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> Front surface dome mirror, aka first surface convex spherical mirror
simhopp
post Jul 6 2009, 07:11 PM
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hello, this is my first posting, and hopely this topic wasn't covered before.

I'm thinking of setting up digital projector / dome mirror home planetarium

and looking for dome mirrors, which are readily available as security mirrors
and are fairly inexpensive.

but as mentioned on some other articles, most of them are back surface mirrors.

I guess there is australian source of front surface half dome mirror, but the manufacturers
web site is a bit confusing and doen't really mention any details on it.

I do see several "steel half dome mirrors" offered for sale, on ebay and other web sites.

since these are metal domes, and not clear acrylic or poly-carbonate mirrors,

I'm thinking these must be front surface mirrors?

and they do come in several sizes, 9" to 26" (acrylic domes go up to 48")

I'm assuming bigger is better? can place projectors further away from the mirror etc.

and for people who already tried back surface half dome mirrors, is the effect of back
surface mirror really noticeble on the projected image?

thanks in advance for your input and information.
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Ken Miller
post Jul 7 2009, 09:47 AM
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QUOTE(simhopp @ Jul 6 2009, 06:11 PM) *
hello, this is my first posting, and hopely this topic wasn't covered before.

I'm thinking of setting up digital projector / dome mirror home planetarium

and looking for dome mirrors, which are readily available as security mirrors
and are fairly inexpensive.

but as mentioned on some other articles, most of them are back surface mirrors.

I guess there is australian source of front surface half dome mirror, but the manufacturers
web site is a bit confusing and doen't really mention any details on it.

I do see several "steel half dome mirrors" offered for sale, on ebay and other web sites.

since these are metal domes, and not clear acrylic or poly-carbonate mirrors,

I'm thinking these must be front surface mirrors?

and they do come in several sizes, 9" to 26" (acrylic domes go up to 48")

I'm assuming bigger is better? can place projectors further away from the mirror etc.

and for people who already tried back surface half dome mirrors, is the effect of back
surface mirror really noticeble on the projected image?

thanks in advance for your input and information.

I've seen this idea raised before, but I am pretty sure that the mirrors are steel-backed behind a second-surface acrylic mirror. That is definitely the way they are sold by a couple of manufacturers. If you read the specs, it is described that way.

I haven't seen the results first-hand, but I understand that there are image problems with the second surface mirrors. It has been suggested that the second surface mirror could be used for a proof-of-concept experiment before investing in one of the expensive front surface mirrors.

Last I checked the front surface mirrors were running about $700. Has the rate of exchange affected that price at all?
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Ron Walker
post Jul 7 2009, 12:29 PM
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QUOTE(simhopp @ Jul 6 2009, 06:11 PM) *
hello, this is my first posting, and hopely this topic wasn't covered before.

I'm thinking of setting up digital projector / dome mirror home planetarium

and looking for dome mirrors, which are readily available as security mirrors
and are fairly inexpensive.

but as mentioned on some other articles, most of them are back surface mirrors.

I guess there is australian source of front surface half dome mirror, but the manufacturers
web site is a bit confusing and doen't really mention any details on it.

I do see several "steel half dome mirrors" offered for sale, on ebay and other web sites.

since these are metal domes, and not clear acrylic or poly-carbonate mirrors,

I'm thinking these must be front surface mirrors?

and they do come in several sizes, 9" to 26" (acrylic domes go up to 48")

I'm assuming bigger is better? can place projectors further away from the mirror etc.

and for people who already tried back surface half dome mirrors, is the effect of back
surface mirror really noticeble on the projected image?

thanks in advance for your input and information.


Hi and welcome to OCP.

I've done a little experimenting with an 18 inch second surface mirror. The biggest problem I noticed is with small high contrast projections. Basically stars. With a simple XGA projector (I would recommend a full high-def unit for best reproduction) the stars projected were a bit soft but the real problem are the secondary star blobs projected by the second reflection. With a picture, this secondary projection was washed out fairly well by the main image.

Basically the acceptability of the projected image depends on the level of image quality that is satisfying to you personally. The impact to an all dome image is substantial to say the least, but it will soon wear off. Even the projection of OmniMax is not perfectly clear. A dome is a lot of area to cover with one projector.

