For \(f_{ab}\lt0\), the lens can be made rather compact and is sometimes used as the rear component of some telephoto lenses.

Achromatic doubletlenses

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 \(c_b=\phi_b(n_b-1)\).

Yes, the depth of field can be adjusted on a microscope by changing the aperture of the objective lens or by adjusting the focus of the microscope. Increasing the aperture will decrease the depth of field, while decreasing the aperture will increase the depth of field.

Achromaticlens for telescope

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 1890s. Several significant telescopes, as well as eyepieces, have employed this configuration.

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.

What is anachromaticlens used for

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

Achromaticaberration

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.

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 depth of field can vary in different types of microscopes due to differences in their optical systems. For example, compound microscopes typically have a larger depth of field compared to stereomicroscopes, which have a smaller depth of field but provide a more three-dimensional image. Electron microscopes, on the other hand, have a significantly smaller depth of field compared to light microscopes due to their higher magnification and shorter wavelength of electrons.

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.

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.

Achromatic doubletmeaning

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.

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).

Achromatic DoubletThorlabs

The depth of field is important in microscopy because it allows us to see a three-dimensional image of the specimen. It also helps in determining the thickness and structure of the specimen, which is crucial in many scientific fields such as biology and materials science.

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.

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 \(c\).

Edmund Opticsachromatic doublet

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.

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.

Achromatic doubletformula

The depth of field of a microscope is determined by the numerical aperture of the objective lens, the wavelength of light used, and the refractive index of the medium between the objective lens and the specimen. It can also be affected by the magnification and thickness of the specimen.

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 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 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

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

The depth of field of a microscope refers to the thickness of the specimen that appears in focus at one time. It is the distance between the nearest and farthest points of the specimen that can be seen in sharp focus under the microscope.