JPH0593694A - Method and device for inspecting cylindrical surface - Google Patents

Abstract

PURPOSE:To obtain a device for inspecting a defect such as a flaw or nonuniformity in plating in the surface of a cylinder for a photogravure press or the like. CONSTITUTION:A light emitted by a light source 10 disposed inside a parabolic mirror 8 is made to be a light H of which the cross-sectional shape of the light flux is circular, by a round cover plate 12 covering the central part of the parabolic mirror 8. This light H advances in the direction Y along the surface 2a of a cylinder and it is transmitted through a half mirror 16 and falls on a region T to be inspected of the surface 2a of the cylinder from the direction of a normal line. A reflected light H' thereof follows the forward path reversely and falls on an incident surface of the half mirror 16. The reflected light H' transmitted in the direction Z through the half mirror 16 is reflected in the direction Y by a mirror 18 and projected on a screen 6. An image 22 projected on the screen 6 is an image of the outer peripheral surface of the cylinder 2 in the region T to be inspected and, therefore, a defect in the region T can be detected from the projected image 22.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a cylindrical surface inspection method and apparatus for inspecting defects on the cylindrical surface, such as scratches and plating unevenness on the surface of a cylinder for a gravure printing machine.

[0002]

2. Description of the Related Art Conventionally, in order to detect defects such as scratches and uneven plating on the surface of a cylinder for a gravure printing machine, visual inspection and surface observation with an optical microscope have been conventionally performed. There is no known inspection method or inspection apparatus suitable for the above.

[0003]

However, it is difficult to find minute defects by visual inspection by visual inspection. Further, in surface observation with an optical microscope, it takes time to perform observation over a wide range of the cylinder surface. Therefore, in place of the visual inspection and the optical microscope inspection, there is a demand for the development of an inspection method and an apparatus suitable for the inspection of defects on the surface of the cylinder.

The present invention has been made in order to meet such a demand, and an object thereof is to provide a cylindrical surface inspection method and a cylindrical surface inspection method capable of executing a defect inspection over a wide range of a cylinder surface in a short time. It is to provide a device.

[0005]

In order to achieve the above object, a cylindrical surface inspection method according to the present invention allows light emitted from a light source to be directed to a surface of a region to be inspected formed by at least a part of a mirror-like cylindrical surface. On the other hand, the step of making the light incident from the normal direction of the surface of the test area and the optical path of the reflected light in the normal direction of the surface of the test area to the incident light are converted to one direction along the longitudinal direction of the cylindrical surface. And a step of forming a two-dimensional image corresponding to the surface of the region to be inspected by two-dimensionally projecting the light whose path has been changed.

Further, the cylindrical surface inspection apparatus of the present invention comprises a light source means and a light emitted from the light source means with respect to an area to be inspected formed by at least a part of a mirror-like cylindrical surface. An incident means for making incident light from the normal direction of the surface, a converting means for converting the optical path of the vertically reflected light from the surface of the region to be inspected for the incident light into one direction along the longitudinal direction of the cylindrical surface, and this direction conversion The above-described object is achieved by including a projection unit that forms a two-dimensional image corresponding to the surface of the region to be inspected by two-dimensionally projecting the generated light.

In this case, a longitudinal scanning means for scanning the surface of the test region along the longitudinal direction of the cylindrical surface by integrally moving the incident means and the converting means along the longitudinal direction of the cylindrical surface. It may be further provided.

Another cylindrical surface inspection apparatus of the present invention comprises a light source means and a light emitted from the light source means with respect to an area to be inspected formed by at least a part of a mirror-like cylindrical surface. Incidence means for making the light incident in the normal direction of the surface, conversion means for changing the optical path of the vertically reflected light from the surface of the region to be examined with respect to the incident light, to one direction along the longitudinal direction of the cylindrical surface, and the direction conversion Projecting means for forming a two-dimensional image corresponding to the surface of the region to be inspected by two-dimensionally projecting the generated light, an image capturing means for capturing the two-dimensional image, and an image obtained by the image capturing means. Based on the binarization means for forming a binarized signal corresponding to the light and darkness caused by the surface defect of the inspection area surface, and determining whether there is a defect on the inspection area surface based on the binarized signal And means.

Instead of the judging means, an output means for outputting the binarized distribution of the image based on the binarized signal may be provided.

