Four Element Lens System

1. Field of the Invention

The present invention relates to improvements in optical lens systems providing a real image. In particular, the present invention relates to improvements in providing an optical lens design utilizing duplicate lens component parts for the low cost production of cameras.

2. Description of the Prior Art

Photographic objectives are presently known in the field of low cost cameras. For example, the Altman U.S. Pat. No. 3,194,116 and the Melech U.S. Pat. No. 3,438,697 disclose photographic objectives of the simple triplet type. This lens system has the advantage of providing relatively good correction for aberrations and is frequently referred to as the Cooke triplet. The Altman patent in particular discloses the value from a cost view point of utilizing lens elements made entirely of injection molded plastics. Both of these patents are dependent upon an inner negative biconcave lens element having a relatively thin thickness along the optical axis to permit achromatizing of the entire lens system.

Plastic lens systems utilizing more than three elements are also known in the prior art such as the Willoughby et al U.S. Pat. No. 3,749,477. This reference simply discloses an anamorphic lens system having four lenses made from the same plastic and adapted to be attached as a supplement to a fixed lens camera.

Finally, a glass projection lens system having a 1:1 magnification is disclosed in the McCrobie U.S. Pat. No. 3,817,599. The McCrobie lens system is designed to provide a multi-focal projection lens wherein the basic lens group has a symmetrical conjugate relationship. Basically, the prior art has experienced some limited success in providing low cost cameras with plastic lens. However, manufacturing problems have existed for instance in the injection molding of thin biconcave negative lenses.

The present invention provides a novel lens system embodying a number of features which insure a real image that is adequately corrected for chromatic aberrations, spherical abberrations, coma, and astigmatism and which has a substantially flat image field. The lens system is easily assembled at a low cost in a camera.

The lens system comprises four fixed lens elements comprising a first positive lens element, a second negative lens element, a third negative lens element and a fourth positive lens element. The first and second lens elements having a conjugate relationship to the third and fourth lens elements. An aperture stopper element or its functional equivalent is utilized to create an effective plane between the second and third negative lens elements. The position of the effective plane of the aperture stopper satisfies the following equation: ##EQU2## wherein S is the distance between the elements along the optical axis and S.sub.2 ' is the distance between the surface of the second negative lens and the effective plane of the aperture stopper and S.sub.2 " is the distance between the effective plane of the aperture stopper and the surface of the third negative lens.

In a preferred embodiment, each of the lenses are a meniscus element with the positive lens elements made from methyl methacrylate and the negative lens elements made from a copolymer of polystyrene and methyl methacrylate. The first and fourth lenses and the second and third lenses have respectively identical optical lens characteristics and can be manufactured from a pair of injection molds. The focal length of the first positive lens element, f.sub.1, can be related to the focal length of the second negative lens element, f.sub.2, as follows:

The lens thickness along the optical axis of the first positive lens element, t.sub.1, can be related to the thickness of the second negative lens element, t.sub.2, as follows:

The lesser radius of curvature on the first positive lens element r.sub.1, can be related to the greater radius of curvature on the second negative lens element, r.sub.3, as follows:

The features of the present invention which are believed to be novel are set forth with particularity in the appended Claims. The present invention, both as to its organization and manner of operation, together with further objects and advantages thereof, maybe best understood by reference to the following description, taken in conjunction with the accompanying drawings.

FIG. 1, is a schematic cross sectional view of a conjugate lens system embodying the present invention.

FIG. 2 discloses a graph of the aberration tolerances of example 1.

FIG. 3 discloses a graph of the aberration tolerances of example 2.

FIG. 4 discloses a graph of the aberration tolerances of example 3.

FIG. 5 discloses a graph of the aberration tolerances of example 4.

FIG. 6 discloses a graph of the aberration tolerances of example 5.

FIG. 7 discloses a graph of the aberration tolerances of example 6.

FIG. 8 discloses a graph of the aberration tolerances of example 7.

