The eyepiece in the kepler telescope is a converging lens. kepler telescope

The curiosity and desire to make new discoveries of the great scientist G. Galileo gave the world a wonderful invention, without which it is impossible to imagine modern astronomy - this telescope. Continuing the research of Dutch scientists, the Italian inventor achieved a significant increase in the scale of the telescope in a very short time - this happened in just a few weeks.

Galileo's spotting scope resembled modern samples only remotely - it was a simple lead stick, at the ends of which the professor placed biconvex and biconcave lenses.

An important feature and the main difference between Galileo's creation and the previously existing spotting scopes was the good image quality obtained due to high-quality grinding of optical lenses - the professor personally dealt with all the processes, did not trust delicate work to anyone. The diligence and determination of the scientist bore fruit, although a lot of painstaking work had to be done to achieve a decent result - out of 300 lenses, only a few options had the necessary properties and quality.

The samples that have survived to this day are admired by many experts - even by modern standards, the quality of the optics is excellent, and this is taking into account the fact that the lenses have been around for several centuries.

Despite the prejudices that prevailed during the Middle Ages and the tendency to consider progressive ideas "the machinations of the devil", the spotting scope gained well-deserved popularity throughout Europe.

An improved invention made it possible to obtain a thirty-five-fold increase, unthinkable for the lifetime of Galileo. With the help of his telescope, Galileo made a lot of astronomical discoveries, which made it possible to open the way for modern science and arouse enthusiasm and thirst for research in many inquisitive and inquisitive minds.

The optical system invented by Galileo had a number of drawbacks - in particular, it was subject to chromatic aberration, but subsequent improvements made by scientists made it possible to minimize this effect. It is worth noting that during the construction of the famous Paris Observatory, telescopes equipped with Galileo's optical system were used.

Galileo's spyglass or spyglass has a small viewing angle - this can be considered its main drawback. A similar optical system is currently used in theatrical binoculars, which are, in fact, two spotting scopes connected together.

Modern theater binoculars with a central internal focusing system usually offer 2.5-4x magnification, which is sufficient for observing not only theatrical performances, but also sports and concert events, suitable for sightseeing trips associated with detailed sightseeing.

The small size and elegant design of modern theater binoculars make them not only a convenient optical instrument, but also an original accessory.

The spotting scope is an optical instrument designed to view very distant objects with the eye. Like a microscope, it consists of an objective and an eyepiece; both are more or less complex optical systems, although not as complex as in the case of a microscope; however, we will schematically represent them with thin lenses. In the telescopes, the lens and eyepiece are arranged so that the back focus of the lens almost coincides with the front focus of the eyepiece (Fig. 253). The lens produces a true reduced inverse image of an infinitely distant object in its rear focal plane; this image is viewed through the eyepiece, as through a magnifying glass. If the front focus of the eyepiece coincides with the back focus of the objective, then when viewing a distant object, beams of parallel rays emerge from the eyepiece, which is convenient for observing with a normal eye in a calm state (without accommodation) (cf. § 114). But if the observer's vision is somewhat different from normal, then the eyepiece is moved, setting it "according to the eyes." By moving the eyepiece, the telescope is also “pointed” when viewing objects located at various not very large distances from the observer.

Rice. 253. The location of the lens and eyepiece in the telescope: back focus. Objective coincides with the front focus of the eyepiece

The telescope objective must always be a converging system, while the eyepiece can be either a converging or a diverging system. A spotting scope with a collecting (positive) eyepiece is called a Kepler tube (Fig. 254, a), a tube with a diverging (negative) eyepiece is called a Galilean tube (Fig. 254, b). The telescope objective 1 gives a true inverse image of a distant object in its focal plane. A diverging beam of rays from a point falls on eyepiece 2; since these rays come from a point in the focal plane of the eyepiece, a beam emerges from it parallel to the secondary optical axis of the eyepiece at an angle to the main axis. Once in the eye, these rays converge on its retina and give a real image of the source.

Rice. 254. The course of the rays in the telescope: a) Kepler's tube; b) Galileo's pipe

Rice. 255. The path of the rays in the prism field binoculars (a) and its appearance (b). The change in the direction of the arrow indicates the "reversal" of the image after the rays pass through part of the system

(In the case of the Galilean tube (b), the eye is not shown so as not to clutter up the picture.) Angle - the angle that the rays incident on the lens make with the axis.

Galileo's tube, often used in ordinary theatrical binoculars, gives a direct image of the object, Kepler's tube - inverted. As a result, if the Kepler tube is to serve for terrestrial observations, then it is equipped with a turning system (an additional lens or a system of prisms), as a result of which the image becomes straight. An example of such a device is prism binoculars (Fig. 255). The advantage of the Kepler tube is that it has a real intermediate image, in the plane of which a measuring scale, a photographic plate for taking pictures, etc. can be placed. As a result, in astronomy and in all cases related to measurements, the Kepler tube is used.

Course work

discipline: Applied optics

On the topic: Calculation of the Kepler tube

Introduction

Telescopic optical systems

1 Aberrations of optical systems

2 Spherical aberration

3 Chromatic aberration

4 Comatic aberration (coma)

5 Astigmatism

6 Image field curvature

7 Distortion (distortion)

Dimensional calculation of the optical system

Conclusion

Literature

Applications

Introduction

Telescopes are astronomical optical instruments designed to observe celestial bodies. Telescopes are used with the use of various radiation receivers for visual, photographic, spectral, photoelectric observations of celestial bodies.

Visual telescopes have a lens and an eyepiece and are a so-called telescopic optical system: they convert a parallel beam of rays entering the lens into a parallel beam leaving the eyepiece. In such a system, the back focus of the objective coincides with the front focus of the eyepiece. Its main optical characteristics are: apparent magnification Г, angular field of view 2W, exit pupil diameter D", resolution and penetrating power.

