Patent Publication Number: US-9903758-B2

Title: Spectral measurement device and analysis apparatus

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application claims priority under 35 U.S.C. § 119 to Japanese Patent Application No. 2016-112046 filed on Jun. 3, 2016 and Japanese Patent Application No. 2016-231106 filed on Nov. 29, 2016, the entire contents of which are incorporated herein by reference. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a spectral measurement device and an analysis apparatus. 
     2. Description of the Related Art 
     Spectrometers are typically large and stationary, and researchers have generally used spectrometers in a lab setting for spectroscopic analysis. In recent years, demand for on-site spectroscopic analysis has been growing, and miniaturized spectrometers are being developed. Light of various wavelengths, such as ultraviolet light, visible light, near-infrared light, or infrared light, may be used in spectroscopic analysis depending on the analysis target. Near-infrared light including a wavelength region also referred to as “in vivo window” has high penetration in multi-moisture specimens including biological tissue and can be used to perform noninvasive measurement of a specimen. As such, near-infrared light spectrometers are useful for conducting measurements in various settings including outdoor settings, for example. Thus, efforts are currently being made to develop a miniaturized spectrometer that uses the near-infrared light region. 
     For example, a compact near-infrared spectrometer is known that includes a concave diffraction grating as a spectroscopic element having a wavelength dispersing function and a light collecting function, and a one-dimensional array sensor that detects dispersed light. The one-dimensional array sensor may be configured by a Si photodiode having detection sensitivity in a visible region to a near-infrared region with a wavelength of up to 1100 nm, and an InGaAs photodiode having a detection sensitivity in a near infrared region with a wavelength of 900 nm to 2500 nm, for example. 
     As a method of reducing the size and cost of a spectroscope, one photodiode may be used instead of a one-dimensional array sensor, and the diffraction grating may be rotated, for example. However, it is rather difficult to spectrally separate light with a small device at a low cost using the method of rotating the diffraction grating, and reliable spectral measurements may not be stably obtained owing to influences of vibrations caused by the rotation, for example. 
     [Background Art] Japanese Unexamined Patent 
     
         
         Application Publication No. 2015-148485 
       
    
     SUMMARY OF THE INVENTION 
     An aspect of the present invention is directed to providing a technique for stably obtaining reliable spectral measurements by spectrally separating light using a small device at a low cost. 
     According to one embodiment of the present embodiment, a spectral measurement device is provided that includes a light reflection grating including a plurality of movable gratings arranged side by side along a lateral direction to have a same length in a longitudinal direction and a movable grating drive unit configured to displace the plurality of movable gratings to alter a grating pattern of the light reflection grating, a light detecting element configured to detect light that is incident on the light reflection grating and reflected by the light reflection grating, a storage unit storing a relationship between a light quantity to be detected by the light detecting element and corresponding light intensities at a plurality of different wavelengths for each of a plurality of different grating patterns of the light reflection grating, and a computation unit configured to calculate light intensities at the plurality of different wavelengths of the light incident on the light reflection grating based on a detected light quantity of the incident light detected by the light detecting element for each of the plurality of different grating patterns by altering the grating pattern of the light reflection grating based on the relationship between the light quantity to be detected by the light detecting element and the corresponding light intensities at the plurality of different wavelengths for each of the plurality of different grating patterns stored in the storage unit. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a diagram illustrating an example configuration of a spectrometer; 
         FIG. 2  is a diagram illustrating an example configuration of a spectral measurement device according to a first embodiment of the present invention; 
         FIGS. 3A and 3B  are diagrams illustrating an example configuration of a light reflection grating according to the first embodiment; 
         FIG. 4  is a diagram illustrating an example operation of the light reflection grating according to the first embodiment; 
         FIGS. 5A and 5B  are diagrams illustrating example grating patterns of the light reflection grating according to the first embodiment; 
         FIGS. 6A and 6B  are diagrams illustrating other example grating patterns of the light reflection grating according to the first embodiment; 
         FIG. 7  is a flowchart illustrating an example spectral measurement method implemented by the spectral measurement device according to the first embodiment; 
         FIGS. 8A-8C  are diagrams illustrating other example grating patterns of the light reflection grating according to the first embodiment; 
         FIGS. 9A-9C  are diagrams illustrating an alternative configuration of the light reflection grating according to the first embodiment; 
         FIG. 10  is a diagram illustrating an alternative configuration of the spectral measurement device according to the first embodiment; 
         FIGS. 11A-11C  are diagrams illustrating an example configuration of a light reflection grating according to a second embodiment of the present invention; 
         FIGS. 12A and 12B  are diagrams illustrating an example operation of the light reflection grating according to the second embodiment; 
         FIG. 13  is a diagram illustrating an alternative configuration of the light reflection grating according to the second embodiment; 
         FIG. 14  is a diagram illustrating an example configuration of a spectral measurement device according to a third embodiment of the present invention; 
         FIGS. 15A and 15B  are diagrams illustrating an example configuration of a light reflection grating according to the third embodiment; 
         FIG. 16  is a diagram illustrating an example operation of the light reflection grating according to the third embodiment; 
         FIGS. 17A and 17B  are diagrams illustrating example grating patterns of the light reflection grating according to the third embodiment; 
         FIGS. 18A and 18B  are diagrams illustrating other grating patterns of the light reflection grating according to the third embodiment; 
         FIG. 19  is a flowchart illustrating an example spectral measurement method implemented by the spectral measurement device according to the third embodiment; 
         FIGS. 20A-20C  are diagrams illustrating other example grating patterns of the light reflection grating according to the third embodiment; 
         FIGS. 21A-21C  are diagrams illustrating an alternative configuration of the light reflection grating according to the third embodiment; 
         FIG. 22  is a diagram illustrating an alternative configuration of the spectral measurement device according to the third embodiment; 
         FIG. 23  is a diagram illustrating an example configuration of a light reflection grating according to a fourth embodiment of the present invention; and 
         FIG. 24  is a diagram illustrating an example configuration of an analysis apparatus according to a fifth embodiment of the present invention. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     In the following, embodiments of the present invention are described with reference to the accompanying drawings. Note that in the following descriptions, elements having the same features or functions are given the same reference numerals and overlapping descriptions thereof may be omitted. 
     First Embodiment 
     First, a general configuration of a spectrometer using a concave diffraction grating will be described with reference to  FIG. 1 . The spectrometer of  FIG. 1  includes a concave diffraction grating  902  that diffracts and separates the wavelengths of light incident through a slit  901  formed in a substrate  900 . Light that has been diffracted by the concave diffraction grating  902  is incident on a photodetector array  903  formed on the substrate  900 , and a spectrum of the diffracted light can be obtained by the photodetector array  903 . 
     The wavelength sensitivity (detectable wavelength region) of a photodetector forming the photodetector array  903  is one of the factors determining the measurable wavelength region of the spectrometer having the above configuration. The wavelength sensitivity of the photodetector is determined by the material forming the photodetector. In a commonly used Si photodiode, the detectable wavelength range is up to 1100 nm, but in order to measure a wavelength region that is longer, a compound semiconductor photodiode, such as a InGaAs photodiode, has to be used, for example. Compound semiconductor photodiodes are relatively inexpensive if they are of a single pixel, but when they are used in an array element, such as photodiode array, they may become quite expensive such that a spectrometer using such a photodiode array becomes quite expensive. For this reason, it is difficult to fabricate a spectrometer using a conventional concave diffraction grating that is within a price range for widespread use, and it has been a challenge to develop a compact and inexpensive spectrometer having a wide detection wavelength range. 
