More poppycock 3:
Microscope magnification

In my earlier pages on poppycock terminology, I discussed the concept of image magnification, and how it has been, intentionally or by sheer ignorance, twisted and obfuscated in promotional and technical literature. Here I discuss the magnification claims of a microscope of historical interest claiming to magically achieve magnifications not allowed by photon physics, as well as some toy microscopes and webcam-based digital microscopes.

The realm of the possible

The resolution limit of conventional optical microscopes was established by Ernst Abbe around one and a half centuries ago. Known as the Abbe criterion, it says that the smallest features an optical microscope can resolve are approximately half the size of the wavelength of light. By using shorter wavelengths, one can resolve smaller features, but the shortest wavelengths perceived by human eyes (around 400 nm) place a practical resolution limit at 200 nm for visual observation.

Nothing prevents us to increase the magnification of an optical microscope beyond Abbe's limit, but this only creates empty magnification that does not show any additional detail. For example, you could use the eyepiece of a microscope to project an image on a large projection screen. The image will be very dark and quite blurry, but it does work.

It can also be noted that, with a good optical microscope, it is entirely possible to detect the presence of a particle of a diameter quite a bit smaller than the resolution limit of the microscope, as long as individual particles are located conveniently far from each other. The particle, however, is only visible as a featureless blurred circle, and multiple particles tightly packed together are rendered as a single blur.

Additionally, Abbe's limit is the top theoretical limit to microscope resolution, but there is no bottom limit to the resolution of a poorly built microscope. A good microscope for transmitted illumination with air objectives and air condenser can reach 600x (typically with 10x eyepieces and 60x objective) and still provide a visually sharp image, or 1,000x with a moderately fuzzy image. A better image quality at 1,000x requires a 100x immersion objective and an immersion condenser. To substantially exceed this magnification (e.g. by a factor of 100 or more), you need an electron microscope, X-ray microscope, or atomic-force microscope.

We now know that it is possible to make smaller features than Abbe's limit visible with an optical microscope by cleverly exploiting fluorescence and quantum phenomena. However, they require sophisticated equipment like high-power lasers, near-field meta-optics placed at distances from the subject much smaller than the wavelength of light, or quantum-enhanced microscopes that project quantum-entangled photons outside the range of near fields. You cannot find this level of technology in a toy microscope (not for the next several decades, anyway).

Magnification of a microscope

Magnification of a microscope is specified as the ratio of linear image size seen through the eyepiece(s) to linear subject size. The image size is measured on an image projected in front of the viewers' eyes at the conventional distance of 25 cm.

In practice, magnification of a microscope is calculated by multiplying the magnification of the objective by the magnification of one eyepiece, sometimes additionally multiplied by a tube magnification factor specified on the microscope tube (typically between 1.25 and 2).

Rife microscope

The claims to fame of "inventor" Royal Raymond Rife (1888-1971) are an "oscillating beam ray" device said to be capable of curing almost any disease, and a microscope capable of magnification far beyond any other optical microscope, in spite of using ordinary, commercially available objectives and eyepieces. Some newspapers of the time, for example, reported that the Rife microscopes were capable of a magnification of 17,000x. Other sources report claims of 30,000x. The ray machine was likewise reported in the press to have cured several cases of terminal cancer within 60 days of treatment..

Aside for an internal prism system designed to increase the length of the optical path inside the microscope tube, the Rife microscopes available for inspection and/or documented in photographs do not appear to contain anything capable of fulfilling Rife's claims. In a finite microscope, increasing the optical tube length does increase magnification, but does nothing to increase image resolution. Usually, it decreases the latter by forcing the objective to work outside of its design parameters. Naturally, some proponents of Rife microscopes maintain that a "secret" component has been removed from these microscopes, and even wrote lengthy "explanations" involving multiple stacked optical slits and other unworkable devices. Unfortunately, all these discussions are purely qualitative, and ignore basic aspects of light propagation and diffraction.