The apparent magnification of the optical system is the ratio of the angle at which the image given by the optical system of the device is observed to the angular size of the object when viewed directly by the eye. Apparent magnification of the telescopic system:

G \u003d f "about / f" ok \u003d D / D",

where f "ob and f" ok are the focal lengths of the lens and eyepiece,

D - inlet diameter,

D" - the exit pupil. Thus, by increasing the focal length of the objective or reducing the focal length of the eyepiece, large magnifications can be achieved. However, the greater the magnification of the telescope, the smaller its field of view and the greater the distortion of object images due to the imperfection of the optics of the system.

The exit pupil is the smallest section of the light beam leaving the telescope. During observations, the pupil of the eye is aligned with the exit pupil of the system; therefore, it should not be larger than the pupil of the observer's eye. Otherwise, some of the light collected by the lens will not enter the eye and will be lost. Typically, the diameter of the entrance pupil (lens frame) is much larger than the pupil of the eye, and point sources of light, in particular stars, appear much brighter when viewed through a telescope. Their apparent brightness is proportional to the square of the telescope's entrance pupil diameter. Faint stars not visible to the naked eye can be clearly seen in a telescope with a large entrance pupil. The number of stars visible through a telescope is much greater than what is observed directly by the eye.

telescope optical aberration astronomical

1. Telescopic optical systems

1 Aberrations of optical systems

Aberrations of optical systems (lat. - deviation) - distortions, image errors caused by the imperfection of the optical system. Aberrations, to varying degrees, are subject to any lenses, even the most expensive ones. It is believed that the greater the range of focal lengths of the lens, the higher the level of its aberrations.

The most common types of aberrations are below.

2 Spherical aberration

Most lenses are constructed using lenses with spherical surfaces. Such lenses are easy to manufacture, but the spherical shape of the lenses is not ideal for producing a sharp image. The effect of spherical aberration is manifested in the softening of contrast and blurring of details, the so-called "soap".

How does this happen? Parallel light rays passing through a spherical lens are refracted, rays passing through the edge of the lens merge at a focal point closer to the lens than light rays passing through the center of the lens. In other words, the edges of the lens have a shorter focal length than the center. The image below clearly shows how a beam of light passes through a spherical lens and because of what spherical aberrations appear.

Light rays passing through the lens near the optical axis (closer to the center) are focused in region B, farther from the lens. Light rays passing through the edge zones of the lens are focused in area A, closer to the lens.

3 Chromatic aberration

Chromatic aberration (CA) is a phenomenon caused by the dispersion of light passing through the lens, i.e. breaking down a beam of light into its components. Rays with different wavelengths (different colors) are refracted at different angles, so a rainbow is formed from a white beam.

Chromatic aberrations lead to a decrease in image clarity and the appearance of color "fringes", especially on contrasting objects.

To combat chromatic aberrations, special apochromatic lenses made of low-dispersion glass are used, which do not decompose light rays into waves.

1.4 Comatic aberration (coma)

Coma or coma aberration is a phenomenon seen at the periphery of an image that is created by a lens corrected for spherical aberration and causes light rays entering the edge of the lens at some angle to converge into a comet rather than the desired point. Hence its name.

The shape of the comet is oriented radially, with its tail pointing either toward or away from the center of the image. The resulting blurring at the edges of an image is called coma flare. Coma, which can occur even in lenses that accurately reproduce the point as a point on the optical axis, is caused by the difference in refraction between light rays from a point located outside the optical axis and passing through the edges of the lens, and the main light ray from the same point passing through center of the lens.

The coma increases as the angle of the main beam increases and leads to a decrease in contrast at the edges of the image. A certain degree of improvement can be achieved by stopping the lens. Coma can also cause blurry areas of the image to blow out, creating an unpleasant effect.

The elimination of both spherical aberration and coma for an object located at a certain shooting distance is called aplanatism, and a lens corrected in this way is called aplanatism.

5 Astigmatism

With a lens corrected for spherical and comatic aberration, an object point on the optical axis will be accurately reproduced as a point in the image, but an object point off the optical axis will not appear as a point in the image, but rather as a shadow or line. This type of aberration is called astigmatism.

You can observe this phenomenon at the edges of the image if you slightly shift the focus of the lens to a position in which the object point is sharply depicted as a line oriented in a radial direction from the center of the image, and again shift the focus to another position in which the object point is sharply depicted as a line oriented in the direction of the concentric circle. (The distance between these two focus positions is called the astigmatic difference.)

In other words, the light rays in the meridional plane and the light rays in the sagittal plane are in different positions, so these two groups of rays do not connect at the same point. When the lens is set to the optimal focal position for the meridional plane, the light rays in the sagittal plane are aligned in the direction of the concentric circle (this position is called the meridional focus).

Similarly, when the lens is set to the optimal focal position for the sagittal plane, the light rays in the meridional plane form a line oriented in the radial direction (this position is called the sagittal focus).

With this type of distortion, objects in the image look curved, blurry in places, straight lines look curved, and darkening is possible. If the lens suffers from astigmatism, then it is allowed for spare parts, since this phenomenon cannot be cured.

6 Image field curvature

With this type of aberration, the image plane becomes curved, so if the center of the image is in focus, then the edges of the image are out of focus, and vice versa, if the edges are in focus, then the center is out of focus.

1.7 Distortion (distortion)

This type of aberration manifests itself in the distortion of straight lines. If straight lines are concave, the distortion is called pincushion, if convex - barrel-shaped. Zoom lenses typically produce barrel distortion at wide angle (minimum zoom) and pincushion distortion at telephoto (maximum zoom).

