WO2021054845A9 - Optical systems capable of forming highly-corrected images of 3-dimensional objects - Google Patents

Abstract

Disclosed is a catoptric, catadioptric, or dioptric optical relay system, that is substantially afocal, and which produces a substantially unit-magnitude magnification final image of a finite object. And for which all image aberrations affecting the sharpness of images of point objects, image curvature, and distortion are corrected to an arbitrary order of correction, but at least to the Seidel order, for at least two object-image conjugate plane pairs. The optical relay adds an element that corrects pupil aberration at a location substantially at, or near, the object plane of the original relay, and/or to one or more of the images of this object produced by the system.

Description

Optical systems capable of forming highly-corrected images of 3- dimensional objects.

TECHNICAL FIELD OF THE INVENTION

The present invention is directed to the design of practical, fixed optical systems (systems requiring no adjustable optical elements) capable of producing stigmatic finite images that are free of curvature and distortion, all to some order of residual aberration, over a continuous and wide range of object conjugate distances. In other words, systems capable of producing stigmatic and distortion free images of 3-dimensional volumes in object space.

BACKGROUND OF THE INVENTION

Such systems have been variously referred to as “Ideal Image forming systems” or “Absolute Instruments” and were first described by James Clerk Maxwell.¹’² To be clear from the outset, an Absolute Instrument as first described was capable of producing a perfect image of the entire 3-dimensional object space. Systems described here will all approximate this behaviour to some finite order of residual aberration. For convenience, all such systems shall be referred to as Absolute Instruments or Ideal Image Forming Systems, in this document.

An Absolute Instrument was first shown to be theoretically possible in the design of a system requiring gradient refractive index optical components, the “Maxwell Fisheye”^{1 2}. Flowever, the gradient index material required to implement this design was, and still is, practically unobtainable. Despite obvious technical advantages in a wide range of applications, very few designs for Absolute Instruments have been given for practically realizable systems, which utilize more conventional optical elements such as mirrors or dioptric elements composed of homogeneous refractive index materials. The invention described here comprises a class of optical systems in which these desirable imaging properties are realized without recourse to exotic optical materials. Absolute Instruments

It has been shown by Maxwell and subsequently Wynne, that all Absolute Instruments are necessarily unit-magnitude magnification and afocal optical systems. While a large number of unit magnification, afocal image forming systems exist for which, for a single pair of object/image conjugate planes, a high degree of correction of aberrations affecting stigmatism, curvature and distortion are obtained, images produced by such systems will degrade as the object shifts from its ideal conjugate position.

This patent describes a means by which such systems may be converted to Absolute Instruments (with abovementioned caveats applying) by means of introducing a substantially planar aspheric optical element and/or elements at or near the system object, image or intermediate image, for the purposes of correcting system pupil aberration.

All such systems are subject to the claims of this patent.

When an optical system is used to produce an image of a finite object, this image will in general suffer from three types of defect arising from purely geometrical considerations:

1 ) Errors in stigmatism, arise when rays departing from a point in the object do not all intersect in a point in the image.

2) Error in curvature, give rise to finite curvature in the images of plane objects.

3) Distortion, is an error in linear mapping from points in the object to corresponding points in the image, representing a variation in magnification with field height.

As is generally understood by experts in the field of optical design, these errors can be accurately described by polynomial expressions that are expansions of transcendental functions of system parameters. In general, “correction to a given order” refers to the limiting geometric power of aperture and field to which the infinite set of polynomials in the expansion is truncated to, all terms higher than the given order being referred to as “residuals”. Correction to the lowest order of aberration, “third-order” or “Seidel” aberration is generally considered as a useful degree of correction for defining classes of system. Often, Seidel solutions are used as “starting points” for design, and subsequent ray tracing improves overall system performance by balancing small amounts of re-introduced Seidel aberrations with system residuals, thus minimising overall image defects. All systems currently under consideration in this patent will be corrected to at least the Seidel order of correction.

Catoptric, dioptric or catadioptric optical systems can be produced, which are fully corrected for all aberration terms to the considered order of correction, but only for one specific object-image conjugation. Numerous such systems are described in the literature.

In general, when the object conjugate is shifted from its nominal location in such corrected systems, the resultant shifted images will develop new aberrations. The aberrations of types (1) and (3) from above grow in varying proportions to the shift of the object, and also to terms that depend on the differences in angle that rays entering and leaving the system make to the optical axis of the system and on the spherical aberration of the exit pupil produced by the system. Only the curvature aberration (2) remains unchanged with object/image conjugate shift, in general.

J. C. Maxwell showed that, within what is commonly understood to be the geometrical optics approximation, if an optical system was capable of forming images free of all types (1), (2) and (3) of aberrations as defined above, for any two distinct object/image conjugate pairs, then this system would necessarily form images free from these aberrations for ALL object locations. Thus, the entire volume of object space is imaged perfectly by such systems. This type of optical system was referred to as an “Ideal Imaging System”, or an “Absolute Instrument”. Such systems are free of conjugate-shift aberrations.

Maxwell demonstrated using geometrical arguments¹ that any perfect Absolute Instrument must have unit-magnitude magnification and be afocal. Instruments substantially exhibiting the image correction properties of Absolute Instruments must substantially meet the afocality and unit magnitude magnification requirements.

Maxwell described an Absolute Instrument known as the “Maxwell Fish-Eye”. This system relies on objects and images existing within an “exotic” anisotropic optical medium, a gradient index, or ’’GRIN”, material, of somewhat extreme properties compared to the current state-of-the-art, and thus the Fisheye is not a practical imaging system due to the unavailability of the required material. Maxwell concluded that the only “system” capable of forming ideal images in a homogeneous isotropic optical medium was a flat mirror (or mirrors), a trivial solution, as he termed it. While a flat mirror is an Absolute Instrument its usefulness as an optical instrument is severely limited by the fact that one of its two conjugates is always virtual. A system, on the other hand, that reproduces the image forming capabilities of a flat mirror but also produces a real image from a real object, is certainly not trivial and such systems in fact have a wide range of applications.

C.G. Wynne developed the “conjugate shift equations” ³, to the third-order of expansion of the transverse aberration polynomial, or Seidel aberration. These are shown below.

In these equations the “original system” is described by all of the terms on the right-hand side of equation 1 which are not multiplied by e , i.e. the unstarred S terms. The original system has Seidel aberrations Si, Spherical Aberration, S2, Coma, S₃, Astigmatism, S₄, Field Curvature, S₅, Distortion and the additional term, S₆, which is the Spherical Aberration of the pupil, or in other words, the spherical aberration of the pencil of principal or chief rays.

The angle that the marginal ray makes to the axis is “ϋ". The change of the square of this angle in the object and image spaces respectively is A(u²).

The angle that the chief ray makes to the axis is The change of the square of this

angle in the object and image spaces respectively is Δ(

). “H” is the Smith-Helmholtz- Lagrange invariant. e represents an axial-shift of an object with respect to the object location of the original system. We can consider that an “object-shifted system” with different object conjugate and resultant image conjugate distances is formed when the object from the original system is shifted by e . The optical elements of the system are not perturbed in position with respect to each other. The object-shifted system shall have Seidel aberrations as indicated by the starred quantities in eq. 1., with starred quantities of corresponding index to unstarred quantities referring to the same Seidel aberration polynomial term, but with a new magnitude of coefficient for the object-shifted system .

In an Absolute Instrument, to the order of Seidel aberrations, the initial aberration terms S_t, must all be exactly zero, by definition. The change in all aberrations, with object-shift, must also be exactly zero. Thus, all the starred terms on the L.H.S. of equation (1) must remain exactly zero, for any value of e . Clearly this will be true for S₄*, field curvature, and S₆*, pupil spherical aberration. For these terms there is a simple equality between starred and unstarred terms, with no dependence on e or angle terms.

