JP6362512B2 - Reflect array antenna - Google Patents

Description

  The present invention relates to a reflectarray antenna having a primary radiator such as a horn antenna and a flat reflector.

  Conventionally, a parabolic antenna in which a primary radiator formed of a horn antenna and a parabolic curved reflector are opposed to each other is used as an antenna mounted on an artificial satellite. In general, a parabolic antenna folds a reflector when launched into space and deploys the reflector after launch, so that the structure for deploying the reflector is complicated and has a problem of low reliability during operation.

  Accordingly, a reflectarray antenna using a flat reflector instead of a parabolic reflector has been developed. Such a reflectarray antenna has a simple structure because it uses a flat reflector, and can reduce costs and improve reliability.

  The reflector plate of the reflectarray antenna is composed of a dielectric plate, a metal plate provided on the back surface of the dielectric plate, and a plurality of resonant elements arranged on the surface of the dielectric plate. The electromagnetic wave having a spherical wavefront emitted from the primary radiator is reflected in a predetermined direction by the reflector. The reflected wave includes an electromagnetic wave component reflected by the resonant element (hereinafter referred to as “reflection component”) and an electromagnetic wave component transmitted through the dielectric plate and reflected by the metal plate (hereinafter referred to as “transmission component”). Is included).

  The phase of the reflected wave composed of the reflection component and the transmission component (hereinafter referred to as “reflection phase”) is determined by the shape and size of the resonant elements, the spacing between the resonant elements, and the relative dielectric constant and thickness of the dielectric plate. Is done. The reflector of the reflectarray antenna is controlled so that the reflection phase at each position becomes a desired value by arranging resonant elements of different shapes and sizes depending on the position on the dielectric substrate. Waves are converted into plane waves and reflected.

Here, in the conventional reflectarray antenna, the resonance elements are arranged so that the distance between the center portions of the resonance elements adjacent to each other (hereinafter referred to as “arrangement interval”) d satisfies the following formula (1) ( For example, refer nonpatent literature 1).

を満たすように共振素子を配列したものである。 A reflectarray antenna according to the present invention includes a dielectric plate having a relative dielectric constant ε _r greater than 1 , a metal plate provided on the back surface of the dielectric plate, and a plurality of resonant elements arranged on the surface of the dielectric plate. And a primary radiator that is disposed opposite to the resonant element and radiates electromagnetic waves to the reflective plate, and is free of electromagnetic waves at the highest frequency in the frequency band of electromagnetic waves. The arrangement interval d of the resonant elements is expressed by the following equation, based on the spatial wavelength λ , the incident angle θ at which the incident angle of the electromagnetic wave to the reflecting plate is maximum, and the relative dielectric constant εr of the dielectric plate.

The resonance elements are arranged so as to satisfy the above.

John Huang, Jose A. Encinar, “Reflectarray Antennas”, Wiley-interscience, pp. 83-84, 2008.

  13 and 14 show an example of a conventional reflectarray antenna. A metal plate 21c is provided on the back surface of the dielectric plate 22c, and a plurality of resonance elements 23c are arranged on the surface of the dielectric plate 22c. The metal plate 21c, the dielectric plate 22c, and the resonance element 23c constitute a reflection plate 2c. A primary radiator 1c that radiates electromagnetic waves is disposed on the reflection plate 2c so as to face the resonance element 23c. The primary radiator 1c and the reflecting plate 2c constitute a reflect array antenna 103.

  The reflect array antenna 103 is an antenna having an aperture diameter of 45 centimeters (cm) used in a 12 gigahertz (GHz) band. Each resonance element 23c has a ring shape, has a different diameter depending on the arrangement position on the dielectric plate 22c, and has a desired reflection phase. Usually, the wavelength λ of the electromagnetic wave is 25 millimeters (mm), and the maximum value of the incident angle θ of the electromagnetic wave radiated from the primary radiator 1c and incident on the reflection plate 2c is 60 °. The distance d is set to 13 mm so as to satisfy the formula (1).

  When the performance of the conventional reflectarray antenna 103 and the parabolic antenna having the same aperture diameter are compared, the aperture efficiency of the parabolic antenna is about 75%, whereas the aperture efficiency of the conventional reflectarray antenna 103 is 30%. %.

