WO2017204560A1

WO2017204560A1 - Method and apparatus of detecting particles on upper surface of glass, and method of irradiating incident light

Info

Publication number: WO2017204560A1
Application number: PCT/KR2017/005418
Authority: WO
Inventors: Sungchan HWANG; Jihwa Jung; Taeho Keem; Hyeongcheol Lee; Sungjong Pyo
Original assignee: Corning Precision Materials Co Ltd
Current assignee: Corning Precision Materials Co Ltd
Priority date: 2016-05-25
Filing date: 2017-05-24
Publication date: 2017-11-30
Anticipated expiration: 2018-11-25
Also published as: TW201807404A; CN109564170A; JP6953446B2; JP2019516998A; KR20170133113A

Abstract

A particle detecting method including: disposing a rotatable mirror on a path of light emitted from a light source so that the mirror reflects the light to irradiate an incident light to the upper surface; calculating an incident angle of the incident light so that a first region where the incident light meets the upper surface of the glass and a second region where light transmits through the glass and meets a lower surface of the glass do not overlap with each other when viewed from above; rotating the mirror based on the calculated incident angle; acquiring an image of the first region with a camera disposed above the first region while conveying the glass in a horizontal direction; and detecting particles by analyzing the acquired image. The detected particles are considered as existing on the upper surface.

Description

METHOD AND APPARATUS OF DETECTING PARTICLES ON UPPER SURFACE OF GLASS, AND METHOD OF IRRADIATING INCIDENT LIGHT

This application claims the benefit of priority of Korean Patent Application Serial No. 10/2016/0064134 filed on May 25, 2016, the content of which is relied upon and incorporated herein by reference in its entirety.

The present disclosure relates to a method and an apparatus for detecting particles on an upper surface of a glass, and a method of irradiating an incident light.

Generally, a micro circuit pattern is deposited on only one surface (e.g., an upper surface) of a flat glass which is used for a flat panel display, while the micro circuit pattern is not deposited on the other surface (e.g., a lower surface) of the flat glass. If the micro circuit pattern is deposited on particles which exist on the upper surface of the flat glass, the micro circuit pattern may have some defects. Thus, there is a need for inspecting whether the particles exist on the upper surface of the flat glass or not, before depositing the micro circuit pattern.

To detect only the particles on the upper surface of the flat glass, a conventional flat glass particle detecting apparatus includes: first and second irradiating devices configured to irradiate light to an upper surface and a lower surface of a flat glass at different angles above the flat glass, respectively; and first and second cameras configured to acquire images of an irradiated region of the upper surface and an irradiated region of the lower surface, respectively.

Since the flat glass has a predetermined thickness, the particles on the upper surface are indicated as bright portions and the particles on the lower surface are indicated as dark portions on images. The conventional apparatus is configured to compare and analyze the images acquired by each of the first and second cameras and to detect the particles existing on the upper surface.

However, since the conventional apparatus has two irradiating devices and two cameras, the cost for manufacturing the apparatus as well as the cost for manufacturing the flat glass increase. Further, as the conveying speed of the flat glass has become higher and higher recently, there is a demand for enhancing a detecting speed of the particles on the upper surface of the flat glass. However, since the conventional apparatus must compare and analyze the images acquired by two cameras, it is difficult to satisfy such a demand.

The present disclosure addresses solutions to at least one of the aforementioned problems. The present disclosure provides a method and an apparatus of detecting particles on an upper surface of a glass that can use only one light source and only one camera and a method of irradiating an incident light.

One aspect of the present disclosure provides a method of detecting particles on an upper surface of a glass. The method includes: disposing a rotatable mirror on a path of light emitted from a light source so that the mirror reflects the light to irradiate an incident light to the upper surface; calculating an incident angle of the incident light so that a first region where the incident light meets the upper surface of the glass and a second region where light transmits through the glass and meets a lower surface of the glass do not overlap with each other when viewed from above; rotating the mirror based on the calculated incident angle; acquiring an image of the first region with a camera disposed above the first region; and detecting particles by analyzing the acquired image. The detected particles are considered as existing on the upper surface.

In one embodiment, the incident angle is calculated based on a refractive index and a thickness of the glass.

In one embodiment, the incident angle is calculated based on a maximum value of a horizontal distance between the right end of the first region and the left end of the second region.

