JP2006058070A - Differential pressure measuring system and differential pressure measuring method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a differential pressure measuring system capable of excluding a measurement error resulting from a temperature change, without requiring computer processing. <P>SOLUTION: The system is provided with a light source 4 for emitting light of a first and a second wavelength, a first pressure sensitive section 3 which reflects first reflected light of a first wavelength, a first external pressure and a first temperature are applied to, and has a first thermal expansion coefficient and a first reflection wavelength temperature coefficient being the product of the first thermal expansion coefficient and the first wavelength, a first thermosensitive section 6 which reflects second reflected light of the second wavelength, the first temperature is applied to, and has a second thermal expansion coefficient and a second reflection wavelength temperature coefficient being the product of the second thermal expansion coefficient and the second wavelength, a second pressure sensitive section 13 which reflects third reflected light of the second wavelength, a second external pressure and a second temperature are applied to, and has a second thermal expansion coefficient and a second reflection wavelength temperature coefficient, a second thermosensitive section 16 which reflects fourth reflected light of the first wavelength, a second temperature is applied to, and has the first thermal expansion coefficient and the first reflection wavelength temperature coefficient, and a signal processor 7 for calculating the differential pressure between the first external pressure and the second external pressure, from the fluctuation of the phase difference between a first interference fringe by the first and fourth reflected light and a second interference fringe by the second and third reflected light. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a pressure measurement technique, and more particularly to a differential pressure measurement system and a differential pressure measurement method that eliminate measurement errors caused by ambient temperature changes.

When controlling an oil plant or the like, it may be necessary to measure the differential pressure of the fluid at different locations within the oil plant. As a conventional differential pressure measurement method, there has been proposed a method in which a Fabry-Perot interferometer is arranged at a measurement position and a change in resonance wavelength of the Fabry-Perot interferometer caused by pressure is read with light. However, the phase difference of the Fabry-Perot interferometer changes not only with pressure change but also with temperature change. For this reason, as a method for measuring an accurate differential pressure excluding the influence of the temperature change at the measurement position, a method of arranging a Fabry-Perot interferometer for temperature measurement at the measurement position together with a Fabry-Perot interferometer for pressure measurement has been proposed. In this case, the differential pressure is measured by removing the influence of the temperature change from the measurement signal read by the light irradiated from a halogen lamp or the like with a computer (see, for example, Patent Document 1). However, removal of the influence of temperature changes by a computer requires a high-speed computing device and a large-capacity memory, and computation processing takes time.
Japanese Patent Laid-Open No. 2003-166891

  The present invention provides a differential pressure measurement system and a differential pressure measurement method that do not require complicated computer processing and can eliminate measurement errors due to temperature changes.

  In order to achieve the above object, the first feature of the present invention is: (a) a light source that irradiates light of the first and second wavelengths; and (b) the first reflected light of the first wavelength is reflected; A first pressure-sensitive portion having a first reflection wavelength temperature coefficient obtained by applying an external pressure and a first temperature and multiplying the first thermal expansion coefficient and the first thermal expansion coefficient by the first wavelength; A first thermal part that reflects the second reflected light, has a first temperature applied, and has a second thermal expansion coefficient and a second reflected wavelength temperature coefficient obtained by multiplying the second thermal expansion coefficient by the second wavelength; A second pressure-sensitive part that reflects the third reflected light of the second wavelength, is applied with a second external pressure and a second temperature, and has a second thermal expansion coefficient and a second reflected wavelength temperature coefficient; A second heat sensitive part that reflects the fourth reflected light of the wavelength, is applied with a second temperature, has a first thermal expansion coefficient and a first reflected wavelength temperature coefficient, and (f) the first by the first and fourth reflected light. Due to interference fringes and second and third reflected light And summarized in that the variation of the phase difference between two interference patterns is the differential pressure measurement system comprising a signal processor for calculating a differential pressure of the first and second external pressure.

  The second feature of the present invention is that (a) the step of irradiating light of the first and second wavelengths, and (b) the first external pressure and the first temperature are applied, the first thermal expansion coefficient and the first heat Receiving light at the first pressure-sensitive portion having the first reflection wavelength temperature coefficient obtained by multiplying the expansion coefficient by the first wavelength, and reflecting the first reflected light of the first wavelength; and (c) adding the first temperature. Receiving the light at the first heat sensitive part having the second thermal expansion coefficient and the second thermal expansion coefficient multiplied by the second wavelength and the second reflected wavelength temperature coefficient, and reflecting the second reflected light of the second wavelength; (D) The second external pressure and the second temperature are applied, the light is received by the second pressure sensing unit having the second thermal expansion coefficient and the second reflection wavelength temperature coefficient, and the third reflected light of the second wavelength is reflected. And (e) receiving a light at a second thermal part having a first thermal expansion coefficient and a first reflection wavelength temperature coefficient, wherein the second temperature is applied, and reflecting the fourth reflected light of the first wavelength; And f) calculating a differential pressure between the first and second external pressures from fluctuations in the phase difference between the first interference fringes of the first and fourth reflected lights and the second interference fringes of the second and third reflected lights. The gist is that it is a differential pressure measurement method.

  According to the present invention, it is possible to provide a differential pressure measurement system and a differential pressure measurement method that do not require complicated computer processing and can eliminate measurement errors caused by ambient temperature changes.

  Embodiments of the present invention will be described below. In the following description of the drawings, the same or similar parts are denoted by the same or similar reference numerals. However, the drawings are schematic. Therefore, specific dimensions and the like should be determined in light of the following description. Moreover, it is a matter of course that portions having different dimensional relationships and ratios are included between the drawings.

As shown in FIG. 1, the differential pressure measurement system according to the embodiment of the present invention includes a light source 4 that emits light of a first wavelength λ ₁ and a second wavelength λ ₂ , and a first reflection of a first wavelength λ ₁ . Reflecting light, first external pressure P _O1 and first temperature T ₁ are applied, and first reflection wavelength temperature obtained by multiplying first thermal expansion coefficient E ₁ and first thermal expansion coefficient E ₁ by first wavelength λ ₁ first pressure sensing 3 having coefficients D _1, reflects the second wavelength λ second reflected light _2, the first temperature T ₁ is applied, the second thermal expansion coefficient E ₂ and the second thermal expansion coefficient E ₂ having a first heat-sensitive part 6 having a second reflection wavelength temperature coefficient D ₂ multiplied by the second wavelength lambda ₂ in. The differential pressure measurement system further reflects the third reflected light of the second wavelength λ ₂ , the second external pressure P _O2 and the second temperature T ₂ are applied, the second thermal expansion coefficient E ₂ and the second reflected wavelength temperature coefficient. The second pressure-sensitive part 13 having D ₂ reflects the fourth reflected light of the first wavelength λ ₁ and is added with the second temperature T ₂ , and the first thermal expansion coefficient E ₁ and the first reflected wavelength temperature coefficient D ₁ And the differential pressure between the first and second external pressures from the variation in the phase difference between the first interference fringe due to the first and fourth reflected light and the second interference fringe due to the second and third reflected light. A signal processing device 7 for calculating

As the light source 4, a xenon lamp or the like that can support a continuous spectrum from the ultraviolet region to the infrared region (185 nm to 2000 nm) can be used. As the light source 4, an LED that can emit light of the first wavelength λ ₁ and the second wavelength λ ₂ or a laser oscillator can be used. An optical fiber 30 that propagates the irradiated light is connected to the light source 4. Further, the optical fiber 30 is connected to a splitter 21 that divides the propagation light in two directions. The divided lights are propagated through the optical fiber 31 and the optical fiber 32, respectively.

The first measurement unit 5 is connected to the optical fiber 31. The first measurement unit 5 includes a holder 60a into which an optical fiber 31 having a core 130a and a clad 131a is inserted, and insertion of the optical fiber 31, as shown in FIG. the first heat-sensitive part 6 is arranged on the end face of the by side, arranged in parallel position to the first heat-sensitive part 6, the first sense of the pressure membrane 50a for receiving a first external pressure P _O1, the first sensitive pressure membrane 50a first 1 The first pressure-sensitive portion 3 that is disposed on the surface facing the heat-sensitive portion 6 and receives light transmitted through the first heat-sensitive portion 6, the first interval h ₁ between the first heat-sensitive portion 6 and the first pressure-sensitive portion 3 Has a first measurement housing 43a. In addition, the first measurement unit 5 includes a first pressure-sensitive film 50a, a first measurement housing 43a, and a passage provided in the holder 60a for adjusting the first internal pressure _PI1 in a region surrounded by the holder 60a. The air hole 160a and an open valve 70a for controlling the opening and closing of the air hole 160a are provided. Further, a first measurement sensor base 40a that defines the radius a shown in FIG. 2 of the first pressure-sensitive film 50a to be exposed is disposed outside the first pressure-sensitive film 50a.

