Abstract:
A spectrograph that includes a first mirror having flat a mirror reflective surface and positioned to reflect light traversing a prism, a second mirror having a concave-shaped reflective mirror surface and positioned to reflect light received from the first mirror, a third mirror having a convex-shaped reflective mirror surface and positioned to receive light reflected by the second mirror, a fourth mirror having a spheroidal reflective mirror surface and positioned to receive light reflected by the third mirror, and a field lens comprising a concave mirror surface in combination with a convex mirror surface, wherein light received by said field lens from said fourth mirror enters said convex mirror surface, traverses said field lens, and exits from said concave mirror surface. The fifth mirror is positioned such that the second mirror, third mirror, fourth mirror, and fifth mirror share a common vertex axis.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This non-Provisional Application claims priority from a U.S. Provisional Application filed 26 Oct. 2015 and having Ser. No. 62/246,398, which is hereby incorporated by reference herein. 
     
    
     FIELD OF THE INVENTION 
       [0002]    This invention relates to optical instruments for use in the measurement of properties of light, and specifically to echelle spectrographs. 
       BACKGROUND OF THE INVENTION 
       [0003]    An echelle spectrograph is a spectrograph which uses an echelle grating to diffract light at high resolutions and high diffraction orders. As with other blazed diffraction gratings, the echelle grating consists of a number of grooves, the width of the grooves being close to the wavelength of the diffracted radiation. However, echelle gratings are specifically characterized by the large spacing between the grooves and, therefore, comprises a lower groove density. 
         [0004]    Light incident upon any blazed grating is split into several different diffraction orders. Each order will be comprised of a different but overlapping wavelength range. The dispersion associated with each order will also be different. The overlapping orders make it difficult to associate the correct order numbers with their wavelength ranges. This ambiguity complicates the spectrum and makes it more difficult to determine the correct wavelength emission from the source. 
         [0005]    Although this overlap is generally an unwanted side effect, echelle gratings specifically use this effect to enhance the performance of the spectrograph. A second cross-dispersing element is used to spatially separate the orders. The individual orders, each with a separate (and sometimes overlapping) wavelength range and resolution, can then be analyzed without ambiguity. 
         [0006]    Typical echelle spectrographs have a relatively high effective fvalue, generally f/7 or greater, limiting the total light which reaches the image plane and thereby decreasing the resulting image quality. Further, the high effective fvalue of typical echelle spectrographs prevent their use in certain applications such as Raman spectroscopy where the detection of weak emissions requires the use of a spectrograph with a very low fvalue. Clearly, it is desirable to design an echelle spectrograph with a low fvalue. 
       SUMMARY OF THE INVENTION 
       [0007]    In one implementation, a spectrograph is presented. The spectrograph includes a first mirror having flat a mirror reflective surface and positioned to reflect light traversing a prism; a second mirror having a concave-shaped reflective mirror surface and positioned to reflect light received from the first mirror; a third mirror having a convex-shaped reflective mirror surface and positioned to receive light reflected by the second mirror; a fourth mirror having a spheroidal reflective mirror surface and positioned to receive light reflected by the third mirror; and a field lens comprising a concave mirror surface in combination with a convex mirror surface, wherein light received by said field lens from said fourth mirror enters said convex mirror surface, traverses said field lens, and exits from said concave mirror surface. The fifth mirror is positioned such that the second mirror, third mirror, fourth mirror, and fifth mirror share a common vertex axis. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0008]    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: 
           [0009]      FIG. 1  illustrates the movement of radiation through Applicant&#39;s echelle spectrograph; and 
           [0010]      FIG. 2  shows a different perspective of the Applicant&#39;s echelle spectrograph. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0011]    This invention 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 invention. 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. 
         [0012]    The described features, structures, or characteristics of the invention 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 embodiments of the invention. One skilled in the relevant art will recognize, however, that the invention 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 invention. 
         [0013]    Referring now to the illustrated embodiment of  FIG. 1 , Applicant&#39;s echelle spectrograph  100  comprises an entrance aperture  101 , a collimating mirror  105  with its parent optical axis  107 , a first aperture stop  110 , a second aperture stop  112 , a diffraction grating  130 , a prism  140 , a first mirror  150  having a flat mirror reflective surface with its first axis  152  and a second axis  154 , a second mirror  160  having concave-shaped mirror surfaces, a third mirror  170  having convex-shaped mirror surfaces, a fourth mirror  180  having concave-shaped mirror surface, a field lens  190 , and an image plane  195 . 
