The digital and analog realms typically contribute very little in the way of frequency response distortion. Virtually all of it is found in the acoustic realm, as even the best loudspeakers and headphones struggle to keep their frequency response within a few dB of the intended target [ref] Many examples can be found in the SoundStage database (loudspeakers) and the InnerFidelity database (headphones). [end ref] . It gets worse: the acoustics of home listening rooms (room modes especially) can result in low frequency alterations in the order of 10 dB or more! [ref] Literally any frequency response measurement made in a small room will show this phenomenon. One example can be found in Leduc Michel, 2009, “How Does Listening Room Acoustics Affect Sound Quality?“, Audioholics (graph under “Standing waves” section). A series of representative examples can be found in Toole, Floyd E., Sound Reproduction: Loudspeakers and Rooms, figure 13.9. [end ref] No wonder why these are often said to be the “weakest links” of the audio chain…

Linear distortionamplifier

Ideally, audio components should meet the definition of a linear system as described above; that is, they should be able to accurately track the input signal, such that the output is precisely proportional to the input. Of course that is not the case in practice. Besides noise (which we’ve already covered), consider, for example, that the driver inside a loudspeaker is made from imperfect materials that have imperfect physical properties, so its movement will not perfectly track the signal, instead giving rise to non-linear distortion. One example in the analog realm is crossover distortion that can occur in certain types of amplifiers.

I did not buy the Zeus Pro 2 directly from Zeus Lasers, so I have no acquaintance with their company other than their product.

The power is there. Easily ignites material from 20 feet. The beam/dot was a bit thicker than I was expecting, but impressive to see in the day and just absurd at night. USE THE EYE PROTECTION. Or you'll have blue/purple spots in your vision for a half hour... or worse.

In order to build a high quality audio system, it is necessary to keep signal degradation (i.e. unwanted alteration) under control, and this requires a good understanding of what these alterations might be, what causes them, and how to avoid or alleviate them. Ever since the advent of sound reproduction more than a century ago this topic has been the subject of great debate, some thoughtful and innovative, some misguided or downright counter-productive. Hopefully this blog will do more of the former and less of the latter — but for now, this post serves as a brief introduction to the issues at hand.

Types ofdistortionin communication

The frequency response of a system that amplifies frequencies around 1 kHz by about 6 dB. This particular type of distortion is called a resonance.

In a real-world scenario, noise is only really noticeable when the original signal is relatively quiet, such as when there is a break in a piece of music, because all that remains is the noise itself. Conversely, noise is inaudible when a significantly loud signal is playing, again because of masking (but this time in reverse). In practice, I tend to abide by the following rule of thumb: if you can’t hear anything when playing a silent signal, then your system is probably fine as far as noise is concerned.

Signal alterations can be divided into three broad categories: noise, frequency response distortion, and non-linear distortion. [note] When used by itself without qualification, the term “distortion” can refer to some or all of these categories, depending on context. [end note] Real-world systems exhibit all three kinds in varying amounts. What follows is a brief overview of the issues at hand; future posts will look at each of them more closely.

Linear distortionformula

I have had my green zeus laser for a couple years now and it is still amazing. I have it setup with the 5x beam expander and it is so dam good. Wish i wouldve waited and gotten the more powerful 2watt one they have now or whatever but this one is still amazing. i made sure i didnt leave it on for over 30 seconds at a time and it seems to be the same brightness still :) 10/10 Worth it.

Waveform and spectrum of a 1 kHz sine wave showing symptoms of “hard clipping”, which produces odd-order harmonics (circled in red). The THD in this example is about 7%. [note] Here’s how this number is calculated. First, take the RMS amplitude of the harmonics: 3 kHz -26 dB (0.051) 5 kHz -32 dB (0.025) 7 kHz -46 dB (0.0047) 9kHz -47 dB (0.0043)… the total RMS amplitude of the harmonics is 0.057. The RMS amplitude of the fundamental is 0.78. The THD is the ratio of these two numbers, which is 0.073, or 7.3%. [end note]

So how audible is non-linear distortion? Well, that depends. Because non-linear distortion can take many forms, there is no simple answer. For example, distortion in the lower frequencies is less audible than in higher frequencies, and it is less audible if the newly introduced frequencies are close to the fundamental (thanks, once again, to masking). [ref] Temme, Steve, “Application Note: Audio Distortion Measurements“, Brüel & Kjær, 1992. [end ref] Condensing non-linear distortion measurements into a single, simplistic THD number, as is often done, certainly doesn’t help. With that in mind, real-world examples tend to suggest that a THD of 10% is likely to be audible, 1% is borderline, and 0.1% is unlikely to be audible. [ref] Audioholics, ”Human Hearing - Distortion Audibility Part 3”, 2005. [end ref]

I've collected somewhat of an arsenal of Zeus Lasers& accessories including the pro and the X. But every so often I check the website just to see if anything new has come out, and when I saw this I wrestled with it for a while, thinking 'what can 15 watts do that 7 can't? Then it hit me: a whole bunch of ideas starting off with... Igniting things from 20 feet away. So maybe I talked myself into it, but after it arrived only 4 days later and I was able to fulfill all my curiosity with wonder, I felt lucky that I had found out about these when I did.

