Abstract:
The invention is directed to correcting compound lens forms for 3rd and 5th order ray aberrations. All lens design forms have limiting aberrations. The proposed classes of lenses can be corrected for all 3rd and 5th order ray aberrations. The limiting aberrations are seventh order or higher. A variety of these lenses are disclosed here for the sake of example. These lens design forms can be used in various applications including the objective lens for an endoscope or other optical instrument.

Description:
FIELD OF THE INVENTION 
     The invention is directed to compound lens design forms, and more specifically to correcting compound lens forms for 3 rd  and 5 th  order ray aberrations. 
     BACKGROUND OF THE INVENTION 
     All lens design forms have limiting aberrations. The proposed classes of lenses can be corrected for all 3rd and 5th order ray aberrations. The limiting aberrations are seventh order or higher. A variety of these lenses are disclosed here for the sake of example. These lens design forms can be used in various applications including the objective lens for an endoscope or other optical instrument. 
     Aberrations 
     An optical aberration is a defect in the image forming capability of a lens or optical system, and may be considered to be a departure of the performance of an optical system from the predictions of paraxial optics. In an imaging system, it occurs when light from one point of an object does not converge into (or does not diverge from) a single point after transmission through the system. 
     Aberrations can be expressed as discrepancies from paraxial theory. In terms relating to the underlying mathematics of the system, aberrations can be categorized as first order, third order, fifth order, seventh order, etc. 
     First Order Aberrations 
     Chromatic aberration arises because the index of refraction of a material is different for light of different wavelengths. First order chromatic aberration consists of two components, focus shift, and magnification differences for various wavelengths. A common example of this effect is observed when white light striking a prism breaks up into colored rays. As result of this effect, the image formed by a lens will be different for each color component of light. 
     Third Order Aberrations 
     For finite field angles and apertures, light rays do not focus neatly at a point. Accordingly, no precise image is formed. These deviations from focus may be described by third order theory in terms of the five “Seidel” aberrations. These are monochromatic aberrations characterized by certain geometric effects. 
     Spherical aberration—Spherical aberration is an axial aberration and so may be completely described by meridional rays. Light rays in the paraxial region focus at a different point than light rays going through the periphery of the lens. The distance between the two foci is the lateral spherical aberration. The case where the peripheral rays are more bent than the paraxial rays is called positive spherical aberration. The case where the peripheral rays are bent and the peripheral focus is farther from the lens, is called negative spherical aberration. The lateral spherical aberration is proportional to the square of the entrance pupil diameter. 
     Spherical aberration can be controlled by balancing surfaces having positive spherical aberration with surfaces having negative spherical aberration, or by using a small aperture stop. 
     Coma—Like spherical aberration, coma is an aperture dependent aberration. However, unlike spherical aberration it only affects off-axial rays. The comatic blur is asymmetric and “comet shaped”, hence the name coma. 
     Coma may be eliminated in a lens by appropriate choice of curves. It may be minimized by using a small aperture stop 
     Curvature of field—In curvature of field a plane object is sharply imaged, but on a curved surface. The surface on which the image is formed is called the Petzval surface. 
     Curvature of field may be corrected by balancing components contributing negative field curvature with components contributing positive field curvature. 
     Distortion—In distortion, the object is sharply imaged but does not retain its shape. There are two kinds of distortion, barrel distortion and pincushion distortion, so named because of their effect on the image of a square grid target. 
     Distortion can be corrected by balancing surfaces contributing barrel distortion to those contributing pincushion distortion. A perfectly symmetric system will have no distortion. Changing the aperture size has no effect on distortion. 
     Astigmatism—Astigmatism refers to the differing focal positions for rays in the tangential and sagittal planes. While each plane focuses to a perfect point, in the astigmatic image these focus planes are not coincident. Astigmatism is not present on-axis, but increases as the field angle increases. 
     Astigmatism can be corrected by balancing components contributing negative astigmatism with components contributing positive astigmatism. 
     Fifth Order Aberrations 
     There are nine secondary or fifth-order aberrations: 
     Secondary spherical aberration—there is one form of fifth order spherical aberration, and there are two forms of fifth order oblique spherical aberration. 
     Secondary coma—there is one form of fifth order linear coma, and there are two forms of fifth order elliptical coma. 
     Secondary curvature of field—there is one form of fifth order sagittal field curvature. 
