COMPOUND LENS

A compound lens includes four coaxially aligned lenses: (i) first lens and, in order of increasing distance therefrom, and on a same side thereof, (ii) a second lens, an inter-lens substrate, a third lens, and a fourth lens. The first lens and the third lens are negative lenses. The second lens and the fourth lens are positive lenses.

BACKGROUND

Medical endoscopy, machine vision, eye/face tracking, and other applications require a compact camera that is able to capture a quality image with a wide field-of-view, and is manufacturable via a low-cost process compatible with high-volume manufacturing.

SUMMARY OF THE EMBODIMENTS

Embodiments disclosed herein include lenses that enable such a camera. A compound lens includes four coaxially aligned lenses: (i) first lens and, in order of increasing distance therefrom, and on a same side thereof, (ii) a second lens, an inter-lens substrate, a third lens, and a fourth lens. The first lens and the third lens are negative lenses. The second lens and the fourth lens are positive lenses.

DETAILED DESCRIPTION OF THE EMBODIMENTS

FIG.1is a cross-sectional view of an endoscope195inside a ventricle190that includes a lesion192. Lesion192is on a ventricle sidewall191. Ventricle190may be, for example, a portion of an esophagus or an intestine. Endoscope195includes a camera180, which images lesion192. Camera180includes a lens182, which in part determines a field of view188of camera180. Without departing from the scope hereof, camera180may be part of a device other than an endoscope, such as a security camera, mobile device, or other consumer electronics product.

FIG.2is a cross-sectional view of a compound lens200, which is an example of lens182of camera180. Compound lens200includes a lens210and, in order of increasing distance therefrom, and on a same side thereof, a lens220, a substrate260, a lens230, and a lens240. Lens210and lens230are negative lenses. Lens220and lens240are positive lenses. Lenses210-240are coaxial about a common optical axis201. Lenses210-240have respective object-side surfaces211,221,231, and241, and respective image-side surfaces212,222,232, and242. At least one of surfaces212,221,232, and242may be non-planar and aspheric. At optical axis201, at least one of surfaces212and232may be concave, and at least one of surfaces221and242may be convex.

Compound lens200may also include at least one of a substrate250, a substrate270, a spectral filter280, and a cover glass290. Substrates250,260,270have respective object-side surfaces251,261, and271, and respective image-side surfaces252,262, and272. At least one of surfaces211,222,231,241,251,261,262,271, and272may be planar. Spectral filter280and cover glass290have respective object-side surfaces281and291. An aperture stop of lens200may be at either surface231or271.

Compound lens200has an effective focal length feffbetween a principal plane284and an image plane299, and a total track length T between object-side surface251and image plane299. In embodiments, the ratio T/feffsatisfies 3<T/feff<13, which constrains transverse and longitudinal dimensions of compound lens200. In embodiments, T/feffsatisfies the aforementioned lower and upper bounds at wavelengths between 420 nm and 860 nm.

Lenses210,220,230, and240have respective focal lengths f1, f2, f3, and f4. In embodiments, the ratio R1=(f1+f3)feff/(f1f3) is greater than −2.5 and less than −0.3. A benefit of limiting the ratio R1to the aforementioned range is to balance distortion of compound lens200. In embodiments, the ratio R2=(f2+f4)feff/(f2f4) is greater than 0.4 and less than 3. A benefit of limiting the ratio R2to the aforementioned range is to balance aberrations and improve the modulation transfer function of compound lens200. In embodiments, values of ratio R1and ratio R2are within their respective ranges at wavelengths between 420 nm and 860 nm.

Lenses210and240have respective Abbe numbers V210and V240, which are computed at the blue, green, and red Fraunhofer F-, d- and C-spectral lines: λF=486.1 nm, λd=587.6 nm, and λc=656.3 nm, respectively. In embodiments, V210≥37 and V240≥26, which results in reduced chromatic aberrations such as lateral color and axial color.

FIG.3is a cross-sectional view of a compound lens300, which is an embodiment of compound lens200for imaging at visible wavelengths. Compound lens300includes substrate360, lenses310,320,330, and340, and may also include at least one of substrate350, substrate370, an aperture stop365, an IR-cut filter380, and a cover glass390. Lenses310-340are coaxial about an optical axis301. When compound lens300includes substrate370, aperture stop365is at object-side surface371, and may be an opaque coating on surface371.

