Sensor for identifying position of interface, and liquid level gauge

Abstract

An interface sensor 1 is an interface sensor having a configuration determined by a code system and its specific codeword, and at least one of the following conditions is satisfied: (a) regarding the number e(k) of electrode pairs included in the k-th (k∈[K]) sensor block included in the interface sensor 1, the difference between the maximum value maxk∈[K]e(k) and the minimum value mink∈[K]e(k) of the number e(k) over the set [K] is smaller than that in the prior art; and (b) regarding the number t(j) of electrode pairs connected to the j-th lead (j∈[J]=[Σk∈[K]c(k)], c(k) is the number of leads included in the k-th (k∈[K]) sensor block) included in the interface sensor 1, the difference between the maximum value maxj∈[J]t(j) and the minimum value minj∈[J]t(j) of the number t(j) over the set [J] is smaller than that in the prior art.

Description

Sensors and level gauges for identifying the position of the interface

[0001] The present disclosure relates to a sensor for identifying the position of an interface between two types of substances (hereinafter referred to as an interface sensor), and a liquid level meter including the interface sensor.

[0002] The applicant of the present application is the applicant of Patent Document 1 (International Publication No. WO2023 / 203912A1), Patent Document 2 (International Publication No. WO2023 / 218744A1), Patent Document 3 (International Publication No. WO2023 / 248947A1), and Patent Document 4 (International Publication No. WO2024 / 024325A1).

[0003] Figure 1 is a copy of Figure 9 of Patent Document 1. Figure 2 is a copy of Figure 13 of Patent Document 2. Figure 3 is a copy of Figure 10 of Patent Document 3. Figure 4 is a copy of Figure 16 of Patent Document 4.

[0004] The interface sensor having the configuration shown in FIG. 1 is an interface sensor 2 for identifying the position of an interface between a first material and a second material, comprising K sensor blocks 3, where K is a predetermined integer satisfying 2≦K, and the k-th sensor block 3 of the K sensor blocks 3 comprises M(k) electrode pairs 5 and n(k)+1 conducting wires 7, where k∈{x∈N: 1≦x≦K}, N is the set of all positive integers, n(k) is a predetermined integer satisfying 2≦n(k), M(1)≧8, and for each k∈{x∈N: 1≦x≦K}, m of the M(k) electrode pairs 5 included in the k-th sensor block 3 k The th electrode pair 5 is located in r(k,m) of M(1) planes that are not coincident with each other and are parallel to each other. k ) plane, where m k ∈{x∈N:1≦x≦M(k)}, the M(1) planes are arranged in order according to the magnitude relationship of the elements of the set {x∈N:1≦x≦M(1)}, n(0)=1, and each k∈{x∈N:1≦x≦K} and each m k For ∈{x∈N: 1≦x≦M(k)}, m of the M(k) electrode pairs 5 included in the k-th sensor block 3 kThe th electrode pair 5 is s(m k ) conductor 7, and the other electrode 5b is connected to the n(k)+1 conductor 7, where each k∈{x∈N: 1≦x≦K} and each m k For ∈{x∈N: 1≦x≦M(k)}, That is, the sensor.

[0005] The interface sensor having the configuration shown in FIG. 2 is an interface sensor 2 for identifying the position of an interface between a first material and a second material, comprising a first electrical conductor 5a and K sensor blocks 3, where K is a predetermined integer satisfying 2≦K, and the k-th sensor block 3 of the K sensor blocks 3 comprises M(k) second electrical conductors 5b and n(k) conducting wires 7, where k∈{x∈N: 1≦x≦K}, N is the set of all positive integers, n(k) is a predetermined integer satisfying 2≦n(k), M(1)=4 or M(1)=6 or M(1)≧8, and for each k∈{x∈N: 1≦x≦K}, and m of the M(k) second electrical conductors 5b included in the k-th sensor block 3 k The second electrical conductor 5b is located in the r(k, m) plane among the M(1) planes that are not coincident with each other and are parallel to each other. k ) plane, where m k ∈{x∈N:1≦x≦M(k)}, the M(1) planes are arranged in order according to the magnitude relationship of the elements of the set {x∈N:1≦x≦M(1)}, n(0)=1, and each k∈{x∈N:1≦x≦K} and each m k For ∈{x∈N: 1≦x≦M(k)}, and m of the M(k) second electrical conductors 5b included in the k-th sensor block 3 k The second electrical conductor 5b is s(m) of the n(k) conducting wires 7. k )-th conductor 7, where each k∈{x∈N: 1≦x≦K} and each m k For ∈{x∈N: 1≦x≦M(k)}, That is, the sensor.

[0006] The interface sensor having the configuration shown in FIG. 3 is a sensor 200 for identifying the position of an interface between a first material and a second material, comprising E electrode pairs 500, L conductors 700, and a conductor selector 800, wherein K is a predetermined integer satisfying 2≦K, and for each j∈{x∈N:1≦x≦K}, n(j) is a predetermined integer satisfying 2≦n(j), and N is a set of all positive integers; the E electrode pairs 500 are located on E planes that are mutually disjoint and parallel, in an order according to the magnitude relationship of the elements in the set {x∈N:1≦x≦E}; and for each p∈{x∈N:1≦x≦E-1}, the p-th electrode pair 500 of the E electrode pairs 500 has one electrode 500a connected to the s(p)-th conductor 700 of the L conductors 700, and the other electrode 500b connected to the L-th conductor 700 of the L conductors 700, with the proviso that where n(0)=1, and for each k∈{x∈N: 1≦x≦K}, the k-th set W(k) is the K+1-th set W(K+1) is an empty set and p∈W(r), the E-th electrode pair 500 of the E electrode pairs 500 has one electrode 500a connected to the L-1-th conductor 700 of the L conductors 700 and the other electrode 500b connected to the L-th conductor 700 of the L conductors 700, and the conductor selector 800 can select any one conductor 700 of the L conductors 700, excluding the L-th conductor 700.

[0007] The interface sensor having the configuration shown in FIG. 4 is a sensor 200 for identifying the position of an interface between a first material and a second material, comprising a first electrical conductor 500a, E second electrical conductors 500b, L conductors 700, and a conductor selector 800, wherein: wherein K is a predetermined integer satisfying 2≦K, and for each j∈{x∈N:1≦x≦K}, n(j) is a predetermined integer satisfying 2≦n(j), and N is a set of all positive integers; the E second electrical conductors 500b are located on E planes that are mutually disjoint and parallel to each other, in an order according to the magnitude relationship of the elements in the set {x∈N:1≦x≦E}; and for each p∈{x∈N:1≦x≦E-1}, the p-th second electrical conductor 500b among the E second electrical conductors 500b is connected to the s(p)-th conductive wire 700 among the L conductive wires 700, with the proviso that where n(0)=1, and for each k∈{x∈N: 1≦x≦K}, the k-th set W(k) is the K+1-th set W(K+1) is an empty set, and p∈W(r), the E-th second electrical conductor 500b among the E second electrical conductors 500b is connected to the L-th electrical conductor 700 among the L electrical conductors 700, and the electrical conductor selector 800 can select any one electrical conductor 700 among the L electrical conductors 700.

[0008] WO2023 / 203912A1WO2023 / 218744A1WO2023 / 248947A1WO2024 / 024325A1

[0009] The interface sensors disclosed in Patent Documents 1 to 4 all have an unbalanced configuration. The meaning of "unbalanced" will be mentioned in the "Analysis of Prior Art" section below.

[0010] We disclose an interface sensor having a well-balanced configuration in which the total number of wires drawn from the interface sensor is less than the total number of observation points, and a liquid level meter including the interface sensor.

[0011] The technical matters described herein are not intended to explicitly or implicitly limit the invention described in the claims, nor to enable anyone other than those who benefit from the invention (e.g., the applicant and the right holder) to limit the invention described in the claims, but are provided simply to facilitate understanding of the gist of the invention. The outline of the invention from other perspectives can be understood, for example, from the claims at the time of filing of this patent application.

[0012] The disclosed interface sensor has a configuration determined by the adopted coding system and its specific code words, and a) for the number e(k) of electrode pairs or electrical conductors included in the k-th (k∈[K]) sensor block included in the interface sensor, the maximum value max of the number e(k) in the set [K] k∈[K] The difference between e(k) and the minimum value is min k∈[K] e(k) is smaller than that of the prior art, or b) the jth (j∈[J]=[Σ k∈[K] c(k)], c(k) is the maximum value max on the set [J] of the number t(j) of electrode pairs or electrical conductors connected to the conductors (excluding the number of conductors connected to the e(k) electrode pairs or electrical conductors included in the kth (k∈[K]) sensor block) included in the kth (k∈[K]) sensor block. j∈[J] t(j) and minimum value min j∈[J] The difference in t(j) is smaller than that of the prior art.

[0013] The interface sensor of the present disclosure has a well-balanced configuration in which the total number of conductors drawn out from the interface sensor is smaller than the total number of observation points.

[0014] Copy of Figure 9 of Patent Document 1. Copy of Figure 13 of Patent Document 2. Copy of Figure 10 of Patent Document 3. Copy of Figure 16 of Patent Document 4. A diagram explaining code words in the configuration disclosed in Patent Document 1. A diagram explaining code words in the configuration disclosed in Patent Document 3. First example of the first embodiment. Second example of the first embodiment. Third example of the first embodiment. Another example of the first embodiment. An example of a variation of the first embodiment. Equivalent configuration example 1 of the first embodiment. Equivalent configuration example 2 of the first embodiment. An example of the second embodiment. An equivalent configuration example of the second embodiment. An example of the third embodiment. An equivalent configuration example of the third embodiment. An example of the fourth embodiment. An equivalent configuration example of the fourth embodiment.

[0015] Hereinafter, unless otherwise specified, N is the set of all positive integers. The symbol N is written in bold in mathematical formulas.

[0016] [Analysis of the Prior Art] According to a prior art interface sensor, M planes P(1), ..., P(M) that are not coincident with each other but are parallel to each other are predetermined, and the position of the interface is identified as one of M+1 intervals I(1), ..., I(M+1) defined by the M planes P(1), ..., P(M). Interval I(1) is one of two half-spaces obtained by dividing space by plane P(1) that does not include planes P(2), ..., P(M). Interval I(m) (m∈{x∈N:2≦x≦M}) is the spatial region between adjacent planes P(m−1) and P(m). Interval I(M+1) is one of two half-spaces obtained by dividing space by plane P(M) that does not include planes P(2), ..., P(M). Being able to identify the position of the interface using the interface sensor means that it is possible to assign mutually distinguishable codewords to each of the M+1 intervals I(1), ..., I(M+1). Although there are no restrictions on the codewords, for ease of discussion, hereinafter, a codeword will be represented as a concatenation of K non-negative integers. K is the total number of sensor blocks included in the interface sensor, and satisfies 2≦K.

[0017] In the interface sensor configuration disclosed in Patent Document 1 or Patent Document 2, M+1 code words are systematically assigned to M+1 sections I(1), ..., I(M+1) as follows: When M is expressed as the product of K factors n(k) (see Equation (1)), the k-th sensor block is assigned to one of M planes P(1), ..., P(M) that are different from each other. i=k K Π located on n(i) planes i=k K Since the sensor block contains n(i) electrode pairs (or electrical conductors), the planes on which the electrode pairs (or electrical conductors) are located are used as boundaries, and one of n(k) non-negative integers determined by the number n(k) of conductors is systematically assigned to each of the spatial regions separated by these boundaries. Specifically, M+1 non-negative integers are assigned to M+1 sections I(1), ..., I(M+1) in the k-th (k∈{x∈N:2≦x≦K-1}) sensor block according to formula (2). Formula (2) represents a sequence of non-negative integers, not a matrix. In formula (2), the index Π at the bottom right i=1 k-1 n(i) represents the number of repetitions of each non-negative integer, and the upper right index Π i=k+1 K n(i) represents the number of repetitions of a sequence of non-negative integers. The lower right index for the first sensor block is set to 1, and the upper right index for the Kth sensor block is set to 1. Therefore, the set of M+1 code words assigned to M+1 intervals I(1), ..., I(M+1) is expressed by equation (3). As is clear from equation (3), the code words for interval I(1) and interval I(M+1) are the same. However, the code words for interval I(1) and interval I(M+1) can be distinguished by measuring the capacitance of any one electrode pair (or electrical conductor) included in the Kth sensor block.

