Abstract:
A spectrograph that includes camera focusing optics with a primary mirror having a concave-shaped reflective mirror surface, a secondary mirror having a convex-shaped reflective mirror surface and positioned to receive light reflected by the primary mirror, a tertiary mirror having a concave reflective mirror surface and positioned to receive light reflected by the secondary mirror, and a field correcting lens comprising a convex lens surface in combination with a concave lens surface, wherein light received by said field correcting lens from said tertiary mirror enters said convex lens surface, traverses said field correcting lens, and exits from said concave lens surface. The optional field correcting lens is positioned such that the primary mirror, secondary mirror, tertiary mirror, and the field correcting lens share the common parent vertex axis.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This non-Provisional application is a Continuation-in-Part of a U.S. application having Ser. No. 15/335,315, filed on Oct. 26, 2016, which claims priority from a U.S. Provisional Application filed on Oct. 26, 2015 and having Ser. No. 62/246,398. The disclosure of each of the above-identified applications is incorporated herein by reference in its entirety. 
     
    
     TECHNOLOGY FIELD 
       [0002]    This invention relates to optical instruments for use in the measurement of properties of light, and specifically to spectrographs including echelle, linear array, and imaging spectrographs. 
       BACKGROUND 
       [0003]    An echelle spectrograph is an optical instrument that uses an echelle grating to diffract light with high dispersion and utilizes higher diffraction orders. As with other blazed diffraction gratings, the echelle grating contains a number of grooves. However, echelle gratings are specifically characterized by the large spacing between the grooves and, therefore, are characterized with a lower groove density than standard blazed gratings that are designed to be used in the 1 st  diffraction order. 
         [0004]    Light incident upon any ruled grating is split into several different diffraction orders. Each order is comprised of a different wavelength range that overlaps onto the same spatial location as light that is diffracted into other orders. The dispersion associated with each order is also different. The overlapping ranges of orders diffracted from the grating make it difficult to associate a particular wavelength with a given spatial location in the diffracted light. This ambiguity complicates the output spectrum and makes it more difficult to determine the correct wavelength emission produced by the source. 
         [0005]    Although this overlap between diffraction orders is generally an unwanted side effect, echelle gratings specifically use this effect to enhance the performance of the spectrograph. To this end, a second cross-dispersing element is used to spatially separate the orders. The individual diffraction orders, each with a separate (and sometimes overlapping) wavelength range and resolution, can then be analyzed without ambiguity. 
         [0006]    A lens-based spectrograph can have good resolution and very high throughput (˜f/2) over a limited wavelength range. If the wavelength range of operation needs to be shifted from the design wavelength of the lenses, or if a broad wavelength range is required to be simultaneously acquired such as with an echelle spectrograph, then chromatic aberration limits spectral resolution of a lens-based instrument. 
         [0007]    Typical broadband, all-reflective echelle spectrographs have a relatively high f/number, generally f/7 or greater camera focusing optics, limiting the total light that reaches the image plane and thereby decreasing the resulting image quality. Further, the high f/number of a typical echelle grating-based spectrograph prevents the use of such an instrument in certain applications such as Raman spectroscopy, where the detection of weak levels of light emission necessitates the use of a spectrograph with a very low f/number. 
         [0008]    A linear array spectrograph uses a standard ruled grating, usually (but not always) in the 1 st  order. A 1-D linear array sensor is combined with the spectrograph to make a very compact and inexpensive spectrometer. These instruments have limited wavelength coverage but can be appropriate for some applications such as Raman spectroscopy where a limited wavelength range is possible. All-reflective, linear array spectrographs usually implement camera focusing optics that are f/4 or slower, plus the linear array length and resolution can be limited by the quality of the camera focusing optics. 
         [0009]    An imaging spectrograph is similar to a linear array spectrograph except that it utilizes a 2-D sensor. A tall entrance aperture can be used with an imaging spectrograph because the image plane is better corrected than a linear array spectrograph in the direction perpendicular to the grating dispersion. The tall entrance aperture permits either much better throughput or multiple fiber inputs aligned along the entrance aperture. The multiple fiber inputs can direct light from various light sources enabling simultaneous monitoring of multiple input channels. The tall slit allows the spectrograph to monitor wavelength information along one axis, while simultaneously measuring spatial information along the other axis. All-reflective imaging spectrographs are typically f/4 or slower, plus the size of the 2-D image plane is limited. 
       SUMMARY 
       [0010]    Certain embodiments of the current disclosure include a primary mirror having a concave-shaped reflective mirror surface, a secondary mirror having a convex-shaped reflective mirror surface and positioned to receive light reflected by the primary mirror, a tertiary mirror having a spheroidal (spherical concave) reflective mirror surface and positioned to receive light reflected by the secondary mirror, and a field correcting lens comprising a first lens surface in combination with a second lens surface (positive meniscus lens), wherein light received by said field correcting lens from said tertiary mirror enters said convex lens surface, traverses said field correcting lens, and exits from said concave lens surface. The field correcting lens is positioned such that the primary mirror, secondary mirror, tertiary mirror, and the field correcting lens substantially share the common parent vertex axis. 
         [0011]    Further, in certain embodiments, a spectrograph contains a diffraction grating; a primary mirror having a concave reflective surface and positioned to reflect light that has interacted with the diffraction grating; a secondary mirror having a convex reflective surface and positioned to receive said light from the primary mirror; a tertiary mirror having a concave reflective surface and positioned to receive said light reflected by the secondary mirror, wherein the primary mirror, the secondary mirror, and the tertiary mirror form a three-mirror anastigmat (TMA) with a shared TMA parent vertex axis; an entrance aperture; an aperture stop; and a collimator mirror positioned to receive light that has been transmitted through the entrance aperture and form a collimated beam of light directed towards the diffraction grating through the aperture stop. 