A bigger mirror will place the second reflection closer to the first and my first thought would be that things should look sharper, but on second thought, placing the second reflection closer to the first will at some level look to the viewer as one larger softer image. Not so good.

I would agree that a cheaper mirror is the place to start to see if the level of quality obtained with the system works for you. One can easily imagine the projected image without the secondary reflection especially with star fields.

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charle
post Jul 7 2009, 01:36 PM
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Expanding Ron's experiments using a second surface mirror.

This response is fairly long and bit a bit technical, so feel
free to ignore it in its entirety.

To understand the issues, I have used a good star projector
as the light source, essentially a simple optical planetarium
projector. Normally this rig will project magnitude -2 stars
with less than 5mm diameter image at a distance of 10 feet.
Most stars are projected to points less than 1mm.

Using this setup, the projected image from an 18inch second
surface mirror had a surprising result. When the focus was
to short, the image of a star was a short line, all going the
same direction. When the focus was too long, the image of
a star was a short line and 90 degrees to the under-focus image!
I just thought this phenomena might be of some interest.

The point of "best focus" for this setup occurs when there are no
lines. Each star becomes an unsatisfacory blob that is at least an
order of magnitude larger than the original image.

There is a way to make the secondary mirror more acceptable.
A few simple equations will be helpful here and offer some
general guidance in planning these systems.

Let A be the projection angle of the source machine. This is
determined by direct measurement or the manufacturers
specification.

Let B be the angle representing the portion of the spherical
mirror that is actually used to reflect the source beam. For
example, 45 degrees would represent one eighth of the
circumference of a sphere.

Then the "effective projection angle" C of the system is given
by the equation:

C = 2*B + A

This equation has several usages. For people with a half dome
planetarium needing a 180 degree full horizon projection
with a video projector with 30 degree projection angle, then
the portion of the spherical mirror to be used is 75 degrees.
Mark the mirror for that range, then move the projector in
until the image covers that area.

As a side note, the mirrors used to "magnify" the projection
angle do NOT have to be convex, but I have not seen any
mention of this. The effective projection angle for a concave
mirror is:

C = 2*B - A

So the magnification is less than for a convex mirror, but
can nevertheless be useful. I mention this, because Edmund
still sells a glass first surface mirror with a fairly short radius
for about $60! These are used to make Schmidt cameras etc.
If anybody out there tries this, please let me know how it
worked out.

For the full planetarium problem, with the same parameters,
we would need to use 105 degrees of a concave mirror. More
difficult but doable.

For people who are NOT trying to fill a full dome, the equations
become more helpful. So if I want my 30 degree projector
to have a 90 degree throw, then we only need to use 30 degrees
of the mirror. In this case, a "truck mirror" becomes a more
useful alternative to a full quarter dome mirror which is mostly
unused. Now in this case, the projector can be set up so that the
central line from the projector is only 15 degrees from the edge
ray of the projection. If this were a telescope, it would be called
an "off axis telescope". What this does is significantly reduce
the angle of reflection from the second surface mirror and improves
the quality of the projected image accordingly. This occurs because
the distance between the reflection from the first surface to the reflection
from the second surface is significantly smaller than the full dome case.
This also means that if use a second surface mirror for a full dome,
there is always some part of the image that is really bad because
the distance of first to second reflection is large.

I have tried this with a 15 inch diameter truck mirror and the idea
does work. But the image is still poor compared to any front
surface mirror.

If at least two people are interested in this "discourse" I will put together
a couple of pictures to help illustrate the ideas.







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Ken Miller
post Jul 7 2009, 01:58 PM
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QUOTE(charle @ Jul 7 2009, 12:36 PM) *
If at least two people are interested in this "discourse" I will put together
a couple of pictures to help illustrate the ideas.

Count me for one. I'm sure we have enough interested people to justify continuing with this.
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Ron Walker
post Jul 8 2009, 12:43 PM
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Pictures, Pictures!!!
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charle
post Jul 9 2009, 10:14 PM
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OK, I'm hosting a family reunion this weekend so it
will be about mid next week before I can post the
pictures. Actually, I already have the pictures but
in spite of 1000 words etc. they do need some
explanation.

