Abstract:
A compact F-theta lens suitable for precise mapping and aerial photography has an F# of not more than 4.5 and a full field of view of 60° (high quality field over) 53°. The lens is near-telecentric to less than 6°, apochromatic from 450 nm to 650 nm, and athermal from −15° C. to +40° C. Embodiments have a focal plane diameter of 104 mm and are compatible for use with a CMOS 1.8 gigapixel multiple FPA. In some embodiments the focal length is 101 mm and the back working distance is more than 10 mm. In embodiments the lens includes three groups of optical elements, with an aperture located between the first and second groups. In some of these embodiments, the first group has at least three elements, while the second and third groups have four and three elements respectively, and the diameter of the first two groups, including housing, is less than 65 mm.

Description:
FIELD OF THE INVENTION 
     The invention relates to optical lenses, and more particularly to F-theta lenses. 
     BACKGROUND OF THE INVENTION 
     Off axis light beam refraction through a focusing lens system will produce distorted images in a curved plane as opposed to a more desirable flat surface. A flat field scanning lens is a specialized lens system in which the focal plane is a flat surface. 
     For a typical flat field lens, in the absence of distortion, the beam of light enters the lens at an angle θ compared with the axis of the lens, the position of the spot focused by the lens will be dependent on the product of the focal length (F) of the lens and the tangent of the angle (θ). However, when the lens is designed with built-in barrel distortion, the position of the focused spot can then be made dependent on the product of F and θ, thereby simplifying positioning and image correction algorithms. Lenses designed in this way are called “F-theta” lenses. F-theta lenses are widely used in scanning applications such as laser marking, engraving, and cutting systems. 
     F-theta lenses are also used for surveillance and reconnaissance applications for precise mapping of an observed target. For these applications, the lens must meet several requirements which do not necessarily apply to other applications. It must provide acceptable images over a wide field of view and must have high resolution and high light sensitivity (i.e. have a low F#). In addition, the lens must be compact, and must provide acceptable images over a wide range of light frequencies, being at least achromatic (able to bring two frequencies to a common focal point) and preferably apochromatic (able to bring three frequencies to a common focal point). In addition, F-theta lenses used for surveillance and reconnaissance should be at least near-telecentric, so that it will produce images that are insensitive to the distance between the lens and the focal plane. If the lens is to be used over a range of temperatures, for example mounted to the exterior of an aircraft, then the lens must be athermal, i.e. invariant over a wide range of temperatures. 
     U.S. Pat. No. 4,401,362 (Aug. 30, 1983) discloses an F-theta lens for use in optical scanning devices. In such scanning devices the spot from a light beam should move at a constant velocity across the scanning surface. The &#39;362 lens includes three elements and provides a field of view up to 58.2° and an F# of 50. However, the &#39;362 lens would not be suitable for surveillance and reconnaissance applications, since it transmits a very limited amount of light because of its high F# and it has a low resolution. In addition, the &#39;362 lens is suitable only for monochromatic applications, and cannot be used for applications requiring a wide spectrum. 
     Another example of a prior art F-theta lens is disclosed in U.S. Pat. No. 4,436,383 (Mar. 13, 1984). The &#39;383 lens includes four components and can only be used for monochromatic applications. Its field of view is up to 60.8° and its F# is 19.7. Its resolution is low. For all of these reasons, the &#39;383 lens is only suitable for laser systems applications, and not for surveillance and reconnaissance. 
     Yet another F-theta lens is disclosed in U.S. Pat. No. 5,835,280 (Nov. 10, 1998). The &#39;280 lens is achromatic having the lateral color compensated electronically, but it is not apochromatic. Its field of view is 54° and its F# is not more than 20. In addition, the &#39;280 lens is too large to be used for reconnaissance and surveillance applications. 
     Yet another F-theta lens is disclosed in U.S. Pat. No. 6,388,817 (May 14, 2002). The &#39;817 lens is achromatic, has a field of view of 63°, and has an F# of 50. This lens is not apochromatic and its F# is very large, so it cannot be used in low F# reconnaissance and surveillance systems. 
     The contribution of the optical element to the axial color is the reciprocal of the Abbe number of lens material. 
     The Abbe number V d  is given by
 
 V   d =( n   d −1)/( n   F′   −n   C′ )  (1)
 
where N d  is the index of refraction of the glass at the wavelength of the helium line e (587.6 nm), n F′  is the index of refraction at the blue cadmium line F′ (479.99 nm), and n C′  is the index of refraction at the red cadmium line C′ (643.85 nm).
 
     Accordingly, the smaller the value of V d , the greater the chromatic dispersion of the glass. 
     The characterization of optical glass through refractive index and Abbe number alone is not sufficient for high quality optical systems. A more accurate description of the glass properties can be provided by including relative partial dispersions. 
     The relative partial dispersion Px,y for the wavelengths x and y is defined by the equation:
 
( n   x   −n   y )/( n   F   −n   c )  (2)
 
     The following relationship will approximately apply to the majority of glasses, the so-called “normal glasses”
 
 P   xy   ≈a   xy   +b   xy   V   d   (3)
 
where a xy  and b xy  are specific constants for the given relative partial dispersion P xy . So as to correct the secondary spectrum and provide an apochromatic lens (i.e. color correction for more than two wavelengths), glasses are required which do not conform to this rule. Therefore glass types having partial dispersions which deviate from Abbe&#39;s empirical rule are needed. The ordinate difference ΔP can be used to measure the deviation of the partial dispersion from Abbe&#39;s rule. The ordinate difference is given by the following generally valid equation:
 
 P   xy   =a   xy   +b   xy ·ν d   +ΔP   xy .  (4)
 
The term ΔP xy  therefore quantitatively describes a dispersion behavior that deviates from that of “normal” glasses.
 
     Optical materials expand with rising temperature. The Opto-thermal expansion coefficient β of an optical element is a property of the glass material, and it does not depend on the focal length or shape factor of the individual optics. For a single optical element:
 
β=α+( dn/dT )/( n− 1)  (5)
         where   α=the thermal expansion coefficient of the glass   n=the refractive index of the glass at the current wave length   T=temperature       

     The refractive index of an optical material is also affected by changes in glass temperature. This can be characterized by the temperature coefficient of the refractive index. The temperature coefficient of the refractive index is defined as dn/dt, and varies with wavelength and temperature. 
     There are two ways of expressing the temperature coefficient of refractive index. One is the absolute coefficient (dn/dt absolute) measured under vacuum, and the other is the relative coefficient (dn/dt relative) measured in ambient air (101.3 kPa {760 torr} dry air). 
     The absolute temperature coefficient of refractive index (dn/dt absolute) can be calculated using the following formula:
 
 dn/dT   absolute   =dn/dT   relative   +n·dn   air   /dT   (6)
 
where dnair/dT is the temperature coefficient of refractive index of air listed in the table below.
 