  The reason why the aperture efficiency of the conventional reflectarray antenna 103 is lowered can be explained as follows. That is, in the conventional reflectarray antenna 103, the resonant elements 23c are arranged so that the arrangement interval d satisfies the formula (1), thereby preventing the generation of grating lobes due to the electromagnetic wave of the reflection component. However, even if the arrangement interval d satisfies the formula (1), it may not be possible to prevent the occurrence of grating lobes due to electromagnetic waves of the transmissive component. In this case, there is a problem that the aperture efficiency of the antenna is lowered and the side lobe level is increased.

  The present invention has been made to solve the above-described problems, and is a reflectarray antenna that improves aperture efficiency and reduces side lobes by suppressing the generation of grating lobes due to electromagnetic waves of transmission components. The purpose is to provide.

を満たすように共振素子を配列したものである。 The reflectarray antenna of the present invention is arranged so as to face the resonant element, a metal plate provided on the back surface of the dielectric plate, a flat reflector having a plurality of resonant elements arranged on the surface of the dielectric plate, and the resonant element. A primary radiator that radiates electromagnetic waves to the reflecting plate, and the free space wavelength λ of the electromagnetic waves, the incident angle θ of the electromagnetic waves to the reflecting plate, and the relative dielectric constant εr of the dielectric plate, Arrangement interval d is the following formula

The resonance elements are arranged so as to satisfy the above.

  The reflectarray antenna of the present invention can improve the aperture efficiency and reduce the side lobes by suppressing the generation of grating lobes due to electromagnetic waves of transmission components.

It is a front view which shows the principal part of the reflect array antenna of Embodiment 1 of this invention. It is a side view which shows the principal part of the reflect array antenna of Embodiment 1 of this invention. It is explanatory drawing which shows operation | movement of the reflectarray antenna of Embodiment 1 of this invention. It is explanatory drawing which shows operation | movement of the reflectarray antenna of Embodiment 1 of this invention. It is a front view which shows an example of the principal part of the antenna with an opening diameter of 45 cm for 12 GHz bands by the reflect array antenna of Embodiment 1 of this invention. It is a side view which shows an example of the principal part of the antenna with the aperture diameter of 45 cm for 12 GHz bands by the reflect array antenna of Embodiment 1 of this invention. It is a characteristic view which shows the relationship of the amplitude with respect to the azimuth | direction angle of the reflect array antenna of Embodiment 1 of this invention, the conventional reflect array antenna, and a parabolic antenna. It is a characteristic view which shows the relationship of the aperture efficiency with respect to the frequency of the reflectarray antenna of Embodiment 1 of this invention, the conventional reflectarray antenna, and a parabolic antenna. It is a front view which shows the principal part of the reflect array antenna of Embodiment 2 of this invention. It is a side view which shows the principal part of the reflect array antenna of Embodiment 2 of this invention. It is a front view which shows the principal part of the reflect array antenna of Embodiment 3 of this invention. It is a side view which shows the principal part of the reflect array antenna of Embodiment 3 of this invention. It is a front view which shows an example of the principal part of the antenna with an aperture diameter of 45 cm for 12 GHz bands by the conventional reflectarray antenna. It is a side view which shows an example of the principal part of the antenna with the aperture diameter of 45 cm for 12 GHz bands by the conventional reflectarray antenna.

Embodiment 1 FIG.
With reference to FIG.1 and FIG.2, the reflectarray antenna of Embodiment 1 of this invention is demonstrated.
In the figure, 22 is a dielectric plate. The dielectric plate 22 is made of a disk-shaped dielectric having a relative dielectric constant greater than 1. A metal plate 21 is provided over substantially the entire back surface of the dielectric plate 22. A plurality of ring-shaped resonance elements 23 are provided on the surface of the dielectric plate 22.

The resonant elements 23 are arranged at equal intervals along the first direction (X direction in the figure) on the dielectric plate 22 and along a second direction (Y direction in the figure) orthogonal to the first direction. They are arranged at equal intervals. The resonant elements 23 are arranged so that an interval (arrangement interval) d between the center portions of the resonant elements 23 adjacent to each other along the first direction and the second direction satisfies the following expression (2).

  In Equation (2), λ represents the free space wavelength at the highest frequency in the frequency band of the electromagnetic wave used, εr represents the relative permittivity of the dielectric constituting the dielectric plate 22, and θ represents the primary radiator 1. This represents the maximum value of the incident angle of the electromagnetic wave emitted from and incident on the reflector 2.

