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Screen simulations: flat, curved and torus (lots of pics)  

post #1 of 61
Thread Starter 
As a few of you may already know, a few months ago I decided to write a Matlab simulation program for screens. The reason for performing simulations is to better understand the optical characteristics for different screen materials, curvatures as well as viewing positions. The program uses the so called ray-tracing technique to calculate the reflected “brightness†produced by different parts of the screen. Vector algebra and matrix manipulations are extensively utilized for efficiency.

The algorithm sends out some 20 000 virtual rays from the projector position, all of which are traced to the viewer via the screen. The resulting illumination at the viewing position from each segment of the screen, including gain properties, is calculated to produce a resulting screen illumination matrix. Illumination [lux or lumen/m2] is the physical quantity that more or less directly corresponds to what is commonly known as brightness. For CRT projectors, the color shift can also be calculated through repeating the calculation for each tube position. The projector is assumed to be perfect in that the screen is perfectly evenly illuminated (generally not the case for CRT’s in practice).

The curvature used is circular and may be independent in the horizontal and vertical planes (true toroid). The theoretically optimal shape will almost never be exactly circular, but the deviations from this shape will be so small as to be generally negligible. For example, the optimal curvature in the vertical plane will be very close to elliptical as there are two focal points (PJ and viewer). However, the difference between large and small axis of the ellipse will be a few centimeters or a couple of inches and the resulting practical differences from a circular shape will not be perceivable. To be absolutely correct, the optimal shape will be even more complex than circular/elliptical. Circular curvature means large benefits when it comes to DIY manufacturing of the screens.

For making sense out of the calculated illumination matrix, the data is presented as images. Both the virtual projected image from a full white field and a movie frame can be used for the evaluation.

To provide some insight as to what a few screens may actually look like when projecting an image, I have run a few cases for a typical ceiling mount CRT setup. For a single lense PJ in the same position, the color shift will of course be zero but the brightness variations across the screen will be approximately the same. All of the pictures below have been generated with the following main parameters (1 m = 3.28 ft):

screen width = 2 m (equivalent projected width for curved screens)
screen AR = 16/9
screen - viewer distance = 3 m
lense c/c = 0.18 m (NEC XG135LC)

I have run calculations with published gain curves for four screen materials, 1.0 gain (ideal matte white), 1.3 gain (Stewart Studiotek), 2.0 gain (Stewart Ultramatte) and a generic 2.8 gain material. These materials were chosen because of the availability of usable gain curves and to represent four specific cases, matte white, low gain, mid gain and high gain.

1. All of the pictures have been scaled to the same peak brightness. This means that the brightness increase from high gain screens is not visible. Overall brightness will easily overshadow other differences otherwise. This is of course not completely fair to the high gain screen materials and the scaling can probably be discussed to death (same peak, same average etc etc). The conclusions will still be the same, though.

2. The screen used for viewing the pictures has to have a gamma reasonably close to 2.2 for a correct representation of the illumination. The laptop used for writing this definitely has not – be sure to use a CRT monitor and you should be alright (if you have not fiddled with your graphics card settings, that is).

3. The JPEG compression used introduces some visible “banding†or posterization in the white field plots.

4. Due to the non-linearities of the human visual system and non-ideal viewing conditions in practice, the simulated images will probably not look exactly the same as in practice. Still, they will be reasonbly close and provide valuable insights as to what the subjective response will be like.

First up are flat screens with the viewer horizontally centered:

Full white flat 1.3 gain


Full white flat 2.0 gain


Full white flat 2.8 gain


Note the increasingly bad hot-spot and color shift as gain increases.
post #2 of 61
Thread Starter 
Frame from Gladiator unprocessed


Frame from Gladiator flat 1.3 gain


Frame from Gladiator flat 2.0 gain


Frame from Gladiator flat 2.8 gain


From the pictures above, the following conclusions can be drawn: the 1.3 gain screen has negligible color shift and brightness variation in real-life situations. No wonder it is ISF approved. Still, a keen eye will notice some slight differences to the original (unprocessed) image. Mid and high gain screens will look pretty awful on white fields but probably decent enough in practical use, at least for some viewers. Note how the perception of the Gladiator scene changes a lot with increasing gain, the subjective focus is shifted towards the upper center and the light brown/red cast varies from deeply saturated (left) to pale (right).
post #3 of 61
Thread Starter 
The next logical step is a circular curve screen (r = 3 m) with the viewer horizontally centered (to further optimize this setup, the screen has been tilted backwards to point the screen axis vertically midway between viewer and projector):

