KR102009558B1 - Goggle system for image guide surgery - Google Patents

Abstract

The present invention relates to an image-guided surgical goggles system, the image-guided surgical goggles system includes a camera 11 disposed on the head of the user 1, the optical tissue is applied to the biological tissue to which the fluorescent material is administered Transparent glass disposed in front of the eye of the user 1 to view the image acquisition unit 10 obtained by taking a fluorescent image generated by irradiating the surgery, and the surgical site 3 including the biological tissue ( 20), the image matching unit 30 for processing the fluorescence image so that the fluorescence image is superimposed on the real image seen through the glass 20 in real time, and the image display to display the registration by transmitting the processed fluorescent image to the glass 20 The sending unit 40 is included.

Description

Goggle System for Image-guided Surgery {GOGGLE SYSTEM FOR IMAGE GUIDE SURGERY}

The present invention relates to an image-guided surgical goggles system, and more particularly, to a surgical goggles system that provides a surgical support image that allows the surgeon to more accurately identify the surgical site through a fluorescent image.

Surgery, especially cancer surgery that removes cancerous metastases from normal tissue, results in cancer cell metastasis after surgery if some of the surrounding tissue remains and leads to deterioration of organ function if too large a range is removed. Temperance is very important. To this end, it is necessary to accurately determine the location of cancer and the boundary between surrounding tissue and normal tissue. However, in conventional cancer surgery under a thoracic or open abdominal surgeon, the surgeon can only determine the location and boundaries of the cancer based on his or her own vision and touch. In this case, although various image data acquired through X-ray, CT, PET, etc. were analyzed before the surgery, it was not easy to accurately identify the location of cancer and the boundary between normal tissues in the living organs. . In particular, it was more difficult to identify an inflammation or anatomical variation around the cancer, or chemo and radiation treatment before surgery.

In order to solve this problem, as disclosed in the patent document of the following prior art document, a fluorescence imaging system has been developed. According to the fluorescence imaging system, as shown in FIG. 1, after acquiring a photorealistic image of a surgical site and a fluorescence image emitted by a fluorescent substance administered to a human body through multiple filters, a single photometric image and a fluorescence image are obtained. Output to the monitor. Thus, the surgeon can easily confirm the location and connection of the tumor. However, according to such a fluorescence imaging system, the doctor does not operate while looking at the actual surgical site with his eyes but has a problem of performing surgery while looking at the monitor by turning his head. In this case, a discrepancy between the doctor's field of view and the fluorescence image may occur, and thus, the surgeon's fatigue is increased due to a long operation time.

Meanwhile, a system for transmitting fluorescence images and anatomical images obtained through cameras to eyeglasses has been developed, but the virtual reality-based head mounted display is used to prevent the physical sense of vision through the eyes and to rather inhibit the doctor's sense of distance. Cause inconvenience.

Therefore, there is an urgent need for a solution to solve the problem of the conventional fluorescence imaging system.

KR 10-1630539 B1

The present invention is to solve the above-mentioned problems of the prior art, an aspect of the present invention is to obtain a fluorescent image of the biological tissue by the fluorescent material, and to project the fluorescent image in augmented reality in the field of view of the surgeon in real time To provide an image-guided surgical goggles system used for surgery.

Another aspect of the present invention is an image induction to match the fluorescence image to the real image by correcting in real time difference caused by the disparity of the optical path of the camera is placed on the surgeon's head to obtain the fluorescence image and the doctor's gaze To provide a surgical goggles system.

According to an aspect of the present invention, an image guided goggle system includes an image acquisition unit that includes a camera disposed on a user's head and captures a fluorescent image generated by irradiating light onto a biological tissue to which a fluorescent substance is administered; Transparent glass disposed in front of the eye of the user to see the surgical site including the biological tissue; An image matching unit processing the fluorescent image so that the fluorescent image is superimposed in real time on the real image seen through the glass; And an image transmission unit which transmits the processed fluorescent image to the glass and displays the registration.

In addition, in the image guided surgical goggles system according to the present invention, the image acquisition unit is worn on the head of the user, the head gear to which the camera is attached; further includes.

In addition, in the image-guided surgical goggles system according to the present invention, the image registration unit, the optical path from the camera to the surgical site, and the gaze from the eyes of the user to the surgical site, any arbitrary on the surgical site The head position of the user who meets each other at the point is set as a reference position, and when the user's head position is out of the reference position, the fluorescent image is corrected.

