WO2015111036A1

WO2015111036A1 - Anamorphic optics that resolve off-axis point sources

Info

Publication number: WO2015111036A1
Application number: PCT/IL2014/051088
Authority: WO
Inventors: Shahar NIR; Eyal ARAD; Paula ROIT
Original assignee: Rafael Advanced Defense Systems Ltd.
Priority date: 2014-01-23
Filing date: 2014-12-11
Publication date: 2015-07-30
Also published as: IL230640B; IL230640A0

Abstract

An optical system comprising: an anamorphic optical subsystem that includes: an entrance plane, an exit plane, and at least one optical element, in an optical path from said entrance plane to said exit plane, that effects an aspect ratio distortion, by a factor r>1, on light that has a wavelength in a predetermined wavelength interval and that enters said anamorphic optical subsystem via said entrance plane from an infinitely distant point source at any azimuth and at any elevation of up to at least about five degrees from an optical axis of said anamorphic optical subsystem, such that energy of said light within an Airy disk of said light as said light exits said anamorphic optical subsystem via said exit plane, is at least about f(r) of a diffraction limit value of said energy, wherein f(x) is a monotonic function of x such that f(1)=1, f(1)≥- 0.737, f(2)≥0.6 and f(∞)=0.

Description

ANAMORPHIC OPTICS THAT RESOLVE OFF-AXIS POINT SOURCES

FIELD AND BACKGROUND OF THE INVENTION

The present invention relates to anamorphic optics and, more particularly, to an anamorphic optical system with better off-axis resolution of point sources than those known heretofore.

"Anamorphic optics", as understood herein, are optics that stretch or squeeze the light from a scene rectilinearly. Figures 1A and IB illustrate anamorphic squeezing of a scene. Figure 1A depicts a typical scene as it would be imaged by a camera whose optics are not anamorphic and whose angular field of view is 3.86 times as wide as it is high. Figure IB depicts what image of the scene of Figure 1 A looks like after being squeezed horizontally and/or stretched vertically to be only 1.25 times as wide as it is high.

Conventional infrared detector arrays usually are close to square in shape. An infrared camera with non-anamorphic optics that is to be used for surveillance of a scene such as the scene depicted in Figure 1A would either use a single detector array and capture images that are dominated by the sky above the terrain of interest or would use several side-by-side detector arrays. A camera with anamorphic infrared optics could image just the terrain of interest using a single conventional detector array: the anamorphic optics would squeeze the incident light of a field of view such as the field of view depicted in Figure 1A so that substantially all of the light is focused on substantially all of the detector array.

Figure 2 illustrates the coordinate system used herein. Figure 2 shows the entrance plane and the exit plane of an anamorphic optical system that squeezes the incident angles of incoming light horizontally and stretches the angles of incoming light vertically. The horizontal spread of the incoming angles at the entrance plane is ¼>,:. The vertical spread of the incoming angles at the entrance plane is h,. The horizontal spread of the outgoing angles at the exit plane is w₀. The vertical spread of the outgoing angles at the exit plane is h₀. The aspect ratio of the entrance plane is cti-Wi/hi. The aspect ratio of the exit plane is a<_f=w ih₀. The aspect ratio distortion factor of the anamorphic system is defined herein as r=max(a₀/a_f-, aja₀). The rectilinear coordinate system of the anamorphic optical system is defined so that the exit plane is at z-0 and the z~axis points from the entrance plane to the exit plane, the xz plane is horizontal and the >>z plane is vertical.

A "non-anamorphic" optical system, also called herein a "rotationally symmetric" optical system, is an optical system for which r=\ .

Conventionally, anamorphic optics are designed relative to the desired, performance (at the exit plane) along the x and y axes. See for example US Patent No. 8,049,967 to Hirose that includes several instructive illustrations of on-axis spot diagrams. This results in the smearing of images of off-axis objects. This smearing is acceptable for imaging extended objects but is not acceptable in surveillance applications in which the targets are point sources of light.

DEFINITIONS

The appended claims define the present invention in terms of its effects on light rays from an "infinitely distant point source" that enter the system at certain angles relative to the optical axis of the system.

A "point source" is understood herein as a source of light that is sufficiently compact to be treated for optical modeling purposes as a mathematical point. An "infinitely distant" point source is understood herein as a point source that is sufficiently far from the system of the present invention that all light rays from the point source are effectively parallel.