[0018] 5 shows a specific example of the allocation of M+1 code words to M+1 intervals I(1), ..., I(M+1) in the interface sensor configuration disclosed in Patent Document 1. In this example, M = 30, K = 3, n(1) = 3, n(2) = 5, and n(3) = 2. For example, when k = 2, the value of the exponent in the upper right corner of equation (2) is 2 and the value of the exponent in the lower right corner is 3, so the sequence of non-negative integers according to equation (2) is as follows: 0 4 4 4 3 3 3 2 2 2 1 1 1 0 0 0 4 4 4 3 3 3 2 2 2 1 1 1 0 0 0 Therefore, the code words for each interval according to equation (3) are as follows: I(31):000 I(30):142 I(29):141 I(28):140 I(27):132 I(26):131 I(25):130 I(24):122 I(23):121 I(22):120 I(21):112 I(20):111 I(19):110 I(18):102 I(17):101 I(16):100 I(15):042 I(14):041 I(13):040 I(12):032 I(11):031 I(10):030 I(9):022 I(8):021 I(7):020 I(6):012 I(5):011 I(4):010 I(3):002 I(2):001 I(1):000

[0019] The configuration of the interface sensor disclosed in Patent Document 3 or Patent Document 4 is based on the configuration of the interface sensor disclosed in Patent Document 1 or Patent Document 2. Therefore, in the configuration of the interface sensor disclosed in Patent Document 3 or Patent Document 4, the set of M+1 code words assigned to the M+1 sections I(1), ..., I(M+1) is obtained by modifying the set of code words expressed in equation (3). Specifically, in the configuration of the interface sensor disclosed in Patent Document 3 or Patent Document 4, when M is expressed as the product of K factors n(k) (see equation (1)), the set of code words assigned to each of the M+1 sections I(1), ..., I(M+1) is expressed by equation (4). G k R is a sequence of non-negative integers G kThe k-th (k∈{x∈N:1≦x≦K−1}) sensor block alternately shows the upside-down k and G k R The total number of i=k+1 K n(i).

[0020] FIG. 6 shows a specific example of the allocation of M+1 code words to M+1 sections I(1), ..., I(M+1) in the interface sensor configuration disclosed in Patent Document 3. In this example, M=24, K=3, n(1)=3, n(2)=4, and n(3)=2. The interface sensor configuration conceivable from the disclosure of Patent Document 3 is shown on the left side of FIG. 6, and this configuration is equivalent to the circuit configuration shown on the right side of FIG. 6. For example, when k=2, the sequence of non-negative integers in the second sensor block is as follows: 0 0 0 0 1 1 1 2 2 2 3 3 3 3 3 3 2 2 2 1 1 1 0 0 0 Therefore, the code words for each section according to equation (4) are as follows: I(25):000 I(24):100 I(23):101 I(22):102 I(21):112 I(20):111 I(19):110 I(18):120 I(17):121 I(16):122 I(15):132 I(14):131 I(13):130 I(12):030 I(11):031 I(10):032 I(9):022 I(8):021 I(7):020 I(6):010 I(5):011 I(4):012 I(3):002 I(2):001 I(1):000

[0021] From the above explanation, it can be seen that the set of M+1 code words assigned to the M+1 intervals I(1), ..., I(M+1) in the interface sensor configuration disclosed in Patent Document 1 or Patent Document 2 are codes based on the positional notation system.

[0022] From the above explanation, it can be seen that the set of M+1 code words assigned to the M+1 sections I(1), ..., I(M+1) in the configuration of the interface sensor disclosed in Patent Document 3 or Patent Document 4 is a reflected Gray code when n(K) is an even number, and is a reflected Gray code except for the section I(M+1) when n(K) is an odd number.

[0023] This suggests that the configuration of the interface sensor is determined by the coding scheme and its specific code words.

[0024] In any of the interface sensors disclosed in Patent Documents 1 to 4, the number of electrode pairs (or electrical conductors) is greatest in the first sensor block and least in the Kth sensor block, and the difference between the number of electrode pairs (or electrical conductors) in the Kth sensor block and the number of electrode pairs (or electrical conductors) in the kth sensor block (k∈{x∈N:1≦x≦K−1}) increases multiplicatively as k decreases. In other words, any of the interface sensors disclosed in Patent Documents 1 to 4 have an unbalanced configuration in this respect. Considering that the factorization of M using Equation (1) is not necessarily uniquely determined, in the interface sensors disclosed in Patent Documents 1 and 2, the minimum difference between the number of electrode pairs (or electrical conductors) included in the first sensor block and the number of electrode pairs (or electrical conductors) included in the Kth sensor block is given by Equation (5). In the interface sensors disclosed in Patent Documents 3 and 4, the minimum difference between the number of electrode pairs (or electrical conductors) included in the first sensor block and the number of electrode pairs (or electrical conductors) included in the Kth sensor block is given by Equation (6). Hereinafter, unless otherwise noted, max represents the maximum element of a set, and min represents the minimum element of a set. Hereinafter, unless otherwise noted, the symbol [X] represents the set {x∈N:1≦x≦X} determined by positive integers X. Therefore, [K] is the set {x∈N:1≦x≦K}. Hereinafter, unless otherwise noted, symbols on either side of M / 2 represent floor functions. Hereinafter, unless otherwise noted, symbols resembling a backslash represent the difference set. For example, if M=24 and K=3, the factorization of M is M=2×2×6 or M=2×4×3 (note that the order of the factors is not taken into account). Therefore, F(M, K)={{2, 6}, {2, 3, 4}}. Therefore, the value of equation (5) is 18, and the value of equation (6) is 6.

[0025] As is clear from equations (5) and (6), the value of equation (6) is always smaller than the value of equation (5). Therefore, for the number e(k) of electrode pairs (or electrical conductors) included in the k-th (k∈[K]) sensor block included in the interface sensor, the maximum value max k∈[K]e(k) = max{e(1), ..., e(K)} and the minimum value min k∈[K] If the difference between e(k) = min{e(1), ..., e(K)} is smaller than the value of equation (6), the interface sensor can be said to have a well-balanced configuration compared to prior art interface sensors.

[0026] From another perspective, in any of the interface sensors disclosed in Patent Documents 1 to 4, the number of electrode pairs (or electrical conductors) connected to one conductor (excluding conductors connected to all electrode pairs or electrical conductors included in the sensor block to which this conductor belongs) is greatest in the first sensor block and least in the Kth sensor block, and the difference between the number of electrode pairs (or electrical conductors) connected to one conductor (excluding conductors connected to all electrode pairs or electrical conductors included in the first sensor block) in the first sensor block and the number of electrode pairs (or electrical conductors) connected to one conductor (excluding conductors connected to all electrode pairs or electrical conductors included in the kth sensor block) (k∈{x∈N:1≦x≦K−1}) increases multiplicatively as k decreases. In other words, any of the interface sensors disclosed in Patent Documents 1 to 4 have an unbalanced configuration in this respect. Considering that the factorization of M according to Equation (1) is not necessarily unique, in the interface sensors disclosed in any of Patent Documents 1 to 4, the minimum difference between the number of electrode pairs (or electrical conductors) connected to one conductor in the first sensor block (excluding conductors connecting to all electrode pairs or electrical conductors included in the first sensor block) and the number of electrode pairs (or electrical conductors) connected to one conductor in the Kth sensor block (excluding conductors connecting to all electrode pairs or electrical conductors included in the Kth sensor block) is given by Equation (7). For example, when M = 24 and K = 3, the factorization of M is M = 2 × 2 × 6 or M = 2 × 4 × 3 (note that the order of the factors is not taken into account). Therefore, F(M, K) = {{2, 6}, {2, 3, 4}}. Therefore, the value of Equation (7) is 3.

[0027] Therefore, the jth sensor included in the interface sensor (j∈[J]=[Σk∈[K] c(k)], c(k) is the maximum value max on the set [J] of the number t(j) of electrode pairs (or electrical conductors) connected to the conductors (excluding the number of e(k) electrode pairs or electrical conductors connected to the k-th (k∈[K]) sensor block) included in the k-th (k∈[K]) sensor block. j∈[J] t(j) = max{e(1), ..., e(J)} and the minimum value min j∈[J] If the difference between t(j) = min{e(1), ..., e(J)} is smaller than the value of equation (7), the interface sensor can be said to have a well-balanced configuration compared to prior art interface sensors.

[0028] In short, a sufficient condition for the interface sensor disclosed herein to have a well-balanced configuration compared to prior art interface sensors is that, in an interface sensor having a configuration determined by the adopted coding system and its specific code words, a) with respect to the number e(k) of electrode pairs (or electrical conductors) included in the k-th (k∈[K]) sensor block included in the interface sensor, the maximum value max of the number e(k) in the set [K] is k∈[K] e(k) and minimum value min k∈[K] The difference between e(k) is smaller than the value of equation (6), or b) the jth sensor (j∈[J]=[Σ k∈[K] c(k)], c(k) is the maximum value max on the set [J] of the number t(j) of electrode pairs (or electrical conductors) connected to the conductors (excluding the number of e(k) electrode pairs or electrical conductors connected to the k-th (k∈[K]) sensor block) included in the k-th (k∈[K]) sensor block. j∈[J] t(j) and minimum value min j∈[J] The difference between t(j) is smaller than the value of equation (7), and the following holds true: Based on the results of such analysis of the prior art, the embodiments of the interface sensor disclosed herein will be explained.

[0029] [First embodiment] The interface sensor 1 of the first embodiment is an interface sensor having a configuration determined by the adopted coding system and its specific code words, and satisfies the above-mentioned condition a) for the number e(k) of electrode pairs included in the k-th (k∈[K]) sensor block included in the interface sensor, the maximum value max k∈[K] e(k) and minimum value min k∈[K] The difference between e(k) is smaller than the value of equation (6).

[0030] The interface sensor 1 of the first embodiment is a sensor for identifying the position of the interface between two types of substances (i.e., a first substance and a second substance that are different from each other). An "interface" is a contact boundary between a first substance as a homogeneous phase and a second substance as a homogeneous phase. A "homogeneous phase" is an entity of a material system that is uniform in chemical composition and physical state. In other words, any part V of a substance system entity s The physical and chemical properties of the part V of the substance system s Any part W different from s If the physical and chemical properties of the two planes are the same, the substance system is a "homogeneous phase." In order to accurately identify the position of the interface, the number of interfaces must be 1 or 0 in the range from plane P(1) to plane P(M), which will be described later. The interface sensor 1 detects the Σ k∈[K] e(k) electrode pairs 5 and K+Σ k∈[K] It contains c(k) conductors 7. Σ k∈[K]Each of the e(k) electrode pairs 5 is composed of two electrodes 5a and 5b. The position of the interface between the first and second substances is determined by utilizing a physical quantity generated in the electrode pair 5 according to the properties of the first or second substance present between the two electrodes 5a and 5b constituting the electrode pair 5. If the capacitance between two conductors having equal positive and negative charges is C, the electrical resistance between the two conductors is R, the dielectric constant of the medium between the two conductors is ε, and the electrical resistivity of the medium between the two conductors is ρ, then the relationship RC = ερ holds. Therefore, in the first embodiment, capacitance is used as the physical quantity generated in the electrode pair 5, and an example in which electrical resistance is used as the physical quantity will not be described. A typical example of the interface sensor 1 is a sensor for determining the position of the interface between a liquid (e.g., water) as the first substance and a gas (e.g., air) as the second substance.

[0031] The interface sensor 1 is a sensor having a configuration that satisfies all of the following conditions 1, 2, 3, 4, 5, 6, 7, 8, and 9, or a configuration equivalent to said configuration. First, we will explain the "configuration that satisfies all of conditions 1, 2, 3, 4, 5, 6, 7, 8, and 9" and specific examples thereof, and then we will explain the "equivalent configuration" and specific examples thereof.

[0032] <Condition 1> The interface sensor 1 is composed of K sensor blocks {B k : k∈[K]}. K is a predetermined integer that satisfies 2≦K<M. K preferably satisfies equation (8). Unless otherwise specified, the symbols surrounding log2M represent ceiling functions. M is a predetermined integer that satisfies 8≦M except when K=2, and is a predetermined odd number that satisfies 9≦M when K=2. M determines the resolution of the interface sensor 1. In other words, M is equal to the total number of "observation points" described above.

[0033] K sensor blocks {B k: k∈[K]} are formed on Q substrates 9 each having a flat plate shape, without being limited to the following example. Q is a predetermined integer satisfying 1≦Q≦K. When Q<K, there are substrates 9 having two or more sensor blocks. In each example illustrated later, Q=1. When Q≧2, the Q substrates 9 may be arranged on a single plane, or may be arranged like angle iron or channel iron, or may be arranged like triangular pipes or square pipes, without being limited to the following example.

[0034] <Condition 2> For any k∈[K], there are K sensor blocks {B k : k∈[K]}, k includes e(k) electrode pairs 5 and c(k)+1 conducting wires 7. e(k) is a predetermined integer that satisfies 1≦e(k)<M. c(k) is a predetermined integer that satisfies 2≦c(k)≦e(k) except when e(k)=1, in which case it is 1.

