JP2012181086A - Spectrum measuring apparatus and spectrum measuring method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a spectrum measuring apparatus capable of preventing degradation of S/N ratio by delivering a sufficient light volume to imaging means such as an imaging camera, an imaging element, etc.SOLUTION: A spectrum measuring apparatus 1 comprises: a liquid crystal device 2 as a Fourier transform element; a voltage controller 5 for controlling voltage applied to the liquid crystal device 2; and an imaging device 3 for imaging a transmittance waveform of a measuring object 7 passing through the liquid crystal device 2. A computer 4 executes: a step for storing data about images taken while controlling the voltage applied to the liquid crystal device 2 so that a wave number included in the transmittance waveform after passage through the liquid crystal device 2 has a non-integral multiple relationship; a step for calculating a Fourier component of integral multiple frequency for each pixel in a measurement interval by solving a simultaneous equation based on the multiple pieces of image data which differ in the wave number; and a step for calculating an optical spectrum for each pixel by applying inverse Fourier transform to the calculated Fourier component of integral multiple frequency in each pixel.

Description

  The present invention relates to a spectrum measuring apparatus and a spectrum measuring method for measuring a spectrum of a measurement object.

  One known technique for obtaining a spectral spectrum is a technique in which incident light is split with a prism and the intensity of the split light is measured with a one-dimensional sensor array. However, an image obtained by this method is a one-dimensional image to the last, and has a fatal defect that a measurement object cannot be imaged as a two-dimensional image.

  On the other hand, there are Non-Patent Document 1 and Patent Document 1 listed below as documents disclosing spectroscopic methods capable of capturing a measurement object as a two-dimensional image. The method disclosed in Non-Patent Document 1 is a method of imaging by sequentially exchanging (rotating) a plurality of narrowband spectral filters arranged along the peripheral edge of a disc. In addition, the technique disclosed in Patent Document 1 is a technique that includes a liquid crystal wavelength tunable filter in which a plurality of liquid crystal cells are stacked to form a narrow band filter, and sequentially applies images by varying the voltage applied to the liquid crystal wavelength tunable filter. .

JP 2008-197518 A

http://www.cfme.chiba-u.jp/~haneishi/publication/announcement/announcementPDF/announcement20070608.pdf (searched on February 14, 2011)

  However, the method of Non-Patent Document 1 has a problem that failure is increased because the fixed-wavelength spectral filter must be mechanically replaced (rotated). Further, according to the method of Non-Patent Document 1, data of an arbitrary wavelength of light is not obtained, and only an average value (representative value) in the band of each spectral filter is obtained. For this reason, in order to increase the resolution, the number of spectral filters must be increased, and there is a problem that the apparatus becomes larger.

  On the other hand, the liquid crystal wavelength tunable filter disclosed in Patent Document 1 is advantageous in that it has good operability because it does not have a mechanical portion and can obtain an arbitrary wavelength spectral intensity, but it is half that of a fixed wavelength spectral filter. There is a drawback that only the following brightness can be obtained.

  Furthermore, although common to both methods of Non-Patent Document 1 and Patent Document 1, if a spectral spectrum is to be obtained in more detail, the wavelength band becomes narrower and darker. A two-dimensional sensor such as a CCD or CMOS has a lower limit on the noise (N) side of the S / N ratio, and thus has another problem that the S / N ratio deteriorates when the captured image becomes dark.

  The present invention has been made in view of the above, and a spectrum measuring apparatus and a spectrum measuring method capable of suppressing deterioration of the S / N ratio by passing a sufficient amount of light to an imaging means such as an imaging camera or an imaging device. The purpose is to provide.

  In order to solve the above-described problems and achieve the object, a spectrum measurement apparatus according to the present invention is a spectrum measurement apparatus having a processing unit for calculating a spectrum of a measurement object, and includes a liquid crystal device as a Fourier transform element and A voltage controller that controls a voltage applied to the liquid crystal device; and an imaging device that images a transmittance waveform of the measurement object that has passed through the liquid crystal device, and the processing unit converts the transmittance waveform into the transmittance waveform. By storing image data captured while controlling the voltage applied to the liquid crystal device so that the included wave number has a non-integer multiple relationship, and solving simultaneous equations based on a plurality of image data having different wave numbers , For each pixel, an integer multiple Fourier component calculator for calculating an integer multiple frequency Fourier component in the measurement interval, and the integer multiple Fourier component calculation There is characterized in that and a Fourier inverse transform unit for calculating a spectrum of each pixel by inverse Fourier transform is an integral multiple frequency Fourier component of each pixel calculated.

  According to the spectrum measuring apparatus and the spectrum measuring method according to the present invention, a sufficient amount of light can be passed to an imaging means such as an imaging camera or an imaging device, so that deterioration of the S / N ratio at the time of spectral spectrum measurement is suppressed. There is an effect that can be.