In addition, in the image guided surgical goggles system according to the present invention, the image registration unit is disposed in the camera, the distance sensor for measuring the optical path distance; An eye angle sensor disposed on the glass to measure an eye angle between the eye and the surgical part at the reference distance; And a processor configured to correct the fluorescence image by using the light path distance and the gaze angle.

In addition, in the goggle system for image-guided surgery according to the present invention, the processing unit calculates the viewing angle between the line of sight and the optical path at the reference distance by the formula (1).

[Equation 1]

(b: field of view angle, w: distance between user's eyes and camera, l ₀ : distance of light path from reference position)

In addition, in the image-guided surgical goggles system according to the invention, the image registration unit is disposed in the camera, the optical path for measuring the optical path angle (angle) between the optical path and the surgical site at the reference distance And an angle sensor, wherein the processing unit calculates a viewing angle between the line of sight and the light path at the reference distance by subtracting the line of sight from the light path angle.

In addition, in the goggle system for image-guided surgery according to the present invention, the processing unit calculates the position change amount of the optical path according to the position of the user's head by the following [Equation 2], the fluorescence by the position change amount Adjust the position of the image.

[Equation 2]

(x: position change of light path, a: line of sight, b: angle of view, l ₀ : distance of light path from reference position, l: distance of light path from measurement position)

In addition, in the goggle system for image-guided surgery according to the present invention, the processing unit calculates the ratio of the field of view of the camera to the field of view of the user according to the head position of the user by the following [Equation 3], The size of the fluorescent image is adjusted based on the reciprocal of the size ratio.

[Equation 3]

,

,

(M: size ratio, x: position change of optical path, a: line of sight, b: field of view angle, l ₀ : optical path distance from reference position, l: optical path distance from measurement position)

The features and advantages of the present invention will become more apparent from the following detailed description based on the accompanying drawings.

Prior to this, the terms or words used in this specification and claims are not to be interpreted in a conventional and dictionary sense, and the inventors may appropriately define the concept of terms in order to best explain their invention in the best way possible. It should be interpreted as meaning and concept corresponding to the technical idea of the present invention based on the principle that the present invention.

According to the present invention, by obtaining a fluorescent image of the biological tissue by the fluorescent material, by matching the fluorescent image to the real image of the surgeon looking at the surgical site in real time, the doctor does not rely on a separate monitor By looking directly at the surgical site, the position of the surrounding tissue to be resected and the boundary with normal tissue can be accurately identified. Furthermore, since the vision of the surgery is secured through the eyes, the doctor can make accurate resections without disturbing the sense of distance.

In addition, according to the present invention, when a camera for acquiring a fluorescence image is disposed on the surgeon's head to generate a visual field difference due to a mismatch between the optical path of the camera and the line of sight, the fluorescence image due to the difference is corrected in real time. It can be accurately overlapped with the real image.

1 is a surgical picture using a conventional fluorescence imaging system.
Figure 2 is a block diagram of a goggle system for image induction surgery according to the present invention.
3 is an image photograph matched by the image guided goggles system for surgery according to the present invention.
Figure 4 is a side view showing the line of sight and light path when using the image-guided surgical goggles system according to the present invention.
5A through 5B are diagrams illustrating the image matching unit shown in FIG. 2.
6A is a side view illustrating an optical path when the user's head position retreats from the reference position.
6B is a side view illustrating an optical path when the head position of the user moves forward from the reference position.

The objects, specific advantages and novel features of the present invention will become more apparent from the following detailed description and the preferred embodiments associated with the accompanying drawings. In the present specification, in adding reference numerals to the components of each drawing, it should be noted that the same components as possible, even if displayed on different drawings have the same number as possible. In addition, terms such as “first” and “second” are used to distinguish one component from another component, and the component is not limited by the terms. In the following description, detailed descriptions of related well-known techniques that may unnecessarily obscure the subject matter of the present invention will be omitted.

Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings.

2 is a block diagram of an image-guided surgical goggles system according to the present invention, Figure 3 is an image photograph matched by the image-guided surgical goggles system according to the present invention.

