The basic optics involved in endoscopy includes illumination optics and imaging optics. Optical components used are lens, optical fibers, and prisms. Lenses perform imaging functions or collecting light for illumination. Optical fibers can be used for both illumination light transmission and relaying images. Prisms are for changing the image viewing directions or illumination light direction.

An optical fiber guides light on the basis of a step index structure that causes total internal reflections and directs the coupled light almost without loss from one end to the other. For this to happen the refractive index of the fiber core material (n1) has to be larger than that of the fiber cladding material (n2).

Figure below illustrates how incident light rays within the acceptance cone can be guided through the fiber by total internal reflection, while light with an incidence angle larger than the maximum acceptance angle θa will be partially refracted outside of the fiber. The remaining partially reflected light will eventually get lost after multiple interactions with the fiber core-cladding interface. The maximum acceptance angle θa is determined by the condition for total internal reflection at the core-cladding interface:

Assuming the fiber is in the air with a refractive index of 1, the following holds for the entry surface:

Fig. 1 (a)For visible light, the refractive index n in matter is larger than one. Therefore, light rays are refracted toward the surface normal when entering matter from the vacuum. (b) For hard x-rays, the refractive index n of matter is smaller than one. There-fore, x-rays impinging from vacuum onto a surface are refracted away from the surface normal. (c) If the angle of incidence θ1 falls below the critical angle of total reflection, the x-rays do not propagate deeply into the material but are totally reflected at the surface

With θ′c = 90° − θc, this yields the numerical aperture (N.A.) for the fiber:

Another important characteristics of light transmission through an optical fiber is that light rays entering and exiting the fiber keep the same angle with respect to the fiber’s central axis. Figure 2.7 illustrated this situation for a straight fiber. The incident light ray shown at the left side of the drawing makes an angle, θa, with the fiber’s central axis. It is refracted at point O and enters the fiber at an angle, θ′c, to the fiber’s axis determined by:

The light ray inside the fiber encounters multiple times of total internal reflections and exits at point O′ on the exit face of the fiber. The light ray incident angle at point O′ is the same as θ′c. The light ray exit angle, θ′a, is determined by the law of refraction as follows:

Optical fibers used in an endoscope are required to transmit a broad wavelength range of light (at least covering the visible wavelength range 400–700 nm), therefore, have to be the “multi-mode” type and have a core diameter of larger than about 8 µm.

More than ten thousands of individual glass fibers form fiber bundles of a few mm in size and are used to transmit illumination light or relay the image in an endoscope.

For illumination, fibers with a diameter of larger than 25 µm are used and there is no need to have any precise order in the bundle (incoherent bundle). For relaying an optical image in an endoscope, fibers of smaller diameter (~10 µm size) are used for better image resolution and the fiber bundle must be ordered. Each fiber has to occupy the same relative position at the exit face of the bundle as at the entry face.

This is known as a coherent bundle. These imaging bundles are often used to make flexible endoscopes.
There is a special type of single optical fiber that can also be used to relay optical images. In this special fiber, the refractive index of the core material varies. It has the highest refractive index at the center and decreases gradually towards the edge following a parabolic profile across the radius of the fiber as illustrated in Figure below.
This is called the gradient index (GRIN) fiber or Selfoc (self-focusing) fiber.

Fig. 2 (a) δ/ρ (the index of refraction decrement divided by the density of the material) for Be, Al, and Ni as a function of x-ray energy. (b)Mass attenuation coefficient μ/p for the same elements.

This fiber can periodically focus an image along its length. Therefore, depending on where the end face is cut on the fiber, a Selfoc fiber can act as a converging lens, a planeparallel plate (with or without inversion), or a diverging lens. To form an endoscope, two different types of Selfoc fibers are utilized: one act as the objective lens, the other as the relay lens. The objective lens Selfoc fiber is much shorter than the relay lens Selfoc fiber and is bonded to the end of the relay lens Selfoc fiber.

The objective Selfoc fiber images an object outside of the distal end of the endoscope onto its rear face, while the relay lens Selfoc fiber pass on this image to the proximal end of the endoscope. These endoscopes have smaller diameters and facilitate higher resolution imaging, but are generally rigid because the Selfoc fibers are very fragile.

The illumination optics consists of three parts: light collection from a lamp, light transmission through a flexible light guide, and illumination lenses at the distal end.
Figure (a) shows the complete illumination path for a rigid endoscope, Figure (b),(c) are example variations of the collection optics. In Figure (a), light collection from the lamp is performed by a large collection angle lens (the collection lens).

A spherical reflection mirror placed behind the lamp help in collecting light rays going backwards, i.e., light from both the solid angle α and α′ are collected by the collection lens. This roughly doubles the total power getting into the light guide. A focus lens then focuses the collected light to the flexible light guide. A heat absorbing or heat
reflecting filter (heat filter) is usually placed between the lamp and the collection lens to protect the more dedicated optical components afterward and the light guide.

Another optical filter can be placed between the collection lens and the focus lens, where the light beam is roughly collimated, to further refine the spectral profile of the light source to suit the intended imaging modality. For example, for white light endoscopy, the illumination spectrum is from 400–700 nm.

Fig. 3 Bragg scattering of hard x-rays from a crystalline material. The lattice planes have a spacing d and the x-rays impinge on the lattice planes under the angle θ

There are two common variations to the light collection optics. Figure(b) shows that a parabolic mirror is used to collect and collimate light from the lamp, which is located at the focal point of the parabolic. A focus lens then focuses the collimated beam into the light guide. The heat filter and the spectral shaping filter are placed directly between the lamp and the focus lens. The parabolic mirror is often a dichroic type that reflecting the visible wavelengths and transmitting the infrared (IR) wavelengths.