2. Dimensional calculation of the optical system

Initial data:

To determine the focal lengths of the lens and the eyepiece, we solve the following system:

f'ob + f'ok = L;

f' ob / f' ok =|Г|;

f'ob + f'ok = 255;

f'ob / f'ok =12.

f'ob +f'ob /12=255;

f' ob = 235.3846 mm;

f' ok \u003d 19.6154 mm;

The diameter of the entrance pupil is calculated by the formula D \u003d D'G

D in \u003d 2.5 * 12 \u003d 30 mm;

The linear field of view of the eyepiece is found by the formula:

; y' = 235.3846*1.5o; y'=6.163781 mm;

The angular field of view of the eyepiece is found by the formula:

Prism system calculation

D 1 -input face of the first prism;

D 1 \u003d (D in + 2y ') / 2;

D 1 \u003d 21.163781 mm;

Ray length of the first prism =*2=21.163781*2=42.327562;

D 2 - the input face of the second prism (the derivation of the formula in Appendix 3);

D 2 \u003d D in * ((D in -2y ’) / L) * (f ’ ob / 2+);

D 2 \u003d 18.91 mm;

The length of the rays of the second prism =*2=18.91*2=37.82;

When calculating the optical system, the distance between the prisms is chosen in the range of 0.5-2 mm;

To calculate the prismatic system, it is necessary to bring it to the air.

Let us reduce the path length of the rays of prisms to air:

l 01 - the length of the first prism reduced to air

n=1.5688 (glass refractive index BK10)

l 01 \u003d l 1 / n \u003d 26.981 mm

l 02 \u003d l 2 / n \u003d 24.108 mm

Determination of the amount of eyepiece movement to ensure focusing within ± 5 diopters

first you need to calculate the price of one diopter f ’ ok 2 / 1000 \u003d 0.384764 (the price of one diopter.)

Moving the eyepiece to achieve the desired focus: mm

Checking for the need to apply a reflective coating to the reflective faces:

(permissible deviation angle of deviation from the axial beam, when the condition of total internal reflection is not violated yet)

(limiting angle of incidence of rays on the input face of the prism, at which there is no need to apply a reflective coating) . Therefore: a reflective coating is not needed.

Eyepiece calculation:

Since 2ω’ = 34.9, the required type of eyepiece is symmetrical.

f’ ok =19.6154 mm (calculated focal length);

K p \u003d S ’ F / f ’ ok \u003d 0.75 (conversion factor)

S ’ F \u003d K p * f ’ ok

S ’ F =0.75* f’ ok (back focal length value)

The removal of the exit pupil is determined by the formula: S’ p = S’ F + z’ p

z’ p is found by Newton’s formula: z’ p = -f’ ok 2 / z p where z p is the distance from the front focus of the eyepiece to the aperture diaphragm. In spotting scopes with a prism-enveloping system, the aperture diaphragm is usually the lens barrel. As a first approximation, we can take z p equal to the focal length of the lens with a minus sign, therefore:

z p = -235.3846 mm

The removal of the exit pupil is equal to:

S’ p = 14.71155+1.634618=16.346168 mm

Aberration calculation of optical system components.

The aberration calculation includes the calculation of eyepiece and prism aberrations for three wavelengths.

Eyepiece aberration calculation:

The calculation of the eyepiece aberrations is carried out in the reverse course of the rays, using the ROSA software package.

δy' ok \u003d 0.0243

Calculation of aberrations of the prism system:

The aberrations of the reflective prisms are calculated using the formulas for the third order aberrations of an equivalent plane-parallel plate. For BK10 glass (n=1.5688).

Longitudinal spherical aberration:

δS ' pr \u003d (0.5 * d * (n 2 -1) * sin 2 b) / n 3

b’=arctg(D/2*f’ ob)=3.64627 o

d=2D 1 +2D 2 =80.15 mm

dS’ pr \u003d 0.061337586

Position chromatism:

(S' f - S' c) pr \u003d 0.33054442

Meridian coma:

δy "= 3d (n 2 -1) * sin 2 b '* tgω 1 / 2n 3

δy" = -0.001606181

Lens aberration calculation:

Longitudinal spherical aberration δS’ sf:

δS’ sf \u003d - (δS ’ pr + δS ’ ok) \u003d -0.013231586

Position chromatism:

(S’ f - S’ c) rev \u003d δS’ xp = - ((S’ f - S’ c) pr + (S’ f - S’ c) ok) \u003d -0.42673442

Meridian coma:

δy’ to = δy’ ok - δy’ pr

δy’ to =0.00115+0.001606181=0.002756181

Definition of structural elements of the lens.

Aberrations of a thin optical system are determined by three main parameters P, W, C. Approximate formula prof. G.G. Slyusareva connects the main parameters P and W:

P = P 0 +0.85(W-W 0)

The calculation of a two-lens glued lens is reduced to finding a certain combination of glasses with given values ​​of P 0 and C.

Calculation of a two-lens lens according to the method of prof. G.G. Slyusareva:

) Based on the values ​​of the lens aberrations δS’ xp, δS’ sf, δy’ k. obtained from the conditions for compensating for aberrations of the prism system and the eyepiece, the aberration sums are found:

S I xp = δS’ xp = -0.42673442

S I \u003d 2 * δS 'sf / (tgb ') 2

S I =6.516521291

S II \u003d 2 * δy to '/(tgb') 2 *tgω

SII =172.7915624

) Based on the sums, the system parameters are found:

S I xp / f 'ob

S II / f'ob

) P 0 is calculated:

P 0 = P-0.85(W-W 0)

) According to the graph-nomogram, the line crosses the 20th cell. Let's check the combinations of glasses K8F1 and KF4TF12:

) From the table are the values ​​of P 0 ,φ k and Q 0 corresponding to the specified value for K8F1 (not suitable)

φk = 2.1845528

for KF4TF12 (suitable)

) After finding P 0 ,φ k, and Q 0, Q is calculated by the formula:

) After finding Q, the values ​​a 2 and a 3 of the first zero ray are determined (a 1 \u003d 0, since the object is at infinity, and 4 \u003d 1 - from the normalization condition):

) The values ​​of a i determine the radii of curvature of thin lenses:

Radius Thin lenses:

) After calculating the radii of a thin lens, the lens thicknesses are selected from the following design considerations. The thickness along the axis of the positive lens d1 is the sum of the absolute values ​​of the arrows L1, L2 and the thickness along the edge, which must be at least 0.05D.

h=D in /2

L \u003d h 2 / (2 * r 0)

L 1 \u003d 0.58818 2 \u003d -1.326112

d 1 \u003d L 1 -L 2 + 0.05D

) According to the obtained thicknesses, calculate the heights:

h 1 \u003d f about \u003d 235.3846

h 2 \u003d h 1 -a 2 *d 1

h 2 \u003d 233.9506

h 3 \u003d h 2 -a 3 * d 2

) Lens curvature radii with finite thicknesses:

r 1 \u003d r 011 \u003d 191.268

r 2 \u003d r 02 * (h 1 / h 2)

r 2 \u003d -84.317178

r 3 \u003d r 03 * (h 3 / h 1)

The control of the results is carried out by calculation on a computer using the "ROSA" program:

lens aberration comparison

The obtained and calculated aberrations are close in their values.

telescope aberration alignment

The layout consists in determining the distance to the prism system from the objective and the eyepiece. The distance between the objective and the eyepiece is defined as (S’ F ’ ob + S’ F ’ ok + Δ). This distance is the sum of the distance between the lens and the first prism, equal to half the focal length of the lens, the beam path in the first prism, the distance between the prisms, the beam path in the second prism, the distance from the last surface of the second prism to the focal plane and the distance from this plane to eyepiece.

692+81.15+41.381+14.777=255

Conclusion

For astronomical lenses, the resolution is determined by the smallest angular distance between two stars that can be seen separately in a telescope. Theoretically, the resolving power of a visual telescope (in arc seconds) for the yellow-green rays to which the eye is most sensitive can be estimated by the expression 120/D, where D is the diameter of the entrance pupil of the telescope, expressed in millimeters.

The penetrating power of a telescope is the limiting stellar magnitude of a star that can be observed with this telescope under good atmospheric conditions. Poor image quality, due to jitter, absorption and scattering of rays by the earth's atmosphere, reduces the maximum magnitude of actually observed stars, reducing the concentration of light energy on the retina, photographic plate or other radiation receiver in the telescope. The amount of light collected by the entrance pupil of a telescope grows in proportion to its area; at the same time, the penetrating power of the telescope also increases. For a telescope with an objective diameter of D millimeters, the penetrating power, expressed in stellar magnitudes for visual observations, is determined by the formula:

mvis=2.0+5 lgD.

Depending on the optical system, telescopes are divided into lens (refractors), mirror (reflectors) and mirror-lens telescopes. If a telescopic lens system has a positive (collecting) objective and a negative (diffusing) eyepiece, then it is called a Galilean system. The Kepler telescopic lens system has a positive objective and a positive eyepiece.

Galileo's system gives a direct virtual image, has a small field of view and a small luminosity (large exit pupil diameter). The simplicity of the design, the short length of the system and the possibility of obtaining a direct image are its main advantages. But the field of view of this system is relatively small, and the absence of a real image of the object between the lens and the eyepiece does not allow the use of a reticle. Therefore, the Galilean system cannot be used for measurements in the focal plane. At present, it is used mainly in theater binoculars, where high magnification and field of view are not required.

The Kepler system gives a real and inverted image of an object. However, when observing celestial bodies, the latter circumstance is not so important, and therefore the Kepler system is most common in telescopes. The length of the telescope tube in this case is equal to the sum of the focal lengths of the objective and the eyepiece:

L \u003d f "ob + f" approx.

The Kepler system can be equipped with a reticle in the form of a plane-parallel plate with a scale and cross hairs. This system is widely used in combination with a prism system that allows direct imaging of lenses. Keplerian systems are mainly used for visual telescopes.

In addition to the eye, which is the receiver of radiation in visual telescopes, images of celestial objects can be recorded on photographic emulsion (such telescopes are called astrographs); a photomultiplier and an electron-optical converter make it possible to amplify many times a weak light signal from stars distant at great distances; images can be projected onto a television telescope tube. An image of an object can also be sent to an astrospectrograph or an astrophotometer.

To point the telescope tube at the desired celestial object, a telescope mount (tripod) is used. It provides the ability to rotate the pipe around two mutually perpendicular axes. The base of the mount carries an axis, about which the second axis can rotate with the telescope tube rotating around it. Depending on the orientation of the axes in space, mounts are divided into several types.

In altazimuth (or horizontal) mounts, one axis is vertical (the azimuth axis), and the other (the zenith distance axis) is horizontal. The main disadvantage of an altazimuth mount is the need to rotate the telescope around two axes to track a celestial object moving due to the apparent daily rotation of the celestial sphere. Altazimuth mounts are supplied with many astrometric instruments: universal instruments, transit and meridian circles.

Almost all modern large telescopes have an equatorial (or parallactic) mount, in which the main axis - polar or hourly - is directed to the celestial pole, and the second - the declination axis - is perpendicular to it and lies in the plane of the equator. The advantage of a parallax mount is that to track the daily movement of a star, it is enough to rotate the telescope around only one polar axis.

Literature

1. Digital technology. / Ed. E.V. Evreinova. - M.: Radio and communication, 2010. - 464 p.

Kagan B.M. Optics. - M.: Enerngoatomizdat, 2009. - 592 p.

Skvortsov G.I. Computer Engineering. - MTUCI M. 2007 - 40 p.

Attachment 1

Focal length 19.615 mm

Relative aperture 1:8

Angle of view

Move the eyepiece by 1 diopter. 0.4mm

Structural elements

19.615; =14.755;

Axial beam

Main beam

Meridional section of an oblique beam

Interchangeable lenses for cameras with Vario Sonnar lenses

Instead of an introduction, I propose to look at the results of hunting for ice butterflies using the photogun above. The gun is a Casio QV4000 camera with a Kepler tube type optical attachment, composed of a Helios-44 lens as an eyepiece and a Pentacon 2.8 / 135 lens.