Full white circular 2.8 gain


Frame from Gladiator circular 2.8 gain


Notice how the hotspot has widened to fill the screen in the horizontal direction – a lot better than flat but still far from perfect. The colorshift is gone. This screen is very easy to build so if you want a quick and nice DIY high gain screen, this is a no brainer - go ahead.

I am not going to compare the previous pictures with the same screen materials for a spherical screen and a horizontally centered viewing position. Why not? Because the images are virtually PERFECT! The brightness is even more constant than for the flat matte white screen. Also, a curved screen should not be used with a low gain material as internal screen cross reflections will completely destroy the image. Actually, a gain curve with a hump of some +-25 degrees width and complete cutoff otherwise would be the best option. This is why only the 2.0 and 2.8 gain materials are used in the torus screen simulations.
post #4 of 61
Thread Starter 
Now what is really interesting is what happens for a viewer placed off-center horizontally. To emphasize the effects, the viewing position is placed 1 m from center, i.e. level with the screen edge (18 degrees off-axis).

Full white spherical 2.8 gain red tube side


Full white spherical 2.8 gain blue tube side


The above pictures reveal severe but almost constant color shift. This is due to extreme viewer positioning and the “peaky†gain curve of the 2.8 gain material. With a wider gain curve “hump†and less extreme viewing position, the color shift will not be as pronounced.

The same viewing position for a flat screen will produce a hot-spot shifted to the side:

Full white flat 2.8 gain blue tube side

post #5 of 61
Thread Starter 
A movie frame comparison between flat and spherical, viewing position 1 m off-center:

Frame from Gladiator unprocessed


Frame from Gladiator spherical 2.8 gain blue tube side


Frame from Gladiator flat 2.8 gain blue tube side


Note the slight red shift for the spherical screen and the much worse hot-spot of the flat screen changing the visual focus completely.
post #6 of 61
Thread Starter 
Remember the slightly red tinted spherical screen full white for the off-center viewing position above? Well there is still hope - Enter the Toroid. A toroidial screen shape allows two radi, one horizontal and one vertical. It turns out in this case that the optimal radi (optimized for minimum brightness variation) for the 1 m off-center viewer is some 2.7 m horizontal and 3.2 m vertical (2.8 gain) and some 2.6 m horizontal and 3.3 m vertical (2.0 gain). The reason for the deeper curvature horizontally is that the distance to the vertical far screen edge is longer. Illumination is inversely proportional to distance squared and this is compensated by the higher angle. This of course means a slightly less perfect image from the centered viewing position, but the difference is negligible. If even less color variation is desired, use the 2.0 gain material instead. There is a lot more to real optimization than described above (for starters: what to optimize for?), but in general terms rather small deviations from a spherical shape may provide worthwhile benefits for off-center viewers. Also, note that neither the circular nor spherical screens have been fully optimized, the radius of curvature has been fixed to 3 m for these cases.

Optimized toroidial screen, viewing position 1 m off-center

Full white toroidial 2.8 gain blue tube side


Frame from Gladiator unprocessed


Frame from Gladiator toroidial 2.8 gain blue tube side


The red shift is still visible but the brightness variation is minimized.

And finally, this is what a toroid screen may look like, including coordinate system definitions useful for the table below.


In the table below I have defined two ratios, Brightness Ratio (BR) and Color Ratio (CR). BR is defined as maximum illumination R+G+B divided by minimum illumination R+G+B for all screen segments – unity is ideal. CR is defined as the max ratio of R to B or R to G or G to B (or inverted) for any individual screen segment – unity is ideal. The average viewer will probably readily accept a BR of 1.5-2.0, even if BR closer to unity will of course be better. The CR is more critical and should be kept below some 1.3 for subjectively good results and perhaps below 1.15 for perfect results. BR and CR are not necessarily optimized for the same radi. CR for off-center viewers is mainly a function of the lense distance of the PJ and the screen material. Still, it is almost constant for curved screens while it varies from blue-shift to red shift over the screen area for flat screens.

post #7 of 61

This is some great work!