As shown in Figure 2, the image-guided surgical goggles system according to the present invention includes a camera 11 disposed on the head of the user 1, generated by irradiating light to the biological tissue to which the fluorescent material is administered The image acquisition unit 10 obtained by taking a fluorescence image, the transparent glass 20 disposed in front of the eye of the user 1 so that the surgical site 3 including the living tissue is visible, the fluorescence image The image matching unit 30 for processing the fluorescent image, and the image transmitting unit 40 for transmitting the processed fluorescent image to the glass 20 so as to overlap the real image seen through the glass 20 in real time. Include.

The present invention relates to an image-guided surgical goggles system, which displays a bioluminescent tissue to be excised by administering a fluorescent substance into the human body, and projects the fluorescent image obtained by augmented reality onto the surgeon's field of vision to remove the biological tissue. Allows you to check the position of and the boundaries of normal tissue. Surgical surgery, in particular in the case of cancer surgery in which cancer cells are metastasized from normal tissues, requires accurate resection due to fear of post-operative cancer cell metastasis or deterioration of organs. Thus, after acquiring a live image and a fluorescence image of the surgical site, a fluorescence imaging system for outputting each image to one monitor or glasses has been developed. However, in the conventional fluorescence imaging system, the surgeon does not operate by looking at the surgical site with his eyes but rather turns the head to look at the monitor, or the image is transmitted to the glasses, so the operation is performed. The sense of distance is hampered by the problem that precise surgery is not performed. Therefore, as a solution to the problem of the conventional fluorescence imaging system, an image-guided surgical goggle system according to the present invention has been devised.

In detail, the image induction system according to the present invention includes an image acquisition unit 10, a glass 20, an image matching unit 30, and an image transmission unit 40.

Here, the image acquisition unit 10 obtains a fluorescent image displayed on the biological tissue by using a fluorescent material. When the fluorescent substance is administered to the human body, a specific substance is generated during the material conversion process by metabolism in the body, thereby showing fluorescence expression in a predetermined biological tissue. Representative fluorescent materials include organic dyes and organic quantum dats (QDs). Organic dyes such as indocyanin green (ICG) and methylene blue are mainly used. . However, the fluorescent material is not necessarily limited thereto.

After the fluorescent material is injected into the biological tissue, when the light having a predetermined wavelength region is irradiated, the fluorescent light is emitted, and at this time, a fluorescent image is obtained by capturing the fluorescent light. The wavelength of the irradiated light can be controlled through the light source 5. On the other hand, the fluorescence image is an image of a tumor, blood vessels, etc., if the cell or tissue capable of emitting light according to the fluorescent material can obtain a fluorescence image without particular limitation.

Here, the image acquisition unit 10 includes a camera 11 to obtain such a fluorescent image. At this time, the camera 11 uses a near-infrared camera, a visible light camera, etc., but the type is not limited as long as it can take a fluorescent image. On the other hand, the camera 11 is arranged on the head of the user 1, that is, the surgeon. Therefore, even if the user 1 changes his or her gaze direction by turning his head, the fluorescent image can be taken according to the gaze direction. Here, since the camera 11 is arrange | positioned at the head of the user 1, it is suitable to use an ultralight camera.

In addition, in order to secure a clear fluorescence image, an optical system such as a lens and a filter may be additionally used, and this is selected in consideration of weight reduction and surgical conditions. For example, an infinity lens and a near-infrared filter may be used, and since the distance between the camera 11 and the operating table is about 20 to 70 cm, a lens is selected between 25 and 50 mm, and a filter suitable for the emission wavelength band of the fluorescent material. Select. However, the optical system is not necessarily limited thereto, and the user 1 may determine a wide range in consideration of various conditions.

In order for the camera 11 to be disposed on the head of the user 1, the image acquisition unit 10 may further include a head gear 13. Here, the head gear 13 is not particularly limited as long as it is formed to be worn on the head of the user 1. The headgear 13 is formed with a cradle for mounting the camera 11, it is possible to fix the camera 11 to the head of the user (1). Here, the holder may be formed integrally with the head gear 13 or may be manufactured separately and attached to the head gear 13.

The fluorescent image photographed by the camera 11 of the head of the user 1 is finally displayed on the glass 20.

Glass 20 is provided in the form of glasses or goggles to be placed in front of the eyes of the user 1, made of a transparent material. Accordingly, the user 1 may directly recognize the reality image of the surgical site 3 through the glass 20. That is, the surgical field of view by the eyes of the user 1 is secured.

