Longitudinal chromatic aberration (LCA) can limit the optical performance in refractive optical systems. Understanding a singlet’s chromatic change of effective focal leads to insights and methods to control LCA. Long established, first order theory, shows the chromatic change in focal length for a zero thickness lens is proportional to it's focal length divided by the lens V number or inverse dispersion. This work presents the derivation of an equation for a thick singlet's chromatic change in effective focal length as a function of center thickness, t, dispersion, V, index of refraction, n, and the Coddington shape factor, K. A plot of bending versus chromatic focal length variation is presented. Lens thickness does not influence chromatic variation of effective focal length for a convex plano or plano convex lens. A lens's center thickness'influence on chromatic focal length variation is more pronounced for lower indices of refraction.
An achromatic component shares a common focus at two wavelengths and is a commonly used device in optical assemblies. This work explores the cost versus performance tradeoff for several types of achromatic lenses: conventional doublets with homogenous glass elements, hybrid doublets with a diffractive surface, axial GRadient INdex (GRIN) lenses (where the index of refraction changes along the length of the lens), and radial GRIN lenses (where the index of refraction changes depending on radial position). First order achromatic principles will be reviewed and applied to each system as a starting point and refined through the use of ray trace software. Optical performance will be assessed in terms of focusing efficiency and imaging. Cost will then be evaluated by accounting for current manufacturing costs and retail price through several distributors.
Constraining the Seidel aberrations of optical surfaces is a common technique for relaxing tolerance sensitivities in the optimization process. We offer an observation that a lens’s Abbe number tolerance is directly related to the magnitude by which its longitudinal and transverse color are permitted to vary in production. Based on this observation, we propose a computationally efficient and easy-to-use merit function constraint for relaxing dispersion tolerance sensitivity. Using the relationship between an element’s chromatic aberration and dispersion sensitivity, we derive a fundamental limit for lens scale and power that is capable of achieving high production yield for a given performance specification, which provides insight on the point at which lens splitting or melt fitting becomes necessary. The theory is validated by comparing its predictions to a formal tolerance analysis of a Cooke Triplet, and then applied to the design of a 1.5x visible linescan lens to illustrate optimization for reduced dispersion sensitivity. A selection of lenses in high volume production is then used to corroborate the proposed method of dispersion tolerance allocation.
The use of aspheres has become common in minimizing aberrations, reducing weight and the overall package. With new
technology for fabrication and metrology being introduced, aspheres have experienced increasing use in wide
applications. Although new techniques allow for tighter tolerance and steeper geometries, there still remains a
significant challenge in designing aspheres for manufacturability and testing. While the topic of designing for
fabrication and metrology limitations has been highlighted over the years, the design process continues to be complex
and may prevent the optical designer from reaching an optimum solution that meets both optical performance and
In achieving such goals, it is important to not only have a fundamental understanding of aspheres and its uses, but also
the flow for a design process using such elements. Without adding the correct constraints and varying them at the
correct time, the design may take extreme forms and hence eliminate fabrication options. In this paper, we present a
method for optimizing aspheres which can be applied to designing simple on-axis single elements all the way to high
numerical aperture multi-element systems. It will outline the procedure of the necessary steps, configurations to pay
attention to, and potential courses of action in order to design for the appropriate solution. Understanding these issues
will enable the optical designer to efficiently produce an asphere meeting optical requirements and fabrication
This paper will demonstrate a graphical method for selecting a pair of optical components to simultaneously achromatize and passively athermalize an imaging lens for use in a housing with a particular coefficient of thermal expansion. The effort will be presented for a generic spectrum, so readers may apply the method to whatever waveband and set of materials that are of interest. The term “component” is used in place of “material” since this paper will explore combinations of refractive and diffractive optics. The method for creating an achromat with two refractive materials will be reviewed. To create an athermal doublet, or lens that does not change focus under temperature changes, the same color equations are used with a slight modification to include housing thermal effects. The paper will culminate by demonstrating how a set of two materials can be used to both color correct and passively athermalize a single lens; these materials can be quickly chosen to match a particular housing material via nomograph. A sample chart for a common waveband will be demonstrated.
Long wave infrared (LWIR) optical systems are prone to defocus with changes in temperature. IR refractive materials
are more thermally sensitive compared to conventional visible glass due to their larger therm-optic coefficients. LWIR
systems can be designed to be passively athermal (little or no change to focus with varying temperatures). Chalcogenide
glasses provide additional material choices for IR lens designers. In particular, AMTIR5 has been engineered so its
therm-optic coefficient matches the coefficient of thermal expansion (CTE) of aluminum, allowing for an athermal
singlet. This paper explores the benefits of using engineered chalcogenide glass for color corrected, passively athermal
Initially, we present color corrected and passively athermal doublets that are designed with different materials and / or
diffractive surfaces. Their thermal and color performance are cataloged for axial beams only. These are intended to be
starting components, which readers may then insert into common design forms, such as Petzval, Double Gauss,
Telephoto, and Inverse Telephoto.