Here, when the first heat sensitive unit 6 receives the light emitted from the light source 4, as shown in FIG. 8 (a), the first heat sensitive unit 6 converts the light in the second wavelength band WB ₂ where the intensity peak appears at the second wavelength λ _2. reflect. The first thermosensitive part 6 is made of a silicon (Si) -based material having a second reflection wavelength temperature coefficient D ₂ equal to a value obtained by multiplying the second thermal expansion coefficient E ₂ and the second thermal expansion coefficient E ₂ by the second wavelength λ _2. It consists of a multilayer film. The “reflection wavelength temperature coefficient” is a coefficient indicating the degree of change in the reflection wavelength caused by the temperature change in the multilayer film. This “reflection wavelength temperature coefficient” is adjusted, for example, by selecting the material of the multilayer film or the number of stacked layers. Further, the second wavelength λ ₂ of the reflected light of the first heat sensitive part 6 is also adjusted by the number of deposited multilayer films. The graph shown in FIG. 4 shows an example in which when the number of stacked multilayer films is 5, reflected light having a center wavelength of 870 nm and a bandwidth of 10 nm can be obtained. The graph shown in FIG. 5 shows an example in which when the number of stacked layers is 30, reflected light having a center wavelength of 1300 nm and a bandwidth of 0.3 nm can be obtained. As shown in FIG. 1, the distance from the splitter 21 to the first heat sensitive unit 6 is _defined as a first heat sensitive light distance L _1r .

The first pressure sensing unit 3 receives the transmitted light from the first heat sensing unit 6 and reflects the light in the first wavelength band WB ₁ in which the intensity peak appears at the first wavelength λ ₁ as shown in FIG. 8 (a). The first pressure sensing unit 3 is a multilayer made of a Si-based material having a first reflection wavelength temperature coefficient D ₁ equal to a value obtained by multiplying the first thermal expansion coefficient E ₁ and the first thermal expansion coefficient E ₁ by the first wavelength λ _1. It consists of a membrane. As shown in FIG. 1, the distance from the splitter 21 to the first pressure sensing unit 3 is defined as a first pressure sensitive light distance L _1s .

The first pressure-sensitive film 50a shown in FIG. 3 does not bend in the “steady state” where the first internal pressure _PI1 and the first external pressure _PO1 are equal. However, as shown in FIG. 6, when the increased compared to the first internal pressure P _I1 is the first external pressure P _O1 is first sensitive pressure membrane 50a is bent in an inward direction. Further, as shown in FIG. 7, when the smaller first external pressure P _O1 as compared with the first internal pressure P _I1, the first sense of the pressure membrane 50a is bent in the outside direction. The first measurement unit 5 is used to measure the first external pressure _PO1 by detecting the deflection w of the first pressure-sensitive film 50a shown in FIGS.

As shown in FIG. 6, the deflection w of the first pressure-sensitive film 50a when the first external pressure _PO1 is applied is as follows when the first pressure-sensitive film 50a has the radius a as shown in FIG. ) Expression. :
w = (P _O1 -P _I1 ) × (a ² -r ² ) ² / (64 × D)… (1)
Here, r (r: 0 ≦ r ≦ a) is a distance from the center position M of the first pressure-sensitive film 50a to the measurement position. D is given by the following equation (2). :
D = E × c ³ / {12 × (1-υ ² )}… (2)
In equation (2), E is the Young's modulus of the first pressure-sensitive film 50a, c is the thickness of the first pressure-sensitive film 50a, and υ is the Poisson's ratio of the first pressure-sensitive film 50a. (1) By using the equation, it is possible to calculate the first external pressure P _O1 from the deflection w of the first sensitive pressure membrane 50a.

FIG. 9 is a graph plotting the relationship between the first external pressure _PO1 and the deflection w when the thickness c of the first pressure-sensitive film 50a shown in FIGS. 3 to 7 is 50 μm. In FIG. 9, the plots are plotted for the cases where the radius a of the first pressure-sensitive film 50a shown in FIG. 2 is 0.01 mm, 0.10 mm, and 1.00 mm. FIG. 10 is a graph plotting the relationship between the first external pressure _PO1 and the deflection w when the thickness c of the first pressure-sensitive film 50a is 1 μm. In FIG. 10, the plots are plotted for the cases where the radius a of the first pressure-sensitive film 50a is 0.01 mm, 0.10 mm, and 1.00 mm. As shown in FIGS. 9 and 10, the pressure sensitivity with respect to the first external pressure _PO1 can be adjusted by appropriately selecting the radius a and the thickness c of the first pressure-sensitive film 50a.

Note first sense pressure membrane 50a shown in FIGS. 2-7, in addition to deflect in the first external pressure P _O1, to expand or contract depending on the variation amount [Delta] T ₁ of the first temperature T ₁ of the surroundings. Also, each of the first heat sensitive part 6 and the first pressure sensitive part 3 expands or contracts depending on the fluctuation amount ΔT ₁ of the surrounding first temperature T ₁ . Furthermore, the refractive index of each of the first heat sensitive part 6 and the first pressure sensitive part 3 changes depending on the fluctuation amount ΔT ₁ of the surrounding first temperature T ₁ , and a wavelength shift may occur in the reflected light. Therefore, the first sense of pressure membrane 50a which depends on the variation amount [Delta] T ₁ of the first temperature T _1, each of the expansion or the refractive index change of the first heat-sensitive part 6 and the first pressure sensing 3 of the first external pressure P _O1 It becomes a measurement error factor. A mechanism in which the differential pressure measurement system shown in FIG. 1 removes the measurement error of the first measurement unit 5 caused by the fluctuation amount ΔT ₁ of the first temperature T ₁ will be described in detail later. As shown in FIG. 1, the reflected light from the first measurement unit 5 is propagated to the light receiving element 8 by the optical fiber 33 connected to the splitter 21.

The second measurement unit 15 is connected to the optical fiber 32. As shown in FIG. 11, the second measurement unit 15 includes a holder 60b into which an optical fiber 32 having a core 130b and a clad 131b is inserted, a second heat sensitive unit 16 disposed on the end face on the side where the optical fiber 32 is inserted, arranged parallel position to the second heat-sensitive part 16, the second sense pressure membrane 50b for receiving a second external pressure P _O2, disposed in the second heat-sensitive part 16 and the facing surface of the second sensitive pressure membrane 50b, the second heat-sensitive A second pressure-sensitive part 13 that receives light transmitted through the part 16, and a second measurement housing 43b that defines a _second distance h2 between the second heat-sensitive part 16 and the second pressure-sensitive part 13. The second measuring unit 15, the second sense of pressure membrane 50b, the second measuring housing 43b and vent hole provided in the holder 60b to adjust the second internal pressure P _I2 of the area surrounded by the holder 60b 160b and an open valve 70b for controlling the opening and closing of the vent hole 160b. Further, outside the second pressure sensitive film 50b, there is a second measurement sensor base 40b similar to the first measurement sensor base 40a that defines the radius a shown in FIG. 2 of the second pressure sensitive film 50b to be exposed. Be placed.

When receiving the light emitted from the light source 4, the second heat sensitive unit 16 reflects the light in the fourth wavelength band WB ₄ in which the intensity peak appears at the first wavelength λ ₁ as shown in FIG. 8 (b). The second heat sensitive part 16, similarly to the first heat-sensitive part 6, a multilayer film of Si-based material having a first thermal expansion coefficient E ₁ and a first reflection wavelength temperature coefficient D _1. As shown in FIG. 1, the distance from the splitter 21 to the second heat sensitive unit 16 is a second heat sensitive light distance L _2r .

The second pressure sensing unit 13 receives the transmitted light from the second heat sensing unit 16 and reflects the light in the third wavelength band WB ₃ in which the intensity peak appears at the second wavelength λ ₂ as shown in FIG. 8 (b). Second pressure sensing 13, like the first heat-sensitive part 6, a multilayer film of Si-based material having a second thermal expansion coefficient E ₂ and the second reflection wavelength temperature coefficient D _2. As shown in FIG. 1, the distance from the splitter 21 to the second pressure sensing unit 13 is defined as a second pressure sensitive light distance L _2s .

Second spacing h ₂ shown in FIG. 11 may be the same as the first distance h ₁ of the first measuring unit 5 shown in FIG. 3, may be a different intervals. Other components of the second measurement unit 15 shown in FIG. 11 have the same structure as the first measurement unit 5 shown in FIG. 3, and the second internal pressure _PI2 is set to be the same as the first internal pressure _PI1. . Thus, in the deflection w of the second sense pressure membrane 50b of the second measurement unit 15 is 0, when the second respective temperature T ₂ of the first temperature T ₁ and the second measuring unit 15 of the first measuring unit 5 is equal to As shown in FIGS. 8 (a) and 8 (b), the reflection spectra of the first heat-sensitive part 6 and the second pressure-sensitive part 13 are equal. In w is 0 flexure of the first sense pressure membrane 50a of the first measuring unit 5, if the second respective temperature T ₂ of the first temperature T ₁ and the second measuring unit 15 of the first measuring unit 5 are equal As shown in FIGS. 8 (a) and 8 (b), the reflection spectra of the first pressure-sensitive part 3 and the second heat-sensitive part 16 are equal.

Second pressure sensing thick film 50b shown in FIG. 11, in addition to deflect the second external pressure P _O2, to expand or contract depending on the variation amount [Delta] T ₂ of the second temperature T ₂ ambient. Further, each of the second heat sensitive part 16 and the second pressure sensitive part 13 expands or contracts depending on the fluctuation amount ΔT ₂ of the surrounding second temperature T ₂ . Further, the refractive index of each of the second heat sensitive part 16 and the second pressure sensitive part 13 changes depending on the fluctuation amount ΔT ₂ of the surrounding second temperature T ₂ , and a wavelength shift may occur in the reflected light. Therefore, the second sense pressure membrane 50b that depends on the variation amount [Delta] T ₂ of the second temperature T _2, each stretch or refractive index change of the second heat-sensitive part 16 and the second pressure sensing 13 of the second external pressure P _O2 It becomes a measurement error factor. A mechanism in which the differential pressure measurement system shown in FIG. 1 removes the measurement error of the second measurement unit 15 caused by the fluctuation amount ΔT ₂ of the second temperature T ₂ will be described in detail later.

