Abstract:
An optical imaging assembly is provided, having an optical axis; an object axis defined by an object being imaged; an aperture stop disposed on the optical axis; a light-transmissive sleeve enclosing the object axis, being disposed in object space defined by the object axis; and at least three refractive lens elements being arranged between the object and the aperture stop without any other intervening optical component, at least one of the elements having surfaces having at least one of cylindrical and acylindrical prescription, with an image plane, wherein the object being imaged lies within the sleeve.

Description:
CROSS-REFERENCE 
       [0001]    The present application is a Continuation application of U.S. patent application Ser. No. 15/133,486 filed Apr. 20, 2016, which is also a Continuation application of U.S. patent application Ser. No. 14/169,633 filed Jan. 31, 2014, now U.S. Pat. No. 9,360,658, which is incorporated herein by reference. 
     
    
     TECHNICAL FIELD 
       [0002]    The present disclosure relates generally to optical imaging and measuring systems, and more specifically to such a system used for calibrating fluid flow to a medical infusion pump. 
       BACKGROUND 
       [0003]    One way to measure the rate of flow of a fluid is to cause the fluid flow to be in a continuous stream of drops of known volume, and then count the number of droplets per unit time to deduce the flow rate. This approach is very coarse because it has a measurement granularity equal to the volume of the droplets, and it assumes that the volume of each droplet is the same as it detaches from its orifice. Indeed, this “drop counting” approach has measurement accuracy that is inadequate for many applications, such as medical infusion. The granularity problem can be eliminated if the volume of the droplets can be measured in real-time as the droplets form and detach from the supporting orifice. 
         [0004]    One way to measure the volume is to capture a two-dimensional image of a pendant drop suspended from its orifice, and then measure its width along several points from the tip of the droplet to the orifice. If rotational symmetry is assumed, the droplet can be represented as a series of stacked disks where the volume of each disk is V=πH(Width/2) 2 , where H is the distance between points along the axis of rotation. The volume of the drop is the sum of the volume of all the disks. To obtain good droplet volume accuracy, it is important to obtain good estimates of the width of the droplet. The rate of fluid flow can then be more accurately determined by measuring the time rate of change of droplet volume, by for example, collecting and processing a series of images in quick succession, such as a series of video images. 
         [0005]    Complicating the imaging process is the fact that the pendant drop of an infusion tube is enclosed in a generally cylindrical drip chamber that introduces enormous amounts of optical distortion in the direction that the width of the droplet is to be measured. Further complicating matters is that splashes and condensation can cause fluid droplets to form on the inner surface of the drip chamber that can occlude or partially occlude the edge of the droplet from the image. Lastly, due to manufacturing, assembly, and even usage processes, the imaging assembly must be able to tolerate changes in distance between the axis of the pendant droplet and the lens without causing an appreciable change in the calculated volume of the droplet. 
       SUMMARY 
       [0006]    Accordingly, an optical imaging assembly is prescribed that is optically fast, corrects for optical distortion introduced by a sleeve co-axial with an axis of the object, and is telecentric in object space. The present assembly employs combinations of cylindrical or acylindrical, and spherical or aspherical lens elements to correct optical distortion and other aberrations. In addition, the present disclosure relates to an optical imaging assembly for use with an infusion tube, or, more particularly, for imaging the pendant drop within an infusion tube. The present optical imaging assembly corrects for the optical distortion caused by the infusion tube, is optically fast so that droplets and other artifacts residing on the wall of the infusion tube are out of focus and not imaged by the imaging system, and is telecentric so the magnification of the object is substantially independent of the distance between the object and the first lens element. 
         [0007]    According to aspects illustrated herein, there is provided an optical imaging assembly, including: an optical axis connecting an object plane and an image plane; an object axis within the object plane and perpendicular to the optical axis; a first optical element with a substantially planar input surface and acylindrical output surface where the axis of acylindricity intersects the optical axis and is parallel to the object axis; a second optical element with a substantially planar input surface and acylindrical output surface where the axis of acylindricity intersects the optical axis and is parallel to the object axis and the acylindrical output surface of the second optical element is spaced away from the acylindrical output surface of the first optical element; a third optical element with input and output surfaces having rotational symmetry and centered on the optical axis; an aperture stop; and a fourth optical element with input and output surfaces having rotational symmetry and centered on the optical axis. 