     (Spectral Measurement Device) 
     In the following, a spectral measurement device  100  according to a first embodiment of the present invention will be described with reference to  FIG. 2 . 
     In  FIG. 2 , the spectral measurement device  100  according to the present embodiment includes a first substrate  10  and a second substrate  20 . The first substrate  10  is provided with a light entrance portion  11  and a light exit portion  12  that penetrate through the first substrate  10  from one surface to the other surface of the first substrate  10 . Also, on one surface of the first substrate  10 , a light reflection grating  30  is provided between the light entrance portion  11  and the light exit portion  12 . Also, a first concave light reflecting portion  21  and a second concave light reflecting portion  22  are provided on one surface of the second substrate  20 . Further, a light detecting element  50  is provided on the other surface of the first substrate  10  where the light exit portion  12  is formed. The light detecting element  50  may be a single pixel photodiode chip made of Si, Ge, or InGaAs, for example. 
     The spectral measurement device  100  according to the present embodiment also includes a movable grating drive power source  60  as a movable grating drive unit that is connected to the light reflection grating  30 , and a control unit  70  that is connected to the movable grating drive power source  60  and the light detecting element  50 . The control unit  70  includes a grating control unit  71 , a computation unit  72 , and a storage unit  73 . 
     The broken line arrows in  FIG. 2  represent an optical path of light incident into the light entrance portion  11 . In the spectral measurement device  100  according to the present embodiment, light entering the light entrance portion  11  is reflected by the first concave light reflecting portion  21  of the second substrate  20  to be incident on the light reflection grating  30  formed on the first substrate  10  and reflected by the light reflection grating  30 . The light reflected by the light reflection grating  30  is reflected by the second concave light reflecting portion  22  of the second substrate  20  and focused by the light exit portion  12  of the first substrate  10  to form an image. The light focused in the above-described manner is detected by the light detecting element  50 . 
     Note that the first substrate  10  and the second substrate  20  are fixed in place by a spacer  40  that are provided between the first substrate  10  and the second substrate  20  such that one surface of the first substrate  10  and one surface of the second substrate  20  face each other. Also, when fixing the first substrate  10  and the second substrate  20  by the spacer  40 , the first substrate  10  and the second substrate  20  are aligned so as to be in a desired position. 
     Note that a spectral measurement device according to an embodiment of the present invention is not limited to the wafer-level spectral measurement device  100  as illustrated in  FIG. 2  as long as it includes a light reflection grating as described below. Also, although the light entrance portion  11  and the light exit portion  12  are provided on the first substrate  10  in the spectral measurement device  100  of  FIG. 2 , in other embodiments, slits formed in a separate substrate from the first substrate  10  may be provided as a light entrance portion and a light exit portion, for example. 
     (Light Reflection Grating) 
     In the following, the light reflection grating  30  according to the present embodiment will be described with reference to  FIGS. 3A and 3B .  FIG. 3A  is a cross-sectional view of the light reflection grating  30  across a longitudinal direction of a grating forming the light reflection grating  30 , and  FIG. 3B  is a cross-sectional view of the light reflection grating  30  across a lateral direction perpendicular to the longitudinal direction of the light reflection grating  30 . Note that in the figures illustrating the light reflection grating  30  according to the present embodiment, direction X represents the lateral direction of the light reflection grating  30 , direction Y represents the longitudinal direction of the light reflection grating  30 , and direction Z represents a direction perpendicular to direction X and direction Y. 
     Also, in the following descriptions of embodiments of the present invention, a plurality of fixed electrodes  32   a  to  32   l  may generically be referred to as “fixed electrode  32 ” and a plurality of movable gratings  33   a  to  33   l  may generically be referred to as “movable grating  33 ”. Further, in the light reflection grating  30  according to the present embodiment, twelve fixed electrodes  32   a  to  32   l  and twelve movable gratings  33   a  to  33   l  are provided as an example. However, the number of fixed electrodes  32  and the number of movable gratings  33  provided in the light reflection grating  30  is not limited to twelve. 
     The light reflection grating  30  according to the present embodiment includes a substrate  31  having a recess  31   a  formed therein. The fixed electrodes  32   a  to  32   l  are formed on a bottom surface  31   b  of the recess  31   a . Also, the movable gratings  33   a  to  33   l  are formed on an upper surface  31   c  of an outer edge of the substrate  31  surrounding the recess  31   a , and in this way, the movable gratings  33   a  to  33   l  cover the recess  31   a . The plurality of fixed electrodes  32   a  to  32   l  and the plurality of movable gratings  33   a  to  33   l  are arranged to extend the same length in the longitudinal direction and are arranged side by side in the lateral direction. 
     Also, as illustrated in  FIG. 3A , the two longitudinal direction side ends of each of the movable gratings  33   a  to  33   l  are supported by the upper surface  31   c  of the outer edge surrounding the recess  31   a  of the substrate  31 . In this way, the movable grating  33  is arranged to have a doubly supported beam configuration. In the present embodiment, for example, the depth D of the recess  31   a  formed in the substrate  31  may be 10 μm to 100 μm, and the length L in the longitudinal direction of the fixed electrode  32  may be 100 μm to 3 mm. The width W of the fixed electrode  32  and the movable grating  33  in the lateral direction may be 1 μm to 100 μm, and the thickness t of the movable grating  33  may be 1 μm to 10 μm. 
     In the present embodiment, the fixed electrode  32  and the movable grating  33  form a pair to face each other. That is, the fixed electrodes  32   a  to  32   l  and the movable grids  33   a  to  33   l  are respectively arranged to face each other. Specifically, the fixed electrode  32   a  and the movable grating  33   a , the fixed electrode  32   b  and the movable grating  33   b , the fixed electrode  32   c  and the movable grating  33   c , the fixed electrode  32   d  and the movable grating  33   d , the fixed electrode  32   e  and the movable grating  33   e , and the fixed electrode  32   f  and the movable grating  33   f  are arranged to face each other. Further, the fixed electrode  32   g  and the movable grating  33   g , the fixed electrode  32   h  and the movable grating  33   h , the fixed electrode  32   i  and the movable grating  33   i , the fixed electrode  32   j  and the movable grating  33   j , the fixed electrode  32   k  and the movable grating  33   k , and the fixed electrode  32   l  and the movable grating  33   l  are arranged to face each other. More specifically, the fixed electrodes  32   a  to  32   l  and the movable gratings  33   a  to  33   l  are arranged such that one surface of each of the fixed electrodes  32   a  to  32   l  face one surface of the corresponding movable gratings  33   a  to  33   l.    
     The substrate  31  may be made of an insulator or a semiconductor such as Si. The light reflection grating  30  according to the present embodiment may be formed on one surface of the first substrate  10 , or on a substrate other than the first substrate  10 . In the case where the light reflection grating  30  according to the present embodiment is formed on one surface of the first substrate  10 , the first substrate  10  can be used as the substrate  31  of the light reflection grating  30 , and in this way, further downsizing and cost reduction can be achieved. Also, in the case where the substrate  31  is made of a semiconductor, an insulating film is formed on the bottom surface  31   b  of the recess  31   a  of the substrate  31 , and the fixed electrodes  32   a  to  32   l  are formed on the insulating film. An insulating film is also formed on the upper surface  31   c  of the substrate  31 , and the movable gratings  33   a  to  33   l  are formed on the insulating film. Further, in some embodiments, an insulating film may be formed on the entire surface that is exposed in the recess  31   a  of the substrate  31 , for example. 