FIG. 9 is a schematic view of the lens system embodying the present invention.

The following description is provided to enable any person skilled in the optical design art to make and use the invention and it sets forth the best mode contemplated by the inventors of carrying out their invention. Various modifications, however, will remain readily apparent to those skilled in the art, since the generic principles of the present invention have been defined herein specifically to provide a relatively economical and easily assembled lens system.

Subsequent to the advent of fast electronic computers, the field of optical designing has been revolutionized and it is now possible to perform comprehensive image analysis in a relatively short time. The derivation of the formulae and relationships set forth herein have been accomplished with the assistance of a computer. The present invention represents the parameters of a compromised balance of acceptable aberrations in a relatively easily manufactured and low cost lens system for utilization in a camera. For a reference to the techniques of computer design, which are not necessary for either an understanding or the practice of the present invention, the reader is directed to "LENS ABERRATION DATA" by J. M. Palmer, American Elsevier Publishing Co., Inc., 1971 and "OPTIMIZATION TECHNIQUES IN LENS DESIGN" by T. M. Jamieson, American Elsevier Publishing Co. Inc. 1971. In addition, reference is made to "GEOMETRICAL OPTICS" by L. C. Martin, Pitman & Sons Ltd. 1955. These references are incorporated herein, simply as supplementing the present disclosure.

The present invention includes two pairs of meniscus lens elements in a conjugated relationship. Each pair of lens comprises a positive and negative lens element. The lens arrangements are a mirror image of each other, that is, viewing the lens elements sequentially from the object side of the lens system to the image side, the first positive meniscus lens element will have a convex surface towards the object, while the second negative meniscus lens will also have a convex surface towards the object. Both the third negative meniscus lens and the fourth positive meniscus lens will have convex surfaces towards the image plane.

In the present lens system the positioning of the effective plane of the aperture stopper or an effective equivalent of the aperture stopper is important in correcting coma and chromatic aberrations for permitting an acceptable photographic image from infinity to a portait distance. The position of the aperture stopper or its functional equivalent, can be seen with reference to FIG. 1 and FIG. 9. A schematic aperture stop 12 as shown in FIG. 8 and in trace lines in FIG. 1. The actual aperture stopper element in the commercial embodiment of FIG. 1 is physically formed by both the object and image side edges of the lens mounting shoulder 8 to define the intersection point of the maximum field angle principle rays with the optical axis. That is, the lower object side edge and the upper image side edge of the mounting shoulder 8 defines the position of the maximum field principle ray as schematically shown in FIG. 1. The same intersection point for the other maximum field angle principle rays are similarly defined by a simple rotation about the annular shoulder edges. The effective plane of the aperture stopper can be further defined as a plane extending normal to the optical axis and containing the junction or intersection point of the maximum field angle principle rays with the optical axis.

Referring to FIG. 1, the four element lens system 2 of the present invention is disclosed. A lens barrel 4 has been appropriately molded or machined to accommodate the desired spacings and mounting of the lens elements of the present invention. A first positive meniscus lens of element, L.sub.1 having a pair of convex surfaces directed towards the object is held in place by an appropriate locking ring 6. A second negative meniscus lens element, L.sub.2, is appropriately mounted within the lens barrel 4 to bear against an annular alignment step or shoulder 8 for ease of assembly. In one advantageous embodiment of the invention, the second lens, L.sub.2, if made of plastic, can have an intrinsically molded peripheral spacer portion 10 to appropriately seat and align the outside positive meniscus lens, L.sub.1. As can be readily appreciated by those skilled in the plastic molding art, either lens L.sub.1 or L.sub.2 can be molded with the peripheral spacer. A shim or spacer 14, preferably colored a flat black, can be used to adjust or compensate for any desired spacing between the respective lenses. The relative size of the aperture of the spacer 14 can be dimensioned to eliminate any undesired flare.