Herein, an element ofFIG.3or subsequent figures denoted by a reference number with a specific tens-place value and ones-place value is an example of the element ofFIG.2having the same tens-place value and ones-place value. For example, lens310, surface311, and surface312are respective examples of lens210, surface211, and surface212.

FIG.4is a table400of example parameters of surfaces and substrates of compound lens300. Table400includes columns404,406,408,410,412,414and421-427. Column421denotes surfaces of compound lens300, and also aperture stop365. Column423includes thickness values between adjacent surfaces of compound lens300on optical axis301. For example, the axial distance between surfaces311and312is 0.030 millimeters, which is the axial thickness of lens310. Column426indicates the minimum diameter of each surface sufficient for a ray incident on surface311that passes through aperture stop365to also pass through that surface.

Non-planar surfaces of table400are defined by surface sag zsag, shown in Eqn. 1.

In Eqn. 1, zsagis a function of radial coordinate r, where directions z and r are, respectively, parallel to and perpendicular to, optical axis301. Index i is a positive integer and, in the example ofFIG.4, N=7. In Eqn. 1, the parameter R is the surface radius of curvature, listed in column422of table400. Parameter k denotes the conic constant, shown in column427. Columns404,406,408,410,412, and414contain values of aspheric coefficients α4, α6, α8, α10, α12, and α14, respectively. The units of quantities in table400are consistent with zsagin Eqn. 1 being expressed in millimeters.

Columns424and425list values of material refractive index, at free-space wavelength λd=587.6 nm, and Abbe number, respectively. The refractive index and Abbe number corresponding to a surface characterize the material between the surface and the surface in the row beneath. For example, the refractive index and Abbe number associated with surface311are 1.51 and 61.2, which are the refractive index and Abbe number of lens310, respectively.

Compound lens300has an effective focal length f300=0.43 mm (at λ0=570 nm), a field of view of 125 degrees, and an f-number equal to 4. The total track length of compound lens300is T300=2.08 mm between surface311and an image plane399. The ratio of total track length to effective focal length is T300/f300=1.65.

Lenses310-340have respective focal lengths f1, f2, f3, and f4, each of which may be approximated by the lensmaker's equation using values of radii of curvature, axial thickness, and refractive index from Table 4. The computed focal lengths are f1=−0.38 mm, f2=0.69 mm, f3=−1.86 mm, and f4=0.48 mm, such that R1=−1.55 and R2=1.74. Wavelength dependence of refractive indices and effective focal length between λd=587.6 nm and λ0=570 nm are sufficiently small such that the aforementioned focal length values and ratios apply at both λdand λ0.

FIG.5is a cross-sectional view of a compound lens500, which is an embodiment of compound lens200for imaging at near-infrared wavelengths. Compound lens500includes substrate560, lenses510,520,530, and540, and may also include at least one of substrate550, substrate570, an aperture stop565, and a cover glass590. Lenses510-540are coaxial about an optical axis501. Aperture stop565is at image-side surface562, and may be an opaque coating on surface562.

FIG.6is a table600of example parameters of surfaces and substrates of compound lens500. Table600includes columns604,606,608,610,612,614,616, and621-627, which follow the same convention of Table400described above. Column621denotes surfaces of compound lens500, and also aperture stop565. Columns624and625are analogous to columns424and425of Table400, and therefore include values of material refractive index, at free-space wavelength λd=587.6 nm, and Abbe number, respectively.

Compound lens500has an effective focal length f300=0.49 mm (at λ0=850 nm), a field of view of 103 degrees, and an f-number equal to 1.95. The total track length of compound lens500is T500=2.17 mm between surface511and an image plane599. The ratio of total track length to effective focal length is T500/f500=4.43.

Lenses510-540have respective focal lengths f1, f2, f3, and f4, each which may be approximated by the lensmaker's equation using values of radii of curvature, axial thickness, and refractive index from Table 6. The computed focal lengths are f1=−0.58 mm, f2=0.55 mm, f3=−2.20 mm, and f4=0.74 mm, such that R1=−1.06 and R2=1.56. Wavelength dependence of refractive indices and effective focal length between λd=587.6 nm and λ0=850 nm are sufficiently small such that the aforementioned focal length values and ratios apply at both λdand λ0.

