WO2007008766A1 - Ray correction apparatus and method - Google Patents

Abstract

In a detector system for receiving incoming electromagnetic radiation having a range of chief ray angles (CRAs) that is limited by a stop of the imaging optics, an improvement includes a corrective element that cooperates with imaging optics to ensure that chief rays over the range of CRAs fall within a cone of acceptance angles of the detector. The corrective element may be a tilted lenslet, a diffractive element, a refractive element, a discretized refractive element or a subwavelength structure. A detector system collects a range of chief rays from imaging optics. The system includes an array of detectors, each having a cone of acceptance angles, and a corrective element having one of: an array of lenslets including at least one tilted lenslet; a diffractive element; a refractive element; a discretized refractive element; and subwavelength structures. The corrective element redirects each chief ray to within the cone of acceptance angles.

Description

RAY CORRECTION APPARATUS AND METHOD

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to provisional application serial number 60/697,710, filed July 8, 2005, entitled RAY CORRECTION APPARATUS AND METHOD and provisional application serial number 60/808,698, filed May 26, 2006, entitled OPTICAL SYSTEM WITH A LENSLET CONFIGURATION FOR ACCEPTING LIGHT OVER A RANGE OF INCIDENT ANGLES, both of which applications are incorporated herein by reference.

BACKGROUND

[0002] In detector systems including an array of detectors on a substrate (such as, but not limited to, a silicon wafer or a glass substrate), a lenslet array is often used to aid in the coupling of input electromagnetic radiation to the photodetection regions of the detectors as well as to increase the fill factor of the detector array. However, current state of the art of lenslet arrays may not result in efficient detector systems due to coupling of electromagnetic radiation away from the photodetection regions of the detectors. Namely, currently available lenslet arrays may not efficiently accept electromagnetic radiation of off-normal incidence angles over a wide range of angles of incidence. In the context of the present disclosure, electromagnetic radiation is understood to encompass a range of electromagnetic energy including, but not limited to, ultraviolet, visible and infrared wavelengths.

[0003] Turning now to the figures, wherein like reference numbers are used to refer to like components, FIG. 1 shows a portion 10 forming a portion of a prior art detector array. Portion 10 includes a lenslet 12 optically connected with a detector 14. Incoming light rays 16 (enclosed by a dashed ellipse) are normally incident on lenslet 12 from the left side of FIG. 1. A ray at a center of the bundle of incoming light rays is commonly defined as a chief ray, and its angle with respect to a line that is normal to the detector surface is defined as the chief ray angle ("CRA," e.g., θ_in in Fig. 2). In portion 10, the CRA is zero (i.e., CRA = 0 degrees). Lenslet 12 refracts normally incident light rays 16 such that light rays transmitted through the lenslet are focused near a center of a photodetection region 18 of detector 14. The photodetection region is that region of detector 14 where electromagnetic radiation incident thereon is converted into an electric signal. In the case of a CMOS detector, for example, the photodetection region is equivalent to a photodetection region of a photodetection transistor.

[0004] FIG. 2 shows a cross sectional view of a portion 30 of another prior art detector array system, on which electromagnetic radiation is incident at an angle of incidence away from the detector normal. Portion 30 includes a group of imaging optics 32. Imaging optics 32 may include, for example, lenses 34 and 36 as well as a stop 38. Stop 38 defines an aperture stop for imaging optics 32. Stop 38 includes a center 39, and a ray of electromagnetic radiation passing through center 39 is defined as a chief ray. A plurality of chief rays are present for a given set of imaging optics; for example, a first group of light rays 40A (indicated by a bracket) includes a chief ray 42_A, while a second group of light rays 40_B (also indicated by a bracket) includes a different, chief ray 42β. The angle formed between the chief ray and a normal 44 defined at center 39 of stop 38 is the CRA of that chief ray. In portion 30 as shown in FIG. 2, chief ray 42_A is incident at a CRA of Θ_{CRA A}, while chief ray 42_B is incident at a CRA of Θ_{CRA B} such that a range of CRAs is definable by imaging optics 32.

[0005] Portion 30 also includes a substrate 52 (e.g., a wafer) supporting a detector array 54 thereon (a portion of which is shown in FIG. 2). Detector array 54 includes a plurality of photodetection regions 56 distributed across substrate 52. Portion 30 further includes a lenslet array 58, which includes a plurality of lenslets 12. It is noted that, although each photodetection region 56 is not shown to be physically connected with a corresponding lenslet within lenslet array 58 (i.e., as was the case of portion 10 of FIG. 1), the operating principles of the systems exemplified by portions 10 and 30 are essentially the same. Lenslet array 58 is generally intended, for example, to increase fill factor of detector array 54 by concentrating electromagnetic radiation onto the photodetection regions. Incident electromagnetic radiation 40A, including chief ray 42 _A, is incident on a portion of lenslet array 58 at the CRA indicated as Θ_{CRA A}- While each lenslet 12 in lenslet array 58 may be configured to focus normally incident electromagnetic radiation onto the center of a corresponding photodetection region, without additional modifications lenslet 12 focuses incident electromagnetic radiation away from the center of the corresponding photodetection region (such as exemplified by the focusing of electromagnetic radiation 40A) or, for very large CRAs, at a spot away from photodetection regions 56 (such as exemplified by the propagation of electromagnetic radiation 40_B), such that some of the incident electromagnetic radiation does not fall on a photodetection region and is consequently lost.

[0006] Still referring to FIG. 2, another way to visualize this problem is to compare the range of incoming CRAs to a range of incident angles that is acceptable at each photodetection region. Each photodetection region 56 may be considered to exhibit a cone of acceptance angles 60 over which incident electromagnetic radiation is receivable at that detection region. That is, electromagnetic radiation incident on the photodetection region with an incidence angle within the cone of acceptance angles is detectable at the photodetection region, while electromagnetic radiation with an incidence angle outside of the cone of acceptance angles is lost by, for example, reflection from the photodetection region surface. Considering incident electromagnetic radiation 40_A, chief ray 42_A falls on photodetector 56 at an angle within cone of acceptance angles 60, such that chief ray 42_A is receivable at the photodetection region. In the case of incident electromagnetic radiation 40_B, however, chief ray 42_B does not fall on any of the photodetection regions and is thereby lost.

[0007] Demand for smaller and thinner digital cameras has driven the development of image detector arrays with ever smaller photodetection region pitches, which further exacerbates electromagnetic radiation loss. Moreover, reduction in thickness of digital cameras requires capturing electromagnetic radiation over a large range of CRAs, including electromagnetic radiation incident from highly oblique angles.

[0008] The main types of detectors in these smaller, thinner digital cameras are Charge Coupled Device (CCD) and Complementary Metal Oxide Silicon (CMOS) detectors. While both CCD and CMOS detectors are potentially suitable for use in digital cameras, lower cost and higher flexibility makes CMOS detectors an attractive choice. In particular, since CMOS chip-making processes are well- established and have high-yields, the cost of fabricating a CMOS wafer is approximately one-third the cost of fabricating a CCD wafer. Furthermore, CMOS detectors have other cost advantages; CMOS detectors and associated processing circuitry may be fabricated on the same chip, while CCD fabrication typically does not include processing circuitry on the same chip as the photodetection region. Finally, CMOS detectors can utilize the existing manufacturing infrastructure and circuit libraries available to CMOS chip designers.

[0009] Certain prior art CMOS detectors generated noise and cross-talk, and therefore were mainly used in low-cost cameras. However, recent advances in CMOS technology now provide CMOS detectors capable of image quality comparable to that of CCDs used in high-end digital cameras.

[0010] CCD and CMOS detector arrays are both formed of a plurality of detectors. A principal difference between CCD and CMOS detectors is that, in a CCD, nearly the entire surface area is available for photon-to-electrical signal conversion whereas, in a CMOS detector, a significant portion of detector surface area is occupied by electronic circuitry that does not capture photons. Typical CMOS detectors today have fill factors of approximately 30% (i.e., the photodetection region, where photon-to-electrical signal conversion occurs, takes up approximately 30% of the surface area of each CMOS detector) while CCDs usually have fill factors that are closer to 95%.

[0011] The role of a detector in an imaging system is to collect as much of the electromagnetic radiation that enters the imaging system from a particular direction as possible. Commonly, each detector in a detector array is designed to detect electromagnetic radiation arriving from a different direction such that the pattern of electromagnetic radiation collected at the detector array represents an image of the object from which the electromagnetic radiation emanated. In practice, electromagnetic radiation from a distant source in a given direction relative to the imaging system will be converted by imaging optics into a cone of electromagnetic radiation converging on a given detector, where the angular width of the cone is related to the F/# of the collection imaging optics. In many imaging systems (especially those where the total length of the optics, or optical track, is small), the cone of electromagnetic radiation is tilted away from normal incidence for photodetectioii regions nearer to the edge of the detector array, and is less tilted for photodetection regions closer to the center of the detector array. A ray at the center of each cone of electromagnetic radiation is defined as the chief ray (e.g., chief rays 42A and 42_B in FIG. 2), and its angle with respect to a line that is normal to the aperture stop (e.g., normal 44 in FIG. 2) is defined as the CRA (e.g., ΘCRA _A and Θ_CRA _B, respectively, in FIG. 2).

