Abstract:
A spectrometer includes a beam splitter that receives incident light rays and splits each of the incident light rays into first and second spatially displaced, linearly polarized light rays that respectively have first and second polarization directions orthogonal to each other; an optical member that receives the split incident light rays from the beam splitter and optically converts the split incident light rays into a plurality of light beams that are respectively guided to mutually differing locations so as to generate interference fringes in the respective locations, each of the plurality of light beams including a component of the first linearly polarized light rays and a component of the second linearly polarized light rays; and a detector that detects the interference fringes respectively generated by the plurality of light beams.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    Technical Field 
         [0002]    The present invention relates to a spectrometer and a method of spectroscopy, and more particularly to Fourier transform spectroscopy. 
         [0003]    Background Art 
         [0004]    In one method of Fourier transform spectroscopy, a light ray from a light source is split into two light rays using a beam splitter, and then these two light rays are made to interfere with one another. 
         [0005]    Patent Document 1 discloses an example of a spectrometer used for Fourier transform spectroscopy. In Patent Document 1, a Wollaston prism is used as the beam splitter. A Wollaston prism splits a light ray from a light source into an ordinary light ray and an extraordinary light ray. The ordinary light ray and the extraordinary light ray then interfere with one another on a detector. 
         [0006]    Patent Document 2 also discloses an example of a spectrometer used for Fourier transform spectroscopy. In Patent Document 2, a Savart plate is used as the beam splitter. A Savart plate also splits a light ray from a light source into an ordinary light ray and an extraordinary light ray. The ordinary light ray and the extraordinary light ray are then focused onto a detector using a single lens. In this way, the ordinary light ray and the extraordinary light ray interfere with one another. 
         [0007]    Furthermore, in Patent Document 2, a polarizer is arranged between the Savart plate and the lens. The detector detects an interference fringe (a first interference fringe) created by the light beams that pass through the polarizer. In Patent Document 2, after this interference fringe is detected, the orientation of the transmission axis of the polarizer is changed. The detector then detects the new interference fringe (a second interference fringe) created by the light beams that pass through the polarizer. In Patent Document 2, the difference between the first interference fringe and the second interference fringe is then calculated. Patent Document 2 discloses that calculating this difference removes background noise. 
       RELATED ART DOCUMENTS 
     Patent Documents 
       [0008]    Patent Document 1: Japanese Patent Application Laid-Open Publication No. 2002-168696 
         [0009]    Patent Document 2: Japanese Patent Application Laid-Open Publication No. H2-268234 
       SUMMARY OF THE INVENTION 
       [0010]    In Fourier transform spectroscopy, an interference fringe is detected by a detector, and then a Fourier transform is applied to this interference fringe. However, sometimes the interference fringe is not detected correctly due to pixel defects in the detector (such as a charge-coupled device (CCD) image sensor), for example. 
         [0011]    The present invention was made in light of the foregoing and aims to prevent any negative effects caused by a region of an interference fringe being detected incorrectly when using Fourier transform spectroscopy. Accordingly, the present invention is directed to a scheme that substantially obviates one or more of the problems due to limitations and disadvantages of the related art. 
         [0012]    Additional or separate features and advantages of the invention will be set forth in the descriptions that follow and in part will be apparent from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims thereof as well as the appended drawings. 
         [0013]    To achieve these and other advantages and in accordance with the purpose of the present invention, as embodied and broadly described, in one aspect, the present disclosure provides a spectrometer, including: a beam splitter that receives incident light rays and splits each of the incident light rays into first and second spatially displaced, linearly polarized light rays that respectively have first and second polarization directions orthogonal to each other; an optical member that receives the split incident light rays from the beam splitter and optically converts the split incident light rays into a plurality of light beams that are respectively guided to mutually differing locations so as to generate interference fringes in the respective locations, each of the plurality of light beams including a component of the first linearly polarized light rays and a component of the second linearly polarized light rays; and a detector that detects the interference fringes respectively generated by the plurality of light beams. 
         [0014]    In another aspect, the present disclosure provides a spectrometer, including: a beam splitter that receives incident light rays and splits each of the incident light rays into first and second spatially displaced, linearly polarized light rays that respectively have first and second polarization directions orthogonal to each other; an optical member that receives the split incident light rays from the beam splitter and optically converts the split incident light rays into a plurality of light beams that are respectively guided to mutually differing locations on a virtual plane so as to generate interference fringes in the respective locations in the virtual plane, each of the plurality of light beams including a component of the first linearly polarized light rays and a component of the second linearly polarized light rays; a two-dimensional detector that detects the interference fringes respectively generated by the plurality of light beams on the virtual plane; and a signal processor that applies a Fourier transform to data representing the interference fringes detected by the detector or applies a Fourier transform to data obtained by processing the data representing the interference fringes detected by the detector. 
         [0015]    In another aspect, the present disclosure provides a method of spectroscopy, including: receiving incident light rays and splitting each of the incident light rays into first and second spatially displaced, linearly polarized light rays that respectively have first and second polarization directions orthogonal to each other using a beam splitter; by the optical member, receiving the split incident light rays from the beam splitter and optically converting the split incident light rays into a plurality of light beams that are respectively guided to mutually differing locations so as to generate interference fringes in the respective locations, each of the plurality of light beams including a component of the first linearly polarized light rays and a component of the second linearly polarized light rays; and detecting the interference fringes respectively generated by the plurality of light beams using a detector. 