Being a video novice, I have a bunch of questions, I'll start with a couple and post more later today. That's what I get for being "Audio boy!" (a long learning curve on video stuff).

1) In the first series of Gladiator shots of the desert scene to my eye, the 1.3 gain screen looks best, but the real question ,is which of the images is closest to what was shot (I'm assuming here that the "unprocessed" image is what was delivered on the DVD.

2) You changed from a desert scene to some face closeups midway through the series, which makes it hard to really compare the effects of the various screens. Without a shot of the unprocessed frame, it's also difficult to get a reference. Any chance of doing that to see that compared to the others?

Thanks for the obvious investment in time and computer cycles.

post #8 of 61
Thread Starter 

Thank you very much.

1. The unprocessed image is the reference or original image, straight off the DVD.

2. Note that you should not directly compare the off-center viewing position for the curved screen images with the centered viewing position for the flat screen images. This is one of the reasons I switched scenes. Also, the differences in the color shift for the curved screens is much easier to spot with lots of white and flesh tones, thus the close-up scene. There is an unprocessed image for this scene as well, at the top of the sequence. I think I will add another reference image directly above the toroidial image for easier comparisons, though.

Note that a centered viewing position and spherical or toroidial screen will be virtually impossible to separate from the original image, full white or movie scene, and this is why I omitted images for these cases.
post #9 of 61
This is a very impressive post. I can appreciate the time and effort you put into this research. Even if someone is not interested in a curved screen, your post demonstrates the effects of hot spotting on higher gain screen materials.

It's nice to see that your simulation demonstrates the advantages of the Torus screen. I am designing a Torus screen for my home theater. I was beginning to wonder if the effort was worth the supposedly improved image. I have never seen a live Torus screen. Your post helped me overcome my doubt.

post #10 of 61
This is very cool. (no pun intended)
I can see you spent some time on this.
Don Stewart
post #11 of 61
Amazing post. Thanks for your time and ingenuity. This is just the sort of thing we need!

post #12 of 61
Good information, but I wonder:

1)The only 2.8-gain screen I am aware of (Dalite Hi-Power) is retro-reflective. The nature of this reflectivity negates almost completely any hotspotting effect. Did you take this into account?

2)I dont believe you have been completely fair to high-gain screens, in the sense that your high-gain examples have a *darker* average picture level in your examples. Your 1.3 gain screen should be darker than the higher gain screens, not the other way around. I dont beleive any high-gain screen is <1.0 gain at extreme angles.

Andy K.
post #13 of 61
Thread Starter 

1. The 2.8 gain material I have labeled "generic" is not retro-reflective. Still, it would not be very much trouble to perform calculations for this type of reflective characteristics if necessary.

2. I get to quote myself, great ;):
1. All of the pictures have been scaled to the same peak brightness. This means that the brightness increase from high gain screens is not visible. Overall brightness will easily overshadow other differences otherwise. This is of course not completely fair to the high gain screen materials and the scaling can probably be discussed to death (same peak, same average etc etc). The conclusions will still be the same, though.
I feel that what is really important here is brightness uniformity. That a high gain screen has a very bright hot-spot is self-evident and is also clearly stated in the table at the very bottom of the post (peak relative illumination = 2.71, rel matte white).

3. Both the 2.8 gain and 2.0 gain materials have a gain of less than unity for off-axis angles larger than some 40 degrees.
post #14 of 61
Your 1.3 gain screen should be darker than the higher gain screens, not the other way around.
true, but if the images were adjusted to refelct the above, wouldn't that just make the "hot spot" even more evident/distracting?

post #15 of 61
I'm probably not correct here, but my understanding is that the brightness has been normalized so that differences in coloration won't be overshadowed by a difference in luma level.

post #16 of 61
Excellent work Iceman.

