Angle Sensor

Abstract

To measure an angle in a range larger than 90°.SOLUTION: An angle sensor includes: a bridge circuit 1a as a sensor circuit including a magnetic resistance effect element; magnets 3 and 4 for generating a magnetic field which rotates around the axis A of rotation; a voltage detector 11 for detecting an output voltage of the bridge circuit 1a; and a rotation angle calculation unit 12 for calculating a rotation angle of the magnetic field on the basis of the detected voltage detected by the voltage detector 11. The bridge circuit 1a, the rotary body 2, and the magnets 3, 4 are arranged so that a rotary surface 7 of a magnetic field intersects with a sensor surface 6a with a thin film resistance pattern of the magnetic resistance effect element formed.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to an angle sensor using a magnetoresistive element. [Background technology]

[0002] Conventionally, in chemical plants and the like, positioners are provided for valves used in the flow rate process, and the valve opening is controlled by the positioner. For example, a control valve 100 shown in Fig. 9 includes a valve body 101, a positioner 102, and an actuator 103. The actuator 103 moves a valve stem 104 up and down in response to the output air pressure supplied from the positioner 102, thereby adjusting the valve opening.

[0003] The positioner 102 is equipped with a control calculation unit that determines the deviation between the set opening sent from a higher-level device and the actual opening fed back from the valve, and generates an electrical signal corresponding to this deviation as a control signal; an electro-pneumatic conversion unit that converts the control signal generated by the control calculation unit into a pneumatic signal; and a pneumatic signal amplification unit (pilot relay) that amplifies the pneumatic signal from the electro-pneumatic conversion unit and supplies it to the actuator 103 as output pneumatic pressure (see Patent Document 1).

[0004] The positioner 102 uses an angle sensor 105 as a displacement detection unit that detects the actual opening of the valve as the amount of displacement of the up and down movement of the valve stem 104. The angle sensor 105 has a rotor that rotates in accordance with the amount of displacement of the valve stem 104 via a feedback lever 106. An electrical signal corresponding to the rotation angle of the rotor of this angle sensor 105 is fed back to the control calculation unit as a signal indicating the actual opening of the valve.

[0005] FIG. 10 is a diagram showing the configuration of angle sensor 105. Angle sensor 105 measures the rotation angle of the magnetic field generated by magnets 3 and 4 attached to rotating body 2. A sensor circuit 1 using a magnetoresistive element, a Hall element, or the like is used to measure the angle. In FIG. 10, 5 indicates the direction of the magnetic field generated by magnets 3 and 4, and 6 indicates the measurement surface of sensor circuit 1. Generally, as shown in FIG. 10, the sensor circuit 1 is installed so that the measurement surface and the plane of rotation of the magnetic field are parallel.

[0006] For example, the angle sensor used in the AVP300 positioner manufactured by Azbil Corporation uses anisotropic magnetoresistive effect (AMR) elements as detection elements, and a bridge circuit made up of AMR elements is placed parallel to the plane of rotation of the magnetic field, measuring the angle by utilizing the change in the midpoint potential difference of the bridge circuit depending on the angle of rotation of the magnetic field.

[0007] The output of this angle sensor goes through two cycles per rotation of the magnetic field, and the unique correspondence between the rotation angle of the magnetic field and the output of the angle sensor is at most half that cycle. This means that the angle sensor has the problem of being unable to measure angles greater than 90°. Furthermore, since the error increases near the angle where the output of the angle sensor shows its peak value, the practical angle measurement range becomes even narrower. [Prior art documents] [Patent documents]

[0008] [Patent Document 1] Japanese Patent Application Laid-Open No. 2013-104454 Summary of the Invention [Problem to be solved by the invention]

[0009] The present invention has been made to solve the above-mentioned problems, and has an object to provide an angle sensor that can measure angles in a range wider than 90°. [Means for solving the problem]

[0010] The angle sensor of the present invention comprises a sensor circuit including a magnetoresistive element, a magnetic field generating unit configured to generate a magnetic field that rotates around a rotation axis, an output electrical signal detecting unit configured to detect an output electrical signal of the sensor circuit, and a rotation angle calculating unit configured to calculate the rotation angle of the magnetic field based on the output electrical signal detected by the output electrical signal detecting unit, and is characterized in that the sensor circuit and the magnetic field generating unit are arranged so that the plane of rotation of the magnetic field intersects with the sensor surface on which the thin film resistor pattern of the magnetoresistive element is formed.