  In the differential pressure measurement system shown in FIG. 1, the interference fringes due to the propagation path from the light irradiated from the light source 4 to the light receiving element 8 are the first combination shown in FIG. 12, the second combination shown in FIG. There are four possible combinations of the third combination shown in FIG. 14 and the fourth combination shown in FIG.

In the first combination shown in FIG. 12, light emitted from the light source 4 is guided by the splitter 21 to each of the first pressure-sensitive unit 3 and the second heat-sensitive unit 16. The first pressure sensing unit 3 reflects light having the first wavelength band WB ₁ , and the reflected light travels through the splitter 21 toward the light receiving element 8. The second heat sensitive unit 16 reflects light having the fourth wavelength band WB ₄ , and the reflected light travels through the splitter 21 toward the light receiving element 8. Here, each of the reflection spectrum of the first pressure sensing 3 and the second heat-sensitive portion 16 in the steady state, as shown in FIG. 8 (a) and 8 (b), both of the first wavelength lambda ₁ intensity Overlapping as a peak. Therefore, in the first combination shown in FIG. 12, the light having the first wavelength band WB ₁ and the light having the fourth wavelength band WB ₄ form a first interference fringe on the light receiving element 8.

In the second combination shown in FIG. 13, the light emitted from the light source 4 is guided to each of the first heat sensitive unit 6 and the second pressure sensitive unit 13 by the splitter 21. The light having the second wavelength band WB ₂ is reflected at the first heat sensitive unit 6, and the reflected light travels through the splitter 21 toward the light receiving element 8. The second pressure sensing unit 13 reflects light having the third wavelength band WB ₃ , and the reflected light travels through the splitter 21 toward the light receiving element 8. Here, the respective reflection spectra of the first heat-sensing unit 6 and the second pressure-sensing unit 13 in the steady state have the intensity of the second wavelength λ ₂ as shown in FIGS. 8 (a) and 8 (b). Overlapping as a peak. Therefore, in the second combination shown in FIG. 13, the light having the second wavelength band WB ₂ and the light having the third wavelength band WB ₃ form a second interference fringe on the light receiving element 8.

  In the third combination shown in FIG. 14, the light emitted from the light source 4 is guided to each of the first pressure sensing unit 3 and the second pressure sensing unit 13. Here, as shown in FIG. 8 (a) and FIG. 8 (b), the first pressure-sensitive part 3 and the second pressure-sensitive part 13 have different wavelength bands that can be reflected. Therefore, no interference fringes are formed on the light receiving element 8 in the third combination shown in FIG.

  In the fourth combination shown in FIG. 15, the light emitted from the light source 4 is guided to each of the first heat sensitive unit 6 and the second heat sensitive unit 16 by the splitter 21. Also in the fourth combination, as shown in FIG. 8 (a) and FIG. 8 (b), the first heat-sensitive part 6 and the second heat-sensitive part 16 have different wavelength bands that can be reflected. Therefore, no interference fringes are formed on the light receiving element 8 in the fourth combination shown in FIG.

  From the above, in the differential pressure measurement system shown in FIG. 1, the combination of propagation paths from the light emitted from the light source 4 to the light receiving element 8 is the first combination shown in FIG. 12 and the combination shown in FIG. Only two combinations of the second combination need be considered.

  On the light receiving element 8, which is a photodiode or the like, the first interference fringes and the second interference fringes are overlapped to form a composite interference fringe. The light intensity I of the synthetic interference fringes is expressed by the following equation (3).

I = 2 + 2cos {(2π / λ ₁ ) × (L _1s -L _2r )} + 2cos {(2π / λ ₂ ) × (L _2s -L _1r )}
= 2 + 2cos {2π {(L _1s -L _2r ) / λ ₁ + (L _2s -L _1r ) / λ ₂ }} × cos {2π {(L _1s -L _2r ) / λ _1- (L _2s- L _1r ) / λ ₂ }}… (3)
Here, the first optical path difference L ₁₂ between the reflected light of the first pressure-sensitive portion 3 and the reflected light of the second heat-sensitive portion 16 shown in FIG. 1 is expressed by the following equation (4). Further, the second optical path difference L ₂₁ between the reflected light of the second pressure sensitive unit 13 and the reflected light of the first heat sensitive unit 6 is expressed by the following equation (5).

L ₁₂ = L _1s -L _2r … (4)
L ₂₁ = L _2s -L _1r … (5)
Therefore, from the equations (3) to (5), the light intensity I of the combined interference fringes is expressed by the high frequency component cos {2π (L ₁₂ / λ ₁ + L ₂₁ / λ ₂ )} and the low frequency component cos shown in the following equation (6). It is represented by the product of {2πφ}.

I = 2 + 2cos {2π (L ₁₂ / λ ₁ + L ₂₁ / λ ₂ )} × cos {2πφ}… (6)
In the equation (6), φ is a phase difference between the light having the first wavelength λ _{1 and} the light having the second wavelength λ ₂ expressed by the following equation (7).

φ = L ₁₂ / λ ₁ -L ₂₁ / λ ₂ (7)
Here, in accordance with a variation of the first when the pressure difference is generated between the measuring unit 5 and the second measuring unit 15, the first optical path difference L ₁₂ and the second optical path difference L ₂₁ shown in FIG. 1 position The phase difference φ also varies. However, even if a temperature difference occurs between the first measurement unit 5 and the second measurement unit 15, the phase difference φ can be regarded as not fluctuating by configuring the differential pressure measurement system in the arrangement shown in FIG. it can. The reason why the phase difference φ can be regarded as not fluctuating due to the temperature difference will be described below.

First, the first optical path difference L ₁₂ varies depending on the first external pressure P _O1 applied to the first pressure sensing unit 3, the first temperature T ₁ , and the second temperature T ₂ applied to the second heat sensing unit 16. Therefore, the function of the first external pressure P _O1 , the first temperature T ₁ , and the second temperature T ₂ given by the following equation (8) can be rewritten. The second optical path difference L ₂₁ varies depending on the second external pressure P _O2 applied to the second pressure sensing unit 13, the second temperature T ₂ , and the first temperature T ₁ applied to the first heat sensing unit 6. Therefore, the function of the second external pressure P _O2 , the second temperature T ₂ , and the first temperature T ₁ given by the following equation (9) can be rewritten.

L ₁₂ = L ₁₂ (P _O1 , T ₁ , T ₂ )… (8)
L ₂₁ = L ₂₁ (P _O2 , T ₁ , T ₂ )… (9)
The first wavelength λ ₁ of the light propagating through the path by the first combination shown in FIG. 12 depends on the first temperature T ₁ applied to the first pressure sensitive unit 3 and the second temperature T ₂ applied to the second thermal unit 16 Since the wavelength shifts, the function of the first temperature T ₁ and the second temperature T ₂ given by the following equation (10) can be rewritten. Further, the second wavelength λ ₂ of the light propagating through the path by the second combination shown in FIG. 13 is changed to the first temperature T ₁ applied to the first heat sensitive unit 6 and the second temperature T ₂ applied to the second pressure sensitive unit 13. Since the wavelength shift depends on this, it can be rewritten by a function of the first temperature T ₁ and the second temperature T ₂ given by the following equation (11).

λ ₁ = λ ₁ (T ₁ , T ₂ )… (10)
λ ₂ = λ ₂ (T ₁ , T ₂ )… (11)
Here, when fluctuations occur in each of the first external pressure P _O1 , the second external pressure P _O2 , the first temperature T ₁ and the second temperature T ₂ , the fluctuation of the phase difference φ expressed by the equation (7) The amount Δφ is expressed by the following equation (12).

Δφ = Δ (L ₁₂ / λ ₁ )-Δ (L ₂₁ / λ ₂ )
= ((1 / λ ₁ ) {(δL ₁₂ / δP _O1 ) ΔP _O1 + (δL ₁₂ / δT ₁ ) ΔT ₁ + (δL ₁₂ / δT ₂ ) ΔT ₂ } + L ₁₂ {(δ (1 / λ ₁ ) / δT ₁ ) ΔT ₁ + (δ (1 / λ ₁ ) / δT ₂ ) ΔT ₂ ]
-[(1 / λ ₂ ) {(δL ₂₁ / δP _O2 ) ΔP _O2 + (δL ₂₁ / δT ₁ ) ΔT ₁ + (δL ₂₁ / δT ₂ ) ΔT ₂ } + L ₂₁ {(δ (1 / λ ₂ ) / δT ₁ ) ΔT ₁ + (δ (1 / λ ₂ ) / δT ₂ ) ΔT ₂ ]… (12)
The sections (12), the variation amount [Delta] P _O1 of the first external pressure P _O1, respectively, the variation [Delta] P _O2 of the second external pressure P _O2, variation [Delta] T ₁ of the first temperature T _1, and the second temperature T to summarize in the section having the _second variation amount [Delta] T _2, the following equation (13) is derived.

Δφ = (1 / λ ₁ ) (δL ₁₂ / δP _O1 ) ΔP _O1- (1 / λ ₂ ) (δL ₂₁ / δP _O2 ) ΔP _O2
+ ((1 / λ ₁ ) (δL ₁₂ / δT ₁ ) + L ₁₂ (δ (1 / λ ₁ ) / δT ₁ )-((1 / λ ₂ ) (δL ₂₁ / δT ₁ ) _{+ L 21 (δ (1 /} λ 2) / δT 1)}] ΔT 1
+ [(1 / λ ₁ ) (δL ₁₂ / δT ₂ ) + L ₁₂ (δ (1 / λ ₁ ) / δT ₂ )-((1 / λ ₂ ) (δL ₂₁ / δT ₂ ) + L ₂₁ (δ (1 / λ ₂ ) / δT ₂ )}] ΔT ₂ (13)
Further transforming equation (13) leads to equation (14) below.

