There are now readily available a number of proprietary eyepieces which are supplied by their manufacturers with illuminated reticle systems. They have completely transformed amateur double-star astrome-try.2 The Celestron Micro Guide eyepiece provides a typical example, but other makes are essentially similar (this section refers specifically to the Celestron version). Reticle eyepieces of this type require the use of a motor-driven equatorial mount, with remote slow-motion controls to both axes. This section describes two methods of using the Micro Guide. The first is simple yet very effective, while the more advanced procedure is considerably slower but promises even greater accuracy.
The Celestron Micro Guide is an orthoscopic eyepiece of 12.5-millimetre focal length incorporating a laser-etched reticle and a battery-powered variable illumination system (Figure 12.5). The Meade version uses a different reticle layout (Figure 12.6). In both cases, however, there is a 360° protractor scale at the edge of the field and a linear scale at the centre. The linear scale, which is used to measure separation, is a ruler graduated at 100-micron intervals. Position angles may be determined either by means of an external position circle or, more elegantly and more simply, by using the drift method described in this section.
The first step is to calibrate the linear scale by determining the scale constant, i.e. the number of arcsec-onds per division. The smaller the constant, the more accurate the measures will be. This dictates as great an
Figure 12.5. The reticle of the Celestron Micro Guide eyepiece. The thickness of the inscribed lines and circles is 15 |m.
Figure 12.5. The reticle of the Celestron Micro Guide eyepiece. The thickness of the inscribed lines and circles is 15 |m.
effective focal length as possible. Ideally, the focal length should be 5 metres or more, and certainly not less than 3 metres. Since most amateur telescopes have a focal length of between only 1 and 2 metres, it is
Figure 12.6. The reticle of the Meade astrometric eyepiece.
Figure 12.6. The reticle of the Meade astrometric eyepiece.
obvious that a Barlow lens will usually be necessary in order to amplify the image scale at the telescopic focus.
To calibrate the eyepiece, time the passage of a star along the entire length of the linear scale. Select a star that is neither too bright nor too faint - magnitude 5 or 6 will probably be about right for small or medium apertures. In order to minimise the effects of timing errors, choose a star of relatively high declination, but without straying too close to the celestial pole. I have found that a declination of between 60° and 75° is suitable. Rotate the eyepiece until the star drifts exactly parallel to the linear scale. Then use a stopwatch to time the star's journey from one end of the scale to the other. Repeat the process at least 30 times, preferably spread over several nights, and take the mean. To convert the result into arcseconds, multiply by 15.0411 cos S, where S is the star's declination. Then divide by the number of divisions in the scale; in the case of the Micro Guide this is 60, but the equivalent scale in the Meade version has 50 divisions. The resulting scale constant, z, will always remain valid for the same optical set-up.
The simpler of the two methods of measuring the separation of a double star is as follows. Rotate the eyepiece until the linear scale is exactly parallel with the pair's axis, ensuring that the primary star is closer to the zero point (or the 90° point in the Meade version) on the 360° protractor scale; although this precaution has no bearing on the separation measure, it will assume importance when it comes to measuring the position angle at a later stage. Then, estimating to the nearest 0.1 division, count the number of divisions separating the two components and multiply the result by the scale constant to obtain the separation in arcseconds.
Measuring the position angle is a slightly more involved process. One way of going about it is to use an external position circle or dial as described in the previous section, but this is actually quite unnecessary.3 By allowing a star to drift across the field, it is possible to obtain accurate position angles from the 360° protractor scale etched on the reticle itself.
The procedure is as follows: having completed the separation measure, leave the motor running and the orientation of the eyepiece undisturbed so as to preserve the alignment of the reticle. Use the slow-motion controls to bring a star to the exact centre of the field, which on the Micro Guide will be found to
Figure 12.7. Using the simpler method, the pair's separation is measured against the linear scale. The position angle can be found by switching off the telescope's clock drive until the pair drifts to the protractor scale, where the angle is noted. It is important not to bypass or hasten the drift process by using the telescope's RA motor, as unless the polar alignment is perfect, the result will be incorrect. Reproduced courtesy of Sky Publishing Corporation
Figure 12.7. Using the simpler method, the pair's separation is measured against the linear scale. The position angle can be found by switching off the telescope's clock drive until the pair drifts to the protractor scale, where the angle is noted. It is important not to bypass or hasten the drift process by using the telescope's RA motor, as unless the polar alignment is perfect, the result will be incorrect. Reproduced courtesy of Sky Publishing Corporation lie between the "30" markings on the linear scale. For this purpose, any convenient star will do; it does not even have to be a component of the pair being measured. Once the star is accurately centred, switch off the motor drive and allow the Earth's rotation to carry the star towards the western edge of the field of view. The direction of drift, by definition, corresponds to the true position angle 270° When the star reaches the 360° protractor scale, switch the motor on and read and record the angle indicated by the star on the protractor scale (Figure 12.7). For a conventional inverted field, the outer (clockwise) set of figures should be used. The inner (anticlockwise) figures are for use with a reversed image, as produced by a right-angle prism. Although the scale is only graduated at intervals of 5°, it is perfectly feasible to estimate to the nearest 0°5, which is sufficient for all practical purposes.
Subject to one possible correction, the reading indicated by the star shows the position angle of the pair. When using the Celestron Micro Guide, it is necessary to add 90° to the protractor reading in order to arrive at the true position angle. If the final result exceeds 360, just subtract 360 to bring the answer within the range 0-360. With the Meade version, which employs a different layout, no correction is necessary.
As with other techniques of measurement, observations should be repeated over a number of nights and means taken. Used in this way, a reticle eyepiece is capable of making good measures of pairs of any separation lying comfortably within the telescope's resolving ability. It is important to eliminate the effects of parallax by ensuring that the reticle and the star images are focused in exactly the same plane. To achieve this, adjust the telescope focus and the eyepiece dioptre control until you can move your head from side to side without inducing any relative movement between image and reticle.
The beauty of the drift method is that it effectively eliminates index error and places considerably less stringent demands upon the accuracy of the mount's alignment by comparison with a conventional position circle. It follows that this particular technique of measurement lends itself especially well to portable equato-rials. Perhaps for that reason, it has become steadily more popular among amateur observers since it was first described in print.3
In an alternative, more advanced procedure, the observer uses the reticle eyepiece to measure pairs of angles in each of which both components of the pair are bisected by markings on the linear scale. Employed in this fashion, the eyepiece effectively becomes a degenerate form of filar micrometer. It is a method which produces greater accuracy in the measurement of separation, but it is also slower than the basic procedure already described.
The first step is to rotate the eyepiece until the linear scale is parallel with the axis of the pair to be measured, remembering to ensure that the primary star lies closer to the zero point on the 360° protractor scale. The observer counts the number, n, of whole divisions on the linear scale separating the two components. In the example illustrated in Figure 12.7, it will be seen that n = 3. With the motor drive running, the eyepiece is rotated and the slow-motion controls adjusted until a pair of scale markings n divisions apart bisects the two stars as shown in Figure 12.8a. Leaving the orientation of the eyepiece undisturbed, the observer uses the slow-motion controls to bring a star to the exact centre of the field, turns off the drive and notes the angle, 6X, indicated by the 360° protractor circle at the point where the star drifts across it. In Figure 12.8a, the reading is 60°.
Figure 12.8. The advanced method: a measuring 91; b measuring 02.
Reproduced courtesy of Sky Publishing Corporation
Figure 12.8. The advanced method: a measuring 91; b measuring 02.
Reproduced courtesy of Sky Publishing Corporation
Next, the eyepiece is rotated in the opposite direction, past the original position at which the axis and linear scale are parallel, until both components are once more bisected by two markings on the linear scale (see Figure 12.8b). Again, the observer measures the angle, 02, as before. In the example shown, the reading is 20°.
If one of the two angles happens to fall within the first quadrant (0-90°) and the other in the fourth quadrant (270-360°), add 360 to the lower of the two figures. This is necessary in order to avoid numerical complications at a later stage in the process of reduction.
The position angle of the pair, 0, is given by the mean of the two angles:
to which (in the case of the Celestron version) the 90° correction must be added. The separation, p, is given by:
cos a where n represents the number of whole divisions separating the components, z the scale constant, and a is half the difference between the two angles 01 and 02:
In the example shown, a = 20°. Assuming a scale constant, z, of 5'', the corresponding separation is therefore
cos 20
Table 12.3. This observation of £1442 was made on 2000, Mar 25 with a 21.5-cm Newtonian reflector and Celestron Micro-Guide eyepiece (z = 6'.'25). Each set of measures occupies a numbered row. The first angle is 01, the next a direct PA measure made by the simple "drift" method, and the third 02; note all these angles appear in their uncorrected forms. The penultimate column shows the corrected position angle, obtained by adding 90° to the mean of the three preceding entries. The final column gives the separation, derived from 01 and 02 by the method described in the text. The overall mean position angle and separation appear in the last row
0, |
02 |
0 |
P | |||
1 |
45 |
68.5 |
85 |
156? 17 |
13' |
'30 |
2 |
49 |
66 |
88.5 |
157? 83 |
13' |
'28 |
3 |
43 |
66 |
94 |
157? 67 |
13' |
'85 |
4 |
48 |
67 |
89 |
158? 00 |
13' |
'35 |
157? 42 |
13' |
'45 |
Again, the procedure should be repeated over a series of nights, and means taken of the position angle and separation. In each set of observations, it is a sensible practice to include a number of direct determinations of the position angle made by the simple method, as shown in Table 12.3.
Because this method of using a reticle eyepiece is insensitive to variations in (01 - 02), it is capable of yielding separation measures far more accurate than those obtained by means of the standard technique. In theory, the precision is not constant, since the uncertainty increases with a. But since it is easier to judge simultaneous bisection at high values of a than at lower values, the competing practical and theoretical considerations probably cancel out.
The range of measurement is restricted by the layout of the reticle. For obvious reasons, the lower limit is set by z, the value of the scale constant. However, it is possible to measure closer binaries by turning the eyepiece through 90° and bisecting the stars with the two long parallel lines, which are only 50 microns apart. Provided the line nearer to the semicircular protractor scale always bisects the primary star, this expedient will also remove any need for a 90° correction; in the case of the Meade version it will, of course, introduce such a correction.
It is the inconveniently short graduation markings on the linear scale that impose an upper limit on the range of continuous measurement. At certain separa-
tions beyond about 6z, the observer will find it impossible to bisect both components simultaneously, with the result that gaps begin to appear in the measurement range. For wider pairs, the Barlow lens may always be dispensed with, but this will require the reticle to be recalibrated.
The more advanced method of using an illuminated reticle eyepiece places extreme demands on the observer's patience and dexterity. Not everyone will find the gain in accuracy is really worth the extra time and effort. While it may be useful for occasional measurements, where time is not a consideration, or for the observer who has to make do with a relatively short effective focal length, the amateur who wishes to pursue a systematic programme involving the study of as many pairs as possible will probably prefer to master the simpler technique in conjunction with a telescope having an effective focal length of not less than 5 metres.
Irrespective of the procedure adopted, the illuminated reticle enjoys great advantages over other methods. It is readily obtainable at a reasonable cost and is capable of considerable accuracy.4 It eliminates index error, is comparatively tolerant of errors in polar alignment and is, therefore, particularly suitable for portable instruments. Its main disadvantage lies in the raising of the magnitude threshold by reason of the illumination system.
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