     Each of the fixed electrodes  32   a  to  32   l  is made of an electrode material used in various semiconductor devices, such as aluminum (Al), platinum (Pt), gold (Au), and other conductive metal materials, for example. Each of the movable gratings  33   a  to  33   l  may be made of a conductive metal material or a semiconductor material. A reflection film  34  for reflecting light is formed on the other surface of the movable gratings  33   a  to  33   l  on the opposite side of the one surface facing the corresponding fixed electrodes  32   a  to  32   l . The reflection film  34  is a metal film that may be made of aluminum, silver, gold or the like according to the wavelength of light to be spectrally analyzed. 
     In the spectral measurement device  100  according to the present embodiment, the movable grating drive power source  60  is connected to the fixed electrodes  32   a  to  32   l  and the movable gratings  33   a  to  33   l , and the movable grating drive power source  60  is configured to apply a voltage between the corresponding pairs of the fixed electrodes  32   a  to  32   l  and the movable gratings  33   a  to  33   l.    
     When the potential difference between the fixed electrode  32  and the movable grating  33  is 0V, the movable grating  33  is not displaced, and the fixed electrode  32  and the movable grating  33  are spaced apart by a distance D 1  as illustrated in  FIG. 3A . On the other hand, when a predetermined voltage, such as a voltage that causes a potential difference between the fixed electrode  32  and the movable grating  33  to be several dozen volts (V), is applied between the fixed electrode  32  and the movable grating  33 , the fixed electrode  32  and the movable grating  33  are attracted to each other by an electrostatic attractive force, and the movable grating  33  is displaced toward the fixed electrode  32  as illustrated in  FIG. 4 . As a result, the movable grating  33  moves toward the fixed electrode  32 , and the distance between the movable grating  33  and the fixed electrode  32  becomes distance D 2 , which is shorter than the distance D 1 . 
     In the present embodiment, the grating pattern of the light reflection grating  30  can be altered by changing a combination of voltages applied or changing the voltage applied between the fixed electrodes  32   a  to  32   l  and the movable gratings  33   a  to  33   l.    
       FIG. 3B  illustrates an example case where no voltage is applied to the fixed electrodes  32   a  to  32   l  and the movable gratings  33   a  to  33   l , such as a case where the applied voltage is 0 V. In this case, the movable gratings  33   a  to  33   l  are not displaced, and as such, light incident on the reflective film  34  arranged on the light entering side surface of the movable gratings  33   a  to  33   l  is specularly reflected without deviation. 
       FIG. 5A  illustrates an example case where a voltage is alternately applied to every other movable grating  33 . That is, a predetermined voltage is applied between the fixed electrode  32   b  and the movable grating  33   b , the fixed electrode  32   d  and the movable grating  33   d , the fixed electrode  32   f  and the movable grating  33   f , the fixed electrode  32   h  and the movable grating  33   h , the fixed electrode  32   j  and the movable grating  33   j , and the fixed electrode  32   l  and the movable grating  33   l . In this case, the grating pattern of the light reflection grating  30  is arranged such that every other movable grating  33 , that is, the movable gratings  33   b ,  33   d ,  33   f ,  33   h ,  33   j , and  33   l , is displaced downward. 
       FIG. 5B  illustrates an example case where a voltage is alternately applied and not applied to every two adjacent movable gratings  33 . That is, a predetermined voltage is applied between the fixed electrode  32   a  and the movable grating  33   a , the fixed electrode  32   b  and the movable grating  33   b , the fixed electrode  32   e  and the movable grating  33   e , the fixed electrode  32   f  and the movable grating  33   f , the fixed electrode  32   i  and the movable grating  33   i , and the fixed electrode  32   j  and the movable grating  33   j . In this case, the grating pattern of the light reflection grating  30  is arranged such that every two movable gratings  33 , that is, the movable gratings  33   a ,  33   b ,  33   e ,  33   f ,  33   i , and  33   j , are displaced downward. 
       FIG. 6A  illustrates an example case where a voltage is applied between the pairs of fixed electrode  32  and the movable grating  33  other than the pairs of the fixed electrode  32   a  and the movable grating  33   a , the fixed electrode  32   e  and the movable grating  33   e , and the fixed electrode  32   i  and the movable grating  33   i . In this case, the grating pattern of the light reflection grating  30  is arranged such that the movable gratings  33   b ,  33   c ,  33   d ,  33   f ,  33   g ,  33   h ,  33   j ,  33   k , and  33   l  are displaced downward. 
       FIG. 6B  illustrates an example case where a predetermined voltage is applied between the fixed electrode  32   b  and the movable grating  33   b , the fixed electrode  32   c  and the movable grating  33   c , the fixed electrode  32   d  and the movable grating  33   d , the fixed electrode  32   f  and the movable grating  33   f , the fixed electrode  32   j  and the movable grating  33   j , and the fixed electrode  33   k  and the movable grating  33   k . In this case, the grating pattern of the light reflection grating  30  is arranged such that the movable gratings  33   b ,  33   c ,  33   d ,  33   f ,  33   j , and  33   k  are displaced downward. 
     Note that in a given grating pattern of a light reflection grating, the relationship between the voltage V of incident light detected by a light detecting element and the intensities Iλ1 to Iλn of the light at a plurality of different wavelengths λ1 to Δn can be expressed by the following equation (1). The voltage V detected by the light detecting element corresponds to the light quantity of the light incident on the light detecting element. Also, in the following equation (1), “a1” to “an” represent coefficients that vary depending on the grating pattern of the light reflection grating.
 
V= a 1× Iλ 1+ a 2× Iλ 2+ . . . + an×Iλn   (1)
 
     The storage unit  73  stores the relationship between positions of the movable gratings  33  in each of a plurality of different grating patterns of the light reflection grating  30  and the corresponding coefficients “a1” to “an” for each of the different grating patterns. That is, the storage unit  73  stores the relationship between a voltage based on a light quantity to be detected by the light detecting element  50  and corresponding light intensities at the plurality of different wavelengths for each of the plurality of different grating patterns. The grating control unit  71  of the control unit  70  performs control for altering the grating pattern of the light reflection grating  30  to a different grating pattern. Under control of the grating control unit  71 , the movable grating drive power source  60  applies a voltage between corresponding pairs of the fixed electrodes  32   a  to  32   l  and the movable gratings  33   a  to  33   l . That is, the grating control unit  71  controls the movable grating drive power source  60  to apply a voltage between predetermined pairs of the fixed electrodes  32   a  to  32   l  and the movable gratings  33   a  to  33   l  so that the light reflection grating  30  is arranged into one of the grating patterns stored in the storage unit  73 . 
     In the present embodiment, the grating pattern of the light reflection grating  30  is rearranged into n or more different grating patterns, the light detecting element  50  detects voltages V1 to Vn for each of the different grating patterns, and an inverse operation is performed based on a determinant represented by the formula indicated below. In this way, the intensities Iλ1 to Iλn of light at the plurality of different wavelengths λ1 to λn can be calculated. Note that in the formula indicated below, “a11” to “ann” represent coefficients. The inverse operation based on the determinant represented by the formula below is performed by the computation unit  72  of the control unit  70 . 
     
       
         
           
             
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     The spectral measurement device  100  according to the present embodiment can obtain spectral characteristics of incident light based on the intensities Iλ1 to Iλn of light at the wavelengths λ1 to λn that have been obtained by the above inverse operation. 
