Classifications

• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B13/00—Optical objectives specially designed for the purposes specified below
  • G02B13/02—Telephoto objectives, i.e. systems of the type + - in which the distance from the front vertex to the image plane is less than the equivalent focal length
• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B13/00—Optical objectives specially designed for the purposes specified below
• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B13/00—Optical objectives specially designed for the purposes specified below
  • G02B13/18—Optical objectives specially designed for the purposes specified below with lenses having one or more non-spherical faces, e.g. for reducing geometrical aberration
• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
  • G02B27/0012—Optical design, e.g. procedures, algorithms, optimisation routines

Definitions

• This invention relates generally to lens systems using free form
• lenses and more particularly relates to lens systems configured to provide matching of the object space to the image space according to the application for which the lens system is used.
• An aspect of this invention relates generally to lens systems using double plane symmetry freeform lenses, and more particularly relates to lens systems using double plane symmetry lens elements for time of flight and machine vision applications where the surface or Z-sag of the double plane symmetry surface is defined by an X-Y polynomial
• Rotational symmetry is widely used in conventional lenses, with the field of view and the aperture stop both being rotationally symmetric. With only rare exception, this results in the final design comprising rotationally symmetric elements.
• An example of such a conventional design is shown in Figure 1 .
• Lens designs using only rotationally symmetric lenses attempt to achieve as good as possible image quality (IQ) inside the circular image space field of view.
• the objective includes minimizing optical aberrations such as spherical errors, coma, astigmatism, field curvature, distortion, axial and lateral aberration, color, and others.
• An inherent characteristic of rotationally symmetric designs is that the optical errors in the lenses are the same at all points equidistant from the center of the lens, even though points outside the area of the sensor are of no consequence to the stored image.
• optimal lens performance cannot be matched to the sensor’s field of view, and the result is similar to that shown in Figure 3.
• the present invention provides a plurality of optical designs using free form lenses which overcome the limitations of conventional rotationally symmetric designs while also taking into consideration the particular application and the considerations associated with that application.
• the optical designs of the present invention permit - depending upon the application - different optical power, field of view, aberration correction, and so on to be made along the X axis than along the Y axis.
• one or more optical elements having double plane symmetry or other free form characteristics is introduced into the optical system.
• a freeform optical element as contemplated by the present invention can have one optical surface with double plane symmetry, while the other surface is rotationally symmetrical.
• both surfaces can have double plane symmetry, or one surface may have another form of asymmetry, such as a surface defined by a Zernike or Chebyshev polynomial, or a hybrid Zernike lens element, or a lens element with a diffractive surface.
• Multiple such freeform optical elements are also possible in the optical system. In the case of multiple elements having double plane symmetry, the orientation of the freeform elements in the assembly has to be aligned.
• the image projected onto the sensor is better matched to the field of view of the sensor, resulting in enhanced resolution of the captured imaged and, effectively, higher resolution.
• This better matching offers significant benefits in many optical applications, including lens modules for smartphone cameras, virtual reality and augmented reality optics, time of flight systems, machine vision systems, security cameras, and so on.
• One example of the benefits of such better matching is in the virtual reality context, where dewarping an image taken with conventional rotational optics can take two days or more, while dewarping of that same image when captured with an appropriately designed free form lens system may take only a few hours.
• the lens design of the present invention is particularly well suited to wide angle lenses, but in some implementations is also advantageous for normal and telephoto or zoom lenses.
• the lens design can be implemented as a fixed focal length lens attachment to an existing lens, such as might be integrated into a smart phone.
• lens characteristics are optimized around narrow wavelength bands such as infrared or near infrared.
• the present invention makes possible numerous machine vision solutions not available with conventional rotationally symmetric lenses. Such solutions can be implemented across a wide range of wavelengths, for example from 350 nanometers to 2500 nanometers.
• the materials used for the optical elements will typically be optimized for the relevant wavelength to ensure proper transmittance,
• Perspective aberration can be corrected with these types of free form optical elements.
• perspective aberration results in an elongation, or stretching, of the object on the image plane of the sensor.
• Traditional optical system typically results in a constant effective focal length of the optical system throughout the field of view.
• the use of such freeform lens elements in accordance with the present invention implements a varying effective focal length of the optical system with respect to the field of the view.
• the changing effective focal length can be implemented for lenses that are rotationally symmetric, as discussed below in connection with Figure 22.
• This changing effective focal length can, alternatively, be implemented with different rates of change of focal length along the X-axis and Y-axis. In an embodiment, this minimizes perspective aberration and can be
• the image plane on the sensor is a circle that does not completely fill the sensor.