Wynne showed that to drive the remaining starred terms of equation (1) to zero for any e, it is necessary that the delta angle terms are all zero as well. This condition is only possible to be met by unit-magnitude magnification, afocal systems. Wynne stated, echoing Maxwell, that “no non-trivial solutions exist” to the Conjugate Shift equations.

This growth of aberration with conjugate shift is often undesirable in practical optical systems, but despite the fact that conjugate shift aberrations are problematic in a large number of practical cases, there are currently very few practical optical designs, composed of conventional optical elements, which are corrected to at least Seidel order for all object conjugates,

Some recent work has been done extending Maxwell’s Fisheye concept to include systems in which object and image conjugates lie in air, but these systems still rely on exotic gradient index material.

Offner produced a system combining an Offner monocentric catoptric relay, an earlier design by Offner which is a unit-magnification afocal system corrected for aberration at ONE object/image conjugate pair, with a Maksutof- Bowers meniscus lens. This system fully corrected conjugate-shift aberrations to fifth-order⁴. C. G. Wynne also in 1986 produced some variants on the meniscus-corrected-pupil Offner in US Pat. No. 4796984, which replaced the mirrors used by Offner with Mangin mirrors. Shafer produced versions of meniscus-corrected-pupil Offner’s incorporating multi-element refracting correctors, which produced an Absolute Instrument to 5^th order⁵, described in reference 5 and also in US Pat. No. 4711535. Shafer also produced an all-reflective system, requiring six reflections, that corrected conjugate shift aberrations to third-order⁵ without requiring any refractive components. The current state-of-the-art therefore provides a limited range of options for systems corrected over a volume. Such known designs require either meniscus refractive correctors, multi-element refractive correctors or large numbers of aspheric mirrors. Meniscus refracting correctors introduce chromatic errors to broad-band applications and are limited by absorption in various bands from Infra-red through UV and soft-Xray.

In the case of systems free of refractive components, as are useful for example in soft-X- ray lithography, systems requiring less than 6 reflections are currently unknown.

It is to be understood in all of the following description, that the various conditions such as “afocality” or “unit-magnitude magnification” or “corrected Seidel aberration” may be considered as “substantially so” and it is commonly understood to experts in the field of optical design that small perturbations may be introduced to the specifications of any optical system by means of which optimum balances may be sought. In this sense, for example a system of focal ratio of f/30 or more may be considered “substantially afocal”, and a system producing magnifications of +/- 1 +/- 10% may be thought of as substantially unit-magnification, and so on.

A novel class of Absolute Instruments.

As noted above, there exist a number of known unit-magnitude magnification, afocal systems, for which near-perfect imaging is achieved at only one pair of conjugate planes.

Well-known examples of such systems are the Offner catoptric relays, constituting an entire class of monocentric, object centred unit-magnification, afocal catoptric relays comprised entirely of spherical mirrors, and the Dyson catadioptric relay⁶⁷. Other examples exist, with some using more complex forms such as aspheric or free-form surfaces, and/or departing from strict co-axiality of optical components, such as is the case with “Schiefspiegler” systems. More examples of can be found in US 7,573,655, US 7,177,099, US 7,116,496, KR101130594B1 , and PCT WO2012145335A1.

It is notable that in WO2012145335A1 , the exact text “Meniscus elements can be used to reduce or remove the spherical aberration of principal rays parallel to the optical axis, see the publication entitled "Achievements in Optics" by A. Bouwers” given on page 2, lines 25-30, is in fact copied directly from US Pat. No. 4711535. However, the systems subsequently described in WO2012145335A1 do not correct the spherical aberration of the pupil and make no further mention of the correction of principal rays, beyond this copied text, copied from the patent describing a system already noted to be an Absolute Instrument. It is clear the system presented in WO2012145335A1 is not an Absolute Instrument.

In general, systems comprising the class so-far described, suffer from pupil aberration. The pupil, which is necessarily at a different object distance to the relay optics than the nominal object surface, will in general, be imaged with aberration by such systems. As the object is moved axially from the location in which it is imaged stigmatically by the system, aberrations will grow in proportion to the pupil-aberration dependent term.

It is an object of the present invention to provide the public with a useful new range of choices in this area. It is an object of the present invention to provide a new class of Absolute Instruments, to some useful degree of correction, or to provide a real world implementation of an Absolute Instrument that does not rely on exotic materials, said systems having the characteristics of being of being substantially afocal and of substantially unit-magnitude magnification, for which near-perfect imaging, or at least full correction of Seidel aberrations, is achieved for all object-image conjugate plane pairs, to provide the first such system that is purely catoptric incorporating less than 6 mirrors, or to overcome the above shortcomings or address the above desiderata, or to at least provide the public with a useful choice.

BRIEF DESCRIPTION OF THE INVENTION

In a first aspect the present invention may be said to comprise of: a catoptric, catadioptric, or dioptric optical relay system, that is substantially afocal,

- and which produces a substantially unit-magnitude magnification final image of a finite object

- and for which all image aberrations affecting the sharpness of images of point objects, image curvature, and distortion are corrected to an arbitrary order of correction, but at least to the Seidel order, for at least two object-image conjugate plane pairs, and to which an element that corrects pupil aberration is added at a location substantially at, or near, the object plane of the original relay, and/or to one or more of the images of this object produced by the system.

The particular placement of the pupil correcting element in the near vicinity of the object or one of its intermediate or final images, allows for the control of the pupil aberration without otherwise disturbing the correction of the aberrations of types (1) or (3) of the base system. It should be noted that the introduced element must be of substantially zero optical power, i.e., of substantially zero curvature, or substantially planar, so as not to introduce curvature aberration.

Any and all systems, as described in the first two paragraphs of this section above, are systems that can be “converted” to Absolute Instruments, to some order of correction, by the application, of a substantially flat, aspheric pupil correction element. In all cases the pupil correction discussed occurs at or near the object, and/or one or more of its images.

The following preferences broaden and generalize the first description of the invention given above.

Preferably the optical relay system to which a pupil correcting element is added is any one of the systems claimed by Offner in US Patent 3,748,015 (1973) “Unit Power Imaging Catoptric Anastigmat”. Preferably the optical relay system to which a pupil correcting element is added is any one of the systems claimed in US 7,573,655, US 7,177,099, US 7,116,496, KR101130594B1 , and PCT WO2012145335A1 .

Preferably the optical relay system to which a pupil correcting element is added, at or near the object and/or its image or images, is a pair of unit-magnification afocal confocal Cassegrain or Gregorian telescopes, as described by Wetherell.⁸

Preferably the optical relay system to which a pupil correcting element is added, at or near the object and/or its image or images, is any qualifying known, or yet to be discovered, optical relay. By “qualifying” it is understood that the optical relay in question will be: a) Corrected at least to Seidel order for aberrations affecting image stigmatism, curvature and distortion. b) Unit magnification (or unit magnitude magnification, of either sign). c) Afocal.

Preferably the pupil aberration correction, at or near the object and/or its image or images, is achieved by at least one refracting aspheric optical element or elements.

Preferably the pupil aberration correction, at or near the object and/or its image or images, is achieved by at least one reflecting aspheric optical element or elements.

Preferably the pupil aberration correction, at or near the object and/or its image or images, is achieved by at least one deformable “active” or “adaptive optic” optical element or elements.

Preferably the pupil aberration correction, at or near the object and/or its image or images, is achieved by a tilted or refractive optical component with a long-radius spherical profile, capable of introducing astigmatism to correct the pupil aberration. A long radius spherical element introduces some curvature but for very long radii, not “substantially” so. Such an element tilted can introduce aberration capable of correcting pupil aberration, particularly for eccentric-pupil systems. Preferably the pupil aberration correction, at or near the object and/or its image or images, is achieved by a tilted or diffractive optical component capable of introducing wavefront aberration (such as a computer generated hologram) to correct the pupil aberration.