         [0016]    The present invention makes it possible to prevent any negative effects caused by a region of an interference fringe being detected incorrectly when using Fourier transform spectroscopy. 
         [0017]    It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory, and are intended to provide further explanation of the invention as claimed. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0018]      FIG. 1A  is a side view illustrating a configuration of a spectrometer according to Embodiment 1.  FIG. 1B  is a top view illustrating the configuration of the spectrometer according to Embodiment 1. 
           [0019]      FIG. 2  is a detailed view of a beam splitter illustrated in  FIGS. 1A and 1B . 
           [0020]      FIG. 3  illustrates an example of a plurality of interference fringes created by the spectrometer illustrated in  FIGS. 1A and 1B . 
           [0021]      FIGS. 4A and 4B  illustrate a modification example of  FIGS. 1A and 1B .  FIG. 4A  is a side view of the spectrometer, and  FIG. 4B  is a top view of the spectrometer. 
           [0022]      FIG. 5A  is a side view illustrating a configuration of a spectrometer according to Embodiment 2.  FIG. 5B  is a top view illustrating the configuration of the spectrometer according to Embodiment 2. 
           [0023]      FIG. 6  illustrates an example of a plurality of interference fringes created by the spectrometer illustrated in  FIGS. 5A and 5B . 
           [0024]      FIGS. 7A and 7B  illustrate Modification Example 1 of  FIGS. 5A and 5B .  FIG. 7A  is a side view of the spectrometer, and  FIG. 7B  is a top view of the spectrometer. 
           [0025]      FIGS. 8A and 8B  illustrate Modification Example 2 of  FIGS. 5A and 5B .  FIG. 8A  is a side view of the spectrometer, and  FIG. 8B  is a top view of the spectrometer. 
           [0026]      FIG. 9A  is a side view illustrating a configuration of a spectrometer according to Embodiment 3.  FIG. 9B  is a top view illustrating the configuration of the spectrometer according to Embodiment 3. 
           [0027]      FIG. 10  illustrates an example of a plurality of interference fringes created by the spectrometer illustrated in  FIGS. 9A and 9B . 
           [0028]      FIGS. 11A and 11B  illustrate a modification example of  FIGS. 9A and 9B .  FIG. 11A  is a side view of the spectrometer, and  FIG. 11B  is a top view of the spectrometer. 
           [0029]      FIG. 12A  is a side view illustrating a configuration of a spectrometer according to Embodiment 4.  FIG. 12B  is a top view illustrating the configuration of the spectrometer according to Embodiment 4. 
           [0030]      FIG. 13  illustrates an example of a plurality of interference fringes created by the spectrometer illustrated in  FIGS. 12A and 12B . 
           [0031]      FIGS. 14A and 14B  illustrate Modification Example 1 of  FIGS. 12A and 12B .  FIG. 14A  is a side view of the spectrometer, and  FIG. 14B  is a top view of the spectrometer. 
           [0032]      FIGS. 15A and 14B  illustrate Modification Example 2 of  FIGS. 12A and 12B .  FIG. 15A  is a side view of the spectrometer, and  FIG. 15B  is a top view of the spectrometer. 
       
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
       [0033]    Next, embodiments of the present invention will be described with reference to figures. Note that the same reference characters are used in all of the figures for components that are the same, and redundant descriptions of these components will be omitted as appropriate. 
         [0034]    Moreover, in the following descriptions, a signal processor  80  is intended to be a functional block rather than a specific hardware component. The signal processor  80  may implemented using any combination of hardware and software, such as primarily any computer CPU, memory, programs implemented according to the configurations illustrated in the figures that are loaded into the memory, storage media such as a hard disk for storing the programs, and an interface for connecting to a network. Furthermore, the methods and devices used to implement the signal processor  80  may be modified in various ways. 
       Embodiment 1 
       [0035]      FIG. 1A  is a side view illustrating a configuration of a spectrometer according to Embodiment 1.  FIG. 1B  is a top view illustrating the configuration of the spectrometer according to the present embodiment. The spectrometer includes a beam splitter  40 , a fly&#39;s-eye lens  50  (an optical member), and a detector  70 . The beam splitter  40  splits each of incident light rays from a light source  10  into an ordinary light ray (first linearly polarized light rays) eo and an extraordinary light ray (second linearly polarized light rays) oe. The fly&#39;s-eye lens  50  optically converts light rays that includes the ordinary light rays eo and the extraordinary light rays oe into a plurality of light beams. Each light beam of this plurality of light beams includes an ordinary light ray eo component and an extraordinary light ray oe component. The fly&#39;s-eye lens  50  focuses the plurality of light beams onto mutually differing regions. The detector  70  detects the interference fringes respectively created by the plurality of light beams. The details of this will be described below. 
         [0036]    The light source  10  emits incident light that is to be measured by the spectrometer. This light may be light that passed through a sample, light that was scattered by a sample, or light that was emitted by a sample, for example. In addition, this light may be infrared light, for example, or may alternatively be visible light or ultraviolet light. 
         [0037]    The light from the light source  10  passes through a lens  20 . The lens  20  converts the light from the light source  10  to collimated light. In other words, the lens  20  is a collimating lens. 
         [0038]    The light from the lens  20  enters a polarizer  30 . In the example illustrated in  FIGS. 1A and 1B , the polarizer  30  is arranged such that the transmission axis of the polarizer  30  is inclined by an angle of 45° towards one of the sides going from the height direction of the spectrometer (the Y direction in the figure) towards the width direction of the spectrometer (the X direction in the figure). Therefore, light that passes through the polarizer  30  oscillates in the same direction as the transmission axis of the polarizer  30 . 
