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# Curved Screen Equations

Greetings,

Im currently looking at buying my first CRT, and asthetics are making some demands on the projector (see CRT forum if interested). I was wondering if anyone has any equations to calculate the increase in gain given by a curved screen.

Also, when diagonal screen size is quoted in relation to a curved screen, I assume that this would not be the surface area of the screen, but rather what the size would be if a surface was tensioned between the edges. Is that correct ?

Can curved screens be used will all screen materials, or would retroreflective materials cause problems ?

Laslty, I would imagine that having the curved screen tilted downward to face the viewers, with the projector lenses perpendicalar and centred on this screen would provide the optimum results ?

Daniel.

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Good list of Issues:

Based on my experience I would say that the gain would vary from

achieving 3.5 from a 2.8 pearlescent white screen.

To achieving a 7 gain from a 3.5 silver screen.

To achieving 11 from a 5 gain screen.

The later 2 I would not recommend..

The Diagonal is measured Corner to corner, not surface area.

The only rermaining curved screen manufacturer Vu tec makes a
6 x 8 curved screen that they sell with that stupid looking foil. I cannot believe that they never tried it with a high gain white pearlescent.

In addition the VUTEC cannot be cut down past 16 x 9. As my name points out I am a curved cinemascope kind of guy.

If there is an australian curved screen mnufacturer that can produce a 2.35 ratio screen 8 feet or wider please let me know.

The relation of the screen to len is perpendicalur.

Normal angularly reflective screens give you a 5 to 7 dgree + - Range from perfectly perpendicular. This fine adjustment is used to dial in the brightnes to the audience also reflecting away side ambient light.

Curved screens are fantastic I encourage you to experiment with the retroreflective like the dalite super, it could be the curved screen from hell..

------------------
The Artist formerly known as PANARAMAX.....
Snaggs
I have a different but related question.

With respect to a concave curved screen. As the area of the screen increases, does the screen gain -

A. Increase (and under certain circumstances approach infinity,

B. Decrease, or

C. Stay exactly the same.

My guess now is "A" but I would love to hear of a proof either way.

Thanks,
Mike
You are not a Millionaire!

All parameters of curvature satying the same the gain is unaffected by the surface. The lumen output of the projector is a different story, larger screen requires larger lumens. But the ratio remains the same.

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The Artist formerly known as PANARAMAX.....
Hi Peter.

I'm trying to use my audience lifeline here. Consider this hypothetical setup.

1. A screen that is a section of a perfect sphere.

2. Light source and eyeball at the exact center of this sphere.

3. A 100% reflective surface (perfect mirror).

Under these circumstances, all light reaching the screen would be reflected to the eye. As the screen size increases, the light to the eye would remain constant while the light from a reference flat 1.0 gain screen would decrease and approach zero. The ratio, or gain, would therefore approach infinity. No?

Obviously there are other variables at play, but it seems that the contribution to gain of the curve itself is not constant with respect to size.

Thanks,
Mike

[This message has been edited by Mike2 (edited 10-05-2000).]
I'll have to respond to that one, like I have had when asked questions about folding space in space exploration....

The answer is the same GWB gave when asked about the name of ministry of defense of Mombawe. Uhmmmmm? ......no.

In screens from 7 feet wide to 16 feet wide that where properly degigned the gain remained consistently proportional to basic screen gain to luminosity. With the torus that linearity is given +- 2% for evry seat or portion of the screen.

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The Artist formerly known as PANARAMAX.....
Surely we can get more scientific than that.

Consider this one as a corollary.

2 screens of equal area. One flat white 1.0 gain reference and the other curved with an identical white surface. The curved screen has a gain higher than 1.0. Correct?

Now imagine shrinking each screen identically. As the size decreases, they both approach the same shape- a single point. As the shape and size of the 2 screens approach equality, the gain of the screens should also approach equality - i.e. the curved screen gain decreases with decreasing size and approaches 1.0

Uhhhhhm....yes?
Ah...I believe people are misunderstanding what a curved screen does.

A curved screen allows one to have higher gain with no hotspotting.