Preferably the pupil aberration correction, at or near the object and/or its image or images, is achieved by a volume phase hologram component capable of introducing wavefront aberration to correct the pupil aberration.

Preferably the pupil aberration correction, at or near the object and/or its image or images, is achieved by a binary optical element.

Preferably the pupil aberration correction, at or near the object and/or its image or images, is achieved by some combination of more than one of the means described in the forgoing text.

Preferably the pupil aberration correction, at or near the object and/or its image or images, is achieved by a means not listed here, but because of the location of the pupil correction, at or near the object of one or more of its images, and the nature of the relay as specified in this patent, a system corrected to some order for conjugate shift is achieved. .

Preferably the optical relay system is used to produce an imaging spectrograph.

Preferably the optical relay system is used to produce an industrial imaging system.

Preferably the optical relay system is used as a subsystem of a directed energy weapon system.

Preferably the optical relay system is used as a subsystem of an earth imaging system.

Preferably the optical relay system is used to produce a spectrograph or a spectrograph relay.

Preferably the optical relay system is used to produce a lithography system..

Preferably the optical relay system is used to produce an all-reflective lithography system. Preferably at least one intermediate pupil is accessible in the optical relay system.

Preferably the optical relay system is used to produce a variant with non-unit magnification, where extended depth of focus (over a reduced range of object conjugate distances) is achieved by balancing re-introduced pupil aberration against conjugate shift terms containing non-zero delta-angle products.

In another aspect the present invention may be said to broadly consist in an adaptive optics relay, comprised of a system such as described in the foregoing.

In another aspect the present invention may be said to broadly consist in augmented reality system that produces sharply defined intermediate pupil(s) and/or image(s), and stigmatic imaging of multiple object conjugates, comprised of a system such as described in the foregoing, and utilizes these pupils or intermediate images for the addition of information using means common to such systems. The aberration control of the intermediate pupils or images afforded by this invention render them attractive for such systems; improved aberration correction in this case allows for increased introduced information content possible with the “image overlay system” when comparing two systems of otherwise identical parameters.

In another aspect the present invention may be said to broadly consist in a catoptric, catadioptric or dioptric optical system that produces a unit-magnitude magnification image of a finite object as described herein with reference to any one or more of the accompanying drawings.

The term “accessible pupil” refers to as is defined by an optical pupil (that is, an optical surface at or in which paraxial principal rays from all object points intersect) that is formed within the bounds of the optical system - that is, between the object and image planes (and, in a specific embodiment - between the first and second elements or second and third elements of the optical system of the invention), and that is spatially-distinguished and separated from a surface of an optical element of the system at hand.

Unit magnification: in the context of this discussion this will refer to systems for which the absolute magnitude of the ratio of ray heights in the image and the object is unity.

Afocal system: an afocal system is an optical system that produces no net convergence or divergence of the beam, i.e. the system has an infinite effective focal length. Doubly Telecentric: For the purposes of this discussion a system shall be described as “ doubly telecentric” if, when its aperture stop is placed such that its entrance pupil is located at an infinite distance in object space, the exit pupil will also be located at infinity. Systems described here as “doubly telecentric” may be made non-telecentric by placing the aperture stop at a location for which the entrance and exit pupils of the system are at finite distances, but in those cases the “atelecentricity”, or the finite angle that the chief ray makes to the optical axis will be equal in object and image spaces. Such systems are, by definition, afocal.

Seidel aberration: The well-known set of five aberrations indexed as S_j for which the first three terms, spherical aberration, coma and astigmatism, lead to the blurring of images of point source objects, the fourth term leads to the mapping of points from a plane object to a curved focal surface and the fifth term, distortion, which causes a field-dependent change in magnification. For Seidel aberrations, expressed as deformation of a wavefront of light in the system, the sum of the exponents of aperture and field in the polynomial expression for each term is four. These aberrations are often described as “third-order aberrations” referring to the order of similar exponent sums for expressions describing aberration as transverse errors of the ray in the image surface.

High-Order aberration: Aberrations for which the sum of pupil and field exponents in the particular aberration expression (for wavefront deformations) sum to even numbers greater than four.

Object/image conjugates: A reversible pair of points for which, in the absence of aberration, all rays leaving one and passing through the optical system, will pass exactly through the other.

Object Conjugate Shift: A movement of the object in the direction of the optical system axis of symmetry, either towards or away from the optical system.

Catoptric system: a system composed entirely of reflective optical elements Catadioptric system: a system composed of some combination of refracting and reflecting elements.

Dioptric system: a system composed entirely of refracting components.

As used herein the term “and/or” means “and” or “or”, or both.

As used herein “(s)” following a noun means the plural and/or singular forms of the noun. The term “comprising” as used in this specification means “consisting at least in part of”. When interpreting statements in this specification which include that term, the features, prefaced by that term in each statement, all need to be present, but other features can also be present. Related terms such as “comprise” and “comprised” are to be interpreted in the same manner.

It is intended that reference to a range of numbers disclosed herein (for example, 1 to 10) also incorporates reference to all rational numbers within that range (for example, 1 , 1.1 ,

2, 3, 3.9, 4, 5, 6, 6.5, 7, 8, 9 and 10) and also any range of rational numbers within that range (for example, 2 to 8, 1.5 to 5.5 and 3.1 to 4.7).

The entire disclosures of all applications, patents and publications, cited above and below, if any, are hereby incorporated by reference.

To those skilled in the art to which the invention relates, many changes in construction and widely differing embodiments and application of the invention will suggest themselves without departing from the scope of the invention as defined in the appended claims. The disclosures and the descriptions herein are purely illustrative and are not intended to be in any sense limiting.

Other aspects of the invention may become apparent from the following description which is given by way of example only and with reference to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

Preferred forms of the present invention will now be described with reference to the accompanying drawings. The first 9 figures serve to illustrate the performance of a system that is highly corrected at only one pair of conjugate planes. It is seen how the performance degrades drastically as the object conjugate is shifted away from the nominal location, even if the image conjugate is refocused, i.e., shifted to the position that minimizes the aberrations. In comparison drawings from the 10th and subsequent figures illustrate the performance of the corresponding Absolute Instrument to which the correcting element or elements have been added as per the descriptions given above.

The here named “Schmidt-Offner” systems are given as prime examples of this invention and their performance is shown to be markedly superior to that of the corresponding “Offner System” as the object conjugate is placed at locations other than the Offner’s nominal.

The Schmidt-Offner, in either its Catoptric or Catadioptric forms (i.e. with reflecting or refracting corrector(s)), represents one of the simplest possible Absolute Instruments in terms of total number and optical elements and of aspheric surfaces.

Figure 1 Shows an Offner unit-magnification, afocal distortion-free, flat-field anastigmatic relay, as described in US Pat. 3,748,015,

Figure 2 is a Seidel diagram showing that aberrations arising at mirrors D, F and G from figure 1 , sum to zero in the image (r.h.s. of the diagram)

Figure 3 shows a Geometrical Spot Diagram for the Offner system of figure 1 ,

Figure 4 shows that if for the system in Figure 1 , the object is moved to the left, (A) the image moves to the right (B), and unit-magnitude magnification and afocality are maintained,

Figure 5 shows the Seidel diagram for the conjugate-shifted image. When this is compared to figure 2 it is seen that the system Seidel sum is no longer zero, Figure 6 shows the Geometrical Spot Diagram for object shifted system of Figure 4 and when Compared to Figure 3, and noting that the scale is 10x greater in that figure, it is clear that the image quality is severely degraded in this conjugate-shifted Offner system,

Figure 7 shows the Offner system as a pupil relay, in this system the pupil and the object planes are swapped, this system, first given by Reed, relays the pupil. It can be considered as a pair of confocal off-axis “plateless-Schmidt telescopes”, with the common focal plane lying on the surface of the convex mirror,