[0011] Furthermore, one configuration example of the angle sensor of the present invention is characterized in that the reference position at which the output electrical signal of the sensor circuit is zero is coincident with or parallel to the intersection line between the rotation plane of the magnetic field and the sensor surface. In one configuration example of the angle sensor of the present invention, the rotation angle calculation unit calculates a rotation angle θ of the magnetic field on the sensor surface based on the output electrical signal detected by the output electrical signal detection unit, and calculates φ=tan -1 The rotation angle φ of the magnetic field on the plane of rotation is calculated by (tan θ / cos α).

[0012] Furthermore, one configuration example of the angle sensor of the present invention is characterized in that the reference position at which the output electrical signal of the sensor circuit is zero is not on the intersection line between the rotation plane of the magnetic field and the sensor surface. In one configuration example of the angle sensor of the present invention, the rotation angle calculation unit calculates a rotation angle θ of the magnetic field on the sensor surface based on the output electrical signal detected by the output electrical signal detection unit, and calculates φ=tan θ based on the rotation angle θ, an inclination angle α of the rotation plane of the magnetic field with respect to the sensor surface, and an angle β between the reference position on the sensor surface and the intersection line. -1 {tan(θ-β) / cosα}+tan -1The rotation angle φ of the magnetic field on the plane of rotation is calculated by (tan β / cos α).

[0013] In addition, in one configuration example of the angle sensor of the present invention, the rotation angle calculation unit calculates the rotation angle θ from the output electrical signal detected by the output electrical signal detection unit using an approximation function that indicates the relationship between the output electrical signal of the sensor circuit and the rotation angle θ. Moreover, one configuration example of the angle sensor of the present invention is characterized in that the magnetic field is saturated with respect to the magnetoresistive effect element of the sensor circuit regardless of the rotation angle. [Effects of the Invention]

[0014] According to the present invention, by arranging the sensor circuit and magnetic field generating unit so that the plane of rotation of the magnetic field intersects with the sensor surface on which the thin film resistor pattern of the magnetoresistive effect element is formed, angles can be measured over a range wider than 90°. [Brief explanation of the drawings]

[0015] [Figure 1] FIG. 1 is a circuit diagram of a bridge circuit configured with AMR elements. [Figure 2] FIG. 2 is a diagram showing the configuration of an angle sensor according to a first embodiment of the present invention. [Figure 3] FIG. 3 is a diagram showing the trajectory of the magnet accompanying the rotation of the rotor in the angle sensor according to the first embodiment of the present invention. [Figure 4] FIG. 4 is a diagram showing the relationship between the range of measurable rotation angles of the magnetic field and the tilt angle of the rotation plane of the magnetic field relative to the sensor surface. [Figure 5] FIG. 5 is a diagram showing the relationship between the rotation angle of the magnetic field when the tilt angle is 45° and the ratio of the midpoint potential difference to the amplitude of the bridge circuit. [Figure 6] FIG. 6 is a diagram showing the trajectory of the magnet accompanying the rotation of the rotor in the angle sensor according to the second embodiment of the present invention. [Figure 7]FIG. 7 is a diagram showing the relationship between the tilt angle of the rotation plane of the magnetic field relative to the sensor surface, the angle of the reference position on the sensor surface relative to the intersection line between the rotation plane of the magnetic field and the sensor surface, and the range of measurable rotation angles. [Figure 8] FIG. 8 is a block diagram showing an example of the configuration of a computer that realizes the angle sensors according to the first and second embodiments of the present invention. [Figure 9] FIG. 9 is a diagram showing an example of a control valve. [Figure 10] FIG. 10 is a diagram showing the configuration of a conventional angle sensor. DETAILED DESCRIPTION OF THE INVENTION

[0016] [Conventional example] Before describing the embodiments of the present invention, a conventional angle sensor will be described in detail. Fig. 1 shows a bridge circuit 1a composed of AMR elements whose electrical resistance changes depending on a magnetic field. The bridge circuit 1a is formed by connecting in parallel a first series circuit 10-5 in which a first AMR element 10-1 and a second AMR element 10-2 are connected in series, and a second series circuit 10-6 in which a third AMR element 10-3 and a fourth AMR element 10-4 are connected in series.

