Doublet
Introduction
An objective with the crown lens in front is the usual form, originally known as the Fraunhofer objective. The positive crown element of this air-spaced doublet is in front, the negative flint at the rear. The interior radius of curvatures are unequal, and air-space is small (about 2-5 mm).
The Steinheil, or „flint-in-front“, objective is less used because of the greater suscepttibility of the flint glass (less stable than crown glass) to atmospheric attack. The Steinheil objective is also used when offers better correction of aberrations. However, because it has stronger curves, it is seldom used unless necessary.
Design and Optimization
The design of an achromatic refractor doublet is a trial and error process. The designer varies the available degrees of freedom until the aberrations have been reduced to an acceptable level. It is important to work systematically. The design procedure includes four steps. These are:
To start design select from the pull down menu "Refractor | Doublet". The Achromatic Doublet design and analysis applet appears and you can input/change the general doublet data, such as clear diameter, system focal length, edge thickness of the positive lens and center thickness of the negative lens. For a 200 mm lens the minimum edge thickness for the positive lens and the minimum axial thickness for the negative lens will be around 15 mm. In a positive lens the center thickness is always larger than the edge thickness.
The last input is the glass type selection. This is maybe the most important element of the design whose success depends upon the correct glass selection. The following rules apply to the choice of glass:
Now we can proceed to the optimization (iterative process) by using the scroll bars for the corresponding six optimization parameters. What do we need to know for the optimization procedure of an achromatic doublet.
For a cemented doublet, the width of the air space (air gap) is zero, and R2=R3. In an air spaced doublet, the air gap between the lenses is typically set to 1 or 2 millimeters. The initial values of the radii of curvatures are not very critical, but it is useful to study some existing designs before starting. We might assume an initial R1 equal to 2/3 of the focal length of the objective. Making R2 and R3 different is an effective tool in reducing spherical aberration. Suppose we set R3/R2 equal to 1.01 for a Fraunhofer design and to 0.99 for a Steinheil type.
After bending the two lenses so that longitudinal spherical aberration is corrected, you will often discover that the red light and the blue light curves are not crossed and we must move the blue curve with respect to the red curve. This is accomplished by giving the first lens a slightly stronger power (i.e. shorter focal length). The lens power factor of the first lens in a Fraunhofer type doublet normally lies between 1.00 and 1.01, while that of the negative first lens of a Steinheil objective lies between 1.01 and 1.02.
In summary, we can see that for a given set of glasses, the design process works by altering only three parameters:
Other Optimization Parameters
If the designer cannot reduce the aberrations for a particular combination of glasses, a number of degrees of freedom remain. These are the thicknesses of the elements and the width of the air gap, if there is one. The air space is most useful in controlling spherical aberration. Making the air gap larger can reduce spherochromatism. This approach leads to a design called the Clark objective.
Another reason for selecting a larger lens separation is that the designer can achieve an aplanatic system with equal R2 and R3. This simplifies fabrication because the surfaces can be tested against each other by interference. If the ratio R3/R2 approaches unity as the separation of the elements is increased, then this goal can be achieved.
Unfortunately, a large lens distance has some disadvantages: it is very sensitive to decentering, and lateral color may occur. For this reason, the Clark objective is not often used.
The designer may also opt for a Steinheil objective rather than a Fraunhofer. However, only in exceptional cases can a better design be achieved with the Steinheil form.
An objective with the crown lens in front is the usual form, originally known as the Fraunhofer objective. The positive crown element of this air-spaced doublet is in front, the negative flint at the rear. The interior radius of curvatures are unequal, and air-space is small (about 2-5 mm).
The Steinheil, or „flint-in-front“, objective is less used because of the greater suscepttibility of the flint glass (less stable than crown glass) to atmospheric attack. The Steinheil objective is also used when offers better correction of aberrations. However, because it has stronger curves, it is seldom used unless necessary.
Design and Optimization
The design of an achromatic refractor doublet is a trial and error process. The designer varies the available degrees of freedom until the aberrations have been reduced to an acceptable level. It is important to work systematically. The design procedure includes four steps. These are:
- Input doublet diameter, focal length edge thickness of positive lens and center thickness of negative lens.
- Select the design wavelengths including the primary wavelength
- Select the types of glass
- Correct spherical aberration, minimizing spot size diameter
To start design select from the pull down menu "Refractor | Doublet". The Achromatic Doublet design and analysis applet appears and you can input/change the general doublet data, such as clear diameter, system focal length, edge thickness of the positive lens and center thickness of the negative lens. For a 200 mm lens the minimum edge thickness for the positive lens and the minimum axial thickness for the negative lens will be around 15 mm. In a positive lens the center thickness is always larger than the edge thickness.