What is gain? A 1.0 gain screen with (theoretically) disperse light evenly in a hemisphere, think of a spotlight on a wall. You can see the circle of light cast by the spotlight from anywhere in a room. This is 1.0 gain. A mirror has a gain of infinity, you can only see the circle of light cast by the spotlight if you are in the reflected path. Gain measures how much light is dispersed and how much if reflected. A 2.0 gain screen would show a spot twice a bright as a 1.0 gain screen if you shone a flashlight at it. This light has the come from somewhere and the farther you are from the reflected light the less bright it will be (because more is being reflected and less is dispersed). Anyways, what you need to know about gain is that it can multiply the lumens outputed by your projector (2.0 gain * 1300 lumes = 2600 lumes), but with some limitations.

What is hotspotting? Hotspotting looks like someone has dimmed the corners of your screen, like a brighter circle in the center of the screen that slowly falls off to a dimmer image at the edges. This is a sign of too much gain. It means that too much light is being reflected and not enough dispersed and you are noticing it in the corners of the screen most because you are farthest away from the reflected light from the corner.

A curved screen directs more of the reflected light back to the audience instead of off into the back of the room and into the walls, this allows you to use a higher gain and avoid hotspots. It's almost like a curved mirror that focuses light onto a point. This makes it pretty bright at the point, but kinda dim elsewhere, however there's no one sitting outside of the point so that's OK. Cool, no? It makes better use of your available lumens.

Regards,

Kam Fung
Kam Fung,

I cheerfully admit I don't have a complete understanding of what a curved screen does. I'm posting in the hopes that someone who does will respond and help educate me. I've observed first-hand, as Peter and others have posted previously, that there can be a dramatic improvement in picture quality and brightness with a CRT/compound curved screen and I would like to better understand why.

"Because I said so" is helpful to a certain extent (seriously), but understanding the actual relevant equations - as Snaggs initially asked - might have the added benefit of saving considerable time and money when designing, building, or buying these screens.

It appears we may be using different definitions of gain. I apologize for not stating mine at the outset. My simple definition for the purposes of the "Millionaire" question above was, Gain = Light reaching a particular point (eyeball, perpendicular and centered) from screen X divided by light reaching the same point from a same size reference 1.0 surface. I've seen several definitions of gain here and elsewhere but comparing the amount of light actually reaching our eyes from the screen seems to be what we are most interested in doing. If there is a better term than "gain" for this ratio, I would like to learn it and will use it instead.

I also made the assumption that for any given surface material the gain from a curved screen is higher than that of a flat screen of identical size.

What definition of gain are you using that gives a mirror a gain of infinity? (Mine yields the opposite- flat mirror gain approaches 0.) Yours implies the gain of curved and flat screens are identical as a curved mirror and flat mirror would then each have infinite (equal) gain.

Mike
Guys:

I validate your points theoretically. However Based on my TORUS experiences, I assure you that a 2.8 custom designed pearlescent STEWART surface exhibited a gain of 3.2 to 3.5. Could it be Collimation of light , concentrated in that center? Mike may be a millionaire after all . What can be said is that in sizes from 7 wide to 16 wide, no gain change/ratio
has been observed. And I seldom have installed flat screens.

A properly designed Curved screen with a pearlescent coating( I have done 20 in 54" x 96" )on Barco 700's enhanced the color dynamics and apparent resolution where in many ways it beat a 9 inch Barco 1200 hd costing 4 times more.

The reason that curved screen was not promoted was Joe Kane and Joel Silver who know a lot of theory that in reality ignores that the eye/brain
can be the most perspicas instrument.

So yes the Silver curved screens are horrendous. But there was a company Beiner that went out of Business, that did not exhibit rgb color shift reflections.

Let's call an ace , an ace. Did you see Lethal Weapon 4. Well?
To paraphrase: Joe & Joel "F*CK*D" most of "you,they really realy F*CK*D you". In fact, most of you, projecting pcrt's unto flat fixed screens without masking or perforations,following the ISF guidelines,and those not projecting on a curved screen, where a curved screen could have been used -that excludes those that needed a rolloup situation.) make all the prostitutes in the Amsterdam red light district, on any given night, seem like a theater full of girls scouts, no more like a nun convention at the vatican.