In one embodiment, the maximum value of the horizontal distance is calculated based on the following equation:

where L' is the horizontal distance,

d is the thickness of the glass,

n is the refractive index of the glass,

θ is the incident angle of the incident light, and

W is a width of the incident light.

In one embodiment, rotating the mirror is performed before the glass is conveyed.

In one embodiment, the camera is installed so that the right end of the first region is positioned at the right end of a field of view of the camera.

In one embodiment, calculating the incident angle and rotating the mirror are performed when at least one of a refractive index and thickness of the glass is changed.

Another aspect of the present disclosure provides a method of irradiating an incident light to an upper surface of a glass for detecting particles on the upper surface. The method includes: disposing a rotatable mirror on a path of light emitted from a light source so that the mirror reflects the light to irradiate the incident light to the upper surface; calculating an incident angle of the incident light based on a refractive index and a thickness of the glass so that a first region where the incident light meets the upper surface and a second region where light transmits through the glass and meets a lower surface of the glass do not overlap with each other when viewed from above; and rotating the mirror based on the calculated incident angle. Calculating the incident angle and rotating the mirror are performed when at least one of a refractive index and thickness of the glass is changed.

〔Math.1〕

where L' is the horizontal distance,

d is the thickness of the glass,

n is the refractive index of the glass,

θ is the incident angle of the incident light, and

W is the width of the incident light.

Yet another aspect of the present disclosure provides an apparatus of detecting particles on an upper surface of a glass. The apparatus includes: a light source configured to emit light; a rotatable mirror disposed on a path of the light and configured to adjust an incident angle of an incident light to be irradiated to the upper surface; a controller configured to control the rotation of the mirror so that a first region where the incident light meets the upper surface and a second region where light transmits through the glass and meets a lower surface of the glass do not overlap with each other when viewed from above; and a camera configured to acquire an image of the first region. The controller is configured to detect particles by analyzing the acquired image and considers the detected particles as existing on the upper surface.

In one embodiment, the controller is configured to control the rotation based on a refractive index and a thickness of the glass.

In one embodiment, the controller is configured to control the rotation based on a maximum value of a horizontal distance between a right end of the first region and a left end of the second region.

〔Math.1〕

where L' is the horizontal distance,

d is the thickness of the glass,

n is the refractive index of the glass,

θ is the incident angle of the incident light, and

W is a width of the incident light.

In one embodiment, the camera is configured so that the right end of the first region is positioned at the right end of a field of view of the camera.

FIG. 1 is a schematic side view showing an apparatus of detecting particles on an upper surface of a glass according to one embodiment.

FIG. 2 is a partially enlarged view of FIG. 1.

FIG. 3 is a partially enlarged view of FIG. 2.

FIG. 4 is a graph showing the relationship between an incident angle and a horizontal distance when the apparatus shown in FIG. 1 is used.

FIG. 5 is a flowchart showing a method of detecting particles on an upper surface of a glass according to one embodiment.

FIG. 6 is a flowchart showing a method of irradiating an incident light according to one embodiment.

Hereinafter, embodiments of methods and an apparatus for detecting particles on an upper surface of a glass and a method of irradiating an incident light will be described with reference to the accompanying drawings.

A 2-dimensional Cartesian coordinate system (X axis and Y axis) is used in FIGS. 1 to 3 of the accompanying drawings. In the descriptions below, a positive X-axial direction and a positive Y-axial direction indicate a rightward direction and an upward direction, respectively. Further, a negative X-axial direction and a negative Y-axial direction indicate a leftward direction and a downward direction, respectively.

In the descriptions below, the terms "upper", "lower", "above", "below", "right", "left" etc. are referencing relative spatial relationship as shown in the accompanying drawings, where the glass is assumed to be conveyed horizontally and are not intended to represent absolute spatial relationships depending on the direction of the glass conveyance.

As shown in FIGS.1 and 2, an apparatus of detecting particles on an upper surface of a glass 100 (hereinafter, briefly referred to as "a particle detecting apparatus") according to one embodiment includes: a light source 110; a mirror 120; a controller 130; and a camera 140.