According to the embodiment of the present invention, the cylindrical surface inspection apparatus having the image pickup means is configured such that the incident means, the conversion means, and the image pickup means are integrally moved along the longitudinal direction of the cylindrical surface so that the cylindrical surface is inspected. It further comprises a longitudinal scanning means for scanning the surface of the test region along the longitudinal direction of the surface.

According to an embodiment of the present invention, the cylindrical surface in the method and apparatus described above is the outer surface of a subject having a cylindrical shape. However, this cylindrical surface may be the inner surface of the subject having a hollow cylindrical shape.

[0012]

According to the method and apparatus of the present invention, the optical path of the reflected light reflected from the surface of the test area in the normal direction with respect to the light incident on the surface of the test area in the normal direction is defined by the longitudinal direction of the cylindrical surface. By being converted into one direction along the direction, the test area surface as a curved surface is projected as a planar image.

[0013]

DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 1 shows, as a first embodiment of the present invention, a conceptual apparatus configuration for achieving the cylindrical surface inspection method of the present invention. In this embodiment, for simplicity of explanation, it is assumed that there is no optical path shield such as a mechanical device existing on the optical path.

In FIG. 1, the cylinder 2 to be measured is shown.
Is, for example, a cylinder for a gravure printing machine, and its outer surface is mirror-finished by plating or the like. In the following description, the direction along the longitudinal direction of the cylinder 2 is the Y-axis direction, and the radial direction of the cylinder 2 is the Z-axis direction.
A surface light source 4 and a screen 6 are arranged on both ends of the cylinder 2 in the Y-axis direction.

As shown in FIG. 2, in particular, the surface light source 4 includes a parabola mirror-8, a light source 10 disposed inside the parabola mirror-8, and a circular shield plate 1 for covering a central portion of the parabola mirror-8 in a circular shape.
2 and. The light (hereinafter, referred to as measurement light) H emitted from the surface light source 4 is a plane light having a circular cross-sectional shape of the light flux. That is, the measurement light H emitted from the surface light source 4 travels in a virtual hollow cylindrical shape as indicated by reference numeral 24.

Referring again to FIG. 1, the cylinder 2 is
The measurement light H emitted from the surface light source 4 is arranged coaxially with the hollow cylindrical shape and on the inner peripheral side of the hollow cylindrical shape.

Here, the cylindrical surface formed by the surface in a partial area T of the cylinder 2 in the longitudinal direction is taken as the inspection surface. An annular half mirror 16 is arranged coaxially with the cylinder 2 on the optical path of the measurement light H on the outer peripheral side of the cylinder 2 on the front side of the area T when viewed from the surface light source 4.
The half mirror 16 has an inner peripheral surface facing the surface light source 4 as a transmissive surface and an outer peripheral surface facing the screen 6 as a reflective surface.

Further, an annular mirror 18 is coaxially arranged on the outer peripheral side of the half mirror 16. This mirror 1
The outer peripheral surface of the cylinder 2 and the inner peripheral surface of the cylinder 8 facing the screen 6 are reflection surfaces.

FIG. 3 shows the optical system as described above in the cylinder 2
The figure which showed the cross section along the longitudinal direction of FIG. However, since the above optical system is substantially rotationally symmetric with respect to the longitudinal axis of the cylinder 2, only the cross section above the cylinder 2 is shown.

The operation of the apparatus of the first embodiment will be described below with reference to FIGS. 1 and 3.

The measurement light H emitted from the surface light source 4 travels in the direction of the arrow along the Y-axis direction, and is inspected (area T) on the cylinder surface 2a along the Z-axis direction by the half mirror 16.
(Cylindrical surface at) is reflected toward. That is, the measurement light H is incident on the inspection surface of the cylinder surface 2a from the direction normal to the inspection surface.

Next, the reflected light H'reflected on the inspection surface of the cylinder surface 2a is reflected upward in the Z-axis direction so as to follow the forward path in the reverse direction, and further mirror-18. Is reflected toward the screen 6 along the Y-axis direction. The reflected light H'reflected by the mirror 18 is projected on the screen 6. The projected image 22
Corresponds to an image in which the surface to be measured on the surface of the cylinder 2 is two-dimensionally shown as a ring. From this projected image 22, the inspection surface of the cylinder surface 2a can be observed. Also, each Mira-16,1
The inspection surface can be scanned along the longitudinal direction of the cylinder surface 2a by moving the mirror group including 8 or the cylinder 2 along the Y-axis direction by an appropriate means.

