Ultrafine focusing: myth or reality?
What is the ultrafine focusing? A human eye can be presented as a certain composite lens with the optical power of 50–60 diopters from the optical point of view, consisting of cornea, crystalline lens, crystalline humor and input variable diaphragm with 1.8–7.5mm diameter (according to some information it is 1–8 mm diameter), i. e. eye pupil plus eyelids (squint) that it is possible to be replaced simply with an ideal lens in total, having forgotten about absorption, scattering and other optical distortions. This allowed scientists-theorists to assume that the laser radiation can be focused in a spot with a diameter of 10 microns when arranging an ideal aspheric lens with 60 dioptres optical power (it is practical at accommodation on 50 dioptres infinity point) on the course of a single-mode laser bunch with the constriction which is on infinity point. According to the theory this fact is confirmed only when observing some prerequisites, i. e. diameter of a bunch is less than eye pupil (diffraction) and an action occurs in a distant zone z >> Lр.
; , (1)
θ is the energy divergence at 1/е 2 level,
Fгл is an eye focal distance,
М2 is an М index (for TEM00 M2= 1, super-Gaussian beam M2= 5–10, FlatTop M2= 30–40)
; dz = d0 ≈ θz, (2)
where z is the running coordinate from a front mirror to an eye, d0 is a constriction diameter on an output mirror at 1/e 2 level. Any accommodation changes nothing, and it does not reduce beam diameter on retina. Reality is far from theory everything is much greater.
The authors of ultrafine focusing of a laser radiation in an eye have invented nothing better, than to to abandon the discrete elements method, even without regard for the sun. Angular scale of the sun is 0.5°. Energy density of solar energy power on the earth is Ps = 1 000 W/m 2 as an eye focuses on radiation from 0.3 to 1.4 microns. Let us accept density of power of the solar energy received by an eye for 500 W/m 2. Having 60 dioptres eye power, the image of the Sun with 150 microns is built on a retina. Having 2 mm eye pupil diameter, 1.5 mW sun energy passes through it. Power density (3) is equal to 84 mW/mm 2 or 21 mJ/mm 2 in case of radiation during 0.25 sec.
It is obvious that the direct view of the sun in a zenith is dangerous for sight. In case of accepting the condition that when 10 microns focusing 0.1 mW radiation is dangerous, the allowed density of power in an eye (4) is equal to 1.27 W/mm 2. It looks quite strange.
And is ultrafine focusing of laser radiation on eye retina possible in real life?
Statements contained in different versions of discussing on laser safety of Mr. G. I. Zheltov include statements on certain data obtained from doctors who have found some microdamages of eye retina of Не-Nе lasers adjuster, and about certain overdetermined experiment, or just misprints on wavelength of helium-neon laser radiation [1,2] or the note that "maximum-permissible energetic parameters for lasers of the 1st, 2nd and 3rd classes differ according to distinctions of discrete elements method and maximum allowable limit". These statements have nothing to do with reality . There are some questions to the author of the theory and certainly to co-authors who have maniac diligence when deal with arithmetic, and who obviously have little understanding of laser beams, and therefore they consider an injury of eye retina made by laser beams of He-Ne laser and they are difficult to see with the naked eye. It should be reminded that this maximum allowable limit is a result of approximation (extrapolation) of real results of laser radiation focusing measurements on an eye retina from the area of 150 microns to the area of estimated diameter of 10 microns ultrafine focusing .
Domestic and foreign measurements data of 70th and 80th belong to the range of minimum possible spot diameters on a retina from 50 microns to 150 micron, and it is a reality in most cases.
ANSI developers have included a 10-time hygienic allowance for all errors.
Is it possible at least to approach to ultrafine focusing in reality? Authors of ultrafine focusing suppose that duties of a person of which include placing his eye on optical axis that it the same as a laser beam axis pretend to be a subject, i. e. it is referred to laser resonator adjuster who uses collimation method (collimator ) in his work.
Let us describe the standard technology of adjustment made by collimation method. For observation of reflected light from remote mirror it is necessary to disadjust a near mirror to avoid glares from the walls forming a border of the active medium (capillary in the gas laser). Further it is necessary to excite the active medium, to receive a light flow and surely to use tinted glasses (better protective goggles). After nontransmitting mirror adjustment by means of diopter tube, an adjustment is made for output mirror returned on the place and beforehand an adjustment according to a cross position in a cold state is performed, combining cross reflection from the mirror with the middle of the mirror visible through mirror’s discharge channel that is illuminated from resonator reverse side. Attention (!), if no generation appears, its search is performed by a collimation method through a nontransmitting mirror in goggles. It is a standard adjustment of visible gas lasers, as is, actually, matter of disputes. Such method of adjustment is applied extremely seldom and is urgent in the most difficult resonators, i. e. in the single-mode and curved ones when it is necessary to bring a working body to resonator axis at amplification optimum. An eye is necessary only for tracking the power indicator as generation is received by means of a common scanning of an output mirror by oscillation on two axes, to maximum value. And there is a myth about eye retina microdamage by gas lasers adjusters violating the adjustment technology in dry residual. And this myth is not a single one.