In the particle detecting apparatus 100, a target to be inspected is a glass 10 which is conveying in a horizontal direction (e.g., the rightward direction). In the particle detecting apparatus according to another embodiment, the target to be inspected may be a glass which is not conveyed and is stationary. The glass 10 includes an upper surface 11 on which a micro circuit pattern is deposited and a lower surface 12 on which the micro circuit pattern is not deposited. In another embodiment, the glass 10 may include a flat glass, a glass substrate, a flat glass substrate, etc., which have a predetermined thickness and a predetermined width and extends along the leftward direction or a rightward direction. For a better explanation on the particle detecting apparatus 100, in FIGS. 1 to 3 the glass 10 is illustrated as having a magnified thickness which is shown as being thicker than an actual thickness of the glass 10 (e.g., approximately several millimeters to several micrometers).

The light source 110 is disposed above the glass 10 so as to emit a light 31 in a perpendicular direction with respect to the glass 10. Since the camera 140 is also disposed above the glass 10, the light source 110 can be manufactured integrally with the camera 140, thereby reducing the size of the particle detecting apparatus 100. The light source 110 may cover concepts of a light emitting device, an illuminating device, a lamp, and a beam former, etc. In another embodiment, the light source 110 may be disposed above the glass 10 so as to emit the light 31 in an inclined direction with respect to the glass 10. In one embodiment, the light 31 may include a ray, and a laser beam, etc. In one embodiment, the light source 110 may include a focusing lens 111 for focusing the light 31 to a predetermined irradiating region. The focusing lens 111 may be configured to adjust a size of the irradiating region by the light 31 emitted from the light source 110.

The mirror 120 is disposed on a path of the light 31 emitted from the light source 110 so that an incident light 32 is irradiated to the upper surface 11 of the glass 10. An incident angle θ of the incident light 32 is adjusted by the mirror 120 disposed on the path of the light 31. Thus, the incident light 32 may be irradiated to the upper surface 11 of the glass 10 at relatively large range of incident angle θ compared to the conventional apparatus where the light source is directly inclined with respect to the glass. The mirror 120 is electrically connected to the controller 130 to be rotated based on control signals from the controller 130. The mirror 120 is rotatable about a rotating shaft 121 in a clockwise direction or a counterclockwise direction. To this end, the mirror 120 may include a driving mechanism and a power transmission mechanism. In one embodiment, the driving mechanism may include a driving motor, an electric motor, etc. In one embodiment, the power transmission mechanism may include a pulley and belt, a sprocket and chain, a driving gear and driven gear, etc. In one embodiment, the mirror 120 may cover concepts of a reflecting mirror, a reflecting device, a reflector, etc. In the description below, the incident light 32 means a light which advances from when the light 31 is reflected by the mirror 120 to when the light 31 reaches the upper surface 11 of the glass 10.

The controller 130 is configured to calculate an incident angle θ of the incident light 32, control a rotation of the mirror 120 based on the calculated incident angle θ, detect particles by analyzing images acquired by the camera 140 and determine that the detected particles are considered as existing on the upper surface 11 of the glass 10.

Specifically, the controller 130 is configured to calculate the incident angle θ of the incident light 32 so that a first region 41 and a second region 42 do not overlap with each other when viewed from above. Herein, the first region 41 is a region where the incident light 32 meets the upper surface 11 of the glass 10, while the second region 42 is a region where a transmitted light 33 transmitted through the glass 10 meets the lower surface 12 of the glass 10. In other words, the controller 130 is configured to calculate the incident angle θ of the incident light 32 so that a horizontal distance L' between a right end of the first region 41 and a left end of the second region 42 is greater than zero.

If the first region 41 and the second region 42 do not overlap with each other when viewed from above, it is possible to acquire an image of the first region 41 without acquiring an image of the second region 42 by using the camera 140 above the glass 10. In this case, since an image of an irradiated region (i.e., the second region 42) on the lower surface 12 of the glass 10 is not acquired by the camera 140, an image of the particles on the second region 42 cannot be acquired by the camera 140. Further, since any one of the lights does not reach the particles existing on a non-irradiated region (i.e., the rest region except the second region 42) on the lower surface 12 of the glass 10, an image of the particles cannot be acquired by the camera 140. As such, only the image of the upper particles 21 on the first region 41 can be acquired by the camera 140, while the image of lower particles existing on the lower surface 12 of the glass 10 cannot be acquired by the camera 140.

In one embodiment, the controller 130 may include a computer having a program storage part. Any program or programs related to calculating the incident angle θ, rotating the mirror 120, and analyzing the images can be stored in the program storage part. For example, the program storage part may include computer-readable hard disc, flexible disc, compact disc, magnet-optical disc, and memory card, etc.

