An achromatic lens or achromat is a lens that is designed to limit the effects of chromatic and spherical aberration. Achromatic lenses are corrected to bring two wavelengths (typically red and blue) into focus on the same plane. Wavelengths in between these two then have better focus error than could be obtained with a simple lens.
The most common type of achromat is the achromatic doublet , which is composed of two individual lenses made from glasses with different amounts of dispersion. Typically, one element is a negative (concave) element made out of flint glass such as F2, which has relatively high dispersion, and the other is a positive (convex) element made of crown glass such as BK7, which has lower dispersion. The lens elements are mounted next to each other, often cemented together, and shaped so that the chromatic aberration of one is counterbalanced by that of the other.
In the most common type (shown), the positive power of the crown lens element is not quite equalled by the negative power of the flint lens element. Together they form a weak positive lens that will bring two different wavelengths of light to a common focus. Negative doublets, in which the negative-power element predominates, are also made.
Theoretical considerations of the feasibility of correcting chromatic aberration were debated in the 18th century following Newton's statement that such a correction was impossible (see History of the telescope). Credit for the invention of the first achromatic doublet is often given to an English barrister and amateur optician named Chester Moore Hall. [1] [2] Hall wished to keep his work on the achromatic lenses a secret and contracted the manufacture of the crown and flint lenses to two different opticians, Edward Scarlett and James Mann. [3] [4] [5] They in turn sub-contracted the work to the same person, George Bass. He realized the two components were for the same client and, after fitting the two parts together, noted the achromatic properties. Hall used the achromatic lens to build the first achromatic telescope, but his invention did not become widely known at the time. [6]
In the late 1750s, Bass mentioned Hall's lenses to John Dollond, who understood their potential and was able to reproduce their design. [2] Dollond applied for and was granted a patent on the technology in 1758, which led to bitter fights with other opticians over the right to make and sell achromatic doublets.
Dollond's son Peter invented the apochromat, an improvement on the achromat, in 1763. [2]
Several different types of achromat have been devised. They differ in the shape of the included lens elements as well as in the optical properties of their glass (most notably in their optical dispersion or Abbe number).
In the following, R denotes the radius of the spheres that define the optically relevant refracting lens surfaces. By convention, R1 denotes the first lens surface counted from the object. A doublet lens has four surfaces with radii R1 through R2. Surfaces with positive radii curve away from the object (R1 positive is a convex first surface); negative radii curve toward the object (R1 negative is a concave first surface).
The descriptions of the achromat lens designs mention advantages of designs that do not produce "ghost" images. Historically, this was indeed a driving concern for lens makers up to the 19th century and a primary criterion for early optical designs. However, in the mid 20th century, the development of advanced optical coatings for the most part has eliminated the issue of ghost images, and modern optical designs are preferred for other merits.
Uses an equiconvex crown glass lens (i.e. R1 > 0 with −R1 = R2 ) and a complementary-curved second flint glass lens (with R3 = R2 ). The back of the flint glass lens is flat ( R4 = ∞ ). A Littrow doublet can produce a ghost image between R2 and R3 because the lens surfaces of the two lenses have the same radii.
The first lens has positive refractive power, the second negative. R1 > 0 is set greater than −R2, and R3 is set close to, but not quite equal to, −R2. R4 is usually greater than −R3. In a Fraunhofer doublet, the dissimilar curvatures of −R2 and R3 are mounted close, but not quite in contact. [7] This design yields more degrees of freedom (one more free radius, length of the air space) to correct for optical aberrations.
Early Clark lenses follow the Fraunhofer design. After the late 1860s, they changed to the Littrow design, approximately equiconvex crown, R1 = R2 , and a flint with R3 ≃ R2 and R4 ≫ R3 . By about 1880, Clark lenses had R3 set slightly shorter than R2 to create a focus mismatch between R2 and R3, thereby avoiding ghosting caused by reflections within the airspace. [8]
The use of oil between the crown and flint eliminates the effect of ghosting, particularly where R2 ≈ R3 . It can also increase light transmission slightly and reduce the impact of errors in R2 and R3.
The Steinheil doublet, devised by Carl August von Steinheil, is a flint-first doublet. In contrast to the Fraunhofer doublet, it has a negative lens first followed by a positive lens. It needs stronger curvature than the Fraunhofer doublet. [9]
Dialyte lenses have a wide air space between the two elements. They were originally devised in the 19th century to allow much smaller flint glass elements down stream since flint glass was hard to produce and expensive. [10] They are also lenses where the elements can not be cemented because R2 and R3 have different absolute values. [11]
The first-order design of an achromat involves choosing the overall power of the doublet and the two glasses to use. The choice of glass gives the mean refractive index, often written as (for the refractive index at the Fraunhofer "d" spectral line wavelength), and the Abbe number (for the reciprocal of the glass dispersion). To make the linear dispersion of the system zero, the system must satisfy the equations
where the lens power is for a lens with focal length . Solving these two equations for and gives
Since and the Abbe numbers are positive-valued, the power of the second element in the doublet is negative when the first element is positive, and vice versa.