FIG. 1 is a diagram illustrating a configuration example of a spectrum measuring apparatus according to an embodiment. FIG. 2 is a schematic configuration diagram of a liquid crystal wavelength tunable filter disclosed in Patent Document 1 (prior art). FIG. 3 is a diagram showing the transmittance of each liquid crystal cell (polarizing plate dust) and the total transmittance which is the product of them. FIG. 4 is a diagram illustrating a detailed configuration of the liquid crystal cell according to the embodiment. FIG. 5 is a diagram illustrating an example of a spectrum of a measurement object. FIG. 6 is a diagram showing a calculation process and a data flow in the computer. FIG. 7 is a diagram illustrating a processing image for acquiring image data. FIG. 8 is a diagram showing a calculation process and a data flow when the integer multiple Fourier component calculation process is unnecessary.

  Hereinafter, a spectrum measuring apparatus and a spectrum measuring method according to embodiments of the present invention will be described with reference to the accompanying drawings. In addition, this invention is not limited by embodiment shown below.

(Embodiment)
FIG. 1 is a diagram illustrating a configuration example of a spectrum measuring apparatus according to an embodiment of the present invention. A spectrum measuring apparatus 1 according to an embodiment of the present invention includes a liquid crystal device 2, an imaging apparatus 3, a calculator 4, and a voltage controller 5, as shown in FIG.

  The liquid crystal device 2 is a device including a liquid crystal cell in which a liquid crystal element is enclosed, and operates as a Fourier transform element (device) in the present invention. The voltage controller 5 is a controller that controls the voltage applied to the liquid crystal device 2. When the voltage applied to the liquid crystal cell 2 is a certain value, the liquid crystal device 2 is controlled to have a transmittance characteristic as shown in the illustrated balloon. The imaging device 3 is a device that captures an image of the measurement object 7 that passes through the liquid crystal device 2. The computer 4 is a processing unit having a calculation function, a control function, and a storage function, controls the voltage applied to the liquid crystal device 2, and stores image data (pixel values for each pixel) captured by the imaging device 3. Then, the processing shown in the calculation formula described later is performed to calculate and display the spectral component of the measuring object 7.

(Description of Patent Document 1)
Next, the principle of the invention (invention name: liquid crystal wavelength tunable filter) disclosed in Patent Document 1 will be described. In addition, it is considered that understanding of the invention of Patent Document 1 is very effective for clarifying the difference from the present invention.

  FIG. 2 is a schematic configuration diagram of the liquid crystal wavelength tunable filter disclosed in Patent Document 1 (FIG. 1 of the same document), and shows the basic configuration of the liquid crystal wavelength tunable filter when three liquid crystal cells are stacked. Is. In FIG. 2, P1, P2, P3, and P4 are polarizers (polarizing plates), and LC1, LC2, and LC3 are liquid crystal cells, which are arranged in the order of signs from the incident side. The liquid crystal alignment directions 15 of the liquid crystal cells LC1, LC2, and LC3 are parallel to each other, and the absorption axes 20 of the polarizers P1, P2, P3, and P4 are parallel to each other (parallel Nicols). The axis 20 forms an angle of 45 degrees.

  FIG. 3 is a diagram showing the transmittance of each liquid crystal cell (polarizing plate dust) and the total transmittance which is the product of them. In FIG. 3, the waveform shown at the top of “Liquid Crystal Cell 1” is the transmittance characteristic of the liquid crystal cell LC 1. In the same manner, the waveform shown in the upper middle part of the liquid crystal cell 2 is the transmittance characteristic of the liquid crystal cell LC2, and the waveform shown in the lower middle part of the liquid crystal cell 3 is the transmittance of the liquid crystal cell LC3. It is a characteristic. Also, the product of all these transmittance characteristics is the total transmittance characteristic (product of transmittance) at the bottom. That is, the liquid crystal wavelength tunable filter of Patent Document 1 applies a different voltage so that each liquid crystal cell has a transmittance waveform with a different wave number, and only a portion where the peaks of the transmittance waveforms coincide with each other is a narrowband bandpass filter. To do.

  Since the liquid crystal wavelength tunable filter of Patent Document 1 has no mechanical part, it has good operability and can obtain an arbitrary wavelength spectral intensity. However, this liquid crystal wavelength tunable filter has a drawback that only half or less brightness can be obtained compared to a fixed wavelength spectral filter. The reason is that the liquid crystal cell is sandwiched between two polarizers, so that in principle, only half of the polarized light can be used. In other words, it is necessary to stack a large number of cells (5 to 7), so that absorption loss due to the polarizing plate (particularly, absorption on the short wavelength side (blue) is a problem) increases. In addition, the fixed wavelength spectral filter can achieve a spectral transmittance of 90% or more when multilayer film deposition is used, whereas the liquid crystal wavelength tunable filter has a spectral transmittance of 30% near blue (λ = 400 nm). It is one of the drawbacks.