On the other hand, the fluorescent image is displayed on the glass 20 to be placed within the field of view of the user 1, in this case, as shown in Figure 3, the fluorescent image 7 is superimposed in real time on the real image (9). When the fluorescent image 7 is projected to the augmented reality in the field of view of the user 1, the user 1 can accurately check the position of the surrounding tissue to be excised and the boundary with the normal tissue. In addition, since the sense of distance is not impaired due to securing the vision through the eyes, it is possible to aim a surgical tool such as a scalpel in the correct position.

The image matching unit 30 processes the fluorescence image so that the fluorescence image is matched at an accurate position with a size corresponding to the real image. In the present invention, since the camera 11 is disposed on the head of the user 1, there is an advantage that the biological tissue can be taken in the direction of the user 1's eye, but if the user 1 moves the head during surgery, the camera ( 11) Depending on the position change, the captured fluorescent image may not be matched. Thus, the image matching unit 30 is set to analyze and match the fluorescent image obtained by the camera 11, and also corrects this. The setting and correction processing method will be described later.

The image transmission unit 40 receives the fluorescent image processed by the image matching unit 30 and transmits the image to the glass 20 to display the image. Here, the image transmitter 40 includes a communication module, and an augmented reality module. The communication module is a communication device capable of transmitting and receiving fluorescent image data, and may transmit data by wire or wirelessly. Meanwhile, the augmented reality module displays a fluorescent image on the glass 20 using an augmented reality program, and all known devices for synthesizing and displaying an augmented reality image as long as the fluorescent image can be displayed and matched with a real image. Include.

Overall, according to the image-induced surgical goggles system according to the present invention, a fluorescent image of a living tissue is obtained by a fluorescent material, the fluorescent image is matched to a real image of a surgeon looking at the surgical site, and displayed in real time. By doing this, the doctor can check the position of the surrounding tissue to be resected and the boundary with the normal tissue while looking directly at the surgical site without relying on a separate monitor. Furthermore, since the vision of the surgery is secured through the eyes, the doctor can make accurate resections without disturbing the sense of distance.

Hereinafter, the fluorescence image processing by the image matching unit 30 will be described.

Figure 4 is a side view showing the line of sight and light path when using the image-guided surgical goggles system according to the present invention, Figures 5a to 5b is a configuration diagram of the image matching unit shown in Figure 2, Figure 6a is a user Is a side view showing an optical path when the head position is retracted from the reference position, Figure 6b is a side view showing an optical path when the user's head position advances from the reference position.

As shown in FIG. 4, in the image guided goggles system according to the present invention, since the camera 11 is disposed at the head of the user 1 (see FIG. 2), the gaze e and the light path l are mutually different. Does not match Here, the gaze (e) is a virtual straight line extending from the eye 2 of the user 1 to the surgical site 3, the optical path (l) is the reflected light reflected from the surgical site (3) of the camera 11 It means a straight path passing through the lens.

Thus, the image matching unit 30 acquires the fluorescent image at the reference position, sets the fluorescent image to match the real image, and when the fluorescent image is obtained at the position outside the reference position, the position and size of the fluorescent image. Calibrate Here, the reference position is a position where the field of view of the eye 2 and the field of view of the camera 11 coincide with each other, and the position of the camera 11 which photographs the fluorescent image used for the initial registration, that is, the head position of the user 1. to be. This reference position may be determined as the head position when the line of sight e and the optical path l ₀ meet with each other at any point on the surgical site 3 on. At this time, the arbitrary point may be, for example, the surgical site (3), or the center point of the biopsy being excised, and at any one point, as long as the line of sight (e) and the optical path (l ₀ ) meet each other, there is a need for special limitation. There is no. When the fluorescent image is photographed at the reference position, the position and size of the fluorescent image are initially set so that the fluorescent image is matched with the real image at the position.