     Secondary distortion—There is one form of fifth order distortion. 
     Secondary astigmatism—there is one form of fifth order astigmatism 
     Optical Systems 
     A lens or group of lenses can be arranged to form an optical system. The lenses in such systems are typically arranged such that they are all coaxial with the same optical axis, although for some applications this may not necessarily be the case. Over the history of lens design, various categories of optical systems have been explored. Some examples of lens designs include five element lens designs, reverse telephoto lens designs, and Biogon™ type lens designs. 
     However, prior lens designs of each of these types have not been known to be correctable for all 3 rd  and 5 th  order aberrations. 
     It is therefore desired to provide lens design forms that account for these deficiencies 
     SUMMARY OF THE INVENTION 
     Accordingly, it is an object of the invention to provide a five element lens design that is correctable for all 3 rd  and 5 th  order aberrations. 
     It is a further object of the invention to provide a reverse telephoto lens design that is correctable for all 3 rd  and 5 th  order aberrations 
     It is another object of the invention to provide a six element Biogon type lens design that is correctable for all 3 rd  and 5 th  order aberrations. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a diagram illustrating a five element lens design according to aspects of the invention. 
         FIG. 2  is a diagram illustrating another five element lens design according to aspects of the invention. 
         FIG. 3  is a diagram illustrating a further five element lens design according to aspects of the invention. 
         FIG. 4  is a diagram illustrating a reverse telephoto lens design according to aspects of the invention. 
         FIG. 4   a  is an enlarged view of the reverse telephoto lens design illustrated by  FIG. 4 . 
         FIG. 5  is a diagram illustrating Biogon-type lens design according to aspects of the invention. 
         FIG. 6  is a diagram illustrating a four element lens design according to aspects of the invention. 
         FIG. 7  is a diagram illustrating another five element lens design according to aspects of the invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       FIG. 1  is a diagram illustrating a five element lens design  100  which is correctable for all 3 rd  and 5 th  order aberrations according to aspects of the invention. 
     Lens design  100  includes the following lenses, arranged coaxially and in order, described from the object (not shown) to the image plane  101 : 
     Lens  110 , which is a positive meniscus lens, arranged with its concave side oriented toward the object. 
     Lens  120 , which is a negative meniscus lens, arranged with its concave side oriented toward the object. Lens  120  may form a doublet with  110 . 
     Lens  130 , which is a negative meniscus lens, arranged with its convex side oriented toward the object. 
     Lens  140 , which is a biconvex lens. 
     Lens  150 , which is a negative meniscus lens, arranged with its concave side oriented toward the object. 
     Lens design  100  can be made achromatic with the addition of one further element. 
       FIG. 2  is a diagram illustrating a five element lens design  200  which is correctable for all 3 rd  and 5 th  order aberrations according to aspects of the invention. 
     Lens design  200  includes the following lenses, arranged coaxially and in order, described from the object (not shown) to the image plane  201 : 
     Lens  210 , which is a positive meniscus lens, arranged with its convex side oriented toward the object. 
     Lens  220 , which is a positive meniscus lens, arranged with its concave side oriented toward the object. 
     Lens  230 , which is a negative meniscus lens, arranged with its concave side oriented toward the object. This lens may form a doublet with Lens  220 . 
     Lens  240 , which is a biconvex lens. Lens  240  may have a side oriented toward the object having a greater convexity than the side oriented toward the image. 
     Lens  250 , which is a negative meniscus lens, arranged with its concave side oriented toward the object. 
     Lens design  200  can be made achromatic with the addition of one further element. 
       FIG. 3  is a diagram illustrating a five element lens design  300  which is correctable for all 3 rd  and 5 th  order aberrations according to aspects of the invention. 
     Lens design  300  includes the following lenses, arranged coaxially and in order, described from the object (not shown) to the image plane  301 : 
     Lens  310 , which is a negative meniscus lens, arranged with its convex side oriented toward the object. 
     Lens  320 , which is a positive meniscus lens, arranged with its convex side oriented toward the object. Lens  320  may form a doublet with lens  310 . 
     Lens  330 , which is a positive meniscus lens, arranged with its concave side oriented toward the object. 
     Lens  340 , which is a biconvex lens, arranged with a side having greater convexity oriented toward the object. 
     Lens  350 , which is a negative meniscus lens, arranged with its concave side oriented toward the object. 