         [0012]    Moreover, the diffraction grating is positioned to receive and diffract light that has passed through the aperture stop into a plurality of beams spatially dispersed by wavelength; the diffraction grating is configured to be rotatable about a first axis that is perpendicular to the surface of a first plane of the grating such that a dispersion direction is caused to be perpendicular to a second plane, the second plane passing through the primary mirror, the secondary mirror, and the tertiary mirror of the TMA; the diffraction grating configured to be rotatable about a second axis such that a rotation angle is substantially close to a blaze angle of the grating, wherein the second axis is parallel to a groove direction on the surface of the diffraction grating; and the diffraction grating configured to be rotatable in the first plane of the grating about a third axis at an angle chosen to result in cancellation of the geometric distortion and causing said plurality of beams to intersect an image plane along a straight line in the center of the image plane, wherein the third axis is perpendicular to the groove. 
         [0013]    In addition, in certain embodiments, the diffraction grating is positioned to receive and diffract light that has passed through the aperture stop into a plurality of beams spatially dispersed by wavelength; the diffraction grating is configured to be rotatable about a first axis that is perpendicular to the surface of a first plane of the grating such that a dispersion direction is caused to be parallel to a second plane, the second plane passing through the primary mirror, the secondary mirror, and the tertiary mirror of the TMA; the diffraction grating configured to be rotatable about a second axis such that a rotation angle is substantially close to a blaze angle of the grating, wherein the second axis is parallel to a groove direction on the surface of the diffraction grating. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0014]    The disclosure will be better understood from a reading of the following detailed description taken in conjunction with the drawings in which like reference designators are used to designate like elements, and in which: 
           [0015]      FIG. 1  illustrates the movement of radiation through one embodiment of the echelle spectrograph; 
           [0016]      FIG. 2  shows a different embodiment of the echelle spectrograph; 
           [0017]      FIG. 3  demonstrates two components of the embodiment of the echelle spectrograph illustrated in  FIG. 1 ; 
           [0018]      FIG. 4  demonstrates the echelle spectrograph&#39;s wavelength coverage and resolution (top image) and a standard Czerny-Turner imaging spectrograph&#39;s wavelength coverage and resolution (bottom image); 
           [0019]      FIGS. 5A, 5B and 5C  illustrate the effect of the fold mirror rotation on resolution for the echelle spectrograph; 
           [0020]      FIG. 6  illustrates the embodiment of the echelle spectrograph in  FIG. 2  with dimensions; 
           [0021]      FIG. 7  shows a different perspective of the embodiment of the echelle spectrograph in  FIG. 2  with dimensions; 
           [0022]      FIG. 8  illustrates another embodiment of the echelle spectrograph with different dimensions; 
           [0023]      FIG. 9  shows a different perspective of the embodiment of the echelle spectrograph in  FIG. 8 ; 
           [0024]      FIG. 10  illustrates yet another embodiment of the echelle spectrograph with different dimensions; 
           [0025]      FIG. 11  shows a different perspective of the embodiment of the echelle spectrograph in  FIG. 10 ; 
           [0026]      FIG. 12  illustrates an embodiment of a linear array or a 2-D imaging sensor with the use of the three mirror anastigmat (TMA), without a corrective field lens in the camera focusing optics component; 
           [0027]      FIG. 13  shows a different perspective of the embodiment of the imaging or linear array spectrograph in  FIG. 12 ; 
           [0028]      FIG. 14A  is a different embodiment of a linear array or a 2-D imaging sensor whereas the grating has been rotated 90 degrees about an axis that is perpendicular to a plane of a grating, thereby resulting in a change of a general direction in which the diffracted light is spatially dispersed;  FIG. 14B  shows the location of 6 wavelengths along a 500 μm×12.8 mm linear array sensor for the embodiment in  FIG. 14A . 
           [0029]      FIG. 15  shows a different perspective of the embodiment of the imaging or linear array spectrograph illustrated in  FIG. 14A ; 
           [0030]      FIG. 16A  and  FIG. 16B  illustrate an embodiment wherein the grating is rotated to cancel the geometric distortion on the image plane, as shown in  FIG. 16B . 
           [0031]      FIG. 17  illustrates the difference in root mean square (RMS) spot diameter when offsetting the entrance slit from the nominal parent vertex location and by tilting the secondary mirror. 
           [0032]      FIG. 18  illustrates yet another embodiment of a linear array or a 2-D imaging sensor including a field correcting lens; and 
           [0033]      FIG. 19  shows a different perspective of the embodiment of the imaging or linear array spectrograph illustrated in  FIG. 18 . 
       
    
    
     DETAILED DESCRIPTION 
       [0034]    This disclosure is described in preferred embodiments in the following description with reference to the Figures, in which like numbers represent the same or similar elements. Reference throughout this specification to “one embodiment,” “an embodiment,” or similar language means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present disclosure. Thus, appearances of the phrases “in one embodiment,” “in an embodiment,” and similar language throughout this specification may, but do not necessarily, all refer to the same embodiment. 
         [0035]    The described features, structures, or characteristics of the disclosure may be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are recited to provide a thorough understanding of the embodiments of the disclosure. One skilled in the relevant art will recognize, however, that the disclosure may be practiced without one or more of the specific details, or with other methods, components, materials, and so forth. In other instances, well-known structures, materials, or operations are not shown or described in detail to avoid obscuring aspects of the disclosure. 
         [0036]    Referring to  FIG. 3 , in certain embodiments, an echelle spectrograph  100  can be divided into two sets of components. The first set of components is light collimating and dispersing optics  310 , and the second set of components is camera focusing optics  320 . Referring to  FIGS. 1 and 2 , the first set  310  includes an entrance aperture  101 , a collimator mirror  105 , an aperture stop  110 , a diffraction grating  130 , a cross-dispersing prism  140 , and a fold mirror  150 . In certain embodiments, the fold mirror  150  comprises a reflector with a flat surface. Moreover, the fold mirror  150  has a first axis  152  that is defined in the plane of the mirror  150  (and, in reference to  FIG. 1 , substantially perpendicular to the plane of  FIG. 1 ) and a second axis  154  that is contained in the same plane of the mirror  150  perpendicular to the first axis  152 . 
