کارآموری سیستم های اندازه گیری

The Autocollimator is a single instrument combining the functions of a collimator and a telescope to detect small angular displacements of a mirror by means of its own collimated light
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کارآموری سیستم های اندازه گیری

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Auto-collimators

The Auto-collimator is a single instrument combining the functions of a collimator and a telescope to detect small angular displacements of a mirror by means of its own collimated light.

The two reticles are positioned in the focal plane of the corrected objective lens, so that the emerging beam is parallel. This usual configuration is known as infinity setting, i.e the auto-collimators are focused at infinity.

When moving the reticles out of the focal plane of the objective lens, the auto-collimator can be focused at finite distances, and the beam becomes divergent (producing a virtual image) or convergent (real image). This results in a focusing auto-collimator. The shape of the beam -convergent or divergent- depend on the direction in which the reticles are moved

The main components of a standard auto-collimator i.e. focused at infinity are:

  • Tube mounted objective lens
  • Beam splitter mount which contains two reticles
  • Eyepiece
  • Illumination device

The illuminated reticle projected over the beam splitter towards the lens is known as collimator reticle. The second reticle placed iin the focus of the eyepiece is the eyepiece reticle.

The beamsplitter mount together with the eyepiece and the illumination device form a main unit called: Auto-collimator head.

A focusing auto-collimator (finite distance setting) is similary built. The auto-collimator head containing the two reticles is now mounted on a draw out tube for focusing adjustment.

Auto-collimation is an optical technique of projecting an illuminated reticle to infinity and receiving the reticle image after reflection on a flat mirror. The reflected image is brought to the focus of the objective lens in which the eyepiece reticle is located. Thus the reflected image of the collimator (illuminated) reticle and the eyepiece reticle can be simultaneously observed.

When the collimated beam falls on a mirror which is perpendicular to beam axis, the light is reflected along the same path. Between the reflected image and the eyepiece reticle -which are seen superimposed- no displacement occures.

If the reflector is tilted by an angle (in radians), the reflected beam is deflected by twice that angle i.e. 2. The reflected image is now laterally displaced with respect to the eyepiece reticle. The amount of this displacement “d” is a function of the focal length of the auto-collimator and the tilt angle of the reflector: d = 2 f.

The tilt angle can be ascertained with the formula:

= d / 2f

where f is the effective focal length EFL of the auto-collimator.

Since the f is a constant of the auto-collimator, the eyepiece reticle can be graduated in angle units and the tilt angle can be directly read off.

The Autocollimator and its reflections

I have long had a feeling that the existing descriptions of the autocollimator and its mode of operation have not been based on a clear understanding. This analysis attempts to describe the reflections seen and their positions as functions of miscollimation and builds on a discussion in the Yahoo Collimate_Your_Telescope forum.

The autocollimator is a flat mirror mounted in a short tube made to fit a Newtonian telescope focuser, and set accurately perpendicular to the tube’s axis. Centered in it is a small peephole or pupil that you look through. If the primary mirror’s center is marked with a bright or reflective spot, you can see the spot (reflected in the secondary) and a few more reflections of the spot after several reflections back and forth. This picture shows a 2” autocollimator (INFINITY, ™ by Jim Fly).

To use it, you first do a fairly close collimation with a sight tube and a Cheshire collimator (or, if you prefer, with a laser with a Barlow attachment), then insert the autocollimator and fine-adjust the collimation. When collimation is ideal, the reflections will appear “stacked” or coincident – but if they are not, how do you proceed? To answer this vital question, I believe you need a clear understanding of how the reflections are generated.


http://web.telia.com/~u41105032/Acoll/acoll1max.gif

This figure (click this or later images for a larger version!) shows, greatly exaggerated and not to scale, the primary and autocollimator (the secondary mirror is ignored, not to introduce even more confusion). The primary’s optical axis starts at the center mark P and goes to COC, the center of curvature of the mirror. Midway between P and COC is F, the focus of the primary mirror.

The autocollimator’s axis is perpendicular to the mirror and centered in it, at the pupil. There is a combined collimation error shown: the primary’s axis misses the autocollimator pupil by a distance A (elsewhere I have called this a 1A error!), and the autocollimator(=focuser) axis misses the primary’s center by B (1B error).


http://web.telia.com/~u41105032/Acoll/acoll2max.gif

To trace the reflections:

Draw a line (green) from P, parallel to the autocollimator axis, to V1 via H5, and another parallel line from F to H3. Also, draw a line parallel to them from COC to H2, and a third line V2 to “2”, parallel and with a distance V2-COC equal to COC-V1.

At V1 is a virtual image of P by the autocollimator. This virtual image is reflected to a focused virtual image (the details are not shown) V2, also at the level of the COC. This virtual image is again reflected in the autocollimator down to a real image “2” at the primary. This reflection can be seen as an “inverted”, or more accurately rotated by 180°, but (just like P) sharp when seen with an eye or camera focused at one focal length.

Also another reflection “1” can be seen (this will be shown later), by intercepting the light going towards the image V2 – its projected position on the primary is found by drawing a line V2 to autocollimator pupil, extending it down to the primary.

The real image at “2” is projected by the reverse path back to P, accurately on top of it after another 180° rotation, thus ending for good the series of reflections. But before this, a reflection “3” can be seen, formed from “3” in analogy to how the reflection “1” is formed from P. Both “1” and “3” are seen as bundles of converging light, as if focused at minus one focal length – if imaged with a camera focused at P, they will appear noticeably defocused (if the camera is focused at infinity, all images will appear defocused by the same amount).


http://web.telia.com/~u41105032/Acoll/acoll3max.gif

Now we can determine the relative positions of the reflections (positive to the right in the figure):

The distance P to H3 is A+B, as is H3 to H2. H2 to “2” equals p to H2 =2A+2B, the total displacement P to “2” is 4A+4B.

By similar reasoning, the distance from H4 to the autocollimator pupil is 4A+3B, and from “2” to “1” twice this – thus the displacement of “1” from P is -4A-2B. The displacement of “3” from P is 2B, remarkably enough independently of any miscollimation of the primary.

This figure shows the paths of reflections “1” (bold red) and “2” (bold green) seen in the autocollimator after 2 and 4 reflections respectively (note that the reflection at H6 should rightly have occurred much farther to the right!). The reflections of “3”, (if you include the reflections in the secondary, there are 13!) are left as an exercise to the reader.

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