  The arrangement interval d is set to a value larger than the sum of the radii of the adjacent resonance elements 23 along the first direction and the second direction, so that the plurality of resonance elements 23 do not overlap. Yes.

  The size of the resonance element 23 differs depending on the arrangement position on the dielectric plate 22. The metal plate 21, the dielectric plate 22, and the resonance element 23 constitute a flat reflector 2.

  The primary radiator 1 is disposed so as to face the resonance element 23. The primary radiator 1 is composed of a horn antenna, for example, and radiates electromagnetic waves to the reflector 2. The primary radiator 1 and the reflection plate 2 constitute a reflect array antenna 100.

Next, with reference to FIGS. 3 and 4, the operation of the reflectarray antenna 100 will be described focusing on the operation of the transmission antenna.
3 and 4, in order to explain the operation principle in an easy-to-understand manner, using the reflector 2 having an infinitely large area, resonance elements 23 having the same shape and size are arranged infinitely at an arrangement interval d. It shall be. Further, it is assumed that an infinitely large uniform amplitude distribution plane wave is incident on the reflector 2 from the primary radiator 1.

  First, the incident wave A radiated from the primary radiator 1 is incident on the reflector 2 at an incident angle θ. As a result, an electric current is induced in the resonant element 23, and an electromagnetic wave of a part (reflected component) B of the incident wave A is reflected by the resonant element 23 at the reflection angle θ and becomes a part of the reflected wave D. On the other hand, the electromagnetic wave of the remaining component (transmission component) C1 is transmitted through the inside of the dielectric plate 22 at the transmission angle θt and reflected by the metal plate 21 on the back side. The reflected electromagnetic wave of the transmission component C1 passes through the inside of the dielectric plate 22 and enters the resonance element 23 again. A current is induced in the resonance element 23 by the electromagnetic wave of the transmission component C1, the electromagnetic wave of a part of the transmission component C1 is reflected again toward the metal plate 21, and the electromagnetic wave of the remaining component C2 is a part of the reflected wave D. It becomes. Hereinafter, by repeating the same operation, almost all electromagnetic wave components included in the incident wave A become the reflected wave D.

  The reflection phase of the reflected wave D is determined according to the size and shape of the resonant element 23, the arrangement interval d, and the relative dielectric constant εr and thickness of the dielectric plate 22. In the actual reflectarray antenna 100, by arranging the resonance elements 23 having different shapes and sizes depending on the positions on the dielectric plate 22, the reflection phase at each position is controlled to have a desired value, and the incident light is incident. The resulting spherical wave is converted to a plane wave and reflected.

  At this time, a grating lobe may be generated by the electromagnetic wave of the transmission component. That is, as shown in FIG. 4, the electromagnetic wave of a part of the transmission component E1 of the incident wave A is transmitted through the dielectric plate 22 at a transmission angle different from the transmission angle θt and reflected by the metal plate 21. The reflected electromagnetic wave of the transmission component E1 passes through the inside of the dielectric plate 22 and enters the resonance element 23 again. A current is induced in the resonant element 23 by the electromagnetic wave of the transmissive component E1, a part of the electromagnetic wave of the component E3 of the transmissive component E1 is reflected again toward the metal plate 21, and the electromagnetic wave of the remaining component E2 is a part of the scattered wave F. It becomes. Thereafter, by repeating the same operation, almost all electromagnetic wave components included in the transmission component E1 become the scattered wave F. The scattered wave F is an unnecessary radiation wave that is reflected in a direction different from the reflected wave D, and forms a grating lobe.

However, the resonant elements 23 of the reflectarray antenna 100 are arranged at an arrangement interval d that satisfies the condition of the above formula (2). This equation (2) is obtained by the following equation (3) showing the condition of the arrangement interval d that prevents the generation of the grating lobe due to the electromagnetic wave of the transmission component. This is obtained by substituting the following equation (4) indicating the relationship with the transmission angle θt of C1.

  As a result, since the expression (2) of the arrangement interval d of the reflect array antenna 100 of the first embodiment includes the expression (3), according to the arrangement of the resonant element 23, the scattered wave F shown in FIG. Can be prevented. That is, it is possible to suppress the generation of grating lobes due to electromagnetic waves of the transmission component, improve the aperture efficiency, and reduce the side lobes.

