1.  Field of the Invention
The present invention relates, generally, to anamorphic lenses, and in particular embodiments, to a rear anamorph that provides high image quality and is small enough in size to make it suitable for use with both prime and zoom lenses. 
2.  Description of Related Art
Conventional anamorphic formats.  In the early 1950s, as a result of the perceived threat of television, motion pictures began to be released in various widescreen formats.  Until this time the majority of feature films and television programs were released with frames having an aspect ratio of 1.33:1 (4:3). 
To capture a widescreen image onto a standard-sized film frame, a special lens known as an anamorphic lens is used to horizontally squeeze (i.e. compress) a wide field of view down to the size of the standard film frame.  Anamorphic lenses are essentially astigmatic; the magnification in the horizontal direction is different from the magnification in the vertical direction.  To project this squeezed image, another anamorphic lens is used to horizontally unsqueeze (i.e. stretch or expand) the image so that the projected image is restored to the wide field of view at which the image was originally taken.  Although numerous widescreen formats were introduced in the 1950s, most of these formats have become obsolete.  The predominant widescreen format in use today is Panavision®, an anamorphic optical system with a 2:1 horizontal squeeze and a 2.40:1 aspect ratio (0.825 inches by 0.690 inches). 
FIG.  1 illustrates the SMPTE 195-2000 projection aperture standard for a film frame generated using the Panavision® anamorphic format.  Area 100 is the full camera aperture, but area 102 (having an aspect ratio of approximately 1.2:1) is the portion of the film frame that is actually projected.  The optical image in area 102 has been squeezed in a 2:1 ratio, and thus exemplary image 104, although appearing as an oval, is actually a circular image that has been photographed.  The image capture area 102 in FIG.  1 is typically converted directly to release print film without changing or otherwise manipulating the format, because traditional methods of stretching or squeezing the captured image on an optical bench to produce the release print image would further degrade the image quality.  As mentioned above, when projecting the release print film, another anamorphic lens is used to unsqueeze the image.  When unsqueezed during projection, area 102 will have an aspect ratio of approximately 2.40:1 (the Panavision® widescreen format), and the oval exemplary image 104 will return to its correct circular shape. 
The area 102 in FIG.  1 is off-centered to leave area 106 for an optical soundtrack.  This technique of generating an off-centered, right-shifted frame (a.k.a. “ Academy frame”) was developed because historically, the original film would be put in contact with another piece of film and the soundtrack would be recorded optically onto that piece of film to generate the release print film.  Even today, this optical soundtrack is needed on release print film.  Therefore, original film is still frequently shot “Academy centered” to leave room for the optically recorded soundtrack and other digital soundtracks. 
The Panavision® anamorphic format employs a 2:1 horizontal squeeze to maximize the available image area on the film frame while leaving an area for the optical soundtrack.  In general, anamorphic optics are inferior to their spherical counterparts, and produce a degraded image.  The greater the amount of anamorphosis (squeezing or stretching), the greater the degree of image degradation.  Nevertheless, the use of anamorphosis can produce improved overall image quality because the increased image area on the original and release print film reduces the amount of magnification needed to project the image on a theater screen, and there is a direct correlation between magnification and image degradation, when viewed from the same distance. 
New and improved anamorphic formats.  As mentioned above, because conventional methods of stretching or squeezing the captured image on an optical bench to produce the release print image would further degrade the image quality, the image capture area 102 in FIG.  1 was typically converted directly to release print film without changing or otherwise manipulating the format.  However, new techniques for electronic processing of the captured image (i.e. digital intermediate processing) are able to stretch or squeeze the captured image to produce a release print image without any significant degradation of the image.  This technological advance allows the image to be captured in a format that is different from the final release print format.  Captured images need not leave room for the optical soundtrack (see 106 in FIG.  1), and can extend to the entire usable width of the film or electronic detector. 
As illustrated in FIG.  2, related U.S. patent application entitled “Anamorphic Three-Perforation Imaging System,” in recognition of this expansion of the usable image capture area, discloses an anamorphic imaging system that utilizes a maximized image capture area 202 only three perforations in height and extending to practically the entire usable width of the film frame or electronic detector 200 for either cine or digital applications.  In film applications, because the image capture area 202 is only three perforations high, the amount of original film needed can be reduced.  In digital applications, because digital imagers for electronic cinematography applications are being designed with an aspect ratio of 16:9 and a size that happens to approximate the area of three-perforation film, the image capture area 202 maximizes the active area of digital imagers. 
The maximized image capture area 202 reduces magnification and image degradation due to magnification when displayed, and reduces the amount of anamorphic squeeze required during photography, which in turn lowers image degradation due to anamorphosis.  The amount of anamorphic squeeze used during image capture is, for example, in the ratio of 2.40:1 over 16:9 or approximately 1.34 to maximize the image capture area.  Note than an anamorphic squeeze other than this ratio will not maximize the image capture area and thus will not maximize overall image quality. 