Charle'

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charle
post Jul 17 2009, 12:07 AM
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Formulas for Planning a Spherical Mirror Projection System

These notes relate to formulas that may be useful
for planning a projection system using spherical mirrors.
This idea has been recently popularized by Paul Bourke
who has developed an approach for adding modern digital
imaging to classic planetarium installations. The results
to date have been remarkable based on the number of sites
that have implemented the approach. Paul is well deserving
of the recognition given him by the planetarium community.

I will assume that the reader is generally familiar with the
idea. I am simply reporting some basic formulas that my be of
some use in the consideration of such systems by planetarium
professionals as well as amateur experimenter ... perhaps more
useful for amateurs.

Figure 1 illustrates some details of the projection path between
a projector at point A, a section of a spherical mirror with
center at point B. The portion of sphere used to reflect the
projector image is the section C to D. The projection angle will
be called "A" (geometrically the angle DAC). The projection
angle is determined from manufacturers specifications or by
direct measurement. If the focal length of the projection lens
is known, and the size of the imaging array is known then the
projection angle is given by the formula:

A = 2* arctan(d/2/f)

where f is the focal length, and d is the diagonal of the image
source (LCD array, slide etc.) Sometimes the projector spec sheet
will give the final image size of a projection for a given distance
to the screen. In this case, use the same formula but use d as
the image size on the screen and f is the distance from the
projector to the screen.

The second main piece of information that we need is the radius
of curvature of the mirror. This is always specified directly.
The angle B (actually CBD) is the portion of the spherical
mirror actually used. As we will see, this is a fundamental design
choice and significantly affects the result. Given the angles
A and B we can determine the resulting projection angle C (Lines E
to F) by the formula:

C = A + 2*B

This formula is derived as follows. One side of the projected
image is the line AC which is reflected by the mirror on line CE.
The line that bisects this angle is of course a line from the surface
of the sphere to the center of the sphere. The angle of reflection
is equal on each side of the bisector based on the law of reflection.
Orthogonal to the bisector is the tangent line CG. Similarly, the
line AD is the extreme of the other side of the projection path.
The reflection of this line represents of the line DF. The bisector
of the reflection angle ADF is the radius line DB with tangent line
DH. The angle between the two tangent lines represents the amount of
increase in the projection angle of the entry line of point D
compared to point C. Using the similarity properties of the triangles
formed by the radius lines CB and DB to the tangent lines,
we see that the angle between the tangent lines is the same
as the angle B. This angle is added to each side of the reflection
at point D so the resulting projection angle is 2*B greater
than the original angle A thus demonstrating the derivation of the
formula.

A simpler way of viewing this is to start with a flat mirror
that is flexible and has the property that it always bends
in the arc of a circle. When the mirror is flat, the reflection
angle at point D is the same as at point C plus the projection
angle A. We then start bending the mirror at point D
leaving point C rigid. For each degree that we bend the
mirror at point D (increase in the angle between the
tangents) the reflection angle is changed by 2 degrees, one
degree on each side of the bisector. The formula results
when we have bent the mirror by the amount B. The figure
shows an example numerical case that may be of further
help. In the figure, the angle A is 20 degrees and the
angle B is 31.74 degrees resulting in a final projection
angle of 83.48 degrees, which is four times wider
than the original angle.

In a way, we can view the spherical mirror as a "wide
angle converter". The interesting thing is that we have
considerable control over the final projection angle
by moving the projector closer to the mirror or further
away. This is a mixed blessing in that this distance
must be made fairly precisely to get the desired result.