Further, since the dielectric plate 22 is made of a dielectric having a relative dielectric constant εr larger than 1, the arrangement interval d satisfying the above equation (2) causes generation of grating lobes due to electromagnetic waves of the reflection component. The following expression (5) indicating the condition to be prevented is satisfied at the same time.

  Therefore, it is possible to suppress both the generation of the grating lobe due to the reflection component electromagnetic wave and the generation of the grating lobe due to the transmission component electromagnetic wave, thereby further improving the aperture efficiency and further reducing the side lobe.

  The reflectarray antenna 100 has the same electromagnetic characteristics between the receiving antenna and the transmitting antenna according to the so-called “reversible theorem”. For this reason, illustration and description of the operation of the receiving antenna are omitted.

Next, the effect of the reflectarray antenna 100 will be described.
5 and 6 show an example of an antenna having an aperture diameter of 45 cm used in the 12 GHz band, which is configured by the reflectarray antenna 100 according to the first embodiment. The wavelength λ of the electromagnetic wave is 25 mm, the maximum value of the incident angle θ of the electromagnetic wave radiated from the primary radiator 1 and incident on the reflection plate 2 is 60 °, and the relative dielectric constant of the dielectric constituting the dielectric plate 22 Since εr is 2.65, the arrangement interval d is set to 9.5 mm so as to satisfy Expression (2).

  FIG. 7 is a characteristic diagram showing the amplitude (Amplitude) of the electromagnetic wave with respect to the azimuth angle (Azimuth) of the antenna. A characteristic line I indicates the characteristic of the reflectarray antenna 100 according to the first embodiment shown in FIGS. 5 and 6. A characteristic line II indicates a characteristic of a parabolic antenna having an aperture diameter equivalent to that of the reflect array antenna 100 as a comparison target.

  As shown in FIG. 7, when the azimuth angle is in the range of about −5 ° to + 5 °, the amplitudes of the characteristic line I and the characteristic line II are equal, and a main lobe is formed. When the azimuth angle is in the range of −60 ° to −5 ° and in the range of + 5 ° to + 60 °, the amplitude of the characteristic line I is approximately −30 decibels (dB) or less like the characteristic line II. Particularly, when the azimuth angle is in the range of −20 ° to −5 ° and in the range of + 5 ° to + 20 °, the amplitude of the characteristic line I is smaller than that of the characteristic line II, and the side lobe is reduced.

  FIG. 8 is a characteristic diagram showing the aperture efficiency (aperture efficiency) of the antenna with respect to the frequency (frequency) of electromagnetic waves. A square plot I shows the aperture efficiency of the reflectarray antenna 100 of the first embodiment shown in FIGS. 5 and 6. A triangular plot II shows the aperture efficiency of the conventional reflectarray antenna 103 shown in FIGS. 13 and 14 as a comparison object. A rhombus plot III shows the aperture efficiency of a parabolic antenna having an aperture diameter equivalent to that of the reflectarray antenna 100 as a comparison object.

  As shown in FIG. 8, the aperture efficiency of the parabolic antenna is about 75% to 80% over the frequency range of 11.7 GHz to 12.4 GHz. On the other hand, the aperture efficiency of the conventional reflectarray antenna 103 is about 25% to 30% over the frequency range of 11.7 GHz to 12.4 GHz. In contrast, the aperture efficiency of the reflectarray antenna 100 of the first embodiment exceeds 60% over a wide frequency range of 11.8 GHz to 12.4 GHz, and the aperture efficiency is higher than that of the conventional reflectarray antenna 103. It has risen by over 30%.

  In other words, the reflectarray antenna 100 according to the first embodiment maintains the superiority over the parabolic antenna that the cost can be reduced and the reliability can be improved by using the flat reflector 2. An aperture efficiency close to that of a parabolic antenna can be realized by raising the aperture efficiency as compared with the antenna 103.

  In the reflectarray antenna 100 with the arrangement interval d of 9.5 mm, when the frequency of the electromagnetic wave is 12.7 GHz, a grating lobe due to a transmission component is generated when the incident angle θ is 59.1 ° or more. However, since the incident angle θ is 59.1 ° or more is only an extremely narrow portion at the end of the reflector 2, it is considered that the influence on the aperture efficiency was small.