Figure 8 shows the contributions to spherical aberration and field curvature from the two “plateless-Schmidt” concave mirrors are equal and sum, now there is no cancelling spherical aberration from the convex mirror because this mirror is at the focus of the two concave mirrors, the Field Curvature contribution from the convex mirror exactly balances the field curvature from the two concave mirrors,

Figure 9 shows the Spot diagram for the Reed/Offner pupil relay of Figure 7 note that in this object-at-infinity conjugate the image is also at infinity and so angular units must be used in the spot diagram, the spots are clearly very aberrated compared to the Airy discs. The elongation shows astigmatism and the top to bottom asymmetry shows coma,

Figure 10 shows the “Schmidt-Offner” Layout, note the addition of a Schmidt-like plate at H, when comparing to the conventional Offner of figure 1 ,

Figure 11 shows the Seidel diagram for the Schmidt-Offner layout with the object at the normal Offner object position, the plate introduces virtually no aberration, and aberrations are practically identical to those for the conventional Offner in figure 2,

Figure 12 shows the Spot diagram for the Schmidt-Offner arrangement of figure 10,

Figure 13 shows the Schmidt-Reed-Offner pupil relay, collimated light enters and exits the system and the object and image are at infinity, Figure 14 Figure 14 Schmidt-corrected Reed-Offner, comparing with figure 8 we see now that the new plate spherical aberration cancels mirror spherical aberration, as in a Schmidt telescope,

Figure 15 Shows the Spot diagram for Schmidt-corrected Reed-Offner system, note that the spot diagram is on a scale of 1/20th of that in figure 9, the RMS spot radii here are ~ 30x smaller diameter, giving ~900x higher energy concentration than those of the corresponding system in Figure 9,

Figure 16 Shows the Object-shifted Schmidt-Offner, note that in practical implementations the plate must be sized to pass the rays from all object conjugates considered in the design,

Figure 17 Shows the Seidel diagram for Schmidt-Offner with displaced object at finite distance. Noting also the correction shown in figures 12 and 13 we see that the Schmidt-Offner is corrected at two distinct object conjugates, “infinity” and at the common centre of curvature of the mirrors. Therefore, following Maxwell’s arguments, all object conjugates are corrected,

Figure 18 Shows the Spot diagram for Schmidt-Offner with displaced object at finite distance

Figure 19 Shows a design, similar to that of Figure 10, but with the Schmidt plate now split into two plates,

Figure 20 Shows the Seidel diagram showing aberrations for the system of Figure 19,

Figure 21 Shows a further Seidel diagram for the split plate version of the Schmidt- Reed-Offner system, which is the Schmidt-Offner system with object at infinity, and entrance and exit pupils coplanar and containing the centres of curvature of the mirrors.

Figure 22 shows the Seidel diagram for an intermediate object version of the Schmidt-Offner system, Figure 23 Shows an object relay system having an accessible intermediate pupil,

Figure 24 Shows a first Seidel diagram for the object relay systems of Figure 23,

Figure 25 Shows a second Seidel diagram for the object relay systems of Figure 23, now used in the Reed-pupil relay mode,

Figure 26 Shows a third Seidel diagram for the object relay systems of Figure 23 used to relay an object at some distance away from the nominal location of the corresponding Offner, and

Figure 27 Shows an object relay system as an imaging spectrograph configured to the present invention.

DETAILED DESCRIPTION OF THE INVENTION

Examples of preferred embodiments will now be described with reference to Figures 1 through 26 with application to two known qualifying relays

The following detailed description of the invention uses two versions of the Offner monocentric relay as a starting point and demonstrates the advantages to be gained by applying the present invention to convert this system to an “Absolute Instrument to third- order” in this case, by the addition of an aspheric plate at the Object or one or more of its images.

It will be understood from the foregoing that these examples are only representative samples from the numerous possible embodiments of this invention.

In particular it will be understood that in the case of the following example, the refracting aspheric pupil correcting element can practically be replaced with a reflecting aspheric correcting element, making an all-reflective variant.

Before demonstrating a corrected volume-imaging system, we can begin by considering the aberrations of the Offner catoptric relay, shown in Figure 1 , for several object/image conjugate pairs. In the example of Figure 1 , the red vertical plane contains an extended object (A), its unit-magnitude magnification image (B) and the combined centers of curvatures of all the mirrors in the system (C). C is located at the intercept of the axis of symmetry of the system and the object/image plane (I). Note that there is no unique axis to the mirror system as C is at the centre of all mirrors so any ray L from C is a radius of all optical surfaces in the system. A unique axis of symmetry, D, for the system can be defined with respect to the plane containing C, a finite plane object and its unit- magnification plane image. D is normal to that plane and passes through C.

Light leaving A travels to the first concave spherical mirror E, and is reflected towards B. This light is intercepted by the convex spherical mirror at F, which has half of the radius of the mirror at E, and subsequently travels towards the second concave spherical mirror at G, appearing now to originate from A. This second concave spherical mirror at G has the same radius of curvature as the first concave spherical mirror at E. Light subsequently travels to the image at B. It is noticeable that the central rays L for every object point and the central rays of every image point are parallel to each other and to the axis of symmetry of the system. These rays come to foci respectively at the entrance pupil and the exit pupil, which are both at infinity, and so the system is seen to be doubly telecentric, and therefore afocal.

This fact can be proven algebraically for any set of three monocentric mirrors arranged to be in sequence concave, convex, concave and for which the Petzval sum is zero (Seidel field curvature, S₄, is then zero).

Table 1 Optical design data for the Offner system shown in figure 1.

As is well known, this system is free of all Seidel image aberrations. The Seidel aberrations arising at each spherical mirror (at surfaces 7, 8 and 10 as indicated in table 1 corresponding to mirrors E, F and G from Figure 1) sum and cancel each other perfectly in the image. This is shown in a “Seidel Diagram” in Figure 2.

A geometrical spot diagram for this system, shown in Figure 3 shows black rings (M) which are “Airy Discs” indicating diffraction-limits to the image sharpness. The very tight collection of spots (N) within the black rings indicates very good image quality. The residual aberration is 5^th order tangential astigmatism.

However, this optical system has spherical aberration, coma, astigmatism and distortion that grow if the object (A) moves away from its location in the red object/image plane (I) indicated in Figure 1.

For example, in Figure 4, the object (A) is shifted to the left of this plane (I), away from the Offner system. The image conjugate plane (B) moves to the right. It is noticeable in the image that unit-magnification and afocality are maintained. If we consider the Seidel aberrations that result from this object conjugate shift, as shown in the Seidel diagram in Figure 5, it is clear that the balance of aberrations shown in Figure 2 is now not maintained and significant aberration exists in the image. It is noticeable in Figure 5 that the Field Curvature system (light blue) sum is still zero, as is to be expected from equations 1 for the S₄ term.

Comparing the spots in Figure 6 to those produced by the original system in Figure 3, we see that the RMS spot radius (N) has increased by a factor of 25. This indicates the image quality is relatively very poor.

The system by Reed, shown in Figure 7, who’s publication in fact preceded that of Offner, swaps object A and pupil F plane locations with those of the Offner, so that the object A is at infinity and the pupil K is in the same plane I as the centres of curvature of the mirrors discussed and shown in Figure 1 . In Figure 7 the pupils K now sit where the position of the object and image for the system in Figure 1 were. In this system the two individual concave spherical mirrors can be considered as the mirrors of two Schmidt telescopes (each used with a pencil of rays off-axis in the pupil), but without a corresponding Schmidt plate. As with the Schmidt telescope, the aperture stop is at the centre of curvature of each of the spherical mirrors. The focus of each of these “plate-less” Schmidt telescopes is the convex secondary mirror, which therefore contributes no image aberration to the system (because the intermediate image lies on this surface). This surface however does still contribute to system field curvature.

It can be seen in Figure 7 that unit-magnitude magnification and angle invariance for rays in the object and image spaces is conserved.

