Triplet
Introduction
After Fraunhofer and Steinheil objectives, the triplet is thethird type of objective commonly used in refracting telescopes. This is a photo-visual objective. The use of three different glasses permits a considerable reduction of chromatic difference of focus over a given spectral range to be obteined. This objective is almost equally good for photographic and visual wavelengths, and at one time was popular for astronomical use at apertures up to about 12“.
Additionally, triplet refractors can be designed to work at focal ratios between f/6 and f/10, as compared with the f/15 focal ratio of a conventional doublet. A triplet corrected for three colors is called an apochromat, whereas a triplet corrected for four colors is termed a superachromat (by Max Herzberger). The first element is biconvex, the second biconcave, and the third element biconvex.
The steep curves of the centre component, making centering difficult, and the early use of unstable varieties of flint glass, have detracted, however, from the value of these lenses.
Design and Optimization
The designing a triplet is nearly the same as designing a doublet. But there are some important differences. When designing a triplet, the choice of a proper glass combination is very important, so much so that it is the coice of glass, and not the design process, that is the most time-consuming part of making a new design.
With a triplet, the number of design parameters is higher than with a doublet. The additional parameters are the curvature ratio R5/R4 and the lens power ratio F3/F2. Because there are more ways to achieve very low spherical aberration and OSC with apochromatic color correction, designing a triplet is considerably more complex than designing a doublet.
In general a suitable combination of glasses for a triplet consists of:
When we require that the lens bring four colors to a common focus (violet, blue, green and red), the three glasses must satisfy an additional condition. It can be shown mathematically that when four colors are to be corrected, the three glasses in the P-P (Pec-Pge) diagram will lie on a straight line. This is the case for the combination that includes TiF2. The glass combination with BaFN10 glass does not satisfy the straight line condition and with this combination only three color can be brought into a common focus.
In the design of a broken triplet, we use the variables R1, R3/R2 and R5/R4 to correct spherical aberration and coma, while lens power ratios F2/F1 and F3/F2 are used to minimize the influence of spherochromatism. We start with changing the values of R3/R2 and R5/R4 for one starting value of R1 (default value is 1.04 of the triplet focal length). Through trial and error, we determine what particular combination of both variables gives the smallest LA and OSC. We repeat the procedure for other values of R1 until the best values of LA and OSC are obtained. During the first trials, the three desired colors generally do not focus at a common point on the LA-curves. As soon as the value of LA has been sufficiently decreased, we vary slightly the powers of the first and second lens with respect to the third lens.After several trials, the colors are made to coincide and intersect somewhere between to 70% and 100% zone. After correcting spherochromatism, we continue to optimize LA and OSC.
Designing cemented and immersion objectives is difficult because the airgraps are fixed at zero and both curvature ratios are fixed at unity. Only R1 and the lens power are free parameters. In this case all other radii depend on the chosen value of R1. Often it is not possible to correct LA and OSC sufficiently with R1 alone and we must vary with F2/F1 and F3/F2 to achieve a good design.
After Fraunhofer and Steinheil objectives, the triplet is thethird type of objective commonly used in refracting telescopes. This is a photo-visual objective. The use of three different glasses permits a considerable reduction of chromatic difference of focus over a given spectral range to be obteined. This objective is almost equally good for photographic and visual wavelengths, and at one time was popular for astronomical use at apertures up to about 12“.
Additionally, triplet refractors can be designed to work at focal ratios between f/6 and f/10, as compared with the f/15 focal ratio of a conventional doublet. A triplet corrected for three colors is called an apochromat, whereas a triplet corrected for four colors is termed a superachromat (by Max Herzberger). The first element is biconvex, the second biconcave, and the third element biconvex.
The steep curves of the centre component, making centering difficult, and the early use of unstable varieties of flint glass, have detracted, however, from the value of these lenses.
Design and Optimization
The designing a triplet is nearly the same as designing a doublet. But there are some important differences. When designing a triplet, the choice of a proper glass combination is very important, so much so that it is the coice of glass, and not the design process, that is the most time-consuming part of making a new design.
