Ball lens

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A photograph through a ball lens Through the lens ball - a different view (2020-07-31 13.15.20 by Kaarina Dillabough).jpg
A photograph through a ball lens

A ball lens is an optical lens in the shape of a sphere. Formally, it is a bi-convex spherical lens with the same radius of curvature on both sides, and diameter equal to twice the radius of curvature. The same optical laws may be applied to analyze its imaging characteristics as for other lenses.

Contents

As a lens, a transparent sphere of any material with refractive index (n) greater than air (n > 1.00) bends parallel rays of light to a focal point. For most glassy materials the focal point is only slightly beyond the surface of the ball, on the side opposite to where the rays entered. Ball lenses have extremely high optical aberration, including large amounts of coma and field curvature compared to conventional lenses.

Ball lenses or "lensballs" are used by photographers to take novel extreme wide-angle photos.

Optical coupling

A ruby ball lens atop a green laser pointer. The 520 nm light is absorbed and remitted as red fluorescence, showing how the lens focuses the light into a cone within. Ball lenses are often used to connect optical fibers to light sources. Ruby ball fluorescence @ 520nm laser illumination.jpg
A ruby ball lens atop a green laser pointer. The 520 nm light is absorbed and remitted as red fluorescence, showing how the lens focuses the light into a cone within. Ball lenses are often used to connect optical fibers to light sources.

The first lenses were likely spherical or cylindrical glass containers filled with water, which people noticed had the ability to focus light. Simple convex lenses have surfaces that are small sections of a sphere. A ball lens is just a simple lens where the surfaces' radii of curvature are equal to the radius of the lens itself.

A ball lens refracts light at the interface between its surface and its surroundings. Light from a collimated source is bent into a converging cone. The rays travel in straight lines within the lens, and then are bent again when they exit, converging to a focal point which is typically just outside the ball.

The focal length of a ball lens is a function of its refractive index and its diameter. The effective focal length (EFL) of a ball lens is much larger than the back focal length (BFL), the distance from the back surface of the lens to the focal point. Ball lenses have the shortest possible focal length for a given lens diameter (for a spherical lens). Due to the optical invariant, this allows light from a collimated beam to be focused to smaller diameters than could be achieved with other spherical lenses. Similarly, a point source of light placed at the focal point will produce a collimated beam emanating from the opposite side of the lens, and the lens's large ratio of diameter to focal length (large numerical aperture) allows more light to be captured than would be possible with other spherical lenses. This makes ball lenses particularly suited for coupling light from a laser to a fiber-optic cable or a detector, or from one fiber-optic cable to another, or for micro-optical systems. In addition, ball lenses are omnidirectional, which eases alignment of optical couplings over other types of lens because all that is necessary is to keep everything centered. Ball lenses for optical coupling are typically small, ranging from 5 millimeters down to as tiny as 110 micrometers, with focal lengths ranging from 100 to 250 micrometers. They tend to be made of high-quality optical glass such as borosilicate glass or quartz glass, or crystals such as synthetic sapphire with refractive indices ranging from 1.5 to 1.8. Higher indices produce a shorter focal length for a given size ball. [1]

Fiber optics

Ball lenses are often used in fiber optics. Due to their short focal lengths and the subsequently small waist diameters they produce in a laser beam, they are ideally suited to focus nearly all of the light from a laser into an optical fiber core. The numerical apertures of the fiber and lens need to match. The fiber can usually be placed in direct contact with the ball, helping to ease alignment.

In addition, a ball lens can be used on the output side of a fiber-optic cable to collimate the output back into a beam. In this way, two lenses placed back to back can be used to couple two cables to one another. [2]

Microscopy

Ball lenses are rarely used for imaging applications due to their high optical aberration. Their very short focal lengths allow them to be used to make very simple microscopes, however. A 3 mm ball lens can magnify an image 100 to 200 times, while a 1 mm ball will produce images 200 to 350 times larger than their actual size. [3] In addition, because they are omnidirectional and have large aperture for their focal length, ball lenses convert such images into Bessel wavefronts, which have reduced diffraction effects and can be imaged in the far field as well as in the near field. [4] In 1677, Antonie van Leeuwenhoek used a small ball lens to create a single-lens microscope with 300× magnification, allowing the first observation of spermatozoa. Ball lenses have found uses in many micro-imaging applications, ranging from electron microscopes to single-lens smart-phone microscopes to nano-microscopy. [5]

Omnidirectional lens

A Campbell-Stokes recorder Campbell-Stokes recorder.jpg
A Campbell–Stokes recorder

Unlike other types of lens, the image-forming properties of a ball lens are omnidirectional (independent of the direction being imaged). This effect is exploited in the Campbell–Stokes recorder, a scientific instrument which records the brightness of sunlight by burning the surface of a paper card bent around the sphere. The device, itself fixed, records the apparent motion and intensity of the sun across the sky, burning an image of the sun's motion across the card.[ citation needed ]

