# Fibre Optics and Endoscopy

Endoscopy is a non-ionising imaging technique used in medical physics to examine the interior of the human body. The difference between other imaging techniques and endoscopy is that endoscopy uses a device called an endoscope, which is inserted directly into the human body. This classifies it as an invasive medical procedure, unlike other imaging techniques based on radiation or sound.

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## Is fibre optics used in endoscopy?

Fibre optics is used in endoscopy. Optical fibres are flexible and transparent fibres with a diameter just a little bigger than a human hair. They are primarily used for transmitting light.

In fibre optics, a core is usually surrounded by a transparent cladding material with a lower index of refraction. The way light is transmitted in fibre optics, which allows doctors to use endoscopes to see the body’s interior, depends on the total internal reflection principle.

### The total internal reflection principle

Total internal reflection is the optical event in which light waves reach the boundary between two media. The light is not refracted to the opposite medium but is completely reflected back to the initial medium instead. This phenomenon occurs when the opposite medium has a higher refractive index than the initial medium.

Refractive index (n) is the number that shows how fast light can travel through the medium. The refractive index and the speed of light in the medium are inversely proportional.

We can calculate the refractive index of a medium with this equation:

$n = \frac{c}{v}$

Here, c is the speed of light in a vacuum (3.00 ⋅ 108m/s), and v is the phase velocity of light in the medium.

For this phenomenon to occur, the angle of incidence at the boundary between two mediums must be greater than the critical angle. Lets say that a light beam travels from a medium that has a refractive index of n1 to a second medium with a refractive index of n2, and n2 ≤ n1. We can then find the critical angle (θc) with this equation:

$\theta_c = \arcsin \Big(\frac{n_2}{n_1} \Big)$

#### When the angle of incidence is lower than the critical angle

If the angle of incidence (θ1) is lower than the critical angle, then the wave will refract to the opposite medium with an angle of θ2 (yellow arrows in the illustration below). We can now find the relation between these angles with this equation:

$n_1 \cdot \sin \theta_1 = n_2 \sin \theta_2$

#### When the angle of incidence is equal to the critical angle

If the angle of incidence (θ1) is equal to the critical angle (θc), then the wave will continue on its way in alignment with the boundary (purple arrows in the illustration).

#### When the angle of incidence is greater than the critical angle

If the angle of incidence is greater than the critical angle, total internal reflection occurs, and the wave will reflect back to the initial medium with the same angle it had initially (red arrows in the illustration).

Behaviour of a wave related to the refractive index and angle of incidence

## Fibre optic endoscopy procedure

When using endoscopes with fibre optics, a light source in the tip of the endoscope illuminates the passageways. The light is reflected from the passageways back into this tip. Light is guided by a step-index structure inside the optical fibre that induces total internal reflection and directs coupled light from one end to the other without loss. For this to happen, the refractive index of the fibre core material (n1) must be greater than that of the fibre cladding material (n2).

Lights paths inside an optical fibre.

Light with an incidence angle greater than the maximum acceptance angle θa will be partially refracted outside of the fibre. Light with an incidence angle less than the maximum acceptance angle θa will be partially refracted inside the fibre. After several encounters with the fibre core-cladding interface, the residual partly reflected light is finally lost.

The requirement for 100% internal reflection at the core-cladding contact determines the maximum acceptance angle θa. To determine the acceptance angle θa, remember that to find the critical angle θc, we use the equation:

$\sin(\theta_c) = \frac{n_2}{n_1}$

Thus, assuming the fibre is in the air with a refractive index of 1, the following equation helps us find the acceptance angle θa. Note that θc' = 90° - θc.

$\sin (\theta_a) = \frac{n_1}{1} \cdot \sin(\theta'_c)$

Another important characteristic of fibre optics in an endoscope is that light will enter and exit the optical fibre with the same angle with regard to the fibres central axis. This means that in the illustration above, θa = θa'. This important characteristic is valid for a curved fibre as well.

In conclusion, the light wave, which reflects from the passageways of the human body and enters the optical fibres in the endoscope, travels through the optical fibres with total internal reflection. As a result, the light exits the optical fibres in the same way it entered them (with the same angle). The image is then transferred for a viewer to examine.

## What are the applications of endoscopy?

Endoscopy is currently used in a variety of applications in medical physics. While endoscopy is mainly used in surgeries to allow surgeons to visualise the interior of the human body while operating, other uses include looking into the passageways of the human body to determine any abnormalities. Here are some other uses of endoscopy:

• Panendoscopy for plastic surgery (triple endoscopy).
• Orthopaedic surgeries, such as knee surgeries and hand surgery.
• Examining the foetus and the amnion during pregnancy.
• Examining the female reproductive system.
• Looking into the interior of the ear.

## Fibre Optics and Endoscopy - Key takeaways

• Endoscopy is a procedure that allows doctors to examine the bodys passageways. It is also used in various surgical procedures so that doctors have a visual of the interior of the human body.
• The biggest difference between other imaging techniques and endoscopy is that endoscopy uses an endoscope inserted directly into the human body. This makes it an invasive procedure.
• Optical fibres are flexible and transparent fibres with a diameter that is just a little bit bigger than a human hair. They are mostly used to transmit light and are currently used in endoscopes.
• The way light is transmitted in fibre optics, which allows doctors to use endoscopes to see the bodys interior, depends on the total internal reflection principle.
• Endoscopy is currently used in a variety of applications in medical physics, such as examining the foetus and the amnion during pregnancy and examining the inside of the human ear.

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How are fibre optics used in endoscopy?

Fibre optics is used in endoscopy, and it is primarily used for transmitting light. In fibre optics, a core is usually surrounded by a transparent cladding material with a lower index of refraction. The way light is transmitted in fibre optics, which allows doctors to use endoscopes to see the body’s interior, depends on the total internal reflection principle.

What is fibre optic endoscopy?

Fibre optic endoscopy is an imaging technique that uses fibre optic endoscopes in order to look into the passageways of the human body.

What is the disadvantage of endoscopy?

One disadvantage of endoscopy is that it is an invasive procedure unlike other imaging techniques based on radiation or sound.

## Test your knowledge with multiple choice flashcards

The core with the refractive index of n1 in the optical fibres in an endoscope is surrounded by a cladding material with a refraction index of n2. Which of the following describes the relation between n1 and n2?

If the angle of incidence is greater than the critical angle, then total internal reflection will occur and the wave will reflect back to the initial medium at which angle?

What is the relation between the angle at which light enters the optical fibre and the angle at which it exits the optical fibre?

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