A third negative meniscus lens element, L.sub.3, can be the identical molded lens as the second negative lens element, L.sub.2. Lens element, L.sub.3, will accordingly have an integral peripheral spacer 10 for spacing a lens element, L.sub.4. The convex surface of L.sub.3 will be directed towards the image plane of the lens system. The fourth positive meniscus lens element, L.sub.4, will be identical to the first positive meniscus lens element, L.sub.1. Lens, L.sub.4, will have its convex surface also directed towards the image plane.

The thickness of each lens element as measured along the optical axis of the lens system, OA, is appropriately designated as t with the subscript numbers referring to a specific lens element sequentially from the object side of the lens system to the image side. Likewise, the spacer distances along the optical axis are set forth as S.sub.1, the distance between the lens L.sub.1 and L.sub.2. The distance between the image side surface of the second negative meniscus lens, L.sub.2, and the effective plane of the aperture stopper 12 or its functional equivalent traversed to the optical axis, OA, is denoted as S.sub.2 '. The distance between the effective plane of the aperture stopper 12 and the surface of the third meniscus lens, L.sub.3, is S.sub.2 ". The total distance between lens L.sub.2 and L.sub.3 is S.sub.2. Finally, the distance between the adjacent surfaces of lens, L.sub.3 and L.sub.4, is set forth as S.sub.3. The radii of curvature of the lens surface uses the symbol r with the sub numbers referring to the individual radius of curvatures of the respective lens surfaces sequentially from the object side to the image side of the lens system.

To maximize the advantages of the present invention in low cost cameras, the preferred embodiment will utilize injection molded optical plastics for each of the lens elements. Some of the plastics which could be utilized are methacrylate (Nd 1.492, V 57.4) and polystyrene (Nd 1.591, V 30.8), polycarbonate (Nd 1.586, V 34.8) and polysulfone (Nd 1.633).

In the preferred embodiment the negative meniscus lens system L.sub.2 and L.sub.3, can be molded from a methyl methacrylate and styrene copolymer having an index of refraction Nd of 1.57 and an Abbe index of dispersion, V of 34.6. The positive meniscus lens systems L.sub.1 and L.sub.4 can be molded from acrylic (Nd 1.492, V 57.4). The use of plastics are highly advantageous with respect to the cost of material and the elimination of grinding or finishing steps required in conventional optical glass. Further the use of plastic permits the integral molding of peripheral spacers on one of the lens elements for positioning the other lens element. Plastic is particularly advantageous in the lens design of the present invention in that the lens dimensions are capable of being manufactured with relatively high quality. Further, due to the relative dimensions of the negative lens elements L.sub.2 and L.sub.3, of the present invention, as compared to the double concave lens elements used in the conventional Cooke triplet lens system, pressure stresses that are developed during the molding are not a problem and birefringence stress rings are not produced. That is, the thinness of the meniscus lens of the present invention eliminates conventional optical problems that can occur with molding. The manufacture of the present four element lens system can be accomplished with only a production cost of two separate molds, since the lens elements are duplicated in the assembled conjugate four element lens system. The use however, of a symmetrical conjugate lens system in the present invention requires the aperture stopper 12 or its functional equivalent to be positioned in accordance with the following derived formula: ##EQU3## By adhering to formula (1) it is possible to adequately correct coma flare and color aberrations that would result from a completely symmetrical conjugate lens system.

The above formula (1) establishes the junction of the principle rays defining the maximum field angle with the optical axis, OA, as shown in FIG. 1.