  As described above, the liquid crystal wavelength tunable filter according to the related art can capture a two-dimensional image with good operability, but has a drawback of being dark. Even when a fixed-wavelength spectral filter is used, there is a problem that when the band of the filter is narrowed, it becomes dark and the S / N ratio in the image sensor deteriorates.

  Next, the principle of the present invention will be described. Although the theoretical details will be described later, the present invention uses a liquid crystal cell as a Fourier transform element, and converts the transmittance waveform passing through the liquid crystal cell to a plurality of non-integer multiple frequencies (frequency having a relationship of non-integer multiples). A first step of imaging while changing, and a second step of calculating a Fourier component of an integral multiple frequency of a measurement interval for each pixel by solving simultaneous equations from a plurality of captured image data. And a third step of obtaining a spectral spectrum for each pixel by inverse Fourier transforming the integer multiple frequency Fourier component of each pixel. We consider these series of steps a new concept that has never been proposed before. Therefore, in the present application, a measurement technique including a series of these steps is named “Fourier spectroscopy”.

  FIG. 4 is a diagram showing a detailed configuration of the liquid crystal device 2 according to the embodiment of the present invention. The liquid crystal device 2 includes a liquid crystal cell 22 in which liquid crystal is sealed, a polarizing plate 21 disposed on the incident side of the liquid crystal cell 22, and a polarizing plate 23 disposed on the exit side of the liquid crystal cell 22. Is done. In FIG. 4, the solid line arrows indicate the transmission polarization directions in the polarizing plates 21 and 23, and the broken line arrows indicate the slow axis direction in the liquid crystal cell 22.

  Next, the operation of the liquid crystal device 2 will be described. In the following description, the wavelength dispersion characteristic of the liquid crystal cell is not considered in view of briefly explaining the gist of the invention. Even under such assumptions, the generality of the present invention is not lost.

  The light incident on the polarizing plate 21 is converted into a transmission polarization direction indicated by a solid arrow in FIG. The liquid crystal molecules enclosed in the liquid crystal cell 22 have refractive anisotropy, and the electric field oscillation direction of light that has a high refractive index becomes the slow axis, and the axis orthogonal to the slow axis is the fast axis. (Dashed arrow in FIG. 4).

  As shown in FIG. 4, the liquid crystal cell 22 is oriented so that the slow axis is inclined by 45 degrees with respect to the incident linearly polarized light. It experiences different optical distances (actual distance × refractive index) due to the axial vibration, and becomes elliptically polarized light when exiting the liquid crystal cell 22. Such an optical distance difference between the fast axis direction and the slow axis direction is generally called “retardation”, and the applied voltage V to the liquid crystal cell 22 is changed. The value can be changed.

  In the polarizing plate 23 on the emission side, the component in the transmission axis direction is extracted from the incident elliptically polarized light. FIG. 4 shows an arrangement (parallel Nicol) in which the transmission polarization direction of the polarizing plate 21 and the transmission polarization direction of the polarizing plate 23 are parallel to each other, but “the size of retardation (hereinafter referred to as“ Ret ”)”. That is, by changing the optical distance difference between the fast axis direction and the slow axis direction, an arrangement in which the transmitted polarization direction of the polarizing plate 21 and the transmitted polarization direction of the polarizing plate 23 are orthogonal (crossed Nicols). It is also possible to adopt.

  When Ret is 0, the incident light to the polarizing plate 23 remains the original linearly polarized light, and thus the transmittance is 1 (here, for the sake of convenience, the light after passing through the first polarizing plate) The ratio that can pass through the last polarizing plate is defined as the transmittance). Further, when Ret is 1/4 with respect to the wavelength λ of light, the light incident on the polarizing plate 23 is circularly polarized, and thus the transmittance is ½. Further, when Ret is ½ with respect to the wavelength λ of the light, the incident light to the polarizing plate 23 is linearly polarized light that is orthogonal, so that the transmittance is zero.

From the above, the transmittance T can be expressed as the following equation as a function of “Ret” and “λ”.
T = {cos (π · Ret / λ)} ² = {1 + cos (2π · Ret / λ)} / 2

  When the transmittance T is represented by a graph with the wavelength of light λ on the horizontal axis, the waveform becomes longer as the wavelength increases (“liquid crystal cell 1” and “liquid crystal cell 2” or “liquid crystal cell 3” in FIG. 3). See the transmission waveform for On the other hand, when the horizontal axis represents the wave number k of light, which is the reciprocal of the light wavelength λ, a sine waveform is obtained. Since the Fourier transform uses a sinusoidal waveform for sampling, the calculation is easier when the wave number k of light is used instead of the wavelength λ of light.