It is called a cold mirror and also helps reduce the heat to the light guide. Figure(c) shows that an elliptical mirror is used in light collection. The lamp is located at one of the two foci of the elliptical mirror, while the collected light is focused to the other focal point of the elliptical mirror. A collection lens is placed after the focused beam to accept and collimate the light beam and a focus lens then focuses the collimated beam to the light guide. Similar to Figure 2.9(a), the heat filter is placed before the collection lens, while the spectral shaping filter is placed between the collection lens and the focus lens. The elliptical mirror is also often a dichroic type. Usually the parabolic mirror and elliptical mirror help collect light from a larger solid angle than the spherical mirror configuration.

In the early days, tungsten lamps were used for endoscopy illumination. Now high-pressure Xenon arc lamps and metal halide lamps are used, which have a more flat spectral profile and are brighter with a smaller arc size, making it easier to focus to the light guide.
For a flexible endoscope (both the fiber endoscope and video endoscope), a single light guide based on an incoherent fiber bundle is used to conduct light from the light source to the distal end of the endoscope. This light guide has a diameter of millimeters with an individual fiber size of 25 µm or greater. From the light source to the endoscope proximal end, the light guide is packed within an umbilical cord that also contains pipes to transmit air and water.
For a rigid endoscope with no requirements for air and water transmission, the light guide takes the form of a two segments design. Usually a flexible liquid light guide is used between the light source and the proximal end of the endoscope. A mechanical adapter, allowing the liquid light guide to be detachable, then helps connect the liquid light guide with an incoherent fiber bundle-based light guide inside the endoscope to transmit the light to the distal end. A liquid light is used in the first segment for its higher light transmittance than a fiber bundle.

At the distal end of the fiber bundle, a set of lenses is used to achieve uniform and large field illumination. In endoscopy applications, the object being viewed is usually not flat, but a curved surface. Therefore, the use of regular aberration-free projection lenses does not lead to uniform illumination; instead, aspheric lenses are employed to achieve uniform illumination in endoscopy. Miniaturization requirements deem these lenses to have about the same millimeter scale sizes of the illumination fiber bundle.

The imaging optics for an endoscope could include the objective, the image relay optics, and the eyepiece. Optical design for a rigid endoscope is the most challenging, where image relay is accomplished by as many as 60 individual lenses. A fiber optic flexible endoscope uses a coherent fiber bundle for image relay, simplifying the
optics considerably. In the case of video endoscope, images are captured by placing a miniaturized CCD sensor directly after the objective, eliminating the uses of image relay optics and the eyepiece.

Figure below illustrates the imaging optics involved in a fiber optic endoscope.
Object QP on the tissue surface is imaged by the objective to form an image Q’P’ at the entry-face of the distal end of the coherent fiber bundle. The coherent bundle, containing several hundred thousand fibers, relays the image to the proximal endface of the bundle to form an image Q″P″. The eyepiece then create a virtual image Q′″P′″ that presents a magnified view of the object to the observer’s eye.

Optimally the objective should be designed to be telecentric in the image space as shown in Figure above. With the telecentric objective the chief (central) rays of the light cones forming the image Q′P′ all enter normally on the entry-face of the bundle. This is illustrated for the cone of rays forming the image at P′ of the object point P. Because light rays entering and exiting an optical fiber in the bundle keeps the same angle with respect to the fiber central axis, the chief rays of the light cones emerging from the proximal end-face of the fiber bundle are then also perpendicular to the end-face of the bundle. This is exemplified for the cone of light emerging from the fiber at P″ (the relayed image of the object point P).

The chef rays of all emerging cones of light from image Q″P″ are thus parallel to the axis, and they all therefore pass through the back focal point (O′) of the eyepiece. This guarantees that all other rays from each cone can pass the exit-pupil of the system, therefore, achieves uniform detection efficiency over the whole image. If an ordinary objective is used, the rays for any off-axis object point (such as P) emerge from the eyepiece as an annular tube of rays. For details, see (Hopkins 1976). Some rays will fall outside of the exit-pupil, resulting in nonuniform image detection efficiencies (smaller on the edge than in the center).

Figure below shows the imaging optics of a rigid endoscope consisting of the objective, the field lenses, the relay lenses, and the eyepiece. The objective is designed to be telecentric in the image space to facilitate interface with the relay lenses. The objective creates an inverted image Q′P′ of the internal organ QP. Field lens 1 located close to image Q′P′ then redirects the light cones towards the relay lens 1 with the chief rays pass through the center of relay lens. Field lens 2 placed near image Q″P″ helps maintain the chief rays confined within the small tube of the endoscope. Relay lens 2 then conveys the image to Q′″P′″. This series of field lenses and relay lenses are repeated inside the endoscope tube until the image is relayed to the eyepiece, which presents a final magnified image for viewing by the physician.

Figure below also shows that in a modern rigid endoscope the conventional achromatic doublets-based relay lens is replaced by Hopkin’s rod-lens. One advantage of using rod-lens is that the light beam can be confined more tightly to the optical axis by reducing the ray divergence in air gaps between the lenses. This reduces vignetting. Another advantage is that rod-lenses are simpler to mount and have larger clear apertures than thin achromatic lenses

Nowadays, for both the rigid endoscope and fiber optic endoscope, a CCD video camera is often attached to the eyepiece to capture and display the video images on a monitor in real-time. For this purpose a lens adapter is used between the eyepiece and the CCD camera to project the image to the CCD sensor.