Defocus aberration

Last updated November 02, 2023

In optics, defocus is the aberration in which an image is simply out of focus. This aberration is familiar to anyone who has used a camera, videocamera, microscope, telescope, or binoculars. Optically, defocus refers to a translation of the focus along the optical axis away from the detection surface. In general, defocus reduces the sharpness and contrast of the image. What should be sharp, high-contrast edges in a scene become gradual transitions. Fine detail in the scene is blurred or even becomes invisible. Nearly all image-forming optical devices incorporate some form of focus adjustment to minimize defocus and maximize image quality.

In optics and photography

The degree of image blurring for a given amount of focus shift depends inversely on the lens f-number. Low f-numbers, such as f/1.4 to f/2.8, are very sensitive to defocus and have very shallow depths of focus. High f-numbers, in the f/16 to f/32 range, are highly tolerant of defocus, and consequently have large depths of focus. The limiting case in f-number is the pinhole camera, operating at perhaps f/100 to f/1000, in which case all objects are in focus almost regardless of their distance from the pinhole aperture. The penalty for achieving this extreme depth of focus is very dim illumination at the imaging film or sensor, limited resolution due to diffraction, and very long exposure time, which introduces the potential for image degradation due to motion blur.

The amount of allowable defocus is related to the resolution of the imaging medium. A lower-resolution imaging chip or film is more tolerant of defocus and other aberrations. To take full advantage of a higher resolution medium, defocus and other aberrations must be minimized.

Defocus is modeled in Zernike polynomial format as $a(2\rho ^{2}-1)$ , where $a$ is the defocus coefficient in wavelengths of light. This corresponds to the parabola-shaped optical path difference between two spherical wavefronts that are tangent at their vertices and have different radii of curvature.

For some applications, such as phase contrast electron microscopy, defocused images can contain useful information. Multiple images recorded with various values of defocus can be used to examine how the intensity of the electron wave varies in three-dimensional space, and from this information the phase of the wave can be inferred. This is the basis of non-interferometric phase retrieval. Examples of phase retrieval algorithms that use defocused images include the Gerchberg–Saxton algorithm and various methods based on the transport-of-intensity equation.

In vision

In casual conversation, the term blur can be used to describe any reduction in vision. However, in a clinical setting blurry vision means the subjective experience or perception of optical defocus within the eye, called refractive error. Blur may appear differently depending on the amount and type of refractive error. The following are some examples of blurred images that may result from refractive errors:

The extent of blurry vision can be assessed by measuring visual acuity with an eye chart. Blurry vision is often corrected by focusing light on the retina with corrective lenses. These corrections sometimes have unwanted effects including magnification or reduction, distortion, color fringes, and altered depth perception. During an eye exam, the patient's acuity is measured without correction, with their current correction, and after refraction. This allows the optometrist or ophthalmologist ("eye doctor") to determine the extent refractive errors play in limiting the quality of the patient's vision. A Snellen acuity of 6/6 or 20/20, or as decimal value 1.0, is considered to be sharp vision for an average human (young adults may have nearly twice that value). Best-corrected acuity lower than that is an indication that there is another limitation to vision beyond the correction of refractive error.

The blur disk

Optical defocus can result from incorrect corrective lenses or insufficient accommodation, as, e.g., in presbyopia from the aging eye. As said above, light rays from a point source are then not focused to a single point on the retina but are distributed in a little disk of light, called the blur disk. Its size depends on pupil size and amount of defocus, and is calculated by the equation

$d=0.057pD$

(d = diameter in degrees visual angle, p = pupil size in mm, D = defocus in diopters).^[1]

In linear systems theory, the point image (i.e. the blur disk) is referred to as the point spread function (PSF). The retinal image is given by the convolution of the in-focus image with the PSF.

Related Research Articles

In optics, aberration is a property of optical systems, such as lenses, that causes light to be spread out over some region of space rather than focused to a point. Aberrations cause the image formed by a lens to be blurred or distorted, with the nature of the distortion depending on the type of aberration. Aberration can be defined as a departure of the performance of an optical system from the predictions of paraxial optics. In an imaging system, it occurs when light from one point of an object does not converge into a single point after transmission through the system. Aberrations occur because the simple paraxial theory is not a completely accurate model of the effect of an optical system on light, rather than due to flaws in the optical elements.

$Lens Optical device which transmits and refracts light$

A lens is a transmissive optical device that focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (elements), usually arranged along a common axis. Lenses are made from materials such as glass or plastic and are ground, polished, or molded to the required shape. A lens can focus light to form an image, unlike a prism, which refracts light without focusing. Devices that similarly focus or disperse waves and radiation other than visible light are also called "lenses", such as microwave lenses, electron lenses, acoustic lenses, or explosive lenses.