[0012] Due to their high fill factors, CCD detectors are able to accept cones of electromagnetic radiation over a range of CRAs, as most of the surface of the detector CCD consists of photodetection regions. Increased CRA of incoming electromagnetic radiation at the edge of the detector CCD has little effect on the detector CCD's detection efficiency.

[0013] In CMOS detectors, on the other hand, photodetection regions often form less than one-third of total detector surface area. That is, fill factor of a CMOS detector is significantly smaller than fill factor of a CCD detector. Moreover, the photodetection region usually lies deep beneath metal layers, making it especially difficult to direct the incident electromagnetic radiation toward the photodetection region of the CMOS detector. Therefore, a lenslet array is often used with CMOS detectors in order to concentrate incident electromagnetic radiation hitting each detector onto the photodetection region of the detector. However, the characteristics of the CMOS detector geometry make photodetection especially difficult in the presence of large CRAs, even when lenslet arrays are used.

[0014] A lenslet-detector combination such as that shown in FIG. 1, viewed as a miniature optical system in its own right, has a limited field of view ("FOV"). In other words, the lenslet-detector combination will only accept electromagnetic radiation from a given range of incidence angles. In a well-designed camera, for example, the FOV of the lenslet-detector combination is designed to be at least as large as the cone of electromagnetic radiation directed to that lenslet-detector combination by the collection optics. [0015] When a large CRA is present at the detectors at the edge of the detector array, however, the cone of electromagnetic radiation from the imaging optics may lie partially outside the FOV of the lenslet-detector combination, resulting in light loss and reduced detection efficiency. [0016] While one approach to reducing the size of a digital camera is to use detector arrays with smaller detector sizes, such reduction of detector size leads to a further decrease in the photodetection region area and, consequently, the fill factor of CMOS detectors. A reduced fill factor may correspond to a reduction in the overall photosensitivity of CMOS detectors and reduced sensitivity to electromagnetic radiation incident at oblique angles. Additionally, CMOS photodetection regions are often located beneath one or more layers of metal and sometimes also beneath the aforementioned electronic circuitry, further reducing sensitivity of a CMOS detector to electromagnetic radiation incident from oblique angles. Consequently, photosensitivity of a typical CMOS detector tends to be lower than that of a CCD detector. Furthermore, in some cases, a portion of the photons incident on the CMOS detector hits the electronic circuitry rather than the photodetection region, causing extraneous electrical signals in the circuitry and thereby making CMOS detectors potentially more susceptible to noise and crosstalk than CCDs.

SUMMARY [0017] The present disclosure relates generally to optical elements and, more particularly, to an optical solution for redirecting input electromagnetic radiation to desired locations on a substrate.

[0018] Disclosed herein is an improvement for use with a detector system for receiving incoming electromagnetic radiation imaged by imaging optics onto the detector system. The incoming electromagnetic radiation includes chief rays, each having a chief ray angle (CRA) within a range of CRAs limited by a stop of the imaging optics. The improvement includes a corrective element that cooperating with the imaging optics to ensure that all chief rays over the range of CRAs fall within a cone of acceptance angles of the detector. The corrective element may be a tilted lenslet, a diffractive element, a refractive element, a discretized refractive element or a subwavelength structure.

[0019] In another embodiment, a detector system collects a range of chief rays from imaging optics. The system includes an array of detectors, each of the detectors having a cone of acceptance angles. The system also includes a corrective element having one of: (a) an array of lenslets including at least one tilted lenslet; (b) a diffractive element; (c) a refractive element; (d) a discretized refractive element; and (e) subwavelength structures. The corrective element is configured to redirect each of the chief rays to within the cone of acceptance angles. [0020] In another embodiment, a method redirects chief rays within a range of chief ray angles limited by a stop of an optical imaging system. The method includes configuring a corrective element with at least one tilted lenslet, and positioning a corrective element adjacent to an array of detectors such that the chief rays fall within a cone of acceptance angle for each of the detectors. [0021] In another embodiment, a method redirects chief rays within a range of chief ray angles limited by a stop of an optical imaging system. The method includes configuring a corrective element with one or more of diffractive structure, refractive structure, discretized refractive structure and subwavelength structure. The method also includes positioning a corrective element adjacent to an array of detectors such that the chief rays fall within a cone of acceptance angle for each of the detectors.

[0022] In still another embodiment, an optical system for accepting electromagnetic radiation at a normal incidence angle, and over a range of chief ray angles (CRAs) away from the normal incidence angle, is disclosed. The optical system includes a detector array having a plurality of detectors and a plurality of lenslets. Each one of the plurality of lenslets is configured for directing electromagnetic radiation incident thereon onto a corresponding one of the plurality of detectors. Furthermore, at least some of the lenslets are tilted with respect to the normal incidence angle such that electromagnetic radiation incident at the normal incidence angle, as well as over the range of chief ray angles, is receivable at the detector array. [0023] In yet another embodiment, a method of designing an optical system for accepting electromagnetic radiation at a normal incidence angle, as well as over a range of chief ray angles away from the normal incidence angle, at a detector array including a plurality of detectors is disclosed. The optical system includes a plurality of lenslets. The method includes orienting each one of the plurality of lenslets so as to direct electromagnetic radiation incident thereon onto at least a corresponding one of the plurality of detectors such that electromagnetic radiation incident at the normal incidence angle, as well as over the range of chief ray angles, is receivable at the detector array.

BRIEF DESCRIPTION OF THE DRAWINGS

[0024] The present disclosure may be understood by reference to the following detailed description taken in conjunction with the drawings briefly described below. It is noted that, for purposes of illustrative clarity, certain elements in the drawings may not be drawn to scale. [0025] FIG. 1 shows a portion of a prior art detector array including a prior art lenslet optically connected with a detector.

[0026] FIG. 2 shows a cross sectional view of a portion of another prior art detector array system.

[0027] FIG. 3 shows a graphic plot showing a visual representation of CRA correction performed in accordance with the present disclosure.

[0028] FIG. 4 is a diagrammatic illustration, in cross section, of a ray correction system in accordance with the present disclosure.

[0029] FIG. 5 and FIG. 6 are diagrammatic illustrations, in cross section, of a portion of the ray correction system of FIG. 4. [0030] FIG. 7 is a diagrammatic illustration, in cross section, of a ray correction system of the present disclosure including a plurality of corrective elements in a stack over the lenslet array.

[0031] FIG. 8 is a diagrammatic illustration, in cross sectional view, of another embodiment of a ray correction system of the present disclosure including a plurality of corrective elements as well as a color filter array. [0032] FIGS. 9-11 are diagrammatic illustrations, in cross section, of examples of corrective elements suitable for use as corrective elements in the ray correction system of the present disclosure.

[0033] FIG. 12 is a diagrammatic, top view illustration of a portion of a substrate with an array of corrective elements disposed over an array of detectors (not visible), shown here to illustrate an example of a possible shape of the corrective elements.

[0034] FIG. 13 is a diagrammatic illustration, in cross sectional view, of a light ray traveling through an exemplary corrective element, shown here to illustrate a possible type of ray correction provided by a corrective element in the ray correction system of the present disclosure.

[0035] FIG. 14 is a diagrammatic illustration, in cross section, of a light ray traveling through an enhanced corrective element of the present disclosure, shown here to illustrate some of the possible modifications that may be made to the corrective element itself in order to enhance the ray correction.

[0036] FIG. 15 schematically shows one portion of a detector array where a lenslet is tilted with respect to the detector normal, in accordance with the present disclosure.

[0037] FIG. 16 illustrates a portion of a detector array where a lenslet is tilted and shifted with respect to the detector normal, in accordance with the present disclosure.

[0038] FIG. 17 is a schematic diagram illustrating use of an embedded, tilted lenslet configuration with a detector, in accordance with the present disclosure.

[0039] FIG. 18 is a schematic diagram of a large lenslet configuration optically connected with a detector, in accordance with the present disclosure.

[0040] FIG. 19 shows normally incident rays transmitted through a central portion of the large lenslet configuration of FIG. 18.

[0041] FIG. 20 further details light rays transmitted and focused through the central portion of the lenslet configuration of FIG. 19, in accordance with the present disclosure. [0042] FIG. 21 shows light rays incident upon a lenslet, highlighting refraction of a portion of the light rays that are incident at an angle away from normal incidence, towards a detector.

[0043] FIG. 22 shows the lenslet, the detector, and the portion of the light rays that are incident at an angle away from normal incidence, of FIG. 21.

[0044] FIG. 23 shows a detector and a lenslet combination that is similar to the detector and lenslet combination of FIG. 21, with the detector rotated to a horizontal position.

[0045] FIG. 24 shows a lenslet-detector combination that is equivalent to the detector and lenslet combination of FIG. 23.

[0046] FIG. 25 shows a flow diagram of an exemplary design process for designing a lenslet array in accordance with the present disclosure.

[0047] FIG. 26 shows a diagrammatic representation of chief ray propagation through an interface between air and a higher index material. [0048] FIG. 27 shows a graphical solution to a lenslet tilt calculation.

[0049] FIG. 28 shows a schematic diagram of a chirped diffractive grating used in place of a lenslet array in combination with a detector array, in accordance with the present disclosure.

[0050] FIG. 29 shows a schematic diagram of a wavefront transmitted through a subwavelength diffractive grating.