         [0039]    The linearly polarized light (incident light rays) from the polarizer  30  enters the beam splitter  40 . These incident light rays exit the beam splitter  40  as ordinary light rays eo and an extraordinary light rays oe. In the example illustrated in  FIGS. 1A and 1B , the optical axes of the ordinary light ray eo and the extraordinary light ray oe are parallel to one another and extend along the thickness direction of the beam splitter  40  (the Z direction in the figure). The ordinary light ray eo and the extraordinary light ray oe are both linearly polarized light rays. The direction of oscillation of the ordinary light ray eo and the direction of oscillation of the extraordinary light ray oe are mutually orthogonal. More specifically, the ordinary light ray eo oscillates in the height direction of the spectrometer (the Y direction in the figure), and the extraordinary light ray oe oscillates in the width direction of the spectrometer (the X direction in the figure). 
         [0040]      FIG. 2  is a detailed view of the beam splitter illustrated in  FIGS. 1A and 1B . In the example illustrated in  FIG. 2 , the beam splitter  40  is a Savart plate. The beam splitter  40  includes a first crystal plate  42  and a second crystal plate  44 . The first crystal plate  42  and the second crystal plate  44  are bonded to one another. 
         [0041]    The first crystal plate  42  and the second crystal plate  44  are both made from a uniaxial crystal. The first crystal plate  42  is made from the same material as the second crystal plate  44 . Moreover, the thickness of the first crystal plate  42  is equal to the thickness of the second crystal plate  44 . In the example illustrated in  FIG. 2 , the first crystal plate  42  and the second crystal plate  44  are made from yttrium vanadate (YVO 4 ). However, the first crystal plate  42  and the second crystal plate  44  may alternatively be made from calcite (CaCO 3 ), quartz (SiO 2 ), or titanium oxide (TiO 2 ), or from liquid crystal, a birefringent polymer, or a glass made optically anisotropic by poling, for example. 
         [0042]    The first crystal plate  42  is formed such that the optic axis thereof is inclined by 45° from the thickness direction of the first crystal plate  42  (the Z direction in the figure). Similarly, the second crystal plate  44  is formed such that the optic axis thereof is inclined by 45° from the thickness direction of the second crystal plate  44  (the Z direction in the figure). The first crystal plate  42  and the second crystal plate  44  are bonded together such that the optic axis of the first crystal plate  42  and the optic axis of the second crystal plate  44  are mutually orthogonal when the beam splitter  40  (the first crystal plate  42  and the second crystal plate  44 ) is viewed from the thickness direction (the Z direction in the figure). In the example illustrated in  FIG. 2 , the optic axis of the first crystal plate  42  is inclined upwards moving towards the second crystal plate  44  side. The optic axis of the second crystal plate  44  is inclined rightwards moving towards the side opposite to the first crystal plate  42 . 
         [0043]    The light that enters the first crystal plate  42  is split into an extraordinary light ray e (a first extraordinary light ray e) and an ordinary light ray o (a first ordinary light ray o) by the entrance surface of the first crystal plate  42 . The first extraordinary light ray e is refracted by the entrance surface of the first crystal plate  42 . The optical axis of the first extraordinary light ray e is inclined in the same direction from the thickness direction of the first crystal plate  42  (the Z direction in the figure) as the optic axis of the first crystal plate  42 . The first extraordinary light ray e is linearly polarized light. The first extraordinary light ray e oscillates in a direction parallel to the optic axis of the first crystal plate  42 . Meanwhile, the first ordinary light ray o is not refracted by the entrance surface of the first crystal plate  42  and proceeds straight along the thickness direction of the first crystal plate  42  (the Z direction in the figure). The first ordinary light ray o is linearly polarized light. The first ordinary light ray o oscillates in a direction orthogonal to the optic axis of the first crystal plate  42 . 
         [0044]    The extraordinary light ray e from the first crystal plate  42  enters the second crystal plate  44  and becomes an ordinary light ray o (a second ordinary light ray o). The second ordinary light ray o proceeds straight along the thickness direction of the second crystal plate  44  (the Z direction in the figure). The second ordinary light ray o is linearly polarized light. The second ordinary light ray o oscillates in a direction orthogonal to the optic axis of the second crystal plate  44 . Meanwhile, the ordinary light ray o from the first crystal plate  42  enters the second crystal plate  44  and becomes an extraordinary light ray e (a second extraordinary light ray e). The second extraordinary light ray e is refracted by the interface between the first crystal plate  42  and the second crystal plate  44 . The optical axis of the second extraordinary light ray e is inclined in the same direction from the thickness direction of the second crystal plate  44  (the Z direction in the figure) as the optic axis of the second crystal plate  44 . The second extraordinary light ray e is linearly polarized light. The second extraordinary light ray e oscillates in a direction parallel to the optic axis of the second crystal plate  44 . 
         [0045]    The ordinary light ray o from the second crystal plate  44  is not refracted by the exit surface of the second crystal plate  44  and exits the second crystal plate  44  as the ordinary light ray eo. The ordinary light ray eo proceeds straight along the thickness direction of the beam splitter  40  (the Z direction in the figure). Meanwhile, the extraordinary light ray e from the second crystal plate  44  is refracted by the exit surface of the second crystal plate  44 . As a result, the extraordinary light ray e from the second crystal plate  44  exits the second crystal plate  44  as the extraordinary light ray oe. The extraordinary light ray oe proceeds straight along the thickness direction of the beam splitter  40  (the Z direction in the figure). 
