Overview I've been working (slowly) for months on a
new light box for my Takahashi FSQ-106 (4" refractor). It is based
on an 8" x 10" electroluminescent sheet.
Construction The light box is powered by a single 9V battery, which fits in a small kit box that also includes a transformer to raise the voltage.
The battery box attaches to the EL sheet using a snap-together cord
like the kind that mates to the top of a 9V battery.
The key issues that I had to address when building the light box were both related to the diffuser.
First, EL sheets are actually composed of two sheets (a cathode and
an anode), mated side by side. Both sides illuminate identically,
but there is a small (~0.5 mm) insulator between them. When the
sheet is illuminated you can see a thin dark line between the
halves. I needed to ensure that this line was diffused into
invisibility before using the sheet as a flat field light source.
The second use of the diffuser is simply to attenuate the light. EL
sheets are quite bright. With no diffusion the sheet saturates my ST-2000 in less that 0.1 seconds. I ended up using 3/4" of
white "lighted sign" acrylic, 2 x 1/8" sheets and 2 x 1/4" sheets.
The sheets are stacked together using a set of four registration
screws. Behind the light source is a sheet of 1/8" black acrylic to
prevent stray light from ruining my night vision, bothering the
neighbors, etc.
Here is a photo of the front of the panel (click for full size):

Where the battery wires mate to the sheet, a piece of insulating
tape prevents a short circuit. In order to leave room for this tape
while maintaining the flattest possible light source/diffuser
sandwich, I used a Forstner bit to cut a slot in the black acrylic backer
sheet and the first diffuser. You can see the slot and the
insulating tape in this photo of the back of the assembly:

I had to punch holes in the EL sheet in order to pass through the
registration screws. I was concerned about short circuits here
because there was no way to seal off the inside of the holes. So I
used a bit of heatshrink tubing around the base of the screws as an
insulator:

I also trimmed the sheet about 1/8" smaller than the diffuser on all
sides, so that the exposed edges can't shock or short.
The whole assembly cost about $85, basically $65 for the EL sheet
and transformer, and $20 in diffusers. I bought wire leads and a
battery holder at Radio Shack for a few bucks.
How Well Does It Work? Quite well, I believe. (You can evaluate the results for yourself
using the link below.) To use the panel, I aim my FSQ-106 near the
zenith and lay the panel on top of the extended dew hood. The
battery box (not pictured) sits on top of the panel. I can then take
a good series of flats in just a few minutes. With Maxim 4's
sequencing capabilities, RGB filter flats are easy. Because the
light is so strong, I can shoot lots of frames quickly, and not
worry about brightness changes due to battery fade (though I haven't
had to change out the battery yet in any case).
To see for yourself, a sample light, flat (dark-corrected), and dark
frame can be downloaded here (6.8 MB download):
http://www.mightyatom.com/astronomy/flatsamples.zip
Materials Sources LuminousFilm is a good place to buy reasonably priced (for EL anyway) electroluminescent sheets. However, they didn't pack my sheet that well and it came with some creases in it. The creases don't appear to affect the flatness of the light source once the diffusers are in place but you may want to request more careful packaging when ordering from them.
I bought all the acrylic for the project at Tap Plastics.
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