  Here, according to the Fourier spectroscopy according to the present invention, the point of using a liquid crystal cell is the same as that of Patent Document 1, but differs greatly in that only one set of liquid crystal cells is used as shown in FIG. In other words, the Fourier spectroscopy according to the present invention uses only one set of liquid crystal cells and captures an image of the measurement object as a waveform passing through the one set of liquid crystal cells. For this reason, it is possible to pass a sufficient amount of light to the image sensor, and to suppress the deterioration of the S / N ratio related to spectrum measurement.

  Further, since the Fourier spectroscopy according to the present invention uses only one set of liquid crystal cells, only two polarizing plates, ie, an entrance and an exit, may be used, and it is not necessary to pay much attention to the amount of absorption caused by stacking many. Furthermore, the Fourier spectroscopy according to the present invention outputs the transmittance waveform as a wave shape, so that almost half of the light in the measurement section (light wave number space) can pass through, and only half the polarized light can be used. However, the amount of light of the captured image can be increased (that is, brighter) the more it compensates.

Here, regarding the amount of light of the captured image,
(1) When using a "fixed wavelength spectral filter"
(2) When using a “liquid crystal wavelength tunable filter”
(3) When using “Fourier spectroscopy” according to the present invention,
In these three cases, a simple calculation is performed to compare the light amounts of the captured images.

  Note that “Fourier spectroscopy” is a technique that uses Fourier transform in principle. For this reason, when the spectral spectrum of the measurement object has characteristics as shown in FIG. 5, for example, the left end of the measurement section (for example, 400 nm or less) is imaged with a spectral intensity of 0 using an ultraviolet cut filter, At the right end of the measurement section (for example, 700 nm or more), it is preferable to pick up an image with a spectral intensity of 0 using an infrared cut filter. Therefore, in the comparison of the above three methods, the measurement interval is set to a 300 nm interval of [400 nm, 700 nm], and the band in the measurement interval is set to 30 nm.

When white light is measured, the amount of light that reaches the image sensor with respect to all incident light is as follows.
(1) In the “fixed wavelength spectral filter”, even if the spectral transmittance is 100%, 30 nm / 300 nm × 100% = 10%.
(2) In the “liquid crystal wavelength tunable filter”, polarized light is 50%, and if it is near blue, it is absorbed by the polarizing plate or the like and only 60% of it has a spectral transmittance. Therefore, as a whole, 30 nm / 300 nm × 50% × 60% = 3%.
(3) In “Fourier spectroscopy”, the polarization is 50%, and the waveform passing through the liquid crystal device (liquid crystal cell) is wave-like, so that almost 50% is transmitted in the entire section. Therefore, as a whole, 50% × 50 % = 25%.

  That is, “Fourier spectroscopy” has a brightness that is more than 8 times that of “liquid crystal wavelength tunable filter” and 2.5 times that of “fixed wavelength spectral filter”. ing. Of course, this brightness depends on the shape of the spectrum to be measured, but it is not a problem unless an extremely narrow band light source such as an LED or a laser is measured.

  In addition, as our name of “Fourier spectroscopy”, ideally, the transmittance characteristics in the form of sine and cosine waves with an integer number of waves in the measurement interval (in the wave number of light). If the liquid crystal device can be realized, the Fourier components of each pixel can be obtained directly at that stage if images are taken while increasing the number of waves (Fourier frequency) until the necessary bandwidth is reached, and an actual optical spectrum can be obtained. Need only perform an inverse Fourier transform on the Fourier component of each pixel obtained at this stage.

  However, the problem with liquid crystal devices (liquid crystal cells) is that sine waves and cosine waves having an integer number of waves cannot be generated within the measurement interval. It is no exaggeration to say that this was the main reason why “Fourier spectroscopy” could not be realized before the theory of the present invention.

  Next, the meaning of “wave number (k)” in “Fourier spectroscopy” will be described.

  As described above, the transmittance characteristic of the liquid crystal cell becomes a sine wave in the wave number space of light. Accordingly, if all of the spectrum of the measurement object and the transmittance characteristics of the liquid crystal cell are described in the wave number space of light, handling and calculation processing are facilitated.

  When the wave number (k) of light is used, the measurement interval can be expressed as [k0, k1]. In this measurement section [k0, k1], in “Fourier spectroscopy”, the number of waves included in the measurement section of the transmittance curve in the liquid crystal cell that is a sine wave is counted. The “number” is the Fourier frequency itself in “Fourier spectroscopy”. That is, in “Fourier spectroscopy”, “wave number” means “Fourier frequency”. When “wave number” is an integer, it is represented by “m” (m is an integer of 0 or more), and when “wave number” is a non-integer number, “m + δ” (m is an integer part and δ is a fraction part. ).