[0017] As shown by the double-headed arrows in Figure 1, the magnetic sensing direction (the direction of the magnetic field in which the resistance value is minimum) of the facing AMR elements 10-1 and 10-4 is the same, and the magnetic sensing direction of the facing AMR elements 10-2 and 10-3 is the same. In addition, the magnetic sensing directions of adjacent AMR elements are perpendicular to each other.

[0018] When the plane of rotation of the magnetic field generated by the angle sensor's magnet is parallel to the sensor surface on which the thin-film resistance patterns of the four AMR elements 10-1 to 10-4 are formed (a surface parallel to the magnetic sensing direction of the AMR elements 10-1 to 10-4 and parallel to the plane of the paper in Figure 1), if a constant current I is passed through the bridge circuit 1a from a power supply not shown, the midpoint potential difference V(θ), which is the output electrical signal, (the potential difference between the midpoint of the first series circuit 10-5 and the midpoint of the second series circuit 10-6) is expressed by equation (1) depending on the rotation angle θ of the magnetic field.

[0019]

number

[0020] From equation (1), the midpoint potential difference V(θ) is a periodic function with an amplitude of V0 and two periods per rotation of the magnetic field. The rotation angle θ of the magnetic field can be calculated from the midpoint potential difference V(θ) using equation (2).

[0021]

number

[0022] Once the half cycle is exceeded, the rotation angle θ cannot be uniquely determined for the midpoint potential difference V(θ), so the angle measurement range of conventional angle sensors is limited to 90 degrees.

[0023] [First Example] FIG. 2 is a diagram showing the configuration of an angle sensor according to a first embodiment of the present invention, with the same components as those in FIG. 10 being assigned the same reference numerals. In this embodiment, as shown in FIG. 2, a bridge circuit 1a (sensor circuit), a rotor 2, and magnets 3 and 4 (magnetic field generators) are arranged so that the plane of rotation 7 of the magnetic field intersects with a sensor surface 6a on which the thin-film resistor patterns of AMR elements 10-1 to 10-4 are formed, within an inclination angle range of greater than 0 degrees and less than 90 degrees. The magnets 3 and 4 are attached to the rotor 2 and rotate around a rotation axis A as the rotor 2 rotates. An extension of the rotation axis A passes through the center of the diamond-shaped (square) bridge circuit 1a shown in FIG. 1.

[0024] In a magnetically saturated state, the output of AMR elements 10-1 to 10-4 is constant regardless of the distance from magnets 3 and 4, and depends only on the angle of the magnetic field. Therefore, when magnetic field rotation plane 7 is inclined with respect to sensor surface 6a as shown in Figure 2, it is not necessary to consider changes in distance due to the rotation orbit of magnets 3 and 4, as long as the magnetic field strength is strong enough to cause AMR elements 10-1 to 10-4 to be magnetically saturated, even at the position within the measurement range where magnets 3 and 4 are furthest from AMR elements 10-1 to 10-4.

[0025] As the rotor 2 rotates, the magnets 3 and 4 describe a perfect circular trajectory within the plane of rotation 7 of the magnetic field. Here, if the rotation angle of the magnetic field is φ, the angle between the plane of rotation 7 of the magnetic field and the sensor surface 6a is α (0<α<90 degrees), and the rotation angle of the magnetic field on the sensor surface 6a is θ, then, as mentioned above, there is no need to consider the distance from the magnets 3 and 4, and so the rotation of the magnets 3 and 4 can be thought of as an elliptical trajectory rather than a perfect circle. Specifically, if the radius of rotation of the magnets 3 and 4 is R, then the trajectory of the magnets 3 and 4 can be thought of as the trajectory of an ellipse 8 in Figure 3, with a minor axis R and a major axis R / cosα.

[0026] From FIG. 3, formulas (3) to (6) are obtained. cosφ=cosθ (3) sinφ=sinθ / cosα (4) tanφ=sinφ / cosφ=(sinθ / cosα) / cosθ = tanθ / cosα (5) φ=tan -1 (tanθ / cosα) (6)

[0027] Here, equation (8) is obtained from equation (7).

[0028]

number

[0029]

number

[0030] Also, since sin2θ=V(θ) / V0, if we set V(θ) / V0=x, we obtain equation (9).