Therefore, for both film and digital applications, an image may be captured using the same anamorphic lens having an approximate 1.34:1 horizontal squeeze, which is less than the 2:1 horizontal squeeze of the conventional Panavision® anamorphic format.  The reduced degree of anamorphosis combined with using practically the entire area of the three perforation film frame or total digital imaging area results in image quality that is at least equivalent, and potentially superior to, the Panavision® anamorphic format, while still providing an approximate 25% film cost savings over the conventional four perforation format in film applications. 
Front and rear anamorphs.  Contemporary anamorphic lens systems for cinematographic applications usually comprise a spherical lens unit (either fixed focal length or zoom) combined with either a front or rear cylindrical anamorphic unit mainly comprised of cylindrical lens elements.  Note that a cylindrically surfaced element has a radius in one direction (which provides optical power) but is flat in the other direction (which provides no optical power).  A cylindrical lens element is therefore non-rotationally symmetrical (as compared to a sphere, which is an axially rotationally symmetrical element). 
Anamorphic power, or the compression or expansion ratio of the anamorphic lens, is the ratio of the focal lengths of the lens elements of the anamorph.  The compression or expansion ratio of an anamorphic lens is obtained by dividing the focal length measured through the lens in one direction by the focal length measured through the lens in the other direction.  Thus, for cylindrical lens elements, there could be no power in one direction, and all the power in the other direction. 
“Rear anamorphs” are placed at the image side of the lens, while “front anamorphs” are placed at the object side of the lens.  All cylinders (cylindrical lens elements) in conventional rear and front anamorphs are lined up in the same direction.  Therefore, conventional anamorphic units provide a compression or expansion of the object in a single direction (typically the horizontal direction for a front anamorph with compression) at the final image. 
The anamorph could also be placed within the spherical lens, but there is no great benefit to having an anamorph within the spherical lens.  In practice, spherical lenses are generally developed first, and anamorphic lenses are developed later as attachments to the spherical lenses.  By implementing anamorphic lenses as attachments, spherical lenses may be used to generate widescreen as well as conventional formats. 
Front anamorphs have conventionally been preferred because they collect and deliver radiation in nearly collimated light spaces, allowing them to produce low residual aberrations and good image quality.  Front anamorphs are also generally easier to design because the light rays entering and leaving the front anamorph are usually substantially parallel, and also because there are no optics-related restrictions on their size.  However, in practice they cannot be too large due to weight considerations.  This is particularly true for wide angle lenses, where the front anamorph must capture all of the wide field of view.  In conventional front anamorphs, all of the cylindrically surfaced elements line up in the horizontal direction. 
Rear anamorphs are usually not preferred because they collect and deliver radiation in convergent light spaces (where light is heading towards the film or detector), which results in large residual aberrations and poor image quality.  This also makes rear anamorphs harder to design.  The performance of rear anamorphs is also more dependent on the compression or expansion ratios than with front anamorphs.  In addition, rear anamorphs should ideally fit into a limited space between the spherical lens and the film or detector to produce the best image quality.  However, in practice the size of the required lens elements generally forces rear anamorphs to exceed this preferred space, further contributing to poor image quality.  It would be possible to design the spherical lens to enable a longer rear anamorph, but this would result in larger spherical lenses.  Practically speaking, for most fixed focal length lenses such as the Panavision® Primo® fixed focal length lens family, there is about 20 mm of axial space between the last lens element and the reflex mirror in which to fit a rear anamorph.  For most zoom lenses, there is about 25 mm of axial space available.  In conventional rear anamorphs, all of the cylindrically surfaced elements line up in the vertical direction. 
Rear anamorphs do have their advantages, however.  They are generally much smaller and lighter than front anamorphs.  Therefore, although providing relatively poor image quality, rear anamorphs providing a 2:1 squeeze are available.  Rear anamorph attachments are generally not used on fixed focal length lenses, because of limited space.  However, because fixed focal length lenses are not too large as compared to zoom lenses, a front anamorph, although relatively large, is practical.  However, in the case of a contemporary cine zoom lens, which may be over one foot long and have a 4–5″ diameter, a front anamorph would substantially increase the size of the lens.  In addition, the anamorphic elements would be so large that there would be manufacturability problems.  Thus, for zoom lenses there is little choice but to use a rear anamorph. 