• the freeform optical elements of the present invention allow a different effective focal length in the X-axis than in the Y- axis. This results in an image plane that is not a circle and instead may be an oval which fills up more of the rectangle sensor. This increases the effective resolution of the image.
• XY polynomial design characteristics of a double-plane symmetry lens in accordance with one aspect of the present invention can be described by an XY polynomial, for example.
• certain forms of a Zernike polynomial can also be used to describe a double-plane symmetry lens in accordance with the present invention.
• some forms of a Chebyshev polynomial can be used to describe a double-plane symmetry lens according to an aspect of the present invention.
• lens designs can include, but are by no means limited to: panoramic free form lens systems with a low f-number and short total track length; super-wide angle lens systems; lens systems for mobile phone applications with very short track length and very high on-axis performance; hybrid free form lens designs having an f-number in the range of 1.6 while also capable of mating to a large sensor and a short total track length; diffractive free-form lens designs for mobile phone applications; and lens designs for non- imaging applications such as 3D cameras or time of flight systems for applications in, for example, mobile, autonomous and semi-autonomous vehicles, or other machine vision applications.
• lens system designs in accordance with the present invention are suitable for a variety of applications, including security cameras, smart phone attachments, dash cams, action cams, web cams, drone cameras, front facing“selfie” cameras, and a broad variety of machine vision systems including time of flight systems.
• aspects of the present invention can be implemented to provide significant improvement in many imaging and non- imaging sensing applications.
• Figure 1 depicts the relationship between an object plane, a lens and an image plane.
• Figure 2 Prior Art
• Figure 2 illustrates the relationship between the field of view of a rotationally symmetric lens and the field of view of a rectangular sensor.
• Figure 3 Prior Art
• Figure 4 illustrates the improved image quality at the sensor possible with the present invention.
• Figure 5 illustrates an embodiment of a Kepler-type afocal telescopic lens design in accordance with the present invention.
• Figures 6A-6B illustrate in ray diagram and table form details of an embodiment of a lens design in accordance with the invention.
• Figures 7 and 9 shows the improved optical image quality achievable with a lens design in accordance with the present invention.
• Figures 8 and 10 Graphically illustrate optical image quality for a conventional, rotationally symmetric lens design, especially edge softness.
• Figures 1 1 A-1 1 B show an embodiment of a five-element afocal Galileo-type telescopic lens design in accordance with the present invention.
• Figures 12A-12B show a ray path diagram of the lens design of Figures 1 1A-1 1 B.
• Figures 13 and 14 graphically illustrate image quality for the lens design of Figure 1 1A.
• Figure 15 illustrates in ray path form the performance of a low
• Figure 16 shows a double symmetry lens element in accordance with the present invention.
• Figures 17-19 graphically illustrate the performance of a wide angle lens design in accordance with the present invention.
• Figure 20 illustrates the traditional optical systems having a constant effective focal length of the whole field of view of the sensor
• Figure 21 illustrates an optical system where the effective focal length changes with the field on the sensor
• Figure 22 illustrates how the effective focal length changes over the image sensor in a rotationally symmetric manner
• Figure 23 illustrates the effective focal length changes differently along the X-axis and Y-axis on the image plane
• Figure 24 illustrates a conventional image circle for a larger than 180deg FOV lens (left) and a non-circular image circle for increased pixels.
• Figure 25A illustrates in cross-sectional side view an embodiment of the invention, specifically a panoramic or super wide angle lens
• Figure 25B illustrates an example of the highly asymmetrical surface referred to in Figure 25A.
• Figures 26A-26B illustrate graphically the benefits of the lens system of Figures 25A-25B.
• Figure 27A illustrates an embodiment of the invention suited to
• Figure 27B illustrates a free form lens element suited to the
• Figure 27A comprising an aspheric surface and a Zernike surface.
• Figures 28A and 28B illustrate performance characteristics of the embodiment shown in Figure 27A.
• Figure 29A illustrates an embodiment of the invention suited to a mobile implementation having a large sensor and a low f-number, and also a moderately short track length.
• Figure 29B illustrates an embodiment of a free form lens element suited to the embodiment of Figure 29A wherein the lens element comprises a hybrid of a glass base lens having on one surface thereof a UV curable material with a surface defined by a Zernike polynomial.
• Figure 30 shows on axis wavefront error for the embodiment shown in Figure 29A.
• Figure 31 A illustrates an embodiment of the invention suited to a mobile application where a diffractive free form lens enables the use of fewer elements and therefore a particularly short track length.
• Figure 31 B illustrates an example of a diffractive lens element suited for use in the embodiment of Figure 31 A.