Δφ = (1 / λ ₁ ) (δL ₁₂ / δP _O1 ) ΔP _O1- (1 / λ ₂ ) (δL ₂₁ / δP _O2 ) ΔP _O2
+ ((1 / λ ₁ ) (δL ₁₂ / δT ₁ )-(L ₁₂ / λ ₁ ² ) (δλ ₁ / δT ₁ )
-{(1 / λ ₂ ) (δL ₂₁ / δT ₁ )-(L ₂₁ / λ ₂ ² ) (δλ ₂ / δT ₁ )}] ΔT ₁
+ ((1 / λ ₁ ) (δL ₁₂ / δT ₂ )-(L ₁₂ / λ ₁ ² ) (δλ ₁ / δT ₂ )
-{(1 / λ ₂ ) (δL ₂₁ / δT ₂ )-(L ₂₁ / λ ₂ ² ) δλ ₂ / δT ₂ }] ΔT ₂ (14)
Here, the first pressure sensitivity α _P1 ⁽¹⁾ for the first external pressure P _O1 of the first optical path difference L ₁₂ and the second pressure sensitivity α _P2 for the second external pressure P _O2 of the second optical path difference L ₂₁ Each of ⁽²⁾ can be defined by the following equations (15) and (16).

α _P1 ⁽¹⁾ = δL ₁₂ / δP _O1 … (15)
α _P2 ⁽²⁾ = δL ₂₁ / δP _O2 (16)
The thermal expansion amount C ₁₂ with respect to the first temperature T ₁ of the first optical path difference L ₁₂ ^(1), the thermal expansion amount C ₁₂ with respect to the second temperature T ₂ of the first optical path difference L ₁₂ ^(2), second the thermal expansion amount C ₂₁ with respect to the first temperature T ₁ of the optical path difference L ₂₁ ^(1), and each of the thermal expansion amount C ₂₁ with respect to the second temperature T ₂ ⁽²⁾ second optical path difference L _21, following ( 17) to (20) can be defined.

C ₁₂ ⁽¹⁾ = δL ₁₂ / δT ₁ (17)
C ₁₂ ⁽²⁾ = δL ₁₂ / δT ₂ (18)
C ₂₁ ⁽¹⁾ = δL ₂₁ / δT ₁ (19)
C ₂₁ ⁽²⁾ = δL ₂₁ / δT ₂ (20)
Further, the reflection wavelength temperature coefficient D ₁ ⁽¹⁾ to the first temperature T ₁ of the first wavelength lambda _1, the reflection wavelength temperature coefficient D ₁ ⁽²⁾ to the second temperature T ₂ of the first wavelength lambda _1, the second wavelength lambda _The reflection wavelength temperature coefficient D ₂ ⁽¹⁾ for the first temperature T ₁ of ₂ and the reflection wavelength temperature coefficient D ₂ ⁽²⁾ for the second temperature T ₂ of the second wavelength λ ₂ are respectively (21) to (21) It can be defined by equation (24).

D ₁ ⁽¹⁾ = δλ ₁ / δT ₁ (21)
D ₁ ⁽²⁾ = δλ ₁ / δT ₂ (22)
D ₂ ⁽¹⁾ = δλ ₂ / δT ₁ (23)
D ₂ ⁽²⁾ = δλ ₂ / δT ₂ (24)
Therefore, by substituting the equations (15) to (24) into the equation (14), the fluctuation amount Δφ of the phase difference φ is expressed by the following equation (25).

Δφ = (1 / λ ₁ ) α _P1 ⁽¹⁾ ΔP _O1- (1 / λ ₂ ) α _P2 ⁽²⁾ ΔP _O2
+ [(1 / λ ₁ ) C ₁₂ ⁽¹⁾ -(L ₁₂ / λ ₁ ² ) D ₁ ⁽¹⁾
-{(1 / λ ₂ ) C ₂₁ ⁽¹⁾ -(L ₂₁ / λ ₂ ² ) D ₂ ⁽¹⁾ }] ΔT ₁
+ [(1 / λ ₁ ) C ₁₂ ⁽²⁾ -(L ₁₂ / λ ₁ ² ) D ₁ ⁽²⁾
-{(1 / λ ₂ ) C ₂₁ ⁽²⁾ -(L ₂₁ / λ ₂ ² ) D ₂ ⁽²⁾ }] ΔT ₂ … (25)
Also, a first pressure sensing 3 each of the second heat-sensitive portion 16, since a material having a first thermal expansion coefficient E ₁ and a first reflection wavelength temperature coefficient D _1, be approximated to the following (26) Yes, equation (27) holds. Furthermore the first heat-sensitive part 6 each of the second pressure sensing 13, since a material having a second thermal expansion coefficient E ₂ and the second reflection wavelength temperature coefficient D _2, can be approximated to the following (28) In addition, equation (29) holds.

C ₁₂ = C ₁₂ ⁽¹⁾ = C ₁₂ ⁽²⁾ … (26)
D ₁ = D ₁ ⁽¹⁾ = D ₁ ⁽²⁾ … (27)
C ₂₁ = C ₂₁ ⁽¹⁾ = C ₂₁ ⁽²⁾ … (28)
D ₂ = D ₂ ⁽¹⁾ = D ₂ ⁽²⁾ … (29)
In Expressions (26) to (29), C ₁₂ is a first approximate thermal expansion amount of the first optical path difference L ₁₂ with respect to the first temperature T ₁ and the second temperature T ₂ , and C ₂₁ is the second optical path difference L _21. The second approximate thermal expansion amount with respect to the first temperature T ₁ and the second temperature T ₂ is shown. Therefore, from the equations (25) to (29), the fluctuation amount Δφ of the phase difference φ is expressed by the following equation (30).

Δφ = (1 / λ ₁ ) α _P1 ⁽¹⁾ ΔP _O1- (1 / λ ₂ ) α _P2 ⁽²⁾ ΔP <sub>O2
+ [(1 / λ 1)</sub> C 12 - (L 12 / λ 1 2) D 1
-{(1 / λ ₂ ) C _21- (L ₂₁ / λ ₂ ² ) D ₂ }] ΔT <sub>1
+ [(1 / λ 1)</sub> C 12 - (L 12 / λ 1 2) D 1
-{(1 / λ ₂ ) C _21- (L ₂₁ / λ ₂ ² ) D ₂ }] ΔT ₂ … (30)
Further, when the equation (30) is modified, the fluctuation amount Δφ of the phase difference φ is expressed by the following equation (31).

Δφ = (1 / λ ₁ ) α _P1 ⁽¹⁾ ΔP _O1- (1 / λ ₂ ) α _P2 ⁽²⁾ ΔP <sub>O2
+ [(1 / λ 1)</sub> C 12 - (L 12 / λ 1 2) D 1] (ΔT 1 + ΔT 2)
-[(1 / λ ₂ ) C _21- (L ₂₁ / λ ₂ ² ) D ₂ ] (ΔT ₁ + ΔT ₂ )… (31)
Here, the first approximation thermal expansion amount C _12, the following equation (32) in relation holds between the first thermal expansion coefficient E ₁ and the first optical path difference L _12.

C ₁₂ = E ₁ × L ₁₂ … (32)
Therefore, the second term of the equation (31) can be expressed by the following equation (33) using the first thermal expansion coefficient E ₁ .

_{[(1 / λ 1) C} 12 - (L 12 / λ 1 2) D 1] (ΔT 1 + ΔT 2)
_{= [(1 / λ 1)} E 1 × L 12 - (L 12 / λ 1 2) D 1] (ΔT 1 + ΔT 2)
= [(L ₁₂ / λ ₁ ) {E _1- (D ₁ / λ ₁ )}] (ΔT ₁ + ΔT ₂ )… (33)
From the equation (33), the second term of the equation (31) becomes 0 when the relationship shown in the following equation (34) is established.

E _1- (D ₁ / λ ₁ ) = 0
D ₁ = E ₁ × λ ₁ (34)
The second approximation thermal expansion amount C _21, the following equation (35) relationship is established between the second thermal expansion coefficient E ₂ and the second optical path difference L _21.

C ₂₁ = E ₂ × L ₂₁ … (35)
Therefore, the third term in (31) can be expressed by the following equation (36) using a second thermal expansion coefficient E _2.

[(1 / λ ₂ ) C _21- (L ₂₁ / λ ₂ ² ) D ₂ ] (ΔT ₁ + ΔT ₂ )
= [(1 / λ ₂ ) E ₂ × L _21- (L ₂₁ / λ ₂ ² ) D ₂ ] (ΔT ₁ + ΔT ₂ )
= [(L ₂₁ / λ ₂ ) {E _2- (D ₂ / λ ₂ )}] (ΔT ₁ + ΔT ₂ )… (36)
From the expression (36), the third term of the expression (31) becomes 0 when the relationship expressed by the following expression (37) is established.