<span class="mw-page-title-main">Optics</span> Branch of physics that studies light

Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviolet, and infrared light. Because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties.

In optics, chromatic aberration (CA), also called chromatic distortion and spherochromatism, is a failure of a lens to focus all colors to the same point. It is caused by dispersion: the refractive index of the lens elements varies with the wavelength of light. The refractive index of most transparent materials decreases with increasing wavelength. Since the focal length of a lens depends on the refractive index, this variation in refractive index affects focusing. Chromatic aberration manifests itself as "fringes" of color along boundaries that separate dark and bright parts of the image.

A corrective lens is a transmissive optical device that is worn on the eye to improve visual perception. The most common use is to treat refractive errors: myopia, hypermetropia, astigmatism, and presbyopia. Glasses or "spectacles" are worn on the face a short distance in front of the eye. Contact lenses are worn directly on the surface of the eye. Intraocular lenses are surgically implanted most commonly after cataract removal but can be used for purely refractive purposes.

<span class="mw-page-title-main">Eye</span> Organ that detects light and converts it into electro-chemical impulses in neurons

Eyes are organs of the visual system. They provide living organisms with vision, the ability to receive and process visual detail, as well as enabling several photo response functions that are independent of vision. Eyes detect light and convert it into electro-chemical impulses in neurons (neurones). In higher organisms, the eye is a complex optical system which collects light from the surrounding environment, regulates its intensity through a diaphragm, focuses it through an adjustable assembly of lenses to form an image, converts this image into a set of electrical signals, and transmits these signals to the brain through complex neural pathways that connect the eye via the optic nerve to the visual cortex and other areas of the brain. Eyes with resolving power have come in ten fundamentally different forms, and 96% of animal species possess a complex optical system. Image-resolving eyes are present in molluscs, chordates and arthropods.

In optics, a circle of confusion (CoC) is an optical spot caused by a cone of light rays from a lens not coming to a perfect focus when imaging a point source. It is also known as disk of confusion, circle of indistinctness, blur circle, or blur spot.

Angular resolution describes the ability of any image-forming device such as an optical or radio telescope, a microscope, a camera, or an eye, to distinguish small details of an object, thereby making it a major determinant of image resolution. It is used in optics applied to light waves, in antenna theory applied to radio waves, and in acoustics applied to sound waves. The colloquial use of the term "resolution" sometimes causes confusion; when an optical system is said to have a high resolution or high angular resolution, it means that the perceived distance, or actual angular distance, between resolved neighboring objects is small. The value that quantifies this property, θ, which is given by the Rayleigh criterion, is low for a system with a high resolution. The closely related term spatial resolution refers to the precision of a measurement with respect to space, which is directly connected to angular resolution in imaging instruments. The Rayleigh criterion shows that the minimum angular spread that can be resolved by an image forming system is limited by diffraction to the ratio of the wavelength of the waves to the aperture width. For this reason, high resolution imaging systems such as astronomical telescopes, long distance telephoto camera lenses and radio telescopes have large apertures.

$Diffraction-limited system Optical system with resolution performance at the instruments theoretical limit$

In optics, any optical instrument or system – a microscope, telescope, or camera – has a principal limit to its resolution due to the physics of diffraction. An optical instrument is said to be diffraction-limited if it has reached this limit of resolution performance. Other factors may affect an optical system's performance, such as lens imperfections or aberrations, but these are caused by errors in the manufacture or calculation of a lens, whereas the diffraction limit is the maximum resolution possible for a theoretically perfect, or ideal, optical system.

<span class="mw-page-title-main">Astigmatism (optical systems)</span> Optical aberration

An optical system with astigmatism is one where rays that propagate in two perpendicular planes have different foci. If an optical system with astigmatism is used to form an image of a cross, the vertical and horizontal lines will be in sharp focus at two different distances. The term comes from the Greek α- (a-) meaning "without" and στίγμα (stigma), "a mark, spot, puncture".

Visual acuity (VA) commonly refers to the clarity of vision, but technically rates a person's ability to recognize small details with precision. Visual acuity depends on optical and neural factors. Optical factors of the eye influence the sharpness of an image on its retina. Neural factors include the health and functioning of the retina, of the neural pathways to the brain, and of the interpretative faculty of the brain.

<span class="mw-page-title-main">Point spread function</span> Response in an optical imaging system

The point spread function (PSF) describes the response of a focused optical imaging system to a point source or point object. A more general term for the PSF is the system's impulse response; the PSF is the impulse response or impulse response function (IRF) of a focused optical imaging system. The PSF in many contexts can be thought of as the extended blob in an image that represents a single point object, that is considered as a spatial impulse. In functional terms, it is the spatial domain version of the optical transfer function (OTF) of an imaging system. It is a useful concept in Fourier optics, astronomical imaging, medical imaging, electron microscopy and other imaging techniques such as 3D microscopy and fluorescence microscopy.