                                                           TABLE I                   Temperature   dn air /dt (10 −6 /° C.)            Range(° C.)   t   C′   He—Ne   D   e   F′   g               −40 to −20   −1.34   −1.35   −1.36   −1.36   −1.36   −1.37   −1.38       −20 to 0    −1.15   −1.16   −1.16   −1.16   −1.16   −1.17   −1.17        0 to +20   −0.99   −1.00   −1.00   −1.00   −1.00   −1.01   −1.01       +20 to +40   −0.86   −0.87   −0.87   −0.87   −0.87   −0.88   −0.88       +40 to +60   −0.76   −0.77   −0.77   −0.77   −0.77   −0.77   −0.78       +60 to +80   −0.67   −0.68   −0.68   −0.68   −0.68   −0.69   −0.69                    
The refractive index of optical glass change with the temperature is given by:
 
                       ⅆ       n   abs     ⁡     (     λ   ,   T     )           ⅆ   T       =           n   2     ⁡     (     λ   ,     T   0       )         2   ·     n   ⁡     (     λ   ,     T   0       )           ·     (       D   0     +       2   ·     D   1     ·   Δ     ⁢           ⁢   T     +       3   ·     D   2     ·   Δ     ⁢           ⁢     T   2       +         E   0     +       2   ·     E   1     ·   Δ     ⁢           ⁢   T           λ   2     -     λ   TK   2           )               (   7   )               
where
         T 0 : Reference temperature (20° C.)   T: Temperature (° C.)   ΔT: Temperature difference versus T 0      λ: Wavelength of the electromagnetic wave in a vacuum (μm)   D 0 , D 1 , D 2 , E 0 , E 1  and λ TK : constants depending on glass type.       