[0031]

number

[0032] Therefore, the rotation angle φ of the magnetic field can be obtained from the output electrical signal of the bridge circuit 1a. Now, consider how the range of the rotation angle φ of the magnetic field, which corresponds to the 90° range of -45°≦θ≦45°, changes depending on the inclination angle α of the rotation plane 7 of the magnetic field relative to the sensor surface 6a. If sin2θ=V(θ) / V0=x, then within this range of θ, there is a monotonous increase of -1≦x≦1, and the rotation angle φ of the magnetic field reaches a maximum value φ when θ is 45°. max When θ is -45°, the minimum value φ min Take.

[0033]

number

[0034]

number

[0035] Maximum value φ max and the minimum value φ min The difference between these, i.e., the range Δφ of the measurable rotation angle φ of the magnetic field, is given by equation (12).

[0036]

number

[0037] Figure 4 shows the relationship between the range Δφ of the measurable rotation angle φ of the magnetic field and the tilt angle α of the plane of rotation 7 of the magnetic field relative to the sensor surface 6a. According to Figure 4, when the tilt angle α = 0°, φ = θ, so the range of the measurable rotation angle φ of the magnetic field is Δφ = 90°. On the other hand, when the tilt angle α = ±90°, the rotation angle φ is not dependent on the value of θ, so measurement is not possible. Figure 4 indicates that the tilt angle α allows the rotation angle φ to be measured over a range wider than 90°. For example, when the tilt angle α = 45°, the range of the measurable rotation angle φ of the magnetic field is Δφ = 109.5°.

[0038] In an angle sensor, since it is difficult to directly calculate equation (2) to calculate the rotation angle φ of the magnetic field from the output electrical signal of bridge circuit 1a, an approximation curve may be applied to the curve showing the relationship between the rotation angle θ of the magnetic field and the midpoint potential difference V(θ), which is the output electrical signal of bridge circuit 1a. In the case of polynomial approximation, the approximation accuracy deteriorates in the vicinity of θ = ±45°, where the midpoint potential difference V(θ) of bridge circuit 1a is close to its peak, so in order to improve accuracy, it is necessary to increase the degree of the polynomial.

[0039] FIG. 5 shows the relationship between the rotation angle φ of the magnetic field when the tilt angle α is 45° and the ratio x (=V(θ) / V0) of the midpoint potential difference V(θ) to the amplitude V0 of the bridge circuit 1a. In this embodiment, θ=tan -1 Therefore, for example, when measuring -45°≦φ≦45° when the tilt angle α=45°, the range -0.94≦x≦0.94 is sufficient as shown in Figure 5, and accurate approximation is required only within this range, ignoring the area near the peak of the midpoint potential difference V(θ).

[0040] The above explanation is valid in the range of (2n-1 / 2)π<α<(2n+1 / 2)π (n is an integer). In the range of (2n+1 / 2)π<α<(2n+3 / 2)π, the sign of equation (6) is reversed, but the magnetic field rotation angle φ can still be measured at 90° or more.

[0041] 2 supplies a constant current I to the bridge circuit 1a. A voltage detection unit 11 (output electrical signal detection unit) detects a midpoint potential difference V(θ) of the bridge circuit 1a.

[0042] The rotation angle calculation unit 12 of this embodiment calculates the rotation angle θ of the magnetic field on the sensor surface 6a based on the midpoint potential difference V(θ), and calculates the rotation angle φ of the magnetic field (the rotation angle of the rotor 2) using equation (6) based on the rotation angle θ and the known tilt angle α. In this case, the rotation angle calculation unit 12 calculates the rotation angle θ of the magnetic field from the midpoint potential difference V(θ) using a pre-registered approximation function that indicates the relationship between the midpoint potential difference V(θ) and the rotation angle θ of the magnetic field.

[0043] [Second Example] In the first embodiment, the bridge circuit 1a, rotor 2, and magnets 3 and 4 were arranged so that the direction (reference position) in which the midpoint potential difference V(θ) of bridge circuit 1a was zero coincided with or was parallel to the intersection (L in FIG. 3) between the plane of rotation 7 of the magnetic field (the plane of orbit 8 in FIG. 3) and sensor surface 6a. In FIGS. 1 and 3, the reference position is indicated by θ0. In the example of FIG. 1, the reference position θ0 is parallel to the magnetic sensing direction of AMR elements 10-2 and 10-3 and perpendicular to the magnetic sensing direction of AMR elements 10-1 and 10-4.