The last input is the glass type selection. This is maybe the most important element of the design whose success depends upon the correct glass selection. The following rules apply to the choice of glass:
- The glass of the positive lens must have a higher Abbe number than the negative lens.
- A large difference between the Abbe numbers is desirable because less strongly curved surfaces are necessary, allowing spherical aberration and coma to be more easily minimized.
- The negative lens should preferably have a higher refractive index than the positive lens, especially when the lenses are cemented.
- The difference in the relative partial dispersions of the two glasses should be as small as practical so that the secondary spectrum will be small.
- the four radii of curvature R1, R2, R3, and R4
- the correct axial thickness of both lenses
- the power of positive and negative lenses
- air space between two lenses (also optimization parameter)
- effective focal length and back focal length
- two optimization parameters R3/R2 ratio and power ratio
- the difference between two relative partial dispersions dPfe and Abbe numbers dVe
Now we can proceed to the optimization (iterative process) by using the scroll bars for the corresponding six optimization parameters. What do we need to know for the optimization procedure of an achromatic doublet.
For a cemented doublet, the width of the air space (air gap) is zero, and R2=R3. In an air spaced doublet, the air gap between the lenses is typically set to 1 or 2 millimeters. The initial values of the radii of curvatures are not very critical, but it is useful to study some existing designs before starting. We might assume an initial R1 equal to 2/3 of the focal length of the objective. Making R2 and R3 different is an effective tool in reducing spherical aberration. Suppose we set R3/R2 equal to 1.01 for a Fraunhofer design and to 0.99 for a Steinheil type.
After bending the two lenses so that longitudinal spherical aberration is corrected, you will often discover that the red light and the blue light curves are not crossed and we must move the blue curve with respect to the red curve. This is accomplished by giving the first lens a slightly stronger power (i.e. shorter focal length). The lens power factor of the first lens in a Fraunhofer type doublet normally lies between 1.00 and 1.01, while that of the negative first lens of a Steinheil objective lies between 1.01 and 1.02.
In summary, we can see that for a given set of glasses, the design process works by altering only three parameters:
- the curvature ratio R3/R2, which mainly influences the longitudinal spherical aberration
- the radius of curvature of the first surface R1, which mainly influences the coma value
- the lens power factor of the front lens, which influences the relative positions of the longitudinal spherical aberration curves for red and blue light
Other Optimization Parameters
If the designer cannot reduce the aberrations for a particular combination of glasses, a number of degrees of freedom remain. These are the thicknesses of the elements and the width of the air gap, if there is one. The air space is most useful in controlling spherical aberration. Making the air gap larger can reduce spherochromatism. This approach leads to a design called the Clark objective.
Another reason for selecting a larger lens separation is that the designer can achieve an aplanatic system with equal R2 and R3. This simplifies fabrication because the surfaces can be tested against each other by interference. If the ratio R3/R2 approaches unity as the separation of the elements is increased, then this goal can be achieved.
Unfortunately, a large lens distance has some disadvantages: it is very sensitive to decentering, and lateral color may occur. For this reason, the Clark objective is not often used.
The designer may also opt for a Steinheil objective rather than a Fraunhofer. However, only in exceptional cases can a better design be achieved with the Steinheil form.
Applet Tag:
- param value = "Title" value = "Refractor: Fraunhofer Doublet"
- param value = "Doublet Diameter" value = "200.0"
- param value = "Edge Thickness Lens A" value = "10.0"
- param value = "Center Thickness Lens B" value = "10.0"
- param value = "Air Space" value = "2.0"
- param value = "Lens A Glass" value = "FK52"
- param value = "Lens B Glass" value = "KZFSN2"
- param value = "Doublet Focal Length" value = "2000.0"
- param value = "Half Field Angle" value = "0.45"
- param value = "Central Obstruction" value = "0.00"
- param value = "Plot Scale" value = "0.10"
- param value = "TF Start Angle" value = "0.00"
- param value = "TF End Angle" value = "0.45"
- param value = "TF Defocus" value = "0.05"
- param value = "Number of Arms" value = "36"
- param value = "Number of Rings" value = "10"
- param value = "Ray Density" value = "10"
- param value = "Scale Type Index" value = "3"
- param value = "Ray Pattern Index" value = "0"
- param value = "Merrit Function Index" value = "2"
- param value = "Doublet Type Index" value = "0"
- param value = "Air Spaced Index" value = "0"
- param value = "Lens A Catalog Index" value = "6"
- param value = "Lens B Catalog Index" value = "6"
- param value = "Monochr. Color Index" value = "10"
- param value = "WL1 Color Index" value = "1"
- param value = "WL2 Color Index" value = "4"
- param value = "WL3 Color Index" value = "9"
- param value = "Text Color Index" value = "10"