     The change in the refractive index with temperature usually has the largest impact on the lens performance and thermal focus range. 
     To make a lens apochromatic a special combination of glasses, Abbe numbers, and partial dispersions is needed. To make a lens athermal, a special combination of glass refractive indices that change with temperature has to be selected. The solution space is dependent on the configuration of the lens, the number of components, and the component shapes. 
     What is needed, therefore, is a compact F-theta lens having a low F# and a high resolution over a wide field of view, the lens being apochromatic, temperature stable, and near-telecentric over a wide range of light frequencies. 
     SUMMARY OF THE INVENTION 
     A compact F-theta lens has an F# of not more than 4.5 and a full field of view of 60° with a high quality performance field of view of over 53°. The lens is near-telecentric to less than 6°, apochromatic over a light frequency range of at least 450 nm-650 nm, and is athermal over a temperature range from −15° C. to +40° C. 
     Embodiments have a focal plane diameter of 104 mm and are compatible for use with a CMOS 1.8 gigapixel multiple FPA (focal plane array) having a 2×2 Bayer filter geometry and a pixel size of 2.2 μm×2.2 μm, wherein each CMOS image sensor pixel includes a series of dielectric layers above the photo detector, with a micro lens on top of each pixel to focus light onto the active area of the pixel floor, thereby minimizing both the amount of light lost and the amount of light incident on adjacent photodiodes. In various embodiments, secondary color is corrected so as to take full advantage of a high resolution FPA. 
     In some embodiments, the lens is athermal over the specified temperature range, so that there is no need for a special stage to move lens components or the focal plane to compensate for environmental temperature variations. In some embodiments the focal length is 101 mm and the back working distance is more than 10 mm. 
     In various embodiments, the lens comprises three groups of optical elements, and the aperture is located between the first and second groups (i.e. the two groups furthest from the FPA). In some of these embodiments, the first two groups can be contained within a housing having an outer diameter of 65 mm. In certain of these embodiments the first group includes at least three optical elements, the second group includes exactly four optical elements, and the third group includes exactly three optical elements. 
     In some of these embodiments, one of the first two groups of optical elements corrects the lens for spherical aberration and astigmatism across the field and corrects axial chromatism, spherochromatism, coma and astigmatism without causing distortion, while satisfying relationships required to achieve high resolution of the lens. The other of the first two groups corrects residual chromatic aberration, spherical aberration, coma and astigmatism across the field, while achieving athermalization of the lens through the desired spectrum. And the third optical group corrects field curvature, astigmatism and distortion. 
     The present invention is an F-theta lens that includes a first optical group including a plurality of optical elements, a second optical group, including a plurality of optical elements, an aperture located between the first and second optical groups, and a third optical group, including a plurality of optical elements. The F-number of the lens is not more than 4.5. The lens has a full field of view of at least 60°, with a quality performance field of 53°. The lens is telecentric to less than 6°, apochromatic over a range of at least 450 nm to 650 nm, and is functionally insensitive to temperature over a range of at least −15° C. to +40° C. 
     In embodiments, the second optical group includes exactly four optical elements, and the third optical group includes exactly three optical elements. In some of these embodiments the first optical group includes exactly five optical elements. In other of these embodiments, the first optical group includes exactly three optical elements, one of the optical elements being made of sapphire. 
     In various embodiments, the lens is athermal over the temperature range of at least −15° C. to +40° C. 
     In certain embodiments, the lens has a focal plane of at least 104 mm. In some of these embodiments the lens is compatible for use with a CMOS 1.8 gigapixel multiple FPA (focal plane array) having a 2×2 Bayer filter geometry and a pixel size of 2.2 μm×2.2 μm, wherein each CMOS image sensor pixel includes a series of dielectric layers above the photo detector, with a micro lens on top of each pixel to focus light onto the active area of the pixel floor, thereby minimizing both the amount of light lost and the amount of light incident on adjacent photodiodes. 
     In some embodiments the lens is secondary color corrected. In other embodiments the first two optical groups can be contained within a housing having an outer diameter of 65 mm. And in certain embodiments at least one surface of one of the optical elements in the first optical group is aspherical, and at least one surface of one of the optical elements in the third optical group is aspherical. 
     In various embodiments one of the first two optical groups corrects the lens for spherical aberration, axial chromatism, spherochromatism, coma, and astigmatism without causing distortion, the other of the first two optical groups corrects the lens for residual chromatic aberration, spherical aberration, coma, and astigmatism while achieving athermalization of the lens through the range of at least 450 nm to 650 nm, and the third optical group corrects field curvature, astigmatism and distortion. 
     In certain embodiments, all three optical groups have positive powers, whereby: 
     the first optical group includes five optical elements, having, in order, a negative optical power, a positive optical power, a negative optical power, a positive optical power and a positive optical power, the first optical group being arranged to converge light received from an object and to direct the converged light onto the second optical group; 
     the second optical group includes four optical elements, having, in order, a negative optical power, a positive optical power, a positive optical power and a negative optical power, the second optical group being arranged to further converge light received from the first optical group and to direct the converged light onto the third optical group; 
     the third optical group includes three optical elements having, in order, a negative optical power, a positive optical power and a positive optical power, the third optical group being arranged to focus the light from the second optical group onto the imaging surface; and 
     the optical groups and optical elements satisfy the relationships described in paragraph [0087] below. 
     In some of these embodiments, the first optical element of the first optical group is a double concave lens, the second optical element of the first optical group is a double convex lens, the third optical element of the first optical group is a double concave lens, the fourth optical element of the first optical group is a double convex lens, and the fifth optical element of the first optical group is shaped as a meniscus whose concave surface faces toward the image. 
     In some of these embodiments the second surface of the first element of the first optical group is aspherical. In other of these embodiments the first surface of the fifth element of the first optical group is aspherical. 
     In other of these embodiments the first optical element of the second optical group is shaped as a meniscus whose concave surface faces toward the image, the second optical element is a double convex lens, the third optical element is a double convex lens, and the fourth optical element is a double concave lens. 
     In still other of these embodiments the first optical element of the third optical group is shaped as a negative meniscus lens whose concave surface faces toward the object, the second optical element of the third optical group is shaped as a positive meniscus whose concave surface faces toward the object, and the third optical element is a double convex lens. 
     In various of these embodiments the second surface of the first element of the third optical group is aspherical. And in other of these embodiments the first surface of the third element of the third optical group is aspherical. 
     In certain embodiments: 
     the first optical group has a negative optical power, and the second and third optical groups have positive optical powers, the first optical group includes five optical elements, having, in order a negative optical power, a positive optical power, a positive optical power, a negative optical power and a positive optical power, the first optical group being arranged to diverge light received from an object and to direct the diverged light onto the second optical group; 
     the second optical group includes four optical elements, having, in order, a positive optical power, a positive optical power, a positive optical power and a negative optical power, the second optical group being arranged to converge light received from the first optical group and to direct the converged light onto the third optical group; 
     the third optical group includes three optical elements having, in order, a negative optical power, a positive optical power and a positive optical power, the third optical group being arranged to focus light from the second optical group onto an imaging surface; 
     the aperture stop is positioned between the first and the second optical groups; and 
     the optical groups and elements satisfy the relations give in paragraph below. 
     In some of these embodiments, the first optical element of the first optical group is a double concave lens, the second optical element of the first optical group is shaped as a meniscus whose concave surface faces toward the object, the third optical element of the first optical group is shaped as a meniscus whose concave surface faces toward the object, the fourth optical element of the first optical group is shaped as a meniscus whose concave surface faces toward the object, and the fifth optical element of the first optical group is shaped as a meniscus whose concave surface faces toward the object. 
     In some of these embodiments, the second surface of the first element of the first optical group is aspherical. In other of these embodiments, the second surface of the second element of the first optical group is aspherical. 
     In certain of these embodiments the first optical element of the second optical group is shaped as a positive meniscus whose concave surface faces toward the image, the second optical element is a double convex lens, the third optical element is in a double convex lens, and the fourth optical is a double concave lens. 
     In other of these embodiments the first optical element of the third optical group is shaped as a negative meniscus lens whose concave surface faces toward the object, the second optical element of the third optical group a double convex lens, and the third optical element of the third optical group is a double convex lens. In some of these embodiments the second surface of the first element of the third optical group is aspherical. In other of these embodiments the first surface of the third element of the third optical group is aspherical. 