Optical aberrations other than just color are present in all lenses. For example, coma remains after spherical and chromatic aberrations are corrected. In order to correct other aberrations, the front and back curvatures of each of the two lenses remain free parameters, since the color correction design only prescribes the net focal length of each lens, and separately This leaves a continuum of different combinations of front and back lens curvatures for design tweaks ( and for lens 1; and and for lens 2) that will all produce the same and required by the achromat design. Other adjustable lens parameters include the thickness of each lens and the space between the two, all constrained only by the two required focal lengths. Normally, the free parameters are adjusted to minimize non-color-related optical aberrations.
Lens designs more complex than achromatic can improve the precision of color images by bringing more wavelengths into exact focus, but require more expensive types of glass, and more careful shaping and spacing of the combination of simple lenses:
In theory, the process can continue indefinitely: Compound lenses used in cameras typically have six or more simple lenses (e.g. double-Gauss lens); several of those lenses can be made with different types of glass, with slightly altered curvatures, in order to bring more colors into focus. The constraint is extra manufacturing cost, and diminishing returns of improved image for the effort.
In optics and lens design, the Abbe number, also known as the Vd-number or constringence of a transparent material, is an approximate measure of the material's dispersion, with high values of Vd indicating low dispersion. It is named after Ernst Abbe (1840–1905), the German physicist who defined it. The term Vd-number should not be confused with the normalized frequency in fibers.
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.
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.
In optics, chromatic aberration (CA), also called chromatic distortion, color aberration, color fringing, or purple fringing, 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. Since the focal length of the lens varies with the color of the light different colors of light are brought to focus at different distances from the lens or with different levels of magnification. Chromatic aberration manifests itself as "fringes" of color along boundaries that separate dark and bright parts of the image.
Dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency. Sometimes the term chromatic dispersion is used to refer to optics specifically, as opposed to wave propagation in general. A medium having this common property may be termed a dispersive medium.
The Cooke triplet is a photographic lens designed and patented in 1893 by Dennis Taylor who was employed as chief engineer by T. Cooke & Sons of York. It was the first lens system that allowed the elimination of most of the optical distortion or aberration at the outer edge of the image.
A refracting telescope is a type of optical telescope that uses a lens as its objective to form an image. The refracting telescope design was originally used in spyglasses and astronomical telescopes but is also used for long-focus camera lenses. Although large refracting telescopes were very popular in the second half of the 19th century, for most research purposes, the refracting telescope has been superseded by the reflecting telescope, which allows larger apertures. A refractor's magnification is calculated by dividing the focal length of the objective lens by that of the eyepiece.
An optical telescope gathers and focuses light mainly from the visible part of the electromagnetic spectrum, to create a magnified image for direct visual inspection, to make a photograph, or to collect data through electronic image sensors.
John Dollond was an English optician, known for his successful optics business and his patenting and commercialization of achromatic doublets.
An apochromat, or apochromatic lens (apo), is a photographic or other lens that has better correction of chromatic and spherical aberration than the much more common achromat lenses.
An eyepiece, or ocular lens, is a type of lens that is attached to a variety of optical devices such as telescopes and microscopes. It is named because it is usually the lens that is closest to the eye when someone looks through an optical device to observe an object or sample. The objective lens or mirror collects light from an object or sample and brings it to focus creating an image of the object. The eyepiece is placed near the focal point of the objective to magnify this image to the eyes. The amount of magnification depends on the focal length of the eyepiece.
In optics, a doublet is a type of lens made up of two simple lenses paired together. Such an arrangement allows more optical surfaces, thicknesses, and formulations, especially as the space between lenses may be considered an "element". With additional degrees of freedom, optical designers have more latitude to correct more optical aberrations more thoroughly.
Crown glass is a type of optical glass used in lenses and other optical components. It has relatively low refractive index (≈1.52) and low dispersion. Crown glass is produced from alkali-lime silicates containing approximately 10% potassium oxide and is one of the earliest low dispersion glasses.
The achromatic telescope is a refracting telescope that uses an achromatic lens to correct for chromatic aberration.
Chester Moore Hall was a British lawyer and inventor who produced the first achromatic lenses in 1729 or 1733 . He used the achromatic lens to build the first achromatic telescope, a refracting telescope free from chromatic aberration.
Athermalization, in the field of optics, is the process of achieving optothermal stability in optomechanical systems. This is done by minimizing variations in optical performance over a range of temperatures.
A dialyte lens is a compound lens design that corrects optical aberrations where the lens elements are widely air-spaced. The design is used to save on the amount of glass used for specific elements or where elements can not be cemented because they have dissimilar curvatures. The word dialyte means "parted", "loose" or "separated" in Greek.
The Gauss lens is a compound achromatic lens that uses two uncemented elements; in its most basic form, a positive meniscus lens on the object side and a negative meniscus lens on the image side. It was first proposed in 1817 by the mathematician Carl Friedrich Gauss for a refracting telescope design, but was seldom implemented and is better known as the basis for the Double-Gauss lens first proposed in 1888 by Alvan Graham Clark, which is a four-element, four-group compound lens that uses a symmetric pair of Gauss lenses.
Low-dispersion glass is a type of glass with reduced chromatic aberration, meaning the refractive index does not change as strongly with different wavelengths of light. In other words, the light passing through the glass has a smaller spread or dispersion between its constituent colors, resulting in a reduced "rainbow effect" at high-contrast edges. Wavelength dispersion in a certain material is characterized by its Abbe number; LD glass has a higher Abbe number than conventional types. Crown glass is an example of a relatively inexpensive low-dispersion glass.