         [0014]    In certain embodiments, a cone of light enters through entrance aperture  101  and travels toward collimating mirror  105  as a cone of light  202 . In the illustrated embodiment of  FIG. 1 , the collimating mirror  105  comprises a Conic Constant of −1 and Radius of Curvature of 72 mm (concave). 
         [0015]    Light  202  is reflected off collimating mirror  105  to give collimated light  210 . Collimated light  210  passes through aperture stop  110 , which located on the parent axis  107  of the collimating mirror  105 . In certain embodiments, collimating mirror  105  is interchangeable. This being the case, the focal length of collimating mirror  105  is adjustable. If entrance aperture  101  is located correctly, there are practically no aberrations in light  210 , and therefore, light  210  comprises nearly perfect collimated light. 
         [0016]    Light  210  passes through aperture stop  110  and produces light  220 . Light  220  is directed onto diffraction grating  130 . Light  220  comprises a polychromatic beam, i.e., light  220  comprises electromagnetic radiation containing a plurality of wavelengths. The nature of the light source determines the constituent wavelengths of light  220 . 
         [0017]    As those skilled in the art will appreciate, echelle grating  130  separates incident light  220  into a plurality of constituent wavelengths, i.e., light  220  is dispersed by echelle grating  130 . When light  220  is incident on echelle grating  130  with an angle θi (measured from the normal of the grating), that light is diffracted into several beams. The beam that corresponds to direct transmission (or specular reflection in the case of a reflection grating) is called the zero order, and is denoted m=0. The other orders correspond to diffraction angles which are represented by non-zero integer values for m. For a groove period d and an incident wavelengh λ, the grating equation (4) gives the value of the diffracted angle θm(θ) in the order m: 
         [0000]      d(sinθm(λ)+sin θi)=Mλ(4)
 
         [0018]    The diffracted beams corresponding to consecutive orders may overlap, depending on the spectral content of the incident beam and the grating density. The higher the spectral order, the greater the overlap of light into the next order. 
         [0019]    Light  230  that is reflected from diffraction grating  130  comprises a plurality of beams dispersed by wavelength. Light  230  is directed onto dispersive prism  140 . As those skilled in the art will appreciate, light changes speed as it moves from one medium to another, for example, from air into the matrix of prism  140 . Under Huygens principle, such a speed-change causes light striking the boundary between two media at an angle to be refracted and enter the new medium at a different angle. 
         [0020]    In accordance with Snell&#39;s law, the degree of bending of a light path is a function of, inter alia, the ratio between the refractive indices of the two media. The refractive index of a medium varies with the wavelength of the light. This being the case, light  230  traveling through prism  140  is further dispersed by wavelength, but in a direction orthogonal to the dispersion direction of the grating. 
         [0021]    Echelle grating  130  can be replaced with another grating of different groove density or blaze angle. Changing the blaze angle or groove density of grating  130  will provide different spectral characteristics at image plane  195  that will affect spectral resolution and order spacing. Echelle grating  130  is interchangeable with a wide range of groove densities and blaze angles that can be used in different embodiments. 
         [0022]    Prism  140  controls the total range of wavelengths passing through to image plane  195 . By changing prism  140 , different wavelength ranges can be utilized at image plane  195 . For example, the standard embodiment of echelle spectrograph  100  includes a fused silica (FS) prism  140 . The wavelength range using the FS prism  140  is about 180 nm up to about 1.1 microns. If prism  140  comprises a CaF2 prism, the wavelength range can be extended down to about 150 nm. Another embodiment can include a BK7 glass prism  140 . BK7 has higher dispersion than FS or CaF2 but it does not transmit light below 350 nm. The wavelength range of the echelle spectrograph  100  would be from about 350 nm up to about 1.1 microns, but the spectral order separation is larger because dispersion is higher with BK7 glass. A taller entrance aperture  101  can then be used to increase the etendue of the instrument for this embodiment with a BK7 glass prism  140 . 
         [0023]    Light  240  exits prism  140 , and is directed onto the first mirror  150 . The first mirror  150  comprises a flat mirror reflective surface. In certain embodiments, the first mirror  150  tilts along the first axis  152  thereof, then tilts along the second axis  154  thereof. The first mirror  150  is titled in a way such that no obstruction of light  250 ,  260 ,  270 , and  280 . Further, the first mirror  150  is disposed at an angle such that minimal obstructions occur with the grating  130  when mounting a camera. The image plane  195  is located within a sensor. In certain embodiments, a sensor is a scientific, digital CCD camera used to collect image data of the light from an emitting source. With this configuration of the first mirror  150 , the dimension of the echelle spectrograph  100  is allowed to decrease and generate a hand-held echelle spectrograph. 
