Need to Know: Visual Metrics

Optical quality of the images formed in the human eye can be assessed using key optical quality metrics. These include the modulation transfer function (MTF), optical transfer function (OTF), phase transfer function (PTF), point spread function (PSF), and the Strehl ratio. Visual perception or visual transfer function (VTF) is contributed to by the optical transfer function (OTF) and the neural transfer function (NTF). Let us understand each of these terms.

The optical transfer function describes how details or different spatial frequencies are transferred by the human eye’s optical system. It consists of the MTF and the PTF and is the Fourier transform of the PSF. A reduction in OTF results in loss of high spatial frequencies or fine details.

OTF = MTF (amplitude/magnitude) + PTF (phase shift).

Modulation transfer function

Image performance is characterized by resolution and contrast. Resolution is the ability to distinguish object detail and is measured in terms of line pairs per millimetre (lp/mm), cycles per millimetre, or frequency. Inverse of frequency gives the spacing between two resolved line pairs. Contrast is the difference in light intensity between an object and its background. It can be degraded by diffraction effects, optical aberrations, and vignetting. Contrast = (Imax − Imin)/(Imax + Imin), where ‘I’ refers to intensity.

MTF is a performance metric that measures the ability of an optical system to transfer all the various levels of detail (spatial frequencies) from object to image. Thus, it describes contrast loss/preservation (how much image contrast is degraded as compared to object contrast) at different spatial frequencies. It is the optical contribution to contrast sensitivity function (CSF) and refers to the ratio of image contrast to object contrast as a function of spatial frequency.

To determine MTF, a sinusoidal pattern with 100% contrast is used as the object, and MTF is plotted on the y-axis (representing contrast transfer) with spatial frequency on the x-axis. It is also often plotted in comparison to that of a perfect, aberration-free, diffraction-limited system.

As spatial frequency of the lines increases (i.e., line spacing decreases), the contrast of the image decreases due to optical limitations such as diffraction, aberrations (both lower and higher order), and scatter (e.g., media abnormalities, such as corneal haze or cataracts). A high MTF allows contrast in fine details while a low MTF diminishes contrast, resulting in blurry, washed-out images. Degradation makes distinguishing small features in the image more difficult. Low illumination can affect MTF; therefore, testing is generally set to photopic conditions, although charts may also be plotted at different illumination levels.

MTF is the absolute value or magnitude of OTF, derived from the Fourier transform of the PSF. The human eye has low MTF and consequently a low OTF for high spatial frequencies, so very fine details are not perfectly transmitted, thus limiting resolution of vision.

PTF describes phase distortions across different spatial frequencies—the light waves that shift in phase affecting sharpness and alignment of details. This is especially necessary to describe aberrations (like coma and astigmatism) where MTF alone is not sufficient, as these create a shift in image features without decreasing contrast. Symptoms of phase distortions include ghosting, diplopia, and asymmetrical blur.

Point spread function

The PSF is the image of the point source formed by the human eye or any other optical system. A point source constitutes the most fundamental object and is the basis for more complex objects. A perfect optical system should image a point source of light as a single point. However, aberrations, diffraction, and imperfections spread the image into a blurry spot. The PSF for a perfect optical system is the Airy disc, which is the Fraunhofer diffraction pattern for a circular pupil. PSF is the inverse Fourier transform of the OTF; A larger PSF implies a poorer image quality.

A Strehl ratio is the ratio between peak intensity of the real PSF and a theoretically perfect, diffraction-limited PSF. A higher Strehl ratio indicates sharper vision, while a lower ratio indicates worse PSF and lower MTF. The average value for the human eye is approximately 0.1–0.3, which is secondary to aberrations.

NTF refers to the processing of spatial frequency information within the retina and the brain that further refines visual perception. Factors affecting NTF include:

Photoreceptor sampling: The cone density of the fovea limits the amount of detail perception. The Nyquist sampling theorem states that the maximum resolvable spatial frequency is half the photoreceptor sampling rate. The Nyquist limit refers to the highest frequency the retina can process without aliasing artefacts (false patterns). In the fovea, cone spacing allows a theoretical Nyquist limit of approximately 60 cycles per degree (cpd). However, the actual perceived limit is slightly lower (approximately 40–50 cpd) due to neural optimization.

Neural contrast enhancement: This works through lateral inhibition and cortical processing. Lateral inhibition reduces the activity of neighbouring neurons when one neuron is stimulated. In the visual process, surrounding signals are suppressed by horizontal and amacrine cells to enhance contrast and colour discrimination. It sharpens edges via the Mach band effect—an optical illusion of edges appearing darker or lighter than in reality. Cortical processing by the visual cortex is responsible for further enhancement and higher-level interpretation via edge detection, orientation sensitivity, and motion perception. NTF enhances mid-spatial frequencies, improving edge detection. It also suppresses very high spatial frequencies (above 60 cpd) to filter out noise and aliasing and reduce the perceptual impact of optical aberrations.

While neural processing can compensate for some optical aberrations, an excess decline in MTF, and consequently OTF and VTF (explained later), can cause loss of detail. Wavefront-guided, wavefront-optimized, and topography-guided LASIK, intracorneal ring segments, CAIRS, and aberration-modifying IOLs, among others, are all attempts to improve the optical transfer function of the eye. Adaptive optics aid in researching wavefront modification.

Stiles–Crawford effect

The Stiles–Crawford effect (SCE) is an optical and retinal phenomenon that gives different weightage to light entering the eye through different pupil locations. Cones are 200-fold more tightly packed in the foveal region. Foveal cones are also taller and thinner than peripheral cones (1.5–2.0 μm at the fovea versus 4.0–10.0 μm in the peripheral retina). The shape and high refractive index of the foveal cones compared to the surrounding intercellular medium give them optical waveguide-like properties.

Similar to an optical fibre, foveal cones guide and preferentially transmit axial light entering at angles closer to their optical axis. SCE-I explains how light rays entering at the centre of the pupil are perceived as brighter and more effective for vision than those entering near the periphery of the pupil, even if their physical intensities are the same. SCE-I therefore pre-filters retinal input, providing a better optical signal to the retina by suppressing peripheral rays that are more affected by aberrations. SCE-II refers to the perceived colour of light changing slightly depending on the pupil entry location. This effect is greatest for red and blue light where chromatic dispersion is maximum. SCE-II compensates for chromatic aberration by altering neural perception of colour differences.

VTF describes the final perceived visual quality and is secondary to the combined effect of OTF and NTF.

Adaptive optics

In visual research, adaptive optics (AO) help to correct aberrations using a combination of wavefront sensors, real-time feedback control systems, and deformable mirrors or liquid crystal spatial light modulators that correct distortions. AO is used to study higher-order aberrations, design and simulate the effect of custom corrections, and understand neural adaptations. It is also used in retinal imaging to compensate for image distortion secondary to ocular aberrations.

This is the fourth in a multipart tutorial on higher-order aberrations. Previous articles in the series can be found at escrs.org/eurotimes.

Dr Soosan Jacob is Director and Chief of Dr Agarwal’s Refractive and Cornea Foundation at Dr Agarwal’s Eye Hospital, Chennai, India, and can be reached at dr_soosanj@hotmail.com.