     In the following, an example spectral measurement method implemented by the spectral measurement device  100  according to the present embodiment will be described with reference to  FIG. 7 .  FIG. 7  is a flowchart illustrating an example spectral measurement method that is controlled by the control unit  70  of the spectral measurement device  100  according to the present embodiment. In the present example, it is assumed that the relationship between 1st to n-th grating patterns and the corresponding coefficients “a11” to “ann” of the above formula representing the determinant is obtained in advance through measurement and/or calculation and stored in the storage unit  73 . 
     In step S 102 , a variable “i” is set to “1” (i=1). 
     Then, in step S 104 , the movable grating drive power source  60  applies a voltage to the movable gratings  33  under control of the grating control unit  71  such that the grating pattern of the light reflection grating  30  is arranged into an i-th grating pattern. 
     Then, in step S 106 , a voltage Vi corresponding to the light quantity of light incident on the light detecting element  50  while the light reflection grating  30  is in the i-th grating pattern is obtained. The detected voltage Vi is temporarily stored in the control unit  70 . 
     Then, in step S 108 , a value obtained by adding 1 to the current value of the variable “i” is set up as a new value for the variable “i”. 
     Then, in step S 110 , a determination is made as to whether the value of “i” exceeds “n”. If the value of “i” exceeds “n”, the process proceeds to step S 112 . If the value of “i” does not exceed “n”, the process goes back to step S 104  and the processes of steps S 104  to S 108  are repeated. 
     Then, in step S 112 , based on information stored in the storage unit  73  and the voltages V1 to Vn detected by the light detection element  50  for each of the different grating patterns, the computation unit  72  performs the inverse operation based on the determinant represented by the above formula. In this way, the intensities Iλ1 to Iλn of light at the wavelengths λ1 to λn can be obtained, and the spectral characteristics of the incident light can be obtained. 
     According to an aspect of the present embodiment, the number of movable gratings  33  may be increased to thereby increase the wavelength resolution, for example. Further, the light reflection grating  30  may be rearranged into more than n different grating patterns, and the light detecting element  50  may detect the light quantity for each of the different grating patterns. In this way, accuracy of the obtained light spectrum may be further improved, for example. 
     Note that in the example described above, the light reflection grating  30  is arranged into n different grating patterns. However, in other examples of the present embodiment, the amount of displacement of the movable gratings  33  may be varied while the light reflection grating  30  is in the same grating displacement pattern. Specifically, for example, the light reflection grating  30  may be arranged such that every other movable grating  33  is displaced downward. In such a state, the amount of displacement of the displaced movable grating  33  may be increased as illustrated in  FIG. 8A , or the amount of displacement of the displaced movable gratings  33  may be decreased as illustrated in  FIG. 8B , and the light detecting element  50  may measure the light quantity of incident light for each variation in the amount of displacement of the movable gratings  33 . For example, displacement of the movable gratings  33  may be controlled to be in n different amounts of displacement, the light detecting element  50  may detect voltages V1 to Vn for the respective amounts of displacement, and an inverse operation may be performed using the determinant represented by a formula similar to the above formula but with different coefficients. In this way, the intensities Iλ1 to Iλn of light at wavelengths λ1 to λn may be calculated. Note that  FIG. 8C  illustrates an example case where no voltage is applied between the fixed electrodes  32  and the movable gratings  33 . 
     Also, the light reflection grating  30  of the spectral measurement device  100  according to the present embodiment may have an alternative configuration as illustrated in  FIGS. 9A-9C  in which one common fixed electrode  32  is provided in place of the plurality of fixed electrodes  32   a  to  32   l  on the bottom surface  31   b  of the recess  31   a  of the substrate  31 . Even with such a configuration, a desired grating pattern of the light reflection grating  30  can be obtained by controlling the potential of the fixed electrode  32  to be constant and varying the voltage applied to each of the movable gratings  33   a  to  33   l .  FIG. 9A  illustrates an example case where the movable gratings  33  are displaced in four different amounts of displacement. Specifically, a voltage V1 is applied between the fixed electrode  32  and the movable gratings  33   a ,  33   e , and  33   i . A voltage V2 is applied between the fixed electrode  32  and the movable gratings  33   b ,  33   f , and  33   j . A voltage V3 is applied between the fixed electrode  32  and the movable gratings  33   c ,  33   g , and  33   k . A voltage V4 is applied between the fixed electrode  32  and the movable gratings  33   d ,  33   h , and  33   l . Note that the voltages V1 to V4 have the following relationship: V1&gt;V2&gt;V3&gt;V4.  FIG. 9B  illustrates an example case where the voltages V1 to V4 are increased while maintaining the relationship V1&gt;V2&gt;V3&gt;V4.  FIG. 9C  illustrates an example case where no voltage is applied between the fixed electrode  32  and the movable grating  33 . 
     Further, the spectrum measurement device  100  according to the present embodiment may have an alternative configuration as illustrated in  FIG. 10  in which the light detecting element  50  is arranged in the first substrate  10  on one surface of the first substrate  10 . In this case, the light exit portion  12  does not have to be provided in the first substrate  10 . The light detecting element  50  is arranged at a position where light incident through the light entrance portion  11  and reflected by the first concave light reflecting portion  21 , the light reflection grating  30 , and the second concave light reflecting portion  22  is brought into focus. By forming the light detecting element  50  within the first substrate  10  on one surface of the first substrate  10 , further miniaturization of the spectral measurement device may be achieved. Also, assembly of the spectral measurement device may be simplified as compared with the configuration in which the light detecting element  50  is provided outside, and in this way, manufacturing costs can be reduced. Note that in a case where the light detecting element  50  is a Si photodiode, for example, the light detecting element  50  may be formed by a CMOS process using a Si substrate or an SOI (Silicon on Insulator) substrate. 
     In the spectral measurement device  100  according to an aspect of the present embodiment, the light detecting element  50  is configured to detect the light quantity of incident light for each of a plurality of grating patterns in which one or more of the movable gratings  33  forming the light reflection grating  30  are displaced, and the light intensities of the light at various wavelengths are calculated based on the detected light quantity. With such a configuration, the light reflecting grating  30  does not have to be rotated, and as such, the spectral measurement device  100  may be miniaturized and manufactured at a relatively low cost, for example. Further, because no drive system for rotating the light reflection grating  30  has to be provided, reliability of the spectral measurement device  100  may be improved, for example. 
     Second Embodiment 
     In the following, a second embodiment of the present invention will be described. In the second embodiment, a movable grating forming a light reflection grating is supported not by two ends but by one end to have a cantilever configuration. Specifically, as illustrated in  FIGS. 11A-11C , a fixing support portion  136  is provided on a substrate  131 , and one end of each of the movable gratings  133   a  to  133   l  is supported by the fixing support portion  136 . Note that in the following description of the present embodiment, the movable gratings  133   a  to  133   l  may simply be referred to as “movable grating  133 ”.  FIG. 11A  is a front view of the light reflection grating according to the embodiment,  FIG. 11B  is a top view, and  FIG. 11C  is a side view of the same. 
       FIGS. 12A and 12B  illustrate a more detailed configuration of the light reflection grating according to the present embodiment. As illustrated in  FIGS. 12A and 12B , the light reflection grating according to the present embodiment includes a fixed electrode  132  formed on one surface of the substrate  131 . A movable grating electrode  135  is formed on one surface of the movable grating  133 , and a reflective film  134  made of a metal material is formed on the other surface of the movable grating  133 . Note that the fixed electrode  132 , the reflective film  134 , and the movable grating electrode  135  are omitted from the illustrations of  FIGS. 11A-11C  for the sake of convenience. 