         [0008]    More specifically, an optical imaging assembly is provided, including an optical axis, with an object axis, having a light-transmissive sleeve enclosing the object axis, telecentric in object space, having at least three refractive lens elements, in two of the lens elements, at least one of the elements having surfaces with at least one of cylindrical and acylindrical prescription, with an image plane, wherein the object being imaged lies within the sleeve. 
         [0009]    In one embodiment, an assembly includes four lens elements arranged in a manner such that the resulting optical imaging assembly is able to correct for large amounts of optical distortion, is telecentric in object space, has an f-number of 1.5 or less. Two of the lens elements have aspherical prescriptions, and the other two lens elements have acylindrical surfaces, wherein the two acylindrical surfaces are separated from one another. The optical imaging assembly is well adapted for use in a liquid flowmeter system in which the fluid flows in a series of droplets enclosed in a drip chamber. 
         [0010]    In another embodiment, an imaging assembly is configured for removing optical distortion from an image generated by an object located within a light transmissive sleeve. The assembly includes a first optical element acting in conjunction with a second optical element; both optical elements have cylindrical and/or acylindrical surfaces that together remove optical distortion from the image. 
         [0011]    In yet another embodiment, an optical imaging assembly is provided, having an optical axis; an object axis defined by an object being imaged; an aperture stop disposed on the optical axis; a light-transmissive sleeve enclosing the object axis, being disposed in object space defined by the object axis; and at least three refractive lens elements being arranged between the object and the aperture stop without any other intervening optical component, at least one of the elements having surfaces having at least one of cylindrical and acylindrical prescription, with an image plane, wherein the object being imaged lies within the sleeve. 
         [0012]    In yet another embodiment, an imaging assembly is provided, having an optical axis; an object axis defined by an object being imaged; an aperture stop disposed on the optical axis; four lens elements disposed on the optical axis, at least three of the four lens elements being arranged between the object and the aperture stop without any other intervening optical component; and a light-transmissive sleeve being disposed in object space defined by the object axis. The imaging assembly has an optical speed f-number of 1.5 or less, two of the four lens elements have aspherical prescriptions, and the other two of the four lens elements have acylindrical surfaces, and the two acylindrical surfaces are separated from one another. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0013]    The nature and mode of operation of the present optical imaging assembly will now be more fully described in the following detailed description taken with the accompanying drawing figures, in which: 
           [0014]      FIG. 1  is a schematic top-view of the present optical imaging assembly; 
           [0015]      FIG. 2  is a schematic side-view of the present optical imaging assembly; 
           [0016]      FIG. 3  is an isometric view of the object, the sleeve about the object, and objective lens elements of the present optical imaging assembly; 
           [0017]      FIG. 4  is a top-view ray-trace plot showing how a fan of rays originating at the edge of the field in the object plane propagate through the optical imaging assembly to the image plane; 
           [0018]      FIG. 5  is a representative image of a pendant drop within a sleeve having inner surface droplets in which the optical imaging assembly is not optically fast; 
           [0019]      FIG. 6  is a representative image of a pendant drop within a sleeve having inner surface droplets in which the optical imaging assembly is optically fast; 
           [0020]      FIGS. 7A, 7B, and 7C , are a prescription of an embodiment of the present optical imaging assembly, created by the Zemax lens design program; 
           [0021]      FIGS. 8A and 8B  are graphs from the Zemax lens design program illustrating the amount of optical distortion of the optical imaging assembly in the directions parallel to the object axis and perpendicular to the object axis, respectively, with a cylindrical sleeve located about the object; 
           [0022]      FIG. 9  are spot diagrams from the Zemax lens design program showing the size and shape of the images produced by the present optical imaging assembly in which the object consists of delta-functions at six field locations with a sleeve located about the object; and 
           [0023]      FIG. 10  is a block diagram illustrating how the present optical imaging assembly is used in a flow-rate measurement system. 
       
    
    
     DETAILED DESCRIPTION 
       [0024]    At the outset, it should be appreciated that like drawing numbers on different views identify identical, or functionally similar, elements of the present disclosure. 