The angular coordinate system used to describe the orientation of the incoming rays relative to the optical axis of the system at the entrance plane uses the "azimuth" and the "elevation" of a spherical coordinate system. The azimuth, in the interval [-180°,180°], is measured relative to the xz plane, as shown in Figure 2. The elevation, in the interval [0°,90°], is measured relative to the optical (z) axis, as shown in Figure 3, in which the direction of propagation of the light is from left to right.

SUMMARY OF THE INVENTION

According to the present invention there is provided an optical system including: (a) an anamorphic optical subsystem that includes: (i) an entrance plane, (ii) an exit plane, and (iii) at least one optical element, in an optical path from the entrance plane to the exit plane, that effects an aspect ratio distortion, by a factor r>\, on light that has a wavelength in a predetermined wavelength interval and that enters the anamorphic optical subsystem via the entrance plane from an infinitely distant point source at any azimuth and at any elevation of up to at least about five degrees from an optical axis of the anamorphic optical subsystem, such that energy of the light within an Airy disk of the light as the light exits the anamorphic optical subsystem via the exit plane, is at least about fir) of a diffraction limit value of the energy, wherein fix) is a monotonic function of x such tha 1 )=1 ,f(l )>-0.737, f(2)>0.6 and_, (∞)=0.

According to the present invention there is provided an optical system including: (a) an entrance plane; (b) a detector; and (c) at least one optical element, in an optical path from the entrance plane to the detector, that: (i) focuses, onto the detector, light, from an infinitely distant point source, that enters the optical system via the entrance plane at any azimuth and at any elevation of up to at least about five degrees from an optical axis of the optical system and that has a wavelength in a predetermined wavelength interval, and (ii) that effects an aspect ratio distortion, by a factor of r>l, on the light, such that energy of the light within an Airy disk of the light as focused on the detector is at least about fir) of a diffraction limit value of the energy, wherein fix) is a monotonic function of x such that fil)=\ , f(l)≥-0.737, f(2)>0.6 andfi∞ =0.

One basic embodiment of the present invention is an optical system that includes an anamorphic optical subsystem. The anamorphic optical subsystem includes an entrance plane, an exit plane and one or more optical elements, in the optical path from the entrance plane to the exit plane, that effect(s) an aspect ratio distortion, by a factor r>\, on light that has a wavelength in a predetermined interval and that enters the subsystem via the entrance plane from an infinitely distant point source at any azimuth and at any elevation up to at least about five degrees from the optical axis of the subsystem. The energy of the light within the Airy disk of the light as the light exits the subsystem via the exit plane is at least about /(r) of the diffraction limit value of that energy, where fix) is a monotonic function of x such that/f l)=l , /(l)≥-0.737, f(2)>0.6 and/loo)-0.

The preferred functional form of f(x) \sfix)-x^'' where n<0.737. Preferably, n<0.515. More preferably, n<0.322. Most preferably, n≤0.152.

The optical element(s) may be refractive and/or reflective optical elements. In the preferred embodiments described below, the optical elements are refractive optical elements. Preferably, 1.5<r<8. if r≤4, then preferably the condition on the energy of the light within the Airy disk is satisfied for any azimuth and for any elevation up to about six degrees. If r<2, then preferably the condition on the energy of the light within the Airy disk is satisfied for any azimuth and for any elevation up to about ten degrees.

In some preferred embodiments, the predetermined wavelength interval is in the mid-infrared (3 microns to 8 microns), most preferably between about 3.6 microns and about 4.9 microns. In other preferred embodiments, the predetermined wavelength interval is an interval in the long wavelength infrared (8 microns to 15 microns), most preferably between about 8 microns and about 13 microns.

Preferably, the system also includes a detector of the light and a rotationally symmetric optical subsystem that receives the light from the exit plane and. focuses the light on the detector. Most preferably, the energy of the light within, the Airy disk of the light as focused on the detector also is at least about fir) of a diffraction limit of that energy.