There is something wrong with the modeling of color shift though. In reality, with a crt/2.8 gain spherical screen, the shift is quite subtle, even from as far as 60 degrees off axis.

Are you assuming a perfectly smooth screen surface for your model? That might be the problem.

post #17 of 61
I'm probably not correct here, but my understanding is that the brightness has been normalized so that differences in coloration won't be overshadowed by a difference in luma level.
Actually, if you think about it...why would you use a higher-gain screen? to compensate for a lower-output projector. The result in the real-world would be to arrive at an image that has the same resultant overall "brightness" when averaging the brightness of the projector and the gain of the screen...regardless of which projector/screen combination your looking at.

So in that sense having all the images look the same overall brightness regardless of the gain of the screen makes sense. In real life all of these screens *would* be driven by a projector to compliment their gain to the same effect.

post #18 of 61
I'll stay away from the brightness issue - maybe you were right, it just confuses things :)

I think it would be quite instructive to plot a retro-reflective screen example as well, since the Da-Lite High Power is easily the most popular high gain screen.

I'm trying to track down the plot from thier website, but I do recall that for the High Power the gain never dropped below unity. I extrapolated that to assume that this was true of all gain screens, but perhaps I'm mistaken.

Nevertheless, thanks a bunch for the already presented info!

Andy K.
post #19 of 61
There are lots of varying gain materials out there from the major players (ie Stewart)...they just don't list them all for the HT web site. Its not a problem finding proper gain in "plain" reflective.
post #20 of 61
Thread Starter 

Regarding the scaling issue, one should not forget that the peak scaling was the most easily implemented alternative. You could certainly have objections to this. Nevertheless, I found the brighter images looking almost too good in ambient lighting on my crappy laptop LCD screen (as they should), so there were several reasons that made me choose to scale to peak illuminance. Average may be more appropriate and I will see what can be done here. This would perhaps even closer correspond to David's line of reasoning, which I have contemplated myself.


Interestingly for very extreme viewing angles, the color shift for the spherical screen almost completely disappears (CR = 1.05-1.10)! BR is quite high though, as it should be. Yes the screen surface is mathematically perfect, but I believe the point lense modelling might be the culprit when the viewing angle is more normal. I will try to model the lenses with a few finite elements instead. Damn, there go my quick calculation times :p. Another important factor may be that your gain curve is flatter than the quite peaky one I have used and does not reach 2.8 gain in practice. Last but not least, subjectively you will usually not have access to the direct A/B comparison provided by the images. Especially large fields of a whitish nuance tend to look white if there is no reference - I know my house looks white in the summertime, now it looks dirt yellow compared to the snow :D.

A general caution about simulated results should probably be issued. As is almost always the case with any simulation, the results tend to come out generally correct but perhaps too idealized. This is to be expected, though, as statistics will dictate that a certain "practical noise" will overlay the calculated results and blur the differences somewhat.
post #21 of 61
Thread Starter 
I have taken a quick look at the lense area issue and this will affect the results only slightly. Point modelling seems to be allright.

In the image below I have plotted CR and BR vs viewing angle for a viewing distance of 3 m for a spherical (r = 3 m) screen. The gain curves I have generated from hard-to-read data are not perfect so some small "hickups" may be present in the plots.


Note the serious hump in the CR for angles around 15-20 degrees! Very interesting indeed.
post #22 of 61

I think the main problem is your screen surface model. If the surface is "computer perfect" smooth, then you have essentially modeled a white mirror and not a movie screen. The fine texture of a real screen surface contributes significantly to the degree of hotspotting and color shift. A perfectly smooth model will exaggerate these. The error from using point sources for R,G,+B is small.

post #23 of 61
Thread Starter 

Should not the gain curve reflect the surface properties as well? I certainly think so. If I enter a gain curve for a "mirror" (now this is a peaky curve!) I also get mirror results.

Upon further thought, what we are seeing in the local maxima in the CR curve above is just the maximum rate of change for the gain curves. This is really elementary and very logical. Also, as the viewing angle gets more extreme, the gain curves usually flatten out and become almost constant. This will minimize color variations.