Each mirror-16, 18 as shown in FIGS.
According to the arrangement, the width along the Y direction of the inspection surface per inspection is determined according to the size of each of the mirrors 16 and 18. For example, as shown in FIGS. 4 and 5, when each of the mirrors 16, 18 is small (FIG. 4), the width T _{1 of the} inspection surface is also small and each of the mirrors 16, 18 is large (FIG. 5). Has a large width T ₂ of its inspection surface (T ₂ > T ₁ ).

Therefore, the number of inspections can be suppressed to a necessary minimum by appropriately selecting the sizes of the respective mirrors 16 and 18, and more reliable inspection can be performed over the entire surface of the cylinder 2. Become. Further, since the inspection light H is incident on the surface of the cylinder 2 in the normal direction, each mirror-1
By appropriately selecting the inner diameters of 6 and 18, it is possible to inspect cylinders having various diameters.

Next, the image 22 projected on the screen 6
6 and 7 for a method for detecting defects on the inspection surface from
Will be described.

When there is a defect, for example, a convex portion 26 (FIG. 6) due to uneven plating or the like and a concave portion 28 (FIG. 7) such as a relatively large scratch, on the inspection surface of the cylinder surface 2a, the inspection surface with respect to the incident direction. The reflected light H'which should be reflected vertically is disturbed by the scratch, travels with a spread proportional to the distance L from the inspection surface to the screen 6, and is projected on the screen 6 in a light-dark distribution. It That is, the distribution of the reflected light rays of the reflected light H'is dense in the bright portion W on the light-dark distribution, and is also sparse in the dark portion B. On the screen 6, this difference in brightness is magnified to a size that can be sufficiently visually confirmed.

When a relatively small scratch is present as a defect on the inspection surface of the cylinder surface 2a, the reflected light H'from the inspection surface is reflected from the scratch and from a portion without the scratch. Includes light that interferes with light. Therefore, interference fringes are observed in the projected image 22 on the screen 6.

In the above-mentioned embodiment, since it is assumed that there are no optical path shields such as mechanical elements, the inspection surface in one inspection is assumed to extend over the entire circumference in the region T of the cylinder 2. The projected image 22 is projected as a continuous ring. However, in an actual device, the optical path is blocked by a mechanical device or the like, so that the inspection surface that can be inspected by one inspection is a part of the region T in the circumferential direction. Therefore, each of the mirrors 16, 18 does not necessarily have an annular shape, and may have an arc shape that covers a part of the region T in the circumferential direction. Similarly, the cross-sectional shape of the luminous flux of the measurement light H emitted from the surface light source 4 does not necessarily have to be an annular shape, and may be an arc shape that is a part of the annular shape.

FIG. 8 shows a second embodiment of the present invention. In this embodiment, each mirror-1 in the apparatus shown in the first embodiment is
6, 18 and the drive system for the cylinder 2 are provided, and the same components as those in the first embodiment are designated by the same reference numerals.

In FIG. 8, the detection unit 30 has a built-in mirror group consisting of the respective mirrors 16, 18 (not shown in FIG. 8). The positional relationship of the mirror group with respect to the cylinder 2 is the same as in the first embodiment. The detection unit 30 is fixed to a moving rail 32 that is arranged near the cylinder 2 along the Y-axis direction. This moving rail 3
2 is driven by the Y-axis motor 34 to detect the detection unit 30.
It is movable integrally with the Y-axis direction.

Further, one end of the rotary shaft 36, which substantially coincides with the longitudinal center axis of the cylinder 2, is connected to the drive shaft 40a of the θ-axis motor 40 via the drive side bearing portion 38, and the other end is connected to the driven side bearing portion 42. It is rotatably supported by. Therefore, by driving the θ-axis motor 40, the cylinder 2 rotates in the θ direction around the rotation shaft 36.

The Y-axis motor 34 and the θ-axis 40 are controlled by the motor controller 44. Commands for driving, stopping, and rotating speed of the motors 34, 40 by the motor control unit 44 are
It is given by the operator operating an input device such as a control box 46 attached to the motor control unit 44.