         [0037]    Further, the camera focusing optics  320  ( FIG. 3 ) contains the optics configured to focus light onto the image plane, commonly referred to as the “camera focusing optics”. This camera focusing optics  320  includes a combination of three mirrors aggregately configured as a three mirror anastigmat (TMA). Specifically, and referring again to  FIG. 1 , the TMA within the camera focusing optics  320  includes a primary mirror  160  having concave-shaped reflecting surface, a secondary mirror  170  having convex-shaped reflecting surface, and a tertiary mirror  180  having concave-shaped reflecting surface. The TMA is optically followed by a field correcting lens  190 , which relates light incident thereon on an image plane  195 . In some embodiments, the field correcting lens  190  is a positive meniscus field correcting lens. Further, the field correcting lens  190  is formed from an off-axis portion of a positive meniscus lens. In other embodiments, the field correcting lens  190  is a biconvex, piano-convex, piano-concave, or negative meniscus lens. In yet other embodiments, the field correcting lens  190  is a bi-concave corrective element. With different types of the field correcting lens used, the parent axis of the field corrective lens is located on or substantially close to the TMA parent vertex axis  322  shown in  FIG. 3 . “Substantially close” is defined as the vertex axis of the field corrective lens is translated in X or Y by less than a millimeter from the TMA parent vertex axis  322  or the parent vertex axis of the field corrective lens is tilted less than 1 degree with respect to the TMA parent vertex axis  322 . The field correcting lens  190  is located between the tertiary mirror  180  and the image plane  195 . 
         [0038]    Referring to  FIG. 1 , light incident onto the fold mirror  150  is directed by the fold mirror  150  to first strike the primary mirror  160 , and is further reflected to the secondary mirror  170 . The mirror  170 , in turn, redirects this light to the tertiary mirror  180 . The TMA, with three off-axis mirrors, provides a much better corrected angular field of view than other types of camera focusing optics that utilize only one or two corrective surfaces. The more corrective surfaces an optical design has available, the smaller the optical aberrations can become and the larger the useable field of view. As an example,  FIG. 4  shows comparison images from a standard Czerny-Turner (CT) type of spectrograph (bottom image) with an existing TMA-based EMU-120/65 spectrograph (EMU) from Catalina Scientific Instruments, LLC (top image). The EMU has three corrective surfaces in the camera focusing optics while the CT design has a single corrective element. The TMA-based EMU provides a highly corrected 2D image plane allowing multiple spectral orders to be displayed simultaneously on the image plane, resulting in excellent spectral resolution and very broad wavelength coverage. The CT design is limited to a very narrow wavelength band and can only operate in one diffraction order, typically 1 st  order. 
         [0039]    Referring to  FIG. 1  again, in certain embodiments, a cone of light is accepted by the echelle spectrograph  100  through the entrance aperture  101  and then propagated toward the collimator mirror  105  as a cone of light  202 . In the embodiments illustrated in  FIGS. 1 and 2 , the off-axis section of the collimator mirror  105  has a conic constant of −1 (rendering this off-axis section to be a parabolic section of the reflector  105 ) and radius of curvature of 1200 mm (rendering this off-axis section to be a concave portion of the reflector). 
         [0040]    In further reference to  FIGS. 1 and 2 , light beam  202  is reflected by the collimator mirror  105  to produce a collimated beam of light  210 . The beam  210  passes through the aperture stop  110 , which is centered ( 107 ) on the bundle of rays arriving to the stop  110  from the collimator mirror  105 . If the entrance aperture  101  is located at the focal point of the collimator parent vertex axis  312 , the optical aberrations present in a wave front of the beam  210  are minimized or substantially absent, and therefore, the beam  210  approximates the perfectly collimated beam of light. In some embodiments, the entrance aperture  101  may be offset from the parent collimator mirror by less than 1 mm. Astigmatism introduced into the spectrograph by offsetting the entrance aperture can be used to cancel residual astigmatism found in the camera focusing optics  320  in  FIG. 3 . 
         [0041]    As those skilled in the art readily appreciate, an aperture stop limits the brightness of an image by restricting the size of the angular cone of light passing through the entrance aperture and collimator mirror. Therefore, the aperture stop  110  is one of the primary components of an embodiment of the present system that controls the amount of light transmitted through echelle spectrograph  100 . In certain embodiments, the aperture stop size can be user interchangeable to allow the desired amount of light into echelle spectrograph  100 . Neglecting the effects of diffraction, a smaller aperture stop usually produces a sharper image at the image plane  195  as a result of reducing optical aberrations. Echelle spectrograph  100  can be optimized for maximum light throughput with a large aperture stop  110  or best spectral resolution with a small aperture stop  110 . In the embodiment in  FIG. 1 , the aperture stop has been located half way between the collimator mirror and grating. Aperture stop  110  can also be located near the grating or anywhere between the collimator and diffraction grating as long as it does not block rays  202  going to collimator  105  or rays  230  traveling from grating  130  to prism  140 . 
         [0042]    Light beam  210  passes through the aperture stop  110 , and forms the beam of light  220 . Beam  220  is further directed onto the diffraction grating  130 . The beam of light  220  carries polychromatic light that is electromagnetic radiation at a plurality of wavelengths. The nature of the light source determines the specific constituent wavelengths of light  220 . 
         [0043]    As those skilled in the art will readily appreciate, the echelle grating  130  spatially separates incident light beam  220  into a plurality of beams at respectively corresponding constituent wavelengths, i.e., light  220  is dispersed by echelle grating  130 . When light beam  220  is incident on echelle grating  130  at an angle θ i  (measured from the normal to the surface of the grating), the incident light is diffracted into several beams. The beam that corresponds to direct transmission (or specular reflection in the case of a reflection grating) forms the zeroth order of diffraction, and is denoted with an index m=0. The other diffraction orders correspond to diffraction angles that are different from the specula angle of reflection and are represented by non-zero integer values of the index m. For a groove (grating) period d and an incident wavelength λ, the grating equation (1) gives the value of the diffracted angle θ m (λ) in the order m: 
         [0000]        d ×(sin θ m (λ)+sin θ i )= m×λ   (1)
 
         [0044]    In a related embodiment, the echelle grating  130  can be replaced with another grating of different groove density or blaze angle. Changing the blaze angle or groove period of grating  130  results in different spectral characteristics of light at the image plane  195 , which in turn affects spectral resolution and diffraction order spacing. In different implementations, different echelle gratings  130  with different groove periods and/or blaze angles can be used. 