Another basic embodiment of the present invention is an optical system that includes an entrance plane, a detector, and one or more optical elements in the optical path from the entrance plane to the detector. The optical element(s) focus(es), onto the detector, light, from an infinitely distance point source, that enters the system via the entrance plane at any azimuth and at any elevation up to at least about five degrees and that has a wavelength in a predetermined wavelength interval. The optical element(s) also effect(s) an aspect ratio distortion by a factor of r>l, on the light. The energy of the light within the Airy disk of the light as focused on the detector is at least about fir) of the diffraction limit value of that energy, where fix) is a monotonic function of x. such

BRIEF DESCRIPTION OF THE DRAWINGS

Various embodiments are herein described, by way of example only, with reference to the accompanying drawings, wherein:

FIGs. 1 A and IB illustrate anamorphic squeezing of a scene;

FIG. 2 illustrates the coordinate system used herein and also the definition of "azimuth";

FIG. 3 illustrates the definition of "elevation"; FIGs. 4A and 4B are horizontal and vertical cross sections of exemplary r=2 anamorphic optics;

FIG. 5 shows plots of the fraction of enclosed energy within circles centered on the centroid of the light at the exit plane of the optics of FIGs 4A and 4B, as a function of the radii of the circles, for several entrance angles;

FIG. 6 shows plots similar to those of FIG. 5 for r=2 prior art anamorphic optics;

FIGs. 7A and 7B are horizontal and vertical cross sections of exemplary r=4 anamorphic optics;

FIG. 8 shows plots of the fraction of enclosed energy within circles centered on the centroid of the light at the exit plane of the optics of FIGs 7A and 7B, as a function of the radii of the circles, for several entrance angles;

FIGs. 9 A and 9B are horizontal and vertical cross sections of exemplary r=S anamorphic optics;

FIG. 10 shows plots of the fraction of enclosed energy within circles centered on the centroid of the light at the exit plane of the optics of FIGs 9A and 9B, as a function of the radii of the circles, for several entrance angles;

FIG. 11 is a high-level block diagram of a complete system of the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The principles and operation of anamorphic optics according to the present invention may be better understood with reference to the drawings and the accom anying description.

Referring again to the drawings, Figures 4A and 4B are horizontal and vertical cross sections of exemplary / -2 anamorphic optics 10 of the present invention, for mid-infrared wavelengths between 3.6 microns and 4.9 microns. Lenses 16 and 18 are made of germanium. The spacing apart of entrance plane 12, lenses 16 and 18 and exit plane 14 are as shown in Figure 4A. Surface 22 of lens 16 is a spherical surface of radius 147.7466 mm, concave towards exit plane 14. Surface 26 of lens 18 is a spherical surface of radius 35.3941 1 mm, convex towards exit plane 14. Lenses 16 and 18 are rendered anamorphic by their surfaces 20 and 24, which are defined by mixed toroidal-Zernike coefficients. 6 2014/051088

Mixed toroidal-Zernike surfaces are defined herein similarly to their definition in the ZEMAX™ Optical Design Program Users Manual of 8 July 2011 with the radius of revolution set equal to zero. Toroidal surfaces are formed by defining a curve in eyz plane and then translating the curve parallel to the x-axis. The curve in the yz plane is defined by

z = a y² + ₂y⁴ + a^y⁶

The resulting surface is modified by the addition of the following Zernike terms:

where the Zernike polynomials Z are as defined by Noll, p is the normalized radial coordinate (normalized to equal 1 at the circular edge of the lens surface) and φ is the angular coordinate. In surfaces 20 and 24 the only non-zero Zernike coefficients are A\, A4, As, A_{\ \t} An, A i4, A22, A24, A.26 nd ^g- The corresponding polynomials are:

Ζ_\(ρ,φ) = 1

Ζ₆( = j6(p² cos 2φ)

Ζ ,φ) =^Ιΐθ(4ρ⁴ - 3p²) cos2<p

Zu(p,<p) = -JlQp⁴ cos 4<p ¾( > ) = ^7(20 ⁶ - 30p⁴ + Up² - 1)

Ζ₂₄(ρ,φ)

- 20p + 6 ²)cos2<p

¾(/> ) = Vl4 (6p⁶ - 5p ) cos 4φ

The coefficients that define surfaces 20 and 24 are as in the following table.

The diameter of the aperture at entrance plane 12 is 40.58 mm. Lens 16 has a diameter of 38.52 mm at surface 20 and a diameter of 36 mm at surface 22. Lens 18 has a diameter of 17.24 mm at surface 24 and a diameter of 1 .06 mm at surface 26. The diameter of the aperture at exit plane 14 is 7.7 mm.