         [0046]    Alternatively, the beam splitter  40  may be a Wollaston prism. The following description assumes that the beam splitter  40  is a Savart plate. 
         [0047]    Return to  FIGS. 1A and 1B . The ordinary light ray eo and the extraordinary light ray oe enter the fly&#39;s-eye lens  50 . The fly&#39;s-eye lens  50  includes a plurality of lenses that are arranged in a two-dimensional array when viewed from the direction running parallel to the optical axis of the light (the ordinary light ray eo and the extraordinary light ray oe) that enters the fly&#39;s-eye lens  50  (the Z direction in the figure). This plurality of lenses is arranged within a plane orthogonal to the optical axis of the light (the ordinary light ray eo and the extraordinary light ray oe) that enters the fly&#39;s-eye lens  50 . More specifically, the plurality of lenses is arranged in a 4×4 array. 
         [0048]    When viewed from the direction running parallel to the optical axis of the light (the ordinary light ray eo and the extraordinary light ray oe) that enters the fly&#39;s-eye lens  50  (the Z direction in the figure), each of the lenses in the fly&#39;s-eye lens  50  is positioned within the spot of the ordinary light ray eo and the spot of the extraordinary light ray oe. Therefore, the ordinary light ray eo and the extraordinary light ray oe enter all of the lenses in the fly&#39;s-eye lens  50 . As the ordinary light ray eo and the extraordinary light ray oe pass through the lenses in the fly&#39;s-eye lens  50 , the ordinary light ray eo and the extraordinary light ray oe are split into a plurality of light beams. Each of these light beams includes an ordinary light ray eo component and an extraordinary light ray oe component. 
         [0049]    The plurality of light beams from the fly&#39;s-eye lens  50  then pass through a polarizer  60 . The polarizer  60  is arranged such that the transmission axis of the polarizer  60  is oriented in the same direction as the transmission axis of the polarizer  30 . More specifically, the transmission axis of the polarizer  60  is inclined by an angle of 45° towards one of the sides going from the height direction of the spectrometer (the Y direction in the figure) towards the width direction of the spectrometer (the X direction in the figure). As a result, the light that passes through the polarizer  60  oscillates in the same direction as the transmission axis of the polarizer  60 . Alternatively, the transmission axis of the polarizer  60  may be oriented in a different direction than the transmission axis of the polarizer  30 . For example, the transmission axis of the polarizer  60  may be orthogonal to the transmission axis of the polarizer  30  when viewed from the direction running parallel to the optical axis of the light that passes through the polarizer  30  and the polarizer  60  (the Z direction in the figure). 
         [0050]    Each of the light beams that passes through the polarizer  60  creates an interference fringe on the detector  70 . More specifically, these interference fringes are created due to interference between the ordinary light ray eo component and the extraordinary light ray oe component included in each light beam. The detector  70  detects these interference fringes. More specifically, in the example illustrated in  FIGS. 1A and 1B , the detector  70  is an image sensor that includes a plurality of photoelectric conversion elements arranged in a matrix. Even more specifically, the detector  70  is a charge-coupled device (CCD) image sensor. 
         [0051]      FIG. 3  illustrates an example of the plurality of interference fringes created by the spectrometer illustrated in  FIGS. 1A and 1B . In the example illustrated in  FIG. 3 , the plurality of interference fringes are shown as viewed from the front side of the detector  70 . As described with reference to  FIGS. 1A and 1B , the fly&#39;s-eye lens  50  includes a plurality of lenses arranged in a 4×4 array. As a result, like the plurality of lenses in the fly&#39;s-eye lens  50 , the plurality of interference fringes are arranged in a 4×4 matrix pattern. 
         [0052]    Return to  FIGS. 1A and 1B . The plurality of interference fringes detected by the detector  70  are processed by a signal processor  80 . More specifically, the signal processor  80  calculates the average of the plurality of interference fringes. The signal processor  80  then applies a Fourier transform to the data that represents that average (interference fringe). This makes it possible to obtain the spectrum of the light from the light source  10 . In this case, even if some of the interference fringes are detected incorrectly due to pixel defects in the detector  70 , for example, using this data that represents the average (interference fringe) makes it possible to prevent any negative effects due to such incorrect detections. Moreover, the signal processor  80  does not need to process all of the interference fringes detected by the detector  70  and may just process at least two of the interference fringes detected by the detector  70 . 
         [0053]      FIGS. 4A and 4B  illustrate a modification example of  FIGS. 1A and 1B .  FIG. 4A  is a side view of the spectrometer, and  FIG. 4B  is a top view of the spectrometer. As illustrated in  FIGS. 4A and 4B , the polarizer  60  may be arranged between the beam splitter  40  and the fly&#39;s-eye lens  50 . In this case, after passing through the polarizer  60 , the ordinary light ray eo and the extraordinary light ray oe both oscillate in the same direction as the transmission axis of the polarizer  60 . The light rays from the polarizer  60  are then split into a plurality of light beams by the fly&#39;s-eye lens  50 . In the example illustrated in  FIGS. 4A and 4B , interference fringes are created on the detector  70  due to interference between the ordinary light ray eo component and the extraordinary light ray oe component contained in each of these light beams. 
