The design of an achromatic doublet using the Gee-Wyld Acrhomatic Doublet Design Tool is in two simple steps. First, the user selects optical glass types that will be used in the doublet. Glass selection may itself depend upon the wavelengths of interest; two wavelengths generally denoting this band are also selected along with the glass. The second step in the design is the specification of parameters prior to optimization of the actual design.
Selecting the Glass Types
The calculator has a small set of glass catalogs. The easiest option is to use the glass catalogs to select the desired optical glass for the doublet. A crown and a flint glass must be selected. After selecting the catalog for each glass, the glass type may be selected from within that catalog.
Selecting the Band of Interest
The band of interest is selected with the choice of a wavelength of minimal color error and a wavelength of minimal zonal error. These are simple user-editable fields. The wavelengths are expressed in microns. The initial values of both wavelengths have been selected to provide a reasonable amount of visual correction (Photopic).
Accepting the Glass and Band Selection
When the desired glass types and band of interest have been entered, that selection is accepted by hitting the button marked "Accept". This action also calculates the design constants for the selected glass types and band. Those constants include the central refractive index, the dispersion, and Abbe numbers as well as in-band and out-of-band partial dispersions and variation of those partial dispersion from the "normal" line.
Alternative Methods
If the user is unfamiliar with the glass catalogs, but knows the desired glass type, the "empty" catalog (first in the list) may be selected. The Glass Type field for that glass (crown or flint) is then an editable field. Enter the selected glass type (case insensitive), ending with the "Enter" key. That will start a search of all the internal glass catalogs for the desired glass type. One note: The user must also select the equation type from the four available types (more on this later). Newer glass types typically use either the Sellmeier or Ohara equations while older glass types typically use the Cauchy or Schott equations. In addition, the Sellmeier and Ohara equations are logically equivalent, so either may be selected for the given glass type to be found. Similarly the Cauchy and Schott equations are logically equivalent.
For those more familiar with glass equations, the coefficients may be entered directly. Warning: the "empty" glass catalog must be selected and the glass type must be blank or the user-entered values may be overwritten when the Accept button is hit.
Sometimes glass catalogs do not provide dispersion equation coefficients. In this case, the user may enter the glass constants directly. However, when this method is used, the band selection is not modifiable, as only certain predefined sets of constants are available. If partial dispersions are not available, making them blank (including the differences from the normal curve) will substitute a fit to "normal" glass types.
Initial Design
The doublet is parameterized by it aperture and focal ratio, both of which are selectable via user-editable fields. The aperture may be expressed in any units (inches, mm, etc.). Where applicable, results will be expressed in the same units.
The user-provide aperture is the "Clear Aperture". The lenses themselves will be somewhat larger in order to allow mounting within a lens cell. The Gee-Wyld design tool expresses this "extra" diameter as the percentage needed to obtain the desired clear aperture. This extra is selectable via a user-edittable field.
Lens thickness is expressed as a percentage of the semi-diameter. For convex lenses, the thickness is at the edge of the lens. For concave lenses the thickness is at the center of the lens.
The initial values provided in the tool yield an example. The design is for a 100 mm f/15 doublet. The desired focal length is 1500 mm. The lens diameter is larger than the required 100 mm, the "extra" being 5 percent, so that lens diameter is about 105.263 mm (i.e.: 5 percent of 105.263 mm is 5.263 mm, giving the 100 mm clear aperture). The convex lens of the doublet will have an edge thickness in the initial design of 12.5 percent of the semi-diameter, or about 6.57895 mm. The concave lens will have a center thickness of 14 percent of the semi-diameter or about 7.36842 mm. Exact quantities are not usually required here (more later).
The initial design is generated by clicking the "Design" button. The initial system will be calculated and evaluated. The design values provided are the three thicknesses (the two lenses and the potential air-space between them) and the four radii of curvature of the lenses (front and back, two lenses). The thicknesses (t1, t2 and t3) are actually provided as both the thickness at the center and the thickness at the edge pf the lenses. Both the thicknesses and the radii of curvature are numbered from front to back.
