Classical Optics Review of the Source of the Fraunhofer Diffraction Limit
To understand how the magnification and resolving power of the Rife microscope can go beyond that of the commonly used optical microscope, it is necessary to understand the cause of the magnification and resolving power limitations of the ordinary optical microscope. Figure 1 shows the simplest form of a microscope. The object (1) for the objective lens has its image (2) as the object for the eyepiece lens. This object (2) has a final real image formed on the eye retina (4) by the combined lens system of the eyepiece lens and eye lens. And finally, the brain interprets the real image (4) as coming from a virtual object (3). From the point of view of geometrical optics alone, the objective and eyepiece of Figure 1 can each be replaced with lens combinations to give unlimited magnification. However, due to diffraction phenomenon, namely Fraunhofer diffraction, and lens aberration phenomenon there is a practical limit to useful magnification. From theory and experiment it has been found that Fraunhofer diffraction phenomenon is usually by far the dominant limiting factor in determining the resolution ability of a lens system to form an image in currently used microscopes. Figure 2 shows a plano convex lens which has two objects, O and O’. From these the lens form images I and I’ are formed in Figure 2 using only geometrical optics principles. Note that O and O’ are represented by small black dots. Further, note that Figure 2 is a symbolic diagram and therefore the white background could be replaced by black and the black lines and curves could be replaced by any color, yellow for example. The symbolic information contained in the Figure would remain the same. Now let O and O’ be sources of yellow light. I and I’ will now be yellow dots. Let the diameter (size) of the yellow light sources O and O’ become smaller and smaller. The diameter of the images I and I’ will, by geometrical optics principles, also become smaller and smaller. In fact, by geometrical optics principles, as the diameters of O and O’ go to zero so will the diameters of I and I’. However, due to Fraunhofer diffraction phenomenon as the diameters of O and O’ go to zero, the diameters of the images I and I’ converge to a finite non zero size. In fact the images I and I’ of point (zero diameter) light sources O and O’ are concentric light and dark zones as qualitatively illustrated in Figure 3. The light intensity pattern produced in space as illustrated in Figure 3 is that found along any line passing through the center of I (or I’) and at right angles to the shortest line segment joining I (or I’) and O (or O’).
So looking back at Figure 2 we see that if the distance s between the two point (zero diameter) light sources O and O’ becomes small enough, their images I and I’ will begin to overlap. This means that any two self luminous point light sources O and O’ located on an object of interest (the specimen) can not be observed independently unless they are far enough apart so that the center bright zone of theirFraunofer diffraction patterns do not appreciably overlap. In optics the standard derived relationship between s, w, n, and i for the lens of Figure 2 is:
S = (1.22 w) / 2n sin i ; Equation 1.
Where s is the minimum separation between O and O’ where they are just resolved, w is the wavelength of light used, n is the index of refraction of the medium between O (or O’) and the lens surface, and i is the angle as indicated in Figure 2. Substituting appropriate values of w, n, and i into Equation 1, for commonly used high power optical microscopes, gives values for s of around 2,000 Angstroms or .2 microns, which is significantly larger than the mean radius of viruses in general. However, this .2 micron resolution limit is still too optimistic when other distortion effects of lens systems are taken into account. The minimum resolving distance given by Equation 1 does not explicitly contain the diameter (D) of the lens. However, direct examination of Figure 2 clearly shows how i is dependent on D. It is now evident that no matter how much the eyepiece lens magnifies the object (2) of Figure 1, the corresponding size resolution in the final virtual image (3) can be no better than approximately .2 microns.
How Dr. Rife Suppressed the Fraunhofer Diffraction Limitations in Optical Microscopes
Rife found a way to overcome or suppress the Fraunhofer diffraction limitation, that enabled him to build a microscope that could see viruses and the fine details of bacterial structures that currently used microscopes can not see at all. What Rife did was to apply the Principle of Reversibility in a new and novel way. The Principle of Reversibility states: If a reflected or refracted ray is reversed in direction, it will retrace its original path. This principle has more than a purely geometrical foundation, and can be shown to follow from the application of corresponding mechanics principles to wave motion. In other words diffraction phenomenon (wave phenomenon) is also undone by reversing the path of the light ray (effectively time reversal). In Figure 4 we see a equiconvex lens which has formed the image I, in space, from a point light source object O. As indicated, the image I is not a point but has the form of concentric light and dark zones just as in Figure 3. Now by the Principle of Reversibility, if the diffraction pattern image I of Figure 4, which is formed in space, not on a screen, is sent back through the equiconvex lens (effectively time reversal), the original point image O will be formed, not the normally found diffraction pattern image from a point light source, such as in Figure 3. Note again that, the diffraction pattern image of Figure 4 is formed in space not on a screen. The diffraction pattern image that is being sent back through the lens is effectively a time reversal of light “image”. It is not light back scattered from and image formed on a material screen. Now consider Figure 5 which shows a compound lens objective as used in a high power optical microscope being used to form an image I in space, not on a screen, of a point light source O. As with the single lens objective a point image will not be formed. Instead a Fraunhofer diffraction pattern will be formed as shown. For simplicity theFraunhofer diffraction pattern shown is that of a single lens, however the actual pattern would be a composite of the separate Fraunhoferdiffraction patterns from the three lens in the system. The actual pattern would qualitatively be the same as shown, a strong central light disk, known as the Airy’s disk, surrounded by faint darker and lighter concentric zones. And just as before, if the diffraction pattern image formed in space not on a screen were sent back through the objective lens system a light point image would be formed, not a diffraction pattern image.