     In yet other embodiments: 
     the first optical group has a negative optical power, and the second and third optical groups have positive optical powers; 
     the first optical group includes three optical elements, having, in order, a negative optical power, a positive optical power and a negative optical power, the first optical group being arranged to diverge light received from an object and to direct the diverged light onto the second optical group; 
     the second optical group includes four optical elements, having, in order, a negative optical power, a positive optical power, a positive optical power and a negative optical power, the second optical group being arranged to converge light received from the first optical group and to direct the converged light onto the third optical group; 
     the third optical group comprises three optical elements having, in order, a negative optical power, a positive optical power and a positive optical power, the third optical group being arranged to focus the light from the second optical group onto the imaging surface; 
     the aperture stop is positioned between the first and the second optical groups; and 
     the optical groups and the optical elements satisfy the third embodiment relations described below. 
     In yet other embodiments, the first optical element of the first optical group is a double concave lens, the second optical element of the first optical group is a double convex lens, and the third optical element of the first optical group is shaped as a meniscus whose concave surface faces toward the object. In some of these embodiments the first surface of the first element of the first optical group is aspherical, and in other of these embodiments the second surface of the second element of the first optical group is aspherical. 
     In various of these embodiments the first optical element of the second optical group is shaped as a meniscus whose concave surface faces toward the image, the second optical element of the second optical group is a double convex lens, the third optical element of the second optical group is in a form of a double convex lens, and the fourth optical element of the second optical group is a double concave lens. 
     In other of these embodiments, the first optical element of the third optical group is shaped as a negative meniscus lens whose concave surface faces toward the object, the second optical element of the third optical group a double convex lens, and the third optical element of the third optical group is a double convex lens. In some of these embodiments the second surface of the first element of the third optical group is aspherical. And in some of these embodiments the first surface of the third element of the third optical group is aspherical. 
     And in certain of these embodiments the second optical element of the second optical group is made from sapphire. 
     The features and advantages described herein are not all-inclusive and, in particular, many additional features and advantages will be apparent to one of ordinary skill in the art in view of the drawings, specification, and claims. Moreover, it should be noted that the language used in the specification has been principally selected for readability and instructional purposes, and not to limit the scope of the inventive subject matter. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a cross sectional side view illustrating a first embodiment of the present invention; 
         FIG. 2  presents a wave front analysis of the embodiment of  FIG. 1 ; 
         FIG. 3A  is a graph presenting MTF data for the embodiment of  FIG. 1 ; 
         FIG. 3B  is a graph presenting additional MTF data for the embodiment of  FIG. 1 ; 
         FIG. 4A  includes a plurality of graphs presenting RIM RAY curves for the embodiment of  FIG. 1 ; 
         FIG. 4B  includes additional graphs presenting RIM RAY curves for the embodiment of  FIG. 1 ; 
         FIG. 5A  presents a graph of field aberration data for the embodiment of  FIG. 1 ; 
         FIG. 5B  presents a graph of distortion data for the embodiment of  FIG. 1 ; 
         FIG. 6  is a graph presenting environmental analysis for the embodiment of  FIG. 1 ; 
         FIG. 7  is a listing of properties of optical elements for the embodiment of  FIG. 1 ; 
         FIG. 8  is a cross sectional side view illustrating a second embodiment of the present invention; 
         FIG. 9  presents a wave front analysis of the embodiment of  FIG. 8 ; 
         FIG. 10A  is a graph presenting MTF data for the embodiment of  FIG. 8 ; 
         FIG. 10B  is a graph presenting additional MTF data for the embodiment of  FIG. 8 ; 
         FIG. 11A  includes a plurality of graphs presenting RIM RAY curves for the embodiment of  FIG. 8 ; 
         FIG. 11B  includes additional graphs presenting RIM RAY curves for the embodiment of  FIG. 8 ; 
         FIG. 12A  presents a graph of field aberration data for the embodiment of  FIG. 8 ; 
         FIG. 12B  presents a graph of distortion data for the embodiment of  FIG. 8 ; 
         FIG. 13  is a graph presenting environmental analysis for the embodiment of  FIG. 8 ; 
         FIG. 14  is a listing of properties of optical elements for the embodiment of  FIG. 8 ; 
         FIG. 15  is a cross sectional side view illustrating a third embodiment of the present invention; 
         FIG. 16  presents a wave front analysis of the embodiment of  FIG. 15 ; 
         FIG. 17  is a graph presenting MTF data for the embodiment of  FIG. 15 ; 
         FIG. 18  includes a plurality of graphs presenting RIM RAY curves for the embodiment of  FIG. 15 ; 
         FIG. 19A  presents a graph of field aberration data for the embodiment of  FIG. 15 ; 
         FIG. 19B  presents a graph of distortion data for the embodiment of  FIG. 15 ; 
         FIG. 20  is a graph presenting environmental analysis for the embodiment of  FIG. 15 ; and 
         FIG. 21  is a listing of properties of optical elements for the embodiment of  FIG. 15 . 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  is a cross section of a first embodiment of the F-theta athermal lens  10  of the present invention. The lens includes a front window  21 , a first optical group  20 , a second optical group  30 , a third optical group  40 , and a back window  44  in order from the object to the image plane. An aperture stop  12  is located between the first and the second optical groups. An image of a target is formed on a focal plane array  60 . In embodiments, the focal plane array incorporates CMOS with micro lenses, 2×2 Bayer filter geometry, and 1.8 Giga pixels. In other embodiments the image surface  60  incorporates CCD or a direct viewing screen. 
     The first optical group  20  has an overall positive optical power and is configured to receive light from the remote object and to direct the converged light onto the second optical group  30 . The first optical group  20  includes five optical elements  22 ,  23 ,  24 ,  25  and  26 , having, in order from the object to the image plane, a negative optical power, a positive optical power, a negative optical power, a positive optical power and a positive optical power. As can be seen in  FIG. 1  the first optical element  22  of the first optical group  20  has a negative optical power and is a double concave lens. The second surface  22   a  of the element  22  is aspherical so as to correct oblique spherical aberration and to provide the low F# of the lens  10 . The second optical element  23  has a positive optical power and is a double convex lens. The third optical element  24  has a negative optical power and is a double concave lens. The fourth optical element  25  has a positive optical power and is a double convex lens. The fifth optical element  26  has a positive optical power and is shaped as a meniscus whose concave surface faces toward the image. The first surface  26   a  of the fifth optical element is aspherical so as to correct spherical aberration and astigmatism across the field of view. 
     The mutual configuration of the five optical elements  22 ,  23 ,  24 ,  25  and  26  of the first optical group  20  provides correction of axial chromatism, spherochromatism, coma, and astigmatism without introducting a distortion, while satisfying relationships required among the optical elements to achieve high resolution of the lens  10 . 
     The second optical group  30  has a positive overall optical power and is configured to further converge light from the first optical group  20  and to direct the converged light onto the third optical group  40 . The second optical group includes four optical elements  31 ,  32 ,  33  and  34 , having in order from the object to the image plane a negative optical power, a positive optical power, a positive optical power, and a negative optical power. The first optical element  31  of the second optical group  30  is shaped as a meniscus whose concave surface faces toward the image, the second optical element  32  is a double convex lens, the third optical element  33  is a double convex lens, and the fourth optical element  34  is a double concave lens. 
     The mutual configuration and choice of glasses of the elements in the second optical group  30  provides correction of residual chromatic aberration, spherical aberration, coma, and astigmatism across the field of view, while achieving athermalization of the lens  10  through the wavelength range of 450 nm-650 nm. 
     The third optical group  40  has a positive overall power and is configured to further converge the light from the second optical group  30  and to focus the light onto the focal plane array  15 . The third optical group  40  includes three optical elements  41 ,  42  and  43 , having, in order from the object to the image plane, a negative optical power, a positive optical power, and a positive optical power, respectively. The first optical element  41  of the third optical group  40  has a negative optical power and is shaped as a negative meniscus lens whose concave surface faces toward the object. The second surface  41   a  of the first element  41  is aspherical so as to correct residual astigmatism across the field of view. The second optical element  42  of the third optical group is shaped as a positive meniscus lens whose concave surface faces toward the object. The third optical element  43  is a double convex lens. The first surface  43   a  of the third optical element  43  is aspherical so as to correct residual coma and distortion shape across the field of view, and to provide telecentricity for the beam at the focal plane. 
     The mutual configuration of the third optical group elements provides correction of field curvature, astigmatism and distortion. 
     The mutual combination of glass refractive indices and Abbe numbers of the optical elements in the three optical groups  20 ,  30  and  40  provides apochromatic correction of the lens  10 . The axial color and lateral color are corrected as well. The mutual combination changes of refractive indes with temperature provides athermalization of the lens  10  over the temperature range −15° C. to +40° C. 
     In the embodiment of  FIG. 1  the optical groups  20 ,  30 ,  40  and their constituent optical elements satisfy the following relations:
 
