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Performance of Representative Lenses

This is a continuation from the previous tutorial - laser oscillation and laser cavity modes.


Figures 27 – 38 present the performance of lenses representing a variety of lens types. The measures of performance provided in each figure have been selected for utilization purposes. Diffraction effects have not been included.

Each figure is divided into four sections \(a-d\).

Section \(a\) is a drawing of the lens showing the aperture stop.

Section \(b\) contains two set of plots. The solid line is for the distortion versus field of view (\(\theta\)) in degrees while the dashed lines show the transmission of the lens versus field of view for three F-numbers. Transmission in this case is one minus the fractional vignetting. No loss for coatings, surface reflection, absorption, etc., is included.

The rms diameter of the geometric point source image versus field of view for three F-numbers is presented in section \(c\). The spot sizes are in angular units and were calculated for the central wavelength only, i. e., monochromatic values. Note that the ordinate is logarithmic.

The final section, \(d\), contains angular transverse ray plots in all three colors for both the on-axis and near-extreme field angles with \(y_\text{ep}\) being measured in the entrance pupil. The lower right plot shows the axial aberrations while the upper left plot represents the tangential/meridional aberrations and the upper right plot presents the sagittal aberrations.

The X included on some of the tangential plots represents the location of the paraxial principal ray. The legend indicating the relationship between line type and wavelength is included.

The linear spot size is computed by multiplying the \(efl\) by the angular spot size. This value can be compared against the diffraction-limited spot size given by \(2.44(\lambda/D_\text{ep})\).

If the geometric spot is several times smaller than the diffraction-limited spot, then the lens may be considered to be diffraction-limited for most purposes. If the geometric spot is several times larger, then the lens performance is controlled by the geometric spot size for most applications.


Figure 27  Rapid Rectlinear: This lens is an aplanat which is symmetrical with the rear half corrected for spherical aberration and flat tangential field. A compact configuration is realized by having a large amount of coma in each half. Symmetry removes the lens system coma, distortion, and lateral color. This type of lens is one of the most popular camera lenses ever made.



Figure 28  Celor: F/5.6 with 50° total field of view. Also known as an airspaced dialyte lens.



Figure 29  Symmetrical double anastigmat or Gauss homocentric objective: basic form of Double-Gauss lens using a pair of Gauss telescope objectives. First patented by Alvan Clark in 1888.



Figure 30  Triplet: F/2.8 with 50° total field of view.



Figure 31  Tessar: F/4 with 50° total field of view.



Figure 32   Unsymmetrical Double-Gauss: This lens was designed in 1933 for Leitz and was called the Summar. F/2 with 60° total field of view. This lens was replaced by the Leitz Summitar in 1939, due to rapidly degrading off-axis resolution and vignetting. Compare this lens with the lens shown in Fig. 33.



Figure 33  Unsymmetrical Double-Gauss: This lens type was designed in 1939 for Leitz and was called the F/2 Summitar. Kodak had a similar lens called the F/1.9 Ektar. A later example of this design form is shown and operates at F/1.4 with 30° total field of view.



Figure 34   Unsymmetrical Double-Gauss: F/1.75 with 50° total field of view. Similar to the 1949 Leitz F/1.5 Summarit. This lens has a split rear element which produces improved resolution of the field of view and less vignetting than the earlier Summar type lens.



Figure 35  Unsymmetrical Double-Gauss : F/5.6 with 70° field of view. This lens is a variant of the 1933 Zeiss F/6.3 Topogon and is the Bausch & Lomb Metrogon. The principal difference is the splitting of the front element. 



Figure 36  Reverse Telephoto: This lens was developed by Zeiss in 1951 and is known as the Biogon. It operates at F/2.8 with 70° field of view. This lens comprises two reverse-telephoto objectives about a central stop. 



Figure 37  Petzval: Example of Kodak projector lens operating at F/1.4 with 24° total field of view. The front lens group has its power shared between a cemented doublet and a singlet for aberration correction. Note that the aperture stop is located between the front and rear groups rather than the more common location at the front group. Resolution in the region near the optical axis is very good although it falls off roughly exponentially. The limiting aberrations are oblique spherical and cubic coma.



Figure 38  Fish-eye: The Hill Sky lens was manufactured by Beck of London in 1924. The lens has moderate resolution and enormous distortion characteristic of this type of lens.


The next tutorial introduces rapid estimation of lens performance


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