Jan. 06, 2025
The complexity of optical elements comes from the difference between simplified elements used for simulation and real optical elements that comes with limitation and defaults. Doublets are a way to minimise some optical default in your optical system, lets learn more about them.
CLZ contains other products and information you need, so please check it out.
A doublet lens is a assembly of two lenses of different material cemented together.
Every optical material is subject to chromatic dispersion, defined by their Vd value. This chromatic dispersion will cause scattering of a signal at different wavelengths.
The objective of manufacturing a doublet lens is two use to 'complementary' dispersing material to compensate the chromatic dispersion and have a resulting doublet lens with identical focusing power on it's whole wavelength range.
These lenses are also called : achromatic lens, meaning lens with no chromatic dispersion, achromatic doublet is also a common name.
Achromatic doublets are usually made out of two kinds of glass : Flint glass and Crown glass. A concave lens will be made usually in Flint glass and a convex lens in Crown glass with similar radius of curvature so they can easily be cemented together.
Flint glass are high refringent glass, meaning that they will cause a high scattering of light rays according to their wavelength. While Crown glass are low dispersion glass. It is easy to find is a glass is Flint or Crown as its name will include a 'F' for Flint or a K for Crown (for example in the most common : N-BK7 ( Schott) or H-K9L (CDGM).
Cementing of the two lenses to form the doublet, is done with very thin, optically neutral glue material and hardened with UV light. Positioning of both lenses during the cementing and the hardening of the cementing medium is the key factor to the success of the manufacturing of the achromatic lens.
In order to increase optical transmission of the lens, it is not unusual to have a antireflect coating added on external surfaces after the cementing.
Doublets improve the optical quality of a lens reducing both chromatic dispersion and spherical aberration. Their were first discovered in the XVIII century in England for telescopes applications.
Currently many imaging applications in the visible are using doublets :
Designing of a a doublet lens is not very difficult but need the experience of an optician to better understand the material possibilities and define the surface shapes of the two optics.
Design deliverable will be a separate drawing including optical glass selection for each component and eventually an assembly drawing of the doublet that will state the coating requirements and may also request blackening of the doublet edge.
Once the design completed, precision optics manufacturers with the experience and ability to assemble doublet lenses, will be able to quote for its manufacturing.
The complexity of optical elements comes from the difference between simplified elements used for simulation and real optical elements that comes with limitation and defaults. Doublets are a way to minimise some optical default in your optical system, lets learn more about them.
View Details
A doublet lens is a assembly of two lenses of different material cemented together.
Every optical material is subject to chromatic dispersion, defined by their Vd value. This chromatic dispersion will cause scattering of a signal at different wavelengths.
The objective of manufacturing a doublet lens is two use to complementary dispersing material to compensate the chromatic dispersion and have a resulting doublet lens with identical focusing power on its whole wavelength range.
These lenses are also called : achromatic lens, meaning lens with no chromatic dispersion, achromatic doublet is also a common name.
Achromatic doublets are usually made out of two kinds of glass : Flint glass and Crown glass. A concave lens will be made usually in Flint glass and a convex lens in Crown glass with similar radius of curvature so they can easily be cemented together.
Flint glass are high refringent glass, meaning that they will cause a high scattering of light rays according to their wavelength. While Crown glass are low dispersion glass. It is easy to find is a glass is Flint or Crown as its name will include a F for Flint or a K for Crown (for example in the most common : N-BK7 ( Schott) or H-K9L (CDGM).
Cementing of the two lenses to form the doublet, is done with very thin, optically neutral glue material and hardened with UV light. Positioning of both lenses during the cementing and the hardening of the cementing medium is the key factor to the success of the manufacturing of the achromatic lens.
In order to increase optical transmission of the lens, it is not unusual to have a antireflect coating added on external surfaces after the cementing.
Doublets improve the optical quality of a lens reducing both chromatic dispersion and spherical aberration. Their were first discovered in the XVIII century in England for telescopes applications.
