TRANSMISSION OF AN OPTICAL IMAGE ALONG A CURVED PATH USING A FLEXIBLE FIBER-OPTIC LIGHT GUIDE

It is often necessary to transmit an optical image along a curved path. In particular, such devices are used in medicine for examining internal organs (cystoscopes, gastroscopes, bronchoscopes, etc.). In this case the requirement is imposed that the image-transmitting system be flexible and easily adaptable to the conditions of its introduction into the organ under investigation. Existing instruments intended for these purposes, which are complex systems of lenses, prisms, and mirrors, have a number of major shortcomings. First of all, they either consist of rigid joints or have extremely limited flexibility. Further, owing to the enormous number of optical surfaces (in a modern gastroscope the number of lenses reaches 50), they are characterized by large losses of light and a strong scattering background. In addition, the image quality proves to be very poor as a result of all possible aberrations. Finally, and this is especially important, these instruments have an extremely small aperture.

The authors of the notes reviewed\(^{1,2}\) have developed a new method for solving this problem, largely free of the indicated shortcomings and, in essence, reproducing the structure of the eye of certain insects.

It is well known that light entering a curved glass rod or jet of water will, under known conditions, undergo total internal reflection at its surface and can emerge only at its end. This phenomenon will also occur in the case of a thin fiber of glass or another transparent material situated in a medium with a lower refractive index. In other words, a thin glass fiber can act as a light guide: light entering one of its ends emerges from its other end, practically independently of its shape (provided, of course, that there are no kinks). Theoretical consideration shows that this is true for fibers whose diameter is greater than approximately \(0.01\) mm, since otherwise differential phenomena become important—the fiber will act as a waveguide and energy will be propagated through its walls. Experiments show\(^{2}\) that indeed, in the case of a borosilicate-glass fiber having a diameter of \(0.025\) mm and a length of \(750\) mm, light entering one of the ends of the fiber emerges from its other end.

If the length of the fiber is \(L\), and the angle made by the light ray with the axis of the fiber is \(\varphi\), then along the path through the fiber the ray undergoes

\[ \frac{L \operatorname{tg}\varphi}{D} \]

reflections (\(D\) is the diameter of the fiber). In particular, for \(\varphi = 10^\circ\), \(D = 0.025\) mm, and \(L = 25\) mm, the ray undergoes 116 reflections. Thus, practically only those rays for which \(\frac{\pi}{2} - \varphi\) is greater than the angle of total internal reflection will pass along the fiber. In this case the intensity of the transmitted light depends substantially on the quality of the surface, including on its cleanliness. The length of the ray path inside the fiber is equal to \(L \sec \varphi\), and (if losses upon reflection are neglected) the transparency of the fiber \(T\) is determined by the relation \(\ln T = -a L \sec \varphi\), where \(a\) is the absorption coefficient of the glass, generally speaking sufficiently small. If the fiber has flat end faces and if the refractive index of the material from which it is made is greater than 1.4, then the aperture angle of the light beam entering the fiber and emerging from it exceeds \(\frac{\pi}{2}\).

Let us now imagine that we have a tightly packed bundle of such fibers. An image of an object is projected onto one of the ends of this bundle (the angle of view may reach \(\pi/2\)). Then the light falling on the end face of any one of the fibers will emerge from its other end face, as a result of which (if, of course, the fibers are not interchanged) an image of the object will be formed at the second end of the bundle. This image will, naturally, not be continuous, but point-like, resembling a television image. However, if the diameter of the fibers is \(10\,\mu\), then details of size \(20\,\mu\) will be distinguishable in the image transmitted by the bundle (taking into account the gaps between the fibers). This corresponds to a resolving power of 5 lines per millimeter, i.e., approximately the resolving power of the unaided eye. In other words, the eye will perceive the image as practically continuous. Experiments carried out by the authors\(^{1,2}\) confirm the considerations set forth above: with the aid of such “fibroscopes” they succeeded in obtaining images of excellent sharpness (in particular, of text). Moreover, bends of the bundle (up to \(360^\circ\)), as well as curvature of its middle part, did not affect the image obtained with its aid.

In practice, for making a fibroscope, glass proved to be the most suitable material—both in its mechanical and in its optical properties (low absorption). Other materials (quartz, nylon, polystyrene) proved considerably worse. In order to improve the conditions for internal reflection and to prevent energy leakage at the points where fibers touch one another, one of the authors\(^{1}\) recommends coating the surface of the fibers with a layer of a transparent substance (plastic) having a lower refractive index, with a thickness of several wavelengths.

A bundle of fibers is made by winding a long fiber onto a drum—layer by layer—followed by fastening and cutting the bundle.

The comparatively high transparency, wide angular aperture, and flexibility, together with sufficient resolving power, apparently ensure broad possibilities for application of the device described. Let us note that it differs from the compound eye of an insect in that in the latter each of the light guides has a separate lens, whereas in the fibroscope there is a single common optical system projecting the image onto the front end surface of the fiber bundle. At the same time, the structure of the image obtained with its aid does not differ from the structure of an image perceived by the eye or by an iconoscope, with the inherent discreteness of the receiving apparatus.

G. R.

References

1. A. C. S. Van Heel, Nature 173, No. 4392, 39 (1954).
2. H. H. Hopkins, N. S. Kapany, ibid.