[0044] In contrast, in this embodiment, a case will be described in which the plane of rotation 7 of the magnetic field is not parallel to the sensor surface 6a and the reference position θ0 of the bridge circuit 1a is not on the intersection L between the plane of rotation 7 of the magnetic field and the sensor surface 6a. In this embodiment, the configuration of the angle sensor is the same as that of the first embodiment shown in Figure 2. As in the first embodiment, the extension of the rotation axis A passes through the center of the bridge circuit 1a, but here we consider a case in which the reference position θ0 of the bridge circuit 1a is shifted by an angle β from the intersection L on the sensor surface 6a and by an angle ψ from the intersection L on the plane of rotation of the magnetic field, as shown in Figure 6.

[0045] By substituting φ → φ-ψ and θ → θ-β in equation (6), equation (13) is obtained.

[0046]

number

[0047] Furthermore, the relationship shown in equation (14) also holds between the angles ψ and β.

[0048]

number

[0049] By substituting equation (14) into equation (13), the rotation angle φ of the magnetic field is given by equation (15).

[0050]

number

[0051] If we rearrange the right-hand side of equation (15) and express it using x, we get equation (16).

[0052]

number

[0053] The range Δφ of the magnetic field rotation angle φ that can be measured in the range of -45°≦θ≦45° varies depending on the inclination angle α of the magnetic field rotation plane 7 with respect to the sensor surface 6a and the angle β of the reference position θ0 on the sensor surface 6a with respect to the intersection L between the magnetic field rotation plane and the sensor surface 6a. Furthermore, from equation (16), it can be seen that the value of the magnetic field rotation angle φ remains the same even if the sign of the inclination angle α is swapped.

[0054] The angles α and β are in the ranges of -90°≦α≦90° and -90°≦β≦90°, respectively, and the maximum value of the rotation angle φ when the rotation angle θ changes by 90 degrees from -45° to 45° is defined as φ max , the minimum value is φ min The range Δφ of the measurable rotation angle φ is defined as φ max -φ min Fig. 7 is a diagram showing the relationship between the angles α and β and the range Δφ of the measurable rotation angle φ. However, in Fig. 7, the range of α<0 is omitted due to symmetry.

[0055] When the tilt angle α of the magnetic field rotation plane 7 relative to the sensor surface 6a is 0°, the measurable range of rotation angles φ, Δφ, is 90°, regardless of the angle β. In the range of β<-45° and β>45°, Δφ<90°, which is narrower than the range of rotation angles θ. Therefore, as the tilt angle α of the magnetic field rotation plane 7 relative to the sensor surface 6a approaches ±90° within the range of -45°≦β≦45°, the measurable range of rotation angles φ, Δφ, widens. However, when the tilt angle α is approximately 65° or greater (or -65° or less), the rotation angle φ becomes discontinuous within the range of -1≦x≦1 depending on the value of angle β, and this must be avoided. Here, discontinuity refers to a 180° shift in the rotation angle φ. In Figure 7, 700 indicates the range including the discontinuity.

[0056] For example, as shown in range 701 in Figure 7, when the angle sensor is used in the range of 40°≦α≦50° and -24°≦β≦24°, the range of measurable rotation angles φ, Δφ, can be made 100° or more. Even if the portion of the midpoint potential difference V(θ) of bridge circuit 1a near the peak is cut out and unused, as long as the cut portion is within a range of 5° in terms of rotation angle φ, the range of measurable rotation angles φ, Δφ, can be made 90° or more. As the tilt angle α approaches 90°, the range of angles β within which the range of measurable rotation angles φ, Δφ, can be made 90° or more widens, approaching -45°≦β≦45°.

[0057] 2 detects the midpoint potential difference V(θ) of the bridge circuit 1a, as in the first embodiment. The rotation angle calculation unit 12 of this embodiment calculates the rotation angle θ of the magnetic field on the sensor surface 6a based on the midpoint potential difference V(θ) of the bridge circuit 1a, as in the first embodiment, and calculates the rotation angle φ of the magnetic field using equation (15) based on the rotation angle θ and the known angles α and β.