[0051] FIG. 30 shows a graph illustrating the effective refractive index as a function of distance along the subwavelength diffractive grating.

[0052] FIG. 31 shows an example of a discretized refractive element, which has been designed in accordance with the present disclosure.

DETAILED DESCRIPTION OF THE DRAWINGS

[0053] In order to compensate for limited fill factor, a CMOS detector often employs a lenslet array placed proximate to the CMOS detector's photodetection region. However, the design of thin cameras may benefit from the availability of detectors that are capable of accepting larger CRAs (i.e., electromagnetic radiation incident from oblique angles away from normal incidence) while maintaining high sensitivity. Likewise, designers of imaging systems may benefit from the availability of additional options when provided with the ability to make use of larger chief ray angles in the optimization of their designs using commonly available optical design tools. The ability to accept larger chief ray angles is beneficial to the design and performance of imaging systems in general and even more so to thin imaging systems, since these systems tend to present a large range of chief ray angles.

[0054] Adjusting the CRA of electromagnetic energy (e.g., light) incident on CMOS detectors may boost the detection efficiency of the CMOS detectors. This change in CRA is referred to as chief ray angle correction ("CRA correction"); it may increase a detector's sensitivity and signal-to-noise ratio while reducing crosstalk by, for example, increasing the amount of electromagnetic radiation directly hitting the photodetection regions of the CMOS detector. Thus, a FOV of the lenslet-detector combination may be configured to be large enough to accept most or all of the electromagnetic radiation from the imaging optics of a given F/#. In the context of the present disclosure, a CRA corrector is understood to be an optical element, or a combination of optical elements, which corrects all incoming CRA over a given range of CRAs to be within the cone of acceptance angles of the photodetection regions of the detector array. Even in cases where the range of CRAs of the incident electromagnetic radiation is greater than the cone of acceptance angles, the CRA corrector corrects the incident CRA to fall within the cone of acceptance angles.

[0055] A graphic representation of CRA correction as performed by a CRA corrector of the present disclosure is for example shown in FIG. 3. FIG. 3 includes a plot 70 of angle as a function of field position for a detector array system. An angle value of zero corresponds to a normal angle with respect to the aperture stop of the imaging optics. Field position is zero at the center of the substrate on which the detector array is supported, and increases toward the edge of the substrate. A line 72 represents incoming CRAs as a function of field position for a given set of imaging optics. A line 74 represents corrected CRAs as a function of field position for a given set of imaging optics. A line 75 represents the maximum acceptance angle of the photodetection regions of the detector array. It may be seen in plot 70 that incoming CRAs increase as a function of field position; that is, CRAs toward edges of the detector array is larger than CRAs near the center of the detector array. Similarly, the corrected CRAs may also increase as a function of field position, but this increase is not at the same rate as the CRA of the incoming electromagnetic radiation. Furthermore, the corrected CRAs are all less than the maximum acceptance angle of the photodetection regions, while some of the incoming CRAs are larger than this angle. A CRA corrector therefore serves, in this example, to reduce the CRA of the incoming electromagnetic radiation (as indicated by a series of downward arrows 76) for all chief rays within a particular range of CRA. Details of the CRA corrector are further discussed immediately hereinafter.

[0056] FIG. 4 illustrates a portion of a detector array system 100, in a cross sectional view, in accordance with the present disclosure. System 100 has a number of components in common with portion 30 shown in FIG. 2; in particular, system 100 includes substrate 52 supporting detector array 54, including a plurality of photodetection regions 56, and lenslet array 58 including a plurality of lenslets 12. Additionally, system 100 includes a ray correction apparatus, generally indicated by a reference numeral 102, in accordance with the present disclosure. In the embodiment shown in FIG. 4, ray correction apparatus 102 includes a substrate 104 with a corrective element 106 attached thereto. Substrate 104 maybe, for example, transparent to wavelengths to be received at photodetection regions 56. It should be noted that corrective element 106 may be on the top or bottom, or both, of substrate 104. Corrective element 106 may include one or more optical elements, or a combination thereof, including but not limited to refractive elements and diffractive elements, such as diffraction gratings and discretized elements, as will be discussed below. Ray correction apparatus 102 is configured such that incident electromagnetic radiation 40 (see FIG. 2) may be received over a range of CRAs (one such CRA is indicated as Θ_CRA) and still reach one of the plurality of photodetection regions 56. That is, more of incident electromagnetic radiation 40 may reach detector array 54 regardless of Θ_CRA with the presence of ray correction apparatus 102 than without the apparatus. In essence, ray correction apparatus 102 aids in correcting for non-ideal (i.e., away from the substrate normal) angles of incidence of the chief ray so that the incident electromagnetic radiation reaches one of the plurality of photodetection regions 56, even when the incidence angle is far from normal, hi this way, detector array system 100 may accept input electromagnetic radiation over a large cone of incidence angles and still function effectively. In the embodiment shown in FIG. 4, ray correction apparatus 102 may be positioned near lenslet array 58 such that chromatic dispersion and cross-talk may be minimized.

[0057] Turning now to FIGS. 5 and 6, details of the effect of the presence of a corrective element in the detector array system are illustrated. In FIG. 5, a system 130 includes a corrective element 132 added to the system of FIG. 2, such that incident electromagnetic radiation 40 passes through corrective element 132 before it reaches lenslet array 58. Corrective element 132 receives incident electromagnetic radiation 40 at a CRA (indicated as Θ_CRA) from normal 44. Corrective element 132 is configured to compensate for off-normal incidence such that incident electromagnetic radiation 40 passes through corrective element 132 and is directed toward lenslet array 58 at a near-normal angle such that the electromagnetic radiation is focused onto one of photodetection regions 56.

[0058] FIG. 6 shows a system 150 including a corrective element 152 that is placed in the path of the incident electromagnetic radiation propagation between lenslet array 58 and photodetection regions 56. As was shown in FIG. 2, without corrective element 152, lenslet array 58 would focus incident electromagnetic radiation 40 between photodetection regions 56. However, corrective element 152 serves to correct the direction of propagation of the resulting electromagnetic radiation such that the electromagnetic radiation then falls on one of photodetection region 56.

[0059] FIGS. 7 and 8 show other embodiments of the ray correction apparatus of the present disclosure. FIG. 7 shows a portion 200 of a detector system that has a ray correction apparatus 202 including a plurality of corrective elements 106, 204, 206, 208, 210 and 212. These corrective elements maybe supported by a plurality of substrates, such as substrate 104 supporting corrective elements 106 and 204, and a substrate 214 supporting corrective elements 210 and 212. Alternatively, corrective elements may be independently stacked (e.g., as shown for corrective elements 206 and 208). Stacking a plurality of corrective elements may yield greater ray corrective effects than would be possible with a single corrective element, such that more compensation may be effected. For instance, a plurality of corrective elements may enable utilization of a large range of chief ray angles, a wider range of wavelengths or a higher diffraction efficiency. Ray correction apparatus 202 may also fabricated as a stack of layers, for example covering an entire wafer on which the plurality of photodetection regions is fabricated, thus potentially reducing fabrication cost. [0060] FIG. 8 shows a portion 250 of a detector system that is similar to portion 200 of FIG. 7, but also includes a color filter array 260 for color separation. Portion 250 includes detector array 54, lenslet array 58, ray correction apparatus 252 (including a stacked configuration of corrective elements 106, 204, 208, 210 and 212 and transparent substrates 104, 214) and color filter array 260. Corrective elements 106, 204, 208, 210 and 212 may be configured such that ray correction effected by ray correction apparatus 252 is tailored for a variety of wavelengths corresponding to the colors in the color filter. For example, ray correction apparatus 252 may be configured such that a green component of the incident electromagnetic radiation is directed specifically through the detector/color filter combination configured to detect green light, thus performing color separation in addition to CRA correction.

Optionally, color filter array 260 may be removed if the color separation performed by ray correction apparatus 252 is sufficiently effective, thereby potentially resulting in increased detector sensitivity.

[0061] FIGS. 9-11 illustrate three examples of possible elements that are suitable for use as corrective elements in the ray correction apparatus in accordance with the present disclosure. FIG. 9 shows a CRA corrector element implemented as a smooth, refractive element 302 that corrects for varying CRA as a function of radial position (e.g., position of a given photodetection region 56 with respect to a center of substrate 52, FIG. 4). That is, refractive element 302 may be placed in close proximity of a detector array and provide different degrees of CRA correction according to the position of a given detector within the detector array. The localized slope of a top surface 303 of refractive element 302 maybe expressed by Snell's Law. Refractive element 302 may or may not exhibit optical power. In either case, refractive element 302 may be disposed in close proximity to a detector array such that its optical power (or lack thereof) has little effect on the position at which incident light may be brought to a focus by separate, imaging optics in the combined imaging system. [0062] FIG. 10 shows a discretized element 304, which may also serve as a CRA corrector element in accordance with the present disclosure. Discretized element 304 is formed, for example, by creating discontinuities in the top surface of a smooth, refractive element, such as refractive element 302 of FIG. 9. Such discontinuities may be created, for instance, at regular intervals such as, but not limited to, every 20 μm of sag. Discretized element 304, with or without power, provides an effect similar to that of refractive element 302 of FIG. 9 but may be thinner than refractive element 302 along an optical axis. Discretized element 304 includes a ridged surface 306 that provides the chief ray corrective effect. That is, discretized element 304 may be considered, for instance, as a collection of small prisms, each prism being designed to direct light incident thereon toward a particular detector within a detector array. The surface angle orientation of the small prisms is more acute near the edges of discretized element 304 because more CRA correction is needed at these edges. In the center, where not as much CRA correction may be required, the prism surface angle may be shallower. Taking this analogy further, the effect provided by these small prisms may be approximated by a smooth surface, such as that provided in refractive element 302 of FIG. 9. Refractive element 302 has an advantage that smooth surface 303 provides continuously varying CRA correction across a detector array, while discretized element 304 may be advantageous in that the same amount of CRA correction as refractive element 302 may be provided by a thinner optical element, thereby allowing discretized element 304 to be placed closer to the detector array. Also, discretized element 304 may be readily reproducible by techniques such as, for example, stamping.