         [0045]    Light  230  that is reflected by and/or diffracted at the diffraction grating  130  forms a plurality of beams dispersed according to the wavelength of light. The diffracted beams corresponding to consecutive diffraction orders spatially overlap, thereby making it difficult to determine the correct wavelength for a chosen spectral feature. 
         [0046]    Light  230  is further directed onto a cross-dispersive prism  140 , where it is further dispersed upon traversal of the prism  140  according to wavelength, but in a direction perpendicular to the dispersion direction of the grating. 
         [0047]    Prism  140  controls the total range of wavelengths passing through to the image plane  195 . By either changing the apex angle  142  of prism  140  or by changing the material of prism  140 , different wavelength ranges can be utilized at the image plane  195 . For example, in one embodiment of the echelle spectrograph  100  includes a fused silica (FS) prism  140 . The resulting range of wavelengths delivered to the plane  195  is from about 180 nm to above 1.1 microns. As used herein, “about” means plus or minus 10% difference in any measurements. If prism  140  is made of CaF2, one limit of the wavelength range at the plane  195  can be extended down to about 150 nm. Another embodiment can include a BK7 glass prism  140 . BK7 has higher dispersion than that of FS or CaF2, but it does not transmit light below about 340 nm. The wavelength range of the echelle spectrograph  100  in this case would be from about 340 nm to about 1.1 microns; at the same time, the spectral order separation is larger when using BK7 prism. A taller entrance aperture  101  can then be used to increase the throughput of this embodiment of the instrument containing a BK7 glass prism  140 . 
         [0048]    Many optical materials including FS, CaF2 and glass have good transmission above 1.1 microns. However, silicon based sensors cannot detect wavelengths longer than 1.1 microns, so spectrographs are limited to a maximum wavelength of 1.1 microns when using silicon-based sensors. When using InGaAs or other infrared sensitive detectors, the TMA-based echelle spectrograph can have good sensitivity beyond 1.1 μm. The long-wavelength limit is determined by the detector sensitivity, and the transmission characteristics of the prism and the corrective field lens. The wavelength range of an echelle spectrograph is also dependent on the useable area of the image plane. The larger the image plane, the more spectral orders can be located on the sensor, resulting in larger wavelength coverage. 
         [0049]      FIG. 1  shows light  240  exiting prism  140  and then directed onto the folding mirror  150 . In certain embodiments, the folding mirror  150  is configured to rotate only about the first axis  152  by 42 degrees as shown in  FIG. 1 . In other embodiments, folding mirror  150  is first configured to rotate about the first axis  152  and then is configured to rotate about the second axis  154  in the plane of the mirror.  FIG. 2  shows an embodiment where the fold mirror has been rotated about both the first axis  152  and the second axis  154 . It has been rotated −5 degrees about axis  152  and then rotated by +45 degrees about the second axis  154 . 
         [0050]    Referring again to  FIG. 1 , the folding mirror  150  is tilted in such a way as to prevent obstructions to light beams  250 ,  260 ,  270 , and  280  that propagate towards and between the mirrors of the TMA. Further, the folding mirror  150  is disposed at such an angle as to present no optical obstruction to other spectrograph components. As illustrated in  FIG. 2 , by rotating the folding mirror  150  about both axes  152 ,  154  in the plane of the mirror, the volume of the echelle spectrograph  100  can be decreased to create a more compact design.  FIG. 3  shows the location of a parent vertex axis  322 , which is defined as the vertex axis of the full-sized parent mirrors (only portions of the full-sized parent mirrors are shown in the figures) of each of the three mirrors within the TMA. The off-axis primary mirror  160 , the off-axis secondary mirror  170 , and the off-axis tertiary  180 , which are respectively subsections of each one&#39;s parent mirror, substantially share the TMA parent vertex axis  322 . “Substantially share” is defined as following: in some embodiments, the primary mirror  160 , the secondary mirror  170 , and the tertiary mirror  180  shares the parent vertex  322 ; and in other embodiments, the secondary parent vertex axis can be tilted +1.0 degree to about −1.0 degree relative to the parent vertex axis  322 . Alternatively or in addition, the parent vertex axis  322  and the secondary parent vertex axis can be separated (translated) with respect to one another by as much a +2.0 mm to −2.0 mm in X or Y directions and still be considered to be “substantially shared.” Such tilt can help cancel residual astigmatism in the TMA for a sharper focus at image plane  195 . The compact design in  FIG. 2  allows the camera focusing optics  320  to be located closer to the parent vertex axis  322  which minimizes spectrograph aberrations, as one skilled in optical design appreciates. In certain embodiments, the primary mirror  160  can be located closer to the tertiary mirror  180 , without causing obstructions to rays  260  passing between the primary mirror  160  and secondary mirror  170  by the fold mirror  150 . The rays  260  approaching the secondary mirror  170  have a shallow angle relative to the parent vertex axis  322  and rays  280  departing the secondary mirror  170 , also have a small angle relative to the parent vertex axis  322  as rays  280  approach the tertiary mirror  180 . The shallower the angle of rays relative to the TMA vertex axis, the better and sharper the image quality at the image plane  195 , as those skilled in the art will appreciate. 
         [0051]    As an example of the image resolution improvement,  FIGS. 1 and 2  show similar optical designs with fold mirror  150  rotated about axis  152  in  FIG. 1  and with the fold mirror axis  150  rotated about both  152  and  154  axes in  FIG. 2 . The resulting image quality for the two embodiments are shown in  FIGS. 5A-5C , which show the RMS spot diameter across  3  different orders on the image plane. The RMS spot diameter is a measure of the smallest focal spot diameter that can be measured on the image plane (excluding diffraction effects) and it is a measurement of the optical aberrations in the system. The smaller the RMS spot diameter, the better the spectral resolution. Referring to  FIGS. 5A-5C , the dashed lines represent the RMS spot diameter obtained with the embodiment of the spectrograph wherein the fold mirror  150  was rotated about axis  152  and the solid lines represent the RMS spot diameter obtained with the embodiment of the spectrograph wherein the fold mirror  150  was rotated about both axes  152  and  154 . The solid lines show decreased RMS spot diameter under different diffraction orders compared to the dashed lines, thus, the embodiment of the spectrograph illustrated in  FIG. 2  has better spectral resolution than the embodiment of the spectrograph illustrated in  FIG. 1 . The improved resolution is achieved because there is less interference among mirrors  150 ,  160 ,  170 , and  180  and their associated rays  250 ,  260 ,  270  and  280  so mirrors  150 ,  160 ,  170 , and  180  can be disposed closer together. Since the mirrors  150 ,  160 ,  170 , and  180  are closer together, the mirrors are closer to on-axis relative to their substantially shared TMA parent vertex axis  322 , shown in  FIG. 3 . 