A F/1.3, 20° full field of view, aspheric Petzval lens design form is explored and the MTF is evaluated for -50°C to 85°C
in an aluminum housing. From this design, we explore the tradeoffs between using chalcogenide versus crystalline
materials, diffractive versus pure refractive surfaces, and engineered chalcogenide (AMTIR5) versus "catalog" materials.
Infrared detector technology has progressed to include many fused wavebands. This has been
driven by the need of military systems to image over diverse spectrums. Imaging systems can
now operate in both the short wave infrared (SWIR) as well as the long wave infrared (LWIR).
Reflective optics seems like a natural solution to such a large waveband, but they will have
more restrictive size and field of view constraints. This paper will demonstrate the steps to
achieve a Petzval lens with fast aperture and moderate field that is achromatic in the SWIR and
has low axial color in the LWIR. The lens achieves a high resolution solution in terms of
modulation transfer function (MTF).
With the increasing availability of InGaAs detectors for imaging applications in the short wave infrared (SWIR, 0.9 - 1.7 μm), the need for diffraction limited lenses optimized for this spectrum is rising as well. With an abundance of commercially available optical glasses that are transparent in the SWIR, correcting chromatic aberration over the broader SWIR waveband might seem only a moderately difficult task for the optical designer. As it turns out, it is considerably more difficult because the dispersive nature of most of the common glass flints is decreased in the SWIR, limiting the
availability of strong flints for achromatization. Fortunately, a limited selection of highly dispersive SWIR transparent materials can be found among materials used for mid-wave and long wave infrared (IR) optics. However, some of these IR materials have a strong absorption edge in close proximity to the SWIR waveband which presents the optical designer with a different challenge. This paper examines challenges and tradeoffs specific to material selection for color correction in the design of diffraction limited lenses for the SWIR. Solutions are proposed for achromatic and apochromatic lenses. A discussion of material properties and the SWIR glass map is included.
While researching various gradient index glass families for superb color correction using ZEMAX<SUP>1</SUP> optical design program, the authors found that certain solutions could only be found using the Hammer routine<SUP>2</SUP>. Hammer is a genetic algorithm that breeds a particular lens configuration with variations of itself<SUP>3</SUP>. It is not intended to be a global search routine. Hammer is typically used after the best performance is obtained using the standard damped least squares (DLS) algorithm with the default merit function (MF) based on minimizing root mean square (RMS) spot size. Upon this discovery, the authors proceeded to explore the benefit of using the genetic Hammer algorithm on three different lens systems. To make the solution space more complicated, two axial gradient index (AGRIN) elements were used in each lens type; a bi- AGRIN cemented doublet; a bi-AGRIN air spaced triplet with CaF2 as the center element, and a double Gauss with four AGRIN elements and two CaF2 elements. AGRIN elements were used in each lens to provide a more complex solution space and to make optimization more difficult. After optimization, the performance of each lens was compared wiht the conventionally optimized counterpart using the default MF with a DLS algorithm. After this comparison was made, another trade study was done between the Hammer and DLS algorithms, but in this case, the optimization used a custom MF instead of the default MF. The authors believe this study shows the importance of MF construction over that of using the default RMS spot size metric. A significant improvement was obtained for all lenses with the default MF using the Hammer over the DLS technique, but that improvement was less obvious when a custom MF was used.
This paper presents an approach for correcting conformal missile domes with a non-rotationally symmetric optical element called an arch. A parametric study in terms of aerodynamics, fineness ratio, maximum seeker look angle and dome index of refraction will demonstrate its capabilities for correcting conformal domes. A nomograph for trading optical performance versus relative missile range will also be presented.
This paper discusses a novel approach to correct conformal missile dome aberrations with the addition of unique correction elements. For purposes of this study, an elliptical conformal dome with a fineness ratio of 1.0 and an index of refraction of 1.7 is used. A rotationally symmetric element, referred to as a 'fixed corrector', is capable o f some correction for roll-nod or azimuth- elevation gimbaling schemes. A non-rotationally symmetric corrector, referred to as an 'arch corrector' is capable of correcting roll-nod gimbaled missile seekers. Both methods are compared and the performance in terms of aberrations versus gimbal angle are reported.