  The transmittance of the liquid crystal cell can be only 0 or 1 (all half polarized light is passed) at k = 0 (1 / λ = 0) depending on the arrangement method of the polarizing plates. Since the measurement interval [k0, k1] is away from the origin k = 0, when only the measurement interval [k0, k1] is viewed, only a half-sine phase sine wave that is neither a sine wave nor a cosine wave has transmittance characteristics. Can not take as. On the other hand, in the Fourier transform, two components, a Fourier component having a sine wave as a sampling waveform and a Fourier component having a cosine wave as a sampling waveform, are essential. Therefore, it is impossible or difficult to use a Fourier transform as in a textbook for a liquid crystal cell.

  Further, “Fourier spectroscopy” proposed in the present application includes a new mathematical technique “Fourier transform at a non-integer multiple frequency”. The essence of this technique is that “when observed with a sampling waveform having an integer number of waves, only the same integer frequency component of the spectrum to be measured remains in the integral, whereas the Fourier component is found in a one-to-one correspondence, When observed with a sampling waveform having a non-integer number of wave numbers, all frequency components of the spectrum to be measured remain in the integration with the phase, so if the wave number is changed in the fractional part, the phase is 90 degrees like sine and cosine. Even if it is not, it is possible to obtain an integer frequency component (Fourier component) of the spectrum to be measured by solving simultaneous equations (matrix). It seems that there was no one who focused on this point and pointed out the theory before this application.

  Although described in the section “When the wave number for sampling is an integral multiple” described later, the integral multiple frequency Fourier component is not obtained from the sampling data of the non-integer multiple frequency, and each band of the target spectrum is obtained. Assuming a representative value, it is not possible to obtain the representative value directly from non-integer multiple sampling data because it is mathematically incorrect.

  Next, the mathematical explanation about the “Fourier spectroscopy” described above and the theory of the “Fourier spectroscopy” are proved to be correct. The description will be made in the order of “notation”, “when the sampling wave number is an integral multiple”, “when the sampling wave number is a non-integer multiple”, and “solution of simultaneous equations when the sampling wave number is a non-integer multiple”.

(notation)
First, when a measurement section in the wave number space of light is represented by [k ₀ , k ₁ ], a variable k ′ and a section width T shown in the following equations are defined.

Further, when the spectrum to be measured is represented by x (k ′), this x (k ′) is expressed by using the Fourier component C _{m ′} and the phase φ _{m ′} for the wave number m ′ that is an integral multiple of the entire interval. It can be expressed as an expression.

  In the above equation (2), the upper limit value of m ′ is finite (<∞) in order to prevent the Fourier series value from diverging.

On the other hand, when the filter characteristic of the liquid crystal cell is represented by f (m, n, k ′), m is an integer, δ is a fractional part, and the wave number m + δ _{m, n} and the phase α _{m, n} are non-integer multiples over the whole interval. And can be expressed as:

In the above equation (3), m is an integer that satisfies m ≧ 0, and δ _{m, n} is a decimal that satisfies 0 <δ _{m, n} <1. When m = 0 and δ _{m, n} = 0, the DC component may be measured with α _{m, n} = 0. The wave number m + δ _{m, n} and the phase α _{m, n} are uniquely determined by the retardation. Furthermore, in actual measurement, since the number of times is different with different retardations for the same m, it is possible to distinguish by adding a subscript n like δ _{m, n} and α _{m, n} .

In Equation (3), m substantially corresponds to a measurable resolution (wave number of section division number), and δ _{m, n} and α _{m, n} substantially correspond to sampling with changing phases. When the highest measurement wave number is m, the division number (resolution) is 2 m. However, in the case of non-integer multiple sampling described later, it is possible to measure up to 2 m ′ exceeding the maximum measurement wave number m. This point will be described later.

(When sampling wave number is an integer multiple)
The case where the sampling wave number is an integral multiple is a special case of the above equation (3). In this case, since δ _{m, n} = 0, α _{m, n} has only one type with respect to _m, and is expressed as α _m . At this time, the spectrum (measured value) S _m of the measurement object passing through the liquid crystal cell is expressed by the following equation in the form referring to (2) and (3).

  In the equation (4), for DC (direct current) component, since m ′ is an integer, each integral value of “cos in Σ” is zero, and the number of additions of Σ is finite. It is expressed concisely as follows.

  For m ≧ 1, the following equation is modified.

  In the above equation (6), since the integral value of the term “cos” in the second and third terms is zero, it is simplified as the following equation.

  In addition, the integral value of the second term in the above equation (7) is zero, and the integral value of the third term remains only when m = m ′, and is further simplified as the following equation.

That, the DC component is confirmed by the measurement of S _0, by subtracting the DC component from the measured values of the S _m, are two unknowns C _m and phi _m remains in the S _m. Furthermore, since cos (α _m −φ _m ) has indefiniteness that it has two solutions different by π when the value is other than ± 1, it is necessary and sufficient to measure with different phases α _m for the same m. (It is synonymous with the need for two processes of cos transform and sin transform in ordinary Fourier transform).