Lensball photography

Landscape photograph taken through a lensball Hanstholm Fyr - The crystal ball (10).jpg
Landscape photograph taken through a lensball

Ball lenses are used by photographers to take novel extreme wide-angle photos. [6] [7] [8] The ball lens is placed fairly close to the camera and the camera's own lenses are used to focus an image through it. The light is focused to a small spot at the output surface of the ball, and reaches its focal point just outside the surface. From there the light diverges, flipping both the right/left and the top/bottom axes. Thus, if the camera is too close to the ball lens, the background around the ball will be completely blurred. The further the camera lies from the ball lens, the better the background will come into focus. [9]

Special types

Extremely refractive glass

For materials with refractive index greater than 2, objects at infinity form an image inside the sphere. The image is not directly accessible; the closest accessible point is on the sphere's surface directly opposite the source of light. Most clear solids used for making lenses have refractive indices between 1.4 and 1.6; only a few rare materials have a refractive index of 2 or higher (cubic zirconia, Boron nitride (c‑BN & w‑BN), diamond, moissanite). Many of those few are either too brittle, too soft, too hard, or too expensive for practical lens making (columbite, rutile, tantalite, tausonite). For a refractive index of exactly 2.0, the image forms on the surface of the sphere.[ citation needed ]

Gradient index

A Luneburg lens is a ball lens that has a radially varying index of refraction that follows a certain profile. A Luneberg lens has foci outside the lens and can perfectly image a spherical object. Luneberg lenses designed for radio wavelengths are used in some radar systems and radio antennas.

See also

Related Research Articles

<span class="mw-page-title-main">Optical aberration</span> Deviation from perfect paraxial optical behavior

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.

<span class="mw-page-title-main">Lens</span> 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.

<span class="mw-page-title-main">Numerical aperture</span> Characteristic of an optical system

In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. By incorporating index of refraction in its definition, NA has the property that it is constant for a beam as it goes from one material to another, provided there is no refractive power at the interface. The exact definition of the term varies slightly between different areas of optics. Numerical aperture is commonly used in microscopy to describe the acceptance cone of an objective, and in fiber optics, in which it describes the range of angles within which light that is incident on the fiber will be transmitted along it.

The focal length of an optical system is a measure of how strongly the system converges or diverges light; it is the inverse of the system's optical power. A positive focal length indicates that a system converges light, while a negative focal length indicates that the system diverges light. A system with a shorter focal length bends the rays more sharply, bringing them to a focus in a shorter distance or diverging them more quickly. For the special case of a thin lens in air, a positive focal length is the distance over which initially collimated (parallel) rays are brought to a focus, or alternatively a negative focal length indicates how far in front of the lens a point source must be located to form a collimated beam. For more general optical systems, the focal length has no intuitive meaning; it is simply the inverse of the system's optical power.

<span class="mw-page-title-main">Spherical aberration</span> Optical aberration

In optics, spherical aberration (SA) is a type of aberration found in optical systems that have elements with spherical surfaces. Lenses and curved mirrors are prime examples, because this shape is easier to manufacture. Light rays that strike a spherical surface off-centre are refracted or reflected more or less than those that strike close to the centre. This deviation reduces the quality of images produced by optical systems. The effect of spherical aberration was first identified by Ibn al-Haytham who discussed it in his work Kitāb al-Manāẓir.

<span class="mw-page-title-main">Collimated beam</span> Light all pointing in the same direction

A collimated beam of light or other electromagnetic radiation has parallel rays, and therefore will spread minimally as it propagates. A perfectly collimated light beam, with no divergence, would not disperse with distance. However, diffraction prevents the creation of any such beam.

<span class="mw-page-title-main">Reflecting telescope</span> Telescopes which utilize curved mirrors to form an image

A reflecting telescope is a telescope that uses a single or a combination of curved mirrors that reflect light and form an image. The reflecting telescope was invented in the 17th century by Isaac Newton as an alternative to the refracting telescope which, at that time, was a design that suffered from severe chromatic aberration. Although reflecting telescopes produce other types of optical aberrations, it is a design that allows for very large diameter objectives. Almost all of the major telescopes used in astronomy research are reflectors. Many variant forms are in use and some employ extra optical elements to improve image quality or place the image in a mechanically advantageous position. Since reflecting telescopes use mirrors, the design is sometimes referred to as a catoptric telescope.

Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior 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.

<span class="mw-page-title-main">Objective (optics)</span>

In optical engineering, an objective is an optical element that gathers light from an object being observed and focuses the light rays from it to produce a real image of the object. Objectives can be a single lens or mirror, or combinations of several optical elements. They are used in microscopes, binoculars, telescopes, cameras, slide projectors, CD players and many other optical instruments. Objectives are also called object lenses, object glasses, or objective glasses.

<span class="mw-page-title-main">Gradient-index optics</span>

Gradient-index (GRIN) optics is the branch of optics covering optical effects produced by a gradient of the refractive index of a material. Such gradual variation can be used to produce lenses with flat surfaces, or lenses that do not have the aberrations typical of traditional spherical lenses. Gradient-index lenses may have a refraction gradient that is spherical, axial, or radial.