$Refractive error Problem with focusing light accurately on the retina due to the shape of the eye$

Refractive error, also known as refraction error, is a problem with focusing light accurately on the retina due to the shape of the eye and or cornea. The most common types of refractive error are near-sightedness, far-sightedness, astigmatism, and presbyopia. Near-sightedness results in far away objects being blurry, far-sightedness and presbyopia result in close objects being blurry, and astigmatism causes objects to appear stretched out or blurry. Other symptoms may include double vision, headaches, and eye strain.

Inverse synthetic-aperture radar (ISAR) is a radar technique using radar imaging to generate a two-dimensional high resolution image of a target. It is analogous to conventional SAR, except that ISAR technology uses the movement of the target rather than the emitter to create the synthetic aperture. ISAR radars have a significant role aboard maritime patrol aircraft to provide them with radar image of sufficient quality to allow it to be used for target recognition purposes. In situations where other radars display only a single unidentifiable bright moving pixel, the ISAR image is often adequate to discriminate between various missiles, military aircraft, and civilian aircraft.

In visual perception, the far point is the farthest point at which an object can be placed for its image to be focused on the retina within the eye's accommodation. It is sometimes described as the farthest point from the eye at which images are clear. The other limit of eye's accommodation is the near point.

<span class="mw-page-title-main">High-resolution transmission electron microscopy</span>

High-resolution transmission electron microscopy is an imaging mode of specialized transmission electron microscopes that allows for direct imaging of the atomic structure of samples. It is a powerful tool to study properties of materials on the atomic scale, such as semiconductors, metals, nanoparticles and sp²-bonded carbon. While this term is often also used to refer to high resolution scanning transmission electron microscopy, mostly in high angle annular dark field mode, this article describes mainly the imaging of an object by recording the two-dimensional spatial wave amplitude distribution in the image plane, similar to a "classic" light microscope. For disambiguation, the technique is also often referred to as phase contrast transmission electron microscopy, although this term is less appropriate. At present, the highest point resolution realised in high resolution transmission electron microscopy is around 0.5 ångströms (0.050 nm). At these small scales, individual atoms of a crystal and defects can be resolved. For 3-dimensional crystals, it is necessary to combine several views, taken from different angles, into a 3D map. This technique is called electron tomography.

The Strehl ratio is a measure of the quality of optical image formation, originally proposed by Karl Strehl, after whom the term is named. Used variously in situations where optical resolution is compromised due to lens aberrations or due to imaging through the turbulent atmosphere, the Strehl ratio has a value between 0 and 1, with a hypothetical, perfectly unaberrated optical system having a Strehl ratio of 1.

The contrast transfer function (CTF) mathematically describes how aberrations in a transmission electron microscope (TEM) modify the image of a sample. This contrast transfer function (CTF) sets the resolution of high-resolution transmission electron microscopy (HRTEM), also known as phase contrast TEM.

The eye, like any other optical system, suffers from a number of specific optical aberrations. The optical quality of the eye is limited by optical aberrations, diffraction and scatter. Correction of spherocylindrical refractive errors has been possible for nearly two centuries following Airy's development of methods to measure and correct ocular astigmatism. It has only recently become possible to measure the aberrations of the eye and with the advent of refractive surgery it might be possible to correct certain types of irregular astigmatism.

$Subjective refraction Technique to determine the combination of lenses that will provide the best corrected visual acuity$

Subjective Refraction is a technique to determine the combination of lenses that will provide the best corrected visual acuity (BCVA). It is a clinical examination used by orthoptists, optometrists and ophthalmologists to determine a patient's need for refractive correction, in the form of glasses or contact lenses. The aim is to improve current unaided vision or vision with current glasses. Glasses must also be comfortable visually. The sharpest final refraction is not always the final script the patient wears comfortably.

References

Smith, Warren J., Modern Optical Engineering, McGraw–Hill, 2000, Chapter 11, ISBN 0-07-136360-2

↑ Strasburger, Hans; Bach, Michael; Heinrich, Sven P. (2018). "Blur Unblurred—A Mini Tutorial". i-Perception. 9 (2): 204166951876585. doi:10.1177/2041669518765850. PMC 5946648 . PMID 29770182.

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[blur_unblurred-1] Strasburger, Hans; Bach, Michael; Heinrich, Sven P. (2018). "Blur Unblurred—A Mini Tutorial". i-Perception. 9 (2): 204166951876585. doi:10.1177/2041669518765850. PMC 5946648 . PMID 29770182.

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