         [0054]    In the present embodiment as described above, the fly&#39;s-eye lens  50  makes it possible to create a plurality of interference fringes. This makes it possible for the signal processor  80  to calculate the average of this plurality of interference fringes. In this case, even if some of the interference fringes are detected incorrectly due to pixel defects in the detector  70 , for example, using the average described above makes it possible to prevent any negative effects due to such incorrect detections. 
       Embodiment 2 
       [0055]      FIG. 5A  is a side view illustrating a configuration of a spectrometer according to Embodiment 2 and corresponds to  FIG. 1A  in Embodiment 1.  FIG. 5B  is a top view illustrating the configuration of the spectrometer according to the present embodiment and corresponds to  FIG. 1B  in Embodiment 1. The spectrometer according to the present embodiment has the same configuration as the spectrometer according to Embodiment 1 except for the following points. 
         [0056]    In the example illustrated in  FIGS. 5A and 5B , a first polarizer  62  and a second polarizer  64  are arranged between a fly&#39;s-eye lens  50  and a detector  70 . Furthermore, in the example illustrated in  FIGS. 5A and 5B , the first polarizer  62  and the second polarizer  64  are aligned with one another in the direction going from the fly&#39;s-eye lens  50  towards the detector  70  (the Z direction in the figure). The transmission axis of the first polarizer  62  and the transmission axis of the second polarizer  64  are oriented in different directions. More specifically, the transmission axes of the first polarizer  62  and the second polarizer  64  are mutually orthogonal when viewed from the direction running parallel to the optical axis of the light that passes through first polarizer  62  and the second polarizer  64  (the Z direction in the figure). Even more specifically, the transmission axis of the first polarizer  62  is inclined by an angle of 45° towards one of the sides going from the height direction of the spectrometer (the Y direction in the figure) towards the width direction of the spectrometer (the X direction in the figure), and the transmission axis of the second polarizer  64  is inclined by an angle of 45° towards the other of the sides going from the height direction of the spectrometer (the Y direction in the figure) towards the width direction of the spectrometer (the X direction in the figure). 
         [0057]    Some of the light beams that exit from the fly&#39;s-eye lens  50  enter the first polarizer  62 . The rest of the light beams that exit from the fly&#39;s-eye lens  50  enter the first polarizer  64 . More specifically, in the example illustrated in  FIGS. 5A and 5B , when viewed from the direction running parallel to the optical axis of the light beams that enter the fly&#39;s-eye lens  50  (the Z direction in the figure), the fly&#39;s-eye lens  50  includes a plurality of first lenses arranged in two rows running in the width direction of the spectrometer (the X direction in the figure) and a plurality of second lenses arranged beneath the plurality of first lenses and also in two rows running in the width direction of the spectrometer (the X direction in the figure). The light beams that enter the first polarizer  62  are the light beams that exit from the first lenses of the fly&#39;s-eye lens  50 . The light beams that enter the second polarizer  64  are the light beams that exit from the second lenses of the fly&#39;s-eye lens  50 . 
         [0058]      FIG. 6  illustrates an example of a plurality of interference fringes created by the spectrometer illustrated in  FIGS. 5A and 5B  and corresponds to  FIG. 3  in Embodiment 1. In the example illustrated in  FIG. 6 , the plurality of interference fringes are shown as viewed from the front side of the detector  70  Like the plurality of lenses in the fly&#39;s-eye lens  50 , the plurality of interference fringes are arranged in a 4×4 matrix pattern. Furthermore, the interference fringes in the top two rows (the interference fringes in region  72  in the figure) are interference fringes (first interference fringes) created by the light beams that passed through the first polarizer  62 . Meanwhile, the interference fringes in the bottom two rows (the interference fringes in region  74  in the figure) are interference fringes (second interference fringes) created by the light beams that passed through the second polarizer  64 . Moreover, as illustrated in  FIG. 6 , when the interference fringes in the region  72  and the interference fringes in the region  74  are overlaid on top of one another, the bright areas of one group of interference fringes overlap with the dark areas of the other group of interference fringes. 
         [0059]    Return to  FIGS. 5A and 5B . A signal processor  80  calculates the average (a first interference fringe for calculation) of the plurality of interference fringes created by the light beams that passed through the first polarizer  62 . Likewise, the signal processor  80  calculates the average (a second interference fringe for calculation) of the plurality of interference fringes created by the light beams that passed through the second polarizer  64 . The signal processor  80  then calculates the difference between these two averages and applies a Fourier transform to the data that represents this difference. 
         [0060]    More specifically, the intensity distribution I 1  of the interference fringes created by the light beams that passed through the first polarizer  62  can be given by formula (1) below. 
         [0000]      &lt;#1&gt; 
         [0000]        I   1 =∫ 0   ∞   I (σ)(1+cos 2πσΔ) dσ   (1)
 
         [0000]    Here, I(σ) is the intensity distribution of the light from a light source  10 , where σ is wavenumber, and Δ is the optical path difference between the ordinary light ray eo component and the extraordinary light ray oe component. Meanwhile, the phase difference between the ordinary light ray eo component and the extraordinary light ray oe component of the light beams that passed through the second polarizer  64  is shifted by exactly π from the phase difference between the ordinary light ray eo component and the extraordinary light ray oe component of the light beams that passed through the first polarizer  62 . Therefore, the intensity distribution I 2  of the interference fringes created by the light beams that passed through the second polarizer  64  can be given by formula (2) below. 
         [0000]      &lt;#2&gt; 
         [0000]        I   2 =∫ 0   ∞   I (σ)(1−cos 2πσΔ) dσ   (2)
 
         [0061]    As described above, the signal processor  80  then calculates the difference between the intensity distribution I 1  and the intensity distribution I 2 . This difference is given by formula (3) below. 