[0063] FIG. 11 shows a diffractive element 310 including a surface 312 with a spatially varying grating period for altering the local CRA of incident electromagnetic radiation. Diffractive element 310 may be configured, for example, to correct for arbitrary variations of the chief ray angle. In one embodiment, surface 312 may include features that are smaller than the wavelength of the electromagnetic radiation incident thereon. Such sub-wavelength features aid in the performance of CRA correction in the presence of photodetection regions with very small pitches (e.g., on the order of the wavelength of electromagnetic radiation) without "shadowing" portions of the incident electromagnetic radiation. Also, CRA correction effected by diffractive element 310 may be made to be wavelength dependent by selection of feature size - that is, by selecting features that are smaller than a certain range of electromagnetic radiation of interest, diffractive element 310 provides CRA correction for that certain range of electromagnetic radiation, while allowing electromagnetic radiation of other wavelengths to pass through unaffected. Diffractive element 310 maybe made even thinner than discretized element 304 while providing an equivalent CRA corrective effect. As shown in FIGS. 7 and 8, a variety of corrective elements (e.g., those shown in FIGS. 9-11) maybe combined or cascaded for greater design flexibility. [0064] FIG. 12 shows a top view of a detector system 400 including an array of corrective elements 420 positioned over substrate 52. As shown, for example, in FIG. 4, substrate 52 includes a plurality of photodetection regions 56 (not visible in FIG. 12). The array of corrective elements 420 is placed over the plurality of photodetection regions so as to provide ray correction for electromagnetic radiation incident thereon. The shape of each of corrective elements 420 may be tailored for the size and shape of the incident electromagnetic radiation. Therefore, the elongated octagonal shape of corrective elements 420 as shown in FIG. 12 is to be regarded as exemplary and not limiting.

[0065] FIGS. 13 and 14 illustrate ray correction by exemplary corrective elements. In FIG. 13, a corrective element 502 is a refractive element for receiving electromagnetic radiation 504 that impinges on a top surface 506 of corrective element 502 at an incidence angle O₁ (measured with respect to a normal angle of an underlying substrate, not shown in this view). When exiting from a ridged, bottom surface 508 of corrective element 502, electromagnetic radiation 504 emerges at an output angle O₂, which is less than the incidence angle G₁. Corrective element 502 would be suitable for use as a ray correction apparatus of the present disclosure.

[0066] FIG. 14 shows a corrective element 512 of includes a top surface 514 with a reflection suppression coating 516 formed thereon. Reflection suppression coating 516 allows coupling of electromagnetic radiation from a large cone of angles away from the normal such that a CRA (Θ_CRA) may be any angle less than 90-degrees, depending on the specific coating design. That is, reflection suppression coating 516 provides an advantage that reflection of incident electromagnetic radiation with large CRA from top surface 514 may be suppressed such that incident electromagnetic radiation, even with large CRA, would be directed into and through corrective element 512 for CRA correction. Corrective element 512 further includes a bottom surface 518, which in turn includes a plurality of alternating refractive surfaces 520 and transitional surfaces 522. The refractive surfaces are designed to yield a ray correction that directs electromagnetic radiation 504 at an output angle θ_out that is less than Gj_n. The transitional surfaces are sloped such that minimum electromagnetic radiation is scattered by the transitional surfaces; for example, at a particular spot on the corrective element, transitional surfaces 522 may be disposed at approximately θ_out, the chief ray output angle at that spot. The orientation of the refractive and transitional surfaces may be tailored for a given type of electromagnetic radiation source, such as one including input optics that provide an incident cone of electromagnetic radiation rather than a collimated beam. Corrective element 512 would be suitable for use as a ray correction apparatus of the present disclosure. [0067] Looking more specifically at individual lenslet-detector combinations, a lenslet paired with each photodetection region may additionally be tilted or shifted with respect to the detector normal to accommodate a desired range of CRAs. By tilting and/or shifting the lenslet, the FOV of the lenslet-detector combination is matched to the incoming CRA, so that a photodetection region of the detector accepts all of the incident light, reducing light loss. Furthermore, since the CRA is typically different for each detector within an imaging system, each lenslet- detector combination may be designed to have a tilt and/or shift that compensates for the CRA tilt at the detector.

[0068] It should be noted that, while the present disclosure concentrates on an example of CRA correction in an embodiment including a CMOS detector, this CRA correction is applicable in other applications requiring adjustment of the chief ray angle of electromagnetic radiation incident upon a device. Therefore, the embodiments including a CMOS detector, as described hereinafter, should be considered exemplary and not limiting. [0069] Without CRA correction, as CRA increases, electromagnetic radiation is increasingly intercepted and blocked by the underlying detector structure, so that less electromagnetic radiation reaches the CMOS photodetection region, where photons are converted into electronic signals. CRA correction may increase the largest CRA accepted by a CMOS detector array given a minimum accepted detector efficiency. CRA correction thus converts electromagnetic radiation rays with a large CRA into rays with a smaller CRA, allowing the detector to be utilized with optical modules that benefit from being compatible with a larger maximum CRA. The larger CRA may then be used to design optical modules with reduced total track, thereby addressing consumer applications that require thinner optical modules (e.g., digital still cameras, cell phone cameras and portable still and video cameras), or to reduce aberrations and improve performance of imaging systems, when reduced total track is not a primary goal, or a combination of both effects (e.g., somewhat reduced total track with reduced aberrations).

[0070] CRA correction may include, for instance, tilting (with respect to the detector normal) and/or shifting one or more lenslets within a lenslet array that is used with a detector array. Shifting of the lenslets with respect to incident electromagnetic radiation may compensate for some range of incident electromagnetic radiation with varying incident chief ray angle. The current disclosure provides for a combination of tilts and shifts of lenslets to tilt the electromagnetic radiation acceptance cone angle of a lenslet-detector combination to an angle that matches the incoming cone angle, thereby preventing light loss. Since, in a given optical system, the CRA is typically different for each detector, each detector within the detector array may require a unique amount of lenslet tilt/shift in order to compensate for the particular CRA at that detector.

[0071] Field-dependent asymmetric (i.e., tilted and/or shifted) lenslets may facilitate integration of optical elements into a lenslet array. In particular, such tilted lenslets may be fabricated at low cost and/or provide high reliability image capturing devices since few components (e.g., additional optical elements) or assembly steps may be required. The tilt of lenslets in such an array may, for example, vary from the center of the array (zero tilt) to greater and greater tilts at outer edges of the array. CRA correction for a single lenslet-detector combination within a detector array system is examined more closely in the following figures.

[0072] FIG. 15 schematically shows one portion 600 (generally indicated by an arrow) of a detector array system for detecting electromagnetic radiation over a large range of chief ray angles, in accordance with the present disclosure. As shown in FIG. 15, portion 600 includes a tilted lenslet 602 that is optically connected with a detector 604. Incoming light rays 606 (encircled by a dashed ellipse) in FIG. 15 are incident on portion 600 of the detector array system at a large CRA. [0073] Continuing to refer to FIG. 15, lenslet 602 is tilted with respect to normal incidence - as compared to (non-tilted) lenslet 12 shown in FIG. 1 - such that a larger percentage of incident light rays 606 focus to a point near a photodetection region 608 of detector 604. The result is higher detector sensitivity, higher efficiency, higher detector signal-to-noise ratio and lower crosstalk, as compared to lenslet 12 of FIG. I₅ since less of the incident electromagnetic radiation travels toward neighboring detectors.

[0074] Still referring to FIG. 15, lenslet 602 is tilted with respect to normal incidence in order to accommodate incident electromagnetic radiation with large CRA. The amount of tilt of lenslet 602 may be calculated by Snell's law as a function of the CRA and the index of refraction of the material forming lenslet 602. For example, light rays 606 with a large CRA are incident at an oblique angle with respect to the surface of the lenslet array. As known to those skilled in the art, light rays incident on an optical surface incur reflection losses that increase as a function of CRA. To minimize such losses, a front surface 602A of lenslet 602 encountered by light rays 606 may be coated with an anti-reflection coating (not shown). Further, the shape of lenslet 602 may be customized to account for the particular shape and placement of structures (e.g., photodetection region 608) in the actual detector design. The shape may be further customized depending on location of a particular detector in the detector array. For example, less CRA correction (e.g., less lenslet tilt) may be required for detectors near the center of the detector array system, while more CRA correction (e.g., more lenslet tilt) may be required for detectors at the edges of the substrate.