• Figures 32A and 32B show, respectively, on-axis wavefront error and on-axis point spread for the embodiment shown in Figure 31 A.
• Figure 33 illustrates an embodiment of the invention suited for
• Figure 34 illustrates an embodiment of the invention suited to time- of-flight systems, which can be considered a specific application of machine vision.
• Figure 35 shows an embodiment of a lens system suited to use in mobile and similar applications where the free form lens surfaces are defined using extended X-Y Polynomial.
• Figure 36 shows in table form the constituent elements of the
• Figures 37A-37D show in table form exemplary coefficients for the embodiment shown in Figure 35.
• FIG. 4 illustrated therein is a general description of the improvement in image quality that can be achieved by the use of a free form lens and permitting different optimization at different distances from the axis of the lens.
• the area of the sensor, indicated at 100 is shown to have best image quality, while areas outside of the sensor, indicated at 1 10, are permitted a reduced quality since these areas are irrelevant to the image captured by the sensor.
• FIG. 5 and 6A-6B an embodiment of a lens system in accordance with one aspect of the invention can be better appreciated.
• a seven element lens system is shown in perspective and ray trace form, although not necessarily shown to scale.
• Figure 6B presents in table form the details of the lens elements, while Figures 7 and 9 illustrate image quality and distortion information of the design as compared to the image quality and distortion information of a conventional rotationally symmetric lens shown in Figures 8 and 10.
• the first lens element, 500 can be seen to be aspheric and fabricated from a plastic such as E48R or equivalent.
• the second lens element, 505 is spherical and can fabricated from Schott SF14.
• the third element, 510 is also spherical but can be made from E48R plastic.
• Element 515 is, in the embodiment shown, aspherical and can be made from OKH4HT plastic.
• Element 520 is aspherical and can be made from E48R plastic, while element 525 is spherical in the embodiment shown and can be made from N-PK51 Schott glass.
• element 530 is double plane symmetrical in shape and can be made from E48R plastic.
• Elements 500-515 comprise the objective portion
• lenses 520-530 comprise the eyepiece portion.
• both portions have positive optical power.
• the resulting lens has a nominal field of view of 17.4 degrees along the X axis, and 13.1 degrees along the Y axis, with a magnification of 4X, a total track of 31 mm, a distance from the last surface to the exit pupil of 3 mm, and an objective and eyepiece f-number of 1.67.
• the lens design of Figure 5 is particularly useful as an afocal
• the lens of Figure 5 is indicated as portion I
• a smart phone camera is indicated as portion II.
• the lens of the smart phone camera is presumed to be an ideal lens.
• the distance D1 the distance from the front surface of element 500 to the entrance to the phone’s camera, can be ⁇ 30 mm, which the distance D2, total track, can be ⁇ 34 mm.
• Figure 7 shows a geometric map of the lens’ modulation transfer function (MTF) at 220 cyc/mm frequency
• Figure 8 which shows the geometric MTF of a rotationally symmetric lens system having the same technical specifications other than features of the present invention.
• the advantages of the present invention can be understood most easily by comparing the edges of the field view.
• green zones depict a higher MTF value, and thus the green zones at the edges of Figure 7, compared to the blue zones at the edges of Figure 8, demonstrates the performance improvement.
• Figures 9 and 10 are grid distortion maps for, respectively, the lens of Figure 5 and a conventional rotationally symmetric lens.
• grid distortion for the lens of Figure 9 is less that 0.63%
• the lens of Figure 10 shows a distortion of less than 0.78%. While both values are acceptable in some instances, the benefits of the present invention offer significant value in more demanding applications.
• a Galileo type afocal telescopic system in accordance with an
• FIGS. 1 1A-14 The lens system of Figure 1 1 , shown in cross-sectional ray path view in Figure 12A, again comprises two parts, both with positive optical power.
• Elements 1 100-1 1 10 comprise the Objective, while elements 1 1 15-1 120 comprise the Eyepiece part, to project an image onto sensor 1 125.
• Element 1 100 is a double plane symmetric lens, while the other four elements are rotationally symmetric lenses.
• the field of view along the X axis is 21 .9 degrees
• the field of view along the Y axis is 16.5 degrees.
• the magnification is 3x, with an f-number of 2.3.
• the total track is 35 mm, with a one mm distance from the last lens surface to the exit pupil.
• these characteristics are exemplary and not limiting, and are provided simply to aid in understanding the benefits of the present invention as well as the ease of implementation.
• FIG. 12A the relationship between the afocal lens of one aspect of the present invention, indicated as portion I, and a camera with an existing lens such as a smart phone camera indicated as portion II, can be better appreciated.
• the table of Figure 12B provides details regarding each element, similar to Figure 6B.