[0035] If e(k)≠1, then K sensor blocks {B k : k∈[K]}, k The e(k) electrode pairs 5 included in the above equation have the same capacitance C when the gap between the electrodes 5 a and 5 b of each of the e(k) electrode pairs 5 is filled with, for example, the first substance. k The kth sensor block B k The capacitance C of each of the e(k) electrode pairs 5 included in k is the jth (j≠k) sensor block B j The capacitance C of each of the e(j) electrode pairs 5 included in j Each of the c(k)+1 conducting wires 7 is connected to one of the K sensor blocks {B k : k∈[K]}, and as will be described later in relation to condition 5, the interface sensor 1 has Σ k∈[K]At least one of the e(k) electrode pairs 5 is connected to the electrode pair 5. The c(k)+1 conductors 7 are connected to a measuring circuit, which will be described later. In the drawing, for ease of viewing, only some of the electrode pairs and some of the conductors are labeled.

[0036] <Condition 3> The Σ that interface sensor 1 has k∈[K] Each of the e(k) electrode pairs 5 is located in one of M planes P(1), ..., P(M) that are mutually disjoint and parallel to each other. k∈[K] At least one of the e(k) electrode pairs 5 is located on the plane P(1). That is, there is no plane among the M planes P(1), ..., P(M) on which an electrode pair 5 is not located. The M planes P(1), ..., P(M) are arranged in space in an order according to the element order relation of the set [M] = {x∈N: 1≦x≦M} (i.e., a binary relation < on N (note that a binary relation < is a strict total order)). Specifically, between the first plane P(1) and the pth plane P(p) (p∈{x∈N: 3≦x≦M}), the qth plane P(q) (q∈{x∈N: 2≦x≦p-1}) exists. More simply stated, when the normal direction of the M parallel planes P(1), ..., P(M) is referred to as the first direction, the M planes P(1), ..., P(M) are arranged in this order in the first direction. For any g∈{x∈N:1≦x≦M−2} and any h∈{x∈N:g+1≦x≦M−1}, the distance between the gth plane P(g) and the g+1th plane P(g+1) may or may not be equal to the distance between the hth plane P(h) and the h+1th plane P(h+1). For example, it is advisable to narrow the interval between adjacent planes in a measurement range where the position of the interface is desired to be more accurately identified. Note that when the first direction is the vertical direction, the term "plane" may be rephrased as, for example, "level."

[0037] <Condition 4> For any k∈[K], there are K sensor blocks {B k : k∈[K]}, k The i-th electrode pair 5 of the e(k) electrode pairs 5 included ink,i The th plane P(p k,i ), equation (9) holds. Unless otherwise specified, the symbol "x" represents a Cartesian product, and A x B = {(a, b): a∈A ∧ b∈B}.

[0038] <Condition 5> For any (k, i)∈[K]×[e(k)], there are K sensor blocks {B k : k∈[K]}, k In this case, one electrode 5a of the i-th electrode pair 5 among the e(k) electrode pairs 5 is connected to the s k,i The other electrode 5b is connected to the c(k)+1-th conductor 7 of the c(k)+1 conductors 7. k,i is expressed by equation (10). Unless otherwise specified, the symbol mod represents a modulo operation, and a mod b is the remainder obtained by Euclidean division of the dividend a by the divisor b. In equation (10), the dividend of the modulo operation is i-1. In this example, the electrode 5a and s of the i-th (i∈[e(k)]) electrode pair 5 are k,i The i-th (i∈[e(k)]) electrode pair 5 and the c(k)+1-th conductor 7 are connected to each other via a branch line 7x, and the other electrode 5b of the i-th (i∈[e(k)]) electrode pair 5 and the c(k)+1-th conductor 7 are connected to each other via a branch line 7y.

[0039] <Condition 6> Non-negative integer g m,k is defined by equation (11), and the codeword h(m) is defined as K non-negative integers g m,k When the codeword h(m) is defined as a sequence of (k∈[K]) by equation (12), equation (13) or equation (14) holds. m,k is given as a sequence arranged in ascending order of the order relation of k∈[K]. In other words, h(m)=(g m,1 g m,2 ... g m,K) In equation (13) or (14), h(m1) ≠ h(m2) means a mismatch between two code words h(m1) and h(m2). The mismatch between two code words is defined by equation (15). Although the code word is not limited to a concatenation of K non-negative integers, there is no loss of generality if the code word is expressed as a concatenation of K non-negative integers.

[0040] Let I(1) be the half-space that does not include planes P(2), ..., P(M) of the two half-spaces obtained by dividing space by plane P(1), let I(m) (m∈{x∈N:2≦x≦M}) be the spatial region between adjacent planes P(m-1) and P(m), and let I(M+1) be the half-space that does not include planes P(2), ..., P(M) of the two half-spaces obtained by dividing space by plane P(M). Clearly, there exists a bijection between the M+1 codewords h(m) (m∈[M+1]) and the M+1 intervals I(m) (m∈[M+1]). However, the bijective image of h(m) is I(m) (m∈[M+1]). That is, in the interface sensor 1, a one-to-one correspondence is established between the M+1 code words h(m) (m∈[M+1]) and the M+1 intervals I(m) (m∈[M+1]). Therefore, specifying the position of the interface using the interface sensor 1 is equivalent to specifying the interval, and specifying the interval is nothing more than determining a K-digit code word based on the physical quantity occurring in the electrode pair 5. In other words, by determining a K-digit code word based on the physical quantity occurring in the electrode pair 5, it is possible to specify the interval in which the interface exists. This will be described in detail below as a method for specifying the position of the interface.

[0041] If equation (14) holds, the code word for section I(1) and the code word for section I(M+1) are the same. In this case, the code word for section I(1) and the code word for section I(M+1) can be distinguished by measuring the capacitance of any one electrode pair included in any sensor block.

[0042] For r(k) (k∈[K]) defined in condition 6, if equation (13) holds, then equation (16) holds, and if equation (14) holds, then equation (17) holds.

[0043] <Condition 7> max({d H (h(m),h(m+1)) : ∀m∈[M]}) = 1 holds. However, d H (h(m), h(m+1)) is the Hamming distance between codeword h(m) and codeword h(m+1). In other words, the coding system in the first embodiment is a Gray code.

[0044] <Condition 8> From condition 2, the kth (k∈[K]) sensor block B k contains c(k)+1 conducting wires 7. Therefore, in order for the total number of conducting wires 7 drawn out from the interface sensor 1 to be less than the total number of observation points, i.e., the number of planes M, it is sufficient that the formula (18) is established. Meanwhile, according to the condition 5, the kth (k∈[K]) sensor block B k In the kth (k∈[K]) sensor block B, the c(k)+1th conductor 7 is connected to the e(k) electrode pairs 5. In other words, the c(k)+1th conductor 7 provides a reference potential to the e(k) electrode pairs 5. Therefore, the kth (k∈[K]) sensor block B k The c(k)+1 th conductor 7 and the j th (j∈[K], j≠k) sensor block B j In the extreme case, the c(j)+1 th conductor 7 in the sensor block B k The c(k)+1th group of conducting wires 7 in (k) can be replaced with one conducting wire. Therefore, it is sufficient that the formula (19) holds.

[0045] <Condition 9> Equation (20) is established. Equation (20) corresponds to the above-mentioned condition a). The left side of the inequality in Equation (20) is the kth (k∈[K]) sensor block B included in the interface sensor 1. k Regarding the number e(k) of electrode pairs 5 included in k∈[K] e(k) and minimum value min k∈[K]represents the difference between e(k). The right-hand side of the inequality in equation (20) is the same as equation (6). The value of K on the right-hand side of the inequality in equation (20) is the same as the value of K on the left-hand side of the inequality in equation (20). The set F(M, K) is a set whose elements are the union of singletons, each of which has K factors n(k) (k∈[K]) of M excluding 1 as its elements. Again, please note that the factorization of M is not necessarily unique. For example, if M = 24 and K = 3, the factorization of M using K factors excluding 1 is M = 2 × 2 × 6 or M = 2 × 4 × 3 (note that the order of the factors is not taken into account). Therefore, F(M, K) = {{2, 6}, {2, 3, 4}}. The symbol F for the set F(M, K) is written in calligraphy in mathematical formulas. An element F of a set F(M, K) is written in German letters in mathematical formulas. If M cannot be expressed as a product of K factors excluding 1, the inequality in formula (20) holds (vacuous truth).

[0046] [Example of coding system] As an example, M=2 K -1 holds, the coding system that gives the codeword h(m) (m∈[M+1]) is a K-digit max({r(k):k∈[K]})-ary counting sequence. As another example, if r(k)=2 for any k∈[K] in condition 6, the coding system that gives the codeword h(m) (m∈[M+1]) is a K-digit binary Gray code. Furthermore, d H If (h(M+1),h(1))=1 holds, then the coding system that gives the codeword h(m) (m∈[M+1]) is cyclic. For more information on such coding systems, please refer to Document A. (Document A) I Nengah SUPARTA, "Counting Sequences, Gray Codes and Lexicodes", Dissertation at Delft University of Technology, 2006, ISBN 90-8559-176-7

[0047] [Design] An example of the design of the interface sensor 1 will be briefly described. The essence (groundwork) of the design of the interface sensor 1 is to determine the code word h(m) (m∈[M+1]). When the coding system that gives the code word h(m) (m∈[M+1]) is, for example, balanced Gray codes or uniform counting sequences, the process of determining the code word h(m) (m∈[M+1]) is disclosed in Literature A (Literature A discloses several examples of balanced Gray codes or uniform counting sequences as transition sequences (see, for example, Example 3.2.6)). Once the balanced Gray codes or uniform counting sequences are determined, it is easy to design the interface sensor 1 that satisfies conditions 1 to 9. For example, when a code word h(m) (m∈[M+1]) having three or more predetermined digits is determined as a balanced Gray code, K is the number of digits of the code word h(m) (m∈[M+1]), and M=2 K -1 and condition 7 are naturally determined, and e(k) (k∈[K]) is determined from the transition counts of the k-th digit of the codeword h(m) (m∈[M+1]) (i.e., the sum of the number of transitions from 0 to 1 and the number of transitions from 1 to 0). k,i ) (i∈[e(k)]) is defined as the position of the transition (i.e., a change from 0 to 1 or a change from 1 to 0) in the k-th digit of the codeword h(m) (m∈[M+1]), and furthermore, c(k) = r(k) = 1 + max({g m,k:m∈[M+1]})=2(k∈[K]), it is possible to easily design an interface sensor 1 that satisfies conditions 1 to 9. Note that if the set of all configurations of the interface sensor 1 that satisfy conditions 1 to 9 is denoted as X1, and the set of all configurations of the interface sensor 1 determined by the balanced Gray codes or uniform counting sequences disclosed in Document A is denoted as X2, then X2 ⊂ X1 holds, but the reverse does not hold. Therefore, the configuration of the interface sensor 1 that satisfies conditions 1 to 9 is not limited to the configuration of the interface sensor 1 determined by the balanced Gray codes or uniform counting sequences disclosed in Document A.

[0048] Several examples of the interface sensor 1 according to the first embodiment will be described with reference to the drawings. In each drawing, in consideration of ease of viewing the drawing, when two or more identical components are present, one or more, but not all, of the two or more identical components are given reference numerals.

[0049] 7 shows a first example of the first embodiment. In the first example, K=4, M=15, e(1)=4, e(2)=3, e(3)=4, e(4)=4, Σ k∈[K] e(k)=15 c(1)=2, c(2)=2, c(3)=2, c(4)=2 p 1,1 = 4, p 1,2 = 9, p 1,3 = 11, p 1,4 =14 p 2,1 = 3, p 2,2 = 5, p 2,3 =10 p 3,1 = 2, p 3,2 = 6, p 3,3 = 8, p 3,4 =12 p 4,1 = 1, p 4,2 = 7, p 4,3 = 13, p 4,4 = 15 s 1,1 = 1, s 1,2 = 2, s 1,3 = 1, s 1,4 = 2 s 2,1 = 1, s 2,2 = 2, s 2,3 = 1 s 3,1 = 1, s 3,2= 2, s 3,3 = 1, s 3,4 = 2 s 4,1 = 1, s 4,2 = 2, s 4,3 = 1, s 4,4 =2 r(1)=2, r(2)=2, r(3)=2, r(4)=2 h(16)=0100 h(15)=0101 h(14)=1101 h(13)=1100 h(12)=1110 h(11)=0110 h(10)=0010 h(9) =1010 h(8) =1000 h(7) =1001 h(6) =1011 h(5) =1111 h(4) =0111 h(3) =0011 h(2) =0001 h(1) =0000 max({d H (h(m),h(m+1)):∀m∈[M]})=1. It can be easily confirmed that equations (13), (16), and (19) hold. Since M cannot be expressed as a product of K factors excluding 1, equation (20) holds (vacuous truth). The coding system in the first example is cyclic 4-digit binary Gray codes.