E _2- (D ₂ / λ ₂ ) = 0
D ₂ = E ₂ × λ ₂ (37)
Therefore, (34) as indicated formula, each of the first value of the reflection wavelength temperature coefficient D ₁ of the first pressure sensing 3 and the second heat-sensitive portion 16, the first wavelength to the first thermal expansion coefficient E ₁ equal to the value obtained by multiplying the lambda _1, and (37) as indicated formula, each of the second values of the reflection wavelength temperature coefficient D ₂ of the second pressure sensing 13 and the first heat-sensitive part 6, the second heat If the system of FIG. 1 is configured with a material that is equal to the value obtained by multiplying the expansion coefficient E ₂ by the second wavelength λ ₂ , the second and third terms of the equation (31) are eliminated, and the amount of fluctuation of the phase difference φ Δφ is expressed by the following equation (38).

Δφ = (1 / λ ₁ ) α _P1 ⁽¹⁾ ΔP _O1- (1 / λ ₂ ) α _P2 ⁽²⁾ ΔP _O2 … (38)
Therefore, if a pressure difference occurs between the first measurement unit 5 and the second measurement unit 15 shown in FIG. 1, the phase difference φ varies, but even if a temperature difference occurs, the phase difference φ does not vary. Can be considered. Note first sense pressure membrane 50a shown in FIG. 3 have the same first thermal expansion coefficient E ₁ and the first pressure sensing 3, second pressure sensing thick film 50b shown in FIG. 11 is the same as the second pressure sensing 13 It is desirable to have a _second coefficient of thermal expansion E2.

In practice, if the approximate expression is satisfied even if the expressions (34) and (37) are not strictly established, the second and third terms of the expression (31) are sufficiently small to approximate the expression (38). it can. For example, the first wavelength λ ₁ is 1.30 μm, the first optical path difference L ₁₂ is 10 μm, and the first thermal expansion coefficient E ₁ is 4.13 × 10 ^{−6 in} the material of the first pressure-sensitive part 3 and the second heat-sensitive part 16. When single crystal Si of / K is used, the first approximate thermal expansion C ₁₂ is 4.13 × 10 ⁻¹¹ m / K from the equation (32). Further, when the film formation conditions of the first pressure sensing 3 and the second heat-sensitive part 16 first reflection wavelength temperature coefficient D ₁ is set to be ^{5.30 × 10 -12 m / K,} (31) second term of the equation Is represented by the following equation (39).

_{[(1 / λ 1) C} 12 - (L 12 / λ 1 2) D 1] (ΔT 1 + ΔT 2)
^{= (3.18 × 10 -5 - 3.14} × 10 -5) × (ΔT 1 + ΔT 2)
= 0.04 × 10 ^-5 × (ΔT ₁ + ΔT ₂ )… (39)
The second wavelength λ ₂ is 1.31 μm, the second optical path difference L ₂₁ is 5 μm, and the second thermal expansion coefficient E ₂ is 4.13 × 10 ⁻⁶ / When K single crystal Si is used, the second approximate thermal expansion C ₂₁ is 2.06 × 10 ⁻¹¹ m / K. Furthermore, when the film formation conditions of the first heat sensitive part 6 and the second pressure sensitive part 13 are set so that the second reflection wavelength temperature coefficient D ₂ is 5.30 × 10 ⁻¹² m / K, the third term of the equation (31) Is represented by the following equation (40).

-[(1 / λ ₂ ) C _21- (L ₂₁ / λ ₂ ² ) D ₂ ] (ΔT ₁ + ΔT ₂ )
^{= - (1.57 × 10 -5 -} 1.54 × 10 -5) × (ΔT 1 + ΔT 2)
=-0.03 × 10 ^-5 × (ΔT ₁ + ΔT ₂ )… (40)
Therefore, since the equation (31) is expressed by the following equation (41) under the above conditions, the equation (38) can be approximated.

Δφ = (1 / λ ₁ ) α _P1 ⁽¹⁾ ΔP _O1- (1 / λ ₂ ) α _P2 ⁽²⁾ ΔP _O2
+ 1.00 × 10 ^-7 × (ΔT ₁ + ΔT ₂ )
≒ (1 / λ ₁ ) α _P1 ⁽¹⁾ ΔP _O1- (1 / λ ₂ ) α _P2 ⁽²⁾ ΔP _O2 … (41)
The light receiving element 8 shown in FIG. 1 converts the light intensity I into an electric signal and outputs it to the signal processing device 7. The signal processing device 7 observes the fluctuation amount Δφ expressed by the equation (38) of the phase difference φ between the light of the first wavelength λ _{1 and} the light of the second wavelength λ ₂ expressed by the equation (7). Here, since the respective values of the first wavelength λ ₁ , the second wavelength λ ₂ , the first pressure sensitivity α _P1 ⁽¹⁾ , and the second pressure sensitivity α _P2 ⁽²⁾ are known, from the equation (38) The signal processing device 7 can calculate the differential pressure between the first external pressure _PO1 and the second external pressure _PO2 .

As indicated above, the differential pressure measurement system shown in Figure 1, the error in the pressure measurement by each of the first temperature T ₁ and the second temperature T ₂ by the first pressure sensing 3 and the second pressure sensing 13 Even if it can occur, the variation Δφ of the phase difference φ between the light of the first wavelength λ _{1 and} the light of the second wavelength λ ₂ is not affected by the first temperature T ₁ and the second temperature T _2. Yes.

Accordingly, in the differential pressure measurement system shown in FIG. 1, it is not affected by the first temperature T ₁ and the second temperature T _2, the first external pressure P _O1 of the differential pressure between the second external pressure P _O2 When calculating, there is no need to perform complicated calculations for removing errors caused by temperature changes. Therefore, the differential pressure between the first external pressure P _O1 and the second external pressure P _O2 can be calculated instantaneously from the equation (38).

  Next, a method for manufacturing the first measurement unit 5 according to the embodiment shown in FIGS. 2 to 7 will be described with reference to FIGS.

(a) First, as shown in FIG. 16, a first semiconductor layer 141 such as Si, a first pressure sensitive film 50a that is an insulating film such as silicon oxide (SiO ₂ ) disposed on the first semiconductor layer 141, and A silicon-on-insulator (SOI) substrate including a second semiconductor layer 142 such as Si disposed on the first pressure-sensitive film 50a is prepared. The second semiconductor layer 142 has a thickness h _1. Next, after a resist film is applied to the surface of the second semiconductor layer 142, patterning is performed by a lithography method or the like to form resist masks 161a and 161b as shown in FIG.

 (b) A part of the second semiconductor layer 142 exposed from the resist masks 161a and 161b is selectively removed by anisotropic etching or the like until the first pressure-sensitive film 50a is exposed as shown in FIG. Then, the first measurement housing 43a and the recess 121 are formed. After removing the resist masks 161a and 161b with an alkaline solution or the like, a resist film is applied to the surface of the first semiconductor layer 141. The resist film is patterned by a lithography method or the like to form resist masks 162a and 162b as shown in FIG.

(c) A part of the first semiconductor layer 141 exposed from the resist masks 162a and 162b is selectively removed by anisotropic etching or the like until the first pressure sensitive film 50a is exposed as shown in FIG. Then, the first measurement sensor base 40a and the recess 123 are formed. After removing the resist masks 162a and 162b with an alkaline solution or the like, a metal mask 180 is disposed on the second semiconductor layer 142 as shown in FIG. By depositing a multilayer film of Si-based material by a vacuum deposition method or the like, the first feeling that exposed by the first thermal expansion coefficient E ₁ and a first reflection wavelength temperature coefficient D ₁ first pressure sensing 3 a recess 121 having a It is formed on the pressure film 50a.

(d) A holder 60a having a through hole 62 and a vent hole 160a shown in FIG. 22 is newly prepared. Next, as shown in FIG. 23, the optical fiber 32 having the core 130a and the clad 131a is inserted into the through hole 62, and the end face of the optical fiber 32 is polished. Next, a metal mask 181 is disposed below the end face of the optical fiber 32 as shown in FIG. 24, and a second thermal expansion coefficient E ₂ and a second reflection wavelength temperature coefficient are formed of a multilayer film of Si material by vacuum deposition or the like. A first heat sensitive part 6 having D ₂ is formed. Furthermore, the holder 60a and the first measurement housing 43a shown in FIG. 21 are joined to complete the first measurement unit 5 shown in FIGS.

Note the second measurement unit 15 shown in FIG. 11 also, by depositing a second pressure sensing 13 having a second thermal expansion coefficient E ₂ and the second reflection wavelength temperature coefficient D ₂ in FIG. 21, the first heat in 24 If the second heat-sensitive film 16 having the expansion coefficient E ₁ and the first reflection wavelength temperature coefficient D ₁ is deposited, it can be manufactured in the same manner as the first measurement unit 5, and thus detailed description is omitted.

  Next, a differential pressure measuring method using the differential pressure measuring system shown in FIG. 1 will be described with reference to FIG.

(a) In step S101, light is emitted from the light source 4 shown in FIG. In step S102, the first has a thermal expansion coefficient E ₁ and a first reflection wavelength temperature coefficient D _1, emitted from the light source 4 in the first external pressure P _O1 and a first temperature T ₁ is the first pressure sensing 3 applied The reflected light is received and the first reflected light having the first wavelength λ ₁ is reflected. Further in step S103, has a second thermal expansion coefficient E ₂ and the second reflection wavelength temperature coefficient D _2, receives the light emitted from the light source 4 in the first heat-sensitive portion 6 first temperature T ₁ is applied, the Second reflected light having two wavelengths λ ₂ is reflected.

