Optical lens design

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Optical lens design is the process of designing a lens to meet a set of performance requirements and constraints, including cost and manufacturing limitations. Parameters include surface profile types (spherical, aspheric, holographic, diffractive, etc.), as well as radius of curvature, distance to the next surface, material type and optionally tilt and decenter. The process is computationally intensive, using ray tracing or other techniques to model how the lens affects light that passes through it.

Contents

Design requirements

Performance requirements can include:

  1. Optical performance (image quality): This is quantified by various metrics, including encircled energy, modulation transfer function, Strehl ratio, ghost reflection control, and pupil performance (size, location and aberration control); the choice of the image quality metric is application specific. [1] [2] [ citation needed ]
  2. Physical requirements such as weight, static volume, dynamic volume, center of gravity and overall configuration requirements.
  3. Environmental requirements: ranges for temperature, pressure, vibration and electromagnetic shielding.

Design constraints can include realistic lens element center and edge thicknesses, minimum and maximum air-spaces between lenses, maximum constraints on entrance and exit angles, physically realizable glass index of refraction and dispersion properties.

Manufacturing costs and delivery schedules are also a major part of optical design. The price of an optical glass blank of given dimensions can vary by a factor of fifty or more, depending on the size, glass type, index homogeneity quality, and availability, with BK7 usually being the cheapest. Costs for larger and/or thicker optical blanks of a given material, above 100–150 mm, usually increase faster than the physical volume due to increased blank annealing time required to achieve acceptable index homogeneity and internal stress birefringence levels throughout the blank volume. Availability of glass blanks is driven by how frequently a particular glass type is made by a given manufacturer, and can seriously affect manufacturing cost and schedule.

Process

Lenses can first be designed using paraxial theory to position images and pupils, then real surfaces inserted and optimized. Paraxial theory can be skipped in simpler cases and the lens directly optimized using real surfaces. Lenses are first designed using average index of refraction and dispersion (see Abbe number) properties published in the glass manufacturer's catalog and through glass model calculations. However, the properties of the real glass blanks will vary from this ideal; index of refraction values can vary by as much as 0.0003 or more from catalog values, and dispersion can vary slightly. These changes in index and dispersion can sometimes be enough to affect the lens focus location and imaging performance in highly corrected systems.

The lens blank manufacturing process is as follows:

  1. The glass batch ingredients for a desired glass type are mixed in a powder state,
  2. the powder mixture is melted in a furnace,
  3. the fluid is further mixed while molten to maximize batch homogeneity,
  4. poured into lens blanks and
  5. annealed according to empirically determined time-temperature schedules.

The glass blank pedigree, or "melt data", can be determined for a given glass batch by making small precision prisms from various locations in the batch and measuring their index of refraction on a spectrometer, typically at five or more wavelengths. Lens design programs have curve fitting routines that can fit the melt data to a selected dispersion curve, from which the index of refraction at any wavelength within the fitted wavelength range can be calculated. A re-optimization, or "melt re-comp", can then be performed on the lens design using measured index of refraction data where available. When manufactured, the resulting lens performance will more closely match the desired requirements than if average glass catalog values for index of refraction were assumed.

Delivery schedules are impacted by glass and mirror blank availability and lead times to acquire, the amount of tooling a shop must fabricate prior to starting on a project, the manufacturing tolerances on the parts (tighter tolerances mean longer fab times), the complexity of any optical coatings that must be applied to the finished parts, further complexities in mounting or bonding lens elements into cells and in the overall lens system assembly, and any post-assembly alignment and quality control testing and tooling required. Tooling costs and delivery schedules can be reduced by using existing tooling at any given shop wherever possible, and by maximizing manufacturing tolerances to the extent possible.

Lens optimization

A simple two-element air-spaced lens has nine variables (four radii of curvature, two thicknesses, one airspace thickness, and two glass types). A multi-configuration lens corrected over a wide spectral band and field of view over a range of focal lengths and over a realistic temperature range can have a complex design volume having over one hundred dimensions.

Lens optimization techniques that can navigate this multi-dimensional space and proceed to local minima have been studied since the 1940s, beginning with early work by James G. Baker, and later by Feder, [3] Wynne, [4] Glatzel, [5] Grey [6] and others. Prior to the development of digital computers, lens optimization was a hand-calculation task using trigonometric and logarithmic tables to plot 2-D cuts through the multi-dimensional space. Computerized ray tracing allows the performance of a lens to be modelled quickly, so that the design space can be searched rapidly. This allows design concepts to be rapidly refined. Popular optical design software includes Zemax's OpticStudio, Synopsys's Code V, and Lambda Research's OSLO. In most cases the designer must first choose a viable design for the optical system, and then numerical modelling is used to refine it. [7] The designer ensures that designs optimized by the computer meet all requirements, and makes adjustments or restarts the process when they do not.

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">Refractive index</span> Ratio of the speed of light in vacuum to that in the medium

In optics, the refractive index of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.