FIG.7is a cross-sectional view of a compound lens700, which is an embodiment of compound lens200for imaging at near-infrared wavelengths. Compound lens700includes substrate760, lenses710,720,730, and740, and may also include at least one of substrate750, substrate770, an aperture stop765, and a cover glass790. Lenses710-740are coaxial about an optical axis701. Aperture stop765is at image-side surface762, and may be an opaque coating on surface762.

FIG.8is a table800of example parameters of surfaces and substrates of compound lens700. Table800includes columns804,806,808,810,812,814,816, and821-827, which follow the same convention of Table400described above. Column821denotes surfaces of compound lens700, and also aperture stop765. Columns824and825are analogous to columns424and425of Table400, and therefore include values of material refractive index, at free-space wavelength λd=587.6 nm, and Abbe number, respectively.

Compound lens700has an effective focal length f300=0.27 mm (at λ0=850 nm), a field of view of 103 degrees, and an f-number equal to 1.95. The total track length of compound lens700is T700=2.21 mm between surface711and an image plane799. The ratio of total track length to effective focal length is T700/f700=8.19.

Lenses710-740have respective focal lengths f1, f2, f3, and f4, each which may be approximated by the lensmaker's equation using values of radii of curvature, axial thickness, and refractive index from Table 8. The computed focal lengths are f1=−0.58 mm, f2=0.55 mm, f3=−2.20 mm, and f4=0.74 mm, such that R1=−1.06 and R2=1.56. Wavelength dependence of refractive indices and effective focal length between λd=587.6 nm and λ0=850 nm are sufficiently small such that the aforementioned focal length values and ratios apply at both λdand λ0.

Combinations of Features

Features described above as well as those claimed below may be combined in various ways without departing from the scope hereof. The following enumerated examples illustrate some possible, non-limiting combinations:(A1) A compound lens includes four coaxially aligned lenses: (i) first lens and, in order of increasing distance therefrom, and on a same side thereof, (ii) a second lens, an inter-lens substrate, a third lens, and a fourth lens. The first lens and the third lens are negative lenses. The second lens and the fourth lens are positive lenses.(A2) In embodiments of (A1), the second lens has a planar image-side surface on a planar object-side surface of the inter-lens substrate. The third lens has a planar object-side surface on a planar image-side surface of the inter-lens substrate.(A3) Either of embodiments (A1) or (A2) further includes an image-side substrate; the fourth lens has a planar object-side surface on a planar image-side surface of the image-side substrate.(A4) Any of embodiments (A1)-(A3) further includes an object-side substrate; the first lens has a planar object-side surface on a planar image-side surface of the object-side substrate.(A5) In any of embodiments (A1)-(A4), the first lens, second lens, third lens, and fourth lens collectively have an effective focal length feffsuch that an image is formed at an image plane located a distance T from an object-side surface of the object-side substrate, and the ratio T/feffsatisfying 3<T/feff<13.(A6) In any of embodiments (A1)-(A5), the Abbe number of the first lens is at least 37, and the Abbe number of the fourth lens is at least 26.(A7) In any of embodiments (A1)-(A6), the first lens, second lens, third lens, and fourth lens collectively have an effective focal length feffsuch that an image is formed at an image plane.(A8) In any of embodiments (A1)-(A7), the first lens and the third lens have respective focal lengths f1and f3, and the ratio (f1+f3)feff/(f1f3) is greater than −2.5 and less than −0.3.(A9) In any of embodiments (A1)-(A8), the second lens and the fourth lens have respective focal lengths f2and f4, and the ratio (f2+f4)feff/(f2f4) is greater than 0.4 and less than 3.(A10) In any of embodiments (A1)-(A9), an image-side surface of the first lens is concave at the optical axis of the four coaxially aligned lenses.(A11) In any of embodiments (A1)-(A10), an object-side surface of the second lens and an image-side surface of the third lens are convex and concave, respectively, at the optical axis of the four coaxially aligned lenses.(A12) In any of embodiments (A1)-(A11), an object-side surface of the fourth lens is convex at the optical axis of the four coaxially aligned lenses.

Changes may be made in the above methods and systems without departing from the scope of the present embodiments. It should thus be noted that the matter contained in the above description or shown in the accompanying drawings should be interpreted as illustrative and not in a limiting sense. Herein, and unless otherwise indicated, the phrase “in embodiments” is equivalent to the phrase “in certain embodiments,” and does not refer to all embodiments. The following claims are intended to cover all generic and specific features described herein, as well as all statements of the scope of the present method and system, which, as a matter of language, might be said to fall therebetween.