Less well know is the fact that a concave mirror can also
be used as a wide angle converter, although it is not as
efficient as the convex mirror. The argument is essentially
the same with one major difference: for each degree that
we bend the mirror inward, the reflected angle is decreased
by 2 degrees giving the formula C = A - 2*B. This may seem
counter productive, but the trick is to make the angle large
enough to still make the result substantially wider than
the original angle. For large B, the formula gives a
negative result which just means that the image has been
reversed (this is a fairly standard thing in optics
analysis). To avoid confusion, I prefer to express the
formula as C = 2*B - A. In the shown numerical example, the
angle A is 20 degrees as before, the angle B is 29.12 degrees
and the resulting angle is 38.24 degrees. The dimensions
specified are for the six inch first surface concave mirror sold
by Edmund Scientific (the Anchor Optics division). This lens
has a radius of curvature of 300 mm (11.798 inches) and has
various usages including home built Schmidt cameras. I have
used this as an example because its the only first surface
mirror available to the amateur at a reasonable price (about
$80 USD). Note that the angle 29.12 degrees is the largest
value of B possible with that specific mirror. The concave
quarter dome mirror would achieve a much larger projection
angle.

Now for a couple of quick application demonstrations. Figure 3
shows the basic structure of Bourke's planetarium projector.
Bourke uses a value of B = 58 degrees in his demonstration
model with a half dome mirror of radius 300 mm (about 12 inches).
He does not specify the projector angle, since this
value is vendor specific. I have used a value of 15 degrees
which is fairly typical. The resulting projection angle
is then 131 degrees. I have chosen to position the projector
and mirror so that the full 180 degrees of the dome is filled
with no gaps. I did this just to show that it is possible
because in practice, the projector and mirror are elevated
to clear the heads of the audience! In that case, a small
portion of the image behind the mirror will be missing. I Presume
that the area below Polaris (due North) is picked for this purpose
because who cares what's there (we always get a better view
of these objects when they are on the other side of the NCP).

Figure 4 shows an application that may be of more interest
to the amateur user that has a "square dome" in the living
room. In this case, we wish to project the stellarium image
(or other star chart program) entirely on the ceiling.
We can use a modest 5 inch chrome truck mirror in this case.
This type of mirror is first surface but has about 30% light
loss and typically has many spherical aberrations. But for
my living room ceiling, I'm not to concerned about absolute
accuracy. I have included a second flat mirror so that the
projector sits level instead of pointing downwards which might
mess up the cooling of the unit. The flat mirror can flip up
so that the image can be projected on the far wall. The
zoom lens can be used effectively to increase the image
size for super bowl parties etc. I've also considered
the use of a "moon" hub cap like those used on 1950's
style hot rods ... for the super bowl audience, this would
have MUCH better talk appeal over a perfect glass first surface
reflector! That may be the only way to get these friends
to see a planetarium show. Now if I could only convince the
other occupants of my house ... if anyone tries this, let me
know how it works out. There are endless variations of this
picture that might fit the reader's situation.

Finally, figure 5 is offered to illustrate the fundamental
"zoom" capability of the spherical mirror. The figure
assumes a 12" radius mirror, and shows the projection
angle for three different positions of the projector. In the
case shown, we get about a 2.5:1 zoom ratio.

There is much more to planning a spherical mirror projection
system than these simple formulas, but hopefully you
will find them of some use. Good luck on your project.

Charle' R. Rupp, July 2009 at the Silo Observatory


Attached File(s)
Attached File  fig1.pdf ( 20.3k ) Number of downloads: 77
Attached File  fig2.pdf ( 16.73k ) Number of downloads: 43
Attached File  fig3.pdf ( 54.84k ) Number of downloads: 39
 
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charle
post Jul 17 2009, 12:23 AM
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Here's the last two figures.

Attached File(s)
Attached File  fig4.pdf ( 25.34k ) Number of downloads: 47
Attached File  fig5.pdf ( 22.63k ) Number of downloads: 43
 
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chemed
post Jul 21 2009, 01:06 PM
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hey everyone!
Sorry I haven't posted in awhile. Been busy enjoying the summer.
I am particularly interested in constructing a spherical mirror dome projection system. I have been working on it for some time. I still need a better projector than the one I'm currently using. The specifications on Paul Bourke's page are what I have been using. As far as the mirror goes, what I've found is that if you're looking for a the best projection resolution possible, you need a primary surface mirror. The only company I've found that makes them at a reasonable price is Acril Convex mirrors, based in Australia. I was able to ask a local company, but for them it was a specialty product, and the price was ridiculous. Here's a quote of the correspondence I received from Acril.