In this second embodiment, mechanical elements such as bearings 38 and 42 for supporting the cylinder 2 partially block the optical path, as shown in FIG. Therefore, the image projected on the screen 6 is not the image over the entire circumference of the inspection surface in the circumferential direction, but the image 22 is partially shielded as shown in FIG. Therefore, by operating the control box 46,
By rotating the cylinder 2, the inspection is performed over the entire circumference of the inspection surface in the circumferential direction. Further, by operating the control box 46, the detection unit 30 is moved in the Y-axis direction, and the inspection is repeated while scanning the inspection surface in the Y-axis direction, so that the entire surface of the cylinder surface 2a is finally inspected.

FIG. 11 shows a third embodiment of the present invention. A CCD camera 48 for capturing the image 22 on the screen 6 is attached to the detection unit 30 in this embodiment. In this embodiment, an image obtained from the projected image 22 of the inspection surface is digitally processed by the CCD camera 48 to perform a binarization process of bright / dark (white / black), and the scanning of the inspection surface is automated. , It is intended to automate the inspection. In the third embodiment, the same components as those in the second embodiment are designated by the same reference numerals.

In FIG. 11, the centralized management unit 50 is set with information on the initial condition of the inspection from an input means (not shown) such as a keyboard attached to the centralized management unit 50. Here, the initial condition is the length of the cylinder 2, the binarization level, the determination level of the determination unit 64 described later, and the like. The setting signal S1 as information of these initial conditions is given to the system control unit 52 which controls the entire inspection apparatus. In addition, this system control unit 5
2 generates a monitor signal S2 of each part of the inspection device such as the amount of movement of the CCD camera 48, and feeds this monitor signal S2 back to the central management part 50. Accordingly, the centralized management unit 50 monitors the entire inspection device.

When the system control unit 52, to which the setting signal S1 is applied as described above, applies the inspection start signal S3 to the timing generation unit 54, the inspection is executed as follows.

First, the projected image 22 by the CCD camera 48
The determination of defects based on the image capturing will be described. The timing generation unit 54 gives the image pickup timing signal S5 to the camera control unit 56 which controls the image pickup signal S4 of the CCD camera 48. Thereby, the CCD camera 48 captures the projection image 22.

The surface of the cylinder 2a corresponding to this image pickup area is divided in the longitudinal direction and the circumferential direction of the cylinder 2 according to the field of view of the CCD camera 48, as shown in FIGS. Each cell T _ij in FIG. 12 and FIG.
(i = 1,2,3 ... n, j = 1,2,3 ... n) corresponds to one imaging region.

The image pickup signal of the CCD camera 48 is given to the binarization processing unit 58 via the camera control unit 56 and binarized. The binarization signal S6 by the binarization processing unit 58
Are provided to the image memory 60 and stored therein. The stored binarized signal S6 is given to the counting control unit 62 which controls the white / black counting. Count control unit 62
Counts white / black of the binarized signal based on the count start signal S7 of the timing generation section 54, and gives the count result to the determination section 64. The determination unit 64 determines the presence or absence of a defect based on the counting result of the counting control unit 62, and displays the determination result on a display unit 66 such as a display.

As the display unit 66, a buzzer, a lamp or the like for notifying the operator of the existence of the defect may be used.
Further, instead of the determination unit 64 and the display unit 66, the binarized distribution obtained by the binarization processing unit 58 may be output to an output unit such as a printer or a display. In this case, the operator determines the presence or absence of a defect by referring to the output binarized distribution.

On the other hand, the scan of the inspection surface is given from the timing generating section 54 to the position signal generating section 68.
This is executed based on the movement timing signal S8 of the camera 48. The position signal generator 68 is further supplied with the position information signal S9 of the CCD camera 48 from the system controller 52. The position signal generator 68 determines the amount of movement of the CCD camera 48 based on the movement timing signal S8 and the position information signal S9, and the CCD is sent to the motor controller 44.
A position signal S10 as a movement command for the camera 48 is given. As a result, the motor control unit 44 causes the Y-axis motor 3
The CCD camera 48 is automatically moved in the circumferential direction (column direction in FIGS. 12 and 13) and the length direction (row direction in FIGS. 12 and 13) of the cylinder 2 by driving the 4 and θ-axis motors 40. .. Along with this automatic movement, from the above-mentioned image pickup of the projected image 22 by the CCD camera 48, defect determination based on the image pickup is performed over a desired area or the entire surface of the cylinder surface 2a.