として、このＸ_tを用いて行列形式［Ｓ_m］＝［F_m,t］［Ｘ_t］で表すことが可能かという提言がなされることが予想される。しかしながら、Ｓ₀を除き、上式の変形過程で示したように、積分処理の部分を、フィルタだけの積分と測定対象のスペクトルだけの積分（代表値）との積に分解することができない。このため、このような提言、つまり代表値を用いた行列形式で求めた値は数学的には正しくない。 Note that the entire section is divided into widths Δ, and the representative value of the measurement target spectrum in each section is, for example,

As a result, it is expected that a recommendation will be made as to whether this X _t can be used to represent the matrix form [S _m ] = [F _{m, t} ] [X _t ]. However, except for S ₀ , as shown in the transformation process of the above equation, the integration processing part cannot be decomposed into a product of integration of only the filter and integration (representative value) of only the spectrum to be measured. For this reason, such a recommendation, that is, a value obtained in a matrix format using representative values is mathematically incorrect.

(When sampling wave number is non-integer multiple)
When the sampling wave number is a non-integer multiple, the spectrum (measured value) S _{m, n} of the measurement object passing through the liquid crystal cell is expressed by the following equation in the form referring to (2) and (3).

Here, the DC component measurement (S _0,0 measurement) is the same as in the case of integer multiples (m = 0, δ _{m, n} = 0, α _{m, n} = 0).

On the other hand, when 1> δ _{m, n} > 0 and m ≧ 0 (註: m = 0 is allowed), the following equation is changed.

In the above equation (11), since the integral value of the term “cos” in the third term is zero (註: the second term includes δ _{m, n} which is a non-integer value in the term “cos”). (It does not become zero).

Next, the above equation (12) will be considered. First, when retardation is determined, m, δ _{m, n} and α _{m, n} are uniquely determined. Therefore, unknown values C _{m ′} and φ _{m ′} are included in each measured value S _{m, n} from m ′ = 1 to ∞. include. Here, since the third term of the equation (12) attenuates by 1 / (m + m ′ + δ _{m, n} ) with respect to m ′, the smaller m ′ contributes to S _{m, n} . Further, the fourth term attenuates by 1 / (m−m ′ + δ _{m, n} ) with respect to m ′, and therefore takes a maximum value when m ′ = m, and attenuates as m ′ moves away from m. . However, since both attenuations are on the order of m'-1, rapid attenuation cannot be expected. Therefore, the measurement target spectrum, certain frequency m 'components above _{the MAX,} C _m' for one of m in if Re Shimae assuming = 0 m = 1 to m _'MAX, about 2 times by changing the retardation ( If n = 1, 2), the simultaneous equations can be solved.

Alternatively, if the measurement is performed n times while changing the fractional retardation for one m under the same assumption, wave number components up to m ′ = (n · m) / 2 are obtained as simultaneous equations for the measurement target spectrum. . This means that m may be smaller than m ′ _MAX even if the spectrum to be measured has components up to m ′ _MAX , for example. Replacing this in a physical sense, as measured spectrum had a component of up to m _'MAX, retardation to be prepared indicates that may be those smaller (ie thin cell gap) Yes.

(Solving simultaneous equations when sampling wavenumber is non-integer multiple)
In the above equation (12), in the first and second terms, the DC component is obtained by measuring S ₀ , and δ _{m, n} and α _{m, n} are uniquely determined by the retardation, so that the simultaneous equations are solved. Can be excluded from the simultaneous equations. Therefore, if the first term and the second term are removed from the equation (12) and the coefficient “(1/4) · (T / 2π)” common to the third term and the fourth term is omitted, the following equation is obtained. can get.

In the above equation (13), the unknowns are C _{m ′} · cos (φ _{m ′} ) and C _{m ′} · sin (φ _{m ′} ). Therefore, a 2 · m ′ _MAX × 2 · m ′ _MAX filter is a 2 · m ′ _MAX original vector in which C _{m ′} · cos (φ _{m ′} ) and C _{m ′} · sin (φ _{m ′} ) are arranged. If the coefficient of the above equation (13) determined by retardation is arranged as a matrix, it can be solved as a regular matrix. In the case of δ _{m, n} = 0 due to the selected retardation, an equation for an integer may be applied. The formula in that case is as follows.

When the values of C _{m ′} · cos (φ _{m ′} ) and C _{m ′} · sin (φ _{m ′} ) are obtained in this way, the frequency component C _{m ′} and the phase component φ _{m ′} of the spectrum to be measured are It can obtain | require using a following formula and a following formula.

There are the following two ways to create a filter matrix of 2 · m ′ _MAX × 2 · m ′ _MAX .