On the other hand, when the head position of the user 1 is out of the reference position, the gaze (e) and the optical path (l ₁ , l ₂ ) no longer meet each other on the surgical site (on 3). For example, if the head of the user 1 at the reference position moves away from the surgical site 3, the optical path l ₁ retreats by x (x ₁ ) than at the reference location, and above the surgical site 3. Intersect with line of sight (e) at (up). On the other hand, when the head of the user 1 approaches the surgical site 3, the optical path l ₂ is advanced by x (x ₂ ) than at the reference position, and the gaze (e) and the optical path (l ₂ ) Does not intersect (the extension of each line of sight (e) and light path (l ₂ ) is crossed below the surgical site (3)). In each of these cases, the field of view of the eye and the field of view of the camera 11 also become inconsistent. Therefore, when the initial position and size are applied, the image is not matched, and the image matching unit 30 corrects the fluorescent image at this time.

Specifically, in order for the image matching unit 30 to process the fluorescent image, as shown in FIG. 5A, the image matching unit 30 includes the distance sensor 31, the eye angle sensor 33, and the processing unit 35. It may include.

Here, the distance sensor 31 is disposed in the camera 11 (see FIG. 2) to measure the distance of the optical path (see FIG. 4). The distance sensor 31 is a sensor that calculates distance by reflecting infrared rays, natural light, or ultrasonic waves to the object to be measured and measuring the time, and there is no particular limitation on the measurement method as long as the distance measurement is possible. .

The eye angle sensor 33 is disposed on the glass 20 (see FIG. 2), and measures the angle a between the eye line e (see FIG. 4) and the surgical site (see 3, 4) at the reference position. do. Hereinafter, the angle a measured by this is called eyeball angle. Here, the eye angle sensor 33 may use a gyro sensor, for example, but is not limited thereto, and all known angle sensors may be used.

The processor 35 processes the fluorescence image by using the light path distance measured by the distance sensor 31 and the eye angle measured by the eye angle sensor 33. The parameters required for the processing unit 35 to process the fluorescence image include the optical path (l) distance and the gaze angle (a), and the angle formed by the gaze (e) and the optical path (l) at the reference position. b). Hereinafter, the angle of inclination (b) is referred to as the field of view.

The viewing angle may be calculated by the processing unit 35 by applying Equation 1 below.

Here, b is the viewing angle, w is the distance between the eye 2 of the user 1 and the camera 11, l ₀ is the distance of the light path (l) at the reference position.

However, the viewing angle is not necessarily calculated only by the above Equation 1. For example, as shown in FIG. 5B, the image matching unit 30 may further include the optical path angle sensor 34.

Here, the optical path angle sensor 34 is disposed in the camera 11, and measures the optical path angle (a + b) which is an angle between the optical path l and the surgical site 3 at the reference position. . At this time, as the optical path angle sensor 34, all known angle sensors including a gyro sensor can be used.

When the optical path angle a + b is measured by the optical path angle sensor 34 as described above, the processing unit 35 calculates the visual field angle by subtracting the line of sight angle a from the optical path angle a + b. Can be.

When the field of view angle is calculated in one of the two methods described above, the processor 35 may calculate the position change amount of the optical path l and adjust the position of the fluorescent image based on this. The position change amount of the optical path l is the distance (x, x ₁ , x ₂ ) at which the optical paths l, l ₁ , l ₂ retreat or advanced at the measurement position where the head of the user 1 is located. , May be calculated by Equation 2 below.

Here, x is the position change amount of the optical path (l), a is the viewing angle, b is the field of view angle, l ₀ is the optical path (l) distance from the reference position, l is the optical path (l) distance from the measurement position .

In this case, the x value is a negative value (x ₁ ) when the head of the user 1 moves away from the surgical site 3, that is, when the optical path l ₁ retreats, the optical path l distance increases. Has On the contrary, when the head of the user 1 is moved closer to the surgical site 3 and the light path l ₂ is advanced, the distance of the light path l becomes smaller to have a positive value (x ₂ ).

Therefore, if the x value is negative, the processing unit 35 advances the position of the fluorescent image photographed at the position by x, thereby matching the fluorescent image to the real image. On the other hand, if the x value is positive, the fluorescent image photographed at the position is retracted by x to match the fluorescent image.

On the other hand, the change in the position of the head of the user 1 also affects the size of the field of view of the camera 11, the processor 35 may adjust the size of the fluorescent image. At this time, the processor 35 calculates the field size ratio of the camera 11 with respect to the field of view of the user 1 by Equation 3 below, and scales the fluorescence image with the reciprocal of the size ratio. Adjust it.