• the distance from the front surface of element 1 to the entrance to camera of portion II is ⁇ 35 mm, with a total track of -39.2 mm.
• Performance information for the lens of Figure 1 1 is shown in Figures 13-14, where Figure 13 illustrates geometric MTF and Figure 14 illustrates grid distortion, similar to Figures 7 and 9.
• FIG. 15 is a cross-sectional ray plot of a wide angle lens system comprising six lens elements, where the sixth element is configured with double plane symmetry.
• the performance of such a lens system again designed as an attachment to an existing camera such as a camera integrated into a smart phone, can be appreciated from the plot of Figure 17, which shows polychromatic diffraction MTF, Figure 18, which illustrates field curvature in both millimeters and percent, and Figure 19 which is a plot of grid distortion.
• FIG 21 illustrates an optical system where the effective focal length changes depending on the location within the field of view on the sensor.
• the relationship defining this change in effective focal length can be linear, a polynomial or an equation that varies only with the distance of the coordinate from the optical center of the image plane.
• the effective focal length changes over a plurality of zones with the distance from the center on a lens having rotational symmetry.
• the image projected on the sensor is more oval than circular and thus the shape is defined by an axis or foci rather than the center of a circle.
• Another way that the effective focal length can change to reduce the perspective aberration using double symmetry freeform lenses is to have the same or different rates of change parallel to the X-axis and Y-axis. In this manner, lines parallel to the X-axis or Y-axis in the object plane remains straight in the image plane when captured by the sensor as show in Figure 23. While the double plane symmetry lens elements described above typically have one or more surfaces described by an X-Y polynomial, free form lenses having one or more surfaces configured according to Zernike or Chebyshev polynomials can also provide significant benefits over rotationally symmetric lens systems, as discussed in greater detail hereinafter.
• Figure 24 illustrates a conventional image circle for a larger than 180deg FOV lens.
• the resultant image does not fully utilize the whole sensor and thus obtain the full pixel count.
• a double symmetry or other shape of freeform lens allows a non-circular image to be projected on the sensor to increase the number of usable pixels.
• embodiments reflecting different aspects of the present invention can achieve ultra-wide, or panoramic, fields of view, or can provide a lens system with high MTF as well as high Strehl while at the same time achieving small track length, or can provide a lens system utilizing a hybrid free form lens and suitable for mobile applications with a very low f-number and short track length configured to be mated to a large sensor, or can provide a lens system suitable for mobile applications with fewer lens elements and utilizing a free form lens with a diffractive surface defined by a Zernike polynomial, or can provide a non-imaging lens system suitable for time-of-flight applications and having a wide field of view with relatively uniform illumination, low stray light and low f-number at a chosen frequency such as the infrared or near-infrared range.
• Figures 25A and 25B an embodiment of an aspect of the invention different from the double plane symmetry of Figures 5-7 can be better appreciated. More specifically, Figures 25A and 25B show, respectively, a lens system offering a panoramic or ultra wide field of view, and a free form lens element having a surface defined by a Zernike polynomial (a“Zernike surface”) for use in the lens system of Figure 25.
• a“Zernike surface” a“Zernike surface”
• the embodiment shown in Figure 25A comprises a six element lens system in which any IR filter and the sensor cover glass have been omitted for clarity and simplicity.
• the front element 2500 can comprise a spherical glass element of D-LAF50, followed by a plastic aspheric element 2505 of F52R, then a third aspheric element 2510 of EP8000 plastic, a fourth, aspheric element 2515 of F52R plastic with an aperture stop 2520 between the third and fourth elements, a fifth spherical element 2525 of EP8000 plastic, and, finally, a sixth, free form element 2530 comprised of, for example, F52R having a rear surface [closest to sensor 2535] defined by a Zernike polynomial.
• An exemplary Zernike surface of the sixth element can be better appreciated from Figure 26.
• the sag Z of the Zernike surface of element 2530 is defined by the polynomial
• Z is the Zernike polynomial and the coefficients as, are the corresponding Zernike coefficients.
• Those skilled in the art will recognize that there are several types of Zernike polynomials in the literature, including Standard Zernike, Fringe Zernike, Extended Fringe Zernike, etc.
• the form of Zernike polynomial used herein is the fringe Zernike polynomial which has a total of 37 terms, the same as the Zernike polynomial implemented in Code V software. These 37 terms are defaulted in the simulation package, OSLO [Optics Software for Layout and Optimization, from Lambda
• the polynomial contains essentially two variables, radial coordinate p and the angle Q
• a panoramic lens system designed to create a camera-quality image will preferably have a high MTF, high Strehl, low stray light and low f- number.