In addition, any further color aberrations and spherical aberrations along with astigmatism and the flatness of the image field can be compensated for by arranging the focal length of the positive meniscus lens element L.sub.1 and L.sub.4 to have the following relationship to the focal length of the negative meniscus lens elements L.sub.2 and L.sub.3 wherein f.sub.1 is the focal length of the positive lens elements and f.sub.2 is the focal length of the negative lens elements:

The spherical aberrations can be further minimized by requiring that the absolute value of the radii of curvature r.sub.1 and r.sub.8 of the lesser radius of lens elements L.sub.1 and L.sub.4, should bear the following relationship to the absolute value of the radii of curvature of the larger radius of curvature r.sub.3 and r.sub.6 of the lens elements L.sub.2 and L.sub.3, in accordance with the following equation:

Finally, the color aberrations on the axis and an economical and practical size of the lens diameters and length of the lens systems can be appropriately maintained by having the thickness, t, of the positive lens elements L.sub.1 and L.sub.4 greater than or equal to twice the thickness of the lens thickness of L.sub.2 and L.sub.3. This can be seen in the following equations:

An an alternative embodiment of the present invention, the first lens element L.sub.1, can be made from an appropriately indexed glass to take advantage of the higher resistance of glass to abrasion and static electricity. In addition, a glass lens is easier to coat, because of its higher melting point and accordingly anti-reflective coatings and/or ultra violet coatings can be utilized much more readily on the glass surface. If anti-reflection is a problem in the application of the present plastic lenses, it is possible to utilize a magnesium fluoride coating that can be applied by vacuum deposition.

The parameters of the lens elements of the present invention are listed in the following examples, wherein Nd is the refractive index of the individual spectrum and V is the index of dispersion or Abbe number. The thicknesses of the lens and the spacing between the lens are respectively t and S. A negative sign indicates the radii on centers of curvature lying on the object side of their vertices. In each of the following examples f = 1.0, 1:8 and the maximum field angle is 43.degree..

Reference is made to FIG. 2 to disclose graphically the aspheric, astigmatism and distortion aberration resulting from the lens system of Example 1. As can be readily appreciated by those skilled in the field of photography, these distortions are well within acceptable limits for photographs from infinity to portrait images. FIGS. 3 through 7 correspond to the aberration values respectively of Examples 2 through 6.

As an alternative embodiment of the present invention, one or more of the lens surfaces in the photographic objective can be made aspherical to compensate for aberrations. By permitting the lens surface to depart from a purely spherical form, extra variables are provided the lens designer to correct aberrations of the optical system. The use of aspherical surfaces can reduce the spherical, astigmatism, coma flare, aberrations and the value of the Petzval summation. In general, aspherical lens can permit a higher speed and a wider angle.

Aspherical surfaces are most advantageously utilized with injection molded plastics to eliminate polishing and grinding. As known by lens designers, the aspherical surface of the lens can be defined by a power series function in the radial variable as follows: ##EQU4##

Wherein X is the optical axis of the lens; Y is the orthotropic axis, C.sub.o is a zero-order or Gaussian coefficient of the aspheric surface; C.sub.i .sup..PHI.2i are the higher order coefficients of the aspheric surface and .epsilon. is the eccentricity.

The following examples of conjugate molded plastic lenses are set forth merely as illustrations of the present invention. In each of the following examples, f = 1.0, 1:6.5 and the maximum field angle is 46.degree.;

Reference is made to FIG. 8 to disclose a graphic representation of the resulting aberrations.

The following examples 8 and 9 are cited to disclose conjugate lens systems with a number of aspheric surfaces and design parameters taking into account the higher order aberrations. A polycarbonate plastic is utilized for the lenses L.sub.2 and L.sub.3 in the following example 8.

The present invention permits the manufacturing of a relatively inexpensive photographic objective capable of focusing from infinity to portrait distances. The lenses can be produced from only a pair of mold cavities and are advantageously designed to facilitate their assembly into a lens barrel with integral spacers.

The use of plastic provides a relatively inexpensive lens as compared to glass since it removes any grinding or polishing requirements and further provides the lens designer with the ability to control aberrations with one or more aspheric surfaces.

As can be readily appreciated, it is possible to deviate from the above embodiments of the present invention and will be readily understood by those skilled in the art that the invention is capable of many modifications and improvements within the scope and spirit thereof. Accordingly, it will be understood that the invention is not to be limited by the specific disclosed embodiment but only by the scope and spirit of the appended claims.