  As described above, in the reflectarray antenna 100 of Embodiment 1, the resonant elements 23 are arranged so that the arrangement interval d satisfies the formula (2). Thereby, generation | occurrence | production of the grating lobe by the electromagnetic wave of a permeation | transmission component can be suppressed, an aperture efficiency can be improved, and a side lobe can be reduced.

  The dielectric plate 22 is made of a dielectric having a relative dielectric constant εr larger than 1. As a result, since the arrangement interval d satisfies the expression (2) and simultaneously satisfies the expression (5), both the generation of the grating lobe due to the reflection component electromagnetic wave and the generation of the grating lobe due to the transmission component electromagnetic wave are suppressed. Thus, the aperture efficiency can be further improved and the side lobes can be further reduced.

  In addition, the free space wavelength λ of Expression (2) is set to the free space wavelength at the highest frequency in the frequency band of the electromagnetic wave to be used. The incident angle θ in Expression (2) is set to the maximum value of the incident angle of the electromagnetic wave incident on the reflector 2 from the primary radiator 1. For this reason, it is possible to suppress the generation of grating lobes due to the electromagnetic wave of the transmission component over substantially the entire frequency band of the electromagnetic wave to be used. In addition, it is possible to suppress the generation of grating lobes due to the electromagnetic wave of the transmission component over substantially the entire electromagnetic wave incident on the reflector 2 from the primary radiator 1.

  The antenna used for primary radiator 1 is not limited to a horn antenna. When operating as a transmitting antenna, any antenna may be used as long as it radiates electromagnetic waves to the reflecting plate 2 and when operating as a receiving antenna receives the electromagnetic waves reflected by the reflecting plate 2. .

  Further, the shape of each resonance element 23 is not limited to a ring shape. Depending on the desired reflection phase, the shape may be circular, square, triangular, plus sign or rectangular frame.

  Moreover, the shape of the reflecting plate 2 should just be flat form, and is not limited to disk shape. Depending on the mounting conditions on the satellite and the aperture shape of the antenna used for the primary radiator 1, a reflector 2 having a rectangular plate shape or a polygonal plate shape may be used.

Embodiment 2. FIG.
With reference to FIGS. 9 and 10, a reflectarray antenna in which the arrangement of the resonant elements is different from that in the first embodiment will be described. Components similar to those of the reflectarray antenna 100 of Embodiment 1 shown in FIGS. 1 and 2 are denoted by the same reference numerals, and description thereof is omitted.

  A plurality of ring-shaped resonance elements 23 a are arranged on the surface of the dielectric plate 22. The resonant elements 23a are arranged at equal intervals along the first direction (X direction in the figure) on the dielectric plate 22, and along the second direction (Y direction in the figure) orthogonal to the first direction. They are arranged at equal intervals.

  Here, the arrangement interval dx along the first direction of the resonance element 23a and the arrangement interval dy along the second direction are different from each other. The resonance elements 23a are arranged so that the larger one of the two arrangement intervals dx and dy satisfies the same expression (2) as in the first embodiment. In this way, the reflect array antenna 101 is configured.

  When the larger arrangement interval dx of the arrangement intervals dx and dy satisfies the equation (2), the smaller arrangement interval dy simultaneously satisfies the equation (2). Therefore, the reflect array antenna 101 according to the second embodiment, like the reflect array antenna 100 according to the first embodiment, suppresses the generation of grating lobes due to electromagnetic waves of transmission components, thereby improving the aperture efficiency and reducing the side lobes. can do.

  The dielectric plate 22 is made of a dielectric having a relative dielectric constant εr larger than 1. As a result, both the arrangement intervals dx and dy satisfy Expression (2) and simultaneously satisfy Expression (5). Therefore, as in the first embodiment, both the generation of the grating lobe due to the reflection component electromagnetic wave and the generation of the grating lobe due to the transmission component electromagnetic wave are suppressed to further improve the aperture efficiency and further reduce the side lobe. be able to.

Embodiment 3 FIG.
With reference to FIGS. 11 and 12, a reflectarray antenna in which the arrangement of the resonant elements is different from those in the first and second embodiments will be described. Components similar to those of the reflectarray antenna 100 of Embodiment 1 shown in FIGS. 1 and 2 are denoted by the same reference numerals, and description thereof is omitted.