The figure of merit of the anamorphic optics of the present invention is, for rays of light that enter the entrance plane from an infinitely distant point source, the fraction of the energy of the light within the Airy disk of the light at the exit plane, relative to the value of that energy in the diffraction limit. Figure 5 shows, for anamorphic optics 10, plots of the fraction of enclosed energy within circles centered on the centroid of the light at exit plane 14, as a function of the radii of the circles: one curve for the diffraction limit and four curves for the actual performance of anamorphic optics 10 for the following (azimuth, elevation) pairs for the incident directions:

(0°, 0°) (parallel to optical axis)

(0°, 6°) (in x-z plane, 6° elevation)

(90°, 2.25°) (in y-z plane, 2.25° elevation)

(20.5°, 6.4°) (along entrance plane diagonal)

These curves are weighted averages of curves calculated at wavelengths of 3.6 microns, 4.25 microns and 4.9 microns. The four "actual performance" curves are indistinguishable from each other, and are indistinguishable from the diffraction limit curve except between about 0.5 milliradians and about 0.8 milliradians. In this particular case, the radius of the Airy disk is about 0.7 milliradians.

For reference, Figure 6 shows similar curves for representative anamorphic optics of the prior art. The incident directions illustrated are:

(0°, 0°) (parallel to optical axis) (0°, 6°) (in x-z plane, 6° elevation)

(20.5°, 6.4°) (along entrance plane diagonal)

The two "on-axis" ((0°, 0°) and (0°, 6°)) curves are close to the diffraction limit curve, but the off-axis (20.5°, 6.4°) curve is significantly below the other three curves. At a, radius of about 1 milliradian, the off-axis enclosed energy is about half of the diffraction limit enclosed energy.

Therefore, the first appended claim defines the present invention in terms of the figure of merit, for light from an infinitely distant point source entering the entrance plane at any azimuth (not just on-axis) and at elevations up to about 5°, being as follows. The ratio of the fraction of energy of the light within the Airy disk at the exit plane to what that fraction would, be in the diffraction limit is a function/ of the aspect ration distortion factor r that obeys the following constraints:

fil) - 1 : non-anamorphic optics are excluded from the scope of the claim, f(l)≥ 0.737: as r increases away from 1, the off-axis performance must not decrease faster than this value for the first derivative of ^'with respect to r.

fil)≥ 0.6: the figure of merit at r=2 has to be at least 0.6 of the diffraction limit figure of merit, unlike the prior art in which the figure of merit is at most about half of the diffraction limit figure of merit.

fi∞) = 0: the off-diagonal performance of the prior art designs becomes increasingly worse as r becomes very large.

The preferred function fix) is fix) = x^~"_t with n < 0.737. n = 0.737 gives fil) = 0.6. » = 0.515 gives fi2) = 0.7. n = 0.322 gives fi2) - 0.8. n = 0.152 gives Λ2) = 0.9.

Figures 7A and. 7B are horizontal and vertical cross sections of exemplary r=A anamorphic optics 30 of the present invention, for long infrared wavelengths between 8 microns and 12 microns. Lenses 36, 38, 40 and 42 are made of germanium. The spacing apart of lenses 36, 38, 40 and 42 and exit plane 34 are as shown in Figure 7 A. The entrance plane (not shown) is tangent to surface 44 of lens 36 and perpendicular to the optical axis. Surface 46 of lens 36 is a spherical surface of radius 487.0118 mm, concave towards exit plane 34. Surface SO of lens 38 is a spherical surface of radius 44.8087 mm, concave towards exit plane 34. Surface 54 of lens 40 is a spherical surface of radius 212.26 1 mm, concave towards exit plane 34. Surface 58 of lens 42 is a spherical surface of radius 792.4964, convex towards exit plane 34. Lenses 36 and 42 are rendered anamorphic by their surfaces 44 and 56, which are defined by mixed toroidal-Zemike coefficients, just as surfaces 20 and 24 of lenses 16 and 18 are defined. The coefficients that define surfaces 44 and 56 are as in the following table.

Surface 48 of lens 38 and surface 52 of lens 40 are even aspherical surfaces defined by

z - /?, + fa⁶ + [hs^% + j¾s¹⁰

where s is distance from the optical axis in mm. The coefficients that define surfaces 48 and 52 are as in the following table.

Lens 36 has a diameter of 69.89 mm at surface 44 and a diameter of 68.39 mm at surface 46. Lens 38 has a diameter of 36.63 mm at surface 48 and a diameter of 32. mm at surface 50. Lens 40 has a diameter of 28.61 mm at surface 52 and a diameter of 27.93 mm at surface 54. Lens 42 has a diameter of 16.54 mm at surface 56 and a diameter of 16.26 mm at surface 58.