Where M is the size ratio, x is the positional change of the optical path l, a is the eye angle, b is the viewing angle, l ₀ is the optical path l distance from the reference position, and l is the optical path at the measurement position. (l) Distance.

When the head of the user 1 is away from the surgical site 3 as shown in Fig. 6a, in the above equation, l ₁ is substituted for the optical path distance l at the measurement position, and the size ratio M is calculated. An arbitrary integer K is obtained so that the size ratio M is 1. In this case, K becomes 1 / M, and the size of the fluorescent image matched at that position is adjusted by multiplying the K by the size of the fluorescent image photographed at the measurement position.

6B illustrates a case where the head of the user 1 is close to the surgical site 3, and l ₂ is substituted for the optical path distance l at the measurement position. According to the above formula, the size ratio M and the constant K are obtained, and the size of the fluorescent image is adjusted in the same manner as described above.

Therefore, in the image induction system according to the present invention, a camera 11 for acquiring a fluorescence image is disposed on a surgeon's head so that a visual field difference occurs due to a mismatch between the optical path l of the camera 11 and the line of sight e. In this case, the fluorescence image due to the difference is corrected in real time so that it can be accurately overlapped with the real image.

Although the present invention has been described in detail through specific examples, it is intended to describe the present invention in detail, and the present invention is not limited thereto, and should be understood by those skilled in the art within the technical spirit of the present invention. It is obvious that modifications and improvements are possible.

All modifications and variations of the present invention fall within the scope of the present invention, and the specific scope of protection of the present invention will be apparent from the appended claims.

1: user 3: surgical site
5: light source 7: fluorescent image
9: reality image 10: image acquisition unit
11: camera 13: headgear
20: glass 30: image registration unit
31: distance sensor 33: eye angle sensor
34: optical path angle sensor 35: processing unit
40: video transmission unit

Claims (8)

An image acquisition unit including a camera disposed on a user's head, and photographing and obtaining a fluorescent image generated by irradiating light onto biological tissue to which the fluorescent substance is administered;
Transparent glass disposed in front of the eye of the user to see the surgical site including the biological tissue;
An image matching unit processing the fluorescent image so that the fluorescent image is superimposed in real time on the real image seen through the glass; And
And an image transmission unit for transmitting the processed fluorescent image to the glass and displaying the registration image.
The image matching unit
The position of the head of the user where the light path from the camera to the surgical site and the gaze from the eye of the user to the surgical site meet each other at any point on the surgical site is set as a reference position, and the user's head Correcting the fluorescence image when the position is out of the reference position,
The image matching unit
A distance sensor disposed on the camera to measure the optical path distance;
An eye angle sensor disposed on the glass to measure an eye angle between the eye and the surgical part at the reference position; And
And a processor configured to correct the fluorescence image using the light path distance and the gaze angle.
The method according to claim 1,
The image acquisition unit
A head gear worn on the head of the user and to which the camera is attached;
Image guided surgical goggles system further comprising.
delete delete The method according to claim 1,
The processing unit
An image-guided surgical goggle system for calculating a field of view angle formed by the line of sight and the optical path at the reference position by Equation 1 below.
[Equation 1]

(b: field of view angle, w: distance between user's eyes and camera, l ₀ : distance of light path from reference position)
The method according to claim 1,
The image matching unit
An optical path angle sensor disposed at the camera to measure an optical path angle between the optical path and the surgical site at the reference position;
More,
And the processing unit subtracts the gaze angle from the light path angle to calculate a viewing angle between the line of sight and the light path at the reference position.
The method according to claim 5 or 6,
The processing unit
According to Equation 2, an image guided goggle system for calculating the position change amount of the optical path according to the position of the user's head and adjusting the position of the fluorescent image by the position change amount.
[Equation 2]

(x: position change of light path, a: line of sight, b: angle of view, l ₀ : distance of light path from reference position, l: distance of light path from measurement position)
The method according to claim 7,
The processing unit
According to Equation 3, an image of calculating the field of view ratio of the camera with respect to the field of view of the user according to the position of the user's head, and adjusting the size of the fluorescence image by the reciprocal value of the size ratio Induction Surgical Goggles System.
[Equation 3]

(M: size ratio, x: position change of optical path, a: line of sight, b: field of view angle, l ₀ : optical path distance from reference position, l: optical path distance from measurement position)

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