[0075] As discussed above, tilting of the lenslet may be combined with shifting the lenslet with respect to a photodetection region of its corresponding detector so that the photodetection region captures more or all of the refracted rays. Again, since CRA may vary from detector to detector within an array, an amount of shift required may also be location dependent, usually being minimum (e.g., zero) at a center detector of the array, and maximum at edge detectors.

[0076] Accordingly, FIG. 16 illustrates a portion 620 (generally indicated by an arrow) of a detector array system where a lenslet 622 is tilted and also shifted (by a distance indicated by double-headed arrows 625) with respect to the detector normal in order to accommodate incoming light rays 626 (encircled by a dashed ellipse) with even larger CRA. Lenslet tilt (with or without shift) may be combined with other CRA correction methods - such as the earlier discussed CRA correction apparatus - for even larger CRA correction and/or for other advantages (e.g., higher sensitivity). In this way, incoming light rays 626 are directed to a photodetection region 628 of detector 624.

[0077] FIG. 17 is a schematic diagram illustrating the use of an embedded, tilted lenslet with a detector, in accordance with the present disclosure. A portion 650 of a detector array system includes a lenslet 652 optically connected with a detector 654. Incoming light rays 656 (enclosed by a dashed ellipse) are incident on lenslet 652 with a large CRA. In order for most of the light rays to be focused on a photodetection region 658 of detector 654, lenslet 652 is formed from a combination of a first optical material 659 and a second optical material 661. That is, a refractive surface of the tilted lenslet is formed from an interface 663 defined between materials 659 and 661 and, therefore, is "embedded" within lenslet 652. In one embodiment, as shown in FIG. 17, first material 659 has a higher index of refraction (e.g., n = 1.9) than second material 661 (e.g., n = 1.44) such that lenslet 652 behaves as a positive lens. Consequently, lenslet 652 directs light rays 656 towards photodetection region 658 of detector 654. [0078] Still referring to FIG. 17, the use of lenslet 652 may additionally increase detector efficiency since a larger portion of electromagnetic radiation is directed to photodetection region 658, as is notable by comparing FIG. 17 with FIG. 15. In the embodiment shown in FIG. 15, while the tilt of the lenslet allows insertion of light rays with larger CRA than the prior art, a portion of the incident electromagnetic radiation may be blocked by a back surface 602B of tilted lenslet 602. That is, electromagnetic radiation incident on back surface 602B in FIG. 15 would not be subject to the same CRA correction effects as electromagnetic radiation entering tilted lenslet 602 through front surface 602A. In the embodiment shown in FIG. 17, a back surface 652B of lenslet 652 is exposed to light rays 656 such that incoming light rays may enter lenslet 652 through back surface 652B as well and still be subject to CRA correction. [0079] Continuing to refer to FIG. 17 in conjunction with FIG. 15, losses due to reflections may be reduced and detector efficiency may be increased by utilizing lenslet 652 because light rays 656 are incident at angles that are less oblique with respect to a front surface 652 A of lenslet 652, as compared to incoming ray angles at front surface 602 A of lenslet 602. In addition, front surface 652 A may be anti-reflection coated to reduce reflection losses. Such anti-reflection coating may be simpler to design and have higher performance and/or lower cost than an anti- reflection coating for the front surface of tilted lenslet 602 of FIG. 15, because front surface 652 A is a flat surface while front surface 602 A of lenslet 602 is curved. Moreover, front surface 652A may be tilted towards the incident CRA, thereby further reducing reflection losses.

[0080] FIGS. 18-24 illustrate a procedure for designing tilted and/or shifted lenslets for CRA correction. The procedure involves first designing a large CRA corrector capable of focusing incident electromagnetic radiation, which is incident on the large CRA corrector over an aperture that is larger than a photodetection region that within a detector. Then, portions of the large CRA corrector configuration are extracted to form lenslet-detector combinations for receiving incident electromagnetic radiation at large CRAs.

[0081] First referring to FIG. 18, a configuration 700 includes a large CRA corrector 702 optically connected with a detector 704. Incoming light rays 706 (enclosed by a dashed ellipse) are focused by CRA corrector 702 at, for example, a photodetection region 708 at the back of detector 704. CRA corrector 702 includes a front surface 702 A, the shape of which is optimized using software design tools known in the art. In configuration 700, front surface 702A has been optimized so that CRA corrector 702 is capable of focusing light rays 706 that are incident over a CRA corrector diameter d that is larger than photodetection region 708. CRA corrector diameter d is selected according to the largest CRA to be accommodated by any CRA corrector 702, that is, light rays with the largest CRA incident on any lenslet of a lenslet-detector array of a system will be required to be directed to the photodetection region of a corresponding detector. The assumption of a large, single CRA corrector simplifies the optimization process and enables existing optics optimization software to find better solutions in comparison to optimization procedures using smaller lenslets.

[0082] FIG. 19 illustrates normally incident light rays transmitted through a central portion 720 of configuration 700 of FIG. 18. As discussed earlier, the shape of CRA corrector 702 is optimized such that normally incident electromagnetic radiation transmitted therethrough is brought to a focus at photodetection region 708. Therefore, examining only the central portion of CRA corrector 702, an equivalent small lenslet having the same surface shape as central portion 720 would also focus normally incident electromagnetic radiation at photodetection region 708 (located at a distance z' from central portion 720) of detector 704.

[0083] FIG. 20 shows an equivalent lenslet-detector combination 754 including a lenslet surface 756 that has the same shape as central portion 720 of CRA corrector 702. Lenslet surface 756 is also located at a distance z' away from a photodetection region 758 of lenslet-detector combination 754. Consequently, normally incident light rays transmitted through lenslet surface 756 focus at photodetection region 758. Lenslet-detector combination 754 is suitable for use in a portion of an array of detectors where much of the incident electromagnetic radiation is incident normally thereon, such as near the center of the detector array.

[0084] FIGS. 21-24 illustrate a similar design process for configuring a lenslet surface tilt for off-normal electromagnetic radiation incidence. FIG. 21 shows a lenslet-detector system 800 with light rays 706 incident on a CRA corrector 802 with a front surface 802A, which has the same shape as front surface 702A of CRA corrector 702 described earlier. Attention is directed, this time, to a portion of light rays 706 hitting CRA corrector 802 near a top edge of front surface 802A at an edge portion 820, as indicated by a dashed box. Light rays 706 focus at a point 805 located a distance z' away from front surface 802A. A rotated detector 804 is coupled with CRA corrector 802 at edge portion 820 such that focus point 805 is near the center of a photodetection region 808 of detector 804. Photodetection region 808 is located at a distance z" away from edge portion 820. FIG. 22 shows the same combination of the CRA corrector and the rotated detector as shown in FIG. 21, but only light rays transmitted through edge portion 820 are shown. In examining the angle at which light rays 706, which are normally incident on the center of front surface 802 A of CRA corrector 802, are incident on edge portion 820, it may be seen that light rays 706 hit edge portion 820 at a CRA Θ_CRA away from a local surface normal 822 (indicated by a dashed line). Electromagnetic radiation incident at Θ_CRA on a CRA corrector having a front surface shaped as edge portion 820 focuses at a distance z" away from the front surface of that lenslet.

[0085] FIG. 23 shows a system 800' that is the same as system 800, but rotated by angle θ;_n, so that photodetection region 804 is aligned with an edge of the paper. The rotation is also indicated by a rotation of the y-z axes shown in both FIGS. 22 and 23. FIG. 24 shows an equivalent lenslet-detector combination 850, which includes a lenslet surface 856 having the same shape as edge portion 820 of front surface 802A of CRA corrector 802. As shown in the above analysis of FIG. 22, light rays incident on lenslet surface 856 will focus at a photodetection region 858 located a distance ∑" away from lenslet surface 856. In other words, the design procedure illustrated in FIGS. 18-24 results in a suitable solution for lenslet shapes capable of accommodating incident light rays over a range of CRAs by selecting and rotating portions of a large CRA corrector 702 through respective angles Oj_n up to and including a largest CRA that occurs in a given embodiment.

[0086] The design procedure illustrated in FIGS. 18-24 is outlined in a process 870 shown in FIG. 25. Process 870 begins with a step 872 that identifies a desired detector array geometry and a maximum CRA to be accommodated by the design. Step 874 optimizes design of a large CRA corrector plus detector combination to accommodate the maximum CRA for the given geometry (such as shown in FIG. 18). Then, for each lenslet in the proposed detector array, a corresponding portion of the large CRA corrector with the desired CRA is isolated (e.g., normal incidence, as shown in FIG. 19, or off-normal incidence, as shown in FIG. 21). If necessary, the isolated portion of the large CRA corrector is rotated in a step 878 in order to match the location of a particular detector within the detector array and the corresponding, desired CRA. In other words, the shape of that portion of the large CRA corrector so isolated is the appropriate design for a tilted lenslet at a selected detector location within the detector array. A step 890 determines whether more detector locations need to be analyzed: if the answer is "YES," more detector locations need to be analyzed and the appropriate portion of the large CRA corrector must be identified, so steps 876 and 878 are repeated; and if the answer in step 890 is "NO," then the results of the earlier steps may be combined to yield a design for a detector array with a customized lenslet array for accommodating the desired range of CRA.