In one embodiment, the controller 130 may be configured to control the rotation of the mirror 120 based on the refractive index and the thickness of the glass 10 so that the first region 41 and the second region 42 do not overlap with each other when viewed from above.

For example, the horizontal distance L' may be calculated by the following equation:

〔Math.1〕

where L' is the horizontal distance,

d is the thickness of the glass 10,

n is the refractive index of the glass 10,

θ is the incident angle of the incident light 32, and

W is the width of the incident light 32 in the horizontal direction.

Equation 1 may be derived from the following Equations 2 to 6. First, the horizontal distance L' may be expressed by Equation 2 as follows:

where, referring to FIG. 3, W_A is the horizontal width of the first region 41,

W_B is a horizontal width of the second region 42, and

L is a horizontal distance between the center of W_A and the center of W_B.

In Equation 2, since the thickness of the glass 10 is very thin such as from 0.2 mm to 4 mm, it can be assumed that the horizontal width W_A of the first region 41 effectively equals the horizontal width W_B of the second region 42. Accordingly, the horizontal distance L' may be expressed by Equation 3 as follows:

In Equation 3, L may be expressed using the trigonometric function by Equation 4 that is related to an angle of refraction α:

In Equation 4, the angle of refraction α may be expressed using Snell’s law by Equation 5 that is related to the incident angle θ:

In Equation 3, W_A may be expressed by Equation 6 that is related to the incident angle θ:

If Equations 4 to 6 are applied to Equation 3, Equation 1 is derived. Since the refractive index n, the thickness d, and the width W are a constant in Equation 1, the horizontal distance L' is expressed by a function related to the incident angle θ.

Accordingly, if a specific glass is determined as the target to be inspected, the refractive index and the thickness of the specific glass are also determined. In this case, the incident angle θ can be calculated based on Equation 1 so that the horizontal distance L' is more than zero (i.e., the first region 41 and the second region 42 do not overlap with each other when viewed from above).

Further, Equation 1 is theoretical, and in reality the refractive index may not be uniform throughout the glass. Thus, in order to ensure that the first region 41 and the second region 42 do not overlap with each other, the incident angle θ can be calculated based on Equation 1 so that the horizontal distance L' has a maximum value. For example, when the glass 10 has the refractive index n of 1.5, the width W of 100 ㎛, and the thickness of 500 ㎛, the relationship between the horizontal distance L' and the incident angle θ is illustrated in FIG. 4. Referring to FIG. 4, when the incident angle θ is 58.5 degrees, the horizontal distance L' has the maximum value. In this case, the maximum value of the horizontal distance L' is 154.1 ㎛.

The controller 130 is configured to control the rotation (or an inclined angle) of the mirror 120 based on the incident angle θ calculated through the aforementioned method by driving the driving mechanism of the mirror 120.

As described above, the incident angle θ where the first region 41 and the second region 42 do not overlap with each other depends on the refractive index and the thickness of the glass 10. Therefore, when at least one of the refractive index and the thickness of the glass as the target to be inspected is changed, the controller 130 is configured to calculate the incident angle θ of the incident light 32 based on the changed refractive index or the changed thickness to thereby control the rotation of the mirror 120 in accordance with the calculated incident angle θ.

The camera 140 is disposed above the glass 10 in the perpendicular direction with respect to the glass 10. The camera 140 has a field of view FOV (see the dotted line shown in FIGS. 1 and 2) which extends in the perpendicular direction with respect to the glass 10 downwardly from the camera 140 to meet the upper surface 11 of the glass 10. The camera 140 is configured to acquire an image of the first region 41 without acquiring an image of the second region 42. That is to say, the camera 140 is installed so that the field of view FOV of the camera 140 includes the first region 41 and does not include the second region 42. Since the upper particles 21 existing on the first region 41 of the upper surface 11 scatter the incident light 32 to form scattered lights 34, the image of the upper particles are acquired by the camera 140. The camera 140 is electrically connected to the controller 130. The images acquired by the camera 140 are sent to the controller 130 in a form of electrical signals. In this embodiment, the camera 140 may include a line CCD (Charge Coupled Device) camera. In one embodiment, the camera 140 may cover concepts of a filming device, an imaging device, a detecting device, and a detector, etc.