It is generally believed that devices with a fixed lens have significantly less capabilities than devices with interchangeable lenses. In general, this is certainly true, however, classical systems with interchangeable optics are far from being as ideal as it might seem at first glance. And with some luck, it happens that a partial replacement of optics (optical attachments) is no less effective than replacing the optics entirely. By the way, this approach is very popular with film cameras. More or less painlessly changing optics with an arbitrary focal length is possible only for rangefinder devices with a focal curtain shutter, but in this case we have only a very approximate idea of ​​​​what the device actually sees. This problem is solved in mirror devices, which allow you to see on the frosted glass the image formed by exactly the lens that is currently inserted into the camera. Here it turns out, it would seem, an ideal situation, but only for telephoto lenses. As soon as we start using wide-angle lenses with SLR cameras, it immediately turns out that each of these lenses has additional lenses, the role of which is to provide an opportunity to place a mirror between the lens and the film. In fact, it would be possible to make a camera in which the element responsible for the possibility of placing a mirror would be non-replaceable, and only the front components of the lens would change. An ideologically similar approach is used in reflex viewfinders of movie cameras. Since the path of the beams is parallel between the telescopic attachment and the main objective, a beam-splitting prism-cube or a translucent plate can be placed between them at an angle of 45 degrees. One of the two main types of zoom lenses, the zoom lens, also combines a fixed focal length lens and an afocal system. Changing the focal length in zoom lenses is carried out by changing the magnification of the afocal attachment, achieved by moving its components.

Unfortunately, versatility rarely leads to good results. A more or less successful correction of aberrations is achieved only by selecting all the optical elements of the system. I recommend that everyone read the translation of the article "" by Erwin Puts. I wrote all this only to emphasize that, in principle, the lenses of a SLR camera are by no means better than built-in lenses with optical attachments. The problem is that the designer of optical attachments can only rely on their own elements and cannot interfere with the design of the lens. Therefore, the successful operation of a lens with an attachment is much less common than a well-functioning lens designed entirely by one designer, even if it has an extended rear working distance. A combination of finished optical elements that add up to acceptable aberrations is rare, but it does happen. Typically, afocal attachments are a Galilean spotting scope. However, they can also be built according to the optical scheme of the Kepler tube.

Optical layout of the Kepler tube.

In this case, we will have an inverted image, well, yes, photographers are no strangers to this. Some digital devices have the ability to flip the image on the screen. I would like to have such an opportunity for all digital cameras, since it seems wasteful to fence the optical system to rotate the image in digital cameras. However, the simplest system of a mirror attached at an angle of 45 degrees to the screen can be built in a couple of minutes.

So, I managed to find a combination of standard optical elements that can be used in conjunction with the most common digital camera lens today with a focal length of 7-21 mm. Sony calls this lens Vario Sonnar, lenses similar in design are installed in Canon (G1, G2), Casio (QV3000, QV3500, QV4000), Epson PC 3000Z, Toshiba PDR-M70, Sony (S70, S75, S85) cameras. The Kepler tube I got shows good results and allows you to use a variety of interchangeable lenses in your design. The system is designed to work when the standard lens is set to a maximum focal length of 21 mm, and a Jupiter-3 or Helios-44 lens is attached to it as an eyepiece of the telescope, then extension bellows and an arbitrary lens with a focal length greater than 50 mm are installed.

Optical schemes of lenses used as eyepieces of the telescopic system.

The luck was that if you place the Jupiter-3 lens with the entrance pupil to the lens of the apparatus, and the exit pupil to the bellows, then the aberrations at the edges of the frame turn out to be very moderate. If we use a Pentacon 135 lens as a lens and a Jupiter 3 lens as an eyepiece, then by eye, no matter how we turn the eyepiece, the picture actually does not change, we have a tube with a 2.5x magnification. If instead of the eye we use the lens of the apparatus, then the picture changes dramatically, and the use of the Jupiter-3 lens, turned by the entrance pupil to the camera lens, is preferable.

Casio QV3000 + Jupiter-3 + Pentacon 135

If you use Jupiter-3 as an eyepiece, and Helios-44 as a lens, or make up a system of two Helios-44 lenses, then the focal length of the resulting system does not actually change, however, using fur stretching, we can shoot from almost any distance .

Pictured is a photo of a postage stamp taken by a system composed of a Casio QV4000 camera and two Helios-44 lenses. Camera lens aperture 1:8. The size of the image in the frame is 31 mm. Fragments corresponding to the center and corner of the frame are shown. At the very edge, the image quality sharply deteriorates in resolution and illumination drops. When using such a scheme, it makes sense to use a part of the image that occupies about 3/4 of the frame area. From 4 megapixels we make 3, and from 3 megapixels we make 2.3 - and everything is very cool

If we use long-focus lenses, then the magnification of the system will be equal to the ratio of the focal lengths of the eyepiece and the lens, and given that the focal length of Jupiter-3 is 50 mm, we can easily create a nozzle with a 3-fold increase in focal length. The inconvenience of such a system is the vignetting of the corners of the frame. Since the field margin is quite small, any aperture of the tube lens leads to the fact that we see an image inscribed in a circle located in the center of the frame. Moreover, this is good in the center of the frame, but it may turn out that it is not in the center either, which means that the system does not have sufficient mechanical rigidity, and under its own weight the lens has shifted from the optical axis. Frame vignetting becomes less noticeable when lenses for medium format cameras and enlargers are used. The best results in this parameter were shown by the Ortagoz f=135 mm lens system from the camera.
Eyepiece - Jupiter-3, lens - Ortagoz f=135 mm,

However, in this case, the requirements for the alignment of the system are very, very strict. The slightest shift of the system will lead to vignetting of one of the corners. To check how well aligned your system is, you can close the aperture of the Ortagoz lens and see how centered the resulting circle is. Shooting is always carried out with the aperture of the lens and eyepiece fully open, and aperture is controlled by the aperture of the camera's built-in lens. In most cases, focusing is done by changing the length of the bellows. If the lenses used in the telescopic system have their own movements, then precise focusing is achieved by rotating them. And finally, additional focusing can be done by moving the camera lens. And in good light, even the autofocus system works. The focal length of the resulting system is too large for portrait photography, but a fragment of a face shot is quite suitable for assessing the quality.