[0050] 8 shows a second example of the first embodiment. In the second example, K=3, M=23, e(1)=8, e(2)=8, e(3)=7, Σ k∈[K] e(k)=23 c(1)=3, c(2)=2, c(3)=4 p 1,1 = 5, p 1,2 = 8, p 1,3 = 10, p 1,4 = 11, p 1,5 = 14, p 1,6 = 16, p 1,7 = 18, p 1,8 =20 p 2,1 = 4, p 2,2 = 6, p 2,3 = 9, p 2,4 = 13, p 2,5 = 15, p 2,6 = 19, p 2,7 = 21, p 2,8 =23 p 3,1 = 1, p 3,2 = 2, p 3,3 = 3, p 3,4 = 7, p 3,5 = 12, p 3,6 = 17, p 3,7 = 22 s1,1 = 1, s 1,2 = 2, s 1,3 = 3, s 1,4 = 1, s 1,5 = 2, s 1,6 = 3, s 1,7 = 1, s 1,8 = 2 s 2,1 = 1, s 2,2 = 2, s 2,3 = 1, s 2,4 = 2, s 2,5 = 1, s 2,6 = 2, s 2,7 = 1, s 2,8 = 2 s 3,1 = 1, s 3,2 = 2, s 3,3 = 3, s 3,4 = 4, s 3,5 = 1, s 3,6 = 2, s 3,7 =3 r(1)=3, r(2)=2, r(3)=4 h(24)=203 h(23)=213 h(22)=212 h(21)=202 h(20)=102 h(19)=112 h(18)=012 h(17)=011 h(16)=211 h(15)=201 h(14)=101 h(13)=111 h(12)=110 h(11)=010 h(10)=210 h(9) =200 h(8) =100 h(7) =103 h(6) =113 h(5) =013 h(4) =003 h(3) =002 h(2) =001 h(1) =000 max({d H (h(m),h(m+1)):∀m∈[M]})=1. It can be easily confirmed that equations (13), (16), and (19) hold. Since M cannot be expressed as a product of K factors excluding 1, equation (20) holds (vacuous truth). The coding system in the second example is a 3-digit maximum quaternary code.

[0051] 9 shows a third example of the first embodiment. In the third example, K=5, M=32, e(1)=6, e(2)=6, e(3)=6, e(4)=6, e(5)=8, Σ k∈[K] e(k)=32 c(1)=2, c(2)=2, c(3)=2, c(2)=2, c(3)=2 p 1,1 = 2, p 1,2 = 8, p 1,3=12、p 1,4 =17、p 1,5 =27、p 1,6 =32 p 2,1 =6、p 2,2 =14、p 2,3 =20、p 2,4 =22、p 2,5 =25、p 2,6 =31 p 3,1 =3、p 3,2 =9、p 3,3 =16、p 3,4 =18、p 3,5 =21、p 3,6 =29 p 4,1 =5、p 4,2 =7、p 4,3 =11、p 4,4 =23、p 4,5 =26、p 4,6 =28 p 5,1 =1、p 5,2 =4、p 5,3 =10、p 5,4 =13、p 5,5 =15、p 5,6 =19、p 5,7 =24、p 5,8 =30 s 1,1 =1、s 1,2 =2、s 1,3 =1、s 1,4 =2、s 1,5 =1、s 1,6 =2 s 2,1 =1、s 2,2 =2、s 2,3 =1、s 2,4 =2、s 2,5 =1、s 2,6 =2 s 3,1 =1、s 3,2 =2、s 3,3 =1、s 3,4 =2、s 3,5 =1、s 3,6 =2 s 4,1 =1、s 4,2 =2、s 4,3 =1、s 4,4 =2、s 4,5 =1、s 4,6 =2 s 5,1 =1、s 5,2 =2、s 5,3 =1、s 5,4 =2、s5,5 = 1, s 5,6 = 2, s 5,7 = 1, s 5,8 =2 r(1)=2, r(2)=2, r(3)=2 h(33)=00000=h(1) h(32)=10000 h(31)=11000 h(30)=11001 h(29)=11101 h(28)=11111 h(27)=01111 h(26)=01101 h(25)=00101 h(24)=00100 h(23)=00110 h(22)=01110 h(21)=01010 h(20)=00010 h(19)=00011 h(18)=00111 h(17)=10111 h(16)=10011 h(15)=10010 h(14)=11010 h(13)=11011 h(12)=01011 h(11)=01001 h(10)=01000 h(9) =01100 h(8) =11100 h(7) =11110 h(6) =10110 h(5) =10100 h(4) =10101 h(3) =10001 h(2) =00001 h(1) =00000 max({d H (h(m),h(m+1)):∀m∈[M]})=1. It can be easily confirmed that equations (14), (17), and (19) hold. Since the only factorization of M using K factors excluding 1 is M=2×2×2×2×2, F(M, K)={{2}}. Therefore, equation (20) holds. The coding system in the third example is 5-digit binary balanced Gray codes.

[0052] [Method and Algorithm for Identifying the Position of an Interface] Next, an example of a method for identifying the position of an interface using the interface sensor 1 will be described. In the following example, for any k∈[K], 2≦e(k) and 2≦c(k). The kth sensor block B k (k∈[K]), a measurement circuit (not shown) for measuring capacitance is k (s k ∈[c(k)−1])-th conductor 7, the composite of physical quantities (for example, composite capacitance) C(s k ) and s k+ The composite of the physical quantities (for example, composite capacitance) C(s k +1) and measure the difference C(s k )-C(s k +1) is compared with the threshold value δ. The threshold value δ is determined in advance taking into consideration the relative permittivity of the first material, the relative permittivity of the second material, measurement error, the number of electrode pairs 5 connected to one conductor 7, etc. As a result of the comparison, C(s k )-C(s k +1)≧δ, the k-th non-negative integer of the codeword h(m) (m∈[M+1]) is s k It is determined as follows: k For ∈[c(k)-1], C(s k )-C(s k If the condition (m∈[M+1])≧δ does not hold, the k-th non-negative integer of the codeword h(m) (m∈[M+1]) is determined to be 0. k By performing this measurement process for k∈[K], a K-digit code word is uniquely determined. An interface exists in the interval corresponding to the uniquely determined K-digit code word h(m) among the M+1 code words h(m) (m∈[M+1]). For example, in the interface sensor 1 shown in FIG. 7, if the K-digit code word is determined to be 1010 as a result of the measurement process, the interface exists in interval I(9) (i.e., between planes P(8) and P(9)). Note that if the K-digit code word is 0000, the interface exists in interval I(1) and therefore does not reach plane P(1). If the K-digit code word is 0100, the interface exists in interval I(16) and therefore exceeds plane P(15). The one-to-one correspondence between the M+1 code words h(m) (m∈[M+1]) and the M+1 intervals I(m) (m∈[M+1]) is stored as a lookup table in a memory (not shown), and an arithmetic circuit (not shown) refers to the lookup table to identify the interval corresponding to the K-digit code word obtained by the measurement process of the measurement circuit.

[0053] The measurement circuit may be a component of the interface sensor 1 or may be a physical entity separate from the interface sensor 1. In the latter case, the measurement circuit may be a component of a level meter that includes the interface sensor 1. The measurement circuit may be a component of each s kFor ∈[c(k)], C(s k ) and a measuring instrument to measure each s k ∈[c(k)−1], the difference C(s k )-C(s k The measurement circuit is not limited to a measurement circuit including a comparator that compares c(k)+1) with a threshold value δ, but may further include an AC signal generator that generates an AC signal to be applied to the c(k)+1-th conductor 7 for each k∈[K], or may be a prior art measurement circuit, or may be a measurement circuit including a programmable logic device (PLD). Examples of PLDs include FPGAs (field-programmable gate arrays).

[0054] Table 1 shows an algorithm for identifying the position of an interface using the interface sensor 1. The illustrated algorithm corresponds to the above-described position identification method. In the algorithm, h="" indicates that h is set to an empty string, and h=h+g indicates that a new code word h is obtained by concatenating a non-negative integer g as a character to the code word h. LOOKUP(h, TABLE) indicates the process of determining the interval corresponding to the code word h by referring to the TABLE. This algorithm identifies the interval, i.e., the position of the interface. The illustrated TABLE is based on the example shown in FIG. 7.

[0055] [Variation 1] In the case of a cyclic coding system or in the case where h(1) = h(M+1) is satisfied, a method for easily creating a variation from one embodiment will be explained.

[0056] Step A) In the case of a cyclic coding system, to make the explanation more concrete, the first example shown in FIG. 7 is used as one embodiment. In the first example shown in FIG. 7, M=15. The first example shown in FIG. 7 has a cyclic coding system. In the case of a cyclic coding system, one new electrode pair 5 is added to the M+1-th plane P(M+1). As a result, a code word h(M+2) is also added. The added code word h(M+2) is the same as the code word h(1). The sensor block to which one new electrode is added is the k-th sensor block B, which is determined by k in equation (21) under the condition that h(1)=h(M+2). k In this example, since k=2, one new electrode is added to the second sensor block B2 (see FIG. 10). The configuration shown in FIG. 10 is also an example of the first embodiment.

[0057] Step B) In the configuration obtained by adding one new electrode pair 5 to the M+1th plane P(M+1), shift the M+1 code words h(m) (m∈[M+1]) excluding the code word h(M+2) by a∈N. That is, shift the M+1 code words in the variation configuration by h v (m) (m∈[M+1]), then h v (m)=h(1+((M+m-a) mod (M+1)))(m∈[M+1]) h v (M+2)=h(1), specifically, when a=5, h v (17) =h(1) =0000h v (16) =h(11)=0110h v (15) =h(10)=0010h v (14) = h(9) = 1010 h v (13) = h(8) = 1000 h v (12) = h(7) = 1001 h v (11) = h(6) = 1011 h v (10) = h(5) = 1111 h v (9) =h(4) =0111h v (8) =h(3) =0011h v (7) =h(2) =0001hv (6) =h(1) =0000 h v (5) =h(16)=0100h v (4) =h(15)=0101h v (3) = h(14) = 1101 h v (2) = h(13) = 1100 h v (1) = h(12) = 1110.

[0058] Regarding condition 6), h(1) is always a concatenation of K zeros, but the codeword h v (1) is not a concatenation of K zeros. However, the codeword h v (m) (m∈[M+1]) by applying the remainder operation of the divisor r(k) to each digit of v (m) (m∈[M+1]) is a codeword h that satisfies condition 6). r (m) (m∈[M+1]). Specifically, the m-th codeword h v (m) is the kth non-negative integer of g v m,k Then, the code word h is obtained by equation (22). r (m) (m∈[M+1]) is obtained. Specifically, in this example, r(1) = 2, r(2) = 2, r(3) = 2, r(4) = 2, g v 1,1 = 1, g v 1,2 = 1, g v 1,3 = 1, g v 1,4 = 0, so h r (17) = 0000 h r (16) = 1000 h r (15) = 1100 h r (14) = 0100 h r (13) = 0110 h r (12) = 0111 h r (11) = 0101 h r (10) = 0001 h r (9) = 1001 h r (8) = 1101 h r (7) = 1111 h r (6) = 1110 h r(5) = 1010 h r (4) = 1011 h r (3) = 0011 h r (2) = 0010 h r (1) = 0000. These code words are shown in FIG.

[0059] The structure of this variation is shown in Figure 11. r Since (m) (m∈[M+2]) is determined, as mentioned above, e(k) (k∈[K]) is the codeword h r (m) (m∈[M+2])) (i.e., the total number of non-negative integer changes) of the k-th digit of k,i ) (i∈[e(k)]) is the codeword h r (m) (m∈[M+2]) and further, c(k) = r(k) = 1 + max({g m,k :m∈[M+2]})(k∈[K]), it is possible to easily design an interface sensor 1 that satisfies conditions 1 to 9. In the configuration of the variation shown in Figure 11, K = 4 M = 16 e(1) = 4, e(2) = 4, e(3) = 4, e(4) = 4, Σ k∈[K] e(k)=16 c(1)=2, c(2)=2, c(3)=2, c(4)=2 p 1,1 = 3, p 1,2 = 9, p 1,3 = 14, p 1,4 =16 p 2,1 = 5, p 2,2 = 8, p 2,3 = 10, p 2,4 =15 p 3,1 = 1, p 3,2 = 7, p 3,3 = 11, p 3,4 =13 p 4,1 = 2, p 4,2 = 4, p 4,3 = 6, p 4,4 = 12 s 1,1 = 1, s 1,2 = 2, s 1,3 = 1, s 1,4 = 2 s 2,1= 1, s 2,2 = 2, s 2,3 = 1, s 2,4 = 2 s 3,1 = 1, s 3,2 = 2, s 3,3 = 1, s 3,4 = 2 s 4,1 = 1, s 4,2 = 2, s 4,3 = 1, s 4,4 =2 r(1)=2, r(2)=2, r(3)=2 max({d H (h(m),h(m+1)):∀m∈[M]})=1. The total number of variations using this method is M+1, since it matches the possible values ​​of the shift number. It is easy to verify that equations (14), (17), and (19) hold true for the configuration shown in FIG. 11. Note that in this example, M appearing in equations (14), (17), and (19) has a value of M+1 (i.e., M+1=15+1=16). The only way to factorize M+1 using K factors excluding 1 is M+1=2×2×2×2×2, so F(M,K)={{2}}. Therefore, equation (20) holds true. The coding system in this example is 4-digit binary balanced Gray codes.