  A plurality of ring-shaped resonance elements 23 b are arranged on the surface of the dielectric plate 22. The plurality of resonance elements 23b are arranged so that the three resonance elements 23b adjacent to each other are positioned at the apexes of the equilateral triangle.

  The arrangement interval d of the resonance elements 23b corresponds to the length of one side of the equilateral triangle. The resonance elements 23b are arranged so that the arrangement interval d satisfies the same expression (2) as that in the first embodiment. In this way, the reflect array antenna 102 is configured.

  In the reflectarray antenna 102 of the third embodiment, the arrangement interval d of the resonance elements 23b satisfies the formula (2). Therefore, similarly to the reflectarray antenna 100 of the first embodiment, it is possible to suppress the generation of grating lobes due to electromagnetic waves of transmission components, improve the aperture efficiency, and reduce the side lobes.

  Further, since the dielectric plate 22 is made of a dielectric having a relative dielectric constant εr larger than 1, the arrangement interval d satisfies the expression (2) and simultaneously satisfies the expression (5). Therefore, as in the first embodiment, both the generation of the grating lobe due to the reflection component electromagnetic wave and the generation of the grating lobe due to the transmission component electromagnetic wave are suppressed to further improve the aperture efficiency and further reduce the side lobe. be able to.

  In the present invention, within the scope of the invention, any combination of the embodiments, or any modification of any component in each embodiment, or omission of any component in each embodiment is possible. .

  1,1c primary radiator, 2,2c reflector, 21,21c metal plate, 22,22c dielectric plate, 23,23a, 23b, 23c resonant element, 100,101,102,103 reflectarray antenna.

Claims (3)

A flat plate composed of a dielectric plate having a relative dielectric constant ε _r larger than 1 , a metal plate provided on the back surface of the dielectric plate, and a plurality of resonant elements arranged on the surface of the dielectric plate. Shaped reflector,
A primary radiator disposed opposite to the resonant element and radiating electromagnetic waves to the reflector; and
The free space wavelength λ of the electromagnetic wave at the highest frequency in the frequency band of the electromagnetic wave , the incident angle θ where the incident angle of the electromagnetic wave to the reflecting plate is the maximum value, and the relative dielectric constant ε _{r of the} dielectric plate The arrangement interval d of the resonant elements is

The reflect array antenna, wherein the resonant elements are arranged so as to satisfy A flat plate composed of a dielectric plate having a relative dielectric constant ε _r larger than 1 , a metal plate provided on the back surface of the dielectric plate, and a plurality of resonant elements arranged on the surface of the dielectric plate. Shaped reflector,
A primary radiator disposed opposite to the resonant element and radiating electromagnetic waves to the reflector; and
The plurality of resonance elements are arranged at equal intervals along a first direction at a first arrangement interval, and differ from the first arrangement interval along a second direction orthogonal to the first direction. Arranged at equal intervals in the second arrangement interval,
The free space wavelength λ of the electromagnetic wave at the highest frequency in the frequency band of the electromagnetic wave , the incident angle θ where the incident angle of the electromagnetic wave to the reflecting plate is the maximum value, and the relative dielectric constant ε _{r of the} dielectric plate Thus, the larger arrangement interval d of the resonance elements of the first arrangement interval and the second arrangement interval is expressed by the following formula.

The reflect array antenna, wherein the resonant elements are arranged so as to satisfy A flat plate composed of a dielectric plate having a relative dielectric constant ε _r larger than 1 , a metal plate provided on the back surface of the dielectric plate, and a plurality of resonant elements arranged on the surface of the dielectric plate. Shaped reflector,
A primary radiator disposed opposite to the resonant element and radiating electromagnetic waves to the reflector; and
The plurality of resonant elements are arranged such that three adjacent resonant elements are arranged at the vertices of an equilateral triangle, respectively.
The free space wavelength λ of the electromagnetic wave at the highest frequency in the frequency band of the electromagnetic wave , the incident angle θ where the incident angle of the electromagnetic wave to the reflecting plate is the maximum value, and the relative dielectric constant ε _{r of the} dielectric plate The arrangement interval d of the resonance elements, which is the length of one side of the equilateral triangle, is expressed by the following formula:

The reflect array antenna, wherein the resonant elements are arranged so as to satisfy

Images