There are indeed ways to go slightly beyond Abbe's limit even without quantum-enhanced optics, e.g. by using a slit-like diaphragm instead of a round one. Indeed, some reputable makers of research microscopes used the same method in some of their special-purpose microscopes, where measuring the subject in a single direction was desirable (e.g., the thickness of a fiber, while the length of the fiber and its internal texture were irrelevant). However, this slightly increases resolution in one direction, while simultaneously reducing it in a perpendicular direction. Stacking two slit diaphragms at a right angle to each other, as some of the "explanations" of the Rife microscope propose, produces no net increase in resolution, only a net loss of resolution caused by diffraction in both slits.

Other explanations are simpler nonsense, like the assertion that to make the Rife microscope reach the advertised magnification it is necessary to replace the eyepieces with objectives, because the latter are of better optical quality than eyepieces. This conveniently ignores "details" like the different location of entrance/exit pupils in objectives and eyepieces.

Bracegirdle (2003) provided an account of the Rife microscopes, including one he was able to inspect and test. Like numerous other scientists and microscope experts, he concluded that Rife's claims are impossible. He further suggested, and I concur, that the extremely high number of unnecessary fine mechanical adjustments of the Rife microscopes appears designed to impress laymen, but make the use of the microscope so fiddly to become, at best, impractical. Additionally, a few faults and oversights in its design betray the inexperience of the designer. I believe the unnecessary mechanical complexity is partly smoke and mirrors, and partly a subterfuge to deflect criticism that the device does not work by counter-arguing that the user failed to properly "calibrate" it.

None of the web sites reported at the end of Bracegirdle's paper are still active, although I accessed at least two of them a few decades ago and was able to find them again on the Wayback Machine.

Rife's claims about extremely small "microbes" causing all diseases, and being able to morph into each other, as well as to and from a multitude of different shapes and sizes, are known as Rife's pleomorphism "theory". These claims are frequently repeated and amplified on short-lived web sites promoting "alternative" views on science and medicine. Some of these web sites also publish discussions of the Rife microscopes, probably to reinforce the credibility of the claims about these "microbes", and indirectly of the claims about the effects of "oscillating beam ray" machines.

Later in his life Rife himself, perhaps fearful of being sued for false medical claims, had become slightly more careful with his claims, and limited himself to stating that his microscopes, rather than providing a so-far unheard-of high magnification (which is a demonstrable falsehood even without testing his microscopes), were particularly good for "special applications". This included observing the "microbes" he claimed caused most or all diseases and could be treated by his other main invention, the "oscillating beam ray". Needless to say, no one else could find these shape-shifting microbes with the best medical microscopes of the time, nor with the electron microscopes developed shortly thereafter, and there is no credible documentation of the beam ray devices successfully treating any diseases. Some beam ray devices were tested and found to be DOA - they simply did not turn on, nor did anything at all. Some modern variants do work, in the sense that they produce a visible electrical discharge inside a gas-filled tube and a buzzing sound, but so does a neon sign, and there is no medical proof that neon signs and fluorescent tubes cure diseases like cancer and advanced-stage viral infections. The American Medical Association eventually forbade Rife from treating patients with his machine.

An interesting conceptual variant of the "oscillating beam ray" scam emerged after the Coalition-Iraq wars, when the Iraqi government was scammed by a British company into buying very expensive remote detectors of bomb and mines capable of detecting them at distances up to kilometers (and even drugs, ivory, and other chemicals and materials). These devices were, essentially, empty plastic boxes equipped with a handle, a few fake controls, and a dowsing rod. The makers of these "detectors", confronted with accusations that the devices were a simple fraud, claimed that the person holding the box, and the mental attitudes of this individual, were essential components of the detector. This was tantamount to saying that the detector only worked if held by a person firmly believing that it did work. Any doubter was conveniently blown up by an undetected bomb solely because of his/her own fault. It somehow reminds me of medieval trials for witchcraft designed to prove that any survivor of the tortures had to be a witch, and therefore had to be burned at the stake, because no innocent accused of witchcraft could have survived.