[0087] An example of a calculation method for determining the lenslet tilt for a given angle of incidence ("AOI") is described in detail immediately hereinafter. FIG. 26 shows a diagrammatic representation of chief ray propagation through an interface between two media separated by a tilted plane (for example, air, with refractive index n_aι_r = 1.0, and a lenslet, with index of refraction nι_ensι_et = 1.51). Various angles used in the calculation method are also shown in FIG. 26. A schematic 900 illustrates propagation of a chief ray 902. An optical axis 904 is defined as a surface normal with respect to a detector plane 906 (that is, plane 906 is parallel to a plane of a detector, but is not the location of the detector). Chief ray 902 is incident on a lenslet tilt plane 910, which in turn is a demarcation line of an interface between air 912 and a lenslet 914. Chief ray 902 encounters lenslet tilt plane 910 and is consequently refracted as a refracted chief ray 902'. A lenslet normal 916 is defined with respect to lenslet tilt plane 910.

[0088] Continuing to refer to FIG. 26, the angles used in the lenslet tilt calculation are defined in schematic 900. An angle made by chief ray 902 with optical axis 904 is defined as the CRA. An angle made by chief ray 902 with lenslet normal 916 is an AOI of the chief ray. An angle between optical axis 904 and lenslet normal 916 is defined as θ_t. The angle between refracted chief ray 902' and optical axis 916 is defined as θ_p.

[0089] In calculating lenslet tilt θ_t, certain limits may be set on the AOI and θ_p. For example, in the following exemplary calculation, the absolute value of θ_p is set to be less than or equal to 16.4° (i.e., |θ_p| < 16.4°) because this angle falls within the cone of electromagnetic radiation acceptance for most detectors. Also, the angle of incidence is assumed to be less than or equal to 60° (i.e., AOI < 60.0°) because, for larger values of AOI, reflection of the chief ray at the air/lenslet interface becomes significant.

[0090] As shown in FIG. 26, AOI may be defined in terms of CRA and θ_t as: AOI = CRA ₊ O_{1 Eq (1)}

Also, by Snell's law, the relationship between the indices of refraction, AOI, θ_t and θ_p may be expressed as:

»/«,/* ^sin(^ ^{+ θ}, ) = ⁿair MAOI) _{Eq (2)}

By simple manipulation of Eq. (2) and noting that n_a;_r = 1.0, it is readily shown that the angle between refracted chief ray 902' and optical axis 804 may be expressed as:

Given the empirical limits of θ_p < 16.4° and AOI < 60.0°, it is readily calculable from Eq. (3) that the maximum CRA is CRA_maχ = 41.4° and θ_t < 18.6°.

[0091] The above calculation may also be demonstrated graphically. FIG. 27 shows a graphical solution to a lenslet tilt calculation. A plot 950 includes a mesh 952, which represents a range of valid solutions for the appropriate lenslet tilt with empirical limits of θ_p < 16.4° and AOI < 60.0°. A line 954 graphically indicates a demarcation on plot 950 below which AOI is less than 60.0° (as indicated by an arrow 956). Mesh 952 represents solutions of Eq. (3) for CRA for various values of θ_t with AOI < 60.0° for the case of a chief ray incident from air on a lenslet formed with a material having a refractive index of 1.51.

[0092] Mesh 952 may be drawn using commercial software for providing graphic solutions to numerical problems. For example, mesh 952, as shown in FIG. 27, may be drawn using MATLAB® using the following m-files: [m-file FindLenslet.m]

%FILE: FindLensletm

%Does search thru CRA and Lenslet tilt space for valid solutions %

N = 1.51; N = IOO; M = 50;

CRA = linspace(0,80,N);

Tilt = linspace(0,50,M);

% Tp = zeros (N,M);

AOI = zeros(N,M);

For ϋ = l:N

[tp,aoi] = Lenslet(CRA(ii),Tilt,n); tp(ϋ,:) = tp; AOI(ii,:) = aoi; end

%

%Enforce Limits: ai = abs(AOI)>60; ti = abs(Tρ)>16.4;

%

Tp(ti) = NaN;

Tp(ai) = NaN;

AOI(ti) = NaN; AOI(ai) = NaN;

% figure(l) mesh(Tilt,CRA,Tp) xlabel('Lenslet Tilt') ylabel('CRA Outside Detector')

% [m-file Lenslet.m, as called by FindLenslet.m] function [Tρ,AOI] = Lenslet(CRA,Tilt,n)

%USAGE: [Tp₅AOI] = Lenslet(CRA,Tilt,n); %Calculates chief ray angle inside a detector.

%INPUTS:

% CRA: Chief ray angle outside the detector % Tilt: Angle of lenslet tilt

% n: Refractive index of lenslet-detector material

% (Default: 11 = 1.51)

%OUTPUT: % Tp: Angle of chief ray inside detector

% AOI: Total angle of incidence for chief ray:

% (AOI = CRA + Tilt)

%NOTES:

% Tp is restricted to 16.4 degrees. % AOI must be less than or equal to 60 degrees for n = 1.51

% if nargin < 3 n = 1.51; end ^' % era = deg2rad(CRA); tilt = deg2rad(Tilt);

% tp = asin( sin( cra+tilt ) / n) = tilt; Tp = rad2deg(tp);

% ifnargin > 1

AOI = CRA + Tilt;

End %*****Subfunction Definitions************ function t = deg2rad(T) t = T*pi/180; % * * * * * * * * * * * * * * * * * ** * * * * * * *

Function T = rad2deg(t) T = t*180/pi; [0093] As may be seen in FIG. 27, the maximum CRA for these empirical limits is approximately 41° for a lenslet tilt of approximately 19°, as indicated by arrows 958 and 960, respectively. The maximum CRA is graphically represented in FIG. 27 by a dot 970. These graphically derived values match the maximum values analytically calculated using Eq. (3).

[0094] Plot 950 further indicates additional solutions away from the maximum CRA but still acceptable in a number of applications. For example, using Eq. (3), a calculated CRA for a lenslet tilt value of θ_t = 0 for the same empirical constraints as described above yields a solution that the maximum CRA = 25° with no lenslet tilt. This solution is indicated by a dot 972. A line 974, drawn through dot 970 and 972, indicates a solution boundary of mesh 952 outside of which the empirical limits will not be satisfied. A similar set of solutions, and another solution boundary, may be calculated for high values of lenslet tilt, as indicated by a line 978. Consequently, mesh 952 is confined by lines 954, 974 and 978 such that any point on the mesh within the confines of these lines satisfies the earlier defined empirical limits.

[0095] Although each of the aforedescribed embodiments have been illustrated with various components having particular respective orientations, it should be understood that the embodiments of the present disclosure may take on a variety of specific configurations, with the various components being located in a variety of positions and mutual orientations, and still remain within the spirit and scope of the present disclosure. Furthermore, suitable equivalents may be used in place of or in addition to the various components, the function and use of such substitute or additional components being held to be familiar to those skilled in the art and are therefore regarded as falling within the scope of the present disclosure.

[0096] For example, although each of the aforedescribed embodiments have been discussed mainly for the case of chief ray correction, one or more corrective elements may be combined to provide illumination correction for beam width differences arising from variations in beam angle. An angled, refractive surface, for instance, would be suitable for such an application, and may be further combined with, for example, a diffractive pattern in order to simultaneously correct for chief ray angle. [0097] As another example, a diffractive grating with an increasing grating density may be used in place of the lenslet array for providing a tilted phase. Such a diffractive grating may also be used to separate electromagnetic radiation by wavelength such that electromagnetic radiation of different wavelengths focuses at different locations on a detector, or on different detectors.

[0098] FIG. 28 shows a portion 1500 of a system that utilizes a diffractive grating 1502 in place of a lenslet array. In one embodiment, the diffractive grating is in a form of a linearly chirped grating with sub-wavelength features. In this case, the effective index of refraction increases linearly with space, producing a linearly varying optical path difference (OPD) that is akin to that of a tilted surface. Then, the amount of CRA correction is given by Snell's law, as previously described. In another embodiment, sub-wavelength features may also be used to provide an effective index of refraction that produces an OPD that is equivalent to that produced by a tilted lenslet, and is thus capable of focusing electromagnetic radiation as well as performing CRA correction.

[0099] Furthermore, CRA correction may also be performed using diffractive optical elements. Moreover, the tilted surface described herein may also be implemented using diffractive elements. As another example, the diffractive elements used in the CRA correction elements (such as those shown in FIGS. 11 and 27 may include features that are smaller than the wavelength of the electromagnetic radiation incident thereon (i.e., sub-wavelength features). Such sub-wavelength features are advantageous in that they may exhibit desirable optical characteristics over a broad range of wavelengths. For example, the gratings with sub-wavelength features may be in the form of a surface relief grating fashioned on a material with a high index of refraction. At every point in the surface the effective index seen by electromagnetic radiation incident at a wavelength substantially larger than the grating pitch is given by a weighted average between the indices of the two materials in the boundary, where the concentration of each material determines the weights. The result is that a linear phase profile may be achieved by linearly varying the concentration of the high index material. The same technique may also be used to implement a lens, by creating a surface profile with an effective index that follows the phase variation of the desired lens. Similarly, a tilted CRA corrector may also be implemented by creating a surface profile, using sub-wavelength features, with an effective index that follows that of a tilted lens, generically described by the summation of a parabola and a linear slope.