(b) In step S104, a second thermal expansion coefficient E ₂ and the second reflection wavelength temperature coefficient D _2, the light source in the second external pressure P _O2 and the second temperature T ₂ is the second pressure sensing 13 applied The light irradiated from 4 is received, and the third reflected light having the second wavelength λ ₂ is reflected. In step S105, the first has a thermal expansion coefficient E ₁ and a first reflection wavelength temperature coefficient D _1, it receives the light emitted from the light source 4 at a second temperature T ₂ is the second heat-sensitive part 16 to be added, first The fourth reflected light having the wavelength λ ₁ is reflected.

(c) In step S106, a combined interference fringe of the first interference fringe by the first and fourth reflected light and the second interference fringe by the second and third reflected light is formed on the light receiving element 8. In step S107, the signal processing device 7 calculates the light of the first wavelength λ _{1 and} the light of the second wavelength λ ₂ represented by the above equation (7) from the light intensity of the combined interference fringes formed on the light receiving element 8. The fluctuation amount Δφ expressed by the equation (34) of the phase difference φ is observed. In step S108, the signal processing device 7 uses the known values of the first wavelength λ ₁ , the second wavelength λ ₂ , the first pressure sensitivity α _P1 ⁽¹⁾ , and the second pressure sensitivity α _P2 ^(2). , (34) to calculate the differential pressure between the first external pressure _PO1 and the second external pressure _PO2, and the differential pressure measurement method according to the embodiment is completed.

(Modification 1 of the embodiment)
The differential pressure measurement system according to Modification 1 of the embodiment shown in FIG. 26 differs from FIG. 1 in that the first interference fringes by the first and fourth reflected lights and the second interference fringes by the second and third reflected lights The interferometer 28 is further provided to form the combined interference fringes. In FIG. 26, one light split by the splitter 21 is propagated by the optical fiber 31a, and is split by the first interference splitter 22 into the optical fibers 31b and 36, respectively. The optical fiber 31b is connected to the first measurement unit 5. The reflected light from the first measurement unit 5 is split into an optical fiber 34 connected to the first interference splitter 22.

  The other light split by the splitter 21 is propagated by the optical fiber 32a and split by the second interference splitter 23 into the optical fibers 32b and 37, respectively. The optical fiber 32b is connected to the second measurement unit 15. The reflected light from the second measurement unit 15 is split into an optical fiber 35 connected to the second interference splitter 23.

  The optical fibers 34 and 35 and the light receiving element 8 constitute an interferometer 28. The light propagated by each of the optical fibers 34 and 35 is radiated onto the light receiving element 8 from each end of the optical fibers 34 and 35, as shown in FIG. The emitted light is superimposed on the light receiving element 8 to form a combined interference fringe of the first interference fringe by the first and fourth reflected light and the second interference fringe by the second and third reflected light. As the light receiving element 8, a CMOS image sensor, a linear sensor, a CCD, a photodiode array, or the like can be used. The frequency of the interference fringes is determined by the wavelength of the light emitted from each of the optical fibers 34 and 35 and the optical path difference d. The light intensity I of the interference fringes is expressed by the following formula (42).

I = 2 + 2cos {(2π / λ ₁ ) × d} + 2cos {(2π / λ ₂ ) × d}
= 2 + 2cos {2πd {1 / λ 1 + 1 / λ 2}} × cos {2πd {1 / λ 1 - 1 / λ 2}} ... (42)
Therefore, by replacing each of the first optical path difference L ₁₂ and the second optical path difference L _{21 in} the expressions (6) to (41) shown in the embodiment with the optical path difference d, FIG. 26 and FIG. Even in the illustrated differential pressure measurement system, the fluctuation amount Δφ of the phase difference φ varies when a pressure difference occurs between the first measurement unit 5 and the second measurement unit 15, but does not vary even if a temperature difference occurs. Can be considered. Furthermore, compared with the differential pressure measurement system shown in FIG. 1, the arrangement shown in FIGS. 26 and 27 can be used to further increase the measurement range.

In the interferometer 28, the method of forming the synthetic interference fringes on the light receiving element 8 is not limited to the arrangement shown in FIGS. For example, as shown in FIG. 28, the light emitted from the respective ends of the optical fibers 34 and 35 may be converted into parallel light by the lens 90, and a synthetic interference fringe may be formed on the light receiving element 8 via the prism 91. . In this case, the light incident from the X point of the prism 91 follows the optical path U ₁ and reaches the V ₁ point on the light receiving element 8. The light incident from the Z ₂ point of the prism 91 follows the optical path U ₂ and reaches the V ₁ point on the light receiving element 8. By the optical path U ₁ and the optical path difference of the optical path U ₂ d, and the light traversing the optical path U ₁ in V ₁ point on the light receiving element 8, and the light traversing the optical path U ₂ interferes.

Light incident from the Y point of the prism 91 follows the optical path U ₄ and reaches the V ₂ point on the light receiving element 8. The light incident from the Z ₁ point of the prism 91 follows the optical path U ₃ and reaches the V ₂ point on the light receiving element 8. By the optical path U ₃ and the optical path difference of the optical path U ₄ d, the light traversing the optical path U ₃ at V ₂ points on the light receiving element 8, and the light traversing the optical path U ₄ interferes.

  In the example shown in FIG. 29, the light emitted from each of the optical fibers 34 and 35 is converted into parallel light directed in the x direction by the lens 90, and then the parallel light is converted into two directions by the beam splitter 92 in the x direction and the y direction. To divide. The light traveling in the x direction is totally reflected by the first total reflection mirror 93, then enters the beam splitter 92 again, is reflected in the −y direction, and travels toward the light receiving element 8. The light traveling in the y direction by the beam splitter 92 is totally reflected by the second total reflection mirror 94.

  Here, the first total reflection mirror 93 is arranged perpendicular to the x direction. On the other hand, the second total reflection mirror 94 is arranged with a further tilt of θ from the vertical direction with respect to the y direction. Therefore, an optical path difference d is generated between the light reflected by the first total reflection mirror 93 and directed to the light receiving element 8 and the light reflected by the second total reflection mirror 94 and directed to the light receiving element 8, and a synthetic interference fringe is formed on the light receiving element 8. Is formed.

The first wavelength lambda ₁ is 0.675Myuemu, and synthetic interference fringes when the second wavelength lambda ₂ is 0.687Myuemu, the first wavelength lambda ₁ is 0.669Myuemu, examples of synthetic fringe in the case of the second wavelength lambda ₂ is 0.697μm This is shown in FIG. The signal processing device 7 shown in FIG. 26 measures the interval between the intensity peaks of the combined interference fringes and calculates the reciprocal thereof to obtain the phase difference φ. Alternatively, the phase difference φ may be derived by subjecting the synthetic interference fringes to Fourier transform processing. When the Fourier transform process is performed, the interference fringe envelope is approximated by the equation (6) as shown in FIG. 30, and the low frequency component cos {2πφ} is extracted. When the intensity of the light source 4 is modulated, the signal processing device 7 may perform band-pass filtering on the electrical signal of the combined interference fringes.

(Modification 2 of embodiment)
Noise removal means for removing noise due to disturbance factors may be added to the differential pressure measurement system shown in FIG. For example, the differential pressure measurement system shown in FIG. 31 further includes a lock-in amplifier 27. The lock-in amplifier 27 includes an oscillator 74 that generates a reference signal R having a known frequency, a phase modulator 71 that applies phase modulation A to light emitted from the light source 4 based on the reference signal R, and an electric power output from the light receiving element 8. The amplifier 72 amplifies the signal, the integrator 73 that superimposes the reference signal R on the output of the amplifier 72, and the low-pass filter 75 that is connected to the integrator 73 and that allows only an electric signal having the same frequency as the reference signal R to pass therethrough. The reference signal R generated by the oscillator 74 is expressed by the following equation (43).

R = G ・ sin (2πf ・ t) (43)
In the equation (43), G represents an arbitrary constant, f represents a frequency, and t represents time. The phase modulator 71 is connected to an optical fiber 30a that propagates light emitted from the light source 4. The phase modulation A applied to the light by the phase modulator 71 is given by the following equation (44).

A = ΔL ・ sin (2π ・ f ・ t)… (44)
In equation (44), ΔL represents the optical path length change range. The light subjected to the phase modulation A is propagated to the splitter 21 through the optical fiber 30b connected to the phase modulator 71.

  The amplifier 72 is connected to the light receiving element 8. The integrator 73 is connected to the output of the amplifier 72. The integrator 73 superimposes the reference signal R having a known frequency generated by the oscillator 74 on the electric signal amplified by the amplifier 72. A low-pass filter 75 is connected to the output of the integrator 73. In the low-pass filter 75, only an electric signal having the same frequency as that of the reference signal R can pass, so that noise due to a disturbance factor is removed.

Further, the differential pressure measurement system shown in FIG. 32 further includes phase detection means 127 for removing noise due to disturbance factors as compared with FIG. The phase detection means 127 shown in FIG. 32 delays the reference signal R by delaying the reference signal R, the oscillator 74, the phase modulator 71, the first low-pass filter 76 and the second low-pass filter 77 connected in parallel to the output of the light receiving element 8. delay circuit 176 which outputs the R _D, multiplier 173 for superimposing a delayed reference signal R _D to an electrical signal passed through the first low-pass filter 76, an amplifier 172 for amplifying the electric signal passed through the second low-pass filter 77, and amplifier An adder 175 for adding the output of the integrator 173 to the output of 172 is provided. The principle by which the phase detection means 127 removes noise due to disturbance factors will be described below.