Currently many imaging applications in the visible are using doublets :
Designing of a a doublet lens is not very difficult but need the experience of an optician to better understand the material possibilities and define the surface shapes of the two optics.
Design deliverable will be a separate drawing including optical glass selection for each component and eventually an assembly drawing of the doublet that will state the coating requirements and may also request blackening of the doublet edge.
Once the design completed, precision optics manufacturers with the experience and ability to assemble doublet lenses, will be able to quote for its manufacturing.
This is a continuation from the previous tutorial - two lens systems.
The singlet lens suffers from axial chromatic aberration, which is determined by the Abbe number \(V\) of the lens material and its \(\text{FN}\). A widely used lens form that corrects this aberration is the achromatic doublet as illustrated in Fig. 19.
Figure 19 Typical achromatic doublet lens.An achromatic lens has equal focal lengths in \(c\) and \(f\) light. This lens comprises two lens elements where one element with a high \(V\)-number (crown glass) has the same power sign as the doublet and the other element has a low \(V\)-number (flint glass) with opposite power sign.
Three basic configurations are used. These are the cemented doublet, broken contact doublet, and the widely airspaced doublet (dialyte). The degrees of freedom are two lens powers, glasses, and shape of each lens.
The resultant power of two thin lenses in close proximity, \(s_2\rightarrow0\), is \(\phi_{ab}=\phi_a+\phi_b\) and the transverse primary chromatic aberration \(\text{TPAC}\) is
\[\tag{40}\text{TPAC}=-yf_{ab}\left[\frac{\phi_a}{V_a}+\frac{\phi_b}{V_b}\right]\]
where \(y\) is the marginal ray height.
Featured content:For more Commercial doublet lens wholesalerinformation, please contact us. We will provide professional answers.
Setting \(\text{TPAC}=0\) and solving for the powers of the lenses yields
\[\tag{41}\phi_a=\frac{V_a}{f_{ab}(V_a-V_b)}\]
\[\tag{42}\phi_b=\frac{-V_b\phi_a}{V_a}\]
The bending or shape of a lens is expressed by \(c=c_1-c_2\) and affects the aberrations of the lens. The bending of each lens is related to its power by \(c_a=\phi_a/(n_a-1)\) and \(c_b=\phi_b(n_b-1)\).
Since the two bendings can be used to correct the third-order spherical and coma, the equations for these aberrations can be combined to form a quadratic equation in terms of the curvature of the first surface \(c_1\). Solving for \(c_1\) will yield zero, one, or two solutions for the first lens. A linear equation relates \(c_1\) to \(c_2\) of the second lens.
While maintaining the achromatic correction of a doublet, the spherical aberration as a function of its shape (\(c_1\)) is described by a parabolic curve. Depending upon the choices of glasses, the peak of the curve may be above, below, or at the zero spherical aberration value.
When the peak lies in the positive spherical aberration region, two solutions with zero spherical aberration exist in which the solution with the smaller value of \(c_1\) is called the left-hand solution (Fraunhofer or Steinheil forms) and the other is called the right-hand solution (Gaussian form).
Two additional solutions are possible by reversal of the glasses. These two classes of designs are denoted as crown-in-front and flint-in-front designs. Depending upon the particular design requirements, one should examine all four configurations to select the most appropriate.
The spherical aberration curve can be raised or lowered by the selection of the \(V\) difference or the \(n\) difference. Specifically, the curve will be lowered as the \(V\) difference is increased or if the \(n\) difference is reduced. As for the thin singlet lens, the coma will be zero for the configuration corresponding to the peak of the spherical aberration curve.
With competitive price and timely delivery, Hongsheng sincerely hope to be your supplier and partner.
Although the primary chromatic aberration may be corrected, a residual chromatic error often remains and is called the secondary spectrum, which is the difference between the ray intercepts in \(d\) and \(c\).