         [0000]      &lt;#3&gt; 
         [0000]        I   1   −I   2 =2∫ 0   ∞   I (σ)cos 2 πσΔdσ   (3)
 
         [0000]    As shown in formula (3), taking the difference between the intensity distribution I 1  and the intensity distribution I 2  makes it possible to remove the background noise (the first term in formulas (1) and (2)) in the intensity distributions and multiply the signal component (the second term in formulas (1) and (2)) that depends on the optical path difference Δ by 2. 
         [0062]    Furthermore, the signal processor  80  does not need to calculate the abovementioned average on the basis of all of the interference fringes created by the light beams that passed through the first polarizer  62  (that is, all of the interference fringes in the region  72  in the example illustrated in  FIG. 6 ) and may just calculate the abovementioned average on the basis of at least two of the interference fringes created by the light beams that passed through the first polarizer  62 . Similarly, the signal processor  80  does not need to calculate the abovementioned average on the basis of all of the interference fringes created by the light beams that passed through the second polarizer  64  (that is, all of the interference fringes in the region  74  in the example illustrated in  FIG. 6 ) and may just calculate the abovementioned average on the basis of at least two of the interference fringes created by the light beams that passed through the second polarizer  64 . 
         [0063]    Furthermore, the signal processor  80  may not calculate the abovementioned average for the interference fringes created by the light beams that passed through the first polarizer  62 . Similarly, the signal processor  80  may not calculate the abovementioned average for the interference fringes created by the light beams that passed through the second polarizer  64 . In this case, the signal processor  80  simply calculates the difference between one of the interference fringes created by the light beams that passed through the first polarizer  62  (a first interference fringe for calculation) and one of the interference fringes created by the light beams that passed through the second polarizer  64  (a second interference fringe for calculation), for example. 
         [0064]    Moreover, the signal processor  80  may calculate the difference between the average of the interference fringes created by the light beams that passed through the first polarizer  62  (a first interference fringe for calculation) and one of the interference fringes created by the light beams that passed through the second polarizer  64  (a second interference fringe for calculation), for example. Similarly, the signal processor  80  may calculate the difference between one of the interference fringes created by the light beams that passed through the first polarizer  62  (a first interference fringe for calculation) and the average of the interference fringes created by the light beams that passed through the second polarizer  64  (a second interference fringe for calculation), for example. 
         [0065]    As described above, in the present embodiment, some of the light beams from the fly&#39;s-eye lens  50  pass through the first polarizer  62 , and the rest of the light beams from the fly&#39;s-eye lens  50  pass through the second polarizer  64 . The signal processor  80  then calculates the difference between the interference fringes created by the light beams that passed through the first polarizer  62  and the interference fringes created by the light beams that passed through the second polarizer  64 . Therefore, even when background noise present in the interference fringes detected by the detector  70 , that background noise can be removed. 
         [0066]    Furthermore, the present embodiment makes it possible to detect the interference fringes created by the light beams that passed through the first polarizer  62  and the interference fringes created by the light beams that passed through the second polarizer  64  at the same time. In other words, it is not necessary to detect the interference fringes created by the light beams that passed through the first polarizer  62  and the interference fringes created by the light beams that passed through the second polarizer  64  at different times. Therefore, the abovementioned difference can still be calculated even if time-dependent changes occur in the interference fringes detected by the detector  70 . 
         [0067]      FIGS. 7A and 7B  illustrate Modification Example 1 of  FIGS. 5A and 5B .  FIG. 7A  is a side view of the spectrometer, and  FIG. 7B  is a top view of the spectrometer. As illustrated in  FIGS. 7A and 7B , the first polarizer  62  and the second polarizer  64  may be arranged between the beam splitter  40  and the fly&#39;s-eye lens  50 . In the example illustrated in  FIGS. 7A and 7B , the first polarizer  62  and the second polarizer  64  are aligned with one another in the direction going from the beam splitter  40  towards the fly&#39;s-eye lens  50  (the Z direction in the figure). The light rays that pass through the first polarizer  62  enter the plurality of first lenses of the fly&#39;s-eye lens  50 . The light rays that pass through the second polarizer  64  enter the plurality of second lenses of the fly&#39;s-eye lens  50 . 
         [0068]      FIGS. 8A and 8B  illustrate Modification Example 2 of  FIGS. 5A and 5B .  FIG. 8A  is a side view of the spectrometer, and  FIG. 8B  is a top view of the spectrometer. As illustrated in  FIGS. 8A and 8B , the first polarizer  62  is arranged between the beam splitter  40  and the fly&#39;s-eye lens  50 , and the second polarizer  64  is arranged between the fly&#39;s-eye lens  50  and the detector  70 . The light rays that pass through the first polarizer  62  enter the plurality of first lenses of the fly&#39;s-eye lens  50 . The light beams that enter the second polarizer  64  are the light beams that exit from the second lenses of the fly&#39;s-eye lens  50 . 
       Embodiment 3 
       [0069]      FIG. 9A  is a side view illustrating a configuration of a spectrometer according to Embodiment 3 and corresponds to  FIG. 1A  in Embodiment 1.  FIG. 9B  is a top view illustrating the configuration of the spectrometer according to the present embodiment and corresponds to  FIG. 1B  in Embodiment 1. The spectrometer according to the present embodiment has the same configuration as the spectrometer according to Embodiment 1 except for the following points. 