In one embodiment, as shown in FIG. 2, the camera 140 may be installed so that the right end of the first region 41 is positioned at a right end of the field of view FOV, thereby positioning the field of view FOV the farthest from the second region 42. Thus, it is possible to restrain lights scattered from the lower particles 22 existing on the second region 42 from generating noise in the images acquired by the camera 140.

The controller 130 is configured to consider bright portions on the image as the particles by analyzing the images acquired by the camera 140. As described above, the image of the lower particles 22 existing on the lower surface 12 of the glass 10 is not acquired by the camera 140. Accordingly, the controller 130 is configured to consider that all of the detected particles exist on the upper surface 11 of the glass 10.

As shown in FIG. 5, a method of detecting particles on the upper surface of the glass 200 (hereinafter, briefly referred to as "a particle detecting method") according to one embodiment includes: disposing the mirror S201; calculating the incident angle of the incident light S202; rotating the mirror S203; acquiring an image of the first region S204; and detecting the particles S205.

In disposing the mirror S201, the mirror 120 is disposed on the path of the light 31 emitted from the light source 110. The mirror 120 reflects the light 31 to irradiate the incident light 32 to the upper surface 11 of the glass 10.

In calculating the incident angle of the incident light S202, the incident angle θ of the incident light 32 is calculated so that the first region 41 and the second region 42 do not overlap with each other when viewed from above. The incident angle θ of the incident light 32 may be calculated in the same manner as the particle detecting apparatus 100 according to one embodiment. That is to say, the incident angle θ of the incident light 32 may be calculated based on the refractive index and the thickness of the glass 10. Further, the incident angle θ of the incident light 32 may be calculated based on the maximum value of the horizontal distance L'. Moreover, the maximum value of the horizontal distance L' may be calculated by Equation 1.

In rotating the mirror S203, the mirror 120 is rotated based on the incident angle θ calculated in calculating the incident angle of the incident light S202. In one embodiment, rotating the mirror S203 may be performed before the glass 10 is conveyed. Thus, since the rotation of the mirror 120 is controlled in advance before an inspection of the glass 10 is begun, it is possible to reduce the actual time required for inspecting the glass 10.

In acquiring an image of the first region S204, the camera 140 acquires an image of the first region 41 while the glass 10 is conveyed in a horizontal direction (e.g., the rightward direction). Since the position and the function of the camera 140 has been already described in the particle detecting apparatus 100 according to one embodiment, specific descriptions regarding the above are omitted.

In detecting the particles S205, the particles are detected by analyzing the images acquired in acquiring an image of the first region S202. Specifically, the particles are detected by finding a bright portion displayed by the scattered lights 34 from the images. The particles detected in detecting the particles S205 are considered as existing on the upper surface 11 of the glass 10.

As shown in FIG. 6, a method of irradiating the incident light 300 according to one embodiment includes: disposing the mirror S301; calculating the incident angle of the incident light S302; and rotating the mirror S303. In this embodiment, calculating the incident angle of the incident light S302 and rotating the mirror S303 are performed when at least one of the refractive index and the thickness of the glass 10 is changed.

Since disposing the mirror S301 and rotating the mirror S303 shown in FIG. 6 are identical to disposing the mirror S201 and rotating the mirror S203 shown in FIG. 5, specific descriptions regarding the above are omitted.

In calculating the incident angle of the incident light S302, the incident angle θ of the incident light 32 is calculated based on the refractive index and the thickness of the glass 10 so that the first region 41 and the second region 42 do not overlap with each other when viewed from above. The incident angle θ of the incident light 32 may be calculated in the same manner as the particle detecting apparatus 100 according to one embodiment. That is to say, the incident angle θ of the incident light 32 may be calculated based on the maximum value of the horizontal distance L'. Further, the maximum value of the horizontal distance L' may be calculated by Equation 1.

The technical idea of the present disclosure is not limited to the embodiments described above and the examples shown in the accompanying drawings. It would be obvious to a person of ordinary skill in the art that various substitutions, modifications, and changes are possible within the scope of the technical idea of the present disclosure.

The method and the apparatus of detecting the particles on the upper surface of the glass according to one embodiment is configured to calculate an optimal incident angle of the incident light and control the rotation of the mirror based on the calculated optimal incident angle. Thus, it is possible to precisely detect only particles on the upper surface of the glass by using only one camera. Further, in accordance with the method of irradiating the incident light, it is possible to precisely irradiate the incident light having the optimal incident angle to the upper surface of the glass.