     Lens design  300  can be made achromatic with the addition of one further element. 
       FIG. 4  is a diagram illustrating an example reverse telephoto lens design having a back focal length at least as long as the effective focal length and which is correctable for all 3 rd  and 5 th  order aberrations according to aspects of the invention.  FIG. 4   a  is view of the lens elements of  FIG. 4  which has been enlarged for clarity. 
     Lens design  400  is an example of a family of such lenses having in common the first, second, and third lenses, and having a back focal length at least as long as the effective focal length. Lens design  400  includes the following lenses, arranged coaxially and in order, described from the object (not shown) to the image plane  401 : 
     Lens  410 , which is a positive meniscus lens, arranged with its convex side oriented toward the object. 
     Lens  420 , which is a positive meniscus lens, arranged with its convex side oriented toward the object. 
     Lens  430 , which is a negative meniscus lens, arranged with its convex side oriented toward the object. 
     Lens  440 , which is a plano-convex lens, arranged with its planar side oriented toward the object. 
     Lens  450 , which is a biconvex lens. 
     Lens  460 , which is a positive meniscus lens, arranged with its concave side oriented toward the object. 
     Lens  470 , which is a negative meniscus lens, arranged with its concave side oriented toward the object. Lens  470  may form a doublet with lens  460 . 
     Lens  480 , which is a biconvex lens. 
     Lens  490 , which is a negative meniscus lens, arranged with its concave side oriented toward the object. 
       FIG. 5  is a diagram illustrating a six-element Biogon™ type lens design which is correctable for all 3 rd  and 5 th  order aberrations according to aspects of the invention. 
     Lens design  500  includes the following lenses, arranged coaxially and in order, described from the object (not shown) to the image plane  501 : 
     Lens  510 , which is a negative meniscus lens, arranged with its convex side oriented toward the object. 
     Lens  520 , which is a negative meniscus lens, arranged with its convex side oriented toward the object. 
     Lens  530 , which is a positive meniscus lens, arranged with its convex side oriented toward the object. 
     Lens  540 , which is a biconvex lens. Lens  540  may have a side oriented toward the object having a lesser convexity than the side oriented toward the image. 
     Lens  550 , which is a negative meniscus lens, arranged with its concave side oriented toward the object, and may form a doublet with lens  540 . 
     Lens  560 , which is a plano-concave lens, arranged with its concave side oriented toward the object. 
       FIG. 6  is a diagram illustrating a four element lens design  600  which is correctable for all 3 rd  and 5 th  order aberrations according to aspects of the invention. 
     Lens design  600  includes the following lenses, arranged coaxially and in order, described from the object (not shown) to the image plane  601 : 
     Lens  610 , which is a biconvex lens. Lens  610  may have a side oriented toward the object having a lesser convexity than the side oriented toward the image. 
     Lens  620 , which is a negative meniscus lens, arranged with its concave side oriented toward the object. Lens  620  may form a doublet with  610 . 
     Lens  630 , which is a positive meniscus lens, arranged with its concave side oriented toward the object. 
     Lens  640 , which is a biconcave lens. Lens  640  may have a side oriented toward the object having a greater concavity than the side oriented toward the image. 
       FIG. 7  is a diagram illustrating a five element lens design  700  which is correctable for all 3 rd  and 5 th  order aberrations according to aspects of the invention. 
     Lens design  700  includes the following lenses, arranged coaxially and in order, described from the object (not shown) to the image plane  701 : 
     Lens  710 , which is a biconvex lens. Lens  710  may have a side oriented toward the object having a lesser convexity than the side oriented toward the image. 
     Lens  720 , which is a negative meniscus lens, arranged with its concave side oriented toward the object. Lens  720  may form a doublet with  710 . 
     Lens  730 , which is a positive meniscus lens, arranged with its concave side oriented toward the object. 
     Lens  740 , which is a negative meniscus lens, arranged with its concave side oriented toward the object. 
     Lens  750 , which is a plano-concave lens, arranged with its concave side oriented toward the object. 
     This design has the added advantage that it can be corrected for all first order chromatic aberrations without an additional element. 
     Although the invention has been described with reference to a particular arrangement of parts, features and the like, these are not intended to exhaust all possible arrangements or features, and indeed many modifications and variations will be ascertainable to those of skill in the art.