<span class="mw-page-title-main">Single-mode optical fiber</span> Optical fiber designed to carry only a single mode of light, the transverse mode

In fiber-optic communication, a single-mode optical fiber (SMF), also known as fundamental- or mono-mode, is an optical fiber designed to carry only a single mode of light - the transverse mode. Modes are the possible solutions of the Helmholtz equation for waves, which is obtained by combining Maxwell's equations and the boundary conditions. These modes define the way the wave travels through space, i.e. how the wave is distributed in space. Waves can have the same mode but have different frequencies. This is the case in single-mode fibers, where we can have waves with different frequencies, but of the same mode, which means that they are distributed in space in the same way, and that gives us a single ray of light. Although the ray travels parallel to the length of the fiber, it is often called transverse mode since its electromagnetic oscillations occur perpendicular (transverse) to the length of the fiber. The 2009 Nobel Prize in Physics was awarded to Charles K. Kao for his theoretical work on the single-mode optical fiber. The standards G.652 and G.657 define the most widely used forms of single-mode optical fiber.

<span class="mw-page-title-main">Chromatic aberration</span> Failure of a lens to focus all colors on the same point

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.

<span class="mw-page-title-main">Corrective lens</span> Type of lens to improve visual perception

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">Achromatic lens</span> Lens that is designed to limit the effects of chromatic and spherical aberration

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<span class="mw-page-title-main">Prism (optics)</span> Transparent optical element with flat, polished surfaces that refract light

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<span class="mw-page-title-main">Anti-reflective coating</span> Optical coating that reduces reflection

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<span class="mw-page-title-main">Doublet (lens)</span>

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<span class="mw-page-title-main">Dielectric mirror</span> Mirror made of dielectric materials

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<span class="mw-page-title-main">Refractometer</span> Measurement Tool

A refractometer is a laboratory or field device for the measurement of an index of refraction (refractometry). The index of refraction is calculated from the observed refraction angle using Snell's law. For mixtures, the index of refraction then allows to determine the concentration using mixing rules such as the Gladstone–Dale relation and Lorentz–Lorenz equation.

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The Christiansen effect is named after the Danish physicist Christian Christiansen and describes the reduced scattering of multi-phase microstructures at wavelengths where their refractive indices match.

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Low-dispersion glass is a type of glass with a reduction in chromatic aberration. Crown glass is an example of a relatively inexpensive low-dispersion glass.

<span class="mw-page-title-main">Precision glass moulding</span> Production of optical glass without grinding and polishing

Precision glass moulding is a replicative process that allows the production of high precision optical components from glass without grinding and polishing. The process is also known as ultra-precision glass pressing. It is used to manufacture precision glass lenses for consumer products such as digital cameras, and high-end products like medical systems. The main advantage over mechanical lens production is that complex lens geometries such as aspheres can be produced cost-efficiently.

Fiber-optic filter is an optical fiber instrument used for wavelength selection, which can select desired wavelengths to pass and reject the others. It is Widely used in DWDM systems dynamic wavelength selection, DWDM signal separation, optical performance monitoring, field tunable optical noise filtering and optical amplifier noise suppression, etc. Optical multiplexers (couplers) makes different wavelength coupling into an optical fiber and different wavelength carries different information. At the receiving end, if you want to separate desired wavelengths from optical fiber, it is necessary to use optical filter.

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

A lens antenna is a directional antenna that uses a shaped piece of microwave-transparent material to bend and focus microwaves by refraction, as an optical lens does for light. Typically it consists of a small feed antenna such as a patch antenna or horn antenna which radiates radio waves, with a piece of dielectric or composite material in front which functions as a converging lens to collimate the radio waves into a beam. Conversely, in a receiving antenna the lens focuses the incoming radio waves onto the feed antenna, which converts them to electric currents which are delivered to a radio receiver. They can also be fed by an array of feed antennas, called a focal plane array (FPA), to create more complicated radiation patterns.

References

Notes

  1. Fischer, Robert E.; Tadic-Galeb, Biljana; Yoder, Paul R. (2008). Optical System Design (2nd ed.). New York: McGraw-Hill. pp. 8, 179–198. ISBN   978-0-07-147248-7.
  2. "Modulation Transfer Function".
  3. D.P. Feder, "Automatic Optical Design," Appl. Opt. 2, 1209–1226 (1963).
  4. C. G. Wynne and P. Wormell, "Lens Design by Computer," Appl. Opt. 2:1223–1238 (1963).
  5. "Dr. Erhardt Glatzel (Biography)". The Zeiss Historica Society. Archived from the original on January 27, 2013. Retrieved July 21, 2013.
  6. Grey, D.S., "The Inclusion of Tolerance Sensitivities in the Merit Function for Lens Optimization", SPIE Vol. 147, pp. 63–65, 1978.
  7. Fischer (2008), pp. 171–5.

Bibliography