I inadvertently chose the region of maximum rate of change for the gain curves of my images. You should be able to locate the CR maximum for your screen in practice as well. Please report back as to your findings.
post #24 of 61

This is great!


The differences you see between your screen and the simulation probably have more to do with perception rather than a flaw in Iceman's work. In the abscence of any reference the eye (i.e. a dark theatre) the eye can be very tolerant of colour shift and hotspotting. I'll have to elaborate more later, sleep time. :)


Kam Fung
post #25 of 61
Thread Starter 
Firstly, on the issue of color shift vs viewing angle, I have generated a new image to demonstrate what happens if you just move slightly more off-center than the 1 m (18 degrees) used before.

The screen and setup is the same as before with the only difference being that the viewer is placed 1.5 m off-center (26.5 degrees).

Full white spherical 2.8 gain blue tube side


The color shift is now subjectively quite tolerable (CR = 1.26).

When discussing the very issue of the subjective response to (full area) color shift with a colleague of mine (optics and colorimetry expert - I am just a happy amateur myself), his repsonse was that without a clear reference the human visual system easily adapts to the conditions and "recalibrates". This may very well be a large part of an explanation to what Mike2 sees on his screen. The other possible reason may be a flatter gain curve in his case.
post #26 of 61

These are Redside, Center, and Blueside pics of my setup. (4 ft off center for red and blue pics).

13 ft radius, spherical, 3.1 gain, 9 ft wide screen, 12 ft viewing distance. Ceiling mounted Sony G70.

This is not the ideal shape for this setup. The corner performance would improve with a slightly deeper curve, and even more with a precise torus instead of spherical.


post #27 of 61
Thread Starter 

If you supply the projector to screen center distance and height as well as viewer height I can generate a couple of images for your setup. If you can produce a gain curve for your screen material, the simulation would be complete.

I can tell you right away that your setup (but with the 2.8 gain curve (which actually peaks at almost 2.9) and NEC XG135LC distances) produces a lot less color shift than for the one I used in the original post.
post #28 of 61
"I can tell you right away that your setup (but with the 2.8 gain curve (which actually peaks at almost 2.9) and NEC XG135LC distances) produces a lot less color shift than for the one I used in the original post."

What is it about my system that leads you to believe this? I estimated mine to be merely a scaled up version of your simulation (within a few percent).

Viewing Ht 39"
Screen center ht 60"
lens ht 82"
lens to screen center 12.5 ft
Vutec 3.1 - no gain curve I can find. 120 degree viewing angle acc to their website, if that helps.

Could you estimate the corner vs center brightness as well please? We could cross check hotspotting too.

post #29 of 61
Mike, I assume you've read the other torus thread active now...someone said you have a solid torus screen, is that correct? If so, what' it made of?

Are the measurements your viewing area size? I am interested in the ecact size, others in a foot or so bigger. Any help and insights you can give to our DIY project would be great.

post #30 of 61
Thread Starter 
What is it about my system that leads you to believe this? I estimated mine to be merely a scaled up version of your simulation (within a few percent).
Well, I ran a simulation with estimated data to fill in the gaps. There are a few important differences between the setups, the lens distance that is not scalable and the PJ-screen distance that is somewhat shorter for the NEC (especially when placed slightly closer to the screen than the manual suggests) perhaps being the most important ones.

Since the screen gain curve is paramount and I have no data for the Vutec 3.1, my results will surely differ (at least somewhat) from what you measure. There is often lots of hot air in screen specs and I always feel safer when a gain curve is readily available. The closest I could find with a published gain curve is the Stewart Silver 3D (3.2 gain), so this is what I used for the simulation. Finally, I have used a 16/9 AR.

Full white centered viewer: BR = 1.14, CR = 1.08
Full white off-center viewer 4': BR = 1.69, CR = 1.28

Full white 3.2 gain center


Full white 3.2 gain 4' off-center blue tube side


Also, note that the gain curve of the Stewart 3D material is somewhat better than for the generic 2.8 gain material.

And a final question: your screen depth of curvature is relatively high (some 11"), are you able to focus properly all the way to the edges?
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