Figure 8 shows, for anamorphic optics 30, plots of the fraction of enclosed energy within circles centered on the centroid of the light at exit plane 34, as a function of the radii of the circles: one curve for the diffraction limit ant four curves for the actual performance of anamorphic optics 30 for the following azimuth- elevation pairs:

(0°, 0°) (parallel to optical axis)

(0°, 6°) (in x-z plane, 6° elevation)

(90°, 1.125°) (in y-z plane, 1.125° elevation)

(10.62°, 6.105°) (along entrance plane diagonal)

These curves are weighted averages of curves calculated at wavelengths of 8 microns, 10 microns and 12 microns. All five curves are mutually distinguishable between about 0.5 milliradians and about 2 milliradians but nevertheless are very close to each other. The radius of the Airy disk in this case is about 1.5 milliradians.

Figures 9A and 9B are horizontal and vertical cross sections of exemplary r=8 anamorphic optics 60 of the present invention, for long infrared wavelengths between 8 microns and 12 microns. Lenses 66, 68, 70 and 72 are made of germanium. The spacing apart of entrance plane 62, lenses 66, 68, 70 and lens 72 and exit plane 74 are as shown in Figure A. Surface 76 of lens 66 is a spherical surface of radius 438.5167 mm, concave towards exit plane 34. Surface 80 of lens 68 is a spherical surface of radius 52.28051 mm, concave towards exit plane 64. Surface 84 of lens 70 is a spherical surface of radius 124.5697 mm, concave towards exit plane 74. Surface 88 of lens 72 is a spherical surface of radius 36.72785, convex towards exit plane 74.

Lenses 66 and 72 are rendered anamorphic by their surfaces 74 and 86, which are defined by mixed toroidal-Zernike coefficients, just as surfaces 20 and 24 of lenses 16 and 18 are defined. The coefficients that define surfaces 44 and 56 are as in the following table.

Surface 78 of lens 68 and surface 82 of lens 70 are even aspherical surfaces defined by

z = β_ι5 ⁴ + /½ + + ¾Λ / ² + As¹⁴ + β_Ί*^¼ where s is distance from the optical axis in mm. The coefficients that define surfaces 78 and 82 are as in the following table.

Lens 66 has a diameter of 65.28 mm at surface 74 and a diameter of 63.34 mm at surface 76. Lens 68 has a diameter of 41.31 mm at surface 78 and a diameter of 32.76 mm at surface 80. Lens 70 has a diameter of 27.60 mm at surface 82 and a diameter of 23.56 mm at surface 84. Lens 72 has a diameter of 8.96 mm at surface 86 and a diameter of 9.49 mm at surface 88.

Figure 10 shows, for anamorphic optics 60, plots of the fraction of enclosed energy within circles centered on the centroid of the light at exit plane 64, as a function of the radii of the circles: one curve for the diffraction limit ant four curves for the actual performance of anamorphic optics 60 for the following azimuth- elevation pairs:

(0°, 0°) (parallel to optical axis)

(0°, 5°) (in x-z plane, 5° elevation)

(90°, 0.5°) (in y-z plane, 2.25° elevation)

(5.71°, 5.025°) (along entrance plane diagonal)

These curves are weighted averages of curves calculated at wavelengths of 8 microns, 10 microns and 12 microns. As expected, the curve that deviates the most from the diffraction limit is the (5,71 °, 5.025°) curve. At the Airy disk radius of this case (about 3.2 milliradians), the ratio of the enclosed energy for that curve to the diffraction limit enclosed energy is 0.85, well above even the value of 0.729 that is obtained using/fx)^^"" with x=8 and ra=0.152.