         [0024]    Further, light  240  is reflected from the first mirror  150  as light  250 . For any given wavelength, the beam is still collimated. However, each wavelength reflects off the first mirror  150  at a slightly different angle because of the dispersion by grating  130  and prism  140 . 
         [0025]    Light  250  is incident on the second mirror  160 . In certain embodiments, the second mirror  160  comprises a radius of curvature of about 97.701 mm (concave) and a conic constant of −0.5631. In these embodiments, the second mirror  160  comprises an ellipsoidal mirror. 
         [0026]    Light  250  is reflected convergingly and then divergingly from the second mirror  160  as light  260 . Light  260  converges from the second mirror  160  to an intermediate focus  265  and then diverges from intermediate focus  265  until it strikes the third mirror  170 . In certain embodiments, the intermediate focus  265  comprises a baffle, which is formed to include an aperture. The baffle is disposed in echelle spectrograph  100  such that light  260  converge from the second mirror  160 , passes through said aperture in the baffle, and strikes the third mirror  170 . 
         [0027]    In certain embodiments, the third mirror  170  comprises a radius of curvature of about 70.086 mm (convex) and a conic constant of 0. In these embodiments, the third mirror  170  comprises a spheroidal convex mirror. In other embodiments, the third mirror  170  comprises an ellipsoidal (0.0&gt;conic constant&gt;−1.0, parabolic (conic constant=−1.0) or a hyperbolic (conic constant&lt;−1.0) convex mirror. 
         [0028]    Light  260  is reflected divergingly from the third mirror  170  as light  270 , wherein light  270  passes onto the fourth mirror  180 . In certain embodiments, the fourth mirror comprises an ellipsoidal (0.0&gt;conic constant&gt;−1.0), spherical (conic constant=0), spheroidal, or oblate spheroidal concave mirror (conic constant&gt;0). In general, the smaller the conic constant (more negative), the better the correction but the larger the mirror and spectrograph becomes. 
         [0029]    In certain embodiments, Applicant&#39;s echelle spectrograph utilizes a spherical mirror for the fourth mirror  180  rather than other conic surfaces. The resulting ease of fabrication of the spherical mirror has many important ramifications for Applicant&#39;s echelle spectrograph. 
         [0030]    In certain embodiments, the fourth mirror  180  comprises a radius of curvature of about 78.916 mm (concave) and a conic constant of 0. In these embodiments, the fourth mirror  180  comprises a spheroidal mirror. 
         [0031]    Light  270  is reflected convergingly from the fourth mirror  180  as light  280 . Light  280  is directed onto a correcting, field lens  190  through a second aperture  112 . In certain embodiments, the filed lens  190  is a meniscus lens. Light  280  first passes through first surface  192 . In certain embodiments, surface  192  is spherical and convex. The light exits correcting lens  190  through second surface  194  to define image plane  195 . In certain embodiments, second surface  194  is spherical and concave. Further, in certain embodiments, a field lens  190  parent vertex axis is located on the parent axis shared by the second, third, and fourth mirrors. 
         [0032]    As those skilled in the art will 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. Therefore, aperture stops  110  is one of the primary parameters controlling the amount of light entering echelle spectrograph  100 . 
         [0033]    In certain embodiments, each of the aperture stops comprises an interchangeable device, such that the aperture stop  110  can be adjusted to allow a desired amount of light into echelle spectrograph  100 . A smaller aperture stop will result in a sharper image at image plane  195  by reducing optical aberrations. Echelle spectrograph  100  can be optimized for maximum light throughput (large aperture stop  110 ) or maximum spectral resolution (small aperture stop  110 ). 
         [0034]    One way to change the effective focal length (the “f” value of the input optics) of the echelle spectrograph  100  is to change the focal length of the collimating mirror  105 . For purposes of this discussion, fvalue=1/(2×(sin θ)) where θ is the half angle of light passing through entrance aperture  101 . The numerical aperture (NA) for entrance aperture  101  is defined as NA=sin (θ), or equivalently, 
         [0000]      NA=sin[arctan{D/(2×Fc)}]  (1)
 
         [0035]    and, 
         [0000]      fvalue=1/(2×NA)  (2)
 
         [0036]    where D is the diameter (if circular) of aperture stop  110  and Fc is the effective off-axis focal length of collimating mirror  105 . The NA and fvalue can be generalized by an “averaged NA” or averaged fvalue if D is non-circular. 
         [0037]    A greater fvalue (smaller NA) will cause less total light to reach image plane  195 . Prior art echelle spectrographs comprise approximately f/7 or greater systems. In contrast, Applicant&#39;s echelle spectrograph  100  effectively comprises an f/3 or faster optical system (NA&gt;0.15). This represents approximately a 10× improvement in light throughput compared to prior art devices. 