For the past 48 years, a company called has been running a web page announcing the impending release of what appears to be a modern Rife microscope, with similar claims to the latter and likewise using ordinary commercial objectives and eyepieces. Like the Rife microscopes, they are characterized by extreme mechanical complexity, some of it evidently purposeless even for observers with only a moderate experience of microscopes.

The only developments reported by this company in these 48 years are:

• The death, in 2022, of the "German microscope expert" involved in this project.
• A promise to start delivering microscopes in "Q3, 2022", and a text blaming the Covid pandemic for delays.
• A "nominal" charge of 400 USD for demonstrations of their microscope in Hamburg, Germany.

The company is apparently run from a Las Vegas P.O.Box, with labs and personnel located "in Germany". I will not link to their web site, but if you really want you can easily Google it. Google will also give you an address for the company in Cologne, Germany, which turns out to be a residential apartment block.

The Scientific Papers tab of the company's web site begins with a promising paragraph: "A number of scientific papers have been written using the results obtained with" the company's microscopes, and continues: "We are offering some of these papers for download without further comment." The only paper, scientific or otherwise, available for download is a three-part PDF in German, entitled "Der Blick in die Unendlichkeit". It consists mostly of a haphazard discussion of Rife's pleomorphism "theory" and other pseudo-scientific babble, with mention and references to some of its followers, together with some claims about the company's microscopes.

As of March, 2023, the Scientific Papers tab on the German web site of the company (.de top domain) and PDF no longer seem to be available, but are still available on the US web site (.com top domain). They are also available in the 92 snapshots of the company's US web site on Wayback Machine. The PDF is also available on Yumpu, together with several other tell-tale documents from the same microscope company (e.g. 1, 2, 3, 4, 5, 6).

The PDF is illustrated with pictures reportedly taken by the deceased microscope expert with one of the company's microscopes.

The only significant bits of information worth discussing that I found in the PDF:

1. The assertion, in Part 3, Figure 7, that one of the company's microscopes is capable of a 100 nm resolution, while "ordinary light microscopes" only reach a 400 nm resolution. The purpose of the figure is to assert that the company's microscopes have four times the resolution of an ordinary optical microscope. However:
1. A 100 nm resolution is available by using a 200 nm UV light source and good UV optics (both are commercially available from multiple sources). This capability is far from unique for an optical microscope.
2. The assertion that ordinary light microscopes stop at a resolution of 400 nm is false. 400 nm is violet light still within the visible range, and the resolution at this wavelength is 200 nm according to Abbe's criterion. Therefore, a good visible-light microscope can reach the resolution of 200 nm by using a monochromatic 400 nm illumination, without special optics and still allowing visual observation through the microscope. UV microscopes with a resolution of 170 nm are not too difficult to assemble from off-the-shelf parts that have been available for decades, and obviously require digital cameras or other devices to convert UV to visible images.
2. The assertion in Part 3, Figure 8 that the company's microscope provides (1) a resolution of 100 nm, (2) an enormously higher DOF than other optical microscopes, (3) a "magnification up to approx 25,000x true-color images". This can only prompt one reaction: Poppycock alert! Breaking down the statement:
1. The 100 nm resolution claim is possible, as already discussed, and far from unique.
2. An unlimited DOF can be obtained , with static subjects, by using an image fusion technique called focus stacking, popular in photomacrography, also common in optical microscopy, available in many digital cameras, and even used on Mars by the Curiosity rover. It is not a unique capability of the microscopes of this company. It can be used with any conventional optical microscope equipped with fine focus, after a mechanical modification of this focuser. For example, I am using it on a 35 year old Olympus compound microscope, and some microscopists use it on microscopes built a good one century ago.
3. The 25,000x magnification, on the other hand, is pure, unadulterated poppycock (unless it is empty magnification that shows no more detail than at 1,000x - but what good does it do?). You need a good SEM, TEM or STEM to get 25,000x. As for the "real color" part (a claim also repeated several times on the company's web site), at 25,000x there can be no color because we are at a scale far smaller than the wavelengths of visible light. Hollywood can easily show you the quantum world in dazzling colors, but physics and technology have their limits. Even at 200 nm illumination (100 nm resolution) there can be no "true color". Color is at wavelengths between 400 and 700 nm.