<span class="mw-page-title-main">Catadioptric system</span> Optical system where refraction and reflection are combined

A catadioptric optical system is one where refraction and reflection are combined in an optical system, usually via lenses (dioptrics) and curved mirrors (catoptrics). Catadioptric combinations are used in focusing systems such as searchlights, headlamps, early lighthouse focusing systems, optical telescopes, microscopes, and telephoto lenses. Other optical systems that use lenses and mirrors are also referred to as "catadioptric", such as surveillance catadioptric sensors.

<span class="mw-page-title-main">Aspheric lens</span> Type of lens

An aspheric lens or asphere is a lens whose surface profiles are not portions of a sphere or cylinder. In photography, a lens assembly that includes an aspheric element is often called an aspherical lens.

X-ray optics is the branch of optics that manipulates X-rays instead of visible light. It deals with focusing and other ways of manipulating the X-ray beams for research techniques such as X-ray crystallography, X-ray fluorescence, small-angle X-ray scattering, X-ray microscopy, X-ray phase-contrast imaging, and X-ray astronomy.

<span class="mw-page-title-main">Vergence (optics)</span> Angle between converging or diverging light rays

In optics, vergence is the angle formed by rays of light that are not perfectly parallel to one another. Rays that move closer to the optical axis as they propagate are said to be converging, while rays that move away from the axis are diverging. These imaginary rays are always perpendicular to the wavefront of the light, thus the vergence of the light is directly related to the radii of curvature of the wavefronts. A convex lens or concave mirror will cause parallel rays to focus, converging toward a point. Beyond that focal point, the rays diverge. Conversely, a concave lens or convex mirror will cause parallel rays to diverge.

<span class="mw-page-title-main">Oil immersion</span>

In light microscopy, oil immersion is a technique used to increase the resolving power of a microscope. This is achieved by immersing both the objective lens and the specimen in a transparent oil of high refractive index, thereby increasing the numerical aperture of the objective lens.

<span class="mw-page-title-main">Microlens</span> Small lens, generally with a diameter less than a millimetre

A microlens is a small lens, generally with a diameter less than a millimetre (mm) and often as small as 10 micrometres (µm). The small sizes of the lenses means that a simple design can give good optical quality but sometimes unwanted effects arise due to optical diffraction at the small features. A typical microlens may be a single element with one plane surface and one spherical convex surface to refract the light. Because micro-lenses are so small, the substrate that supports them is usually thicker than the lens and this has to be taken into account in the design. More sophisticated lenses may use aspherical surfaces and others may use several layers of optical material to achieve their design performance.

The design of photographic lenses for use in still or cine cameras is intended to produce a lens that yields the most acceptable rendition of the subject being photographed within a range of constraints that include cost, weight and materials. For many other optical devices such as telescopes, microscopes and theodolites where the visual image is observed but often not recorded the design can often be significantly simpler than is the case in a camera where every image is captured on film or image sensor and can be subject to detailed scrutiny at a later stage. Photographic lenses also include those used in enlargers and projectors.

<span class="mw-page-title-main">Petzval field curvature</span> Optical aberration

Petzval field curvature, named for Joseph Petzval, describes the optical aberration in which a flat object normal to the optical axis cannot be brought properly into focus on a flat image plane. Field curvature can be corrected with the use of a field flattener, designs can also incorporate a curved focal plane like in the case of the human eye in order to improve image quality at the focal surface.

A flat lens is a lens whose flat shape allows it to provide distortion-free imaging, potentially with arbitrarily-large apertures. The term is also used to refer to other lenses that provide a negative index of refraction. Flat lenses require a refractive index close to −1 over a broad angular range. In recent years, flat lenses based on metasurfaces were also demonstrated.

References

  1. Zappe, Hans (2010). Fundamentals of Micro-Optics. Cambridge University Press. pp. 256–257.
  2. Al-Azzawi, Abdul (2007). Light and Optics: Principles and Practice. CRC Press. pp. 9-36–9-37.
  3. Yang (2015). Ambient Diagnostics. CRC Press. p. 244.
  4. Lin, Ming-Tzer; Furlong, Cosme; Hwang, Chi-Hung (2023). Advancements in Optical Methods, Digital Image Correlation, & Micro- and Nanomechanics. Vol. 4. Springer. pp. 1–10.
  5. Skinner, Michael K. (2016). Encyclopedia of reproduction. Elsevier. p. 66.
  6. Bond, Simon (22 December 2016). "Create glass ball landscapes". Lensball. Digital-photography-school. Retrieved 28 February 2020.
  7. "Lensball photography". Refractique. Retrieved 2023-06-06.
  8. "Lensball photography". lensball.com.au. Retrieved 4 March 2019.
  9. "Seven tips for awesome lensball photography". Australian Photography. 31 March 2020. Retrieved 7 June 2023 via australianphotography.com.