Speaking of the POPE. Since FOR A LIMITED TIME ONLY (Y2K), he will forgive all sinners that repent. Maybe if you sell your flat screen and buy a PROPER curved one this year; then and only then, maybe,after coming to terms with yourself, your self esteem, by having undertaken the correct path of: refraining cult-following the industry's "FORNICATING VIDEO-EVANGELISTS",will grow to unimaginable levels, rewarded by the lord with EYE CANDY.

My custom comissioned 2.8 that behaved like a 3.2 torus screen exhibited, on 11' wide on a Barco HD 1200, which I installed in 1993, looks like those double stacked Vidikrons except with a picture area much much larger.

Back to the original topic:

Seems to me that Don Stewart in consultation with Gerald Nash are the only ones that can answer those two questions.

Will Kam fung please post links on his original post on the TORUS. Where we first "met", in that same thread he gave us the patent . I need both links , asap. Please ,please

------------------
The Artist formerly known as PANARAMAX.....
Damn I wrote a reply last night, but it hasn't shown up... http://www.avsforum.com/ubb/frown.gif Must not have pressed "Submit Reply"...

Anyways,

Your definition of gain is intuitively correct, but there is more too it. All surfaces are to some extent mirrors, right? That means that all surfaces bounce light at an angle equal to the angle of incidence to some degree. Your regular white-painted wall is probably doesn't reflect very much light (it doesn't look much like a mirror...). Instead of reflecting light like a mirror it diffuses it equally in all directions. When something doesn't reflect any light, rather it diffuses it all, this is called 1.0 gain. As you raise gain the surface becomes more and more mirror like (although in a screen it's not much like a mirror), so that it reflects more light along an angle equal to the angle of incidence. So mirrors have an infinite gain because they reflect all light and diffuse none of it (theoretically). What the number of the gain represents is how much more light you would get if you were sitting in the reflected path of light from the gain screen over what you would get from a 1.0 gain screen. So a 2.0 gain screen would give you twice as much light if you were sitting in the path of the reflected light, this gain in light falls off the farther off-axis you get. The screen is essentially directing more light in one direction rather than diffusing it evenly. If you ever look at a screen catalogue, you may see a little graph that has angle (of view) on the x-axis and gain on the y-axis. You'll see a little bell-shaped curve centered on 0 degrees, this shows how the screen is directing light that is projected on it. It will reflect more along the 0 degree axis and progressively less as you get farther off axis.

Oh and curved screens do not increase gain, that is a surface property of the screen, gain does not depend on shape. What a curved screen will allow you to do is use a higher gain without hotspotting. What Peter/Cineramax may be refering to is to perceived gain of a curved screen, because more light reaches your eyes from the screen (the corners are not dim like they would be in a flat high-gain screen) it definitely appears brighter, but the center of a curved screen is just a bright as the center of a flat screen (the difference is that the corners of a curved high-gain screen are just as bright as the center and the corners of a flat screen are dimmer).

Hope that helps,

Kam Fung
Thank you Kam Fung.

I think you are mostly correct and problems with my questions are due to my using "gain" differently than others. My (mis)understanding was that gain was the ratio of light energy reaching the viewing area from a particular screen compared to a reference material of equal area.

Something like

Foot-Lamberts (Screen X) / Foot-Lamberts (Reference) = gain.

Where light from the entire screen surface is measured at the eyeballs area, and the angle of projection and viewing can be variable. I'm learning this is not what others are using and am now searching for THE precise definition of gain - if one exists.

So far, every definition I've seen is different. Even the 2 partial definitions you have provided are different- "Gain measures how much light is dispersed and how much if reflected" and "What the number of the gain represents is how much more light you would get if you were sitting in the reflected path of light from the gain screen over what you would get from a 1.0 gain screen"

If you choose to define gain only as some ratio of reflected vs dispersed light perpendicular to a surface material then you have by definition eliminated angles of incidence and reflection from the equation and the shape or size of the screen is indeed irrelevant. mirror gain = infinity

Screen gain as usually discussed here seems to be closer to your definitions than mine - a measure of the maximum relative brightness of a small central screen area viewed perpendicular and center to the screen surface. i.e. a 2.0 gain screen yields twice the brightness only if you are sitting dead center and staring at the exact center of the screen. When you look to the corners, the brightness is less and would approach 0 in the case of a mirror.