Like the company's web site, the text of this PDF seems to have been gradually sanitized of some of the most obvious false claims relating to microscopy, but the figures and their captions seem to have been re-used from earlier materials and have not been revised. The real purpose of the PDF is promoting one of the many variations on the theme of Rife's pleomorphism, especially for what concerns cancer and its "alternative treatments". It would be easy to laugh these claims off, were it not that they are designed to entrap gravely sick people hoping to find a cure, or their desperate relatives grasping at straws to find help for a terminally sick family member that physicians no longer can help, and financially exploit their suffering and trust for financial gain in return for nothing more than false treatments, false promises and false hopes.

There isn't much money to be made by selling microscopes that don't work and have never been available for purchase, so I am convinced that this microscope company is only a side show to increase the credibility of the main scam of selling miraculous treatments that have no basis in science.

I failed to find any information on the supposed journal on which the PDF was published, let alone whether it really was published. Publication on a formally established and indexed science journal, in itself, is no proof of scientific value, because there are thousands of indexed "scientific" predatory journals with high sounding names (sometimes highjacked from respectable journals of the past that are no longer published, other times similar enough to respectable journals to be confused with the latter) that will publish virtually anything as long as the author pays a substantial charge. These journals are mostly based in India, where a single predatory publisher may own a roster of several hundred journals on the most disparate subjects, but quite a few operate from other countries. I myself regularly receive invitations to submit papers for publication in such journals and/or to participate in their editorial and review boards. Quite a few respectable scientists have been duped into lending their prestige and professional credibility to these journals, at least when predatory publishing was still a relatively new phenomenon.

The name of the author of this PDF is found on the web in connection with a few privately published booklets and texts expounding the same general type of pleomorphism theories and other unproven poppycock (one example about "blood flow paintings" that have no place in real medical science, at least in our universe, and another on isopathy, which is apparently related to homeopathy, an "alternative" method of treating diseases apparently popular in Germany, but based on premises not supported by medical research), and apparently designed to attract the attention of cancer patients and other people suffering from medical conditions that medicine cannot yet tackle successfully. The author is also listed as a "health practitioner" in a small German town. For reasons I don't fully understand, even a few modern countries like Germany have a long tradition of allowing self-appointed medical businesses and practitioners to apply "alternative" treatments of doubtful or no medical value on paying private patients.

The Scientific Papers tab on the company's web site additionally links to a few promotional videos, but nothing that could qualify as a scientific paper.

I will not further discuss Rife's claims or those of his followers, other than reporting that the transquantum-based Bull field detector in my lab, which I carefully built after many years of secret research, gives off-the-scale readings when brought close to pictures and descriptions of Rife's and his followers' microscopes and beam ray devices.

Disclaimer: The plans for building my Bull field detector are secret and not for sale (yet - but feel free to ask me again in another 48 years).

Magnification of toy microscopes and digital microscopes

Some cheap toy microscopes are, in a way, comparable to Rife microscopes in the sense that their promotional materials describe them as capable of absurdly high magnifications. In the past, this was especially common in ads on the back cover of comic books. A common trick in these ads was of using a "non-standard" definition of magnification: instead of using linear magnification, they published a figure computed as area magnification, usually without mentioning it, or only as a footnote. In this way, a microscope with 10x eyepiece and 10x objective (100x in total) suddenly became capable of 10,000x magnification (100 times 100). One with 10x eyepiece and 50x objective became a 250,000x microscope, and so on.