         [0025]    Furthermore, it is understood that the present disclosure is not limited to the particular methodology, materials, and modifications as described, and any of these may, of course, vary. It is also understood that the terminology used herein is for the purpose of describing particular aspects only, and is not intended to limit the scope of the present disclosure, which is limited only by the appended claims. 
         [0026]    Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood to one of ordinary skill in the art to which the present disclosure belongs. Although any methods, devices, or materials similar or equivalent to those described herein can be used in the practice or testing of the present disclosure, example methods, devices, and, materials are now described. 
         [0027]      FIG. 1  is a schematic top-view of optical imaging assembly  100 , which includes an optical axis  102 , a first lens element  112  having an input surface  134  and an output surface  136 , a second lens element  114  having an input surface  138  and an output surface  140 , a third lens element  116  having an input surface  142  and an output surface  144 , an aperture stop  118 , and a fourth lens element  120  having an input surface  146  and an output surface  148 . The object plane  104  is perpendicular to the optical axis  102  and contains at least a portion of the object being imaged such as the pendant drop  152  shown in  FIG. 3 . Object space  101  also includes a sleeve  110  having an axis of rotation  108 , the axis of rotation  108  also being substantially coincident with a rotationally symmetric object such as the pendant drop  152  shown in  FIG. 3 . The sleeve  110  is preferably substantially cylindrical, is contemplated as being slightly cone-shaped with a slope of approximately 0.5 to 5.0° for facilitating the molding process, and has an inner surface  130  and an outer surface  132 . The image produced by the optical imaging assembly  100  lies in image plane  106 . 
         [0028]    Also shown in  FIG. 1  is a key to the axes in which the Z-axis is taken to be the optical axis  102 , the Y-axis is perpendicular to the Z-axis in the plane of the drawing, and the X-axis is perpendicular to the Z-axis and perpendicular to the plane of the drawing. The object plane  104  is in the X-Y plane at Z=0. 
         [0029]    Each of the components listed above will be described more fully with reference to  FIGS. 1, 2, and 3 . The first lens element  112  is a refractive optical element having a substantially planar input surface  134  and a cylindrical or acylindrical output surface  136 . Planar surfaces are less costly to produce than non-planar surfaces, and should be used whenever possible to reduce the manufacturing costs of the optical imaging assembly  100 . Furthermore, making input surface  134  planar facilitates placement and replacement of the sleeve  110  in front of the optical imaging assembly  100  so that different objects can be installed in front of the optical imaging assembly  100  as needed. Output surface  136 , being cylindrical or acylindrical, has optical power in the Y-axis direction and little or no optical power in the X-axis. 
         [0030]    The second lens element  114  is a refractive optical element having a substantially planar input surface  138  and a cylindrical or acylindrical output surface  140 . Planar surfaces are less costly to produce than non-planar surfaces, and should be used whenever possible to reduce the manufacturing costs of the optical imaging assembly  100 . The output surface  140 , being cylindrical or acylindrical, has optical power in the Y-axis direction and little or no optical power in the X-axis. 
         [0031]    In  FIGS. 1, 2, and 3 , the cylindrical/acylindrical surfaces are shown to reside on the output surfaces,  136  and  140 , although they could reside on the input surfaces,  134  and  138 , or a combination of input and output surfaces such as input surfaces  134  and output surface  140  or output surface  136  and input surface  138 . 
         [0032]    In  FIGS. 1, 2, and 3 , both cylindrical/acylindrical surfaces have optical power in the Y-direction (i.e., perpendicular to the optical axis  102  and perpendicular to the object axis  108 ), although the optical power could instead be in the X-direction (i.e., the direction parallel to the object axis  108 ), or one cylindrical/acylindrical surface can have optical power in the Y-direction and the other cylindrical/acylindrical surface can have optical power in the X-direction. 
         [0033]    The third lens element  116  is a refractive optical element having a spherical or aspherical input surface  142  whose center of rotation is substantially coincident with the optical axis  102 . Similarly, the output surface  144  is spherical or aspherical and also has a center of rotation substantially coincident with the optical axis  102 . 
         [0034]    An aperture stop  118  is placed between the third lens element  116  and the fourth lens element  120 . The aperture stop  118  can be fabricated from opaque thin sheet material, such as metal or plastic sheeting. The aperture of the aperture stop  118  is nominally round, but can have other shapes as well such as square, rectangular, hexagonal, octagonal, or any shape made from arbitrary lines segments and arcs. The aperture of the aperture stop  118  is nominally centered on the optical axis  102 . A distance from one side to an opposing side of the aperture of the aperture stop  118  can be between 1 mm and 100 mm when measured through the optical axis  102 . 