         [0038]    The total amount of light through entrance aperture  101  is defined by the etendue (E) of the system at aperture stop  110 . At aperture stop  110 , E is proportional to the product of entrance aperture  101  area and the solid angle of the light passing through entrance aperture  101 . Therefore, increasing either the solid angle (proportional to either 1/{fvalue**2} or NA**2) of light passing through entrance aperture  101  or increasing the area of entrance aperture  101  will increase 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 entrance aperture  101 . 
         [0039]    As those skilled in the art will further appreciate, the light passing through echelle spectrograph  100  contains multiple spectral orders that are separated, or dispersed, as light passes through prism  140 . Furthermore, the height of entrance aperture  101  must be less than the distance between the spectral orders at image plane  195 , or cross-talk between the spectral orders will occur. Therefore, the size of the entrance aperture  101  is limited in both height and width to provide good spectral order separation and high spectral resolution at image plane  195 . The best way to increase throughput is to decrease the effective fvalue (increase NA). 
         [0040]    It is important to note that the light source must be optically coupled to entrance aperture  101 . Furthermore, to maximize throughput of light, the fvalue of the optics associated with the light source must perfectly match the fvalue of the input optics defined by Fc and D in module  102  (see equations 1 and 2). Each embodiment of the light source can have a very different fvalue. For example, the typical effective fvalue of an optical fiber is f/2.3 (NA=0.22) and the fvalue of a telescope can be f/16 or higher. 
         [0041]    In certain embodiments, Applicant&#39;s echelle spectrograph  100  can have collimating mirror  105  of a different focal length without changing the mirror diameter. For example, if the focal length of collimating mirror  105  is doubled, then the fvalue of the collecting optics as defined by Equation 2 is increased by a factor of about 2 (NA is half) if D remains unchanged. The magnification of echelle spectrograph  100  is defined by the effective ratio of module  104  (Fi) to module  102  (Fc): 
         [0000]      M=Fi/Fc   (3)
 
         [0042]    When Fc is doubled, 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) will then be approximately half the size as with the original module  102 . It is therefore possible to double entrance aperture  101  (in both height and width) to preserve the total throughput or etendue of echelle spectrograph  100  without degrading spectral resolution or changing any of the optics. 
         [0043]    Applicant&#39;s echelle spectrograph  100  can match any light source from approximately f/2 to &gt;f/16 while maximizing etendue by simply changing Fc and the diameter of the entrance aperture  101 . At the same time, the spectral resolution and order overlap will remain unchanged. The image quality and order location at image plane  195  will also remain unchanged as long as entrance aperture  101  is at the correct location (with the appropriate size) and D remains unaltered. 
         [0044]    The correcting field lens  190  not only adds two more corrective optical surfaces, but also allows for longer effective focal length of the echelle spectrograph  100 . Further, the field lens  190  together with the positon of the first mirror  150  make the echelle spectrograph  100  more compact. When optimizing the first surface  192  and the second surface  194  of the field lens  190 , the concave surface of the second mirror  160 , the convex surface of the third mirror  170 , and the concave surface of the fourth mirror  180  simultaneously, optical aberrations of the echelle spectrograph  100  are reduced compared to optimizing only the concave surface of the second mirror  160 , the convex surface of the third mirror  170 , and the concave surface of the fourth mirror  180  simultaneously. Moreover, the useable size of a sensor is increased, i.e., a much larger corrected area at the image plane  195 , therefore a longer focal length can be with the same spectral orders on a sensor. 
         [0045]    As those skilled in the art will appreciate, the longer focal length of the echelle spectrograph  100  will result in higher spectral resolving power (wavelength/FWHM). In certain embodiments, the spectral resolving power of the echelle spectrograph  100  is up to 200,000. 
         [0046]    Moreover, as those skilled in the art will appreciate, because the spectral orders are located further apart due to the larger useable size of the sensor so a taller entrance aperture  101  can be used without interference between adjacent spectral orders. For example, without employing the field lens  190 , the maximum size of the entrance aperture  101  is about 25 mm without causing too much aberrations. When a field lens  190  is employed, the maximum size of the entrance aperture  101  is about 56 mm without causing too much aberrations. Employing the field lens  190  allows a combination of better spectrograph throughput (taller slit) and better resolving power (higher dispersion). 
         [0047]    Each of U.S. Pat. No. 7,936,454 and U.S. Pat. No. 7,936,455 is incorporated by reference in its entirety to describe the laser induce breakdown spectroscopy (LIBS) implementations of the echelle spectrograph  100 . 
         [0048]    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.