         [0052]    Further, as shown in  FIG. 1 , light  240  is reflected by the folding mirror  150  to form a beam of light  250 . For any given wavelength, this beam remains collimated. However, light at different wavelengths reflects off of the folding mirror  150  at slightly different angles because of the dispersion by grating  130  and prism  140 . 
         [0053]    Light  250 , as shown in  FIG. 3 , is incident on the camera focusing optics. The first mirror of the TMA portion of the camera focusing optics is the primary mirror  160 . In the embodiment displayed in  FIG. 2 , the primary mirror  160  has a radius of curvature of about 604.372 mm (concave) and a conic constant of −0.63642 (rendering this mirror to be ellipsoidal in shape). 
         [0054]    Reflected light  260  in  FIG. 1  converges upon propagation from the primary mirror  160  to an intermediate focus  165  and then diverges upon further propagation from the intermediate focus  165  towards the TMA&#39;s secondary mirror  170 . In certain embodiments, an opaque baffle containing an aperture can be disposed at the intermediate focus  165  such that light  260  passes through this aperture in the baffle, and strikes the secondary mirror  170  afterwards. Such aperture serves to block most of stray light from reaching the image plane  195 . 
         [0055]    In the embodiment shown in  FIG. 2 , the secondary mirror  170  has a radius of curvature of 312.0 mm (convex) and a conic constant of 0. In such embodiment, therefore, the secondary mirror  170  is shaped as a spheroidal convex mirror. In other embodiments, the secondary mirror  170  comprises an ellipsoidal (0.0&gt;conic constant&gt;−1.0), parabolic (conic constant=−1.0) or hyperbolic (conic constant&lt;−1.0) convex mirror. 
         [0056]    Light  260  is reflected by the secondary mirror  170  and forms a diverging beam of light  270 , which passes onto the TMA&#39;s tertiary mirror  180 . In certain embodiments, the tertiary mirror comprises an ellipsoidal (0.0&gt;conic constant&gt;−1.0), spheroidal (conic constant=0), or oblate spheroidal (conic constant&gt;0) concave mirror. In general, it is preferred to have the smaller value of the conic constant, because the smaller the conic constant (that is, the more of a negative value), the better the correction at the image plane (but the larger the mirror and spectrograph become). 
         [0057]    In certain embodiments, the echelle spectrograph utilizes a spherical (spheroidal) mirror for the tertiary mirror  180 . For example, in the embodiment in  FIG. 2 , the tertiary mirror  180  may have a radius of curvature of about 379.681 mm (concave) and a conic constant of 0. The spheroidal mirror is much easier to make than aspherical mirrors, resulting in lower fabrication costs. 
         [0058]    Diverging reflected light  270  from the secondary mirror  170 , as shown in  FIG. 1 , approaches the tertiary mirror  180 . Light reflected from the tertiary mirror  180  converges as a light beam  280 . The beam  280  is directed onto a field correcting lens  190  through a second stray light aperture  112 . Light  280  passes through the first convex surface  192  of the field correcting lens  190 . The light then exits the field correcting lens  190  through its second surface  194 , which is concave, to focus onto the image plane  195 . In other embodiments, the first surface  192  is spherical and concave and the second surface  194  is spherical and convex. In yet other embodiments, the first surface  192  is convex and the second surface  194  is flat. In certain embodiments such as  FIG. 2 , the first surface  192  is spherical and convex with a 149.396 mm radius of curvature. The second surface  194  (of the field correcting lens  190 ) is spherical and concave with a 405.573 mm radius of curvature (positive meniscus lens). Further, in certain embodiments, the field correcting lens  190  parent vertex axis is located on the parent axis shared by the TMA primary  160 , secondary  170 , and tertiary  180  mirrors. 
         [0059]    The embodiment may be further complemented with a camera sensor located at the image plane  195 . In certain embodiments, a sensor is a scientific, digital CCD, ICCD, CID, CMOS, InGaAs, HgCdTe or other optical detector used to collect image data of the light from an emitting source. 
         [0060]    One way to change the f/number of the input optics of the echelle spectrograph  100  is to change the focal length of the collimator mirror  105 . For purposes of this discussion, the f/number=1/(2×(sin θ)), where θ is a half angle of a cone of light passing through the entrance aperture  101 . The numerical aperture (NA) for the entrance aperture  101  is defined as NA c =sin(θ), or equivalently, 
         [0000]        NA   c =sin [arctan { D /(2× F   c )}]˜ D /(2× F   c ) when  F   c   &gt;&gt;D.   (2)
 
         [0000]      and, 
         [0000]        f   c /number=1/(2× NA )− F   c   /D  when  F   c   &gt;&gt;D.   (3)
 
         [0000]    where D is the diameter (if circular) of aperture stop  110  and F c  is the effective off-axis focal length of the collimator mirror  105 . In the situation when the aperture stop  110  is non-circular, the NA and f c /number can be generalized by an “averaged NA” or averaged f c /number. 
         [0061]    The f i /number of the camera focusing optics is independent of the f c /number of the collimator mirror. Equations 2 and 3 are modified to become, 
         [0000]        NA   i =sin [arctan { D /(2× F   i )}]˜ D /(2× F   i ) when  F   i   &gt;&gt;D.   (4)
 
         [0000]      and, 
         [0000]        f   i /number=1/(2× NA   i )˜ F   i   /D  when  F   i   &gt;&gt;D.   (5)
 
         [0000]    where F i  is the effective focal length of the camera focusing optics and D is once again the diameter of the aperture stop. For clarity, the effects of anomorphic magnification introduced by the grating and prism have been ignored in these equations. In some embodiments when large blaze gratings are implemented, the anomorphic f i /number, NA i , and F i  are location dependent on the image plane. 