         [0035]    All refractive lens elements  112 ,  114 ,  116 , and  118  are contemplated as being made from glass or polymer such as acrylic, polycarbonate, or polystyrene, although in general materials having a higher refractive index such as polycarbonate or polystyrene provide for greater optical power, which in turn facilitates a more compact design in which the distance from the object plane  104  to the image plane  106  is reduced. If the choice of material is polymer, any or all of the lens elements  112 ,  114 ,  116 , and  118  can be made from an injection molding process, compression molding process, injection-compression molding process, or even diamond turned. If the choice of material is glass, any or all of the lens elements  112 ,  114 ,  116 , and  118  can be fabricated with a traditional glass grinding and polishing process, an advanced polishing process such as MRF (magneto-rheological finishing), a diamond turned process, or with a molding process. 
         [0036]    The thicknesses of each of the refractive lens elements  112 ,  114 ,  116 , and  118 , as measured from the apex of the input surface to the apex of the output surface along the optical axis, can be from between 1.0 and 25.0 mm. The perimeter of the refractive elements  112 ,  114 ,  116 , and  118  can be rectangular, such as shown, for example, for first lens element  112  in  FIG. 3 , or circular such as shown, for example, for third lens element  116  in  FIG. 3 , or they can have any number of arbitrary curves and sides to facilitate manufacturing. A distance from one side to an opposing side of any or all refractive lens elements  112 ,  114 ,  116 , and  118 , can be between 10 mm and 200 mm when measured through the optical axis  102 . 
         [0037]    If any or all of the refractive lens elements  112 ,  114 ,  116 , and  118  are made with a molding process, then mounting, alignment, or attachment features can be incorporated into the lens element during the fabrication process. 
         [0038]    Due to Fresnel reflection, each surface of the refractive lens elements  112 ,  114 ,  116 , and  118  will back-reflect approximately 4% of the light incident upon it, resulting in diminished light throughput and stray light that can form glints or other artifacts in the image that can corrupt the image processing process. An antireflective coating can be installed onto some or all of the surfaces of the refractive lens elements  112 ,  114 ,  116 , and  118  to reduce the Fresnel surface reflectance to less 1%. The antireflective coating can be a broad-band antireflective coating, or it can be a multi-layer interference film stack. 
         [0039]    Furthermore, the coating on the input surface  134  of the first optical element  112  should have abrasion resistance properties because the drip chamber  300  will need to be replaced at the start of every infusion. Also, abrasion resistance is beneficial since the drip chamber is in close proximity to the input surface  134 , which can be scratched or damaged when the drip chamber  300  is installed. 
         [0040]    Surrounding the object plane  104  and the object  152  is the sleeve  110 . In the preferred embodiment, the substantially cylindrical sleeve  110  is not part of the optical imaging assembly  100 , but instead resides in the object space  101  and is used to enclose, encapsulate, or otherwise contain the object  152 . The sleeve  110  is substantially transparent or translucent to the light being used to image the object  152 , and can be made from a polymer such as acrylic, polycarbonate, polystyrene, or vinyl. The sleeve  110  can be part of an infusion administration set, such as that made by Baxter International, Inc. If the sleeve  110  is part of an infusion administration set, then the sleeve is known as a drip chamber, and the object  152  is a pendant drop residing within the drip chamber and centered or nearly centered on the optical axis  102 . The sleeve drip chamber  110  is nominally centered on the object axis  108 , and has an inner radius of 7.8 mm and an outer radius of 8.8 mm, although the sleeve drip chamber can have other radii in the range of 1.0 mm to 100 mm. 
         [0041]    The sleeve drip chamber  110  introduces severe optical distortion along the Y-axis that must be compensated by the optical imaging assembly  100  for accurate measurement of the width of the object  152 . That is, for best results, the image of the object  152  at the image plane  106  should be substantially free from optical distortion. 