〔Explanations of Reference Numerals〕

10: a glass

11: an upper surface

12: a lower surface

21: upper particles

22: lower particles

31: a light

32: an incident light

33: a transmitted light

34: scattered lights

41: a first region

42: a second region

100: a particle detecting apparatus

110: a light source

111: a focusing lens

120: a mirror

121: a rotating shaft

130: a controller

140: a camera

FOV: a filed of view

200: a particle detecting method

300: a method of irradiating an incident angle

Claims

A method of detecting particles on an upper surface of a glass, comprising:

disposing a rotatable mirror on a path of light emitted from a light source so that the mirror reflects the light to irradiate an incident light to the upper surface;

calculating an incident angle of the incident light so that a first region where the incident light meets the upper surface of the glass and a second region where light transmits through the glass and meets a lower surface of the glass do not overlap with each other when viewed from above;

rotating the mirror based on the calculated incident angle;

acquiring an image of the first region with a camera disposed above the first region; and

detecting particles by analyzing the acquired image,

wherein the detected particles are considered as existing on the upper surface.
The method according to Claim 1, wherein the incident angle is calculated based on a refractive index and a thickness of the glass.
The method according to Claim 2, wherein the incident angle is calculated based on a maximum value of a horizontal distance between the right end of the first region and the left end of the second region.
The method according to Claim 3, wherein the maximum value of the horizontal distance is calculated based on the following equation:

〔Math.1〕

where L' is the horizontal distance,

d is the thickness of the glass,

n is the refractive index of the glass,

θ is the incident angle of the incident light, and

W is a width of the incident light.
The method according to Claim 1, wherein rotating the mirror is performed before the glass is conveyed.
The method according to Claim 1, wherein the camera is installed so that the right end of the first region is positioned at the right end of a field of view of the camera.
The method according to Claim 1, wherein calculating the incident angle and rotating the mirror are performed when at least one of a refractive index and a thickness of the glass is changed.
A method of irradiating an incident light to an upper surface of a glass for detecting particles on the upper surface, comprising:

disposing a rotatable mirror on a path of light emitted from a light source so that the mirror reflects the light to irradiate the incident light to the upper surface;

calculating an incident angle of the incident light based on a refractive index and a thickness of the glass so that a first region where the incident light meets the upper surface and a second region where light transmits through the glass and meets a lower surface of the glass do not overlap with each other when viewed from above; and

rotating the mirror based on the calculated incident angle,

wherein calculating the incident angle and rotating the mirror are performed when at least one of a refractive index and a thickness of the glass is changed.
The method according to Claim 8, wherein the incident angle is calculated based on a maximum value of a horizontal distance between the right end of the first region and the left end of the second region.
The method according to Claim 9, wherein the maximum value of the horizontal distance is calculated based on the following equation:

〔Math.1〕

where L' is the horizontal distance,

d is the thickness of the glass,

n is the refractive index of the glass,

θ is the incident angle of the incident light, and

W is the width of the incident light.
An apparatus for detecting particles on an upper surface of a glass, comprising:

a light source configured to emit light;

a rotatable mirror disposed on a path of the light and configured to adjust an incident angle of an incident light to be irradiated to the upper surface;

a controller configured to control the rotation of the mirror so that a first region where the incident light meets the upper surface and a second region where light transmits through the glass and meets a lower surface of the glass do not overlap with each other when viewed from above; and

a camera configured to acquire an image of the first region,

wherein the controller is configured to detect particles by analyzing the acquired image and considering the detected particles as existing on the upper surface.
The apparatus according to Claim 11, wherein the controller is configured to control the rotation based on a refractive index and a thickness of the glass.
The apparatus according to Claim 12, wherein the controller is configured to control the rotation based on a maximum value of a horizontal distance between a right end of the first region and a left end of the second region.
The apparatus according to Claim 13, wherein the maximum value of the horizontal distance is calculated based on the following equation:

〔Math.1〕

where L' is the horizontal distance,

d is the thickness of the glass,

n is the refractive index of the glass,

θ is the incident angle of the incident light, and

W is a width of the incident light.
The apparatus according to Claim 11, wherein the camera is configured so that the right end of the first region is positioned at the right end of a field of view of the camera.