         [0070]    In the example illustrated in  FIGS. 9A and 9B , the fly&#39;s-eye lens  50  illustrated in  FIGS. 1A and 1B  is replaced by a lens  52  (a first lens) and a plurality of cylindrical lenses  54  (second lenses). In other words, in the example illustrated in  FIGS. 9A and 9B , the optical member (the fly&#39;s-eye lens  50  in the example illustrated in  FIGS. 1A and 1B ) includes the lens  52  and the plurality of cylindrical lenses  54 . The lens  52  is a biconvex Fourier transform lens that makes it possible to focus light rays into a single point. The cylindrical lenses  54  make it possible to focus light beams into straight lines. 
         [0071]    The light rays that exit from a beam splitter  40  pass through the lens  52  and then pass through the plurality of cylindrical lenses  54 . All of the components of the light rays that exit from the beam splitter  40  enter the lens  52 . In the example illustrated in  FIGS. 9A and 9B , two of the cylindrical lenses  54  are arranged in the height direction of the spectrometer (the Y direction in the figure). Each of the cylindrical lenses  54  has a first surface that faces the lens  52  and a second surface on the side opposite to the first surface. When viewed from the width direction of the spectrometer (the X direction in the figure), the first surface of each cylindrical lens  54  is a curved surface, and the second surface of each cylindrical lens  54  is a flat surface. The two cylindrical lenses  54  are arranged such that the second surface of the one of the cylindrical lenses  54  and the second surface of the other of the cylindrical lenses  54  are aligned with one another. 
         [0072]    When viewed from the direction running parallel to the optical axis of the light (an ordinary light ray eo and an extraordinary light ray oe) that enters the plurality of cylindrical lenses  54  (the Z direction in the figure), each of the cylindrical lenses  54  is positioned within the spot of the ordinary light ray eo and the spot of the extraordinary light ray oe. Therefore, the ordinary light ray eo and the extraordinary light ray oe enter all of the cylindrical lenses  54 . 
         [0073]    The cylindrical lenses  54  focus the light beams from the beam splitter  40  into straight lines. In the example illustrated in  FIGS. 9A and 9B , each of the cylindrical lenses  54  focuses the light beams into a straight line that extends in the width direction of the spectrometer (the X direction in the figure). In this way, the light rays from the beam splitter  40  are split into a plurality of light beams by the cylindrical lenses  54 . Moreover, in the example illustrated in  FIGS. 9A and 9B , a light shield  56  is arranged between the plurality of split light beams. In this way, even if a portion of the light beams that passed through the cylindrical lenses  54  stray off path, the light shield  56  blocks that stray light. This makes it possible to prevent stray light from reaching a detector  70 . 
         [0074]    The plurality of light beams split by the cylindrical lenses  54  pass through a polarizer  60  and then arrive at the detector  70 . Each of the light beams split by the cylindrical lenses  54  includes an ordinary light ray eo component and an extraordinary light ray oe component. Therefore, like in the example illustrated in  FIGS. 1A and 1B , a plurality of interference fringes are created. The detector  70  detects this plurality of interference fringes. 
         [0075]    Like in the example illustrated in  FIGS. 1A and 1B , a signal processor  80  calculates the average of the plurality of interference fringes on the basis of the detection results from the detector  70 . The signal processor  80  then applies a Fourier transform to the data that represents that average. 
         [0076]      FIG. 10  illustrates an example of the plurality of interference fringes created by the spectrometer illustrated in  FIGS. 9A and 9B  and corresponds to  FIG. 3  in Embodiment 1. In the example illustrated in  FIG. 10 , the plurality of interference fringes are shown as viewed from the front side of the detector  70 . As described with reference to  FIGS. 9A and 9B , the plurality of cylindrical lenses  54  are arranged in the height direction of the spectrometer (the Y direction in the figure). As a result, the plurality of interference fringes are also arranged in the height direction of the spectrometer (the Y direction in the figure). In the example illustrated in  FIG. 10 , the interference fringe in a region  72  is the interference fringe (a first interference fringe) created by the light beams that passed through the upper cylindrical lens  54 . Meanwhile, the interference fringe in a region  74  is the interference fringe (a second interference fringe) created by the light beams that passed through the lower cylindrical lens  54 . As described with reference to  FIGS. 9A and 9B , each of the cylindrical lenses  54  focuses the light beams into a straight line that extends in the width direction of the spectrometer (the X direction in the figure). As a result, each interference fringe also extends in the width direction of the spectrometer (the X direction in the figure). 
         [0077]      FIGS. 11A and 11B  illustrate a modification example of  FIGS. 9A and 9B  and correspond to  FIGS. 4A and 4B  in Embodiment 1.  FIG. 11A  is a side view of the spectrometer, and  FIG. 11B  is a top view of the spectrometer. As illustrated in  FIGS. 11A and 11B , the light rays from the beam splitter  40  may pass through the polarizer  60  before being split into a plurality of light beams by the plurality of cylindrical lenses  54 . More specifically, in the example illustrated in  FIGS. 11A and 11B , the polarizer  60  is arranged between the lens  52  and the plurality of cylindrical lenses  54 . 
       Embodiment 4 
       [0078]      FIG. 12A  is a side view illustrating a configuration of a spectrometer according to Embodiment 4 and corresponds to  FIG. 5A  in Embodiment 2 and  FIG. 9A  in Embodiment 3.  FIG. 12B  is a top view illustrating the configuration of the spectrometer according to the present embodiment and corresponds to  FIG. 5B  in Embodiment 2 and  FIG. 9B  in Embodiment 3. The spectrometer according to the present embodiment has the same configuration as the spectrometer according to Embodiment 2 and the spectrometer according to Embodiment 3 except for the following points. 