         [0062]    Broadband (&lt;200-1100 nm wavelength coverage) echelle spectrographs discussed in related art typically contain f i /7 (NA i =0.07) or larger f i /number camera focusing optics. In contradistinction, the camera focusing optics of the echelle spectrograph  100  utilizes an f i /2 optical system (NA i =0.25), in some embodiments. The high NA i  value is approximately an order of magnitude improvement in light throughput compared to devices of related art (assuming similar resolution, wavelength coverage, and equivalent focal length of the camera focusing optics). 
         [0063]    The total amount of light passing through the entrance aperture  101  is defined by the étendue (E) of the system at the aperture stop  110 . At the aperture stop  110 , E is proportional to the product of the area of the entrance aperture  101  and the square of the numerical aperture. Therefore, increasing either the numerical aperture of light passing through entrance aperture  101  or increasing the area of entrance aperture  101  increases total throughput (E) of the instrument. However, as those skilled in the art will appreciate, in general, the spectral resolution (defined by the full width at half maximum of a spectral emission line, FWHM) of an instrument is approximately proportional to the width of the entrance aperture  101  (when aberrations and diffraction effects are excluded). 
         [0064]    As those skilled in the art will further appreciate, the light passing through the echelle spectrograph  100  contains multiple spectral orders that are spatially separated, or dispersed, as light passes through prism  140 . Furthermore, the height of entrance aperture  101  on the image plane is preferably smaller than the distance between the neighboring spectral orders at image plane  195  to reduce or even eliminate cross-talk between the spectral orders. Therefore, the size of the entrance aperture  101  is limited in both height and width to provide for good spectral order separation and high spectral resolving power (wavelength/FWHM) at the image plane  195 . The preferred way to increase throughput is to increase the numerical aperture (or, decrease the f/number). 
         [0065]    It is important to note that the light source is disposed in optical (radiative) communication with (that is, optically coupled to) the entrance aperture  101 . Furthermore, to maximize throughput of light, the f/number of the optics associated with the light source that is externally coupled to entrance aperture  101  shown in  FIG. 1  is preferably matching the f c /number of the collimator mirror defined by F c  and D (see equations 2 and 3). Each embodiment of the external optical coupling to the entrance slit can have a very different f/number. For example, a typical effective f/number of an optical fiber is f/2.3 (NA=0.22) and the f/number of a telescope can be f/16 or higher. 
         [0066]    In certain embodiments, echelle spectrograph  100  can have collimator mirror  105  of a different focal length while maintaining the same mirror diameter and aperture stop D. For example, if the focal length of collimator mirror  105  is doubled, then the f c /number of the collimator as defined by Equation 3 is increased by a factor of about two (NA c  is reduced in half) if D remains unchanged. The magnification provided by the echelle spectrograph  100  is defined as a ratio of the effective focal length of the camera focusing optics (Fi) to the off-axis effective focal length of the collimator mirror (Fc): 
         [0000]        M=Fi/Fc   (6)
 
         [0067]    When the value of F c  is doubled, the value of M is halved. The image of entrance aperture  101  projected onto image plane  195  at a given wavelength (or equivalently, the FWHM of a spectral emission line) is then approximately half the size as with the original embodiment. It is therefore possible to double the dimensions of the entrance aperture  101  (in both height and width) to preserve the total throughput (or étendue E) of the echelle spectrograph  100  without degrading spectral resolution or changing any of the optics besides the collimator mirror. 
         [0068]    The echelle spectrograph  100  can be configured to match any light source from approximately f/2 to &gt;f/16 while maximizing étendue by simply changing Fc of the collimator mirror and the size of the entrance aperture  101 . At the same time, the spectral resolving power (wavelength/FWHM) and diffraction order overlap remains unchanged. The image quality and order location at image plane  195  also remains unchanged as long as entrance aperture  101  is at the correct location (with the appropriate size) and D remains unaltered. 
         [0069]    The field correcting lens  190  adds two more corrective optical surfaces when optimized with the other three TMA mirror surfaces for a total of 5 corrective surfaces. After optimization, the effective focal length (F i ) of the camera focusing optics can be increased as compared to that of a design without the field correcting lens. This longer F i  results in higher spectral resolution for a fixed size of the spectrograph. A field correcting lens typically improves field curvature at the image plane when it is added to an existing optical design. The TMA by design may not have field curvature. When simultaneously optimizing the first surface  192  and the second surface  194  of the field correcting lens  190 , and the TMA mirrors ( 160 ,  170 ,  180 ), most camera focusing optics aberrations (spherical, astigmatism, coma, field curvature, etc.) are significantly reduced. For example, using a design without the field correcting lens  190  and a narrow entrance aperture  101 , the average minimum RMS slit image diameter that can be focused on the image plane  195  is 5.4 microns using a 35 mm diameter aperture stop (f i /5.4 camera focusing optics). Including the field correcting lens  190  in a spectrograph with similar F i  and aperture stop, the average RMS spot diameter becomes 3.6 microns. On average, the aberrations have been reduced 33% by including the field correcting lens. Using a 50 mm (f i /3.8) aperture stop  110 , the average minimum RMS slit image diameter becomes 16.6 microns for the spectrograph without the field correcting lens  190 , making it unusable for many applications. The spectrograph with the field correcting lens  190  has a very good 6.4 micron average minimum RMS spot diameter across the image plane  195 , in all orders. In this example, including the field correcting lens  190  in the spectrograph decreased aberrations on average by 61.5%. Moreover, the useable size of a sensor is increased, i.e., a much larger corrected area at the image plane  195  is achieved. This results in higher throughput and resolving power since higher prism and grating dispersion can be utilized. A further advantage of using the field correcting lens  190  is that the distance between the fold mirror  150  and the secondary mirror  170 , and the distance between the secondary mirror  170  and the image plane  195  are increased compared to a spectrograph without the field correcting lens  190 . Thus obstructions of rays  260  by the flat mirror  150  and obstructions of beam  280  by the secondary mirror  170  are minimized. For example, a 50 mm aperture stop  110  would require the fold mirror  150  and secondary mirror  170  to be so large that they would obstruct each other, making a design with a 50 mm aperture stop  110  impractical. 