     The fixed electrode  132  formed on one surface of the substrate  131  and the movable grating electrode  135  formed on one surface of the movable grating  133  face each other, and the movable grating drive power supply  60  is connected to the fixed electrode  132  and the movable grating electrode  135 . In this way, the movable grating drive power supply  60  can apply a voltage between the fixed electrode  132  and the movable grating electrode  135 . 
     In the present embodiment, a predetermined voltage is applied between the fixed electrode  132  and the movable grid electrode  135  by the movable grid drive power source  60 . As a result, an electrostatic attractive force acts between the fixed electrode  132  and the movable grating electrode  135 , and the movable grating  133  having the movable grating electrode  135  formed thereon is deformed and displaced toward the fixed electrode  132  as illustrated in  FIG. 12B  from the position as illustrated in  FIG. 12A . 
       FIG. 13  illustrates an alternative configuration of the light reflection grating according to the present embodiment in which a piezoelectric element  137  that is interposed between electrodes is provided on the other surface of the movable grating  133 . With such a configuration, the fixed electrode  132  does not have to be formed on the substrate  131 . In yet another alternative configuration, the movable grating  133  may be made of a piezoelectric material, and an electrode may be provided on the other surface (back surface) of the movable grating  133 , for example. 
     The light reflection grating according to the second embodiment can be used in place of the light reflecting grating  30  according to the first embodiment in the spectral measurement device  100  illustrated in  FIG. 2  or  FIG. 10 , for example. Note that features of the light reflection grating according to the second embodiment other than those described above may be substantially identical to the first embodiment. 
     Third Embodiment 
     In the following, a spectral measurement device  300  according to a third embodiment of the present invention will be described with reference to  FIG. 14 . 
     As illustrated in  FIG. 14 , the spectral measurement device  300  according to the present embodiment includes the first substrate  10  and the second substrate  20 . The first substrate  10  is provided with the light entrance portion  11  and the light exit portion  12  that penetrate from one surface to the other surface of the first substrate  10 . A light reflection grating  330  is provided between the light entrance portion  11  and the light exit portion  12  on one surface of the first substrate  10 . The second substrate  20  has the first concave surface light reflecting portion  21  and the second concave surface light reflecting portion  22  provided on one surface. The light detecting element  50  is arranged on the other side of the first substrate  10  at a position where the light exit portion  12  is formed. The light detecting element  50  may be a single pixel photodiode chip made of Si, Ge, or InGaAs, for example. 
     In the present embodiment, a movable beam drive power source  360  as a movable beam drive unit is connected to the light reflection grating  330 , and the control unit  70  is connected to the movable beam drive power source  360  and the light detecting element  50 . The control unit  70  includes the grating control unit  71 , the computation unit  72 , and the storage unit  73 . 
     Note that the broken line arrows illustrated in  FIG. 14  represent an optical path of light incident into the light entrance portion  11 . In the spectral measurement device  300  according to the present embodiment, light incident through the light entrance portion  11  is reflected by the first concave light reflecting portion  21  of the second substrate  20 , incident on the light reflection grating  330  formed on the first substrate  10 , and reflected by the light reflection grating  330 . The light reflected by the light reflection grating  330  is reflected by the second concave light reflecting portion  22  of the second substrate  20  to be focused by the light exit portion  12  of the first substrate  10  to form an image. The light focused in this manner is detected by the light detecting element  50 . 
     The first substrate  10  and the second substrate  20  are arranged such that one surface of the first substrate  10  and one surface of the second substrate  20  face each other. The spacer  40  is provided between the first substrate  10  and the second substrate  20  to fix the first substrate  10  and the second substrate  20  in place. Also, when fixing the first substrate  10  and the second substrate  20  in place with the spacer  40 , the position of the first substrate  10  and the second substrate  20  are adjusted to be in a desired position. 
     Note that a spectral measurement device according to the present embodiment is not limited to the wafer-level spectral measurement device  300  as illustrated in  FIG. 14  as long as it includes a light reflection grating as described below. Also, although the light entrance portion  11  and the light exit portion  12  are formed in the first substrate  10  in the spectral measurement device  300  of  FIG. 14 , in other examples, slits forming a light entrance portion and a light exit portion may be separately provided as separate elements from the first substrate  10 , for example. 
     (Light Reflection Grating) 
     In the following, the light reflection grating  330  according to the third embodiment will be described with reference to  FIGS. 15A and 15B . FIG.  15 A is a cross-sectional view across the longitudinal direction of a grating forming the light reflection grating  330  according to the present embodiment, and  FIG. 15B  is a cross sectional view across the lateral direction perpendicular to the longitudinal direction of the light reflection grating  330 . Note that in the figures illustrating the light reflection grating  330  according to the present embodiment, direction X represents the lateral direction of the light reflection grating  330 , direction Y represents the longitudinal direction of the light reflection grating  330 , and direction Z represents a direction perpendicular to direction X and direction Y. 
     Also, in the following descriptions of the present embodiment, the plurality of fixed electrodes  32   a  to  32   l  may generically be referred to as “fixed electrode  32 ”, a plurality of movable beams  333   a  to  333   l  may generically be referred to as “movable beam  333 ”, and a plurality of gratings  336   a  to  336   l  may generically be referred to as “grating  336 ”. Also, note that although an example of the present embodiment in which twelve fixed electrodes  32   a  to  32   l  and twelve movable beams  333   a  to  333   l  are provided will be described below, the number of fixed electrodes  32  and the number of movable beams  333  provided in the light reflection grating  330  according to the present embodiment is not limited to twelve. 
     The light reflection grating  330  according to the present embodiment includes the substrate  31  having a recess  31   a  formed therein and a plurality of fixed electrodes  32   a  to  32   l  formed on the bottom surface  31   b  of the recess  31   a . The light reflection grating  330  also has a plurality of movable beams  333   a  to  333   l  formed on the upper surface  31   c  of the outer edge of the substrate  31  surrounding the recess  31   a  so as to cover the recess  31   a . The plurality of fixed electrodes  32   a  to  32   l  and the plurality of movable beams  333   a  to  333   l  are arranged to extend the same length in the longitudinal direction and are arranged side by side in the lateral direction. 
     As illustrated in  FIG. 15A , the two longitudinal direction side ends of each of the plurality of movable beams  333   a  to  333   l  are supported on the upper surface  31   c  of the outer edge of the substrate  31  surrounding the recess  31   a . That is, the movable beams  333  have a doubly supported beam configuration. In the present embodiment, the depth of the recess  31   a  formed in the substrate  31  may be 10 μm to 100 μm, and the length of the fixed electrodes  32  in the longitudinal direction may be 100 μm to 3 mm, for example. Also, the width Wa of the fixed electrodes  32  and the movable beams  333  in the lateral direction may be 1 μm to 10 μm, and the thickness of the movable beams  333  may be 1 μm to 10 μm, for example. 
     In the present embodiment, the fixed electrode  32  and the movable beam  333  that form a pair are arranged to face each other. That is, the fixed electrodes  32   a  to  32   l  are respectively arranged to face the movable beams  333   a  to  333   l . Specifically, the fixed electrode  32   a  and the movable beam  333   a , the fixed electrode  32   b  and the movable beam  333   b , the fixed electrode  32   c  and the movable beam  333   c , the fixed electrode  32   d  and the movable beam  333   d , the fixed electrode  32   e  and the movable beam  333   e , the fixed electrode  32   f  and the movable beam  333   f  are arranged to face each other. Further, the fixed electrode  32   g  and the movable beam  333   g , the fixed electrode  32   h  and the movable beam  333   h , the fixed electrode  32   i  and the movable beam  333   i , the fixed electrode  32   j  and the movable beam  333   j , the fixed electrode  32   k  and the movable beam  333   k , the fixed electrode  32   l  and the movable beam  333   l  are arranged to face each other. More specifically, the fixed electrodes  32   a  to  32   l  and the movable beams  333   a  to  333   l  are arranged such that one surface of each of the fixed electrodes  32   a  to  32   l  faces one surface of the corresponding movable beams  333   a  to  333   l.    