Figure 11 is a high-level block diagram, of a complete system 100 of the present invention. System 100 includes anamorphic optics 110 (of which anamorphic optics 10 is one embodiment and anamorphic optics 30 is another embodiment), non- anamorphic optics 120 and a detector array 130 such as a CCD detector array. The entrance plane of anamorphic optics 110 is designated in Figure 7 by the reference numeral 112. The exit plane of anamorphic optics 110 is designated in Figure 7 by the reference numeral 114. Anamorphic optics 110 is afocal, and the function of non- anamorphic optics 120 is to focus the light exiting exit plane 114 onto detector array 130, so the entrance plane 122 of non-anamorphic optics 120 coincides with exit plane 114 of anamorphic optics 110. Detector array 130 is placed at the exit plane of non-anamorphic optics 120. The figure of merit of system 100 is similar to the figure of merit of anamorphic optics 110: for rays of light that enter entrance plane 112 from an infinitely distant point source, the fraction of the energy of the light within the Airy disk of the light at detector 130, relative to the value of that energy in the diffraction limit. For light from an infinitely distant point source entering entrance plane 112 at any azimuth and at elevations up to about 5°, the ratio of the fraction of energy of the light within the Airy disk at detector array 130 to what that fraction would be in the diffraction limit is f(r), where r is the aspect ratio distortion factor of anamorphic optics 110.

To the extent that the appended claims have been drafted without multiple dependencies, this has been done only to accommodate formal requirements in jurisdictions which do not allow such multiple dependencies. It should be noted that all possible combinations of features which would be implied by rendering the claims multiply dependent are explicitly envisaged and should be considered part of the invention.

While the invention has been described with respect to a limited number of embodiments, it will be appreciated that many variations, modifications and other applications of the invention may be made. Therefore, the claimed invention as recited in the claims that follow is not limited to the embodiments described herein.

Claims

WHAT IS CLAIMED IS:

1. An optical system comprising:

(a) an anamorphic optical subsystem that includes:

(i) an entrance plane,

(ii) an exit plane, and

(iii) at least one optical element, in an optical path from said entrance plane to said exit plane, that effects an aspect ratio distortion, by a factor r>l , on light that has a wavelength in a predetermined wavelength interval and that enters said anamorphic optical subsystem via said entrance plane from an infinitely distant point source at any azimuth and at any elevation of up to at least about five degrees from an optical axis of said anamorphic optical subsystem, such that energy of said light within an Airy disk of said light as said light exits said anamorphic optical subsystem via said exit plane, is at least about fir) of a diffraction limit value of said energy, wherein fix) is a mono tonic function of x such that y(l)=l, /(l)>-0.737, f(2)>0.6 and^(oo)=0.

2. The optical system of claim 1 , wherein fix)-x^'" and «<0.737.

3. The optical system of claim 2, wherein «<0.515.

4. The optical system of claim 2, wherein 7i<0.322.

5. The optical system of claim 2, wherein n≤0.152.

6. The optical system of claim 1, wherein one of said at least one optical element is a refractive optical element.

7. The optical system of claim 1, wherein one of said at least one optical element is a reflective optical element.

8. The optical system of claim 1, wherein 1.5<r<8.

9. The optical system of claim 8, wherein r<4 and wherein said any elevation is up to about six degrees from said optical axis.

10. The optical system of claim 8, wherein r<2 and wherein said any elevation is up to about ten degrees from said optical axis.

11. The optical system of claim 1, wherein said predetermined wavelength interval is a mid-infrared wavelength interval.

12. The optical system of claim 1 1 , wherein said predetermined wavelength interval is from about 3.6 microns to about 4.9 microns.

13. The optical system of claim 1, wherein said predetermined wavelength interval is a long wavelength infrared wavelength interval.

14. The optical system of claim 13, wherein said predetermined wavelength interval is from about 8 microns to about 13 microns.

15. The optical system of claim 1, further comprising:

(b) a detector of said light; and

(c) a rotationally symmetric optical system that receives said light from said exit plane and focuses said light on said detector.

16. The optical system of claim 15, wherein energy of said light within an Airy disk of said light as focused on said detector is at least about fir) of a diffraction limit value of said energy.

17. An optical system comprising:

(a) an entrance plane;

(b) a detector; and

(c) at least one optical element, in an optical path from said entrance plane to said detector, that:

(i) focuses, onto said detector, light, from an infinitely distant point source, that enters the optical system via said entrance plane at any azimuth and at any elevation of up to at least about five degrees from an optical axis of the optical system and that has a wavelength in a predetermined wavelength interval, and

(ii) that effects an aspect ratio distortion, by a factor of r>l, on said Hght,

such that energy of said light within an Airy disk of said light as focused on said detector is at least about fir) of a diffraction limit value of said energy, wherein fix) is a monotonic function of x such that Xl)=l, (l)>-0.737, f(2)>0.6 dfi∞)=0.