(First method)
The wave number m of the retardation for measurement is moved to the maximum wave number m ′ _{MAX of the} spectrum to be measured _{, and} the value of δ _{m, n} indicating the difference in the fractional part for each m is n = 1, 2 only. In this method, a cell having a large cell gap must be prepared in order to increase the resolution, but the measurement accuracy is higher than that of the second method described below.

(Second method)
The wave number m of the retardation for measurement is kept at a moderate level (it does not move up to the maximum wave number m ′ _MAX ), the number of δ _{m, n} indicating the difference in the decimal part is increased (n> 2), and the number of measurements is Increase (use three or more values to indicate the difference in decimal part for at least one of the wave numbers). If measurement is performed n · m times, a resolution of 2 m ′ = n · m can be obtained for the spectrum to be measured. However, if n is increased too much, the measurement accuracy will drop (it can be understood from the fact that the determinant in the simultaneous equations becomes smaller and the accuracy of the solution will drop), but a cell with a large cell gap is prepared. There is an advantage that the resolution can be increased if the number of measurements is increased.

Note that in normal Fourier transform (integer multiple sampling), only the Fourier component up to the division number of 2m ′ _MAX (the number obtained by dividing the measurement interval by the desired band) can be obtained with respect to the maximum wave number m ′ _MAX . In the case of Fourier transform at a double frequency, the Fourier component having a frequency higher than the integer part remains in the sampling integration, and therefore, using a wave number m smaller than the maximum wave number m ′ _MAX , a Fourier having a division number of 2 m ′ _MAX or more. The component can be measured. That is, in the Fourier transform of the non-integer multiple frequency, it is possible to perform the measurement with the wave number smaller than ½ of the number divided by the band for obtaining the measurement section as the maximum wave number (maximum sampling wave number).

  Next, a specific processing flow when a spectrum measuring apparatus having a function of performing the above-described calculation processing is configured will be described.

  FIG. 6 is a diagram showing a calculation process and a data flow in the computer 4 (see FIG. 1). In FIG. 6, the integer multiple Fourier component calculation unit 31 and the inverse Fourier transform unit 32 are processing units provided in the computer 4. As shown in FIGS. 7A to 7C, “data 1, data 2, data 3,..., Data 2m” input to the integer multiple Fourier component calculation unit 31 are voltages (V1, V2) applied to the liquid crystal cell. (V2, V3,...) Are sequentially changed and the wave number (non-integer) of the sampling waveform is changed as appropriate. The image data is stored in the computer 4. The integer multiple Fourier component calculation unit 31 solves simultaneous equations generated using the imaging data, and calculates the amplitude value and phase of a sine function (cosine function) that is an unknown number. Needless to say, this process is executed for each pixel in the imaging data.

  In this way, the integer multiple Fourier component calculation unit 31 generates “Fourier component data 1, Fourier component data 2, Fourier component data 3,..., Fourier component data 2m” which is Fourier component data of an integral multiple. . Once integer multiple Fourier component data has been generated, these data can be inversely Fourier transformed. This process is performed by the inverse Fourier transform unit 32 to obtain a spectral intensity as shown in the figure.

  Heretofore, the liquid crystal cell has been described as being one sheet for convenience, but is not limited to one sheet. The thinner the liquid crystal cell, the faster the response. Therefore, the operation is faster when a plurality of liquid crystal cells are made. Even in this case, the number of polarizing plates may be two, and they may be arranged on the incident side of the liquid crystal cell closest to the incident portion side and on the emission side of the liquid crystal cell closest to the emission portion side. When the liquid crystal cell is thinned, the response of the liquid crystal cell is fast, so that the imaging time interval and the overall imaging time can be shortened compared to when the liquid crystal cell is thick.

  On the contrary, if the liquid crystal cell is thickened, there is an advantage that the retardation can be increased. As described above, the retardation is an optical distance between the slow axis and the fast axis (corresponding to the thickness of the liquid crystal × the refractive index), and a large retardation leads to an increase in measurement accuracy. In addition, since a liquid crystal cell having a large retardation can be constituted by a single liquid crystal cell, an effect that the configuration of the liquid crystal device can be simplified is also obtained.

  As described above, in the present invention, by controlling the voltage applied to the liquid crystal cell as the Fourier transform element, the image data controlled so that the wave number included in the transmittance waveform that sequentially passes through the liquid crystal cell has a non-integer multiple relationship. And calculating a Fourier component of an integer multiple frequency in the measurement interval for each pixel by solving simultaneous equations generated using a plurality of image data having different wave numbers, and obtaining an integer multiple of each obtained pixel A method for obtaining a spectral spectrum for each pixel by performing inverse Fourier transform on the frequency Fourier component has been described.