If you are assessing only a small central portion of the screen you are by definition also eliminating part or all of the effect of curvature. As the size of a curved surface decreases, it would behave more like a plane. Consider shrinking any curved surface down to the size of 4 points.

So, my previous ramblings here have been addressing an "average gain" of an entire surface and not "gain" per se. Somewhat akin to ANSI lumens vs lumens where measurements are taken from many areas then averaged instead of looking only at a brightest central portion. I didn't realize the importance of that distinction at the outset and for that I will eat crow.

This "average gain" though, seems to me to be a more useful measurement then just gain at the center. Obviously, we view the corners as well as the center of a screen. And, this would account for the apparent increase in brightness of a curved screen vs flat. For a given surface material and size, the central points would appear identical but the corners of the curved would be brighter -

(AVERAGE GAIN of concave curved screen always greater than flat) -

As the size of the screens increase to infinity, the corner brightness of the flat approaches zero while the corners of a perfect curve continue to reflect light back to the viewing area (average gain of curved screen increase with size and approaches infinity).

The practical benefit of all this speculation, IF it is correct, is this.

Increasing the size of a curved screen would require less increase in projector lumens than increasing the size of a flat screen by a similar percentage.

i.e. going from an 8' wide to 10' wide curved or flat screen involves an increase in screen area of around 50%. Approx 50% increased lumens would be required to maintain similar brightness with flat screens. The additional lumens required to maintain similar brightness with curved screens would be something less than 50%.

Therefore, whereas a crt nearing its upper limits might not swing a particular area increase with a flat screen, the same increase may be successful with a torus. This may account for the reported observations of high picture quality on curved screens that are much larger than what is possible with flat even though they may use identical surface materials.

Mike
Mike:

"Therefore, whereas a crt nearing its upper limits might not swing a particular area increase with a flat screen, the same increase may be successful with a torus. This may account for the reported observations of high picture quality on curved screens that are much larger than what is possible with flat even though they may use identical surface materials."

Absolutement correct! My 2 11' feet wide TORUS screens (which is a registered trademark of a patented technique for sucking a screen into Toroidal possition) installations are significantly brighter than many 8 to 9 feet wide installations. A TORUS screen is the only way to resolve 960p with a single 9" crtp on an 11 feet wide, at greater than 16 fl back in 1995 . Incidentally I personally requested from Faroudja to "Double the Doubling" because of the noticeable line structure first noticed during my first TORUS install, he did so in time for the second Torus install, but for the first year and a half, the doubler was sharper.

OFF topic mostly:
I had a handshake with Stallone to redo his 1272 with IFB doubler , he ok'd a budget of 65. By the time I offered both a doubler and a quadrupler for different source material, with the DNP 160" rear screen and an ILA, well, I tripled my budget.

He was very nice, 5'5", Jennifer was massaging his shoulders during the whole conversation with me. I explained that the ILA came with supercontrast option, I told him high contrast was important for some movies , "Like Cliffhanger" he smiled and nodded. I had the deal then.So I thought.

When I presented a propossal for three times 65K, I was not called back.

The entire collection of art work in his house consisted of paintings of him. as rocky, rambo,...... He had a DEAD (Taxidermised) Giraffe
23 feet high in the reception outside his living room.

Maybe is better I did not do his system as the ILA's would require a lot of Maintenance.
Mike,

My use of perpendicular was taken from your initial definition, it is a simplification. My second definition is probably more helpful and accurate. The use of reflected and dispersed light is only a metaphor and not a concrete definition. Actually what will happen is that gain will be the stated number at 0 degrees off the reflected path of light from the projector and the gain will fall off the father off axis you get. The brightest point will probably not be the exact center of the screen, instead it will be the point on the screen that your eyes are on-axis for.