         [0079]    Like in the example illustrated in  FIGS. 5A and 5B , in the example illustrated in  FIGS. 12A and 12B , a first polarizer  62  and a second polarizer  64  are arranged between a plurality of cylindrical lenses  54  and a detector  70 . Furthermore, in the example illustrated in  FIGS. 12A and 12B , the first polarizer  62  and the second polarizer  64  are aligned with one another in the direction going from the plurality of cylindrical lenses  54  towards the detector  70  (the Z direction in the figure). The transmission axis of the first polarizer  62  and the transmission axis of the second polarizer  64  are oriented in different directions. More specifically, the transmission axes of the first polarizer  62  and the second polarizer  64  are mutually orthogonal when viewed from the direction running parallel to the optical axis of the light that passes through first polarizer  62  and the second polarizer  64  (the Z direction in the figure). Even more specifically, the transmission axis of the first polarizer  62  is inclined by an angle of 45° towards one of the sides going from the height direction of the spectrometer (the Y direction in the figure) towards the width direction of the spectrometer (the X direction in the figure), and the transmission axis of the second polarizer  64  is inclined by an angle of 45° towards the other of the sides going from the height direction of the spectrometer (the Y direction in the figure) towards the width direction of the spectrometer (the X direction in the figure). 
         [0080]    The light beams that exit from one of the two cylindrical lenses  54  enter the first polarizer  62 . The light beams that exit from the other of the two cylindrical lenses  54  enter the second polarizer  64 . 
         [0081]    The detector  70  detects an interference fringe (a first interference fringe) created by the light beams that passed through the first polarizer  62  and an interference fringe (a second interference fringe) created by the light beams that passed through the second polarizer  64 . 
         [0082]    A signal processor  80  calculates the difference between the first interference fringe and the second interference fringe. The signal processor  80  then applies a Fourier transform to the data that represents that difference. Here, as described above with reference to formula (3), taking the difference between the intensity distribution I 1  of the first interference fringe and the intensity distribution I 2  of the second interference fringe makes it possible to remove the background noise (the first term in formulas (1) and (2)) in the intensity distributions and multiply the signal component (the second term in formulas (1) and (2)) that depends on the optical path difference Δ by 2. 
         [0083]      FIG. 13  illustrates an example of the plurality of interference fringes created by the spectrometer illustrated in  FIGS. 12A and 12B  and corresponds to  FIG. 10  in Embodiment 3. In the example illustrated in  FIG. 13 , the plurality of interference fringes are shown as viewed from the front side of the detector  70 . As described with reference to  FIGS. 12A and 12B , the plurality of cylindrical lenses  54  are arranged in the height direction of the spectrometer (the Y direction in the figure). As a result, the plurality of interference fringes are also arranged in the height direction of the spectrometer (the Y direction in the figure). In the example illustrated in  FIG. 13 , the interference fringe in a region  72  is the interference fringe (a first interference fringe) created by the light beams that passed through the first polarizer  62 . Meanwhile, the interference fringe in a region  74  is the interference fringe (a second interference fringe) created by the light beams that passed through the second polarizer  64 . Moreover, as illustrated in  FIG. 13 , when the interference fringe in the region  72  and the interference fringe in the region  74  are overlaid on top of one another, the bright areas of one interference fringe overlap with the dark areas of the other interference fringe. 
         [0084]      FIGS. 14A and 14B  illustrate Modification Example 1 of  FIGS. 12A and 12B  and correspond to  FIGS. 7A and 7B  in Embodiment 2.  FIG. 14A  is a side view of the spectrometer, and  FIG. 14B  is a top view of the spectrometer. As illustrated in  FIGS. 14A and 14B , the light rays from the beam splitter  40  may pass through the first polarizer  62  and the second polarizer  64  before being split into a plurality of light beams by the plurality of cylindrical lenses  54 . More specifically, in the example illustrated in  FIGS. 14A and 14B , the first polarizer  62  and the second polarizer  64  are arranged between the lens  52  and the plurality of cylindrical lenses  54 . Furthermore, the first polarizer  62  and the second polarizer  64  are aligned with one another in the direction going from the beam splitter  40  towards the plurality of cylindrical lenses  54  (the Z direction in the figure). 
         [0085]      FIGS. 15A and 15B  illustrate Modification Example 2 of  FIGS. 12A and 12B  and correspond to  FIGS. 8A and 8B  in Embodiment 2.  FIG. 15A  is a side view of the spectrometer, and  FIG. 15B  is a top view of the spectrometer. In the example illustrated in  FIGS. 15A and 15B , some of the light rays from the beam splitter  40  pass through the first polarizer  62  before the light rays from the beam splitter  40  are split by the plurality of cylindrical lenses  54 , and the rest of the light rays from the beam splitter  40  pass through the second polarizer  64  after the light rays from the beam splitter  40  are split by plurality of cylindrical lenses  54 . The first polarizer  62  is positioned between the lens  52  and the plurality of cylindrical lenses  54 , and the second polarizer  64  is positioned between the plurality of cylindrical lenses  54  and the detector  70 . 
         [0086]    Embodiments of the present invention were described above with reference to figures. However, these embodiments are only examples of the present invention, and various configurations other than those described above can be used.