Figure 20 An F/5 airspaced doublet using conventional glasses is shown in (a) and exhibits residual secondary chromatic aberration. A similar lens is shown in (b) that uses a new glass to effectively eliminate the secondary color.Figure 20(a) illustrates an F/5 airspaced doublet that exhibits well-corrected spherical light and primary chromatic aberrations and has notable secondary color. The angular secondary spectrum for an achromatic thin-lens doublet is given by
\[\tag{43}\text{SAC}=\frac{-(P_a-P_b)}{2(\text{FN})(V_a-V_b)}\]
where \(P=(n_\lambda-n_c)/(n_f-n_c)\) is the partial dispersion of a lens material.
In general, the ratio \((P_a-P_b)/(V_a-V_b)\) is nearly a constant which means little can be done to correct the \(\text{SAC}\). A few glasses exist that allow \(P_a-P_b\approx0\), but the \(V_a-V_b\) is often small, which results in lens element powers of rather excessive strength in order to achieve achromatism.
Figure 20(b) shows an F/5 airspaced doublet using a relatively new pair of glasses that have a small \(P_a-P_b\) and a more typical \(V_a-V_b\). Both the primary and secondary chromatic aberration are well corrected. Due to the relatively low refractive index of the crown glass, the higher power of the elements results in spherical aberration through the seventh order. Almost no spherochromatism (variation of spherical aberration with wavelength) is observed. The 80 percent blur diameter is almost the same for both lenses and is 0.007.
Table 3 contains the prescriptions for these lenses.
Table 3 Prescriptions for Achromatic Doublets Shown in Fig. 20When the separation between the lens elements is made a finite value, the resultant lens is known as a dialyte and is illustrated in Fig. 21.
Figure 21 Widely separated achromatic doublet known as the dialyte lens.As the lenses are separated by a distance \(s_d\), the power of the flint or negative lens increases rapidly. The distance \(s_d\) may be expressed as a fraction of the crown-lens focal length by \(p=s_d/f_a\). Requiring the chromatic aberration to be zero implies that
\[\tag{44}\frac{y_a^2}{f_aV_a}+\frac{y_b^2}{f_bV_b}=0\]
By inspection of the figure and the definition of \(p\), it is evident that \(y_b=y_a(1-p)\) from which it follows that
\[\tag{45}f_bV_b=-f_aV_a(1-p)^2\]
The total power of the dialyte is
\[\tag{46}\phi=\phi_a+\phi_b(1-p)\]
Solving for the focal lengths of the lenses yields
\[\tag{47}f_a=f_{ab}\left[1-\frac{V_b}{V_a(1-p)}\right]\]
and
\[\tag{48}f_b=f_{ab}(1-p)\left[1-\frac{V_a(1-p)}{V_b}\right]\]
The power of both lenses increases as \(p\) increases.
The typical dialyte lens suffers from residual secondary spectrum; however, it is possible to design an airspaced achromatic doublet with only one glass type that has significantly reduced secondary spectrum.
Letting \(V_a=V_b\) results in the former equations becoming
\[\tag{49}f_a=\frac{pf_{ab}}{p-1}\qquad{f_b}=-pf_{ab}(p-1)\qquad{s_d}=pf_a\qquad{bfl}=-f_{ab}(p-1)\]
When \(f_{ab}\gt0\), then \(p\) must be greater than unity, which means that the lens is quite long. The focal point lies between the two lenses, which reduces its general usefulness. This type of lens is known as the Schupmann lens, based upon his research in the late s. Several significant telescopes, as well as eyepieces, have employed this configuration.
For \(f_{ab}\lt0\), the lens can be made rather compact and is sometimes used as the rear component of some telephoto lenses.
The next tutorial discusses about triplet lenses.
If you want to learn more, please visit our website Optical Filters export.
Previous: Plano Concave Lenses
Next: Doublet Cemented Lenses
If you are interested in sending in a Guest Blogger Submission,welcome to write for us!
All Comments ( 0 )