[0060] The configuration example obtained by removing the electrode pair 5 located on the plane P(16) from the configuration example shown in FIG. 11 is also an example of the first embodiment.

[0061] To obtain the configuration of variations when h(1) = h(M+1) is satisfied, only step B) needs to be performed. Specifically, M code words h(m) (m∈[M]) excluding code word h(M+1) are shifted by a∈N. In other words, M code words in the configuration of variations are shifted by h v (m) (m∈[M]), then h v (m)=h(1+((M+m-a-1) mod (M)))(m∈[M]) h v (M+1) = h(1). Codeword h v (m) (m∈[M]) to codeword h r The conversion to (m) (m∈[M]) follows equation (22).

[0062] [Variation 2] Another method for easily creating a variation of one embodiment will be described. In a second direction perpendicular to the first direction, K sensor blocks {B k : k∈[K]}. k :k∈[K]}, the total number of possible placement patterns is K! That is, Π ｋ＝１ Ｋ It is k.

[0063] [Equivalent Configurations for the First Embodiment] Next, "configurations equivalent to a configuration satisfying all of Conditions 1, 2, 3, 4, 5, 6, 7, 8, and 9" and specific examples thereof will be described. A "configuration equivalent to a configuration satisfying all of Conditions 1, 2, 3, 4, 5, 6, 7, 8, and 9" is a configuration that has a different configuration from a "configuration satisfying all of Conditions 1, 2, 3, 4, 5, 6, 7, 8, and 9" but has the same function from the perspective of an electrical circuit. Because it is impossible to list all "equivalent configurations," and because a person skilled in the art can easily implement various equivalent configurations, only a few examples of "equivalent configurations" for the first example of the first embodiment will be described.

[0064] max({d H If (h(m), h(m+1)):∀m∈[M]}) is less than K, the electrode pairs 5 can be arranged in Y columns. Y is H (h(m),h(m+1)): ∀m∈[M]})≦Y≦K−1. H Since (h(m),h(m+1)):∀m∈[M]})=1, 1≦Y≦K−1=3. Therefore, the electrode pairs 5 can be arranged in one column. This configuration is shown in FIG.

[0065] Furthermore, as explained in <Condition 8>, K conductors 7--kth (k∈[K]) sensor block B k 12 may be changed to the configuration shown in FIG. 13, since the c(k)+1th group of conducting wires 7 in the above can be replaced with one conducting wire.

[0066] [Second embodiment] The interface sensor 2 of the second embodiment is an interface sensor having a configuration determined by the adopted coding system and its specific code words, and satisfies the above-mentioned condition b) the jth (j∈[J]=[Σ k∈[K] Regarding the number t(j) of electrode pairs connected to the conductors of the kth (k∈[K]) sensor block (excluding the conductors connected to the e(k) electrode pairs or electrical conductors included in the kth (k∈[K]) sensor block), the maximum value max on the set [J] of the number t(j) is j∈[J] t(j) and minimum value min j∈[J] The difference between t(j) is smaller than the value of equation (7). In this respect, the second embodiment differs from the first embodiment.

[0067] Here, the substantial differences between the first embodiment and the second embodiment will be described, and for other technical matters, the description of the first embodiment will be applied mutatis mutandis to the description of the second embodiment. Therefore, the description of the first embodiment, excluding the substantial differences, is expressly incorporated mutatis mutandis herein. By applying the description of the first embodiment to the description of the second embodiment mutatis mutandis, for example, "interface sensor 1" can be rephrased as "interface sensor 2."

[0068] The interface sensor 2 of the second embodiment is a sensor having a configuration that satisfies all of the following conditions 1, 2, 3, 4, 5, 6, 7, and 8, or a configuration equivalent to said configuration. First, the "configuration that satisfies all of conditions 1, 2, 3, 4, 5, 6, 7, and 8" and specific examples thereof will be described, and then the "equivalent configuration" and specific examples thereof will be described.

[0069] <Condition 1> to <Condition 7> Condition 1, condition 2, condition 3, condition 4, condition 5, and condition 6 in the second embodiment are the same as condition 1, condition 2, condition 3, condition 4, condition 5, and condition 6 in the first embodiment, respectively. Condition 7 in the second embodiment is the same as condition 8 in the first embodiment. Therefore, the descriptions of conditions 1, 2, condition 3, condition 4, condition 5, condition 6, and condition 8 in the first embodiment apply mutatis mutandis to the descriptions of conditions 1, 2, condition 3, condition 4, condition 5, condition 6, and condition 7 in the second embodiment. In the second embodiment, conditions 7 and 9 in the first embodiment are unnecessary. Condition 8 in the second embodiment is as follows.

[0070] <Condition 8> Equation (23) is established. Equation (23) corresponds to the above-mentioned condition b). Set S is the union of sets Z(k) and is determined by equation (24). Sets S and Z(k) are written in German letters in the formula. The symbol a|b indicates that integer a is a divisor of integer b. The combination symbol | and symbol / indicates that the integer to the left of the combination symbol is not a divisor of the integer to the right of the combination symbol. The left side of the inequality in equation (23) is the jth (j∈[J]=[Σ k∈[K] Regarding the number t(j) of electrode pairs 5 connected to the conductor 7 of the kth (k∈[K]) sensor block (excluding the conductors connected to the e(k) electrode pairs or electrical conductors included in the kth (k∈[K]) sensor block), the maximum value max on the set [J] of the number t(j) is j∈[J] t(j) and minimum value min j∈[J] The difference between t(j) is specifically expressed using a set. The right-hand side of the inequality in equation (23) is the same as equation (7). When M cannot be expressed as a product of K factors excluding 1, the inequality in equation (23) holds (vacuous truth).

[0071] Several examples of the interface sensor 2 according to the second embodiment will be described with reference to the drawings. In each drawing, in consideration of ease of viewing the drawing, when two or more identical components are present, one or more, but not all, of the two or more identical components are given reference numerals.

[0072] A first example of the second embodiment is the configuration shown in FIG. 7 , a second example is the configuration shown in FIG. 8 , a third example is the configuration shown in FIG. 9 , a fourth example is the configuration shown in FIG. 10 , and a fifth example is the configuration shown in FIG. 11 . In the configuration shown in FIG. 7 , M cannot be expressed as a product of K factors excluding 1, so equation (23) holds (vacuous truth). In the configuration shown in FIG. 8 , M cannot be expressed as a product of K factors excluding 1, so equation (23) holds (vacuous truth). In the configuration shown in FIG. 9 , the only factorization of M using K factors excluding 1 is M=2×2×2×2×2, so F(M, K)={{2}}. Furthermore, S={3, 4}. Therefore, equation (23) holds. In the configuration shown in FIG. 10 , the only factorization of M using K factors excluding 1 is M=2×2×2×2, so F(M, K)={{2}}. Furthermore, S={2}. Therefore, equation (23) holds. In the configuration shown in FIG. 11 , the only factorization of M using K factors excluding 1 is M = 2 × 2 × 2 × 2, so F(M, K) = {{2}}. Furthermore, S = {2}. Therefore, equation (23) holds. These examples of the interface sensor 2 of the second embodiment include examples of the interface sensor 1 of the first embodiment, but this does not necessarily mean that the second embodiment includes the first embodiment.

[0073] 14 shows a sixth example of the second embodiment. In the sixth example, K=4, M=15, e(1)=8, e(2)=7, e(3)=8, e(4)=7, Σ k∈[K] e(k)=30 c(1)=2, c(2)=2, c(3)=2, c(4)=2 p 1,1 = 1, p 1,2 = 2, p 1,3 = 4, p 1,4 = 8, p 1,5 = 9, p 1,6 = 10, p 1,7 = 12, p 1,8 =14 p 2,1 = 3, p 2,2 = 5, p 2,3 = 6, p 2,4 = 9, p 2,5 = 12, p 2,6 = 13, p 2,7 =14 p 3,1 = 1, p 3,2 = 4, p 3,3=7、p 3,4 =8、p 3,5 =10、p 3,6 =11、p 3,7 =12、p 3,8 =15 p 4,1 =1、p 4,2 =2、p 4,3 =6、p 4,4 =7、p 4,4 =9、p 4,4 =13、p 4,4 =14 s 1,1 =1、s 1,2 =2、s 1,3 =1、s 1,4 =2、s 1,5 =1、s 1,6 =2、s 1,7 =1、s 1,8 =2 s 2,1 =1、s 2,2 =2、s 2,3 =1、s 2,4 =2、s 2,5 =1、s 2,6 =2、s 2,7 =1 s 3,1 =1、s 3,2 =2、s 3,3 =1、s 3,4 =2、s 3,5 =1、s 3,6 =2、s 3,7 =1、s 3,8 =2 s 4,1 =1、s 4,2 =2、s 4,3 =1、s 4,4 =2、s 4,5 =1、s 4,6 =2、s 4,7 =1 r(1)=2、r(2)=2、r(3)=2、r(4)=2 h(16)=0101 h(15)=0111 h(14)=1010 h(13)=1111 h(12)=0001 h(11)=0011 h(10)=1001 h(9) =0100 h(8) =1110 h(7) =1101 h(6) =1000 h(5) =1100 h(4) =0110 h(3) =0010 h(2) =1011 h(1) =0000 max({d H(h(m),h(m+1)):∀m∈[M]})=3. It is easy to verify that equations (13), (16), and (19) hold. Since M cannot be expressed as a product of K factors excluding 1, equation (23) holds. The sequence h(m) in the sixth example is a 4-digit binary counting sequence.

[0074] The explanations of [Example of coding system], [Design], [Method and algorithm for identifying the position of an interface], [Variation 1], and [Variation 2] in the first embodiment shall apply mutatis mutandis to the explanations of [Example of coding system], [Design], [Method and algorithm for identifying the position of an interface], [Variation 1], and [Variation 2] in the second embodiment.

[0075] [Equivalent Configurations for the Second Embodiment] Next, "configurations equivalent to a configuration satisfying all of Conditions 1, 2, 3, 4, 5, 6, 7, and 8" and specific examples thereof will be described. A "configuration equivalent to a configuration satisfying all of Conditions 1, 2, 3, 4, 5, 6, 7, and 8" is a configuration that has a different configuration from a "configuration satisfying all of Conditions 1, 2, 3, 4, 5, 6, 7, and 8" but has the same function from the perspective of an electrical circuit. Because it is impossible to list all "equivalent configurations," and because a person skilled in the art can easily implement various equivalent configurations, only an example of an "equivalent configuration" for the sixth example of the second embodiment will be described.

[0076] max({d H If (h(m), h(m+1)):∀m∈[M]}) is less than K, the electrode pairs 5 can be arranged in Y columns. Y is H (h(m),h(m+1)): ∀m∈[M]})≦Y≦K−1. In the sixth example of the second embodiment, max({d H Since (h(m),h(m+1)):∀m∈[M]})=3, 3≦Y≦K−1=3. Therefore, the electrode pairs 5 can be arranged in three columns. Furthermore, K conductors 7--kth (k∈[K]) sensor block B kTherefore, an example of the "equivalent configuration" of the sixth example of the second embodiment (FIG. 14) has the configuration shown in FIG. 15.

[0077] [Third Embodiment] The interface sensor 3 of the third embodiment differs from the first embodiment in that all of the other electrodes 5b are replaced with first electrical conductors. Therefore, the substantial differences between the first and third embodiments will be described here, and the description of the first embodiment will apply mutatis mutandis to the description of the third embodiment for other technical matters. Therefore, the description of the first embodiment, excluding the substantial differences, is expressly incorporated herein mutatis mutandis. By applying the description of the first embodiment to the description of the third embodiment, for example, "interface sensor 1" can be rephrased as "interface sensor 3."

[0078] As will be described later, the interface sensor 3 of the third embodiment has a first electrical conductor 50a and a Σ k∈[K] The first electrical conductor 50a and the second electrical conductor 50b are connected to the lead wire 70. k∈[K] Between the e(k) second electrical conductors 50b, Σ k∈[K] The position of the interface between the first material and the second material is determined by the two electrodes (i.e., the first electrical conductor 50a and the second electrical conductor 50b) that constitute the electrode pair. k∈[K] This is achieved by utilizing a physical quantity that occurs in the electrode pair depending on the properties of the first or second material present between any one of the e(k) second electrical conductors 50 b. For the reasons already mentioned, capacitance is used as the physical quantity that occurs in the electrode pair, and an explanation of an example in which electrical resistance is used as the physical quantity will be omitted.