The Seidel diagram in Figure 8, for the arrangement of Reed in Figure 7, shows the spherical aberration which is to be expected from a pair of “plateless” Schmidt telescopes.

If we consider the field curvature contributions and sums in the three Seidel diagrams, shown in Figures 5 and 8 for conjugate shifted systems, we can see that these remain unchanged from those in the original Offner system (Figure 2) summing to zero in all cases. This is exactly the result expected from equation 1 , where it is given that S₄ = S₄.

The spot diagram for this system, shown in Figure 9, shows elongated spots N, whereas spherical aberration is an aberration with circular symmetry. This arises because the system only considers rays from an off-axis region of the pupil. A circular off-axis cross section of a spherically-aberrated wavefront decomposes into predominantly focus and astigmatism, with some coma. This is quickly recognizable in the spot diagram as seen in Figure 9, to a person knowledgeable in the phenomenology of optical aberrations.

It is clear from the foregoing that the Offner system evolves large conjugate-shift aberrations as the object conjugate is moved from its natural location for the system, in a plane containing also the centres of curvature of the mirrors.

The "Schmidt-Offner". One example of the invention.

It can be deduced from what has been presented so far, that the Offner or Reed/Offner system only produces high-quality images when the object is at, or near, the position indicated in Figure 1. That is, at the object conjugate for which the image-relay system was originally designed.

It can also be deduced from the conjugate shift equations that, given full-correction of Seidels for the system of Figure 1 , and angle invariance from object to image space that naturally arises in afocal, unit-magnification systems, the only term remaining on the right hand side that is non-zero is the S₆ term, the uncorrected spherical aberration of the pupil.

The subject of this invention is the realization that the introduction to ANY such systems, of an aspheric plate, or a part of a Schmidt plate J, or some substantially zero-powered optical element capable of correcting pupil aberration, in the near region of an object, its image or an intermediate, real image, allows for the substantive correction of the pupil aberration of a system such as the one described above without disturbing the correction of the image aberrations or the magnification unity of the original system. This undisturbed correction of the original system is achievable because rays have not substantially diverged from each other in the near region of the object, image or intermediate images.

An example of a Schmidt-Offner system is shown below in Figure 10.

This system shows one approach to correcting the S₆ term, the Seidel spherical aberration of the pupil shown in Figure 8, for the Reed/Offner system. As explained above, the Seidel spherical aberration of the pupil presents as a combination of focus, astigmatism and coma as illustrated in the spot diagram in Figure 9, when the system is used with a laterally displaced portion of the full-system symmetrical pupil, as is most commonly done to allow unobstructed light paths with a system of mirrors.

The dielectric plate (J) in this case supports an aspheric surface that has rotational symmetry about (C), and produces a retardation of incident rays that is typically proportional to even powers of the ray height at the plate. A circular portion of this plate is used that is of the same area as, or slightly larger than, the object A. In practice the 2^nd- degree- in-pupil (wavefront focus) term is typically introduced in systems transmitting some finite bandwidth of light, to allow chromatic focus to offset spherochromatism.

Note that because of the off-axis object and image, off-axis portions of this rotationally symmetrical plate are needed. Because of the symmetry of the Offner and its relationship to a Schmidt, the combination of primarily coma and astigmatic phase retardation required at the plate to correct the pupil is consistent with ratios derived from trepanning an off-axis portion of a symmetrical Schmidt corrector. In more general systems such as Schiefspiegler, the ratios of coma and astigmatism required to correct the pupil are not necessarily those that are consistent with trepanning a part from a rotationally symmetrical parent, and could be described as “free-form”.

As per the caveats at the introduction, higher orders of aberration are also correctable by reintroducing small balancing amounts of low-order aberration.

Table 2 Optical design data for the Schmidt-Offner system shown in figure 10. The 4^th degree aspheric coefficient of the Schmidt plate is also given.

SURFACEDATA SUMMARY:

Table 3 Schmidt plate aspheric coefficient for the system given in table 2.

The Seidel aberrations for this system are shown in Figure 11. It is noticeable that they are identical to those for the Offner system as represented in Figure 2.

Only very slight differences exist in the geometrical spot diagram for this “Schmidt-Offner”, shown in Figure 12, from the original Offner system, as seen in Figure 3. These differences are well below the limit imposed by diffraction in this case.

It can be concluded that that the Schmidt-Offner is effectively indistinguishable in performance from the normal Offner, when the object is conjugated as with the original Offner. The introduction of the Schmidt plate makes no substantive difference to the aberrations of the system, which are well-corrected.

Differences immediately become apparent when we consider the Reed-Offner system, as shown in Figures 7-9, where the same features are marked with the same letters, with the Schmidt plate (J) now included as above, as shown now in Figure 13. As was pointed out earlier, the Reed-Offner system suffers solely from spherical aberration of the pupil. Inspection of Figure 13 shows a system very similar in appearance to the Reed-Offner system shown in Figure 7.

The Seidel diagram in Figure 14, for the arrangement of Figure 13 shows now the effectiveness of the correction. Comparing Figure 14 to Figure 8 it is apparent that now a spherical aberration term has arisen from the plate. This term exactly corrects the spherical aberration of the two concave spherical mirrors of the Reed-Offner system of Figure 7 as seen in figure 8. The result is that the Schmidt-corrected Reed-Offner is as free from aberration as the original Offner system and it therefore performs orders of magnitude better in terms of image quality than the uncorrected Reed-Offner. This becomes more apparent when comparing spot diagrams for the Reed-Offner of Figure 9 and the Schmidt-corrected Reed-Offner shown in Figure 15. It is therefore clear the introduction of the Schmidt Plate (J) near to the object plane of the Offner allows for a system that is corrected for all aberrations at two different object conjugates, at least to the order considered.

As per the earlier Maxwell references, because we now have an optical system that is simultaneously well corrected at two different object conjugates, we can expect to have similar correction at ALL object conjugates. This is also expected from equation 1 , because we have corrected the only outstanding R.H.S. conjugate-shift term of S₆ , the Seidel Spherical aberration of the pupil of the original Offner.

To test this idea, we can look at the Schmidt-Offner system with the object shifted to the same location as was investigated in Figures 4-6.

We see in Figure 16 a system directly comparable to that in Figure 4 with the one exception of the new Schmidt plate (J). The Seidel diagram and spot diagram for this system are given in Figures 17 and 18 respectively. Clearly the performance in the Schmidt-Offner is greatly improved in this case from that of the corresponding Offner.

In Figure 19 we see a design that appears to be very similar to that shown in figure 10.

The difference is that the Schmidt plate (J) that fully corrects the system pupil aberration for the system in figure 2, now is split into two plates. One plate remains at H (now Hi), corresponding to the object location and the location of object in the original Offner relay, and now a second plate occurs close to the image (now H₂). Because of the symmetry of the Offner, in this case each plate has half of the asphericity required to fully correct the pupil aberration. In general the asphericity can be divided arbitrarily between any number of plates, provided they are located as described in this patent, and provided that the algebraic sum of contributions to pupil aberration from the plates fully cancels the total pupil aberration of the system.

In Figure 20 we can see that the Seidel aberrations for this system are the same as for the original Offner (see Figure 3) or the Schmidt Offner (see figure 11). This is expected as the plates are at objects or images.

In Figure 21 we see that for this split-plate version of the Schmidt-Reed-Offner, the pupil correction from the single plate that shows at surface 6 (encircled) in Figure 14, is now evenly divided between surfaces 6 and 17 (with some (yellow) pupil distortion arising at the plane surface of the plate.

In Figure 22 we see that for an intermediate object location version of the split-plate Schmidt-Reed-Offner system the plates now contribute differing values of aberration individually but the balance is maintained in the system sum, which is zero.

An advantage offered by the split plate system is that it allows for the treatment of intermediate pupil or image quality with plates occurring before the intermediate pupil or image, with plates subsequent to this pupil or image providing the required final system pupil correction to make the system a Maxwellian Ideal Imager (to the order of correction considered).