  The inventor of the present application conceived the present invention by paying attention to the fact that the transmittance waveform that has passed through the liquid crystal cell as a Fourier transform element cannot be separated into a sine wave and a cosine wave having an integer number of waves in the measurement section. did. On the other hand, this means that the transmittance waveform that has passed through the Fourier transform element can be separated into a sine wave and cosine wave having an integer number of waves in the measurement interval, that is, the Fourier transform element is an integral multiple. If it is a Fourier transform element, the configuration of the integer multiple Fourier component calculation unit 31 in FIG. 6 can be omitted. FIG. 8 shows a spectrum measuring apparatus or spectrum measuring method configured based on such a viewpoint.

  As shown in FIG. 8, “data 1, data 2, data 3,..., Data 2m” input to the inverse Fourier transform unit 32 has an integer number of wave numbers in the measurement interval and a fixed phase of 90 degrees (sinusoidal wave). Since the observed value corresponds to the Fourier component on a one-to-one basis, the spectral intensity of the measurement object can be obtained simply by performing inverse Fourier transform on these data. it can. The inventor of the present application is a device whose sampling waveform of the measurement object (transmittance waveform in the wave number space of light) has an integer number of waves and has a fixed phase of 90 degrees at the time of filing the present invention. I have no information. However, expecting that a device having such characteristics will be devised in the near future, the technical contents shown in FIG. 8 are also disclosed herein as part of the present invention.

  As described above, the present invention is useful as a spectrum measuring apparatus and a spectrum measuring method capable of suppressing deterioration of the S / N ratio by passing a sufficient amount of light to an imaging unit such as an imaging camera or an imaging element.

DESCRIPTION OF SYMBOLS 1 Spectrum measuring device 2 Liquid crystal device 3 Imaging device 4 Calculator 5 Voltage controller 7 Measuring object 8 Transmittance characteristic 21, 23 Polarizing plate 22 Liquid crystal cell 31 Integer multiple Fourier component calculation part 32 Fourier inverse transformation part

Claims (7)

A spectrum measuring apparatus having a processing unit for calculating a spectrum of a measurement object,
A liquid crystal device as a Fourier transform element;
A voltage controller for controlling a voltage applied to the liquid crystal device;
An imaging device that images the transmittance waveform of the measurement object that has passed through the liquid crystal device;
With
The processor is
The image data captured while controlling the voltage applied to the liquid crystal device so that the wave number included in the transmittance waveform has a non-integer multiple relationship is stored, and simultaneous data based on a plurality of image data having different wave numbers By solving the equation, for each pixel, an integer multiple Fourier component calculation unit that calculates an integer multiple frequency Fourier component in the measurement interval;
A Fourier inverse transform unit that calculates a spectral spectrum for each pixel by inverse Fourier transforming the integer multiple frequency Fourier component of each pixel calculated by the integer multiple Fourier component calculation unit;
A spectrum measuring apparatus comprising:   The spectrum measuring apparatus according to claim 1, wherein the liquid crystal device includes a pair of polarizers and a liquid crystal cell sandwiched between the pair of polarizers.   The spectrum measuring apparatus according to claim 2, wherein the liquid crystal cell includes a plurality of liquid crystal cells with no polarizing plate interposed therebetween. A spectrum measurement method for measuring a spectrum of a measurement object,
A first step of imaging using a liquid crystal cell as a Fourier transform element while changing a transmittance waveform passing through the liquid crystal cell to a plurality of non-integer multiple frequencies;
A second step of calculating, for each pixel, a Fourier component of an integer multiple frequency of a measurement section by solving simultaneous equations based on a plurality of image data obtained in the first step;
A third step of obtaining a spectral spectrum for each pixel by performing an inverse Fourier transform on the integer multiple frequency Fourier component of each pixel obtained in the second step;
A spectral measurement method comprising:   The first step includes a sub-step of changing the wave number of the retardation for measurement. In this sub-step, the wave number is moved to the maximum wave number of the spectrum to be measured, and the difference in the decimal part for each wave number is indicated. The spectrum measurement method according to claim 4, wherein two values are used.   The first step includes a sub-step of changing the wave number of the retardation for measurement, and in this sub-step, the change of the wave number is kept to a value less than the maximum wave number of the spectrum to be measured, while each wave number The spectrum measurement method according to claim 4, wherein three or more values are used as values indicating a difference in the decimal part with respect to at least one of the wave numbers. A spectrum measuring apparatus having a processing unit for calculating a spectrum of a measurement object,
An integer multiple Fourier transform element capable of generating an integer multiple frequency Fourier component;
An imaging device that images the transmittance waveform of the measurement object that has passed through the integer multiple Fourier transform element;
With
The processor is
A Fourier inverse transform unit that stores image data sequentially captured by the imaging device and calculates a spectral spectrum for each pixel by performing an inverse Fourier transform on an integer multiple frequency Fourier component of each pixel of the image data;
A spectrum measuring apparatus comprising:

Images