[0079] The interface sensor 3 is a sensor having a configuration that satisfies all of the following conditions 1, 2, 3, 4, 5, 6, 7, 8, and 9, or a configuration equivalent to said configuration. First, we will explain the "configuration that satisfies all of conditions 1, 2, 3, 4, 5, 6, 7, 8, and 9" and specific examples thereof, and then we will explain the "equivalent configuration" and specific examples thereof.

[0080] <Condition 1> The interface sensor 3 includes a first electrical conductor 50a and K sensor blocks {B k : k∈[K]}. K is a predetermined integer that satisfies 2≦K<M. K preferably satisfies the above formula (8). M is a predetermined integer that satisfies 8≦M except when K=2, and is a predetermined odd number that satisfies 9≦M when K=2. M determines the resolution of the interface sensor 3. In other words, M is equal to the total number of the "observation points" described above.

[0081] The first electrical conductor 50a may be made of, for example, a metal, and may include a single electrical conductor or two or more electrical conductors.

[0082] When the first electrical conductor 50a is a single electrical conductor, the shape of the first electrical conductor 50a is not limited to the following example, and may be a flat plate or a cylinder. When the first electrical conductor 50a has a cylindrical shape, the cross-sectional shape of the cylinder in a cross section perpendicular to the longitudinal direction of the cylinder is, for example, a circle or a rectangle. When the first electrical conductor 50a has a cylindrical shape, K sensor blocks {B k : k∈[K]} is typically, but not necessarily, disposed inside the first electrical conductor 50a.

[0083] When the first electrical conductor 50a includes two or more electrical conductors, the shape of each of the electrical conductors included in the first electrical conductor 50a is not limited to the following examples and may be a flat plate or the shape of each of the components constituting the above-mentioned tube (for example, the shape of an object obtained by cutting the above-mentioned tube in a direction perpendicular to its longitudinal direction (i.e., a tube shorter than the above-mentioned tube), or the shape of an object obtained by cutting the above-mentioned tube in its longitudinal direction (for example, in the case of a cylinder, a 1 / 4 cylinder shape)). When the first electrical conductor 50a includes two or more electrical conductors, the two or more electrical conductors may be independent of each other. However, it is desirable that the two or more electrical conductors included in the first electrical conductor 50a have the same potential, for example, by contacting each other.

[0084] 16 and 17, the first electrical conductor 50a is a single electrical conductor, from the viewpoint of facilitating understanding of the interface sensor 3. In Figs. 16 and 17, in consideration of ease of viewing the figures, the edges of the first electrical conductor 50a are explicitly illustrated, and the first electrical conductor 50a is depicted as if it were transparent.

[0085] <Condition 2> For any k∈[K], there are K sensor blocks {B k : k∈[K]}, k includes e(k) second electrical conductors 50b and c(k) conducting wires 70. e(k) is a predetermined integer satisfying 1≦e(k)<M. c(k) is a predetermined integer satisfying 2≦c(k)≦e(k) except when e(k)=1, in which case it is 1.

[0086] K sensor blocks {B k : k∈[K]} is formed on Q substrates 9 each having a flat plate shape, without being limited to the following example. That is, the second electrical conductor 50b and the conducting wire 70 are formed on the substrate 9. The substrate 9 is waterproof coated except for the second electrical conductor 50b. Q is a predetermined integer satisfying 1≦Q≦K. When Q<K, there is a substrate 9 having two or more sensor blocks. In the examples shown in FIGS. 16 and 17, Q=1. When Q≧2, the Q substrates 9 are not limited to the following example, and may be arranged on a single plane, or may be arranged like angle iron or channel iron, or may be arranged like triangular pipes or square pipes.

[0087] The second electrical conductor 50b is made of, for example, metal. The shape of the second electrical conductor 50b is not limited to the following example, and may be a rectangular flat plate or a circular flat plate. kIn the figure, e(k) electrode pairs are formed between the first electrical conductor 50a and the e(k) second electrical conductors 50b. When e(k)≠1, when the gaps between the e(k) electrode pairs—in other words, the e(k) gaps formed by the first electrical conductor 50a and the e(k) second electrical conductors 50b—are filled with, for example, a first substance, the e(k) electrode pairs have the same capacitance C k From another perspective, when e(k)≠1, "in a state where the spaces between the e(k) electrode pairs are filled with, for example, the first substance, the e(k) electrode pairs have the same capacitance C k In order to satisfy the condition that "has k-th (k∈[K]) sensor block B k The area of ​​the ith (i∈[e(k)]) second electrical conductor 50b among the e(k) second electrical conductors 50b included in the sensor block B and the distance between the ith (i∈[e(k)]) second electrical conductor 50b and the first electrical conductor 50a are appropriately set. For example, the area of ​​the kth (k∈[K]) sensor block B k 16 and 17, the shape of the first electrical conductor 50a is a rectangular flat plate having an area larger than the area of ​​the substrate 9. In the examples shown in Fig. 16 and 17, the kth (kε[K]) sensor block B k is located on one surface of the substrate 9, and the first electrical conductor 50a is located parallel to and faces one surface of the substrate 9. When the interface sensor 3 is viewed from the front (i.e., when the paper of FIGS. 16 and 17 is viewed from the front), the first electrical conductor 50a is located on one surface of the substrate 9. k∈[K] The k-th sensor block B covers e(k) second electrical conductors 50b, and the distance between the edge of the first electrical conductor 50a and each second electrical conductor 50b is sufficiently large. k The capacitance C of each of the e(k) electrode pairs included in kis the jth (j≠k) sensor block B j The capacitance C of each of the e(j) electrode pairs included in j Each of the c(k) conducting wires 70 is connected to one of the K sensor blocks {B k : k∈[K]}, and as will be described later in relation to condition 5, the interface sensor 3 has Σ k∈[K] At least one of the e(k) second electrical conductors 50b is connected to the second electrical conductor 50b. The c(k) conducting wires 70 are connected to the measurement circuit described above. In the drawing, for ease of viewing, only some of the second electrical conductors and some conducting wires are labeled with reference numerals.

[0088] <Conditions 3> to <Conditions 4> Conditions 3 and 4 in the third embodiment are the same as conditions 3 and 4 in the first embodiment. Therefore, the explanation of conditions 3 and 4 in the first embodiment applies mutatis mutandis to the explanation of conditions 3 and 4 in the third embodiment. By applying the explanation of the first embodiment mutatis mutandis to the explanation of the third embodiment, for example, "interface sensor 1" can be rephrased as "interface sensor 3" and "electrode pair 5" as "second electrical conductor 50b."

[0089] <Condition 5> For any (k, i)∈[K]×[e(k)], there are K sensor blocks {B k : k∈[K]}, k In the equation, the i-th second electrical conductor 50b among the e(k) second electrical conductors 50b is the sth second electrical conductor among the c(k) conducting wires 70. k,i It is connected to the s-th conductor 70. k,i is expressed by the above formula (10). In this example, the i-th (iε[e(k)]) second electrical conductor 50b and s k,i The first and second conductors 70 are connected to each other via branch lines 70x.

[0090] <Conditions 6> to <Conditions 7> Conditions 6 and 7 in the third embodiment are the same as conditions 6 and 7 in the first embodiment. Therefore, the explanation of conditions 6 and 7 in the first embodiment applies mutatis mutandis to the explanation of conditions 6 and 7 in the third embodiment. By applying the explanation of the first embodiment mutatis mutandis to the explanation of the third embodiment, for example, "interface sensor 1" can be rephrased as "interface sensor 3" and "electrode pair 5" as "second electrical conductor 50b."

[0091] <Condition 8> From condition 2, the kth (k∈[K]) sensor block B k includes c(k) conducting wires 70. Therefore, in order for the total number of conducting wires 70 drawn out from the interface sensor 3 to be less than the total number of observation points, i.e., the number M of planes, it is sufficient that equation (25) is established.

[0092] <Condition 9> Condition 9 in the third embodiment is the same as condition 9 in the first embodiment. Therefore, the explanation of condition 9 in the first embodiment applies mutatis mutandis to the explanation of condition 9 in the third embodiment. By applying the explanation of the first embodiment mutatis mutandis to the explanation of the third embodiment, for example, "interface sensor 1" can be rephrased as "interface sensor 3" and "electrode pair 5" as "second electrical conductor 50b."

[0093] An example of an interface sensor 3 according to a third embodiment will be described with reference to the drawings. As described above, the third embodiment differs from the first embodiment in that all of the other electrodes 5b are replaced with first electrical conductors. Therefore, only an example of an interface sensor 3 based on the first example of the first embodiment (see FIG. 7) is shown in FIG. 16. In FIG. 16, in consideration of ease of viewing the drawing, when two or more identical components are present, reference numerals are assigned to one or more, but not all, of the two or more identical components.

[0094] The explanations of [Example of coding system], [Design], [Method and algorithm for identifying the position of an interface], [Variation 1], and [Variation 2] in the first embodiment shall apply mutatis mutandis to the explanations of [Example of coding system], [Design], [Method and algorithm for identifying the position of an interface], [Variation 1], and [Variation 2] in the third embodiment.

[0095] [Equivalent Configurations for the Third Embodiment] Next, a "configuration equivalent to a configuration that satisfies all of Conditions 1, 2, 3, 4, 5, 6, 7, 8, and 9" and specific examples thereof will be described. A "configuration equivalent to a configuration that satisfies all of Conditions 1, 2, 3, 4, 5, 6, 7, 8, and 9" is a configuration that has a different configuration from a "configuration that satisfies all of Conditions 1, 2, 3, 4, 5, 6, 7, 8, and 9," but has the same function from the perspective of an electrical circuit. Because it is impossible to list all "equivalent configurations," and because a person skilled in the art can easily implement various equivalent configurations, only the example of the interface sensor 3 shown in FIG. 16 and examples of "equivalent configurations" will be described.

[0096] max({d H If (h(m), h(m+1)):∀m∈[M]}) is less than K, the second electrical conductors 50b can be arranged in Y columns. Y is the sum of max({d H (h(m),h(m+1)): ∀m∈[M]})≦Y≦K−1. H (h(m),h(m+1)):∀m∈[M]})=1. Therefore, 1≦Y≦K−1=3. Therefore, the second electrical conductors 50b can be arranged in one row (see FIG. 17).

[0097] [Fourth Embodiment] The interface sensor 4 of the fourth embodiment is an interface sensor having a configuration determined by the adopted coding system and its specific code words, and has a configuration in which the above-mentioned condition b) is satisfied. In this respect, the fourth embodiment differs from the third embodiment. From another perspective, the fourth embodiment differs from the second embodiment in that all of the other electrodes 5b are replaced with first electrical conductors.

[0098] Here, the substantial differences between the third and fourth embodiments will be described, and with respect to other technical matters, the description of the third embodiment will be applied mutatis mutandis to the description of the fourth embodiment. Therefore, the description of the third embodiment, excluding the substantial differences, is expressly incorporated mutatis mutandis herein. Furthermore, through the incorporation of the description of the third embodiment, the description of the first embodiment is also expressly incorporated mutatis mutandis herein. By applying the descriptions of the first and third embodiments mutatis mutandis to the description of the fourth embodiment, for example, "interface sensor 1" and "interface sensor 3" can be rephrased as "interface sensor 4."

[0099] The interface sensor 4 of the fourth embodiment is a sensor having a configuration that satisfies all of the following conditions 1, 2, 3, 4, 5, 6, 7, and 8, or a configuration equivalent to said configuration. First, the "configuration that satisfies all of conditions 1, 2, 3, 4, 5, 6, 7, and 8" and specific examples thereof will be described, and then the "equivalent configuration" and specific examples thereof will be described.

[0100] <Condition 1> to <Condition 7> Condition 1, condition 2, condition 3, condition 4, condition 5, and condition 6 in the fourth embodiment are the same as condition 1, condition 2, condition 3, condition 4, condition 5, and condition 6 in the third embodiment, respectively. Condition 7 in the fourth embodiment is the same as condition 8 in the third embodiment. Therefore, the descriptions of conditions 1, 2, condition 3, condition 4, condition 5, condition 6, and condition 8 in the third embodiment apply mutatis mutandis to the descriptions of conditions 1, 2, condition 3, condition 4, condition 5, condition 6, and condition 7 in the fourth embodiment. In the fourth embodiment, conditions 7 and 9 in the third embodiment are unnecessary. Condition 8 in the fourth embodiment is as follows.

[0101] <Condition 8> Condition 8 in the fourth embodiment is the same as condition 8 in the second embodiment. Therefore, the description of condition 8 in the second embodiment applies mutatis mutandis to the description of condition 8 in the fourth embodiment.