0.8&lt; F′   10   /F′   20 &lt;1.1
 
0.04&lt; F′   10   /F′   30 &lt;0.07
 
0.3&lt; F′   10   /F′   40 &lt;0.5
 
0.85&lt; n   22   /n   26   =n   22   /n   34   =n   22   /n   42   =n   22   /n   43 &lt;1.15
 
0.95 &lt;n   22   /n   23   =n   22   /n   24   =n   22   /n   31 =&lt;1.25
 
0.80&lt; n   22   /n   25 &lt;1.1
 
1.05&lt; n   22   /n   32   =n   22   /n   33   =n   22   /n   41 &lt;1.35
 
0.8 &lt;V   22   /V   24   =V   22   /V   25   =V   22   /V   26   =V   22   /V   34   =V   22   /V   42   =V   22   /V   43 &lt;1.2
 
1.45 &lt;V   22   /V   23   =V   22   /V   31   =V   22   /V   41 &lt;0.8
 
0.25 &lt;V   22   /V   32 &lt;0.45
 
0.2&lt; V   22   /V   33&lt; 0.4
 
0.0055 &lt;P   32   /V   32   =P   33   /V   33 &lt;&lt;0.0085
 
0.85&lt; dn/dT   22   /dn/dT   26   =dn/dT   22   /dn/dT   34 &lt;1.2
 
0.07&lt; dn/dT   22   /dn/dT   23   =dn/dT   21   /dn/dT   31 &lt;0.1
 
−0.5&lt; dn/dT   22   /dn/dT   24 &lt;−0.3
 
0.2&lt; dn/dT   22   /dn/dT   25 &lt;0.35
 
−0.12&lt; dn/dT   22   /dn/dT   32 &lt;−0.07
 
 dn/dT   22   /dn/dT   42   =dn/dT   22   /dn/dT   43 &lt;0.5
 
−0.04&lt; dn/dT   22   /dn/dT   33′ &lt;−0.02
 
0.035&lt; dn/dT   22   /dn/dT   41′ &lt;0.07
 
where:
 
F′ 10  is the focal length of the lens  10 ;
 
F′ 20 , F′ 30  and F′ 40  are the focal lengths of the first, the second and the third optical groups  20 ,  30  and  40 ;
 
n 22 , n 23 , n 24 , n 25  and n 26  are the refractive indices for the optical elements  22 ,  23 ,  24 ,  25  and  26  of the first optical group  20 ;
 
n 31 , n 32 , n 33  and n 34  are the refractive indices for the optical elements  31 ,  32 ,  33 , and  34  of the second optical group  30 ;
 
n 41 , n 42  and n 43  are the refractive indices for the optical elements  41 ,  42  and  43  of the third optical group  40 ;
 
V 22 , V 23 , V 24 , V 25  and V 26  are Abbe numbers for the optical elements  22 ,  23 ,  24 ,  25  and  26  of the first optical group  20 ;
 
V 31 , V 32 , V 33  and V 34  are Abbe numbers for the optical elements  31 ,  32 ,  33  and  34  of the second optical group  30 ;
 
V 41 , V 42 , and V 43  are Abbe numbers for the optical elements  41 ,  42 , and  43  of the third optical group  40 ;
 
P 32  is the relative partial dispersion for F′-e spectrum for the second optical element  32  of the second optical group  30 ;
 
P 33  is the relative partial dispersion for F′-e spectrum for the third optical element  33  of the second optical group  30 ;
 
dn/dT 22  is the refractive index change with temperature for the first optical element  22  of the first optical group  20 ;
 
dn/dT 23  is the refractive index change with temperature for the second optical element  23  of the first optical group  20 ;
 
dn/dT 24  is the refractive index change with temperature for the third optical element  24  of the first optical group  20 ;
 
dn/dT 25  is the refractive index change with temperature for the second optical element  25  of the first optical group  20 ;
 
dn/dT 26  is the refractive index change with temperature for the second optical element  26  of the first optical group  20 ;
 
dn/dT 31  is the refractive index change with temperature for the first optical element  31  of the second optical group  30 ;
 
dn/dT 32  is the refractive index change with temperature for the second optical element  32  of the second optical group  30 ;
 
dn/dT 33  is the refractive index change with temperature for the third optical element  33  of the second optical group  30 ;
 
dn/dT 34  is the refractive index change with temperature for the fourth optical element  34  of the second optical group  30 ;
 
dn/dT 41  is the refractive index change with temperature for the first optical element  41  of the third optical group  40 ;
 
dn/dT 42  is the refractive index change with temperature for the second optical element  42  of the third optical group  40 ; and
 
dn/dT 43  is the refractive index change with temperature for the third optical element  43  of the third optical group  40 .
 