     Further, as illustrated in  FIG. 15A , the gratings  336   a  to  336   l  are respectively provided on the other side of the movable beams  333   a  to  333   l  opposite the side of the movable beams  333   a  to  333   l  facing the fixed electrodes  32   a  to  32   l . Specifically, the grating  336   a  is arranged on the movable beam  333   a , the grating  336   b  is arranged on the movable beam  333   b , the grating  336   c  is arranged on the movable beam  333   c , the grating  336   d  is arranged on the movable beam  333   d , the grating  336   e  is arranged on the movable beam  333   e , and the grating  336   f  is arranged on the movable beam  333   f . Further, the grating  336   g  is arranged on the movable beam  333   g , the grating  336   h  is arranged on the movable beam  333   h , the grating  336   i  is arranged on the movable beam  333   i , the grating  336   j  is arranged on the movable beam  333   j , the grating  336   k  is arranged on the movable beam  333   k , and the grating  336   l  is arranged on the movable beam  333   l . Note that in the following descriptions, the movable beams  333   a  to  333   l  may also be referred to as movable portion, and the gratings  336   a  to  336   l  may also be referred to as grating portion. 
     The movable beam  333  and the grating  336  are fixed to each other by a connecting member  335 . That is, one surface of each of the gratings  336   a  to  336   l  and the other surface of the corresponding movable beams  333   a  to  333   l  are fixed to the connecting member  335 . The connecting member  335  is arranged at a position of the grating  336  that would be disposed parallel to the fixed electrode  32  even when the movable beam  333  is displaced. Preferably, the connecting member  335  is arranged close to the center of gravity of each of the movable beam  333  and the grating  336 . The height H of the connecting member  335  may be 1 μm to 30 μm, for example. The width of the grating  336  in the lateral direction may be approximately 1 μm to 10 μm, which is approximately the same as the width Wa of the movable beam  333 , and the thickness to of the grating  336  may be 1 μm to 10 μm, for example. Further, the length La of the grating  336  in the longitudinal direction may be 100 μm to 3 mm, for example. Note that the length La of the grating  336  in the longitudinal direction and the height H of the connecting member  335  are determined so as not to interfere with other components when the movable beam  333  is displaced. In particular, the height H of the connecting member  335  is used as an adjustment factor. 
     The substrate  31  may be made of an insulator or a semiconductor such as Si, for example. The light reflection grating  330  according to the present embodiment may be formed on one surface of the first substrate  10  or on a substrate other than the first substrate  10 . In the case where the light reflection grating  330  according to the present embodiment is formed on one surface of the first substrate  10 , the first substrate  10  can be used as the substrate  31  of the light reflection grating  330 , and in this way, miniaturization and cost reduction of the spectral measurement device  300  can be achieved, for example. In the case where the substrate  31  is made of a semiconductor, an insulating film is formed on the bottom surface  31   b  of the recess  31   a  of the substrate  31 , and the fixed electrodes  32   a  to  32   l  are formed on the insulating film. Further, an insulating film is formed on the upper surface  31   c  of the substrate  31 , and the movable beams  333   a  to  333   l  are formed on the insulating film. Further, in some examples, an insulating film may be formed on the entire surface of the substrate  31  that is exposed within the recess  31   a.    
     Each of the fixed electrodes  32   a  to  32   l  is made of an electrode material used in various semiconductor devices, such as Al, Pt, Au, or some other conductive metal material, for example. Also, each of the movable beams  333   a  to  333   l  is made of a conductive metal material or a semiconductor material. A reflection film  334  for reflecting light is formed on the other surface of each of the gratings  336   a  to  336   l  opposite the one surface connected to the connecting member  335 . The reflection film  334  is a metal film that may be made of aluminum, silver, gold or the like according to the wavelength of light to be spectrally analyzed. 
     In the present embodiment, a movable beam drive power source  360  is connected to the fixed electrodes  32   a  to  32   l  and the movable beams  333   a  to  333   l  so that the movable beam drive power source  360  can apply a voltage between corresponding pairs of the fixed electrodes  32   a  to  32   l  and the movable beams  333   a  to  333   l.    
     When the potential difference between the fixed electrode  32  and the movable beam  333  is 0 V, the movable beam  333  is not displaced, and the fixed electrode  32  and the movable beam  333  are separated by a distance Da 1  as illustrated in  FIG. 15A . On the other hand, when a predetermined voltage, such as a voltage that causes the potential difference between the fixed electrode  32  and the movable beam  333  to be several dozen volts (V), is applied between the fixed electrode  32  and the movable beam  333 , the fixed electrode  32  and the movable beam  333  are attracted to each other by an electrostatic attractive force such that the movable beam  333  is displaced toward the fixed electrode  32  as illustrated in  FIG. 16 . That is, the movable beam  333  comes closer to the fixed electrode  32 , and the distance between the movable beam  333  and the fixed electrode  32  becomes distance Da 2 , which is shorter than the distance Da 1 . In the present embodiment, the grating pattern of the light reflection grating  330  may be rearranged into various grating patterns by changing a combination of voltages applied or changing the voltage applied between the fixed electrodes  32   a  to  32   l  and the movable beams  333   a  to  333   l.    
       FIG. 15B  illustrates an example case where no voltage is applied to the fixed electrodes  32   a  to  32   l  and the movable beams  333   a  to  333   l , such as a case where the applied voltage is 0 V. In this case, the movable beams  333   a  to  333   l  are not displaced, and light incident on the reflection film  334  arranged on the light entering surface side of the movable beams  333   a  to  333   l  is specularly reflected by the reflection film  334 . 
       FIG. 17A  illustrates an example case where voltages are alternately applied to the movable beams  333 . That is, a predetermined voltage is applied between the fixed electrode  32   b  and the movable beam  333   b , the fixed electrode  32   d  and the movable beam  333   d , the fixed electrode  32   f  and the movable beam  333   f , the fixed electrode  32   h  and the movable beam  333   h , the fixed electrode  32   j  and the movable beam  333   j , and the fixed electrode  32   l  and the movable beam  333   l . In this case, the light reflection grating  330  is arranged into a grating pattern in which every other movable beam  333 , namely, the movable beams  333   b ,  333   d ,  333   f ,  333   h ,  333   j , and  333   l , are displaced downward, and the corresponding gratings  336   b ,  336   d ,  336   f ,  336   h ,  336   j , and  336   l  are also displaced downward along with the movable beams  333   b ,  333   d ,  333   f ,  333   h ,  333   j , and  333   l.    
       FIG. 17B  illustrates an example case where a voltage is alternately applied and not applied to every two adjacent movable beams  333 . That is, a predetermined voltage is applied between the fixed electrode  32   a  and the movable beam  333   a , the fixed electrode  32   b  and the movable beam  333   b , the fixed electrode  32   e  and the movable beam  333   e , the fixed electrode  32   f  and the movable beam  333   f , the fixed electrode  32   i  and the movable beam  333   i , and the fixed electrode  32   j  and the movable beam  333   j . In this case, the light reflection grating  330  is arranged into a grating pattern in which every two movable beams  333 , namely, the movable beams  333   a ,  333   b ,  333   e ,  333   f ,  333   i , and  333   j , are displaced downward, and the corresponding gratings  336   a ,  336   b ,  336   e ,  336   f ,  336   i , and  336   j  are also displaced downward along with the movable beams  333   a ,  333   b ,  333   e ,  333   f ,  333   i , and  333   j.    