         [0070]    A longer F i  of the echelle spectrograph  100  results in higher spectral resolving power (wavelength/FWHM). In certain embodiments, the spectral resolving power of the echelle spectrograph  100  exceeds 200,000 for a field portable instrument. The typical value of the resolving power for a field portable conventionally-configured echelle spectrograph is on the order of a few thousand.  FIG. 6  (a perspective view as seen along y-axis) and  FIG. 7  (a perspective view as seen along x-axis) show the dimensions of the instrument with f i /3.8 camera focusing optics and resolving power of 200,000. 
         [0071]    Moreover, because the spectral orders are located spatially further apart from one another, due to the larger useable size of the sensor, a larger entrance aperture  101  can be used without causing interference between the adjacent diffraction orders. For example, in one embodiment that does not contain (is devoid of) the field correcting lens  190 , the maximum size of the entrance aperture  101  is about 25 microns without adjacent spectral order cross-talk. When a field correcting lens  190  is employed, however, the maximum size of the entrance aperture  101  can be about 56 microns without causing significant order cross-talk. Employing the field correcting lens  190 , therefore, allows a combination of better spectrograph throughput (taller slit) and better resolving power (higher dispersion characteristics). 
         [0072]    In certain embodiments,  FIG. 8  (a view in the XZ plane) and  FIG. 9  (a view in the YZ plane) show the design and dimensions of a handheld field lens-corrected TMA echelle spectrograph with all of the optics aligned in a single plane with the fold mirror rotated about the axis perpendicular to the plane of the page on  FIG. 8 . The dimensions of the instrument  800  are 110 (l)×50 (w)×75 (h) mm. This handheld design can achieve a spectral resolving power of higher than 10,000 with complete wavelength coverage in the spectral range from 180 to 1100 nm, when the appropriate camera is used.  FIG. 10  (a view in the XZ plane) and  FIG. 11  (a view in the YZ plane) show a similar handheld echelle spectrograph with a 10,000+ resolving power and the 180-1100 nm range of the wavelength coverage, with the fold mirror axis tilted around both axis, which facilitates the reduction of the volume of the device. The dimensions of this instrument  800  could be 75 (l)×60 (w)×50 (h) mm. The folded echelle spectrograph  800  also has better aberration correction than the embodiment with the fold mirror tilted around just the axis perpendicular to the plane of the page. Either design has an order of magnitude better resolving power than existing handheld spectrographs and in many cases, better throughput. 
         [0073]      FIG. 12  displays an embodiment of a spectrograph  1200  in the XZ plane. The spectrograph  1200  can be an imaging spectrograph or a linear array spectrograph. In certain embodiments, the spectrograph  1200  is a compact and handheld instrument.  FIG. 13  displays the YZ plane of the spectrograph  1200  from  FIG. 12 . This embodiment is simpler than an echelle spectrograph and may be appropriate for use with Raman spectroscopy or other applications requiring a limited wavelength coverage with high resolution. This embodiment of the imaging spectrograph is similar to that of the echelle spectrograph illustrated in  FIG. 1 , however, the imaging spectrograph illustrated in  FIG. 12  does not include a prism, a fold mirror, or a field correcting lens. It uses a standard 1 st  order grating  1230  and not an echelle grating. A wavelength sorting filter  1220  is commonly inserted into the beam near an aperture stop  1210  although it can be located anywhere in the light path of the spectrograph. The order sorting filter blocks all wavelengths except the wavelengths associated with a single diffraction order to prevent order confusion on an image plane  1295 . The wavelength coverage for this embodiment is 1.03 to 1.562 microns using a 12.8 mm long sensor and is designed for use with an InGaAs linear array sensor with 25×500 micron pixels. 
         [0074]    The embodiment for the imaging spectrograph in  FIG. 12  has light entering the spectrograph  1200  at entrance aperture  1201 . Rays  1302  forming a cone of light from entrance aperture  1201  reflect from collimator mirror in a collimated beam  1310  toward aperture stop  1210 . Rays  1320  travel through aperture stop  1210  and reflect and diffract from grating  1230 . Grating  1230  can be a standard ruled grating used in 1 st  order or other lower orders. It can also be a holographic, lithographic or other type of grating used in one of the lower grating orders, normally Order  1 . The grating can either be a reflection or transmission grating. Rays  1350  travel from the grating to the TMA camera focusing optics. Rays  1350  reflect from the concave ellipsoidal primary mirror  1260  in a converging beam  1360 . Light next reflects off the spheroidal convex secondary mirror  1270 , forming a diverging beam  1370  that reflects from concave spheroidal tertiary mirror  1280 . Rays  1380  pass through a 2 nd  aperture stop  1212 . The aperture stop  1212  is surrounded by baffles to further block stray light from reaching image plane  1295 . Light travels through aperture stop  1212  and converges on image plane  1295 . The aperture stop  1212  prevents stray light from reaching image plane  1295 . This embodiment can produce RMS spot diameters 3 to 10 times smaller than comparable size and f/number Czerny-Turner type spectrographs commonly used in handheld instruments. The f/number of the spectrograph in this embodiment is about f/4 and the dimensions are 100 (l)×20 (w)×65 (h) mm. The average RMS spot diameter for this embodiment is 18.6 microns which is smaller than a pixel width of 25 microns. 
         [0075]    Referring to  FIGS. 14A and 15 , the grating  1430  is rotated 90 degrees about an axis  1436  perpendicular to the plane of the grating, hence the light dispersion occurs along the YZ plane instead of the XZ plane. Thus, spectrograph  1400  can be configured as an imaging spectrograph or as a linear array spectrograph.  FIG. 15  shows the YZ plane of the spectrograph  1400 . As shown in  FIG. 15 , the primary mirror  1460 , secondary mirror  1470  and tertiary mirror  1480  are very wide in the YZ plane or along a direction of dispersion of light upon interaction with the grating (a dispersion direction), but narrower in the XZ plane shown in  FIG. 14A . This change in width of the optical components results in reduction of spatial interference or obstruction among grating  1430 , primary mirror  1460 , secondary mirror  1470  and tertiary mirror  1480 . Therefore, the mirrors can be much faster, with lower f/numbers. The throughput of spectrograph  1400  corresponds to, in one implementation, f/2.3 and the dimensions are 75 (l)×48 (w)×63 (h) mm. The average RMS spot diameter is 7.7 microns at f/4, and 15.7 microns at f/2.3. The spectrograph  1400  has nearly 4× higher throughput for the same average spot diameter on the image plane as compared to the spectrograph  1200 . However, the spectrograph  1400  is wider in the YZ plane than the embodiment illustrated in  FIGS. 12 and 13 . 