As mentioned earlier there are many real-world systems that could benefit from a practically achievable Absolute Instrument (to the order of correction considered). For example, augmented reality systems could benefit from having a highly corrected image at an intermediate image in a pupil relay, adaptive optics systems could benefit from having highly corrected intermediate pupils or meta pupils, and Infrared relays may benefit from having highly defined pupils on cold-stops, for example.

A final example of variant of the 3-mirror Offner relay involves introducing asymmetry to the relay, so as to produce a pupil K in an accessible location, clear of any interference of rays. In the original Offner 3-mirror system, of Figure 1 , the pupil (K) lies at the convex secondary mirror (F). Metapupils of interest in adaptive optics relays would lie in regions in which rays traversing the system in opposing directions overlapped. It would be impossible to locate a flat deformable mirror for an Adaptive Optics system, or volume holographic element for an Offner Spectrograph, or an LCD screen for an Augmented reality system, at this location without causing obscuration. The Jet Propulsion Laboratory (JPL) have developed especially a technology to produce curved diffraction gratings, so as to allow for the production of Offner spectrographs. The grating must be curved so as to allow it to conform to the convex mirror surface (F) at the location of the pupil (K). The optical advantages offered by the original Offner relay in the case of the Offner spectrograph have motivated an expensive investment in this technology development, to produce curved high-quality gratings. This technology development is not trivial and the technology is not widely available to commercial organizations outside of JPL. The modified Offner system described below offers the advantages of an accessible pupil and nearby metapupils, at which can be located for example flat transmissive or reflective diffractive elements, deformable optics etc. as discussed, while retaining the other advantages of the original Offner, and also avoiding the disadvantages of the JPL technology described above.

The further addition of system pupil correction, as is claimed in this patent, and then also splitting that pupil correction, allows for the very significant improvement of aberration control at these intermediate pupils or images. Furthermore, and critically, for Adaptive Optics systems using laser guide stars, the pupil-corrected unit magnification afocal relay allows for the stigmatic relaying not only of a telescope focal surface, but also of the varying-object-distance focal surfaces of the laser guide stars, which are reimaged to different axial locations from the infinity focus of a telescope, depending on the distance of the telescope to the laser guide star, which varies widely depending on telescope elevation and mesosphere height.

The modified Offner relay described here introduces an asymmetry such that the first and second concave mirrors are allowed to differ significantly in radius, by any ratio.

Characteristic to all such system is the condition that the system Petzval sum must be zero and the centres of curvature of each mirror must be substantially congruent and lying substantially in the plane containing both the object and the image, as per Offer’s patent¹.

In figure 23 we see an example of such a system as an object relay. This system is to be compared to the original unmodified Offner as in Figure 1 , or the Schmidt-Offner of Figure 10, or the Split-Plate Schmidt Offner of Figure 19. It is clear that an accessible intermediate pupil (K) is produced by this modified Offner configuration, and that this intermediate pupil (K) would be an intermediate image if the system was used as a Reed- Offner pupil relay.

Optical data for this system are presented in Tables 4 and 5. Table 4 Prescription data for asymmetric Schmidt-Offner

Table 5 Aspheric coefficients for the plates at surfaces 6 and 16.

The sum of the reciprocals of the two concave radii is equal in magnitude and opposite in sign to the reciprocal of the convex mirror radius. Thus, the Petzval sum for the system is zero. The centres of curvature are congruent and lie in the same plane as the object and image planes.

This system is corrected for all Seidel image aberrations as shown in Figure 24, is unit- magnitude magnification and afocal, and suffers from pupil aberration, just as is the case with the symmetrical Offner system.

However, now because of the asymmetry in the two concave mirrors, the contribution to pupil aberration from each of these elements is uneven. A split plate system is capable of perfectly correcting the pupil aberration occurring before the intermediate pupil (or image in the case of a Reed-Offer pupil relay), whatever it is, with the remaining correction required by the system elements occurring after the corrected intermediate pupil or image, being corrected by the second plate near the final relayed image. Unlike in the case of the symmetrical Split-Plate Schmidt-Offner, in this case, the plates will have different degrees of asphericity.

The Seidel diagrams in Figures 24-26 demonstrate that a Maxwellian Ideal Imager, to the given order of correction, is again produced in this case.

The Schmidt-Offner shown here is an example of an Absolute Instrument, to the given order of correction of the original relay. Very few examples of such systems have been discovered since Maxwell first described their general image forming characteristics.

Since Offner’s systems were patented and published in 1973, there have been no published examples of Schmidt Offners described in the literature, and none of the numerous optical designers working with Offner relays, or other relays of the same ilk, have realized this design path, despite much use being made of the Offner system, and the general desirability of system insensitivity to conjugate shift. Thus it can be argued that even though the path to such systems can be explained in relatively simple terms, it has clearly not been obvious to expert practitioners in the field.

It is clear from the foregoing text that the development and variants discussed above with respect to the Offner 3-mirror relay equally apply to other unit-magnification afocal relays that are corrected for Seidel aberrations. All such systems can be made into Maxwellian Ideal Imagers, to some order of correction, by the suitable addition of pupil correcting elements as discussed. In such cases the pupil correction can occur in a single element or multiple elements. Multiple-element pupil correction allows for the further correction of intermediate images.

Variants of the invention.

It should be clear to any expert practitioner of optical design or optical aberration theory, by way of the preceding invention, that ANY system that is of unit-magnitude magnification, is afocal and is free from (at least) the five Seidel image aberrations, can be transformed into an Maxwellian ideal-imaging system, to the same order of correction as the base relay, by means of an optical element introduced at or near the focus that corrects the pupil aberration of the original relay, to the desired order of correction.

In this section possible variants of the basic invention shall be briefly described, without being analyzed to the same level of detail as the example of the Offner/Schmidt-Offner given above.

Schmidt-Offner variants

It seems to be not generally understood in the field that the 1973 Offner patent described a much more general family of systems than the three-concentric mirror unit-magnitude magnification relay with two equal radius concave mirrors and one convex mirror with half the radius of the concave mirrors. Almost all references to “the Offner system” refer to one particular example from the infinite variety of possible systems Offner described; that is the version shown in Figure 1 for which there are two equal radii concave spherical mirrors and one convex spherical mirror so-disposed.

In fact, Offner’s patent claims any catoptric, monocentric, object-centered, all-spherical relay of three or more mirrors for which the Petzval condition is met (field curvature is zero). Some such systems were demonstrated to have accessible pupils. In general, even the three-mirror system can be generalized to have accessible intermediate pupils. Offner shows that any systems meeting these conditions will be a unit-magnification, afocal relay, with all Seidel aberrations corrected.

Any and all of the systems covered in Offner’s patent claims are convertible to “Schmidt- Offner’s”, as described above, by means of correction of the pupil aberration by means of a correcting element placed at or near the object and/or its conjugate(s).

Any and all of the systems covered by Offner’s patent claims and so converted to Schmidt-Offner’s are subject to the claims of this patent. Possible variants, also claimed, involve systems in which aspheric terms are introduced to improve, for example, the correction of high-order aberration. Such systems may include both conventional rotationally symmetrical or off-axis aspheric optics, or true free-forms, which are not producible from a parent optic of rotational symmetry.

Possible variants, also claimed, involve systems in which free-form and relative position and orientation of any or all optical surfaces are allowed to vary so as to produce a suitably corrected unit-magnitude magnification afocal relay, to which a pupil-correcting element is added.

Means of correction of pupil aberration.

A key concept of this invention is the correction of pupil aberration of systems that are already corrected for all other Seidel aberrations and are unit-magnification, afocal relays. One common feature of the various approaches to correction claimed in this patent is that the correction of pupil aberration will occur at or near an object, an intermediate image or a final image of the system, or with divided correction, at some combination of these. The actual means of providing the required pupil correction can vary.