     Selection of optical powers of optical groups and elements, selection of glass refractive indices, Abbe numbers and partial dispersions along with dn/dT values provides a high resolution imaging lens with chromatic and apochromatic correction while the defocus caused by changes in temperature is less than the depth of focus of the lens. 
     The wave front for the embodiment of  FIG. 1  is presented in  FIG. 2 , and MTF data for the first embodiment is presented in  FIG. 3A  and  FIG. 3B  respectively. The wave front is well corrected over the whole spectrum and polychromatic, and the MTF shows good resolution and contract over the entire field of view. The RIM RAY curves in  FIG. 4A  and  FIG. 4B  show the spherical aberration, coma, and chromatic and apochromatic correction over the wavelength range of 450 nm-650 nm. Astigmatism data is presented in  FIG. 5A  and distortion data is presented in  FIG. 5B . The field is flat and the distortion corresponds to the F-theta law. Data regarding the change of the focus with temperature is presented in  FIG. 6 . The defocus over the temperature range of −15° to 45° is 4 μm, which is much less than the depth of focus. The lack of telecentricity is less than 6° across the field of view. The prescription of the lens of  FIG. 1  is presented in  FIG. 7 . The optical materials used in making the lens of  FIG. 1  include optical glasses that are common and widely available commercially. 
       FIG. 8  is a cross sectional illustration of a second embodiment of the F-theta athermal lens  100  of the present invention. The lens includes a front window  210 , a first optical group  200 , a second optical group  300 , a third optical group  400  and a back window  440  in order from the object to the image plane  150 . The aperture stop  110  is located between the first  200  and the third optical groups. An image of the target is formed on a focal plane array  150 . In embodiments, the focal plane array  150  incorporates CMOS with micro lenses, 2×2 Bayer filter geometry, and 1.8 Giga pixels. In other embodiments, the image surface  150  may include CCD elements or a direct viewing screen. 
     In the embodiment of  FIG. 8 , the first optical group  200  has an overall negative optical power and is configured to receive light from a remote object and to direct the diverged light onto the second optical group  300 . The first optical group  200  includes five optical elements  220 ,  230 ,  240 ,  250  and  260 , having, in order from the object to the image plane, a negative optical power, a positive optical power, a positive optical power, a negative optical power and a positive optical power. As can be seen in  FIG. 8 , the first optical element  220  of the first optical group  200  has a negative optical power and is a double concave lens. The second surface  220   a  of the element  220  is aspherical so as to correct the spherical aberration and coma for the low F#4.5 of the lens  100 . The second optical element  230  has a positive optical power and is shaped as a meniscus whose concave surface faces toward the object. The second surface of the second optical element  230  is aspherical for residual coma and astigmatism correction. The third optical element  240  has a positive optical power and is shaped as a meniscus whose concave surface faces toward the object. The fourth optical element  250  has a negative optical power and is shaped as a meniscus whose concave surface faces toward the object. The fifth optical element  260  has a positive optical power and is shaped as a meniscus whose concave surface faces toward the object. The mutual configuration of the five optical elements  220 ,  230 ,  240 ,  250  and  260  of the first optical group  200  and the choice of glasses combination provides correction of axial chromatism, spherical chromatic aberration, coma, and astigmatism, while satisfying relationships required among the optical elements to achieve high resolution of the lens  100 . 
     The second optical group  300  has a positive overall optical power and is configured to converge light from the first optical group  200  and to direct the converged light onto the third optical group  400 . The second optical group  300  includes four optical elements  310 ,  320 ,  330  and  340 , having in order from the object to the image plane a positive optical power, a positive optical power, a positive optical power and a negative optical power. The first optical element  310  of the second optical group  300  is shaped as a positive meniscus whose concave surface faces toward the image, the second optical element  320  is a double convex lens, the third optical element  330  is a double convex lens, and the fourth optical element  340  is a double concave lens. 
     The mutual configuration and choice of glasses of the optical elements  310 ,  320 ,  330  and  340  in the second optical group  300  provides correction of residual chromatic aberration, residual spherical aberration, coma, and astigmatism across the field of view, while achieving athermalization of the lens  100  through the desired range of temperatures and through a wavelength range of 450 nm to 650 nm. 
     The third optical group  400  has a positive overall power and is configured to further converge the light from the second optical group  300  and to focus the converged light onto the focal plane array  150 . The third optical group  400  includes three optical elements  410 ,  420  and  430 , having, in order from the object to the image plane, a negative optical power, a positive optical power and a positive optical power respectively. The first optical element  410  of the third optical group  400  has a negative optical power and is shaped as a negative meniscus lens whose concave surface faces toward the object. The second surface  410   a  of the first element  410  is aspherical so as to correct a residual saggital astigmatism across the field of view. The second  420  and third  430  optical elements of the third optical group  400  are both double convex lenses. The first surface  430   a  of the third optical element  430  is aspherical so as to correct residual coma and distortion shape across the field of view, and to achieve telecentricity for the beam at the image space. 
     The mutual configuration of the third optical group elements provides correction of field curvature, astigmatism and distortion. The mutual combination of glass refractive indices and Abbe numbers of the optical elements in the optical groups  20 ,  30  and  40  provides apochromatic correction of the lens  100 . The axial color and lateral color are also corrected. The mutual combination of changes of refractive index with temperature provides athermalization of the lens  100  over the temperature range from −15° C. to 40° C. 
     The embodiment of  FIG. 8  satisfies the following relations among the optical groups  200 ,  300 ,  400  and their constituent optical elements:
 
−0.08 &lt;F′   100   /F′   200 &lt;−0.06
 
0.8 &lt;F′   100   /F′   300 &lt;0.9
 
0.2 &lt;F′   100   /F′   400 &lt;0.4
 
0.8 &lt;n   220   /n   230   =n   220   /n   240   =n   220   /n   310   =n   220   /n   340   =n   220   /n   420   =n   220   /n   430 &lt;1.1
 
1.1 &lt;n   220   /n   260   =n   220   /n   320   =n   220   /n   330   =n   220   /n   410 =&lt;1.35
 
0.9 &lt;n   220   /n   250 &lt;1.2
 
0.9 &lt;V   220   /V   230   =V   220   /V   240   =V   220   /V   310   =V   220   /V   340   =V   220   /V   420   =V   220   /V   430 &lt;1.3
 
0.8 &lt;V   220   /V   250 &lt;1.1
 
0.3 &lt;V   220   /V   260   =V   220   /V   320 &lt;0.5
 
0.2 &lt;V   220   /V   330 &lt;0.4
 
0.5 &lt;V   220   /V   410 &lt;0.7
 
0.0055 &lt;P   320   /V   320   =P   330   /V   330 &lt;&lt;0.0085
 
0.2&lt; dn/dT   220   /dn/dT   230   =dn/dT   220   /dn/dT   240   =dn/dT   220   /dn/dT   430 &lt;0.4
 
−0.55&lt; dn/dT   220   /dn/dT   250 &lt;−0.35
 
0.08&lt; dn/dT   220   /dn/dT   260 &lt;0.1
 
0.1&lt; dn/dT   220   /dn/dT   310   =dn/dT   220   /dn/dT   420 &lt;0.3
 
−0.3&lt; dn/dT   220   /dn/dT   320 &lt;−0.08
 
−0.04&lt; dn/dT   220   /dn/dT   330 &lt;−0.02
 
0.9&lt; dn/dT   220   /dn/dT   340 &lt;1.1
 
0.35&lt; dn/dT   220   /dn/dT   410 &lt;0.55
 
where:
 
F′ 100  is the focal length of the lens  100 ;
 
F′ 200 , F′ 300  and F′ 400  are the focal lengths of the first, the second and the third optical groups  200 ,  300  and  400 ;
 
n 220 , n 230 , n 240 , n 250  and n 260  are the refractive indices for the optical elements  220 ,  230 ,  240 ,  250  and  206  of the first optical group  200 ;
 
n 310 , n 320 , n 330  and n 340  are the refractive indices for the optical elements  310 ,  320 ,  330  and  340  of the second optical group  300 ;
 
n 410 , n 420  and n 430  are the refractive indices for the optical elements  410 ,  420  and  430  of the third optical group  400 ;
 