The evaluation values provided are the distance of the [infinity] focus from the back of the lens (back focal length, designated as L'), two measures of spherical aberration (one at 70 percent of the design aperture and one at 100 percent), one measure of coma (the offense against the sine condition, or OSC at 100 percent of the design aperture), and two measures of secondary spectrum (in-band and out-of-band, expressed as a longitudinal difference in focus at the 70% zone).
Refining the Design
The initial design may not be precise. Repeated clicks of the "Iterate" button refine it.
The relative thicknesses given in the lens specification are suggestive, rather than absolute. The iteration toward a refined design does not affect them, even though the radii (and hence sagittae) may change. This aspect may be used to iterate to a design while directly assigning thicknesses. After the initial design, the user may enter t1, t3 or t2 (provided t2 is not variable), followed by the enter key. The new thickness then takes effect. However, the user may also enter an edge thickness followed by the enter key; at that point, the new edge thickness takes effect. This is often especially useful for the air space (t2), as it specifies the thickness of the shim or spacer.
Alternative Design Options
The default doublet design is the Fraunhoefer design, with a [more-or-less] symmetric crown lens in front of a [again, more-or-less] concavoplane flint lens. Toggling the "crown first" option button prior to the initial design step changes the design to look for a Steinheil type of doublet, i.e.: a concave flint meniscus followed by a [more-or-less] convexoplane crown lens.
When the doublet design is tightly constrained (the air space and the relationship between the two inner radii is fixed), it is typical that either OSC (coma) or LA (spherical aberration) may be corrected, but not precisely both. The "for OSC/for LA" toggle button is used to indicate the desired optimization.
The estimate for the condition of minimal spherical aberration results in a quadratic in the overall bending of the doublet. Sometimes, this estimating quadratic does not have a real solution (it normally has two.) When this happens, the indicator on the "for OSC/for LA" button will show "at min LA". At that point, optimization for spherical aberration is not feasible. However, attempting to toggle the "for OSC/for LA" button will force reversion to the original value; if that is optimization for LA, the attempt will be made, even if it is not feasible.
As mentioned above, the estimating equation for zero spherical aberration results in a quadratic in the overall bending of the doublet. That quadratic also often has two solutions. The choice is made internally to choose that solution of the pair that results in the most symmetric crown lens. There are some cases where this is not desired. The "RaC~RbC" may be toggled to choose the alternative design. I have seen few designs where this was needed (a Steinheil CaF2 and Lanthanum Flint doublet is one example); it cannot be ignored as a possibility.
The design of a doublet is often more critical upon the difference between the two inner radii than upon the actual radii themselves. One of the strong simplifications of the design process is then to make the two identical. The "fix R2:R3" button is used to control this. At the initial design stage, enabling this will force the two radii to be equal.
However, after the initial design is complete, the user may actually modify one of the values prior to additional iteration. The altered relationship between R2 and R3 (well, actually C2 and C3) is then maintained over iteration.
Another simplification of doublet design is the maintenance of a fixed air space size. This is controlled with the "fix t2" toggle button.
The Gee-Wyld Acrhomatic Doublet Design Tool may also be used to evaluate externally created designs. After the initial design has been created, the user may change any of the radii or thicknesses and hit the "calculate" button. The user provided design is then evaluated under the same criteria as an internally designed doublet.
The evaluation of LA or OSC is minimally performed at the null zone. The button that "null/color vs OSC/LA" button toggles the fields associated with it. When in the "null/color" mode, it defines the null and color zones (relative to the semi-aperture). When in the "OSC/LA" it controls the relative values of the 100 percent (of null zone) and the 70.7 percent (of null zone) values of OSC or LA as the goal of optimization. This function may be used to create a design in which the desired aspect is minimalized over the entire aperture, rather than nulled at a single zone.
Had enough options? Then get to work. The Gee-Wyld Achromat
Double Design Tool was compiled to be able to run under
any of the 1.4.2, 1.5.0 or 1.6.0 Java run-time, depending
upon the version installed on your system: