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Ever since fitting a set of
Bob's Knobs a few months ago I have been troubled by collimation
difficulties. This has nothing to do with the knobs but more to do with
my collimation method and very poor local seeing conditions. The knobs
are in fact very easy to install and a pleasure to use. The installation
instructions are
here (148k PDF). For an excellent account of collimation by
Thierry
LeGault click
here.
Then some time ago there was a thread on the
Yahoo LX90 Group on using an artificial star made from a bright Light
Emitting Diode (LED) and a pin-hole to collimate SCTs. Were I to
make one of these devices, I could collimate my scope in any seeing
conditions and even during daylight hours. With the assistance of a
couple of good blokes (namely my friend Bert and his mate Andrew), I set to work.
Here is an account of my efforts.
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Components |
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LED (Bright White; 3.6V; 20mA; 8000mcd) - $9.95 from
Dick Smith Electronics (DSE
Cat. No.: Z 3982) |
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LED mounting bezel (with collar) (DSE Cat. No.: H 1910) |
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9V battery clip (DSE Cat. No.: S 6100) |
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270 Ohm 0.25W resistor (DSE Cat. No.: R 1060) |
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Toggle switch |
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Plastic/wooden case |
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Small piece of circuit board |
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9V battery |
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Wire |
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Calculating
the resistance |
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LEDs are current operated devices, which emit light when current flows
in the forward direction. Therefore, any circuit devised for
illuminating an LED MUST have a series resistor to limit the current
through the LED and the LED must be connected the correct way (see the
spec sheet for the LED you get). You can calculate the required
resistance using Ohm's Law:
R = V / I
where R is the required
resistance, V is the net voltage (supplied voltage - forward voltage of
LED) and I is the forward current of the LED in Amps. Here's what we
have using the voltage supply and LED listed above:
R = (9V - 3.6V) / 0.020
R = 270 Ohms
The LED doesn't really care but the resistor should be
1/8 Watt. I couldn't get one of these so 1/4W is fine. By the way, if
the maths for this is in any way hairy, you can find an online LED
circuit resistance
calculator
here.
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Explanatory pictures |
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Here's the
simple circuit diagram schematic incorporating the
electronic components listed above. You can use any DC voltage provided it is
greater than the
value of the forward voltage of the LED and you have a matched resistor
to limit current flowing to the LED. |
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Image showing the innards. In order to
place the LED close to the aluminium foil hole, I had to raise the
circuit board with two pieces of wood (Tasmanian Oak). |
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The artificial star switched on.
The LED
is attached to the circuit board and held upright by the plastic bezel
and collar.
The series resistor is shown on the circuit board. |
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.jpg) |
Image showing the inside of the casing lid with aluminium
foil attached. The pin hole, which is barely visible in this picture,
is centred in the hole drilled into the casing. |
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The relevance of telescope resolution |
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Now for the tricky part. The size of the
pin-hole in the aluminium foil is critical. It must be small enough not to
be resolvable by your telescope at the distance it is placed. First of
all you need to know the resolving power or resolution (Dawes'
Limit) of your telescope using the following
formula (NB: This equation gives
the theoretical resolution and does not take into consideration
secondary mirror obstruction sizes.):
R = 4.54 / Ap
where R is Dawes' Limit (theoretical resolution) and
Ap is aperture in inches (the constant 4.54 becomes 115.32 if dividing by
your aperture in mm). So, for the LX90:
R =
4.45 / 8
R = 0.56 arc sec
What about for other sized scopes?
The table below gives some idea of the resolution (R) for other scopes
of various apertures (Ap) measured in inches:
Ap
R
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4 1.113
6 0.742
8 0.556
10 0.445
12 0.371
13 0.318
16 0.278
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Calculating the size of the pin hole |
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The relationship between the size of
the hole in the aluminium foil and the distance between the scope and
the artificial star is given by any of the following:
Tan (
R ) = H / D
D = H / Tan ( R )
H = D * Tan ( R )
where Rd is the Resolution of your
scope in degrees, H is the hole diameter in mm, and D is the distance
between the scope and the artificial star in mm (Note: H and D can be
any unit of measurement as long as they are the same). As an example,
let's calculate the minimum distance required for a large 1mm diameter hole:
D = H
/ Tan ( Rd )
D = 1 / Tan (0.56 / 3600)
D = 368.33 m
Yikes! You can see that when making
an artificial star it is wise to make the hole as small as possible.
Let's have a closer look at the artificial star hole (H) diameters from 0.1 mm
to 1.0 mm and corresponding minimum distance (D) in metres for the 8 inch LX90:
H D
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0.1 36.83
0.2 73.66
0.3 110.50
0.4 147.33
0.5 184.17
0.6 221.00
0.7 257.83
0.8 294.66
0.9 331.50
1.0 368.33
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How to make a very small hole |
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A number methods for making very small holes shave been used such as
using the tip of a very fine gauge needle to just puncture the aluminium
foil. Andrew, Bert's mate, has used an acupuncture needle, which
apparently is 0.12 mm in diameter. The method I prefer is to use a
single strand of fine gauge wound copper wire. I have no idea about the
diameter of this wire, but it must be very close to 0.1 mm. |
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The finished product |
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The finished product! I found the case at
DSE. It is made of hard plastic and can easily be
drilled. It's solidly constructed and aesthetically pleasing. In this
image the artificial star is in operation and you can see the light
shining through the small hole. |
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All information and images are copyright
© 2003-2004 by P B Langsford. Please ask if you wish to use them or link
to them |