It is impossible to evaluate the work of the lens without focusing on infinity, and although the weather clearly did not contribute to such pictures, I bring them too.

You can put a lens with a shorter focal length than the eyepiece, and that's what happens. However, this is more of a curiosity than a method of practical application.

A few words about the specific installation implementation

The above methods of attaching optical elements to the camera are not a guide to action, but information for reflection. When working with the Casio QV4000 and QV3500 cameras, it is proposed to use the native LU-35A adapter ring with a 58 mm thread and then attach all other optical elements to it. When working with the Casio QV 3000, I used the 46 mm threaded attachment design described in the Casio QV-3000 Camera Refinement article. To mount the Helios-44 lens, an empty frame for light filters with a 49 mm thread was put on its tail section and pressed with a nut with an M42 thread. I got the nut by sawing off part of the adapter extension ring. Next, I used a Jolos adapter wrapping ring from M49 to M59 threads. On the other hand, a wrapping ring for macro photography M49 × 0.75-M42 × 1 was screwed onto the lens, then an M42 sleeve, also made from a sawn extension ring, and then standard bellows and lenses with an M42 thread. There are a great many adapter rings with M42 threads. I used adapter rings for B or C mount, or an adapter ring for M39 thread. To mount the Jupiter-3 lens as an eyepiece, an adapter enlarging ring from the M40.5 thread to M49 mm was screwed into the thread for the filter, then the Jolos wrapping ring from M49 to M58 was used, and then this system was attached to the device. On the other side of the lens, a coupling with an M39 thread was screwed on, then an adapter ring from M39 to M42, and then similarly to the system with the Helios-44 lens.

Results of testing the resulting optical systems placed in a separate file. It contains photographs of the tested optical systems and snapshots of the world, located in the center in the corner of the frame. Here I give only the final table of maximum resolution values ​​in the center and in the corner of the frame for the tested designs. Resolution is expressed in stroke/pixel. Black and white lines - 2 strokes.

Conclusion

The scheme is suitable for work at any distance, but the results are especially impressive for macro photography, since the presence of bellows in the system makes it easy to focus on nearby objects. Although in some combinations Jupiter-3 gives higher resolution, but greater than Helios-44, vignetting makes it less attractive as a permanent eyepiece for an interchangeable lens system.

I would like to wish companies that produce all kinds of rings and accessories for cameras to produce a coupling with an M42 thread and adapter rings from an M42 thread to a filter thread, with an M42 thread internal and an external one for the filter.

I believe that if some optical factory makes a specialized eyepiece of a telescopic system for use with digital cameras and arbitrary lenses, then such a product will be in some demand. Naturally, such an optical design must be equipped with an adapter ring for attaching to the camera and a thread or mount for existing lenses,

That, in fact, is all. I showed what I did, and you yourself evaluate whether this quality suits you or not. And further. Since there was one successful combination, then, probably, there are others. Look, you might be lucky.

These days we are celebrating the 400th anniversary of the creation of the optical telescope - the simplest and most efficient scientific instrument that opened the door to the Universe for mankind. The honor of creating the first telescopes rightfully belongs to Galileo.

As you know, Galileo Galilei began experimenting with lenses in the middle of 1609, after he learned that a telescope had been invented in Holland for the needs of navigation. It was made in 1608, possibly independently by the Dutch opticians Hans Lippershey, Jacob Metius and Zacharias Jansen. In just six months, Galileo managed to significantly improve this invention, create a powerful astronomical instrument based on its principle, and make a number of amazing discoveries.

Galileo's success in improving the telescope cannot be considered accidental. The Italian masters of glass had already thoroughly become famous by that time: back in the 13th century. they invented glasses. And it was in Italy that theoretical optics was at its best. Through the works of Leonardo da Vinci, it turned from a section of geometry into a practical science. “Make glasses for your eyes to see the moon big,” he wrote at the end of the 15th century. Perhaps, although there is no direct evidence for this, Leonardo managed to implement a telescopic system.

Original research on optics was carried out in the middle of the 16th century. Italian Francesco Mavrolik (1494-1575). His compatriot Giovanni Battista de la Porta (1535-1615) devoted two magnificent works to optics: "Natural Magic" and "On Refraction". In the latter, he even gives the optical scheme of the telescope and claims that he was able to see small objects at a great distance. In 1609, he tries to defend the priority in the invention of the telescope, but the actual evidence for this was not enough. Be that as it may, Galileo's work in this area began on well-prepared ground. But, paying tribute to the predecessors of Galileo, let's remember that it was he who made a workable astronomical instrument out of a funny toy.

Galileo began his experiments with a simple combination of a positive lens as an objective and a negative lens as an eyepiece, giving a threefold magnification. Now this design is called theatrical binoculars. This is the most popular optical device after glasses. Of course, in modern theater binoculars, high-quality coated lenses, sometimes even complex ones, made up of several glasses, are used as an objective and eyepiece. They give a wide field of view and excellent image quality. Galileo used simple lenses for both the objective and the eyepiece. His telescopes suffered from the strongest chromatic and spherical aberrations, i.e. gave an image that was blurry at the edges and out of focus in various colors.