These magazine ads have largely disappeared, together with those for "spy cameras" one could hide in the palm of one's hand and "X-ray sunglasses" capable of penetrating women's clothes to reveal their underwear. I still see ads for toy microscopes reaching 1,200x, which is not outside the realm of the possible (especially if it is empty magnification). However, I see a possibly misleading way to specify the magnification of digital microscopes based on cheap webcams, typically advertised on Taobao and Aliexpress, and now making their way also onto Amazon. For example, the following ad titles are common on Aliexpress. Ads and seller names change frequently, so perform a search on Aliexpress.

• 600x 3.6MP Digital Microscope Aluminum Alloy Stand 4.3 Inches HD LCD Video Soldering Microscope PCB Phone Repair Microscope
• 1200X Microscope Digital Portable 7" LCD Video Microscope 12MP for Soldering Electronic PCB Inspection Continuous Zoom

Since these microscopes are designed for repairing electronic PC boards, the 1,200x type has only coarse focusing, and the 600x type lacks a focusing mechanism (you focus by moving the subject held in your hands, or by bending a scarcely practical plastic gooseneck with plenty of backlash). A 600x or 1,200x real magnification, measured as customary for microscopes, would make focusing by these means impossible. Such a magnification would also be way too much for the job of repairing PC boards, and would require sophisticated and expensive optics to provide the working distance of several cm shown in the ads. The NA of these long-working-distance optics would necessarily be low, given the small diameter of the objective.

The magnification specified in the ads is also suspiciously close to that obtained by squaring the estimated linear magnification (25² = 625, and 35² = 1,225), so I cannot exclude that these ads refer to area magnification instead of linear magnification. They may be, in this respect, a reincarnation under a new guise of the misleading magazine ads for toy microscopes.

A 300 Mpixel microscope camera for a few bucks?

At present, dozens of China-based eBay sellers advertise a 300 Megapixel Microscope Module Electronic Eyepiece Camera Module USB2.0 output for around 12-15 USD. A 300 Mpixel digital camera to mount on a microscope, if you can find such a thing, should cost thousands of USD. Most likely you cannot find it, because 300 Mpixel would be a terrible waste of image resolution, considering that 30 Mpixel is probably already overkill for a conventional optical microscope. Additionally, a 300 Mpixel sensor is wasted unless the lens is capable of a comparable resolution, and I can tell you that a 300 Mpixel lens would cost more than a good research-quality microscope.

I cannot imagine a cheap plastic lens with a front optical element 10 mm in diameter having such an image resolution, let alone a 300 Mpixel sensor fitting in the space behind this lens.

Additionally, a USB 2.0 interface as described in the ad would take minutes to transfer a single 300 Mpixel image (almost 1 GB uncompressed for a 24 bit-per-pixel color image).

To put things in perspective, an 8k camera sensor or LCD screen has a resolution of around 33 Mpixel, and 16k is about 132 MPixel. It is just an example of the current attitude of many Chinese retailers that "anything goes, as long as I make a profit".

From the price and picture, I guess they are offering, in the best case, an old and outdated 3 Mpixel generic webcam module (the picture shows a module with a readable 2015-05-19 date on the PC board). I can see no way a honest mistake could cause the resolution to become advertised as 300 Mpixel.

Conclusions

The Rife microscopes are an outstanding example of pseudo-scientific fraud, designed mainly to support and lend credibility to other pseudo-scientific claims of curing/treating a broad range of diseases with an "oscillating beam ray" machine of no medical value. More modest examples of misleading magnification claims can be found in old advertising of toy microscopes and current webcam-based "digital microscopes". Current eBay ads by multiple Chinese sellers misrepresent a cheap and outdated webcam module as a 300 Mpixel microscope camera.