  Since the phase modulator 71 is added, the light intensity I of the combined interference fringe on the light receiving element 8 is expressed by the following equation (45).

I = 2 + 2cos {2π (L ₁₂ / λ ₁ + L ₂₁ / λ ₂ ) + 2πΔL (1 / λ ₁ + 1 / λ ₂ ) sin (2π ・ f ・ t)}
_{× cos {2π (L 12 /} λ 1 - L 21 / λ 2) + 2πΔL (1 / λ 1 - 1 / λ 2) sin (2π · f · t)} ... (45)
If attention is paid to the low frequency component V ₀ in the equation (45), the following equation (46) is derived.

_{V 0 = cos {2π (L} 12 / λ 1 - L 21 / λ 2) + 2πΔL (1 / λ 1 - 1 / λ 2) sin (2π · f · t)}
= cosθ × cos (ηsin (2π ・ f ・ t))-sinθ × sin (ηsin (2π ・ f ・ t))… (46)
In the equation (46), θ and η are defined by the following equations (47) and (48).

θ = 2π (L ₁₂ / λ ₁ -L ₂₁ / λ ₂ ) = 2πφ ... (47)
_{η = 2πΔL (1 / λ 1} - 1 / λ 2) ... (48)
When the equation (46) is rewritten, the low frequency component V ₀ is expressed by the equation (49).

The first low-pass filter 76 attenuates the high-frequency component of the low-frequency component V ₀ and transmits the first transmission component V _LPF1 given by the following equation (50).

V _LPF1 = cosθ × J ₀ (η) (50)
On the other hand, the delay circuit 176 delays the reference signal R generated by the oscillator 74 by π / 2, and outputs a delayed reference signal _RD given by the following equation (51).

R _D = G ・ cos (2πf ・ t) (51)
The integrator 173 is connected to the respective outputs of the first low-pass filter 76 and the delay circuit 176. The integrator 173 superimposes the delayed reference signal _RD on the first transmission component V _LPF1 and outputs an integration component V _A given by the following equation (52).

V _A = G × J ₀ (η) cosθ × cos (2πf ・ t) (52)
The amplifier 172 is connected to the output of the second low-pass filter 77. The amplification factor B of the amplifier 172 is expressed by the following equation (53).

B = J ₀ (η) / 2 J ₁ (η)… (53)
The second transmission component V _LPF2 filtered by the second low-pass filter 77 and amplified by the amplifier 172 is given by the following equation (54).

V _LPF2 = -2B J ₁ (η) sinθ × sin (2πf ・ t)… (54)
The output of the integrator 173 is connected to a band pass filter 178. The band pass filter 178 filters the integrated component V _A. The adder 175 is connected to the respective outputs of the band pass filter 178 and the amplifier 172. The adder 175 adds the second transmission component V _LPF2 to the integrated component V _A and outputs the processed component V _F given by the following equation (55) to the signal processing device 7.

V _F = V _LPF1 + V _LPF2 = G × B × J ₀ (η) cos (θ + 2πf ・ t)
= G × B × J ₀ (η) cos (2π (φ + f ・ t))… (55)
Therefore, the signal processing device 7 can observe the fluctuation amount Δφ of the phase difference φ with higher accuracy.

(Modification 3 of the embodiment)
The first measurement unit 105 according to the third modification of the embodiment shown in FIG. 33 uses fiber Bragg gratings for each of the first heat-sensitive part 106 and the first pressure-sensitive part 103 arranged inside the housing 11. . As shown in FIG. 34, in the first heat sensitive part 106, the first refractive index parts 100a, 100b, 100c,... And the second refractive index parts 200a, 200b, 200c,. Has a periodic structure. The light incident on the first heat sensitive part 106 is selectively reflected only at a specific wavelength by the periodic structure of the first refractive index parts 100a, 100b, 100c,... And the second refractive index parts 200a, 200b, 200c,. The Here, the first refractive index portions 100a, 100b, 100c, ... and a second refractive index portions 200a, 200b, 200c, an average refractive index and n _D2 in ... periodic structure, the interval of the periodic structure second grating spacing Λ as _m2, the second wavelength band WB ₂ light peaks of the second wavelength lambda ₂ to the intensity appears first heat-sensitive part 106 represented by represented 8 below (56) below is reflected.

λ ₂ = 2 × n _D2 × Λ _m2 (56)
33 includes a first pressure-sensitive fiber 107 and a first diffraction grating 108. On the upper part of the first pressure-sensitive fiber 107, a pressure-sensitive window 49 is provided in the housing 11, as shown in FIGS. 35 and 36, which are cross-sectional views seen from the AA direction of FIG. A hollow part 59 is provided in the lower part. Therefore, when the first external pressure _PO1 and the first internal pressure _PI1 inside the hollow portion 59 are equal, the first pressure-sensitive fiber 107 does not bend as shown in FIG. In contrast, when the first external pressure P _O1 is above the first internal pressure P _I1, as shown in FIG. 36, the first pressure sensing fiber 107 is bent in the housing 11 inwardly. The first diffraction grating 108 has the same structure as that shown in FIG. 34 except that the periodic structure has a first grating interval Λ _m1 that is different from the second grating interval Λ _m2 . Assuming that the average refractive index of the first diffraction grating 108 is n _D1 , the first diffraction grating 108 is expressed by the following equation (57), and the first wavelength band WB _{1 in} which an intensity peak appears at the first wavelength λ ₁ shown in FIG. Reflects the light.

λ ₁ = 2 × n _D1 × Λ _m1 (57)
In the first pressure sensing 103, the first pressure sensing fiber 107 deflection by the first external pressure P _O1 shown in FIG. 36, the first pressure sensing piezo-distance L _1s described in FIG changes. Here, each of the first heat sensitive unit 106 and the first pressure sensitive unit 103 expands or contracts depending on the fluctuation amount ΔT ₁ of the surrounding first temperature T ₁ . Further, each of the first heat-sensitive part 106 and the first pressure-sensitive part 103 changes the average refractive index n _D2 , n _D1 depending on the fluctuation amount ΔT ₁ of the surrounding first temperature T ₁ , and the reflected light λ ₂ , A wavelength shift can occur in λ ₁ .

However, a material having a first thermal expansion coefficient E ₁ and a first reflection wavelength temperature coefficient D ₁ constitute a first pressure sensing 103 shown in FIG. 33, the second thermal expansion coefficient E ₂ and the second reflection wavelength temperature coefficient by configuring the first heat-sensitive part 106 of a material having a D _2, it is possible even using a fiber Bragg grating obtain the same effect as that of the embodiment.

(Modification 4 of embodiment)
The differential pressure measurement system shown in FIG. 37 is different from FIG. 1 in that two light sources, a first light source 44 and a second light source 45, are arranged. The first light source 44 emits light corresponding to the first wavelength λ ₁ shown in FIGS. 8A and 8B of the first pressure sensing unit 3 and the second heat sensing unit 16, respectively. The second light source 45 emits light corresponding to the second wavelength λ ₂ of each of the second pressure sensing unit 13 and the first heat sensing unit 6. The second light source 45 shown in FIG. 37 has the light intensity at the second wavelength λ ₂ shown in FIGS. 8 (a) and 8 (b), which is the light intensity at the first wavelength λ ₁ of the first light source 44. A light source having a spectrum similar to that of the first light source 44 is preferable.

  An optical fiber 300a is connected to the first light source 44 shown in FIG. 37, and an optical fiber 300b is connected to the second light source 45. The optical fibers 300a and 300b are connected to the light source splitter 221. When the light source splitter 221 has two-direction output terminals, the optical fibers 30 and 300c are connected to each other. By arranging the first light source 44 and the second light source 45, it is possible to align the intensities of the light propagating through the first combination shown in FIG. 12 and the second combination shown in FIG. 13 with higher accuracy. As a result, differential pressure measurement with higher accuracy is possible.

(Other embodiments)
As described above, the present invention has been described according to the embodiment. However, it should not be understood that the description and drawings constituting a part of this disclosure limit the present invention. From this disclosure, various alternative embodiments, examples, and operational techniques should be apparent to those skilled in the art. For example, in the first measurement unit 5 shown in FIG. 1, the first heat sensitive part 6 and the first pressure sensitive part 3 are arranged in series with respect to the optical fiber 31, but the embodiment is not limited to this. As in the first measurement unit 105 shown in FIG. 38, each of the first pressure-sensitive part 103 and the first heat-sensitive part 106 may be arranged in parallel to the optical fiber 31. Similarly, in the second measurement unit 115, each of the second pressure sensing unit 113 and the second heat sensing unit 116 may be arranged in parallel with the optical fiber 32.

Further, in the embodiment, each of the first heat-sensitive part 6, the first pressure-sensitive part 3, the second heat-sensitive part 16, and the second pressure-sensitive part 13 shown in FIG. 1 is a multilayer thin film made of a Si-based material. I explained that there was. However, the embodiment is not limited to this. For example, the first heat-sensitive portion 6, the first pressure-sensitive portion 3, and the second pressure-sensitive multilayer film made of alternating silicon oxide (SiO ₂ ) and titanium oxide (TiO ₂ ) are used. Each of the heat sensitive unit 16 and the second pressure sensitive unit 13 may be configured. Moreover, you may comprise with an organic type material. As long as the equation (41) can be approximated, various materials can be used for each of the first heat sensitive part 6, the first pressure sensitive part 3, the second heat sensitive part 16, and the second pressure sensitive part 13. Needless to say. Further, each of the first measurement unit 5 and the second measurement unit 15 may be filled with a substance that changes the optical path difference.