Price for the E20534 (primary surface mirror) is $585.00 Australian Dollars (not USD) (approx $410 USD)

Shipping for one mirror to the USA is approx $425.00 AUD

I recommend purchasing 2 mirrors as the cost of freight being high you can save on the freight with 2 mirrors keep one as a spare.

To ship 2 mirrors to the USA is approx $625.00 AUD

Obviously, shipping would be an issue, but I've found it to be around $400 US

Great information Charles! I will be using it as a resource.

-atm
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Ron Walker
post Jul 22 2009, 11:49 AM
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QUOTE(chemed @ Jul 21 2009, 12:06 PM) *
hey everyone!
Sorry I haven't posted in awhile. Been busy enjoying the summer.
I am particularly interested in constructing a spherical mirror dome projection system. I have been working on it for some time. I still need a better projector than the one I'm currently using. The specifications on Paul Bourke's page are what I have been using. As far as the mirror goes, what I've found is that if you're looking for a the best projection resolution possible, you need a primary surface mirror. The only company I've found that makes them at a reasonable price is Acril Convex mirrors, based in Australia. I was able to ask a local company, but for them it was a specialty product, and the price was ridiculous. Here's a quote of the correspondence I received from Acril.

Price for the E20534 (primary surface mirror) is $585.00 Australian Dollars (not USD) (approx $410 USD)

Shipping for one mirror to the USA is approx $425.00 AUD

I recommend purchasing 2 mirrors as the cost of freight being high you can save on the freight with 2 mirrors keep one as a spare.

To ship 2 mirrors to the USA is approx $625.00 AUD

Obviously, shipping would be an issue, but I've found it to be around $400 US

Great information Charles! I will be using it as a resource.

-atm


Have a look at:

http://www.observatorycentral.com/index.ph...ost&p=19809

While we never talked costs, Paul Zacharias, owner of Spectrum Coatings says he has front surfaced plastic dome mirrors before with good results. I can't imagine coating a mirror costing more the $500 but then what do I know. Perhaps if enough people wanted this we could get a deal.
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chemed
post Jul 28 2009, 04:56 PM
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I'm very much interested!
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Ken Miller
post Aug 21 2009, 09:27 AM
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Tony Butterfield posted a message on the Yahoo Small Planetariums Group saying that they were testing some American made front surface mirrors in Houston, and that there will be mirrors available to purchase this Fall.

I looking forward to getting one and experimenting with it.
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chemed
post Aug 25 2009, 07:37 AM
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Ken,

DO you have contact info?

-atm
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Ken Miller
post Aug 25 2009, 01:28 PM
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QUOTE(chemed @ Aug 25 2009, 06:37 AM) *
Ken,

DO you have contact info?

-atm

I do not have direct contact info. Tony has not given out any specific information yet. You can contact him through the group. They hide the personal email addresses these days. I know that he is zacksmumdad@???????. I am very curious as to who is building these mirrors, and I hope to hear more soon. Righ now I'm sorting through dome options so that I have a place to try things out at home before interfering with the planetarium operation at the Children's Natural History Museum. I'm going to start a new topic on my dome adventure as soon as I have time. I don't know anybody else that has set up a dome in a spare bedroom yet. I don't have room for a 10 ft dome, but I'm looking at ways to squeeze in a 9 ft dome.

Ken
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simhopp
post Aug 26 2009, 01:47 PM
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I recently bought a Mitsubishi 1280x720 DLP projector, which cost around $700 for home theatre
purpose.

the DLP projector image projected on screen will show very well defined square pixels if you look up close.
pixel width to gap between pixels ratio is around 50 to 1, ie it looks like each square pixel is defined by thin border lines.




and since I had 24" quarter dome security mirror at hand,

I did a little testing with them, bouncing off projector image to the ceiling of my room.

the security mirror was 2nd surface acrylic dome.

the distance of mirror to projector was around 3 feet, and distance from dome to ceiling was around 7 feet.

and what I can tell is that you don't really see the effect of 2nd surface mirror.

the pixel doesn't look blurry or double image, can't really tell if there is any ghosting.

so I think inexpensive 2nd surface mirror security dome will work just fine for home built planetarium.



however, one thing is for sure, 1280x720 is not enough resolution for planetarium.