The approach described above is to use an aspheric refracting plate in transmission.

An alternative to this, first discussed by Lemaitre⁹, is to use an aspheric mirror that is titled with an appropriate adjustment of the aspheric profile. Lemaitre referred to his systems as “Reflecting Schmidts”. It is clear that the same approach would hold for more general Schiefspiegler systems.

Another approach to introducing the required astigmatic correction to an optical system, is to utilize a very long radius spherical element as a “correcting-fold-mirror”. If such a mirror is placed at or near the object or image or intermediate images of a qualifying unit- magnification relay, a combination of tilt and radius can generally be found that will correct the spherical aberration of the pupil of the type of relay described in this patent, where an off axis portion of the pupil is used and the predominant aberration of the pupil is astigmatic, and render the system as a claimed variant of Maxwellian ideal imager. Other approaches to correct pupil aberration include, but are not limited to, elements that are computer generated holograms, or binary optical elements, or active or adaptive mirrors.

Divided correction of pupil aberration.

“Divided correction” of pupil aberration means, for example, that instead of using one optical element to correct the entire pupil aberration of the system, one element could be located at or near the object and correct some percentage of the system pupil aberration, and subsequently another element or elements at other locations but all closely located object conjugates throughout the system, can correct the remaining pupil aberration. The sum of all of these elements aberration contributions corrects entirely the pupil aberration. Such systems might be of advantage for example where there is interest in maintaining image quality at intermediate images or pupils.

Catadioptric or Dioptric relays.

In the preceding discussion catoptric relays have been used by way of example. Any and all of the descriptions above can apply also to systems for which the original base relay system is comprised of a mix of powered refracting and reflecting components. A famous example is the Dyson relay, which incorporates one refracting surface used in double pass and one spherical mirror. This system is unit-magnification, afocal, and is corrected for all Seidel aberrations, and so it can be corrected for all object distances by correcting the pupil aberration as described above.

This invention has a wide range of possible application areas. Only a subset of the possible application areas of this invention shall be listed below, together with some discussion of the advantages the invention offers to these areas. Application Areas

A) Adaptive Optics Relays.

Such systems relay light from a telescope focus to an instrument or suite of instruments. Internal to the relay are locations which are conjugated to one or more object distances for the telescope, typically above the telescope, at which are placed deformable mirrors. Forming sharp images on these deformable mirrors is advantageous and the pupil correction or divided pupil correction discussed above can give advantages to the design of such systems.

Furthermore, such systems often are simultaneously employed to image light from sodium beacons at various heights in the upper atmosphere. The ability of this relay to provide simultaneously stigmatic images of various object heights is of great advantage to such relays, precluding the need for extra corrective optics in a separated laser path.

Also, the correction of the intermediate pupil and meta-pupils, and the exit pupil is often an important design aspect in such systems and again the “Maxwellian Ideal Imager” features of this invention offer advantages.

B) Spectrographs

Offner imaging spectrographs are an example of a high-performance spectrograph, employing the version of the Offner described in Figure 1 and associated text, or some version of this that is slightly perturbed in its design parameters. A diffractive element is placed at the secondary mirror location which is the pupil for a telecentric system.

A specific improvement to the Offner imaging spectrograph is one in which the radii of the two concave mirrors are made significantly unequal, so that the intermediate pupil K of the system is produced in a region free from the interference of rays travelling in two different directions. Such pupils are generally referred to as “Accessible” as they can be completely enclosed without causing obscuration to the system. Provided that the Petzval sum is maintained at zero, so that the sum of the reciprocal radii of the two concave mirrors is balanced by the reciprocal radius of the convex mirror, the mirrors are substantially monocentric and the system is substantially object centred, such a system will be an Offner. By adding divided pupil correction so that the amount required to correct the spherical aberration of the pupil contributed by the first mirrors preceding the intermediate pupil is in the first plate at the object plane of the relay and the amount of aberration required to correct the spherical aberration of the pupil contributed by the remaining element or elements is in the second plate at or near the final image location, a system that has a substantially perfectly corrected intermediate pupil image (though suffering some uncorrected field curvature) will result. This is advantageous to the design of such spectrographs as aberration at the diffractive element can complicate such designs. The configuration mentioned, in which an asymmetric version of an Offner is used to produce a clear pupil for an Offner spectrograph diffractive element does not appear in the literature and is also a claim of this patent.

One embodiment of the invention configured as an Imaging Spectrograph, in which a flat diffraction grating is disposed not at the surface of the convex mirror but at the location of the accessible pupil that is spatially-separated from the convex mirror, could be considered with reference to Figure 27.

Conventional spectrographs structured according to the Offner design (see, for example, US 2005/0270528) are used for a hyper spectral imaging, and provide advantages over other types of spectrograph for this purpose, as they produce higher image quality and spectral resolution than other kinds for the long slit-length and low f-number required for remote sensing. The higher spectral resolution is beneficial in applications such as anomaly detection, target recognition, and background characterization. At present, hyper spectral imaging is used in a wide variety of technological applications such as scientific research, medical diagnosis, environmental assessment, military applications, quality and safety control, and remote-sensing.

A conventional Offner Imaging spectrograph is configured as follows:

A slit object, that is extended in one dimension, is imaged by a three-mirror Offner afocal relay optical system. As was previously mentioned, for telecentric objects the pupil of the Offner system is coincident with the surface of the convex mirror. At the pupil of the convex mirror, a diffraction grating is formed on the surface of such mirror to spectrally- disperse light (with angle of dispersion being in proportion to wavelength) in directions perpendicular to the direction of the image of the slit. The spectrally-dispersed light is then reflected by a third mirror in the system to form a unit magnification image lying substantially in the same plane as that containing the substantially coincident centers of curvatures of the mirrors and the slit object. As a result, the convention Offner imaging spectrograph produces, in operation, multiple adjacent images of the slit object at multiple wavelengths, such multiple images being distinct and separated from one another.

An operational disadvantage of the Offner imaging spectrograph stems from the fact that the pupil of the system lies on a curved surface (the convex surface) of the secondary mirror. As is recognized in related art, the process of manufacture of high-quality diffraction gratings on curved surfaces is considerably more technically challenging, and therefore expensive, than producing gratings of equivalent quality on flat surfaces, or than producing flat transmissive diffraction gratings (such as those defined by volume phase holograms, for example).

In contradistinction with the conventional Offner Imaging Spectrograph system, an embodiment of the invention employs a diffraction grating J that is configured to be flat - not curved - and that is judiciously placed at the accessible pupil of the embodiment. Accordingly, depending on the specifics of the implementation, such diffraction grating is used either in reflection or in transmission. The grating that is flat (i.e., the rulings of which are defined in a substantially planar surface) could thus be produced with less difficulty and expense, on a flat surface, than is the case for the curved grating required in the Offner system.

As shown in the specific example of Fig. 27, a transmissive diffraction grating J is placed at the accessible pupil K. Light travels from the slit at A (the slit is in the direction into the page) and is sequentially reflected by mirrors E and F. At the grating K the spectrally- different bundles of light are dispersed (separated in angle by wavelength in a direction perpendicular to the slit) and then travels to mirror G to form image B. it is appreciated that, as a result of small modification of the system of Fig 27, a diffraction grating configured to operate in reflection can be used.

C) Industrial imaging systems

There are numerous applications in industrial imaging for which a system that returns unit- magnitude magnification stigmatic image conjugate planes for any object plane will have particular usefulness. Such systems only require a movable detector to produce sharp images of multiple object distances. Depending on the numerical aperture of the system a means of measuring range to objects by determining the image conjugate location accurately is enabled. The properties of afocality and unit-magnitude magnification mean that there is no perspective scale shift in images at different locations.

D) Augmented reality systems

Systems that relay pupils to the human eye pupil and which contain an intermediate image, can be used for augmented reality devices. A means of overlaying a relayed intermediate image with additional light sources is produced at the intermediate image.