         [0042]    The sleeve drip chamber  110  is typically fabricated with a low-cost injection molding process. To reduce fabrication costs, the mold used can have surface imperfections that impart surface imperfections into the cylindrical sleeve that can appear in the image of the object  152 . Furthermore, it is expected that the sleeve drip chamber  110  can have seam lines, flow lines, and particulate imperfections that can all appear in the image. 
         [0043]    When fluids are flowing through the sleeve  110  in operation, i.e., when the object  152  droplets are forming and detaching inside the sleeve drip chamber, splashes from the fluid reservoir at the bottom of the sleeve drip chamber can settle on the inner surface  130  of the sleeve within the field of view of the optical imaging assembly  100 . Furthermore, over long periods of time, the fluid flowing through the sleeve  110  can evaporate and subsequently condense on the inner surface  130  of the sleeve  110  within the field of view of the optical imaging assembly  100 . This condensation can appear as a collection of closely-spaced droplets, and significantly impair the ability of a conventional imaging assembly to image the interior of the sleeve  110 . Both the aforementioned splashes and condensation are shown in  FIG. 3  as sidewall droplets  154 . 
         [0044]    Another challenge facing the optical imaging assembly  100  is the placement of the sleeve  110 , or more particularly the location of the object axis  108  and object  152  relative to the optical imaging assembly  100 . That is, due to instabilities and the flexibility of a vinyl sleeve drip chamber  110 , the distance between the object axis  108  and the input surface  134  of the first lens element  112  can vary by several millimeters. This dimensional problem is exacerbated whenever one sleeve drip chamber  110  is replaced with another like component as typically occurs when one infusion ends and another begins. Since the magnification of a lens typically varies with varying object distance, the varying magnification will cause the image size to vary and the calculated volume of the pendant drop object  152  to be inaccurate, which will in turn cause the computed flow rate to be inaccurate as well. 
         [0045]    The preceding paragraphs have illustrated the need for the optical imaging assembly  100  to have the following set of characteristics: 1) the optical imaging assembly  100  must be telecentric in object space so the magnification does not change with varying object-to-input surface distance; 2) the optical imaging assembly  100  must be optically fast, on the order of F/1.5 or faster, so that sidewall droplets  154  and other undesirable artifacts within the sleeve drip chamber  110  are out of focus and do not appear in the image; and 3) the optical distortion introduced by the sleeve  110  is removed by the optical imaging assembly  100 . An additional desirable characteristic is that the optical imaging assembly  100  be as compact as possible, meaning, for example, that the distance between the object plane  104  and the image plane  106  is small, such as less than 150 mm. The present optical imaging assembly  100  has these four desirable features, whose functions are described in the following paragraphs. 
         [0046]    Telecentricity in object space  101  is that condition where the ray that leaves the object  152  propagating parallel to the optical axis  102  passes through the center of the aperture stop  118 . In  FIG. 4 , that particular ray, also called the chief ray, is seen to be ray  164 C, which leaves the object at location  160  in a direction substantially parallel to the optical axis  102 , and subsequently passes through the aperture stop  118  at location  119 . Note that the location  119  is substantially at the center of the aperture stop  118 , and the chief ray  164 C intersects the optical axis  102  at the location  119 . 
         [0047]    The object space telecentricity condition is determined by the optical power of the third lens element  116 , and the optical distance between the third lens element  116  and the object plane  104 , as well as the optical distance between the third lens element  116  and the aperture stop  118 . 
         [0048]    As described earlier, the drip chamber  110  introduces crippling amounts of optical distortion that are removed by the optical imaging assembly  100 . This optical distortion compensation is achieved with the first optical element  112  acting in conjunction with the second optical element  114 . Both of these optical elements have cylindrical and/or acylindrical surfaces (i.e., output lens surface  136  and output lens surface  140 ) that together remove the optical distortion from the image. Initial attempts at designing the distortion-compensation lens assembly utilized only one optical element having one or two cylindrical and/or acylindrical surfaces; intuitively this approach seemed reasonable since the sleeve  110  is only one optical component (external to the lens proper), and the distortion it introduces should be counteracted with only one lens element having a cylindrical or acylindrical surface. However, it was found that all designs that utilized only one element having a cylindrical or acylindrical surface could not be made optically fast and/or telecentric, or suffered from poor image quality. 