With a triplet, the number of design parameters is higher than with a doublet. The additional parameters are the curvature ratio R5/R4 and the lens power ratio F3/F2. Because there are more ways to achieve very low spherical aberration and OSC with apochromatic color correction, designing a triplet is considerably more complex than designing a doublet.
In general a suitable combination of glasses for a triplet consists of:
- a glass with a relatively high V-value and relatively low P-value, such as a crown with an Abbe number between 60 and 70
- a glass with a relatively low V-value and high P-value such as one of the KzFS glasses
- a glass with low V-value and a P-value even higher than that of the second glass, usually a dense flint
When we require that the lens bring four colors to a common focus (violet, blue, green and red), the three glasses must satisfy an additional condition. It can be shown mathematically that when four colors are to be corrected, the three glasses in the P-P (Pec-Pge) diagram will lie on a straight line. This is the case for the combination that includes TiF2. The glass combination with BaFN10 glass does not satisfy the straight line condition and with this combination only three color can be brought into a common focus.
In the design of a broken triplet, we use the variables R1, R3/R2 and R5/R4 to correct spherical aberration and coma, while lens power ratios F2/F1 and F3/F2 are used to minimize the influence of spherochromatism. We start with changing the values of R3/R2 and R5/R4 for one starting value of R1 (default value is 1.04 of the triplet focal length). Through trial and error, we determine what particular combination of both variables gives the smallest LA and OSC. We repeat the procedure for other values of R1 until the best values of LA and OSC are obtained. During the first trials, the three desired colors generally do not focus at a common point on the LA-curves. As soon as the value of LA has been sufficiently decreased, we vary slightly the powers of the first and second lens with respect to the third lens.After several trials, the colors are made to coincide and intersect somewhere between to 70% and 100% zone. After correcting spherochromatism, we continue to optimize LA and OSC.
Designing cemented and immersion objectives is difficult because the airgraps are fixed at zero and both curvature ratios are fixed at unity. Only R1 and the lens power are free parameters. In this case all other radii depend on the chosen value of R1. Often it is not possible to correct LA and OSC sufficiently with R1 alone and we must vary with F2/F1 and F3/F2 to achieve a good design.
Applet Tag:
- param name = "Title" value = "Refractor: Apochromatic Triplet"
- param name = "Triplet Diameter" value = "200.0"
- param name = "Edge Thickness Lens A" value = "10.0"
- param name = "Center Thickness Lens B" value = "10.0"
- param name = "Edge Thickness Lens C" value = "10.0"
- param name = "Firs Air Space" value = "0.0"
- param name = "Second Air Space" value = "0.0"
- param name = "Lens A Glass" value = "BK7"
- param name = "Lens B Glass" value = "KZFS1"
- param name = "Lens C Glass" value = "TIF3"
- param name = "Triplet Focal Length" value = "2000.0"
- param name = "Half Field Angle" value = "0.45"
- param name = "Central Obstruction" value = "0.00"
- param name = "Plot Scale" value = "0.10"
- param name = "TF Start Angle" value = "0.00"
- param name = "TF End Angle" value = "0.45"
- param name = "TF Defocus" value = "0.05"
- param name = "Number of Arms" value = "36"
- param name = "Number of Rings" value = "10"
- param name = "Ray Density" value = "10"
- param name = "Scale Type Index" value = "3"
- param name = "Ray Pattern Index" value = "0"
- param name = "Merrit Function Index" value = "2"
- param name = "Triplet Type Index" value = "0"
- param name = "Lens A Catalog Index" value = "6"
- param name = "Lens B Catalog Index" value = "6"
- param name = "Lens C Catalog Index" value = "6"
- param name = "Monochr. Color Index" value = "10"
- param name = "WL1 Color Index" value = "1"
- param name = "WL2 Color Index" value = "4"
- param name = "WL3 Color Index" value = "9"
- param name = "Text Color Index" value = "10"