• the MTF and Strehl ratio can be appreciated from Figures 26A-26B.
• Figure 26A illustrates that the lens system of Figure 25A has an on-axis point spread ratio, or Strehl value, that approaches 1.0, close to the diffraction limit.
• Figure 26B shows that the lens system of Figure 25A has a very high MTF value with spatial frequency even at values greater than 360 Ip/mm.
• the Zernike polynomial can be generalized to
• the rotated version can be generalized to f(p) * sin(2 * 0) + g(p) where the additional g(p) term is used to provide correction for distortion, piston, defocus/field curvature, and/or first, second, third, fourth order spherical aberration.
• f(p) sqrt(x 2 +y 2 ).
• the Zernike equations are similar but the (2 * 0) terms will typically be replaced with (3 * 0), (4 * 0), or (n * 0).
• FIG. 27A-27B an embodiment of the invention comprising a four element lens system suitable for mobile applications is shown where the front element, closest to object space, has a free form rear surface, preferably defined by a Zernike polynomial.
• An aperture stop can be implemented in front of the free form element 2700.
• the element 2700 can be cast from APEL plastic.
• a second element 2705 can be an aspheric lens comprised of OKP4 plastic, while third and fourth elements, 2710 and 2715 respectively, can be aspheric elements cast or otherwise fabricated from APEL plastic.
• An IR filter and sensor cover glass, 2720 and 2725 respectively, can be interposed between the rear element 2715 and a sensor 2730.
• the first element 2900 can comprise an aspheric element of APEL plastic.
• An optional aperture stop 2905 can be placed in front of the first element 2900.
• a second element 2910 can be an aspheric element of OKP-1 plastic.
• the third element 2915 is preferably a hybrid element having an aspherical glass base portion 2915A and a UV curable portion 2915B affixed to the back thereof to form a doublet.
• the glass portion can have, in at least some embodiments, a high refractive index, for example, greater than 2.0.
• the portion 2915B can be made, for example, from DELO OM625 or similar, and is configured as a free form surface.
• Fourth and fifth elements, 2920 and 2925 respectively, are both preferably aspherical and comprised of APEL plastic.
• Optional cover glass 2930 and sensor 2935 are shown to the right of the rear element 2925.
• the hybrid lens element 2915 can be better appreciated from Figure 29B.
• the lens system of Figure 29A is particularly well suited to mobile applications involving a large sensor and a low f-number.
• the hybrid element permits reduction of the number of elements and the corresponding reduction in total track length.
• the major characteristics of the lens system of Figure 29A can be appreciated from the table, below.
• a first element 3100 having a front aspheric surface and a rear free form surface 3105 can be comprised of APEL plastic.
• the rear surface 3105 is freeform and defined by a Zernike polynomial, with a micrometer diffractive surface 31 10 over the freeform structure as shown in Figure 31 C.
• the diffractive surface 31 10 comprises a plurality of steps 31 15.
• An optional aperture 3120 may be disposed in front of the first element.
• Second and third elements, 3125 and 3130 respectively, can be aspherical and comprised of APEL plastic. To the right of the element 3130 are shown an IR filter 3135, sensor cover glass 3140, and sensor 3145.
• the first element 3100 can be better appreciated from Figure 31 B, where the aspheric front is shown and the free form Zernike rear surface is also shown. Again, the diffractive surface 31 10 is shown in Figure 31 C.
• the diffractive surface on the free form surface follows a phase
• Figure 33 a still further aspect of the invention can be better appreciated.
• the embodiment of Figure 33 is intended for use in machine vision applications, for example those found in various types of positioning systems.
• One class of such systems is used with autonomous and semi-autonomous vehicles, although other applications include identifying location of moveable equipment, personnel or patients within a hospital, detection by robots of impediments to movement or location of target objects, detection by drones of impediments to flight and proximity to landing zones, and numerous other tasks requiring the determination of the location of an object relative to the surrounding environment.
• the machine vision lens illustrated in Figure 33 can, in one
• a first aspheric meniscus element 3300 followed by an optional aperture 3305, in turn followed by an aspheric double concave element 3310, then an aspheric meniscus lens element 3315, a spherical double convex glass element 3320, a second aspheric meniscus element 3325, and finally a double convex element 3330 having a double plane symmetry rear surface 3335.
• the sensor and cover glass are shown at 3340 and 3345, respectively.
• Each of the elements except 3320 can be comprised of a suitable plastic as discussed for the foregoing embodiments.
• the double plane symmetry surface, for the illustrated embodiment, can be defined by a Zernike or Chebyshev polynomial in the manner shown hereinabove.