       FIG. 18A  illustrates an example case where a voltage is applied between corresponding pairs of the fixed electrode  32  and the movable beam  33  other than the pairs of the fixed electrode  32   a  and the movable beam  333   a , the fixed electrode  32   e  and the movable beam  333   e , and the fixed electrode  32   i  and the movable beam  333   i . In this case, the light reflection grating  330  is arranged into a grating pattern in which the movable beams  333   b ,  333   c ,  333   d ,  333   f ,  333   g ,  333   h ,  333   j ,  333   k , and  333   l  are displaced downward, and the corresponding gratings  336   b ,  336   c ,  336   d ,  336   f ,  336   g ,  336   h ,  336   j ,  336   k , and  336   l  are also displaced downward along with the movable beams  333   b ,  333   c ,  333   d ,  333   f ,  333   g ,  333   h ,  333   j ,  333   k , and  333   l.    
       FIG. 18B  illustrates an example case where a voltage is applied between the fixed electrode  32   b  and the movable beam  333   b , the fixed electrode  32   c  and the movable beam  333   c , the fixed electrode  32   d  and the movable beam  333   d , the fixed electrode  32   f  and the movable beam  333   f , the fixed electrode  32   j  and the movable beam  333   j , and the fixed electrode  32   k  and the movable beam  333   k . In this case, the light reflection grating  330  is arranged into a grating pattern in which the movable beams  333   b ,  333   c ,  333   d ,  333   f ,  333   j , and  333   k  are displaced downward, and the corresponding gratings  336   b ,  336   c ,  336   d ,  336   f ,  336   j , and  336   k  are displaced downward along with the movable beams  333   b ,  333   c ,  333   d ,  333   f ,  333   j , and  333   k.    
     As described above, in a given grating pattern of a light reflection grating, the relationship between the voltage V of incident light detected by a light detecting element and the intensities Iλ1 to Iλn of the light at wavelengths λ1 to Δn can be expressed by equation (1), which is indicated below. The voltage V detected by the light detecting element corresponds to the light quantity of the light incident on the light detecting element. Also, “a1” to “an” of equation (1) represent coefficients that vary depending on the grating pattern of the light reflection grating.
 
V= a 1× Iλ 1+ a 2× Iλ 2+ . . . + an×Iλn   (1)
 
     The storage unit  73  stores the relationship between positions of the movable beams  333  in a plurality of different grating patterns of the light reflection grating  330  and the corresponding coefficients “a1” to “an” for the different grating patterns. That is, the storage unit  73  stores the relationship between a voltage based on a light quantity to be detected by the light detecting element  50  and corresponding light intensities at a plurality of different wavelengths for the plurality of different grating patterns. The grating control unit  71  of the control unit  70  performs control for altering the grating pattern of the light reflection grating  30  to a different grating pattern. Under control of the grating control unit  71 , the movable grating drive power source  60  applies a voltage between corresponding pairs of the fixed electrodes  32   a  to  32   l  and the movable gratings  33   a  to  33   l . That is, the grating control unit  71  controls the movable grating drive power source  60  to apply a voltage between predetermined pairs of the fixed electrodes  32   a  to  32   l  and the movable gratings  33   a  to  33   l  so that the light reflection grating  330  is arranged into one of the grating patterns stored in the storage unit  73 . 
     In the present embodiment, the grating pattern of the light reflection grating  330  is rearranged into n or more different grating patterns, the light detecting element  50  detects voltages V1 to Vn for each of the different grating patterns, and an inverse operation is performed based on the determinant represented by the formula as described above. In this way, the intensities Iλ1 to Iλn of light at the wavelengths λ1 to λn can be calculated. Note that “a11” to “ann” in the above formula are coefficients. The inverse operation based on the determinant represented by the above formula is performed by the computation unit  72  of the control unit  70 . 
     The spectral measurement device  300  according to the present embodiment can obtain spectral characteristics of incident light based on the intensities Iλ1 to Iλn of light at the wavelengths λ1 to λn that have been obtained by the above inverse operation. 
     In the following, an example spectral measurement method implemented by the spectral measurement device  300  according to the present embodiment will be described with reference to  FIG. 19 .  FIG. 19  is a flowchart illustrating an example spectral measurement method that is controlled by the control unit  70  of the spectral measurement device  300  according to the present embodiment. In the present example, it is assumed that the relationship between 1st to n-th grating patterns and the corresponding coefficients “a11” to “ann” of the above formula for the determinant is obtained in advance through measurement and/or calculation and stored in the storage unit  73 . 
     In step S 202 , the variable “i” is set to “1” (i=1). 
     Then, in step S 204 , the movable grating drive power source  60  applies a voltage to the movable beams  333  under control of the grating control unit  71  such that the grating pattern of the light reflection grating  330  is arranged into an i-th grating pattern. 
     Then, in step S 206 , a voltage Vi corresponding to the light quantity of light incident on the light detecting element  50  while the light reflection grating  330  is in the i-th grating pattern is obtained. The detected voltage Vi is temporarily stored in the control unit  70 . 
     Then, in step S 208 , a value obtained by adding 1 to the current value of the variable “i” is set up as a new value for the variable “i”. 
     Then, in step S 210 , a determination is made as to whether the value of “i” exceeds “n”. If the value of “i” exceeds “n”, the process proceeds to step S 212 . If the value of “i” does not exceed “n”, the process goes back to step S 204  and the processes of steps S 204  to S 208  are repeated. 
     Then, in step S 212 , based on information stored in the storage unit  73  and the voltages V1 to Vn detected by the light detection element  50  for each of the different grating patterns, the computation unit  72  performs the inverse operation based on the determinant represented by the above formula. In this way, the intensities Iλ1 to Iλn of light at the wavelengths λ1 to λn can be obtained, and the spectral characteristics of the incident light can be obtained. 
     According to an aspect of the present embodiment, the number of movable beams  333  may be increased to thereby increase the wavelength resolution, for example. Further, the light reflection grating  330  may be rearranged into more than n different grating patterns, and the light detecting element  50  may detect the light quantity for each of the different grating patterns. In this way, accuracy of the obtained light spectrum may be further improved, for example. 
     Note that in the example described above, the light reflection grating  330  is arranged into n different grating patterns. However, in other examples of the present embodiment, the amount of displacement of the movable beams  333  may be varied while the light reflection grating  330  is in the same grating displacement pattern. Specifically, for example, the light reflection grating  330  may be arranged such that every other movable grating  33  is displaced downward. In such state, the amount of displacement of the displaced movable beams  333  may be increased as illustrated in  FIG. 20A , or the amount of displacement of the displaced movable gratings  33  may be decreased as illustrated in  FIG. 20B , and the light detecting element  50  may measure the light quantity of incident light for each variation in the amount of displacement of the movable beams  333 . For example, displacement of the movable beams  333  may be controlled to be in n different amounts of displacement, the light detecting element  50  may detect voltages V1 to Vn for the respective amounts of displacement, and an inverse operation may be performed using the determinant represented by a formula similar to the above formula but with different coefficients. In this way, the intensities Iλ1 to Iλn of light at wavelengths λ1 to λn may be calculated. Note that  FIG. 20C  illustrates an example case where no voltage is applied between the fixed electrodes  32  and the movable beams  333 . 