According to this third embodiment, the detection unit 3
The 0 and / or surface light source 4 need only be large enough to cover the viewing angle of the CCD camera 48. Therefore, the detection unit 30 and / or the surface light source 4 does not need to extend over the entire circumference of the cylinder 2, and may have an arc-shaped cross section that partially covers the peripheral surface of the cylinder 2 as shown in FIG. Is possible. Due to this miniaturization, the work space for the replacement work of the cylinder 2 is largely secured.

Comparing the second and third embodiments, in the second embodiment, as shown in FIG.
The optical path length L of the reflected light H'from the mirror 18 to the screen 6 varies depending on the position in the Y direction, and the defect enlargement ratio changes.

On the other hand, in the third embodiment, the area of one inspection is limited by the viewing angle and resolution of the CCD camera 48 as compared with the second embodiment, and the required number of measurements is increased as compared with the second embodiment. To do. However, at any position of the cylinder 2, the reflected light H ′ from the inspection surface is reflected by the CCD camera 4
Since the distance until reaching 8 is kept constant, there is an advantage that the enlargement ratio does not change.

Although the outer peripheral surface of the cylinder 2 is the surface to be inspected in each of the above embodiments, the present invention is not limited to this, and the inner peripheral surface of the hollow cylindrical object having a mirror-like inner peripheral surface. It is also applicable to the inspection. In this case, the respective mirrors 16 and 18 are arranged on the inner surface side of the hollow cylindrical object so that the optical paths of the measurement light H and the reflected light H ′ pass through the inside of the hollow cylindrical object, so that the same as in the above embodiments. Various inspections can be performed.

[0046]

As described above, according to the method and apparatus for inspecting a cylindrical surface of the present invention, it is possible to project a curved surface of a region to be inspected as a planar image. Defects are easier to detect than inspections and optical microscope inspections, and defect inspections can be performed over a wide range of a cylindrical surface in a short time.

[Brief description of drawings]

FIG. 1 is a configuration diagram conceptually showing a cylindrical surface inspection apparatus according to a first embodiment of the present invention.

FIG. 2 is an explanatory diagram for explaining the operation of the surface light source in FIG.

3 is an optical path diagram showing an optical path in an upper portion of a cylinder of the apparatus shown in FIG.

FIG. 4 is a diagram corresponding to FIG. 3 and is an optical path diagram showing an optical path when a mirror is small.

FIG. 5 is a view corresponding to FIG. 3 and is an optical path diagram showing an optical path when a mirror is large.

FIG. 6 is an explanatory diagram for explaining the principle of defect detection in the method and apparatus of the present invention, and is a diagram showing a light ray distribution on a screen when a convex portion is present on the inspection area surface.

FIG. 7 is an explanatory diagram corresponding to FIG. 6 and is a diagram showing a light ray distribution on the screen when a concave portion is present on the inspection region surface.

FIG. 8 is a configuration diagram showing a second embodiment of the present invention.

9 is a diagram showing the device of FIG. 8 as viewed in the direction of arrows ix-ix.

10 is a plan view showing an image projected on the screen of the apparatus of FIG.

FIG. 11 is a configuration diagram showing a third embodiment of the present invention.

FIG. 12 is an explanatory diagram showing an example in which the inspection area on the cylinder surface is divided according to the viewing angle of the CCD camera in the third embodiment.

13 is a development view showing the cylinder surface in FIG. 12 in a two-dimensional manner.

14 is a diagram showing an example of a cross-sectional shape of the detection unit in FIG.

FIG. 15 is an optical path diagram for explaining a change in the optical path length from the mirror to the screen according to the position of the detection unit.

[Explanation of symbols]

4 ... Surface light source (light source means), 2 ... Cylinder (cylindrical object), 2a ... Cylinder surface (cylindrical surface), 6 ... Screen (projection means), 16 ... Half mirror (conversion means), 18
... Mirror (converting means), 34 ... Y-axis motor (longitudinal direction scanning means), 40 ... θ-axis motor (circumferential direction scanning means), 48
... CCD camera (imaging means), 58 ... Binarization processing section (binarization means), 64 ... Judgment section (judgment means).