For example, the intermediate image of the relay could be produced on a transmissive LCD screen. The divided pupil correction discussed in B) above could also be applied to produce well-corrected intermediate images, enhancing the performance of such devices. The stigmatic relay of various object distances would allow augmented reality systems to produce aberration-free images for a larger range of object distances than would otherwise be the case for a similar relay without the pupil correction.

E) Lithography systems

Lithography has numerous industrial applications, the most famous of those being the production of integrated circuits on silicon wafers. A system capable of rendering diffraction limited images of masks that remain diffraction limited over an extended depth of focus are of general interest. Completely catoptric systems are of interest for such areas as soft-x-ray lithography.

The foregoing description of the invention includes preferred forms thereof. Modifications may be made thereto without departing from the scope of the invention.

References

1 . J. C. Maxwell, “The Laws of Optical Instruments”, The Quarterly Journal of Pure and Applied Mathematics, 2, 232-246, 1858.

2. W. D. Niven (Ed). “The Scientific Works of James Clerk Maxwell”. In two volumes, reproduced by Dover Publications, New York.1965.

3. C.G. Wynne, “Primary aberrations and conjugate change”, Proc. Phys. Soc. 65B, 429-437, 1952.

4. C. G. Wynne "Monocentric Telescopes For Microlithography", Optical Engineering 26(4), 264300 (1 April 1987)

5. D. Shafer, “Some odd and interesting monocentric designs”, Proc. SPIE 5865, Tribute to Warren Smith: A Legacy in Lens Design and Optical Engineering; (2005)

6. J. Dyson, entitled "Unit magnification optical system without Seidel aberrations, " J. Opt. Soc. Am. 49(7), pp. 713-716 (1959) C. G. Wynne, "A unit power telescope for projection copying" Optical Instruments and Techniques, Oriel Press, Newcastle upon Tyne, England (1969) William B. Wetherell, "All-Reflecting Afocal Telescopes," Proc. SPIE 0751 , Reflective Optics, (10 June 1987) G. R. Lemaitre, “Astronomical Optics and Elasticity Theory”, Springer, 2009.

Claims

1 . A catoptric, catadioptric, or dioptric optical relay system that is substantially afocal and which produces a substantially unit-magnitude magnification final image of a finite object and for which, all aberrations to at least Seidel order of the image are substantially corrected, to which a pupil aberration correction is added at a location substantially at the object for correcting system pupil aberration.

2. The system as claimed in claim 1 wherein the correction of the system pupil aberration is achieved by one or more correcting elements each of which is located at, at least one of; the object, one of its intermediate images or the final image, as produced by the system.

3. Any one of the systems described in 3,748,015 , US 7,573,655, US 7,177,099, US 7,116,496, KR101130594B1 , and PCT WO2012145335A1 , to which an element capable of correcting pupil aberration without disturbing the original relay correction is added at the object and or image or intermediate images.

4. The system as claimed in any one of claims 1 to 3 wherein at least one intermediate pupil is accessible in the optical relay system.

5. The system as claimed in any one of claims 1 to 4 wherein the pupil aberration correction is achieved by at least one refracting aspheric optical element or elements.

6. The system as claimed in any one of claims 1 to 5 wherein the pupil aberration correction is achieved by at least one reflecting aspheric optical element or elements.

7. The system as claimed in any one of claims 1 to 6 wherein the pupil aberration correction is achieved by at least one deformable “active” or “adaptive optic” optical element or elements.

8. The system as claimed in any one of claims 1 to 7 wherein the pupil aberration correction is achieved by a tilted or reflective optical component with a long-radius spherical profile, capable of introducing astigmatism to correct the pupil aberration.

9. The system as claimed in any one of claims 1 to 8 wherein the pupil aberration correction is achieved by a tilted or refractive optical component with a long-radius spherical profile, capable of introducing astigmatism to correct the pupil aberration.

10. The system as claimed in any one of claims 1 to 9 wherein the pupil aberration correction is achieved by a tilted or diffractive optical component capable of introducing wavefront aberration (such as a computer generated hologram) to correct the pupil aberration.

11. The system as claimed in any one of claims 1 to 10 wherein the pupil aberration correction is achieved by a volume phase hologram component capable of introducing wavefront aberration to correct the pupil aberration.

12. The system as claimed in any one of claims 1 to 11 wherein the pupil aberration correction is achieved by a binary optical element.

13. The system as claimed in any one of claims 1 to 12 wherein the pupil aberration correction is achieved by some combination of more than one of the means as claimed herein.

14. The system as claimed in any one of claims 1 to 13 wherein the pupil aberration correction is achieved by the location of the pupil correction, and the nature of the relay as claimed herein, an Ideal Maxwellian imager is produced.

15. The system as claimed in any one of claims 1 to 14 wherein the optical relay system is used to produce an imaging spectrograph.

16. The system as claimed in any one of claims 1 to 15 wherein the optical relay system is used to produce an industrial imaging system.

17. The system as claimed in any one of claims 1 to 16 wherein the optical relay system is used as a subsystem of a directed energy weapon system.

18. The system as claimed in any one of claims 1 to 17 wherein the optical relay system is used as a subsystem of an earth imaging system.

19. The system as claimed in any one of claims 1 to 18 wherein the optical relay system is used to produce a spectrograph or spectrograph relay.

20. The system as claimed in any one of claims 1 to 18 wherein the optical relay system modified to allow non-unit magnification and pupil aberration correction with the introduced pupil correcting element is modified so as to optimally balance the resultant conjugate shift components now arising from non-zero delta angle terms. In this way extensions in conjugate shift insensitivity may be achieved in systems with non-unit magnification, when compared to systems without the pupil correcting element as claimed.

21. An adaptive optics relay, that has a in a catoptric, catadioptric or dioptric optical relay arrangement that produces a unit-magnitude magnification image of a finite object and which can be rendered afocal solely by a particular location of a system aperture stop, and for which all Seidel aberrations of the image are corrected, to which a pupil aberration correction is added to a location substantially at, or near, at least one of the object location, or one of its images as produced by the system.

22. An augmented reality system that produces sharply defined intermediate pupils and images, and stigmatic imaging of multiple object conjugates, comprising or including, a catoptric, catadioptric or dioptric optical arrangement that produces a unit-magnitude magnification image of a finite object and which can be rendered afocal solely by a particular location of the system aperture stop, and for which all Seidel aberrations of the image are corrected, to which a means of correcting the pupil aberration is added to a location substantially at at least one of the object location, or one of its images as produced by the system.

23. A head up display that produces sharply defined intermediate pupils and images, and stigmatic imaging of multiple object conjugates, comprising or including, , a catoptric, catadioptric or dioptric optical arrangement that produces a unit-magnitude magnification image of a finite object and which can be rendered afocal solely by a particular location of the system aperture stop, and for which all Seidel aberrations of the image are corrected, to which a means of correcting the pupil aberration is added to a location substantially at least one of the object location, or one of its images as produced by the system.

24. A lithography system that is capable of producing sharply defined images with insensitivity to object displacement. In such systems, for which extremely short wavelengths are to be used a reflecting aspheric plate corrector may be employed to produce a catoptric version. In general systems incorporating powered mirrors will produce ring-field Lithography systems.

25. A catoptric imaging system comprising: no more than three mirrors that include a first mirror having a first curvature characterized by a first radius of curvature and a first center of curvature; a second mirror having a second curvature characterized by a second radius of curvature and a second center of curvature; a third mirror having a third curvature characterized by a third radius of curvature and a third center of curvature; wherein said imaging system is an aplanatic imaging system having an accessible pupil, and wherein said imaging system is a unit-magnification imaging system.

26. A catoptric, catadioptric or dioptric optical system that produces a unit-magnitude magnification image of a finite object as described herein with reference to any one or more of the accompanying drawings.