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Landscape Lenses and the Influence of Stop Position

This is a continuation from the previous tutorial - stimulated atomic emissions.


The first lens used for photography was designed in 1812 by the English scientist W. H. Wollaston about a quarter of a century before the invention of photography.

He discovered that a meniscus lens with its concave surface towards the object could produce a much flatter image field than the simple biconvex lens commonly used at that time in the camera obscuras.

This lens became known as the landscape lens and is illustrated in Fig. 12. Wollaston realized that if the stop was placed an appropriate amount in front of the lens and the F-number was made to be modest, the image quality would be improved significantly over the biconvex lens.


Figure 12  Landscape lens with the aperture stop located to the left of the lens.


The rationale for this can be readily seen by considering the influence on the residual aberrations of the lens by movement of the stop.

Functionally, the stop allows certain rays in the oblique beam to pass through it while rejecting the rest. By simple inspection, it is clear that the movement of the stop (assuming a constant FN is maintained) will not affect the axial aberrations, while the oblique aberrations will be changed.

In order to understand the influence of stop movement on the image quality, a graphical method was devised by R. Kingslake in which he traced a number of rays in the meridional plane at a given obliquity angle as illustrated in Fig. 13.

A plot is generated that relates the intercept height of each real ray at the image plane \(H_i\) to the distance \(s_p\) from the intersection of the ray with optical axis \(P\) to the front surface of the lens.

Each ray can be viewed as the principal ray when the stop is located at the intersection point \(P\). This \(H_i-s_p\) plot provides significant insight into the effect upon image quality incurred by placement of the stop.

The shape of the curve provides information about the spherical aberration, coma, tangential field curvature, and distortion. Spherical aberration is indicated by an S-shaped curve, while the curvature at the principal ray point is a gauge of the coma.

The coma is zero at inflection points. When the curve is a straight line, both coma and spherical aberration are essentially absent. The slope of the curve at the principal ray point is a measure of the tangential field curvature or the sag of the tangential field, i. e., astigmatism.

The difference in height of the real and Gaussian principal rays in the image plane is distortion. For situations where the curve does not exhibit spherical aberration, it is impossible to correct the coma by shifting the stop.


Figure 13   Rays traced at a given obliquity where the intersection of a given ray with the optical axis is \(P\), located a distance \(s_p\) from the front surface of the lens.


Since a simple meniscus lens has stop position and lens bending as degrees of freedom, only two aberrations can be corrected. Typically, coma and tangential field curvature are chosen to be corrected, while axial aberrations are controlled by adjusting the FN of the lens.

The \(H_i-s_p\) plot for the lens shown in Fig. 13 is presented in Fig. 14, where the field angle is 10° and the image height is expressed as a percent of the Gaussian image height.

The lens has a unity focal length, and the lens diameter is 0.275. Table 2 contains the prescription of the lens.

Examination of this graph indicates that the best selection for stop location is when the stop is located at \(s_p=-0.1505\) (left of the lens). For this selection, the coma and tangential astigmatism will be zero since the slope of the curve is zero and an inflection point is located at this stop position.

Figure 15 shows the astigmatic field curves which clearly demonstrate the flat tangential image field for all field angles. Other aberrations cannot be controlled and must consequently be tolerated.

When this lens is used at F/11, the angular blur diameter is less than 300 μradians. It should be noted that this condition is generally valid for only the evaluated field-angle obliquity and will likely be different at other field angles. Nevertheless, the performance of this lens is often acceptable for many applications.

An alternate configuration can be used where the lens is in front of the stop. Such configuration is used to conserve space since the stop would be located between the lens and the image. The optical performance is typically poorer due to greater residual spherical aberration.

The principle demonstrated by the \(H_i-s_p\) plot can be applied to lenses of any complexity as a means to locate the proper stop position. It should be noted that movement of the stop will not affect the coma if spherical aberration is absent nor will astigmatism be affected if both spherical aberration and coma have been eliminated.


Figure 14   The image height \(H_i\) of each ray traced in Fig. 13 is plotted against the intersection length \(s_p\) to form the \(H_i-s_p\) plot. \(H_i\) is expressed as a percent of the Gaussian image height as a direct measure of distortion.



Table 2.  Prescription of Landscape Lens Shown in Fig. 13



Figure 15   Astigmatic field curves for the landscape lens having the stop located at the zero slope location on the \(H_i-s_p\) plot in Fig. 14, which is the flat tangential field position. \(S\) represents the sagittal astigmatic focus while \(T\) indicates the tangential astigmatic focus.



The next tutorial discusses about fiber attenuation loss.



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