I would recommand the highest resolution you can get if you want any kind of decent imagery.

and also dome surface to project to is also necessary, since projecting on flat ceiling distorts images.
unless you have a dome surface to project to, there is no point in using a mirror dome.
it would be better to just directly project images to ceiling without bounding them off a dome mirror,
by pointing projector up.


so, my conclusions from this simple experiments are.

1. 2nd surface mirror dome works pretty well.

2. 1280x720 is not enough resolution.

3. you really need a dome surface to project image onto.
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chemed
post Aug 26 2009, 08:27 PM
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As it turns out, I do have a dome on which to project an image (IMG:http://www.observatorycentral.com/style_emoticons/default/smile.gif)

I also have a security mirror right now, good for testing. In my opinion, as of right now, the quality of a full dome video that has been properly modified to project onto a curved surface won't suffer too much from a second surface mirror of decent quality. The problem is in the projection of digital animations or projection using night sky rendering software. That is, the projection of an animation is much more likely to be distorted by more than one light path. I also think that the "throw distance", the distance from the projector to the projected image could really amplify this problem. That being said, I have seen so called "high quality" digital projection systems that made a real mockery of their projection of the night sky (which is why I am a proponent of using an integrated system). So, maybe all the fuss over the use of primary surface mirrors is about using the highest quality equipment as possible so that any loss of image quality is minimized. After all, this type of digital projection is definitely the cheapest. You can only cut corners so many times before even the cost savings aren't worth the trouble.

BTW, I am working on purchasing a projector that has a native resolution of 1920 x 1080 and can run at WUXGA, 1920 x 1200, which is the native output resolution of my new iMac 24.

Ken,

I was able to contact Tony Butterfield, he estimates that the cost of his mirrors, when available, will be similar to the mirrors coming from the Southern hemisphere.

-atm
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Ken Miller
post Aug 26 2009, 10:48 PM
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QUOTE(chemed @ Aug 26 2009, 07:27 PM) *
Ken,

I was able to contact Tony Butterfield, he estimates that the cost of his mirrors, when available, will be similar to the mirrors coming from the Southern hemisphere.

-atm

Excuse my language, but WTF?????

They can't make them any cheaper? Aside from that, is there any saving when you factor in shipping?

Ken
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Owen Phairis
post Aug 27 2009, 08:42 AM
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QUOTE(chemed @ Aug 26 2009, 07:27 PM) *
As it turns out, I do have a dome on which to project an image (IMG:http://www.observatorycentral.com/style_emoticons/default/smile.gif)

I also have a security mirror right now, good for testing. In my opinion, as of right now, the quality of a full dome video that has been properly modified to project onto a curved surface won't suffer too much from a second surface mirror of decent quality. The problem is in the projection of digital animations or projection using night sky rendering software. That is, the projection of an animation is much more likely to be distorted by more than one light path. I also think that the "throw distance", the distance from the projector to the projected image could really amplify this problem. That being said, I have seen so called "high quality" digital projection systems that made a real mockery of their projection of the night sky (which is why I am a proponent of using an integrated system). So, maybe all the fuss over the use of primary surface mirrors is about using the highest quality equipment as possible so that any loss of image quality is minimized. After all, this type of digital projection is definitely the cheapest. You can only cut corners so many times before even the cost savings aren't worth the trouble.

BTW, I am working on purchasing a projector that has a native resolution of 1920 x 1080 and can run at WUXGA, 1920 x 1200, which is the native output resolution of my new iMac 24.

Ken,

I was able to contact Tony Butterfield, he estimates that the cost of his mirrors, when available, will be similar to the mirrors coming from the Southern hemisphere.

-atm



Interesting, sound to me like it might be easier and even cheaper to go with a first surface flat mirror and a fisheye lens.....

Owen -
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chemed
post Aug 31 2009, 09:14 AM
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fisheye has its own problems, especially with pixelation at and around the springline. Also, with fisheye lenses, efficient use of actual screen space that is utilized by the projector can be much less than mirror projection. Finally, I think they can get quite expensive as well.

-atm
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