[0102] An example of the interface sensor 4 according to the fourth embodiment will be described with reference to the drawings. As mentioned above, the fourth embodiment differs from the second embodiment in that all of the other electrodes 5b are replaced with first electrical conductors. Therefore, only an example of the interface sensor 4 based on the sixth example of the second embodiment (see FIG. 14) is shown in FIG. 18. In FIG. 18, in consideration of ease of viewing the drawing, when two or more identical components are present, reference numerals are assigned to one or more, but not all, of the two or more identical components.

[0103] The explanations of [Example of coding system], [Design], [Method and algorithm for identifying the position of an interface], [Variation 1], and [Variation 2] in the first embodiment shall apply mutatis mutandis to the explanations of [Example of coding system], [Design], [Method and algorithm for identifying the position of an interface], [Variation 1], and [Variation 2] in the fourth embodiment.

[0104] [Equivalent Configurations for the Fourth Embodiment] Next, a "configuration equivalent to a configuration that satisfies all of Conditions 1, 2, 3, 4, 5, 6, 7, and 8" and specific examples thereof will be described. A "configuration equivalent to a configuration that satisfies all of Conditions 1, 2, 3, 4, 5, 6, 7, and 8" is a configuration that has a different configuration from a "configuration that satisfies all of Conditions 1, 2, 3, 4, 5, 6, 7, and 8" but has the same function from the perspective of an electrical circuit. Because it is impossible to list all "equivalent configurations," and because a person skilled in the art can easily implement various equivalent configurations, only an example of an "equivalent configuration" for the example interface sensor 4 shown in FIG. 18 will be described.

[0105] max({d H If (h(m), h(m+1)):∀m∈[M]}) is less than K, the second electrical conductors 50b can be arranged in Y columns. Y is the sum of max({d H (h(m),h(m+1)): ∀m∈[M]})≦Y≦K−1. H (h(m),h(m+1)):∀m∈[M]})=3. Therefore, 3≦Y≦K−1=3. Therefore, the second electrical conductors 50b can be arranged in three rows (see FIG. 19).

[0106] <Appendix 1> The technical features disclosed in the various embodiments and their modifications described above are not necessarily mutually exclusive. As long as there is no contradiction from a technical point of view, the technical features of one embodiment or its modifications may be applied to the technical features of another embodiment or its modifications.

[0107] The claims as of the filing of this application do not necessarily exhaustively claim all inventions disclosed in this specification. In this regard, this should not be understood or construed as meaning that the applicant has pre-filing waived any right to a patent for any invention not claimed at the time of filing this application. To the extent permitted by the laws, regulations, or treaties of any country or region where this application is filed, the applicant reserves the right to a patent for any invention not claimed in this application, the right to file a divisional application for such invention, the right to claim such invention by amendment, and any other rights, unless the applicant expressly and conclusively expresses a contrary intention.

[0108] An example of a summary of the present disclosure based on another aspect is as follows:

[0109] The sensor based on the first aspect is a sensor for identifying the position of the interface between a first material and a second material, and has a configuration that satisfies all of the following conditions 1, 2, 3, 4, 5, 6, 7, 8, and 9, or a sensor having a configuration equivalent to said configuration. Condition 1) The sensor is made up of K sensor blocks {B k : k∈[K]}, where K is a predetermined integer satisfying 2≦K<M, M is a predetermined integer satisfying 8≦M except when K=2, and is a predetermined odd number satisfying 9≦M when K=2, and the symbol [X] represents a set {x∈N:1≦x≦X} determined by positive integers X, and N is a set of all positive integers. Condition 2) For any k∈[K], the k-th sensor block B among the K sensor blocks is kincludes e(k) electrode pairs and c(k)+1 conducting wires, where e(k) is a predetermined integer that satisfies 1≦e(k)<M, and c(k) is a predetermined integer that satisfies 2≦c(k)≦e(k) except when e(k)=1, in which case it is 1. Condition 3) Σ k∈[K] Each of the e(k) electrode pairs is located on one of M planes that are not coincident with each other and are parallel to each other. However, the M planes are arranged in an order according to the order relation of the elements of the set [M], and the Σ k∈[K] At least one electrode pair among the e(k) electrode pairs is located. Condition 4) For any k∈[K], the k-th sensor block B among the K sensor blocks is located k The i-th electrode pair among the e(k) electrode pairs included in k,i When it is located on the th plane, ∀k∈[K],i,j∈[e(k)],i>j ⇒ p k,i >p k,j where ∀(k, i)∈[K]×[e(k)], p k,i ∈[M]. Condition 5) For any (k, i)∈[K]×[e(k)], the k-th sensor block B k In the above, one electrode of the i-th electrode pair among the e(k) electrode pairs is s of the c(k)+1 conducting wires. k,i The other electrode is connected to the c(k)+1-th conductor of the c(k)+1 conductors. Condition 6) Non-negative integer g m,k of, and the codeword h(m) is a) m1, m2∈[M+1], m1≠m2 ⇒ h(m1)≠h(m2), or b) m1, m2∈[M], m1≠m2 ⇒ h(m1)≠h(m2), and h(1)=h(M+1), Condition 7) max({d H (h(m),h(m+1)) : ∀m∈[M]}) = 1 holds. However, dH (h(m), h(m+1)) is the Hamming distance between codeword h(m) and codeword h(m+1). Condition 8) Condition 9) is met. holds true.

[0110] The sensor based on the second aspect is a sensor for identifying the position of the interface between a first material and a second material, and has a configuration that satisfies all of the following conditions 1, 2, 3, 4, 5, 6, 7, and 8, or a sensor having a configuration equivalent to said configuration. Condition 1) The sensor is made up of K sensor blocks {B k : k∈[K]}, where K is a predetermined integer satisfying 2≦K<M, M is a predetermined integer satisfying 8≦M except when K=2, and is a predetermined odd number satisfying 9≦M when K=2, and the symbol [X] represents a set {x∈N:1≦x≦X} determined by positive integers X, and N is a set of all positive integers. Condition 2) For any k∈[K], the k-th sensor block B among the K sensor blocks is k includes e(k) electrode pairs and c(k)+1 conducting wires, where e(k) is a predetermined integer that satisfies 1≦e(k)<M, and c(k) is a predetermined integer that satisfies 2≦c(k)≦e(k) except when e(k)=1, in which case it is 1. Condition 3) Σ k∈[K] Each of the e(k) electrode pairs is located on one of M planes that are not coincident with each other and are parallel to each other. However, the M planes are arranged in an order according to the order relation of the elements of the set [M], and the Σ k∈[K] At least one electrode pair among the e(k) electrode pairs is located. Condition 4) For any k∈[K], the k-th sensor block B among the K sensor blocks is located k The i-th electrode pair among the e(k) electrode pairs included in k,i When it is located on the th plane, ∀k∈[K],i,j∈[e(k)],i>j ⇒ p k,i >p k,jwhere ∀(k, i)∈[K]×[e(k)], p k,i ∈[M]. Condition 5) For any (k, i)∈[K]×[e(k)], the k-th sensor block B k In the above, one electrode of the i-th electrode pair among the e(k) electrode pairs is s of the c(k)+1 conducting wires. k,i The other electrode is connected to the c(k)+1-th conductor of the c(k)+1 conductors. Condition 6) Non-negative integer g m,k of, and the codeword h(m) is a) m1, m2∈[M+1], m1≠m2 ⇒ h(m1)≠h(m2), or b) m1, m2∈[M], m1≠m2 ⇒ h(m1)≠h(m2), and h(1)=h(M+1), Condition 7) Condition 8) holds true.

[0111] A sensor based on the third aspect is a sensor for identifying the position of an interface between a first material and a second material, and has a configuration that satisfies all of the following conditions 1, 2, 3, 4, 5, 6, 7, 8, and 9, or a configuration equivalent to said configuration. Condition 1) The sensor includes a first electrical conductor and K sensor blocks {B k : k∈[K]}, where K is a predetermined integer satisfying 2≦K<M, M is a predetermined integer satisfying 8≦M except when K=2, and is a predetermined odd number satisfying 9≦M when K=2, and the symbol [X] represents a set {x∈N:1≦x≦X} determined by positive integers X, and N is a set of all positive integers. Condition 2) For any k∈[K], the k-th sensor block B among the K sensor blocks is kincludes e(k) second electrical conductors and c(k) conducting wires, where e(k) is a predetermined integer satisfying 1≦e(k)<M, and c(k) is a predetermined integer satisfying 2≦c(k)≦e(k) except when e(k)=1, and is 1 when e(k)=1. Condition 3) Σ k∈[K] Each of the e(k) second electrical conductors is located on one of M planes that are mutually disjoint and parallel, where the M planes are arranged in an order according to the ordering relation of the elements of the set [M], and the Σ k∈[K] At least one second electrical conductor is located among the e(k) second electrical conductors. Condition 4) For any k∈[K], the k-th sensor block B among the K sensor blocks is located among the k-th sensor block B. k The i-th second electrical conductor among the e(k) second electrical conductors included in k,i When it is located on the th plane, ∀k∈[K],i,j∈[e(k)],i>j ⇒ p k,i >p k,j where ∀(k, i)∈[K]×[e(k)], p k,i ∈[M]. Condition 5) For any (k, i)∈[K]×[e(k)], the k-th sensor block B k In the above, the i-th second electrical conductor among the e(k) second electrical conductors is the s k,i connected to the conductor, except that Condition 6) Non-negative integer g m,k of, and the codeword h(m) is a) m1, m2∈[M+1], m1≠m2 ⇒ h(m1)≠h(m2), or b) m1, m2∈[M], m1≠m2 ⇒ h(m1)≠h(m2), and h(1)=h(M+1), Condition 7) max({d H (h(m),h(m+1)) : ∀m∈[M]}) = 1 holds. However, d H(h(m), h(m+1)) is the Hamming distance between codeword h(m) and codeword h(m+1). Condition 8) Condition 9) is met. holds true.

[0112] A sensor based on the fourth aspect is a sensor for identifying the position of an interface between a first material and a second material, and has a configuration that satisfies all of the following conditions 1, 2, 3, 4, 5, 6, 7, and 8, or a configuration equivalent to said configuration. Condition 1) The sensor includes a first electrical conductor and K sensor blocks {B k : k∈[K]}, where K is a predetermined integer satisfying 2≦K<M, M is a predetermined integer satisfying 8≦M except when K=2, and is a predetermined odd number satisfying 9≦M when K=2, and the symbol [X] represents a set {x∈N:1≦x≦X} determined by positive integers X, and N is a set of all positive integers. Condition 2) For any k∈[K], the k-th sensor block B among the K sensor blocks is k includes e(k) second electrical conductors and c(k) conducting wires, where e(k) is a predetermined integer satisfying 1≦e(k)<M, and c(k) is a predetermined integer satisfying 2≦c(k)≦e(k) except when e(k)=1, and is 1 when e(k)=1. Condition 3) Σ k∈[K] Each of the e(k) second electrical conductors is located on one of M planes that are mutually disjoint and parallel, where the M planes are arranged in an order according to the ordering relation of the elements of the set [M], and the Σ k∈[K] At least one second electrical conductor is located among the e(k) second electrical conductors. Condition 4) For any k∈[K], the k-th sensor block B among the K sensor blocks is located among the k-th sensor block B. k The i-th second electrical conductor among the e(k) second electrical conductors included in k,i When it is located on the th plane, ∀k∈[K],i,j∈[e(k)],i>j ⇒ p k,i >pk,j where ∀(k, i)∈[K]×[e(k)], p k,i ∈[M]. Condition 5) For any (k, i)∈[K]×[e(k)], the k-th sensor block B k In the above, the i-th second electrical conductor among the e(k) second electrical conductors is the s k,i connected to the conductor, except that Condition 6) Non-negative integer g m,k of, and the codeword h(m) is a) m1, m2∈[M+1], m1≠m2 ⇒ h(m1)≠h(m2), or b) m1, m2∈[M], m1≠m2 ⇒ h(m1)≠h(m2), and h(1)=h(M+1), Condition 7) Condition 8) holds true.

[0113] The sensor based on the fifth aspect is a sensor based on the third aspect or the fourth aspect, and for any k∈[K], the k-th sensor block B k a distance between one of any two second electrical conductors among the e(k) second electrical conductors included in the sensor array and the first electrical conductor is equal to a distance between the other second electrical conductor and the first electrical conductor.

[0114] A liquid level meter according to the present disclosure includes a sensor based on any one of the first to fifth aspects, wherein the first substance is a liquid and the second substance is a gas. In this liquid level meter, the normal direction of the M planes in the sensor based on any one of the first to fifth aspects may be a vertical direction.

[0115] <Appendix 2> While the present invention has been described with reference to exemplary embodiments, those skilled in the art will recognize that various changes can be made and equivalents can be substituted for elements thereof without departing from the scope of the invention. Furthermore, many modifications can be made to adapt a particular system, device, or component thereof to the teachings of the present invention without departing from the essential scope of the invention. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed for carrying out this invention, but rather that the invention will include all embodiments falling within the scope of the appended claims.