         [0049]    In addition to requiring two lens elements for optical distortion correction (namely the first lens element  112  and the second lens element  114 ), the cylindrical/acylindrical surfaces of these two lens elements are preferably physically separated from one another by a considerable distance, such as 4 mm or more. This separation allows for the distortion-correction characteristics of one cylindrical/acylindrical surface to be leveraged against the second cylindrical/acylindrical surface. That is, because the two acylindrical/cylindrical surfaces (e.g.,  136  and  140 ) are separated, their aberration-compensating effects are not simply additive, but instead interact producing higher-order distortion-compensation terms. This interaction is one of the key components of the present assembly  100 . 
         [0050]    The optical imaging assembly  100  is preferably optically fast, as noted earlier, so obscurations residing within the sleeve  110  drip chamber, or obscurations residing on either the inner surface  130  or outer surface  132 , are out of focus and do not appear in the image. These obscurations do not appear in the image if the optical imaging assembly has an optical speed less than approximately F/2.0, or preferably less than F/1.5. 
         [0051]    It is typically not difficult to design a lens having an f-number of 2.0 or less, although the design of such a lens does become difficult if the object or image field size is large, or if substantial aberrations are present and must be eliminated. Both of these conditions are present in the present operational environment, and the optical imaging assembly  100  preferably provides good image quality over the entire field at the requisite optical speed. This is accomplished with the third optical element  116  and the fourth optical element  120 , both of which have input and output surfaces that have radially symmetric optical power. These four surfaces can be spherical in nature, although better image quality can be obtained if they are aspherical, such as an asphere described by an eighth-order polynomial, although lower order polynomials—such as sixth order—can be used as well. 
         [0052]    The diameter of the aperture of the aperture stop  118  also plays a role in defining the optical speed of the optical imaging assembly  100 . Generally speaking, the greater the width of the aperture the faster the lens, although a larger aperture generally allows more highly aberrated rays to reach the image resulting in poorer image quality. 
         [0053]    To summarize, the first lens element  112  and the second lens element  114  are used to correct the optical distortion introduced by the sleeve  110 ; the third lens element  116  and the aperture stop  118  are used to control the object-space telecentricity of the optical imaging assembly  100 , and the third lens element  116  and the fourth lens element  120  with the aperture stop  118  are used to provide good image quality with low f-number. 
         [0054]      FIG. 3  shows one application of the optical imaging assembly  100  in which the fluid flow rate of an infusion administration set is measured. In such a setup, the object is the pendant drop  152  suspended from an orifice  150 , both of which are substantially located on the object axis  108 . During operation the pendant drop  152  grows in size as the infused fluid flows, then detaches from the orifice  150  when it reaches its terminal weight, and then grows and detaches repeatedly until the desired volume of fluid has been administered. Since the volume of the droplet is less than a milliliter, several thousand drops grow and detach over the course of an infusion. 
         [0055]    During the course of an infusion, droplets  154  can form on the inner surface of the sleeve drip chamber  110 . These droplets  154  can result from splashes from the falling droplet landing in the fluid reservoir at the bottom of the drip chamber. Since the course of an infusion can last several hours, fluid can evaporate from the pendant droplet  152  and from the reservoir of fluid at the bottom of the drip chamber. If the temperature of the inner surface  130  is low enough, then some of the evaporated fluid can condense on the inner surface  130  and present themselves as droplets  154 . 
         [0056]    If the optical speed of the optical imaging assembly  100  is relatively low (i.e., high f-number), then the droplets  154  will be in focus, or partially in focus, at the image plane  106 . For example,  FIG. 5  shows an image of the pendant droplet  152  in the presence of inner surface  130  droplets  154  when the speed of the optical imaging assembly  100  is only f/5.6. Note that the images of the droplets  154  are easily discernible. Worse, some of the droplets  154  lie at the edge of the image of the pendant drop  152 , which, to the image processing software, will make the size of the pendant drop  152  appear to be greater than it actually is, and will cause the fluid flow measurement calculations to produce inaccurate results. 
         [0057]      FIG. 6  shows is an image of the pendant drop  152  with the same set of droplets  154  residing on the inner surface  130  as was made for the image of  FIG. 5 . However, the image of  FIG. 6  was made with an optical imaging assembly  100  having an optical speed of f/1.4. Note that images of droplets  154  are barely noticeable and the edge of the image of the pendant drop  152  has good contrast and fidelity. The image processing software will be able to compute the size of the pendant drop  152  with good accuracy. 
