Some companies feel that if they digitize at 30,000 points per second (30K) or even faster, they get better quality. This belief is false. There may be other reasons they get good quality, but it is not due to the scan speeds.
In fact, the scanners themselves do not see any speed faster than about 12,000 points per second. Thus, at 30,000 points per second, 60% of all points are wasted -- completely unnecessary!
Said another way, you can take a frame digitized at any speed -- 30K, 40K, whatever -- and resample it down to a 12K frame. When laser-projected, this resampled frame will look exactly, precisely 100.00% the same as the original faster frame.
This may be a bit hard to believe, but just go through the reasoning below. At the end, you should understand why LD does not have to go at top speed in order for you to still have excellent graphics.
Standard laser light shows use galvanometer-type scanners. The fastest currently available are Cambridge Technology 6800 scanners with 6588 amps, and General Scanning G-120 scanners with Turbo Track amps.
How fast can these scanners move? To find out, take a sine wave (the easiest wave for scanners to produce) and gradually increase its frequency. At low frequencies, the scanner mirror can move full angle -- 80 degrees for the CT 6800; 60 degrees for the GS G-120's. You will find that at around 1,000 cycles per second (1 KHz), the scan angle begins to shrink. The scanner is moving too fast to go all the way back and forth. As the frequency continues to increase, the scan angle gets smaller and smaller. By 5 KHz, the scanner is not moving at all.
Thus, the limit of today's laser show scanners is about 5,000 cycles per second.
How many points per second is this? A basic tenet of digital signal processing, the Nyquist Theorem, states that if you want to reproduce a signal, you have sample it twice as fast as the highest frequency that you want to keep in the signal.
For example, humans can hear sounds up to about 20,000 cycles per second (20 KHz). Thus, to digitally record audio signals for human ears, the sample rate needs to be twice the cycle rate, or 40,000 samples per second. (To make it a little easier for the playback process, the actual rate used for standard CD-audio discs is set slightly higher, at 44,100 samples per second.)
It is important to keep in mind the difference between the original analog waveform and the resulting digitally sampled equivalent. The analog waveform is measured in Hertz, or cycles per second. The digitally sampled waveform is measured in samples or points per second.
For laser graphics, the Nyquist Theorem states that if we want to reproduce laser signals of 5,000 cycles per second (5 KHz), the fastest we need to go is 10,000 samples per second (10K points per second).
To give ourselves a bit of headroom, let's bump this up to 12,000 points per second (12K). The exact number does not matter. The main principle is that the computer only needs to send points to the scanner amps at a rate of about 12,000 every second in order to reproduce any image that can be shown on laser scanners.*
It does not matter if the original image is from an analog signal generator (older-style planetarium show lissajous generators), from the world's best laser computer (LD, naturally), from music being input into the scanners, or any other signal source. The scanner and amp system cannot go faster than 5,000 cycles per second. Thus, an equivalent waveform can be exactly reproduced using just 10,000 points per second.
Here is another way to consider the situation. A few companies are tuning to, and digitzing at, 40,000 points per second. Think about this for a moment -- this is nearly the same rate at which CD-quality audio is digitized (44,100 samples per second). Are these companies actually claiming that scanners are small, accurate speakers? There are two ways to disprove this.
| Put test signals such as sine waves into scanners. Increase the frequency until the scanner mirror no longer moves. As discussed above, the scanner cannot reproduce any signal above 5,000 Hz -- while audio extends to about 20,000 Hz. |
| Listen to a compact disc being played through scanners. While you do hear music, you hear none of the high frequencies. It is like listening to a cheap transistor radio, or to a stereo with the "Treble" control turned all the way down. This again confirms that scanners cannot reproduce 40,000 samples (points) per second. |
So if points are being wasted, where do they go? It is not as simple as one out of every two or three points being ignored. If this was so, then a resampling algorithm would be trivial -- just remove every second or third point.
Instead, all points are blended together into one waveform. Each point contributes something to the waveform. This is why moving a single point can change the projected image.
This combined waveform contains frequency components above the 5 KHz limit of the scanners. For example, a frame digitized and shown at 40,000 points per second may have measurable energy in the 20 KHz region. But remember that scanners do not see this!
What we are throwing away when we resample is the energy in the region between 5 KHz and 20 KHz. If we were recording music, this would be lost information, since we can hear in this region. But from a laser scanning standpoint, this information is completely wasted since scanners cannot move more than 5,000 times per second (5 KHz).
This is how a resampling algorithm can work. It converts the original digital waveform into its frequency components, throws out all information above 5 KHz, then makes a new waveform containing only the samples necessary to reproduce frequencies below 5 KHz.
The result is a laser frame with 60% fewer points. On the computer screen, the new points have been moved slightly compared to the old points, but the laser-projected frame does not look different in any way.
So why does Lasershow Designer output points faster than 12,000 per second? There are two main reasons.
A human digitizer cannot know exactly where to place points to get perfect results. The human must therefore oversample, or put down more points than are strictly necessary. Once the human is finished, then the computer can resample the frame to have far fewer points.
Pangolin has not yet written a resampling algorithm of sufficient quality. To do 100% accurate resampling takes some time to code. (The algorithms themselves are well-known, as they are the subject of intense study in digital signal processing circles.) Until this time, it is better to have laser companies continue working as they have for the last decade or two.
For these reasons, you should set your default scan speed at a reasonable rate, such as 2/3 of the speed at which your scanners are tuned.
Although you may create and digitize faster than the 12,000 points per second "speed limit", It is still important for you to be aware of this limit:
You should not waste time trying to "beat the system" by tuning faster than the ILDA speeds, or by digitizing at high speeds. Certainly anything beyond 30K is unnecessary. Any alleged benefits from higher-than-normal speeds are really due to the digitizer's skills and experience.
Some laser graphics systems may claim higher speeds because it sounds better in advertising. (One company says they output 300,000 points per second. If the scanners could move at 150 KHz, you could use them for ultrasonic cleaning!) Just based on point output rate, anything over 12,000 points per second is unnecessary.
Pangolin only guarantees Showtime shows up to 30,000 points per second. If Showtime must output points faster, then certain calculations cannot keep up and small "hiccups" may occur in the show. Therefore, keep the point output rate at or below 30K.
This topic seems to be particularly hard for people to understand. If you have any questions about this, please feel free to call or write Pangolin. We would be happy to help discuss it in more depth, so you can see why faster is not always better.
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* Note: The above analysis only addresses X-Y scanners. With a PCAOM, colors can change much faster than 5,000 times per second. If color data is changing faster than point data, higher sample rates would be necessary to accurately retain the color information. But in practical terms, this will not affect any LD frames, because LD cannot change color faster than once per point.