WHAT RIFE APPARENTLY REALIZED WAS THAT TO A GOOD FIRST APPROXIMATION HE COULD ESSENTIALLY ELIMINATE FRAUNHOFER DIFFRACTION PHENOMENON AND ACHIEVE HIGH MAGNIFICATION BY USING A EYEPIECE THAT WAS EXACTLY LIKE THE OBJECTIVE USED (MATCHED PAIR), BUT INSTALLING IT IN THE OPPOSITE ORIENTATION (BACKWARDS) TO THAT OF THE OBJECTIVE, WHILE CONCURRENTLY INSERTING AN OPTICALLY SYMMERTIC LIGHT BEAM EXPANDING (MAGNIFYING) OPTICAL ASSEMBLY BETWEEN THE EYEPIECE AND OBJECTIVE (SEE FIGURE 6).
A news paper article, I uncovered in my research that had no date or publication name, indicates there are probably 6 lens in the cylindrical center section of the microscope between the objective and eyepiece, with these lens being immersed in glycerine. The lens configuration probably used six identical double convex normally converging quartz lens, when used in air, equally spaced apart with the space between the lens filled with glycerine as shown in Figure 6. Since the glycerine has a slightly larger index of refraction (1.473) than quartz (1.46), the immersed double convex normally converging positive lens when used in air can be/are converted to diverging / negative lens making light rays traveling parallel or slightly converging, but nearly parallel rays, entering the lens along the optical axis leave the lens slightly diverging as illustrated in Figure 7A. Figure 7A illustrates qualitatively the light ray paths occurring at the beginning of the optical assembly of spherically convex surfaces of the beam expanding optically symmetric assembly shown in Figure 6. Figures 7A and 7B illustrate how the beam of light from the objective IS EXPANDED IN SUCH A WAY THAT ONLY LIGHT RAYS THAT ARE VERY CLOSE AND NEARLY PARALLEL TO THE OPTICAL AXIS OF THE ENTERING CONVERGING BEAM REACH THE EYEPIECE ENTRANCE. Note that just before the converging beam from the objective lens system comes to its focal point to form an image, it encounters the interface between the lens material medium and the glycerine medium at the spherically convex lens surface. THIS CONVERGING BEAM IS CENTERED ON THE OPTICAL AXIS OF THE SHHERICAL SURFACE OF THE FIRST CONVEX LENS IN THE ASSEMBLY. Upon crossing the spherically convex interface the converging beam is starting to be converted into a diverging (expanding) beam about its center axis. As the beam leaves the second surface of the first double convex lens in the assembly, it is now a diverging beam. As this now diverging beam passes through each additional spherically convex surface the central portion of the beam is again expanded about its axial center, the optical axis of the lens assembly. Only a very small fraction of the expanded light beam from each lens reaches the next lens in the assembly in such a way that it will have both further cross sectional expansion or magnification and still reach the last lens in the assembly. It is this greatly expanded (“magnified”) very small portion of the original beam which is focused down into an “image” by the eyepiece. Of course the optical axis of all the convex lens must coincide as closely as possible with each other. It is only a very small fraction of the spherical surface area of the equiconvex lens that is centered about the optical axis of the lens system that processes the light that will actually reach the eyepiece to form an image. That portion of the expanded light beam leaving the convex surface of the last lens and entering the eyepiece lens system needs to have approximately the same divergence (time reversed convergence) angle as the converging light beam leaving the objective lens system. When the expanded portion of the original beam is focused down into an “image” it still contains the Fraunhofer diffraction pattern structure obtained from its passage through the objective lens system. However, the eyepiece, which is identical as possible (matched pair) to the objective lens system, but installed in the opposite orientation, produces a Fraunhofer diffraction pattern structure which to a first approximation undoes essentially all of the originalFraunhofer diffraction pattern introduced by the objective lens system (Principle of Reversibility). What is obtained is a non inverted image with crystal clear clarity and very high resolution mainly limited by the resolving power of the human eye or camera electro-optics used.