         [0058]    One such embodiment of the optical imaging assembly  100  was designed with Zemax (Radiant Zemax, LLC, Redmond Wash., USA). The prescription of the assembly is given in  FIGS. 7A, 7B, and 7C . Highlights of the design shown in  FIG. 7A  include: a total track of 108.1 mm (the distance from the object plane  104  to the image plane  106 ), a stop radius of 7.5 mm, a working F/# of 1.40, a maximum object field width of 8.8 mm, a magnification of −0.526, and the wavelength of the light is 825 nm. The image quality was set to be optimized at six object field locations, being, in X,Y pairs in millimeters: (0.0, 0.0), (4.0, 0.0), (0.0, 3.0), (0.0, 5.5), (8.8, 0.0), and (6.0, 3.5). 
         [0059]    In  FIG. 7B  it is seen that the optical model consists of an object “OBJ” plane and image “IMA” plane, an aperture stop “STO”, and eleven other surfaces. Surface 1 is a dummy surface used by Zemax for telecentricity optimization. Surfaces 2 and 3 are the inner surface  130  and outer surface  132  of the transparent sleeve  110 , which is made from PVC. Surfaces 4 and 5 are the input surface  134  and the output surface  136  of the first lens element  112 , which is made from polystyrene (POLYSTYR). Surfaces 6 and 7 are the input surface  138  and the output surface  140  of the second lens element  114 , which is also made from polystyrene. Surfaces 8 and 9 are the input surface  142  and the output surface  144  of the third lens element  116 , which is also made from polystyrene. Lastly, surfaces 11 and 12 are the input surface  146  and the output surface  148  of the fourth lens element  120 , which is made from polystyrene as well. 
         [0060]    Further down in  FIG. 7B , and in  FIG. 7C , it is seen that the input surface  134  of the first lens element and the input surface  138  of the second lens element both have no curvature and are in fact planar. Output surface  136  of the first lens element and the output surface  140  of the second lens element both have acylindrical prescriptions. Both surfaces of the third lens element  116  and the fourth lens element  120  are aspherical. 
         [0061]      FIGS. 8A and 8B  are plots of optical distortion present in the image in the X direction (parallel to the object axis  108 ) and the Y direction (perpendicular to the object axis  108 ). In the X direction, the distortion is only a few tens of microns out to a field distance of about 5 mm. In the Y direction, the distortion is only a few tens of microns out to a radial field distance of about 4 mm. Note that in the Y direction, the distortion is undefined at radial field distances greater than the radius of the inner surface  130  of the sleeve  110 . 
         [0062]      FIG. 9  is a collection of image spot diagrams for the six object field locations noted earlier, and optimized by Zemax. Note the scale is 400 um, which is the height and width of each of the six graphs. The RMS width of each of the six spots is substantially less than 100 um. Since a pixel of a CCD or CMOS image sensor is typically 10 um or less, the edges of the pendant drop  152  object will be imaged across about ten pixels, which is ideal for localizing the edge of the image of the object with sub-pixel accuracy with advanced image-processing algorithms. 
         [0063]      FIG. 10  shows how the present optical imaging assembly  100  can be used as part of a flowmeter  200  of a medical infusion device to measure the rate of flow of the infused fluid. The flowmeter includes a bag  312  or container of fluid that is to be infused, a pendant drop  152  of infusion fluid whose rate of flow is to be measured, a drip chamber  300  with exit port  310  and an exit tube  308  carrying infusion fluid to a patient. 
         [0064]    As seen in  FIG. 10 , the flowmeter  200  also includes a backlight  202  that is used to illuminate the pendant drop  152  of infusion fluid, the optical imaging assembly  100 , an image sensor  204  located at the image plane  106 , a communication bus  212  at the output of the image sensor  204  carries image data to a digital processing device  206 , which in turn is connected through a communication bus  220  to a memory element  208  which is used to store image data  216 , other data  214 , and processing instructions  210 . 