  Thus, it should be understood that the present invention includes various embodiments and the like not described herein. Therefore, the present invention is limited only by the invention specifying matters in the scope of claims reasonable from this disclosure.

It is a mimetic diagram of a differential pressure measuring system concerning an embodiment of the invention. It is a top view of the 1st measurement unit concerning an embodiment of the invention. It is sectional drawing (the 1) seen from the AA direction of the 1st measurement unit which concerns on embodiment of this invention. It is a graph (the 1) which shows the reflective characteristic of the 1st heat sensitive part which concerns on embodiment of this invention. It is a graph (the 2) which shows the reflective characteristic of the 1st heat sensitive part which concerns on embodiment of this invention. It is sectional drawing (the 2) seen from the AA direction of the 1st measurement unit which concerns on embodiment of this invention. It is sectional drawing (the 3) seen from the AA direction of the 1st measurement unit which concerns on embodiment of this invention. It is a graph which shows the reflection spectrum which concerns on embodiment of this invention. It is a graph (the 1) regarding the pressure-sensitive film which concerns on embodiment of this invention. It is a graph (the 2) regarding the pressure-sensitive film which concerns on embodiment of this invention. It is sectional drawing of the 2nd measurement unit which concerns on embodiment of this invention. It is a schematic diagram which shows the 1st combination of the propagation path of the light which forms the interference fringe which concerns on embodiment of this invention. It is a schematic diagram which shows the 2nd combination of the propagation path of the light which forms the interference fringe which concerns on embodiment of this invention. It is a schematic diagram which shows the 3rd combination of the propagation path of the light which forms the interference fringe which concerns on embodiment of this invention. It is a schematic diagram which shows the 4th combination of the propagation path of the light which forms the interference fringe which concerns on embodiment of this invention. It is process sectional drawing (the 1) of the 1st measurement unit which concerns on embodiment of this invention. It is process sectional drawing (the 2) of the 1st measurement unit which concerns on embodiment of this invention. It is process sectional drawing (the 3) of the 1st measurement unit which concerns on embodiment of this invention. It is process sectional drawing (the 4) of the 1st measurement unit which concerns on embodiment of this invention. It is process sectional drawing (the 5) of the 1st measurement unit which concerns on embodiment of this invention. It is process sectional drawing (the 6) of the 1st measurement unit which concerns on embodiment of this invention. It is process sectional drawing (the 7) of the 1st measurement unit which concerns on embodiment of this invention. It is process sectional drawing (the 8) of the 1st measurement unit which concerns on embodiment of this invention. It is process sectional drawing (the 9) of the 1st measurement unit which concerns on embodiment of this invention. It is a flowchart which shows the differential pressure measuring method which concerns on embodiment of this invention. It is a schematic diagram of the differential pressure measurement system which concerns on the modification 1 of embodiment of this invention. It is a schematic diagram (the 1) of the interferometer which concerns on the modification 1 of embodiment of this invention. It is a schematic diagram (the 2) of the interferometer which concerns on the modification 1 of embodiment of this invention. It is a schematic diagram (the 3) of the interferometer which concerns on the modification 1 of embodiment of this invention. It is a graph which shows the synthetic | combination interference fringe which concerns on the modification 1 of embodiment of this invention. It is a schematic diagram of the differential pressure measurement system (the 1) which concerns on the modification 2 of embodiment of this invention. It is a schematic diagram of the differential pressure measurement system (the 2) which concerns on the modification 2 of embodiment of this invention. It is a schematic diagram of the 1st measurement unit which concerns on the modification 3 of embodiment of this invention. It is a schematic diagram of the 1st heat sensitive part which concerns on the modification 3 of embodiment of this invention. It is sectional drawing (the 1) of the 1st measurement sensor which concerns on the modification 3 of embodiment of this invention. It is sectional drawing (the 2) of the 1st measurement sensor which concerns on the modification 3 of embodiment of this invention. It is a schematic diagram of the differential pressure measurement system which concerns on the modification 4 of embodiment of this invention. It is a schematic diagram of the differential pressure measurement system which concerns on other embodiment of this invention.

Explanation of symbols

3… First pressure sensing part
4 ... Light source
5… First measurement unit
6 ... 1st heat sensitive part
7 ... Signal processing device
8 ... Light receiving element
11 ... Case
13… Second pressure sensing part
15 ... Second measurement unit
16… The second heat sensitive part
21 ... Splitter
22 ... 1st interference splitter
23… 2nd interference splitter
27 ... Lock-in amplifier
28 ... Interferometer
30, 30a, 30b, 31, 31a, 31b, 32, 32a, 32b, 33, 34, 35, 300a, 300b ... Optical fiber
40a ... First measurement sensor base
40b ... Second measurement sensor base
43a ... First measurement housing
43b… Second measurement housing
44 ... 1st light source
45 ... Second light source
49… Pressure sensitive window
50a ... 1st pressure sensitive membrane
50b… Second pressure sensitive membrane
59… hollow part
60a, 60b ... holder
62 ... Through hole
70a, 70b ... Release valve
71 ... Phase modulator
72, 172 ... amplifier
73, 173 ... Integrator
74 ... Oscillator
75 ... Low-pass filter
76 ... 1st low-pass filter
77… Second low-pass filter
90 ... Lens
91 ... Prism
92 ... Beam splitter
93 ... 1st total reflection mirror
94… Second total reflection mirror
100a, 100b, 100c, ... 1st refractive index part
103 ... 1st pressure sensing part
105 ... 1st measurement unit
106 ... 1st heat sensitive part
107 ... 1st pressure sensitive fiber
108 ... 1st diffraction grating
113… Second pressure sensing part
115… Second measurement unit
116… The second heat sensitive part
121, 123 ... recess
127 ... Phase detection means
130a, 130b ... core
131a, 131b ... clad
141… First semiconductor layer
142… Second semiconductor layer
160a, 160b ... vent
161a, 161b, 162a, 162b ... resist mask
175 ... Adder
176 ... Delay circuit
180, 181 ... metal mask
200a, 200b, 200c …… Second refractive index part
221 ... Splitter for light source

Claims (9)

A light source that emits light of the first and second wavelengths;
Reflecting the first reflected light of the first wavelength, a first external pressure and a first temperature are applied, a first reflected wavelength temperature obtained by multiplying the first thermal expansion coefficient and the first thermal expansion coefficient by the first wavelength A first pressure sensitive part having a coefficient;
The second reflected light of the second wavelength is reflected, the first temperature is added, and a second thermal expansion coefficient and a second reflected wavelength temperature coefficient obtained by multiplying the second thermal expansion coefficient by the second wavelength. 1 heat sensitive part,
A second pressure-sensitive part that reflects the third reflected light of the second wavelength, is applied with a second external pressure and a second temperature, and has the second thermal expansion coefficient and the second reflected wavelength temperature coefficient;
Reflecting the fourth reflected light of the first wavelength, the second temperature is applied, the second thermal part having the first thermal expansion coefficient and the first reflection wavelength temperature coefficient,
A signal processing device that calculates a differential pressure between the first and second external pressures from a variation in the phase difference between the first interference fringes by the first and fourth reflected lights and the second interference fringes by the second and third reflected lights. And a differential pressure measuring system.   2. The differential pressure measurement system according to claim 1, wherein materials of the first and second pressure-sensitive parts and the first and second heat-sensitive parts include silicon.   2. The differential pressure measurement system according to claim 1, wherein the first and second pressure-sensitive parts and the first and second heat-sensitive parts each include silicon oxide and titanium oxide.   4. The differential pressure measurement system according to claim 1, wherein each of the first and second pressure-sensitive parts and the first and second heat-sensitive parts has a multilayer film. 5.   3. The differential pressure measurement system according to claim 1, wherein each of the first and second pressure sensitive units and the first and second thermal sensitive units includes a fiber Bragg grating. 4.   6. The apparatus according to claim 1, further comprising an interferometer that forms a combined interference fringe of the first interference fringe by the first and fourth reflected light and the second interference fringe by the second and third reflected light. The differential pressure measurement system according to any one of the above.   The differential pressure measurement system according to claim 1, further comprising a lock-in amplifier that removes noise added to the first to fourth reflected lights.   The differential pressure measurement system according to claim 1, further comprising phase detection means for removing noise added to the first to fourth reflected lights. Irradiating light of first and second wavelengths;
A first external pressure and a first temperature are applied, and the light is received by a first pressure sensing unit having a first thermal expansion coefficient and a first reflection wavelength temperature coefficient obtained by multiplying the first thermal expansion coefficient by the first wavelength. Reflecting the first reflected light of the first wavelength;
The first temperature is applied, the second thermal expansion coefficient and the second thermal expansion coefficient multiplied by the second wavelength are received by the first heat sensitive part having a second reflection wavelength temperature coefficient, and the second wavelength. Reflecting the second reflected light of
A second external pressure and a second temperature are applied, the light is received by the second pressure sensing unit having the second thermal expansion coefficient and the second reflection wavelength temperature coefficient, and the third reflected light of the second wavelength is reflected. Steps,
Receiving the light at a second thermal part having the second temperature applied, the first thermal expansion coefficient and the first reflection wavelength temperature coefficient, and reflecting the fourth reflected light of the first wavelength;
Calculating a differential pressure between the first and second external pressures from a variation in the phase difference between the first interference fringes of the first and fourth reflected lights and the second interference fringes of the second and third reflected lights. A differential pressure measuring method characterized by comprising.

Images