However, Galileo did not stop, like the Dutch masters, at the “theatrical binoculars”, but continued experiments with lenses and by January 1610 had created several instruments with magnifications from 20 to 33 times. It was with their help that he made his remarkable discoveries: he discovered the satellites of Jupiter, mountains and craters on the Moon, myriads of stars in the Milky Way, etc. Already in mid-March 1610 in Venice in Latin, 550 copies of Galileo's work was published " The Starry Messenger, where these first discoveries of telescopic astronomy were described. In September 1610, the scientist discovers the phases of Venus, and in November he discovers signs of a ring near Saturn, although he does not realize the true meaning of his discovery (“I observed the highest planet in triplet,” he writes in an anagram, trying to secure the priority of discovery). Perhaps not a single telescope of the following centuries made such a contribution to science as the first telescope of Galileo.

However, those astronomy lovers who tried to assemble telescopes from spectacle glasses are often surprised at the low capabilities of their designs, which are clearly inferior in terms of "observation capabilities" to Galileo's handicraft telescope. Often modern "Galilee" cannot detect even the satellites of Jupiter, not to mention the phases of Venus.

In Florence, the Museum of the History of Science (next to the famous Uffizi Picture Gallery) houses two of the first telescopes built by Galileo. There is also a broken lens of the third telescope. This lens was used by Galileo for many observations in 1609-1610. and was presented by him to the Grand Duke Ferdinand II. The lens was later accidentally broken. After the death of Galileo (1642), this lens was kept by Prince Leopold the Medici, and after his death (1675) it was added to the Medici collection in the Uffizi Gallery. In 1793 the collection was transferred to the Museum of the History of Science.

Very interesting is the decorative figured ivory frame made for the Galilean lens by the engraver Vittorio Krosten. Rich and bizarre floral ornamentation is interspersed with images of scientific instruments; several Latin inscriptions are organically incorporated into the pattern. At the top there used to be a ribbon, now lost, with the inscription "MEDICEA SIDERA" ("Medici Stars"). The central part of the composition is crowned by the image of Jupiter with the orbits of 4 of its satellites, surrounded by the text "CLARA DEUM SOBOLES MAGNUM IOVIS INCREMENTUM" ("Glorious [young] generation of gods, great offspring of Jupiter"). Left and right - allegorical faces of the Sun and the Moon. The inscription on the ribbon entwining the wreath around the lens reads: "HIC ET PRIMUS RETEXIT MACULAS PHEBI ET IOVIS ASTRA" ("He was the first to discover both the spots of Phoebus (i.e. the Sun) and the stars of Jupiter"). On the cartouche below the text: "COELUM LINCEAE GALILEI MENTI APERTUM VITREA PRIMA HAC MOLE NON DUM VISA OSTENDIT SYDERA MEDICEA IURE AB INVENTORE DICTA SAPIENS NEMPE DOMINATUR ET ASTRIS" until now invisible, rightly called Medicean by their discoverer, for the sage also rules over the stars.

Information about the exhibit is available on the website of the Museum of the History of Science: link No. 100101; reference no. 404001.

At the beginning of the 20th century, Galileo's telescopes stored in the Florentine Museum were studied (see table). Astronomical observations were even made with them.

Optical characteristics of the first objectives and eyepieces of Galilean telescopes (dimensions in mm)

It turned out that the first tube had a resolution of 20" and a field of view of 15". And the second, respectively, 10 "and 15". The increase in the first tube was 14-fold, and the second 20-fold. The broken lens of the third tube with the eyepieces from the first two tubes would give magnifications of 18 and 35 times. So, could Galileo have made his amazing discoveries with such imperfect tools?

historical experiment

It was this question that the Englishman Stephen Ringwood asked and, in order to find out the answer, he created an exact copy of the best Galilean telescope (Ringwood S. D. A Galilean telescope // The Quarterly Journal of the Royal Astronomical Society, 1994, vol. 35, 1, p. 43-50) . In October 1992, Steve Ringwood recreated the design of Galileo's third telescope and made all sorts of observations with it for a year. The lens of his telescope had a diameter of 58 mm and a focal length of 1650 mm. Like Galileo, Ringwood stopped his lens down to an aperture diameter of D = 38 mm in order to obtain better image quality with a relatively small loss in penetrating power. The eyepiece was a negative lens with a focal length of -50 mm, giving a magnification of 33 times. Since in this design of the telescope the eyepiece is placed in front of the focal plane of the objective, the total length of the tube was 1440 mm.

Ringwood considers the biggest disadvantage of the Galileo telescope to be its small field of view - only 10 ", or a third of the lunar disk. Moreover, at the edge of the field of view, the image quality is very low. Using a simple Rayleigh criterion that describes the diffraction limit of the resolution of the lens, one would expect quality images in 3.5-4.0". However, chromatic aberration reduced it to 10-20". The penetrating power of the telescope, estimated by a simple formula (2 + 5lg D), was expected around +9.9 m . However, in reality, it was not possible to detect stars fainter than +8 m.

When observing the moon, the telescope performed well. It managed to see even more details than was drawn by Galileo on his first lunar maps. “Perhaps Galileo was an unimportant draftsman, or was he not very interested in the details of the lunar surface?” Ringwood wonders. Or maybe Galileo's experience in making telescopes and observing with them was still not great enough? We think that this is the reason. The quality of the glasses, polished by Galileo's own hands, could not compete with modern lenses. And, of course, Galileo did not immediately learn to look through a telescope: visual observations require considerable experience.

By the way, why did the creators of the first spotting scopes - the Dutch - not make astronomical discoveries? Having taken observations with theater binoculars (2.5-3.5 times magnification) and with field glasses (7-8 times magnification), you will notice that there is an abyss between their capabilities. Modern high-quality 3x binoculars make it possible (when observing with one eye!) to hardly notice the largest lunar craters; it is obvious that a Dutch pipe with the same magnification, but of lower quality, could not even do this. Field binoculars, which give approximately the same capabilities as Galileo's first telescopes, show us the Moon in all its glory, with many craters. Having improved the Dutch pipe, having achieved several times higher magnification, Galileo stepped over the “threshold of discoveries”. Since then, in experimental science, this principle has not failed: if you manage to improve the leading parameter of the device several times, you will definitely make a discovery.