Let us consider the common widespread semiconfocal laser resonator where in most cases the radiation escapes from a plane mirror, as we know, for convenience. In case of such resonator adjustment the laser radiation can get to adjuster’s eye unprotected by goggles which is placed most closely to an output plane mirror (20–30 mm). The laser beam constriction of the semiconfocal resonator is on plane mirror surface. The optical layout of retina radiation is provided in fig. 1. Applying the classical equations to Gauss rays (5,6,7):
Accepting we obtain
, and .
As a result is obtained. A well-known result is obtained, i. e. the laser radiation of the semiconfocal resonator cannot be focused on a retina of adjuster’s nearby eye as the constriction of Gauss beam is near the eye focal plane. Accommodation only changes slightly a spot diameter in focus, but at the same time it takes away a constriction from a retina.
Other attempts to place the eye on a visible laser beam can be equated to mutilation, and they are so improbable that they are almost impossible in real life. The probability to find 1 Mrad source divergence with 10 deg antenna (eye) angle reception diagram with consequences at distance of meters even in invisible form by some homo sapiens "foreigner В" (especially to get into a beam in visible form) is insignificant, and it is about one part in a million in case of single eye opening for 0.25 sec. Focusing of the image of the laser beam scattered from objects on eye retina is more real, but in this case the energy of a laser radiation getting into eye is several times lower than the energy of a direct laser beam. And there is not simple particularity related to radiation coherence (speckles).
The creation of laser radiation hitting into a human eye as an integral part of determination of discrete elements method and maximum allowable limit, and everything that was implied is a very simplified abstraction related to ophthalmology (see the appropriate literature on ophthalmology). All these simplifications on eyebulb immovability have independently toughened norms which are convenient for ophthalmologist expert and for a patient for whom Atropinum was applied in the operational machine. The permanent damage of human eye made by laser (total loss of sight of a single eye) is rare phenomenon. Five cases in the world have occurred for 40 years of observation. The value of the acceptable risk is extremely low (one part in ten million). Death rate of miners is one part in ten thousand. Let us remind that maximum allowable limit is the level of energy deposition which causes damage of native tissues with probability of 0.1%. Troubles happen not only to those who have not read rules, but also to those who could not or have not managed to read all volumes concerning troubles of last experience up to the end.
So, the fight against ghosts for health or for something else creates as always, arithmetical monsters (let us do not remind a chronic radiation that is domestic disease too). Requirements that are harmless at first sight lead to serious consequences, and absorb the mass of energy, that is necessary somewhere for preventing serious troubles.
First of all, there are questions concerning invisible, but so obviously dangerous radiation for eyes, against which the person has no receptors. Intuitively it is not clear why 7 mm diaphragm is used for the visible range (bright light). Most likely it is one more 10-time allowance in maximum allowable limit.
Secondly, the hazard classification is itself very conditional. For example, according to an International Electrotechnical Commission 501 mW laser belongs to the 4th class of hazard, and 499 mW one belongs to the 3rd class (for comparing, the 4th class of hazard, is 50 W according to SanPiN 5804–91 ). It is only about potential threat, and 20 kW invisible beam of the technological continuous CO2 laser and 0.5 Watt visible laser that belong to one hazard class are quite bad facts. The concept of a hazard class indicates only a need to analyze a laser and dangerous zone more deeply, but not to make any disastrous conclusions.
According to co-authors  of SanPiN 5804–91, everything is extremely clear: "By the end of the 80th in the USSR advancing results were obtained and at that times the results were more exacting than the western standards without prejudice and not because of someone›s ambitions or according to any administrative instruction. To claim something opposite means accusing medico-biological scientists and expert engineers who spent the considerable parts of lives and rather large amounts of state money for creation of bases of laser safety in Russia".
From the data shown on a review by G. I. Zheltov, no advanced results  are occurred and a wish to be "ahead of the curve" with ultrafine focusing and unfavorable accommodation with corresponding "arithmetic" are available.