V 220 , V 230 , V 240 , V 250  and V 260  are the Abbe numbers for the optical elements  220 ,  230 ,  240 ,  250  and  260  of the first optical group  200 ;
 
V 310 , V 320 , V 330  and V 340  are the Abbe numbers for the optical elements  310 ,  320 ,  330  and  340  of the second optical group  300 ;
 
V 410 , V 420 , and V 430  are the Abbe numbers for the optical elements  410 ,  420 , and  430  of the third optical group  400 ;
 
P 320  is the relative partial dispersion for F′-e spectrum for the second optical element  320  of the second optical group  300 ;
 
P 330  is the relative partial dispersion for F′-e spectrum for the third optical element  330  of the second optical group  300 ;
 
dn/dT 220  is the refractive index change with temperature for the first optical element  220  of the first optical group  200 ;
 
dn/dT 230  is the refractive index change with temperature for the second optical element  230  of the first optical group  200 ;
 
dn/dT 240  is the refractive index change with temperature for the third optical element  240  of the first optical group  200 ;
 
dn/dT 250  is the refractive index change with temperature for the second optical element  250  of the first optical group  200 ;
 
dn/dT 260  is the refractive index change with temperature for the second optical element  260  of the first optical group  200 ;
 
dn/dT 310  is the refractive index change with temperature for the first optical element  310  of the second optical group  300 ;
 
dn/dT 320  is the refractive index change with temperature for the second optical element  320  of the second optical group  300 ;
 
dn/dT 330  is the refractive index change with temperature for the third optical element  330  of the second optical group  300 ;
 
dn/dT 340  is the refractive index change with temperature for the fourth optical element  340  of the second optical group  300 ;
 
dn/dT 410  is the refractive index change with temperature for the first optical element  410  of the third optical group  400 ;
 
dn/dT 420  is the refractive index change with temperature for the second optical element  420  of the third optical group  400 ; and
 
dn/dT 430  is the refractive index change with temperature for the third optical element  430  of the third optical group  400 .
 
     The selection of optical powers of the optical groups, the selection of glass refractive indices, Abbe numbers, and partial dispersions, and the selection of dn/dT values provides a high resolution imaging lens with chromatic and apochromatic correction while the defocus caused by changes in temperature is less than the depth of focus of the lens. 
     Wave front data for the embodiment of  FIG. 8  is presented in  FIG. 9 , and MTF data for the second embodiment is presented in  FIG. 10A  and  FIG. 10B . The wave front is well corrected over the whole spectrum, and the polychromatic MTF shows good resolution and contract over the entire field of view. The RIM RAY curves in  FIG. 11A  and  FIG. 11B  show the spherical aberration, coma and chromatic and apochromatic correction over a wavelength range of 450 nm to 650 nm. Astigmatism data is presented in  FIG. 12A  and distortion data is presented in  FIG. 12B . The distortion corresponds to the F-theta law. Data regarding the change of the focus with temperature is presented in  FIG. 13 . The defocus over the temperature range of −15° to 45° is 9 μm, which is much less than depth of focus. Lack of telecentricity is less than 6° across the field of view. The prescription of the lens of  FIG. 8  is presented in  FIG. 14 . The optical materials of the embodiment include optical glasses that are common and widely available commercially. 
       FIG. 15  is a cross-sectional illustration of a third embodiment of the F-theta athermal lens  1000  of the present invention. The lens  1000  includes a front window  2100 , a first optical group  2000 , a second optical group  3000 , a third optical group  4000  and a back window  4400  in the stated order from the object to the image plane. The aperture stop  1100  is located between the first  2000  and second  3000  optical groups. An image of a remote object is formed on a focal plane array  1500 . In embodiments, the focal plane array  1500  incorporates CMOS with micro lenses, 2×2 Bayer filter geometry, and 1.8 Giga pixels. In other embodiments, the image surface  1500  may incorporate CCD devices or a direct viewing screen. 
     The first optical group  2000  has an overall negative optical power and is configured to receive light from the remote object and to direct the diverged light onto the second optical group  3000 . The first optical group  2000  includes three optical elements  2200 ,  2300  and  2400 , having, in order from the remote object to the image plane, a negative optical power, a positive optical power and a negative optical power. As can be seen in  FIG. 15 , the first optical element  2200  of the first optical group  2000  has a negative optical power and is a double concave lens. The first surface  2200   a  of the first optical element  2200  is aspherical so as to correct the spherical aberration and to achieve the low F# of the lens  1000 . The second optical element  2300  of the first optical group  2000  has a positive optical power and is a double convex lens. The second surface  2300   a  of the second optical element  2300  is aspherical so as to correct pupil spherical aberration and coma. The third optical element  2400  of the first optical group  2000  has a negative optical power and is shaped as a meniscus whose concave surface faces toward the object. The mutual configuration and choice of glasses of the three optical elements  2200 ,  2300 ,  2400  in the first optical group  2000  provide athermalization of the lens  1000 . 
     The second optical group  3000  has a positive overall optical power and is configured to converge light from the first optical group  2000  and to direct the converged light onto the third optical group  4000 . The second optical group  3000  includes four optical elements  3100 ,  3200 ,  3300  and  3400 , having in order from the object to the image plane  1500  a negative optical power, a positive optical power, a positive optical power and a negative optical power. The first optical element  3100  of the second optical group  3000  is shaped as a meniscus whose concave surface faces toward the image. The second optical element  3200  of the second optical group  3000  is a double convex lens. The third  3300  and fourth  3400  optical elements of the second optical group are both double convex lenses. 
     The mutual configuration of the four optical elements  3100 ,  3200 ,  3300  and  3400  in the second optical group  3000  provides correction of axial chromatic aberration and spherochromatism through the wavelength range of 450 nm to 650 nm, while satisfying relationships among the optical elements required to achieve high resolution of the lens  1000 . 
     The third optical group  4000  has a positive overall power and is configured to further converge the light from the second optical group  3000  and to focus the converged light onto the focal plane array  1500 . The third optical group  4000  includes three optical elements  4100 ,  4200  lnd  4300 , having, in order from the object to the image plane a negative optical power, a positive optical power and a positive optical power respectively. The first optical element  4100  of the third optical group  4000  has a negative optical power and is shaped as a negative meniscus lens whose concave surface faces toward the object. The second surface  4100   a  of the first element  4100  is aspherical so as to correct a residual astigmatism across the field of view. The second optical element  4200  of the third optical group is a double convex lens. The third optical element  4300  of the third optical group is a double convex lens. The first surface  4300   a  of the third optical element  4300  is aspherical so as to correct residual coma and distortion shape across the field of view, and to achieve telecentricity for the beam at the image space. 
     The mutual configuration of the third optical group elements provides correction of field curvature, astigmatism and distortion. 
     The mutual combination of glass refractive indices and Abbe numbers of the optical elements in the three optical groups  2000 ,  3000  and  4000  provides apochromatic correction of the lens  1000 . Axial color and lateral color are also corrected. The mutual combination of changes of refractive index with temperature provides athermalization of the lens  1000  over the temperature range −15° C. to +40° C. 
     The embodiment of  FIG. 15  satisfies the following relations among the optical groups  2000 ,  3000 ,  4000  and their constituent optical elements:
 