[0116] Furthermore, the use of terms such as "first," "second," etc., when used in this specification and / or the appended claims, does not denote any order or importance, and terms such as "first," "second," etc., are used to distinguish between elements. The terms used herein are for the purpose of describing embodiments and are not intended to limit the invention in any way. The term "comprises" and its conjugations, when used in this specification and / or the appended claims, reveal the presence of referenced features, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, steps, operations, elements, components, and / or groups thereof. The term "and / or" includes any and all combinations of one or more of the associated listed elements, if any. In the claims and the specification, unless otherwise specified, the use of words such as "connected," "coupled," "joined," "connected," or equivalent words, and all word forms thereof, does not necessarily negate the presence of one or more intermediate elements between two elements that are, for example, "connected" or "coupled" to each other or "connected" to each other. In the claims and the specification, the term "any," if any, should be understood as a term that has the same meaning as the universal symbol ∀, unless otherwise specified. For example, the expression "for any X" has the same meaning as "for all X" or "for each X." Expressions such as "at least one of A, B, and C" (e.g., "at least one of A, B and C," "at least one of A, B or C," "at least one of A, B and / or C"), if any, should be understood as a term that has the same meaning as the universal symbol ∀, unless otherwise specified. S This means that one element is arbitrarily selected from the set P excluding the empty set φ. In this example, S = {A, B, C}, 2 S= {φ, {A}, {B}, {C}, {A, B}, {A, C}, {B, C}, {A, B, C}}, P = {{A}, {B}, {C}, {A, B}, {A, C}, {B, C}, {A, B, C}}, and this example means that one element (e.g., {A, C}) is arbitrarily selected from the set P.

[0117] Unless otherwise specified, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by a person skilled in the art to which this invention belongs. Furthermore, terms such as those defined in commonly used dictionaries should be interpreted to have a meaning consistent with their meaning in the context of the relevant art and this disclosure, and should not be interpreted ideally or excessively formally unless explicitly defined.

[0118] It will be understood that in describing the present invention, many techniques and steps are disclosed. Each of these has distinct advantages, and each can be used in combination with one or more, or in some cases all, of the other disclosed techniques. Therefore, to avoid cluttering, this specification will refrain from describing every possible combination of individual techniques or steps. Nevertheless, the specification and claims should be read with the understanding that such combinations are fully within the scope of the present invention and claims.

[0119] The corresponding structure, material, acts, and equivalents of all functional elements combined with means or steps in the following claims are intended to include the structure, material, or acts, if any, that perform the function in combination with other elements.

[0120] Although the present invention has been described above with reference to exemplary embodiments, it is not limited to these embodiments. Various modifications and variations are possible without departing from the spirit of the present invention. The selected and described embodiments are intended to illustrate the principles of the present invention and its practical application. The present invention may be used in various embodiments with various modifications and variations, which are determined according to the expected use. All such modifications and variations are intended to be included within the scope of the present invention, as defined by the appended claims, and are intended to be accorded the same protection when interpreted in accordance with the breadth that is fairly, legally, and equitably to be given.

[0121] REFERENCE SIGNS LIST 1 Interface sensor 2 Interface sensor 3 Interface sensor 4 Interface sensor 5 Electrode pair 5a Electrode 5b Electrode 7 Conductor 9 Substrate 50a First electrical conductor 50b Second electrical conductor 70 Conductor B k Sensor Block

Claims

A sensor for identifying the position of the interface between a first substance and a second substance, which has a configuration that satisfies all of the following conditions 1, 2, 3, 4, 5, 6, 7, 8, and 9, or a configuration equivalent to said configuration. Condition 1) The sensor is divided into K sensor blocks {B k : k∈[K]}, where K is a predetermined integer satisfying 2≦K<M, M is a predetermined integer satisfying 8≦M except when K=2, and is a predetermined odd number satisfying 9≦M when K=2, the symbol [X] represents a set {x∈N:1≦x≦X} determined by positive integers X, and N is the set of all positive integers. Condition 2) For any k∈[K], the k-th sensor block B k includes e(k) electrode pairs and c(k)+1 conducting wires, where e(k) is a predetermined integer satisfying 1≦e(k)<M, and c(k) is a predetermined integer satisfying 2≦c(k)≦e(k) except when e(k)=1, in which case it is 1. Condition 3) The above sensor has Σ k∈[K] Each of the e(k) electrode pairs is located on one of M planes that are not coincident with each other and are parallel to each other. However, the M planes are arranged in an order according to the order relation of the elements of the set [M], and the Σ k∈[K] At least one electrode pair out of the e(k) electrode pairs is located. Condition 4) For any k∈[K], the k-th sensor block B k The i-th electrode pair among the e(k) electrode pairs included in k,i When it is located in the th plane, ∀k∈[K],i,j∈[e(k)],i>j ⇒ p k,i >p k,j where ∀(k, i)∈[K]×[e(k)], p k,i ∈[M]. Condition 5) For any (k, i)∈[K]×[e(k)], the k-th sensor block B k In the above, one electrode of the i-th electrode pair among the e(k) electrode pairs is s of the c(k)+1 conducting wires. k,i The other electrode is connected to the c(k)+1-th conductor of the c(k)+1 conductors. Condition 6) non-negative integer g m,k of, and the codeword h(m) is In the case where it is determined by a) m1, m2∈[M+1], m1≠m2 ⇒ h(m1)≠h(m2), or b) m1, m2∈[M], m1≠m2 ⇒ h(m1)≠h(m2), and h(1)=h(M+1), holds true. Condition 7) max({d H (h(m),h(m+1)) : ∀m∈[M]}) = 1 holds. However, d H (h(m), h(m+1)) is the Hamming distance between codeword h(m) and codeword h(m+1). Condition 8) holds true. Condition 9) holds true. 　 A sensor for identifying the position of the interface between a first substance and a second substance, which has a configuration that satisfies all of the following conditions 1, 2, 3, 4, 5, 6, 7, and 8, or has a configuration equivalent to said configuration. Condition 1) The sensor is divided into K sensor blocks {B k : k∈[K]}, where K is a predetermined integer satisfying 2≦K<M, M is a predetermined integer satisfying 8≦M except when K=2, and is a predetermined odd number satisfying 9≦M when K=2, the symbol [X] represents a set {x∈N:1≦x≦X} determined by positive integers X, and N is the set of all positive integers. Condition 2) For any k∈[K], the k-th sensor block B k includes e(k) electrode pairs and c(k)+1 conducting wires, where e(k) is a predetermined integer satisfying 1≦e(k)<M, and c(k) is a predetermined integer satisfying 2≦c(k)≦e(k) except when e(k)=1, in which case it is 1. Condition 3) The above sensor has Σ k∈[K] Each of the e(k) electrode pairs is located on one of M planes that are not coincident with each other and are parallel to each other. However, the M planes are arranged in an order according to the order relation of the elements of the set [M], and the Σ k∈[K] At least one electrode pair out of the e(k) electrode pairs is located. Condition 4) For any k∈[K], the k-th sensor block B k The i-th electrode pair among the e(k) electrode pairs included in k,i When it is located in the th plane, ∀k∈[K],i,j∈[e(k)],i>j ⇒ p k,i >p k,j where ∀(k, i)∈[K]×[e(k)], p k,i ∈[M]. Condition 5) For any (k, i)∈[K]×[e(k)], the k-th sensor block B k In the above, one electrode of the i-th electrode pair among the e(k) electrode pairs is s of the c(k)+1 conducting wires. k,i The other electrode is connected to the c(k)+1-th conductor of the c(k)+1 conductors. Condition 6) non-negative integer g m,k of, and the codeword h(m) is In the case where it is determined by a) m1, m2∈[M+1], m1≠m2 ⇒ h(m1)≠h(m2), or b) m1, m2∈[M], m1≠m2 ⇒ h(m1)≠h(m2), and h(1)=h(M+1), holds true. Condition 7) holds true. Condition 8) holds true. 　 A sensor for identifying the position of the interface between a first substance and a second substance, which has a configuration that satisfies all of the following conditions 1, 2, 3, 4, 5, 6, 7, 8, and 9, or a configuration equivalent to said configuration. Condition 1) The sensor includes a first electrical conductor and K sensor blocks {B k : k∈[K]}, where K is a predetermined integer satisfying 2≦K<M, M is a predetermined integer satisfying 8≦M except when K=2, and is a predetermined odd number satisfying 9≦M when K=2, the symbol [X] represents a set {x∈N:1≦x≦X} determined by positive integers X, and N is the set of all positive integers. Condition 2) For any k∈[K], the k-th sensor block B k includes e(k) second electrical conductors and c(k) conducting wires, where e(k) is a predetermined integer satisfying 1≦e(k)<M, and c(k) is a predetermined integer satisfying 2≦c(k)≦e(k) except when e(k)=1, in which case it is 1. Condition 3) The above sensor has Σ k∈[K] Each of the e(k) second electrical conductors is located on one of M planes that are mutually disjoint and parallel, where the M planes are arranged in an order according to the ordering relation of the elements of the set [M], and the Σ k∈[K] At least one second electrical conductor is located among the e(k) second electrical conductors. Condition 4) For any k∈[K], the k-th sensor block B k The i-th second electrical conductor among the e(k) second electrical conductors included in k,i When it is located in the th plane, ∀k∈[K],i,j∈[e(k)],i>j ⇒ p k,i >p k,j where ∀(k, i)∈[K]×[e(k)], p k,i ∈[M]. Condition 5) For any (k, i)∈[K]×[e(k)], the k-th sensor block B k In the above, the i-th second electrical conductor among the e(k) second electrical conductors is the s k,i connected to the conductor, except that Condition 6) non-negative integer g m,k of, and the codeword h(m) is In the case where it is determined by a) m1, m2∈[M+1], m1≠m2 ⇒ h(m1)≠h(m2), or b) m1, m2∈[M], m1≠m2 ⇒ h(m1)≠h(m2), and h(1)=h(M+1), holds true. Condition 7) max({d H (h(m),h(m+1)) : ∀m∈[M]}) = 1 holds. However, d H (h(m), h(m+1)) is the Hamming distance between codeword h(m) and codeword h(m+1). Condition 8) holds true. Condition 9) holds true. 　 A sensor for identifying the position of the interface between a first substance and a second substance, which has a configuration that satisfies all of the following conditions 1, 2, 3, 4, 5, 6, 7, and 8, or has a configuration equivalent to said configuration. Condition 1) The sensor includes a first electrical conductor and K sensor blocks {B k : k∈[K]}, where K is a predetermined integer satisfying 2≦K<M, M is a predetermined integer satisfying 8≦M except when K=2, and is a predetermined odd number satisfying 9≦M when K=2, the symbol [X] represents a set {x∈N:1≦x≦X} determined by positive integers X, and N is the set of all positive integers. Condition 2) For any k∈[K], the k-th sensor block B k includes e(k) second electrical conductors and c(k) conducting wires, where e(k) is a predetermined integer satisfying 1≦e(k)<M, and c(k) is a predetermined integer satisfying 2≦c(k)≦e(k) except when e(k)=1, in which case it is 1. Condition 3) The above sensor has Σ k∈[K] Each of the e(k) second electrical conductors is located on one of M planes that are mutually disjoint and parallel, where the M planes are arranged in an order according to the ordering relation of the elements of the set [M], and the Σ k∈[K] At least one second electrical conductor is located among the e(k) second electrical conductors. Condition 4) For any k∈[K], the k-th sensor block B k The i-th second electrical conductor among the e(k) second electrical conductors included in k,i When it is located in the th plane, ∀k∈[K],i,j∈[e(k)],i>j ⇒ p k,i >p k,j where ∀(k, i)∈[K]×[e(k)], p k,i ∈[M]. Condition 5) For any (k, i)∈[K]×[e(k)], the k-th sensor block B k In the above, the i-th second electrical conductor among the e(k) second electrical conductors is the s k,i connected to the conductor, except that Condition 6) non-negative integer g m,k of, and the codeword h(m) is In the case where it is determined by a) m1, m2∈[M+1], m1≠m2 ⇒ h(m1)≠h(m2), or b) m1, m2∈[M], m1≠m2 ⇒ h(m1)≠h(m2), and h(1)=h(M+1), holds true. Condition 7) holds true. Condition 8) holds true. 　 The sensor according to claim 3 or claim 4, For any k∈[K], the k-th sensor block B k a distance between one of any two second electrical conductors among the e(k) second electrical conductors included in the matrix and the first electrical conductor is equal to a distance between the other second electrical conductor and the first electrical conductor; Sensor. 　 A liquid level meter, A sensor according to any one of claims 1 to 4, the first substance is a liquid; The second substance is a gas, Liquid level gauge.

7. The liquid level meter according to claim 6, The normal direction of the M planes is the vertical direction. Liquid level gauge.

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