You shouldn't use average gain, uniformity is more common. Most people (in the forum http://www.avsforum.com/ubb/smile.gif )will recognize what you mean when you say you have a "2.0 gain screen," in that you have a screen that is twice as bright as a 1.0 gain, but that this effect will likely fall off at the edges of the screen. Instead of using average gain to describe the effects of a toroidal screen, you should probably use uniformity. In the context of a 2.0 gain toroidal screen this would mean that it would have a "uniform 2.0 gain surface". This would mean that a full white field you appear to be the same brightness at all points on the screen (and hopefully from all the viewing positions) with no fall off. In essence, it is directing more of the on-axis (or close to on-axis) light onto the audience as opposed to the walls and ceiling.

It is probably more accurate to view a toroidal screen as giving a high-gain screen greater uniformity rather than a higher "average gain".

What you are saying about the practical uses of a curved screen are not exactly true. A 50% increase in screen area will still require a 50% increase in light output or gain to maintain brightness. The advantage of the curved screen is that it will have better uniformity if you increase gain. However, in the context of your "average gain" your assertions are correct.

Peter,

Don't you ever find it sad that the features that Faroudja charge such astronomical prices for are now reproduced at a fraction of the cost sometimes as little a year after introduction? The DVP-5000 will double 1080i, but I would argue that the current crop of video cards (at \$150-500) may be able to do that (and with the same field-adaptive de-interlacing) and less than a year after the DVP-5k was intro'd. There is still a lot of value in the high quality components and the slightly better scaling and de-interlacing algorithms that Faroudja uses, but not at the horrendously inflated prices they charge.

...or I could just be jealous because I can't afford one http://www.avsforum.com/ubb/biggrin.gif

Regards,

Kam Fung
I'm out.
Mike,

Regards,

Kam
KFung.

What I meant was

1. Comparisons of one screen to another here are using "gain" as the measure of relative brightness.

2. No two people are using gain in exactly the same way.

3. With respect to brightness and predicting screen size, no relevant equations are possible if the underlying terms are not defined first.

IMO, continuing discussion is pointless without first agreeing upon a complete and precise definition of gain. i.e. "What" it is and how it is to be measured. If you can post this, along with your source, it would be very helpful to me.

Thanks,
Mike
Mike,

Gain IS a relative measure of brightness! There are no hard definitions that I know of. The stuff that Sigma sent me does define gain, but only as a measure of relative brightness (almost exactly their words).

Regards,

Kam Fung
"There are no hard definitions that I know of."

I believe you may be correct. Allow me to exaggerate and rephrase -

"As far as we know, gain has not been precisely defined as being either an apple or an orange."

Under some circumstances (small flat screens) it doesn't matter much so long as we're all talking about small round fruit. But, under special circumstances (curved screens, or extreme sizes), a small difference in definition may lead to exact opposite conclusions. e.g. a mirror has infinite gain or 0 gain.

If we are going to use a single measure to compare the perceived brightness of one screen to another, why not choose a measure that IS well defined? Either agree upon a complete and precise definition of gain for this purpose or choose another term?

Mike
Mike,

It seems I haven't done a very good job of helping you! While there may be no rigorous scientific definition of gain (that I am aware of), it IS internally consistent. It is applicable to any size or shape of screen. You may be confused by how gain is often used to represent the light output of an entire screen surface. Gain as a measure of relative brightness applies to only a point on the screen at a time. The "gain" that manufacturers use is the peak gain that you experience when you are "on-axis" (along the path of directly reflected light) this peak gain slowly falls off the farther off axis you get. So for a single point on the screen you get the gain quoted to you by the manufacturer and this falls off the farther off-axis a point on the screen is.

Perhaps an image would be helpful: http://www.draperinc.com/projection/surfaces.html
The graphs here describe the gain characteristics of a screen, as you can see it peaks at 0 degrees and falls off the farther off-axis you get.

I will say again (but differently) a curved screen does not really give you "more gain" it makes all the points on the screen "on-axis" for the audience (or so close that you don't notice the difference in brightness). So, while it DOES reflect more light to your eyes than a regular flat gain screen it DOES NOT change the peak gain that you get when you are on-axis it simply makes more points on the screen on-axis (rather than the single point you get with a flat screen).

David Levinson's "Joys of a Low Gain Screen" http://www.avsforum.com/ubb/Forum9/HTML/000108.html thread has a very good explanation of gain.

Regards,

Kam Fung
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