         [0076]      FIG. 16A , showing the embodiment of a spectrograph  1600 , is a similar design to the spectrograph  1400  depicted in  FIG. 14A . However, the locations of entrance aperture  1401  in  FIG. 14A and 1601  in  FIG. 16A  are different to accommodate different tilts of the diffraction grating. In  FIG. 14A , diffraction grating  1430  is rotated −14 degrees about the Y-axis  1432 , and then −20 degrees about the X-axis  1434 . In  FIG. 16A , the diffraction grating  1630  is rotated −37 degrees about the Y-axis  1632 , and then −24.5 degrees about the X-axis  1634 . The rotations about the X-axes  1434  and  1634  corresponded approximately to the blaze angles of the diffraction gratings  1430  and  1630 . “Approximately” is defined as that the rotations about the X-axes  1434  and  1634  are not necessarily exactly at the blaze angels of the gratings. The blaze angle is optimized to maximize efficiency for the wavelength of the used light and spectral resolving power. The rotation about the Y-axes allows flexibility in the location of the collimator mirrors  1405  and  1605 . A feature of the rotation about the Y-axes is the amount of geometric distortion added to the image plane.  FIG. 14B  illustrates  6  different wavelengths ranging from 1.03 μm on the left end of the sensor up to about 1.6 μm on the right side of a linear array sensor that is 12.8 mm long by 500 μm wide. Note that the wavelengths do not track the centerline axis  1492  of the sensor, and the wavelengths fall upon a curved path. Wavelengths 1.03 μm and 1.60 μm barely strike the active portion of the linear array sensor. The curvature resulted from geometric distortion created by a combination of off-axis camera focusing optics and a grating rotated about the Y-axis. In  FIG. 16B , all wavelengths are aligned along the centerline axis  1692 . The geometric distortion introduced by the camera focusing optics was mostly canceled in spectrograph  1600  by the inverse distortion introduced by increased rotation of the grating Y-axis  1632 . Adjusting the grating rotation is a very useful tool since it allows a linear array to be used at the image plane without light from the slit image missing the sensor. It is equally important to imaging and echelle spectrographs that make use of 2-D sensor arrays since it is much easier to track orders in software when those orders are linear across the sensor instead of parabolic or some other curvature. 
         [0077]    In certain embodiments, as with the echelle design spectrographs, imaging and linear array spectrograph embodiments are improved by offsetting the entrance aperture  1401  in  FIGS. 14A and 15  in X and Y with respect to the collimator parent vertex axis  312  up to approximately 3 millimeters, but typically less than 300 microns on short focal length collimators (&lt;100 mm focal length). Image quality are improved by either offsetting secondary mirror  1470  axis up to a few hundred microns in X and Y, or by rotating the secondary about axis  1474  (X) and axis  1472  (Y) up to a few 10ths of a degree. As those skilled in the art of optical design will appreciate, tilting a spheroidal mirror has the same effect on aberrations as offsetting the mirror location. 
         [0078]    Another improvement in the design of echelle, imaging and linear array spectrographs were achieved by offsetting the entrance aperture in X and Y dimensions while simultaneously tilting the secondary mirror of the TMA. In an exemplary embodiment,  FIG. 17  compares the RMS spot diameters produced at the image plane  1495  in  FIGS. 14A and 14B  by allowing the entrance aperture  1401  to be offset in X and Y dimensions while simultaneously tilting the secondary mirror  1470  to optimize (minimize) aberrations. The offset of the entrance aperture was X=−179.6 μm, Y=215.3 μm relative to the parent collimator focus location. The secondary mirror tilt about the X-axis  1474  is 0.088 degrees and the tilt about the Y-axis  1472  is 0.234 degrees. 
         [0079]      FIGS. 18 and 19  illustrate another embodiment of a spectrograph  1800 , with  FIG. 19  showing the YZ plane. The spectrograph  1800  can be an imaging spectrograph or a linear array spectrograph, and it comprises a positive meniscus field correcting lens  1890 . The dimensions of the spectrograph  1800  are 88 (l)×58 (w)×40 (h) mm. The field correcting lens  1890  improves the throughput to f/1.5 while the volume of the instrument is similar to embodiments without the field lens. The average RMS spot diameter is 18.0 microns at f/1.5, and 7.1 microns at f/2.3. The wavelength coverage with this embodiment is 0.95 to 1.65 microns with the 12.8 μm long linear array. 
         [0080]    While spectrograph embodiments  1200 ,  1400 ,  1600 , and  1800  have been designed for a Raman laser at wavelength of 1.03 or 1.064 microns, being all reflective optics except for the field lens, the same spectrographs can be utilized at any other Raman laser wavelength in the visible (400-700 nm) or near infrared (700-1100 nm). In certain embodiments, an ultraviolet (˜200-400 nm) handheld Raman spectrograph can be designed using a fused silica field lens. 
         [0081]    The imaging and linear array spectrograph embodiments discussed above are for a small handheld Raman spectrograph. Similar embodiments with much higher resolution can be designed for benchtop Raman systems or other systems that require limited wavelength coverage. The imaging and linear array spectrograph embodiments discussed above have superior resolution and throughput compared to traditional Czerny-Turner spectrographs. 
         [0082]    The disclosure of each of U.S. Pat. No. 7,936,454 and U.S. Pat. No. 7,936,455 is incorporated herein by reference in its entirety to describe the laser induced breakdown spectroscopy (LIBS) implementations of the echelle spectrograph  100 . 
         [0083]    While the preferred embodiments of the present invention have been illustrated in detail, it should be apparent that modifications and adaptations to those embodiments may occur to one skilled in the art without departing from the scope of the present invention.