• time of flight sensing is a specific type of machine vision. Time of flight can also be considered a non-imaging application even though a sensor is used for detection of the light impinging thereon to make the timing measurement. In some instances, time of flight sensing utilizes the infrared band, such as between 840 and 950 nanometers, where a freeform element is double plane symmetric and is defined by an X-Y polynomial.
• time of flight sensing can use wavelengths from, for example, 350 nm to 2500 nm, with proper selection of the material for the optical elements to ensure appropriate transmittance.
• time of flight (TOF) applications low stray light is very important as well as low f-number.
• FOV wide field of view
• very good releative illumination is also desirable.
• TOF applications have a different objective.
• the objective is obtain spatially correlated data representative of every object in the field of view, or what can be referred to as a depth map.
• TOF systems create synchronized signals over every pixel such that the time difference of light illuminating objects in the field of view and being reflected back to the sensor can be accurately determined, thus yielding the desired spatial information about those objects in the field of view.
• TOF applications typically include a light source.
• a light source that enables good relative illumination across the field of view becomes important. While a lens system for the camera in a mobile phone operates acceptably with relative illumination at the edge of only 20% or 30% of the on-axis illumination, TOF applications require better off axis performance, and relative illumination is preferably at least 50% of axial illumination.
• Stray light is another characteristic where TOF applications impose tighter requirements. While a mobile phone camera operates acceptably with a reduction ratio of 1.0C10 L -6, stray light for machine vision and TOF applications preferably is at least 1C10 L -7. Likewise, while the f-number for a mobile phone camera can be 1.8, or 2.0, 2.2, or even higher, the f- number for TOF applications is generally smaller, in the range of 1.0 to 1.6. The f-number for other types of machine vision applications can vary from the low f-number s desired for TOF applications to the higher f-numbers suitable for phone cameras, or even higher.
• a first element 3400 can be a spherical meniscus lens, followed by a spherical meniscus second element 3405 and a spherical double convex third element 3410.
• An optional aperture 3415 can be interposed between the second and third elements.
• a spherical double convex element 3420 follows the third element, and, as a fifth element 3425, a double plane symmetric meniscus lens element. All but the fifth element can be comprised of glass, while the fifth element is typically comprised of plastic.
• the image is formed on a sensor 3430. It will be appreciated that, depending upon the size of the lenses and the wavelength used, each of the elements can be of a different material, either all glass, all plastic, or some combination as illustrated by the example.
• the various lens designs disclosed herein can be scaled up to match sensor size.
• the sensors in some embodiments are shown as, approximately, one- fourth inch, one-third inch, or one-half inch, the invention can be equally well adapted to smaller or larger sensors, such as one-sixth inch sensors, one inch sensors, full frame sensors, or even larger.
• sensors can range from less than the eight megapixels typical of some cell phone cameras, all the way to fifty-five or more megapixels typical of some high end DSLR cameras.
• the double plane symmetric element has a freeform surface, or Z-sag, defined by an Extended X-Y polynomial, shown below, The Double Plane Symmetry surface is described through an Extended
• z, x, y are cartesian coordinates of the surface
• c is surface curvature
• r is the surface radial coordinate
• k is the conical constant
• A are polynomial coefficients
• ⁇ (x,y) are polynomials.
• Examples of ⁇ (x,y) are: X 2 Y 2 , X 4 Y 6 , X 8 Y 4 , etc.
• Conical constant k in the illustrated embodiment is 0, but can be of any value as long as the term under the square root is greater than or equal to zero.
• the lens system of Figure 35 is designed for use in the visible light waveband although it will be appreciated by those skilled in the art that alternative implementations usable at different wavelengths such as near infrared, mid infrared or far infrared can be readily configured using the teachings herein.
• lens systems for mobile phone cameras typically operate with different constraints than lens systems for time of flight applications. More specifically, key characteristics of such camera lens systems are low distortion, reasonable field of view but not necessarily wide angle, acceptable f-number where lower is desirable but not always critical, and, perhaps most important, total track length. Typically, the total track length must be less than the Z-height of the phone so that the lens module does not stick out above the phone casing. Thus, shown in the Table, below, are key parameters for the lens system illustrated in Figure 35. The lens elements are detailed in Figure 36.
• the lens system can be seen to comprise a first aspheric meniscus element 3500 (starting, as before, from object space), followed by a second, aspheric meniscus element 3505, and then a third aspheric meniscus element 3510.
• a fourth element 3515 in the illustrated embodiment is double convex, while a fifth element 3520 is again aspheric meniscus.
• the sixth element 3525 is meniscus with a double plane symmetry front and rear surfaces 3530A-3530B.