     Also, the light reflection grating  330  of the spectral measurement device  300  according to the present embodiment may have an alternative configuration as illustrated in  FIGS. 21A-21C  in which one common fixed electrode  32  is provided in place of the plurality of fixed electrodes  32   a  to  32   l  on the bottom surface  31   b  of the recess  31   a  of the substrate  31 . Even with such a configuration, a desired grating pattern of the light reflection grating  330  can be obtained by controlling the potential of the fixed electrode  32  to be constant and varying the voltage applied to each of the movable beams  333   a  to  333   l .  FIG. 21A  illustrates an example case where the movable beams  333  are displaced in four different amounts of displacement. Specifically, a voltage Va1 is applied between the fixed electrode  32  and the movable beams  333   a ,  333   e , and  333   i . A voltage Va2 is applied between the fixed electrode  32  and the movable beams  333   b ,  333   f , and  333   j . A voltage Va3 is applied between the fixed electrode  32  and the movable beams  333   c ,  333   g , and  333   k . A voltage Va4 is applied between the fixed electrode  32  and the movable beams  333   d ,  333   h , and  333   l . Note that the voltages Va1 to Va4 have the following relationship: Va1&gt;Va2&gt;Va3&gt;Va4.  FIG. 21B  illustrates an example case where the voltages Va1 to Va4 are increased while maintaining the relationship Va1&gt;Va2&gt;Va3&gt;Va4.  FIG. 9C  illustrates an example case where no voltage is applied between the fixed electrode  32  and the movable beams  333 . 
     Further, the spectrum measurement device  300  according to the present embodiment may have an alternative configuration as illustrated in  FIG. 22  in which the light detecting element  50  is arranged in the first substrate  10  on one surface of the first substrate  10 . In this case, the light exit portion  12  does not have to be provided in the first substrate  10 . The light detecting element  50  is arranged at a position where light incident through the light entrance portion  11  and reflected by the first concave light reflecting portion  21 , the light reflection grating  30 , and the second concave light reflecting portion  22  is brought into focus. By forming the light detecting element  50  within the first substrate  10  on one surface of the first substrate  10 , further miniaturization of the spectral measurement device may be achieved. Also, assembly of the spectral measurement device may be simplified as compared with the configuration in which the light detecting element  50  is provided outside, and in this way, manufacturing costs can be reduced, for example. Note that in a case where the light detecting element  50  is a Si photodiode, for example, the light detecting element  50  may be formed by a CMOS process using a Si substrate or an SOI (Silicon on Insulator) substrate. 
     In the spectral measurement device  300  according to an aspect of the present embodiment, the light detecting element  50  is configured to detect the light quantity of incident light for each of a plurality of grating patterns in which one or more of the movable beams  33  forming the light reflection grating  330  are displaced, and the light intensities of the light at various wavelengths are calculated based on the detected light quantity. With such a configuration, the light reflection grating  330  does not have to be rotated, and as such, the spectral measurement device  300  may be miniaturized and manufactured at a relatively low cost, for example. Further, because no drive system for rotating the light reflection grating  330  has to be provided, reliability of the spectral measurement device  300  may be improved, for example. 
     Fourth Embodiment 
     In the following, a light reflection grating  430  according to a fourth embodiment of the present invention will be described with reference to  FIG. 23 . 
       FIG. 23  is a cross-sectional view across the longitudinal direction of a grating forming the light reflection grating  430  according to the present embodiment. Note that in  FIG. 23 , direction X represents the lateral direction of the light reflection grating  430 , direction Y represents the longitudinal direction of the light reflection grating  430 , and direction Z represents a direction perpendicular to direction X and direction Y. 
     As illustrated in  FIG. 23 , the light reflection grating  430  according to the present embodiment uses a piezoelectric element  337  as a drive element for displacing the grating  336 . In the light reflection grating  430  according to the present embodiment, the two longitudinal direction side ends of each of the plurality of movable beams  333  are supported on the upper surface  31   c  of the outer edge of the substrate  31  surrounding the recess  31   a . In this way, each of the movable beams  333  is arranged to have a doubly supported beam configuration. Further, the piezoelectric elements  337  are formed on two sides of each movable beam  333 . 
     Each movable beam  333  is made of a conductive metal material or a semiconductor material. The piezoelectric element  337  may be made of a PZT (lead zirconate titanate) thin film, for example. Further, in some examples, electrodes may be formed on the front and back side surfaces of the PZT film, and the movable beam  333  may be arranged to have low resistance such that the movable beam  333  can be used as a single-pole electrode. 
     In a spectral measurement device using the light reflection grating  430  according to the present embodiment, the movable beam drive power source  360  is connected to the piezoelectric element  337  so that the movable beam drive power source  360  can apply a voltage to the corresponding piezoelectric element  337  that drives the grating  336  to be driven. In this way, the movable beam  333  can be displaced, and the grating  336  can be displaced along with the movable beam  333 . 
     The light reflection grating  430  according to the present embodiment can be used in place of the light reflection grating  330  according to the third embodiment. 
     Note that features of the light reflection grating  430  other than those described above may be substantially the same as those of the third embodiment. 
     Fifth Embodiment 
     In the following, an analysis apparatus according to a fifth embodiment of the present invention will be described. The analysis apparatus according to the present embodiment is a mobile analysis apparatus that uses the spectral measurement device according to the first embodiment or the second embodiment. 
       FIG. 24  is a diagram illustrating an example configuration of a mobile analysis apparatus  200  according to the fifth embodiment. In  FIG. 24 , the mobile analysis apparatus  200  includes a light source  211 , the spectral measurement device  100 , a drive circuit  214 , a processing circuit  215 , and a battery  216  corresponding to a power source for the above components. In the present example, the spectral measurement device  100  according to the first embodiment is used. The drive circuit  214  drives the light source  211  and the spectral measurement device  100 , and the processing circuit  215  performs various processes on a detected signal, such as amplification, A/D conversion, and communication of the detected signal. Note that the mobile analysis apparatus according to the present embodiment may use the spectral measurement device according to the second embodiment instead of the spectral measurement device  100 , for example. In this case, the light detecting element  50  is provided on the light exiting side of the spectral measurement device. 
     In the mobile analysis apparatus  200  according to the present embodiment, emitted light  221  that is emitted from the light source  211  is irradiated on an object  230  to be measured, and the emitted light  221  is diffusely reflected by the object  230  while colliding with molecules in the object  230 . The diffusely reflected light  222  enters the spectral measurement device  100  to be detected by the light detecting element  50  provided in the spectral measurement device  100 . In this way, the mobile analysis apparatus  200  according to the present embodiment can obtain a wavelength spectrum characteristic of the molecular structure of the object  230 . 
     According to an aspect of the present embodiment, by using the spectral measurement device according to the first embodiment or the second embodiment, the mobile analysis apparatus  200  can be manufactured at a relatively low cost and miniaturized so that mobility of the mobile analysis apparatus  200  can be improved. Also, note that the analysis apparatus according to the present embodiment does not have to include a battery and may acquire power from an external source, for example. Further, the analysis apparatus according to the present embodiment may use the spectral measurement device according to the third embodiment or the fourth embodiment, for example. With such a configuration, further miniaturization and weight reduction of the analysis apparatus can be achieved such that mobility of the analysis apparatus can be further improved, for example. 
     Although the present invention has been described above with reference to certain illustrative embodiments, the present invention is not limited to these embodiments, and numerous variations and modifications may be made without departing from the scope of the present invention.