[0100] An example of a sub-wavelength diffraction grating is shown in FIG. 29. A portion 1600 of a sub-wavelength diffraction grating 1602 is shown. An incoming wavefront 1604 (indicated by a set of parallel dashed lines) of electromagnetic radiation is incident on sub-wavelength diffraction grating 1602 formed by an interface between a high index material (nπ) and a low index material (U_L). Incoming wavefront 1604 has a chief ray 1606 forming a CRA θ;_n with respect to a normal 1608 (indicated by a dashed line). Sub-wavelength grating 1602 includes a plurality of subwavelength structures 1610 spaced apart with spacing that varies as a function of spatial distance x (indicated by an arrow 1612) along the interface. As a result of the presence of the sub-wavelength structures, sub-wavelength grating 1602 exhibits a spatially- varying effective index of refraction. Consequently, incoming wavefront 1604 is altered as a result of passing through sub-wavelength grating 1602 and emerges as an outgoing wavefront 1614 (indicated by another set of parallel dashed lines) with a chief ray 1616 making a CRA of θ_out with respect to the normal.

[0101] FIG. 30 graphically illustrates the dependence of the effective index of refraction. A graph 1650 of FIG. 30 shows a plot of the effective index of refraction n_eff(x) as a function of x. High index nπ (indicated by a straight, dashed line 1652) and low index n_L (indicated by another straight, dashed line 1654), as well as a mean index n_m (indicated by a straight, dashed line 1656), are indicated on graph 1650. The effective index of refraction n_eff(x), however, varies as a function of distance x and, in the case of sub-wavelength diffraction grating 1600 of FIG. 29, the effective index of refraction n_eφc) increases with x, as indicated by a curve 1660.

The spatial variation of n_eff(x) is seen to be nearly linear with respect to x for a portion of curve 1660, with an effective refraction angle of θ_eff, as indicated between a dashed line 1662, which follows the linear portion of curve 1660, and horizontal line 1664. Following Snell's law, it may be seen that the output CRA following the nκ-nL interface may be expressed as: n_m ^ήn{θ._n - θ_eff)= n_L sin(O_> (Eq- 4) Therefore, given knowledge of the incoming wavefront and the desired CRA of the outgoing wavefront, a desired effective index of refraction n_eff(x) of the sub- wavelength diffraction grating (and consequently the effective refraction angle θ_eff) may be calculated and the sub-wavelength diffraction grating may be designed accordingly.

[0102] FIG. 31 shows an example of a surface sag suitable for use in a discretized refractive element, such as was earlier described in the context of FIG. 10. This particular sag surface, if made fine enough, can approximate a smooth surface such as shown in FIG. 9. FIG. 31 shows a plot 1700 of the depth (in microns) of the sag surface versus distance from the center of the CRA correction element. Plot 1700 has been calculated using a MATLAB© routine as follows:

%FILE: SoInCm

%Calculates discretized refractive element for Chief Ray Angle Correction, close all clear all

%Given Parameters: %Find max extent of array in radius : numX = 2048; %(number of detectors in x direction) numY = 1536; %(number of detectors in y direction) DetSize = 2.2; %(detector size in microns) %Overbuild factor: OB = 1.05; maxX = OB*(numX*DetSize*le-3)/2; maxY = OB*(numY*DetSize*le-3)/2; maxR = sqrt(maxX2 + maxY2); %Add fudge factor for rounding dimensions: maxR = maxR * 1.01 ;

%Max input angle: thetal_max = 35; %Max output angle: theta3_max = 25; %Length of arrays: N - 15000;

%Thickness of Cover Plate (microns):

D = 200; %Distance from Cover Plate to Lenslet array (microns): d = 40; %Index of refraction of Cover Plate: n = 1.4828; %(Index of material ¹Rl' at 0.55 microns) %Maximum depth of cut in Fresnel Lens (microns):

Tmax = 20;

%Set Output (bottom) Radius array increment (microns): %DelR = 6; %(Use for picture)

DeIR = 12; %(Use for Zemax - Small system)

%DelR = 3; %(Use for Zemax - Large system)

%DelR = .1; %(Use for fabrication table) %Radius coordinate along top surface: %Note: this Rmax is adjusted to give a 25 deg output ray at

% the EFFECTIVE edge of the detector: 1.44 mm % (diagonal of 640x480, 3.6 micron detectors) %The last valid facet(s) are replicated to extend the array % to MaxR, the maximum extent of the construction. This is done % to allow for some misalignment of the discretized surface to the array.

Rmax = 2.816 - 0.144; rin = linspace(0,Rmax,N); %Input angle (deg) as a function of rin: thetal = rin * thetal jnax/Rmax; %(degrees)

Thetal = thetal *pi/l 80; %(radians)% %Cal culations:

%Calculate theta2 as a function of rin:

Theta2 = asin(sin(Thetal)/n); theta2 = Theta2 * 180/pi; %Calculate rout as a function of theta2, rin:

%Shift through Cover Plate:

S = D*tan(Theta2); %(microns) s = S*le-3; %(mm) rout = rin + s;

%Linearize the rout array, and interpolate other arrays to fit:

RoutLin = 0:(DelR*le-3):rout(end);

Theta2 = interpl(rout,Theta2,RoutLin); rout = RoutLin; N = length(rout);

%Assume output angle, theta3, is a linear function of rout: theta3 = rout * theta3_max/(max(rout));

Theta3 = theta3*pi/180;

%Calculate the Refracting Facet surface normal: Psi = atan((n*sin(Theta2) - sin(Theta3))./(n*cos(Theta2)- cos(Theta3))); PSi = PSi * 180/ρi;

%Sequentially construct discretized refractive element from center out: %Construction Array is depth of discretized surface (mm) vs. rout:

CA = zeros(size(rout));

ContSurf = zeros(size(rout)); %Continuous surface profile w/ no resets

%Calculate Refracting Facet Slope (=tan(Psi)):

RFS = tan(Psi); %Calculate Transition Facet Slope (avoid singularity at center)

TFS(I )=0;TFS(2:length(Theta2))=tan(pi/2); %No transition angle -> vertical reset %Facet-Transition surface flag: 1 = Facet, 0 = Transition

FTF = I ; %Loop though rout: for ii = 2:N

%Calculate distance from last radius point in microns: rD = (rout(ii)-rout(ii-l))*le3;

ContSurf(ii) = ContSurf(ii-l)+RFS(ii)*rD;

if FTF = 1 %We are doing a Refraction Facet %Check that last value of CA has not reached Tmax: if CA(ii-l) < Tmax

%Calculate next depth from current slope and distance to next point

CA(ii) = CA(ii- 1) + RFS(ii)*rD; %If Tmax is reached, clip and switch to transition facet: if CA(ii) > Tmax,

CA(ii) = Tmax; FTF - 0; %Grab current Transition Facet Slope:

CTS = TFS(ii); end else %Switch to transition facet: CA(U- 1) = Tmax; FTF = 0;

%Grab current Transition Facet Slope: CTS = TFS(ii); end else %We are doing a Transition Facet %Check that last CA is not at 0 if CA(ii- 1) > 0

%Calculate next depth from Transition slope and distance to %next point CA(ii) = CA(U-I) - CTS*rD;

%If zero depth is reached, clip and switch to refraction facet: if CA(ϋ) <= 0 CA(ii) = 0; FTF = I; end else %Switch to refraction facet: CA(ii- 1) = 0; FTF = I; end ^' end end

if FTF == 1 %(Still on last refraction facet)

%Use last Refraction Slope: LastRFS = RFS(end);

LastrD = (rout(end) - rout(end-l))*le3; while CA(end) < Tmax;

ContSurf = [ContSurf (ContSurf(end)+LastRFS *LastrD)] ; NextCA = CA(end) +LastRFS*LastrD; rout = [rout rout(end)+LastrD* 1 e-3] ; if NextCA < Tmax

CA = [CA NeXtCA]; else

CA = [CA Tmax]; FTF = 0; end end end

%Extend last Transition Facet so that it returns to zero: %Use last Transition Slope:

LastCTS = TFS(end); while CA(end) > 0

NextCA = CA(end) - LastCTS *LastrD; CA = [CA NeXtCA]; rout = [rout rout(end)+LastrD*le-3]; NextCont = ContSurf(end) + LastRFS*LastrD; ContSurf = [ContSurf NextCont]; end if CA(end) < 0 CA(end) = 0; end %Check to see if array is defined out to maxR. If not, extend it

% using the last facet angles:

FTF = 1 ; %Starting from zero, so use refraction facet while rout(end) < maxR

NextCont = ContSurf(end) + LastRFS*LastrD; ContSurf = [ContSurf NextCont]; if FTF == 1 %On refraction facet

NextCA = CA(end) + LastRFS*LastrD; rout = [rout rout(end)+LastrD*le-3]; if NextCA < Tmax CA = [CA NeXtCA]; else

CA = [CA Tmax]; FTF = 0; end elseif FTF == 0 %On transition facet

NextCA = CA(end) - LastCTS*LastrD; rout = [rout rout(end)+LastrD* 1 e-3]; if NextCA > 0