• the double plane symmetry front and rear surfaces 3530A-B of element 3525 are defined by the Extended X-Y polynomial shown hereinabove, where the constants have the same meaning.
• the coefficients A thus characterize the double plane symmetry surfaces 3530A-B of element 3525, and can be appreciated from Figures 37A-37D.
• F-number range is in the range of 1.4 - 2.0 (current value is 1.4); the diagonal FOV typically ranges between 45 - 100 degrees (current value is 75 degrees); optical distortion is preferably low, in the range of 0.5 - 10 % (current value is 2%), but can be allowed to increase as a trade-off against a lower f-number; the ratio of the largest diameter element to optical total track length is in the range of 0.5 - 1 (Current value -0.95); and the ratio of Lens Focal Length to 1 st element focal length is in the range of 0.3 - 2 (Current value -0.78).
• This invention relates generally to lens systems using double plane symmetry freeform lenses, and more particularly relates to lens systems using double plane symmetry lens elements for time of flight and machine vision applications where the surface or Z-sag of the double plane symmetry surface is defined by an X-Y polynomial.
• Rotational symmetry is widely used in conventional lenses, with the field view and the aperture stop both being rotationally symmetric. With only rare exception, this results in the final design comprising rotationally symmetric elements.
• most sensors - the photosensitive structures that record the image - are rectangular in shape.
• the image space created by a rotationally symmetric lens creates a circular field of view, while the sensor that records the image is a rectangle.
• Optics for machine vision applications span a wide range of optical solutions.
• One subset of machine vision is time of flight (TOF).
• TOF applications calls for optics that have low f-number, wide field of view, good rejection of stray light, narrow wavelength band, relative uniformity upon illumination, among other considerations, but can tolerate optical distortion.
• Machine vision applications viewed more broadly, often are best served by lens systems suitable for creating a planar image, such as those found in smartphone cameras.
• the present invention provides designs for optical lens systems using at least one double plane symmetry lens element to overcome the limitations of conventional rotationally symmetric designs while also taking into consideration the particular application and the considerations associated with that application.
• the surface or Z-sag of the double plane symmetry lens elements are defined by X-Y polynomials. More
• embodiments of the present invention provide an improved time of flight [TOF] lens system, and an improved visible light machine vision lens system.
• TOF time of flight
• a freeform optical element as contemplated by the present invention can have one optical surface with double plane symmetry, while the other surface is rotationally symmetrical.
• both surfaces can have double plane symmetry.
• Multiple such freeform optical elements are also possible in the optical system. In the case of multiple elements having double plane symmetry, the orientation of the freeform elements in the assembly can be aligned.
• the image projected onto the sensor is better matched to the field of view of the sensor, resulting in enhanced resolution of the captured imaged and, effectively, higher resolution.
• APPENDIX Figure 1 illustrates an embodiment of the invention suited to infrared time-of-flight systems.
• APPENDIX Figure 2 describes in table form exemplary details of the lens elements shown in Figure 1 .
• APPENDIX Figure 4 illustrates an embodiment of the invention suited for visible light machine vision applications where low f-number is desirable.
• time of flight sensing is a specific type of machine vision.
• the lens system of Figure 1 is designed for use in a Time- Of-Flight camera, that is, a range imaging camera system that resolves distance based on the known speed of light, measuring the time-of-flight of a light signal between the camera and the subject for each point of the image.
• Time of flight can also be considered a non-imaging application even though a sensor is used for detection of the light impinging thereon to make the timing measurement.
• time of flight sensing utilizes the near infrared band, and more specifically between 850 and 950 nanometers, where a freeform element is double plane symmetric and is defined by an X-Y polynomial.
• TOF applications typically include a light source.
• a light source that enables good relative illumination across the field of view becomes important. While a lens system for the camera in a mobile phone operates acceptably with relative illumination at the edge of only 20% or 30% of the on-axis illumination, TOF applications require better off-axis performance, and relative illumination can be at least 50% of axial illumination.
• Stray light is another characteristic where TOF applications impose tighter requirements. While a mobile phone camera operates acceptably with a reduction ratio of 1 0C10 L -6, stray light for machine vision and TOF applications can be at least 1C10 L -7. Likewise, while the f-number for a mobile phone camera can be 1 .8, or 2.0, 2.2, or even higher, the f-number for TOF applications is generally smaller, in the range of 1.0 to 1.6. The f- number for other types of machine vision applications can vary from the low f-number s desired for TOF applications to the higher f-numbers suitable for phone cameras, or even higher. Still further, maintaining good optical performance for off-axis objects (or field points) is desirable for machine vision and TOF applications.
• TOF applications low stray light is very important as well as low f-number.