Shiga rear anamorphs.  Previous designs have suffered with the various problems and limitations inherent in conventional anamorphic lenses.  For example, Shiga rear anamorphs, manufactured in Japan, were designed to fit within the axial length generally available for zoom lens rear anamorphs (e.g. about 27 mm).  All of the cylindrical lens elements in Shiga rear anamorphs line up in the vertical direction (i.e. they have curvature in the vertical direction and are flat in the horizontal direction).  Thus, ideally all of the cylindrical power is in the vertical direction, with no power in the horizontal direction. 
In addition, the rear anamorph of Shiga also includes one element with a spherical surface.  This additional spherically surfaced element is adjustable in the axial direction (along the optical axis) either independently or together with all or part of the anamorphic unit to account for manufacturing tolerances so that the image formed by the Shiga rear anamorph will be aligned with the image plane in the camera.  Although this additional spherically surfaced element does align the two focal lengths created by the elements in the horizontal and vertical directions, it does little to enhance the inherent image quality produced by the Shiga rear anamorph, which is generally poor.  It is possible to “stop down” the lens (e.g. change the aperture from f2 to f8) to improve the image quality somewhat, but this technique limits the user to the amount of light allowed in by the closed-down iris, and therefore causes other concerns such as reduced versatility due to the limited lighting. 
The reason for having cylindrically surfaced elements in the vertical direction in rear anamorphs (like the Shiga rear anamorph) instead of in the horizontal direction as in front anamorphs is related to both the image format, which is usually rectangular (i.e. wider than taller), and the difficulty of readily correcting aberrations in an image space where convergent light beams are present.  Because the vertical dimensions in a rear anamorph are smaller than the horizontal dimensions, less refraction is needed in the vertical direction, which translates into better image quality.  In addition, this reduced amount of refraction can be achieved in the limited available axial space. 
To achieve the desired refraction, the rear anamorph should preferably expand the light vertically.  Because the same horizontal unsqueeze projection lens is used for images captured with a front or rear anamorph, a prime or zoom lens with a different effective focal length should be employed in each case in order to produce the same projected image.  For example, assuming that the front anamorph has a horizontal squeeze ratio R and the rear anamorph has a vertical expansion ratio R, then in order to get the same image size after projection utilizing a projection lens of horizontal unsqueeze ratio R, the prime or zoom lens needs an effective focal length L for a front anamorph and an effective focal length L/2 for a rear anamorph.  In other words, the same final projected image size will occur for a front anamorph coupled to a prime or zoom lens with a 50 mm effective focal length, as for a prime or zoom lens with a 37.3 mm effective focal length coupled to a rear anamorph, so long as the front anamorph squeeze (e.g. 1.34:1), rear expansion (e.g. 1.34:1), and projection unsqueeze (e.g. 1.34:1) are related by the same factor. 
The Wallin patent.  To focus a spherical lens, one or more lens elements are moved along the optical axis.  One artifact of this movement is that the image will “breathe.”  When an image breathes, the image will show either slightly more or less field of view, creating a slight zooming effect.  With spherical lenses, the residual distortion (aberrations due to breathing) is the same in the horizontal and vertical directions.  However, with a front anamorph in place, the anamorphic breathing is not the same in the horizontal and vertical directions.  In other words, as the image breathes, the objects in the field of view will not maintain their true shape.  For example, with a front anamorph that produces a horizontal squeeze, as a person gets closer to the camera and the focal length is shortened, the anamorphic breathing will usually cause the person's face to look wider than normal. 
U.S. Pat.  No.  2,890,622 (the Wallin patent) attempts to minimize the effects of anamorphic breathing.  The Wallin patent discloses a front anamorph that includes two cylindrically surfaced elements, one slightly positively powered and one slightly negatively powered, such that if both were put together there would be zero power.  As the focusing lens elements are moved back and forth along the optical axis to focus the image, the two cylindrically surfaced elements of the front anamorph are geared such that they counter-rotate about the optical axis in opposite directions.  Thus, the degree of rotation between the two elements is variable and is dependent on how the lens is being focused.  This counter-rotating action of the two cylindrically surfaced elements cancels most of the anamorphic breathing.  However, although the two elements reduce the anamorphic breathing produced by the anamorph as the lens is focused, they do not change the inherent image quality produced by the anamorph. 
As described above and in related U.S. patent application entitled “Anamorphic Three-Perforation Imaging System,” with the advent of lower cost, yet higher image quality capture mediums such as 3-perforation film and electronic detectors, a rear anamorph with a reduced compression or expansion ratio is now practical.  The reduced compression or expansion ratio enables new design considerations not previously possible, and performance achievements not previously achievable.  For example, if front anamorphs could be replaced by rear anamorphs of the same or better performance, there would be a tremendous weight and size savings. 
Therefore, there is a need for a rear anamorph with a reduced compression or expansion ratio and improved image quality that obviates and mitigates the limitations of current rear anamorphs.