[0058] In the above embodiment, the rotation angle θ of the magnetic field on the sensor surface 6a is calculated based on the midpoint potential difference V(θ) of the bridge circuit 1a. Alternatively, a constant voltage may be applied to the bridge circuit 1a, and the rotation angle θ of the magnetic field on the sensor surface 6a may be calculated based on the current value A(θ) flowing through the bridge circuit 1a. Furthermore, although a positioner is used as an example in the explanation in FIGS. 9 and 10, it goes without saying that the angle sensors of the first and second embodiments can be applied to devices other than positioners.

[0059] The rotation angle calculation unit 12 described in the first and second embodiments can be realized by a computer including a CPU (Central Processing Unit), a storage device, and an interface with the outside, and a program that controls these hardware resources. An example configuration of this computer is shown in FIG. 8. The computer includes a CPU 200, a storage device 201, and an interface device (I / F) 202. The I / F 202 is connected to the hardware of the voltage detection unit 11, etc. The CPU 200 executes the processing described in the first and second embodiments in accordance with the program stored in the storage device 201. [Industrial Applicability]

[0060] The present invention can be applied to a technique for measuring a rotation angle. [Explanation of symbols]

[0061] 1a...bridge circuit, 2...rotating body, 3, 4...magnets, 10-1 to 10-4...AMR elements, 11...voltage detection unit (output electrical signal detection unit), 12...rotation angle calculation unit, 13...power supply.

Claims

1. a sensor circuit including a magnetoresistive element; a magnetic field generating unit configured to generate a magnetic field that rotates around a rotation axis; an output electrical signal detection unit configured to detect an output electrical signal of the sensor circuit; a rotation angle calculation unit configured to calculate a rotation angle of the magnetic field based on the output electrical signal detected by the output electrical signal detection unit, the sensor circuit and the magnetic field generating unit are arranged so that a plane of rotation of the magnetic field intersects with a sensor surface on which a thin film resistance pattern of the magnetoresistive effect element is formed, An angle sensor characterized in that a reference position where the output electrical signal of the sensor circuit becomes zero is coincident with or parallel to the intersection line between the rotation plane of the magnetic field and the sensor surface.

2. 2. The angle sensor according to claim 1, The rotation angle calculation unit calculates a rotation angle θ of the magnetic field on the sensor surface based on the output electrical signal detected by the output electrical signal detection unit, and calculates φ=tan θ based on the rotation angle θ and an inclination angle α of the rotation plane of the magnetic field with respect to the sensor surface. -1 An angle sensor characterized by calculating a rotation angle φ of the magnetic field on the plane of rotation by (tan θ / cos α).

3. A sensor circuit including a magnetoresistive element; a magnetic field generating unit configured to generate a magnetic field that rotates around a rotation axis; an output electrical signal detection unit configured to detect an output electrical signal of the sensor circuit; a rotation angle calculation unit configured to calculate a rotation angle of the magnetic field based on the output electrical signal detected by the output electrical signal detection unit, the sensor circuit and the magnetic field generating unit are arranged so that a plane of rotation of the magnetic field intersects with a sensor surface on which a thin film resistance pattern of the magnetoresistive effect element is formed, a reference position where the output electrical signal of the sensor circuit is zero is not on the intersection line between the rotation plane of the magnetic field and the sensor surface; The angle sensor is characterized in that the rotation angle calculation unit calculates the rotation angle θ of the magnetic field on the sensor surface based on the output electrical signal detected by the output electrical signal detection unit, and calculates the rotation angle φ of the magnetic field on the rotation plane using φ = tan -1 {tan(θ - β) / cos α} + tan -1 (tan β / cos α) based on the rotation angle θ, the inclination angle α of the rotation plane of the magnetic field relative to the sensor surface, and the angle β between the reference position on the sensor surface and the intersection line.

4. 4. The angle sensor according to claim 2, The rotation angle calculation unit calculates the rotation angle θ from the output electrical signal detected by the output electrical signal detection unit using an approximation function that indicates the relationship between the output electrical signal of the sensor circuit and the rotation angle θ.

5. 5. The angle sensor according to claim 1, An angle sensor characterized in that the magnetic field is saturated with respect to the magnetoresistive effect element of the sensor circuit regardless of the rotation angle.

Images