Claims (11)

[Claims] 1. A method for inspecting a mirror-like cylindrical surface, wherein light emitted from a light source is directed to a surface of a test area formed by at least a part of the cylindrical surface in a direction normal to the surface of the test area. The incident light, the step of changing the optical path of the reflected light in the normal direction of the test area surface to the incident light to one direction along the longitudinal direction of the cylindrical surface, and the light path-converted light Forming a two-dimensional image corresponding to the surface of the region to be inspected by two-dimensionally projecting;
A method for inspecting a cylindrical surface, comprising: 2. The cylindrical surface inspection method according to claim 1, wherein the cylindrical surface is an outer surface of an object having a cylindrical shape. 3. The cylindrical surface inspection method according to claim 1, wherein the cylindrical surface is an inner surface of an object having a hollow cylindrical shape. 4. An apparatus for inspecting a mirror-like cylindrical surface, comprising: light source means; and light emitted from the light source means with respect to an area to be inspected formed by at least a part of the cylindrical surface. Incident means for making incident light from the direction normal to the area surface, and conversion means for changing the optical path of vertically reflected light from the area to be inspected for that incident light into one direction along the longitudinal direction of the cylindrical surface, and this direction A cylindrical surface inspection apparatus comprising: a projection unit that forms a two-dimensional image corresponding to the surface of the region to be inspected by two-dimensionally projecting the converted light. 5. A longitudinal direction scanning means for scanning the surface of the test region along the longitudinal direction of the cylindrical surface by integrally moving the incident means and the converting means along the longitudinal direction of the cylindrical surface. The cylindrical surface inspection apparatus according to claim 4, further comprising: 6. An apparatus for inspecting a mirror-like cylindrical surface, comprising: a light source means; and light emitted from the light source means with respect to an area to be inspected formed by at least a part of the cylindrical surface. Incident means for making incident light from the direction normal to the area surface, conversion means for converting the optical path of the vertically reflected light from the area to be inspected for the incident light into one direction along the longitudinal direction of the cylindrical surface, and the above direction. Projecting means for forming a two-dimensional image corresponding to the surface of the region to be inspected by two-dimensionally projecting the converted light, an image capturing means for capturing the two-dimensional image, and an image obtained by the image capturing means. Based on the binarization means for forming a binarization signal corresponding to the lightness and darkness caused by the surface defect of the test area surface, and based on the binarization signal, outputs the binarization distribution of the image. Cylindrical surface inspection characterized by comprising output means Location. 7. An apparatus for inspecting a surface defect of a mirror-like cylindrical surface, comprising: a light source means; and light emitted from the light source means with respect to a surface of a region to be inspected formed by at least a part of the cylindrical surface. Incident means for allowing the light to enter from the normal direction of the surface of the test area, and conversion means for converting the optical path of the vertically reflected light from the surface of the test area with respect to the incident light into one direction along the longitudinal direction of the cylindrical surface. , A projection means for two-dimensionally projecting the direction-converted light to form a two-dimensional image corresponding to the surface of the region to be examined, an imaging means for capturing the two-dimensional image, and an imaging means for obtaining the two-dimensional image. Based on the image, the binarizing means for forming a binarized signal corresponding to the light and darkness caused by the surface defect of the inspection area surface, and the presence or absence of the defect of the inspection area surface based on the binarized signal. Cylindrical surface inspection, characterized by comprising: Location. 8. A longitudinal scan for scanning the surface of the test region along the longitudinal direction of the cylindrical surface by integrally moving the incident means, the converting means and the imaging means along the longitudinal direction of the cylindrical surface. 8. The cylindrical surface inspection apparatus according to claim 6, further comprising means. 9. The method according to claim 9, further comprising a circumferential direction scanning means for moving the cylindrical surface along the circumferential direction of the cylindrical surface to scan the surface of the region to be tested along the circumferential direction of the cylindrical surface. The cylindrical surface inspection device according to any one of 4 to 8. 10. The cylindrical surface inspection apparatus according to claim 4, wherein the cylindrical surface is an outer surface of a subject having a cylindrical shape. 11. The cylindrical surface inspection apparatus according to claim 4, wherein the cylindrical surface is an inner surface of a subject having a hollow cylindrical shape.