By far Galileo's most remarkable discovery was the discovery of the four satellites of Jupiter and the disk of the planet itself. Contrary to expectations, the low quality of the telescope did not greatly interfere with observations of the Jupiter satellite system. Ringwood clearly saw all four satellites and was able, like Galileo, to note their movement relative to the planet every night. True, it was not always possible to focus the image of the planet and the satellite well at the same time: the chromatic aberration of the lens was very disturbing.

But as for Jupiter itself, Ringwood, like Galileo, could not detect any details on the planet's disk. Weakly contrasting latitudinal bands crossing Jupiter along the equator were completely washed out as a result of aberration.

A very interesting result was obtained by Ringwood when observing Saturn. Like Galileo, at a magnification of 33 times, he saw only weak swellings (“mysterious appendages,” as Galileo wrote) on the sides of the planet, which the great Italian, of course, could not interpret as a ring. However, further experiments by Ringwood showed that when using other high magnification eyepieces, clearer features of the ring could still be discerned. If Galileo had done this in due time, the discovery of the rings of Saturn would have taken place almost half a century earlier and would not have belonged to Huygens (1656).

However, observations of Venus proved that Galileo quickly became a skilled astronomer. It turned out that the phases of Venus are not visible at the greatest elongation, because its angular size is too small. And only when Venus approached the Earth and in phase 0.25 its angular diameter reached 45 ", its crescent shape became noticeable. At that time, its angular distance from the Sun was no longer so great, and observations were difficult.

The most curious thing in Ringwood's historical research, perhaps, was the exposure of an old misconception about Galileo's observations of the Sun. Until now, it was generally accepted that it was impossible to observe the Sun with a Galilean telescope by projecting its image onto a screen, because the negative lens of the eyepiece cannot build a real image of the object. Only the telescope of the Kepler system of two positive lenses, invented a little later, made it possible. It was believed that the first to observe the Sun on a screen placed behind the eyepiece was the German astronomer Christoph Scheiner (1575-1650). He simultaneously and independently of Kepler created in 1613 a telescope of a similar design. How did Galileo observe the Sun? After all, he was the one who discovered sunspots. For a long time there was a belief that Galileo observed the daylight with his eye through the eyepiece, using the clouds as light filters or watching the Sun in the fog low above the horizon. It was believed that Galileo's loss of sight in old age was partly provoked by his observations of the Sun.

However, Ringwood discovered that even Galileo's telescope could produce a quite decent projection of the solar image on the screen, with sunspots visible very clearly. Later, in one of Galileo's letters, Ringwood discovered a detailed description of observations of the Sun by projecting its image onto a screen. It is strange that this circumstance was not noted earlier.

I think that every amateur of astronomy will not deny himself the pleasure of "becoming Galileo" for a few evenings. To do this, you just need to make a Galilean telescope and try to repeat the discoveries of the great Italian. As a child, one of the authors of this note made Keplerian tubes from spectacle glasses. And already in adulthood he could not resist and built an instrument similar to Galileo's telescope. The lens used was a 43 mm diameter attachment lens with a power of +2 diopters, and an eyepiece with a focal length of about -45 mm was taken from an old theater binocular. The telescope turned out to be not very powerful, with a magnification of only 11 times, but it also had a small field of view, about 50 "in diameter, and the image quality was uneven, deteriorating significantly towards the edge. However, the images became much better when the lens was apertured to a diameter of 22 mm, and even better - up to 11 mm The brightness of the images, of course, decreased, but the observations of the Moon even benefited from this.

As expected, when viewing the Sun projected onto a white screen, this telescope did indeed produce an image of the solar disk. The negative eyepiece increased the equivalent focal length of the lens several times (telephoto principle). Since there is no information on which tripod Galileo mounted his telescope on, the author observed while holding the pipe in his hands, and used a tree trunk, a fence or an open window frame as a support for his hands. At 11x this was enough, but at 30x, obviously, Galileo could have problems.

We can assume that the historical experiment to recreate the first telescope was a success. Now we know that Galileo's telescope was a rather inconvenient and bad instrument from the point of view of modern astronomy. In all respects, it was inferior even to the current amateur instruments. He had only one advantage - he was the first, and his creator Galileo "squeezed out" everything that was possible from his instrument. For this we honor Galileo and his first telescope.

Be Galileo

This year 2009 was declared the International Year of Astronomy in honor of the 400th anniversary of the birth of the telescope. In the computer network, in addition to the existing ones, many new wonderful sites have appeared with amazing pictures of astronomical objects.

But no matter how full of interesting information Internet sites were, the main goal of the MGA was to demonstrate to everyone the real Universe. Therefore, among the priority projects was the production of inexpensive telescopes available to anyone. The most massive was the "galileoscope" - a small refractor designed by highly professional astronomers-optics. This is not an exact copy of Galileo's telescope, but rather its modern reincarnation. The "galileoscope" has a two-lens glass achromatic lens with a diameter of 50 mm and a focal length of 500 mm. The 4-lens plastic eyepiece gives a magnification of 25x and the 2x Barlow brings it up to 50x. The field of view of the telescope is 1.5 o (or 0.75 o with a Barlow lens). With such a tool, you can easily "repeat" all the discoveries of Galileo.

However, Galileo himself with such a telescope would have made them much larger. The tool's $15-20 price tag makes it truly accessible to the public. Curiously, with a standard positive eyepiece (even with a Barlow lens), the “galileoscope” is actually a Kepler tube, but when used as an eyepiece with a Barlow lens alone, it lives up to its name, becoming a 17x Galilean tube. To repeat the discoveries of the great Italian in such an (original!) configuration is not an easy task.

This is a very convenient and quite mass tool, suitable for schools and beginners in astronomy. Its price is significantly lower than previous telescopes with similar capabilities. It would be highly desirable to purchase such instruments for our schools.