• a wide FOV can be used in many machine vision and TOF applications.
• very good relative illumination is also desirable.
• TOF applications While“normal” cameras such as those in mobile phones are intended to create a planar image, TOF applications have a different objective. In TOF applications, the objective is to obtain spatially correlated data representative of every object in the field of view, or what can be referred to as a depth map. To do so, TOF systems create synchronized signals over every pixel such that the time difference of light illuminating objects in the field of view and being reflected back to the sensor can be accurately determined, thus yielding the desired spatial information about those objects in the field of view.
• a first element 100 can be a spherical meniscus lens, followed by a spherical meniscus second element 105 and a spherical double convex third element 1 10.
• An optional aperture 1 15 can be interposed between the second and third elements.
• a spherical double convex element 120 follows the third element, and, as a fifth element 125, a double plane symmetric meniscus lens element.
• Cover glass 130 and sensor 135 are at opposite ends of the system. All but the fifth element can be comprised of glass, while the fifth element is typically comprised of plastic. Details of each of the lens elements are shown in Figure 2. Key parameters of the TOF lens are shown in Table 1 , below:
• Double Plane Symmetry surface is described through an
• z, x, y are cartesian coordinates of the surface
• c is surface curvature
• r is the surface radial coordinate
• k is the conical constant
• A are polynomial coefficients
• ⁇ (x,y) are polynomials.
• Examples of ⁇ (x,y) are: X 2 Y 2 , X 4 Y 6 , X 8 Y 4 , etc.
• Conical constant k in the illustrated embodiment is 0, but can be of any value as long as the term under the square root is greater than or equal to zero.
• Values for coefficients A, for other embodiments can vary significantly from design to design.
• the following specifications will permit the design of alternative embodiments to the illustrated lens system, but will still define a similar type of lens suitable for infrared time of flight applications: F-number in the range of 1.0 - 2.0 (current value is 1.3); diagonal FOV in the range of 130 - 180 degrees (current value is 160 degrees); optical distortion is less important in this application, can be corrected generally; ratio of largest diameter element to optical Total Track Length is in the range of 0.25 - 0.8 (Current value -0.58); ratio of Lens Focal Length to third element focal length is in the range of 0.3 - 1 (Current value -0.4).
• second order coefficients (e.g. X2Y0) define paraxial (close to optical axis) properties of the optical lens - focal length and etc., while all the other higher orders are used for different aberration correction.
• freeform coefficients A presented in the table of Figures 3A-3C can take dramatically different values within a range of -1 to 1 , but still define a very similar lens.
• FIG. 4 a still further embodiment of the invention can be better appreciated.
• the embodiment of Figure 4 is designed for use in visible light machine vision applications.
• the machine vision lens illustrated in Figure 4 can, in one embodiment and starting from object space, comprise a first aspheric meniscus element 400, followed by an optional aperture 405, in turn followed by an aspheric double concave element 410, then an aspheric meniscus lens element 415, a spherical double convex glass element 420, a second aspheric meniscus element 425, and finally a double convex element 430 having double plane symmetry front and rear surfaces 435A-B.
• Cover glass 440 and sensor 445 are shown for ease of reference.
• Each of the elements except 420 can be comprised of a suitable plastic as discussed for the foregoing
• symmetry front and rear surfaces 435A-B are defined by the same Extended X-Y Polynomial shown and discussed hereinabove, although with different coefficients as shown in Figure 5.
• exemplary coefficients A are shown in Figure 6A-6D-, where Figures 6A-6B show the front surface coefficients and Figures 6C-6D shown the back surface coefficients.
• other front surface charactistics can be radius of 3.27448025, conic of 0.00000000, and semi- diameter of 2.94296383, while other rear surface characteristics can be radius of -1 1 .84566104, conic of 0.00000000, and semi-diameter of
• f-number range is in the range of 1.5 - 1.9 (current value is 1.8); the diagonal FOV typically ranges between 75 - 120 degrees (current value is 120 degrees); optical distortion is preferably low, in the range of 0.5 - 10 % (Current value is 5%), but can be allowed to increase as a trade-off against a lower f-number; the ratio of the largest diameter element to optical Total Track Length is in the range of 0.5 - 1 (Current value -0.66); and the ratio of Lens Focal Length to 4 th element focal length is in the range of 0.3 - 2 (Current value -0.38).
• Lens systems for use in infrared time of flight applications, and visible light machine vision application each with at least one surface of a lens element having double plane symmetry as defined by an X-Y
• the lens elements of the invention can be implemented using existing manufacturing techniques.

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• 2019
  • 2019-10-22 WO PCT/US2019/057467 patent/WO2020086603A1/en unknown
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