sector for the target direction, extract and fit the circular edge, and construct the oversampled ESF by calculating pixel distances to the fitted curve. Differentiate the ESF to get the LSF, apply windowing & apodization, then perform a discrete Fourier transform on the LSF. Finally, take the magnitude and normalize to obtain the Circular - edge MTF in the specified direction. The processing steps are 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 a known spectrum and covers the full range of spatial frequencies. It consists of randomly overlapping circular disks (“coins”) whose radii, gray levels, and positions follow specified probability distributions, and it exhibits a 1/f scale-invariant spectrum. The target is typically designed with a 3:1 low contrast level, in accordance with standards such as CPIQ, to simulate the weak-texture characteristics of natural scenes and avoid signal saturation.

Testing Principle: TThe imaging system captures a dead leaves chart with known spectral characteristics, and a Fourier transform is performed on the captured image to extract its actual power spectral density (PSD). The modulation transfer function (MTF) at different spatial frequencies is then derived by taking the ratio of the measured spectrum to the target’s predefined theoretical spectral model.

Advantages:A single exposure can produce a full-band MTF curve, making the method highly efficient. The statistical characteristics of the low-contrast random texture are close to those of natural scenes, which reduces the influence of edge-sharpening algorithms and makes the results more consistent with human visual perception of fine-detail fidelity.

Limitations:The spatial efficiency of the target is lower than that of the slanted-edge method. The calculation depends heavily on accurate subtraction of the noise power spectral density and on texture-extraction algorithms. The method is highly sensitive to noise and often requires multi-frame averaging to ensure stability. It is also affected by target fabrication accuracy and image-plane uniformity, and its absolute measurement accuracy is slightly lower than that of the high-contrast slanted-edge method.

Applications: The monochrome version is mainly used to assess the basic resolving power of the luminance channel, while the color version is used to diagnose color-detail loss caused by nonlinear denoising algorithms and to evaluate 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