         [0065]    In operation, infusion fluid slowly leaves the fluid bag  312  and forms a pendant drop  152  within the drip chamber  300 . Next, the backlight  202  is used to illuminate the pendant drop  152  through the sleeve  110  of the drip chamber  300 . The light  203  that passes through the sleeve  110  is then collected by the optical imaging assembly  100  which then forms an image of the pendant drop  152  on the image sensor  204 . The output of the image sensor  204  is pixelated image data in the form of a two-dimensional array of integer data, where the integer data corresponds to the brightness of the image at each location of the array. This digital array of brightness data is then transmitted over the communication bus  212  to the processor  206  that processes the image array data to 1) find the edge of the image of the pendant drop  152  within the array, and 2) compute the volume of the pendant drop  152  at the particular instant the image was captured by the image sensor  204 . Knowing the precise time at which successive images are captured by the image sensor  204 , and accurately computing the volume of the pendant drop  152  in each successive frame allows the time rate of change of the pendant drop  152  to be calculated, which is the rate of flow of the fluid. 
         [0066]    It was mentioned earlier that a compact embodiment of the optical imaging assembly  100  is more desirable than an embodiment that is not compact. In some configurations, a more compact embodiment can be achieved by inserting a fold mirror into the assembly, such as between the third lens element  116  and the fourth lens element  120 . Typically the fold mirror will be centered on the optical axis  102 , and tilted at a 45° angle with respect to the optical axis  102  so the imaging path is bent 90°. This can reduce the width of the envelope that the optical imaging assembly  100  occupies by about 30%, although it will increase the size in an orthogonal direction. But this increase in size in an orthogonal direction generally will not increase the overall size of the flowmeter  200 , because other flowmeter components in the orthogonal direction will constrain the size of the flowmeter  200  in this dimension. 
         [0067]    The magnification was mentioned earlier in connection with  FIG. 7A  to be −0.526. The minus sign means that the image is inverted with respect to the object. Indeed, the apex of the pendant drop  152  in  FIG. 3  is seen to be in the downward direction, while the image of the pendant drop in  FIGS. 5 and 6  are seen to be in the upward direction. The magnitude of the magnification, 0.526 means that the size of the image is only 52.6% the size of the object, which is desirable because a smaller and less expensive image sensor  204  can be used as part of the flowmeter  200 . The sign of the magnification of the optical imaging assembly  100  will generally be negative, although the magnitude of the magnification can be tailored to the size of the image sensor  204  and can be between 0.1 and 10.0. 
         [0068]    The wavelength of light was mentioned earlier in connection with  FIG. 7A  to be 825 nm. The wavelength of the light used must be producible by the backlight  202 , transmissible by all of the optical elements of the optical imaging assembly  100 , transmissible by the sleeve  110 , and the image sensor  204  must be responsive to it. The image sensor  204  is generally a silicon device, and is responsive to wavelengths between 400 nm and 1100 nm; the backlight can consist of one or more LED (light emitting diode) sources, which can emit light between 400 nm and 900 nm; and most refractive optical elements can transmit light in the visible and near IR spectral bands, including the wavelengths from 400 nm to 1100 nm. Therefore, the range of light wavelengths that can be used with the optical imaging assembly  100  can be from 400 nm to 900 nm. 
         [0069]    As seen in  FIG. 4 , the center thickness of the fourth lens element  120  is rather thick, being 8.32 mm thick as prescribed in  FIG. 7B . Polymer lens elements having a large thickness can be difficult to mold with good fidelity due to the large amount of shrinkage that the central portion of the lens element undergoes relative to the thinner outer portion as the lens cools after being molded. To remedy this, the fourth lens element  120  can be divided into two separate thinner lens elements. This has the disadvantage of increased material and assembly costs, but also provides two additional degrees of freedom that can be used to improve the image quality with the addition of the two surfaces of a fifth lens element. 
         [0070]    Having thus described the basic concept of the invention, it will be rather apparent to those skilled in the art that the foregoing detailed disclosure is intended to be presented by way of example only, and is not limiting. Various alterations, improvements, and modifications will occur and are intended to those skilled in the art, though not expressly stated herein. These alterations, improvements, and modifications are intended to be suggested hereby, and are within the spirit and scope of the invention. Additionally, the recited order of processing elements or sequences, or the use of numbers, letters, or other designations therefore, is not intended to limit the claimed processes to any order except as may be specified in the claims. Accordingly, the invention is limited only by the following claims and equivalents thereto.