−0.8 &lt;F   1000   /F′   2000 &lt;−0.6
 
1.45 &lt;F′   1000   /F′   3000 &lt;1.75
 
0.25 &lt;F′   1000   /F′   4000 &lt;0.45
 
0.85&lt; n   2200   /n   2400   =n   2200   /n   3400   =n   2200   /n   4100   =n   2200   /n   4200 &lt;1.1
 
0.75 &lt;n   2200   /n   2300   =n   2200   /n   3200   =n   2200   /n   4300 =&lt;0.95
 
0.8 &lt;n   2200   /n   3100 &lt;0.9
 
0.9 &lt;n   2200   /n   3300 &lt;1.15
 
1.15 &lt;V   2200   /V   2300   =V   2200   /V   2400   =V   2200   /V   3400   =V   2200   /V   4100 &lt;1.45
 
2.1 &lt;V   2200   /V   3100   =V   2200   /V   4300 &lt;2.4
 
0.65 &lt;V   2200   /V   3200 &lt;0.85
 
0.5 &lt;V   2200   /V   3300 &lt;0.7
 
0.8 &lt;V   2200   /V   4200 &lt;1.1
 
0.005 &lt;P   3200   /V   3200 &lt;0.007
 
0.2 &lt;dn/dT   2200   /dn/dT   2300   =dn/dT   2200   /dn/dT   2400   =dn/dT   2200   /dn/dT   3400 &lt;0.4
 
3&lt; dn/dT   2200   /dn/dT   3100 &lt;4
 
0.9&lt; dn/dT   2200   /dn/dT   4200 &lt;1.1
 
0.09&lt; dn/dT   2200   /dn/dT   4100 &lt;0.15
 
0.04&lt; dn/dT   2200   /dn/dT   3200   =dn/dT   2200   /dn/dT   4300 &lt;0.06
 
− 0 . 09 &lt; dn/dT   2200   /dn/dT   3300 &lt;−0.06
 
Where:
 
F′ 10  is the focal length of the lens  1000 ;
 
F′ 2000 , F′ 3000  and F′ 4000  are the focal lengths of the first, the second and the third optical groups  2000 ,  3000  and  4000 ;
 
n 2200 , n 2300  and n 2400  are the refractive indices for the optical elements  2200 ,  2300  and  2400  of the first optical group  2000 ;
 
n 3100 , n 3200 , n 3300  and n 3400  are the refractive indices for the optical elements  3100 ,  3200 ,  3300  and  3400  of the second optical group  3000 ;
 
n 4100 , n 4200  and n 4300  are the refractive indices for the optical elements  4100 ,  4200  and  4300  of the third optical group  4000 ;
 
V 2200 , V 2300  and V 2400  are the Abbe numbers for the optical elements  2200 ,  2300  and  2400  of the first optical group  2000 ;
 
V 3100 , V 3200 , V 3300  and V 3400  are the Abbe numbers for the optical elements  3100 ,  3200 ,  3300  and  3400  of the second optical group  3000 ;
 
V 4100 , V 4200 , and V 4300  are the Abbe numbers for the optical elements  4100 ,  4200 , and  4300  of the third optical group  4000 ;
 
P 3200  is the relative partial dispersion for F′-e spectrum for the second optical element  3200  of the second optical group  3000 ;
 
dn/dT 2200  is the refractive index change with temperature for the first optical element  2200  of the first optical group  2000 ;
 
dn/dT 2300  is the refractive index change with temperature for the second optical element  2300  of the first optical group  2000 ;
 
dn/dT 2400  is the refractive index change with temperature for the third optical element  2400  of the first optical group  2000 ;
 
dn/dT 3100  is the refractive index change with temperature for the first optical element  3100  of the second optical group  3000 ;
 
dn/dT 3200  is the refractive index change with temperature for the second optical element  3200  of the second optical group  3000 ;
 
dn/dT 3300  is the refractive index change with temperature for the third optical element  3300  of the second optical group  3000 ;
 
dn/dT 3400  is the refractive index change with temperature for the fourth optical element  3400  of the second optical group  3000 ;
 
dn/dT 4100  is the refractive index change with temperature for the first optical element  4100  of the third optical group  4000 ;
 
dn/dT 4200  is the refractive index change with temperature for the second optical element  4200  of the third optical group  4000 ; and
 
dn/dT 4300  is the refractive index change with temperature for the third optical element  4300  of the third optical group  4000 .
 
     The selection of optical powers of optical groups and elements, the selection of glass refractive indices, Abbe numbers and partial dispersions, and the selection of dn/dT values provides a high resolution imaging lens with chromatic and apochromatic correction while the defocus caused by changes in temperature is less than the depth of focus of the lens. 
     Wave front and MTF data for the embodiment of  FIG. 15  is presented in  FIG. 16  and  FIG. 17  respectively. The wave front is well corrected over the whole wavelength range and is polychromatic. The MTF shows good resolution and contract over the entire field. The RIM RAY curves in  FIG. 18  show the spherical aberration, coma and chromatic and apochromatic corrections over the wavelength range of 450 nm to 650 nm. Astigmatism data is presented in  FIG. 19A  and distortion data is presented in  FIG. 19B . The field is flat and the distortion corresponds to the F-theta law. Data regarding the change of the focus with temperature is presented in  FIG. 20 . The defocus over the temperature range of −15° to 40° is 5 μm, which is much less than the depth of focus. The lack of telecentricity is less than 6° across the field of view. The prescription of the lens of  FIG. 15  is presented in  FIG. 21 . The optical materials of the embodiment include optical glasses that are common and widely available commercially. 
     The foregoing description of the embodiments of the invention has been presented for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed. Many modifications and variations are possible in light of this disclosure. It is intended that the scope of the invention be limited not by this detailed description, but rather by the claims appended hereto.