CA = [CA NeXtCA]; else

CA = [CA O]; FTF = I; end end end

%Calcualate maximum sag of a continuous profile maxCont = max(ContSurf); %Plot the Fresnel approx along w/ the Continuous profile. figure(4); subplot(2,l,l); plot(rout*le3,CA,rout*le3,CA,'.'); subplot(2, 1 ,2); plot(rout* 1 e3 ,ContSurf,rout* 1 e3,ContSurf/.') title(['Refractive Surface vs Continuous profile: Max Cont Sag

num2str(maxCont,'%1.0f) ' μm'])

%Find minimum facet period of refractive surface: pp = fmd(CA==0); ppd = diff(ρp); ppd = ppd*rD;

MinPer = min(ppd); %(microns); % figure(l) plot(rout* 1 e3,CA,rout* 1 e3,CA,'.') a = axis; a(3) = -a(2)/2; a(4) = a(2)/2; axis(a);

%axis equal zoom yon grid title(['Refractive Surface: Minimum Period = ' num2str(MinPer) ' Vtnum']) xlabel('Radius from array center (\mum)') ylabel('Deρth of Fresnel (\mum)')

% if WriteASCII % Write data to an ascii file for use in fabrication fhame= [p filesep 'sagfilej tm '.txt']; %temp location of data fid = foρen( fhame, 'wt^! ); iffid == -l error( sprintf( 'Unable to open file %s!\n', fhame ) ); end fprintf(fid, 'Radial distance (mm)\tDepth of cut (microns)\n'); fclose(fid) sρrintf('Writing File');

% dlmwrite(fname, 'Radial distance (mm)\tDepth of cut • (microns)\n','precisionV%s','newline','pc') dim write(fname, [rout' C A'], 'delimiter', '\t', 'precision', '%6.4f,

'newline', 'pc','-append'); end

%Statements that create a 2-D array for dislay and modeling: %Create 2-D array of surface: x = [-rout(end:-l :l) rout]; [X, Y] = meshgrid(x,x); R = sqrt(X.^Λ2 + Y.^Λ2); if 0 %Clip to round aperture ff= find(R(:) > Rmax);

R(ff) = 0; end %Zero out edges of array: Ed = round(N/20); R([l:Ed end-Ed+l:end],:) = 0; R(:,[l :Ed end-Ed+1 :end]) = 0; %Sort in ascending order:

[RadS,I] = sort(R(:));

%Find corresponding Sags for each element: SagS = interpl(rout,CA,RadS); R(I) = -SagS; % figure(2)

Lgt = [10000 -5000 1250]; surfl(x* 1 e3,x* 1 e3,R,Lgt) axis equal ^" shading('flat') coloπnap(gray) %

%Plot clipped to size of detector array: %Find indices of arrays inside detector array. xx = fmd(abs(x) < maxX); yy = fmd(abs(x) < max Y); figure(3) surfl(x(xx)* 1 e3,x(yy)* 1 e3,R(yy,xx),Lgt) axis equal shading('flat') colormap(gray) camup([0 1 O]) set(gca,'ZTickLabelV') if O xlabel('\mum') ylabel('\mum') title('Refractive surface seen from Detector Side') else set(gca/XtickLabel',") set(gca,'Yticklabel',") set(gca/Ztick',[]) set(gca,Υtick',[]) set(gca,'Xtick',[]) end

Claims

CLAIMSWhat is claimed is:

1. In a detector system for receiving incoming electromagnetic radiation imaged by imaging optics onto the detector system, the incoming electromagnetic radiation including a plurality of chief rays, each having a chief ray angle (CRA) within a range of CRAs limited by a stop of the imaging optics, an improvement comprising: a corrective element configured for cooperating with the imaging optics for ensuring that all chief rays over the range of CRAs fall within a cone of acceptance angles of the detector, the corrective element being one of a tilted lenslet, a diffractive element, a refractive element, a discretized refractive element and a subwavelength structure.

2. The improvement of Claim 1, wherein the corrective element is the diffractive element and includes a grating.

3. The improvement of Claim 1, wherein the corrective element is the discretized refractive element and comprises a plurality of alternating refractive surfaces and transitional surfaces.

4. The improvement of Claim 3, wherein the transitional surfaces are at an angle that is near to an output angle of the chief ray.

5. The improvement of Claim 1, wherein the corrective element is the diffractive element and exhibits wavelength-dependent behavior.

6. The improvement of Claim 5, wherein the corrective element separates the incoming electromagnetic radiation in space according to wavelength.

7. The improvement of Claim 6, the incoming electromagnetic radiation including at least first and second wavelengths, wherein the detector system includes first and second detectors, and wherein the corrective element directs the first wavelength to the first detector and directs the second wavelength to the second detector.

8. The improvement of Claim 1 , wherein the corrective element is the diffractive element and is formed as a layer covering all of the substrate.

9. The improvement of Claim 1 , further comprising a second corrective element that cooperates with the first mentioned corrective element and the imaging optics for ensuring that all chief rays over the range of CRAs fall within the cone of acceptance angles of the detector.

10. The improvement of Claim 9, wherein the first mentioned corrective element and the second corrective element are formed in a stack.

11. A detector system for collecting a range of chief rays from imaging optics, comprising: an array of detectors, each of the detectors having a^" cone of acceptance angles; and a corrective element having one of: (a) an array of lenslets including at least one tilted lenslet; (b) a diffractive element; (c) a refractive element; (d) a discretized refractive element; and (e) subwavelength structures, the corrective element being configured to redirect each of the chief rays to within the cone of acceptance angles.

12. A method of redirecting chief rays within a range of chief ray angles limited by a stop of an optical imaging system, comprising: configuring a corrective element with at least one tilted lenslet; and positioning a corrective element adjacent to an array of detectors such that the chief rays fall within a cone of acceptance angle for each of the detectors.

13. A method of redirecting chief rays within a range of chief ray angles limited by a stop of an optical imaging system, comprising: configuring a corrective element with one or more of diffractive structure, refractive structure, discretized refractive structure and subwavelength structure; and positioning a corrective element adjacent to an array of detectors such that the chief rays fall within a cone of acceptance angle for each of the detectors.

14. An optical system for accepting electromagnetic radiation at a normal incidence angle, and over a range of chief ray angles away from the normal incidence angle, comprising: a detector array including a plurality of detectors; and a plurality of lenslets, wherein each one of the plurality of lenslets is configured for directing electromagnetic radiation incident thereon onto a corresponding one of the plurality of detectors; and wherein at least some of the lenslets are tilted with respect to the normal incidence angle such that electromagnetic radiation incident at the normal incidence angle, as well as over the range of chief ray angles away from the normal incidence angle, is receivable at the detector array.

15. The optical system of claim 14, wherein each one of the plurality of lenslets is further configured for directing a portion of the electromagnetic radiation incident thereon such that the portion of electromagnetic radiation is incident on each one of the plurality of detectors at the normal incidence angle.

16. The optical system of claim 14, further comprising an anti-reflection coating for reducing reflection of the electromagnetic radiation.

17. The optical system of claim 16, wherein the anti-reflection coating is applied to a front surface of each one of the plurality of lenslets.

18. The optical system of claim 16, wherein the anti-reflection coating is applied to a side surface of each one of the plurality of lenslets.

19. The optical system of claim 14, wherein each of the lenslets comprises an interface of two optical materials.

20. The optical system of claim 19, wherein a first one of the optical materials is characterized by an index of refraction that is larger than an index of refraction characterizing a second one of the optical materials.

21. The optical system of claim 19, wherein the electromagnetic radiation is characterized by a plurality of light rays, and wherein each one of the plurality of lenslets is configured so as to increase a detection efficiency of the detector array by increasing a percentage of the light rays that may enter each one of the plurality of lenslets.

22. The optical system of claim 19, further comprising an anti-reflection coating on at least one surface of each one of the plurality of lenslets.

23. The optical system of claim 19, wherein a front surface of the at least one of the lenslets is tilted towards the chief ray angle, to reduce reflection losses.

24. The optical system of Claim 14, wherein at least one of the plurality of lenslets includes a diffraction grating with a non-uniform grating density.

25. A method of designing an optical system for accepting electromagnetic radiation at a normal incidence angle, and over a range of chief ray angles away from the normal incidence angle, at a detector array including a plurality of detectors, the optical system also including a plurality of lenslets, the method comprising: orienting each one of the plurality of lenslets so as to direct electromagnetic radiation incident thereon onto at least a corresponding one of the plurality of detectors such that electromagnetic radiation incident at the normal incidence angle, as well as over the range of chief ray angles away from the normal incidence angle, is receivable at the detector array.

26. The method of claim 25, wherein orienting each one of the plurality of lenslets includes tilting one or more of the lenslets by a tilt angle defined with respect to the normal incidence angle, the tilt angle of tilted lenslets being calculated as a function of position of that lenslet within the optical system.

27. The method of claim 26, wherein tilting further includes positioning at least one of the plurality of lenslets such that a portion of the electromagnetic radiation transmitted therethrough is directed at normal incidence onto at least one of the plurality of detectors.

28. The method of claim 25, further comprising embedding at least one of the plurality of lenslets within an optical material.