I'm pleased with the product. It's well-made. Customer service is very helpful. Overall, a great experience and I highly recommend both the product and this company.

My biggest worry here is that the spring connecting the batteries to the laser unit extends outside of the housing. This means that unless you are careful, the spring can catch the foam in the case and bend it... which will eventually break it off. This laser is almost the length of my forearm when assembled. Another 1/4 inch to cover that vital part would be fine. Or if not possible, a smaller connecting spring.

How is this useful? Well, remember that the frequency domain is often more useful than the time domain when it comes to understanding how audio signals are perceived. Frequency response tells us how a system alters the frequency components of the signal that flows through it. That makes it one the most powerful tools in the audio engineer’s toolbox.

Studies show that frequency response is extremely important when it comes to assessing audio quality in real-world scenarios. For example it has been shown that the human auditory system is capable of detecting frequency response variations as tiny as 0.1 dB [ref] Toole, F. and Olive. S., “The Modification of Timbre by Resonances: Perception and Measurement”, J. Audio Eng. Soc., 36(3), 122–141, (1988). From Fig. 9: coherent sum of 0 dB and -40 dB sources is ~0.1 dB. [end ref] , and that it is by far the most important criterion when it comes to assessing the quality of a loudspeaker [ref] Olive, Sean, “A Multiple Regression Model For Predicting Loudspeaker Preference Using Objective Measurements: Part 1 — Listening Test Results”, presented at the 116th AES Convention, Berlin, Germany, preprint 6113, (May 2004). [end ref] . Make no mistake: this metric is a huge deal, and I expect most posts on this blog will make use of it in one way or another.

Already own a couple of the 7 watt zeus x lasers , and these are like a lightsabre ! love them. So when I saw that there was a 15 watt on sale , I had to look twice ! ,then look twice again... Tried to convince myself that I did not really need this , failed miserably ,lol. This laser is an absolute beast , burns anything instantly , and great for long distance engraving ! So glad I failed to convince myself. LOVE THIS ! LASER HEAVEN ! Thank you zeus , great to do business with you again , so good I bought 2 ! ... now looking at the green 2 watt...LOL

Fokussiert nicht richtig zum Punkt. Ist wohl eher ein kleiner Strich wie schonmal von jemanden erwähnt. Trotzdem sehr stark und man kann so einiges damit an Spaß haben. Vorallem bei Nacht.

Phasedistortion

Linear distortioncalculator

If this relationship is constant, i.e. the same amplitude multiplier is always applied to a given frequency regardless of the shape of the signal, then we are dealing with a linear time-invariant system. We can plot the frequency response on a graph, known as a frequency response graph (or, more technically, a Bode plot). [note] One thing that I’ve omitted to keep things simple is that a linear time-invariant system is not just allowed to change the amplitude of individual frequency components, it can also change their phase. This is conveyed through the phase response. Technically the term “frequency response” encompasses both magnitude response and phase response, though the latter is often dismissed for lack of relevance in most audio discussions. More on the phase response in the next post. [end note]

I was hesitant to purchase something less than practical for so much money, but I enjoy it every time I use it! This thing feels exactly what you expect a lightsaber to be! And turn that thing on, and anything within 10 feet away from you is in danger of being charred! (Focused just right, I got it to light a firecracker almost 12 feet away!) I don't use it all the time, so I only need to recharge it every few months. For improvement, I would like to see a better charger. Mine always has th red light on, and never turns green, even after sitting for 16 hours. I have to time my charges so I don't ruin anything. The laser has nothing to be complained about! I can even burn things underwater!!!! Remember that for lasers this powerful to NEVER have it on for more than 30 seconds. You don't want the focusing and emitting crystals to start deteriorating on you! Thanks Zeus Lasers!

At the beginning of this section I described examples of non-linear distortion that can occur during normal system operation. However, the most egregious, obvious, and audible non-linear distortion issues occur when the system is driven beyond its limits; that is, signal amplitude is pushed too far and the system is unable to keep up. When this happens the peaks of the waveform cannot be reproduced faithfully and the system “bottoms out”, a phenomenon known as clipping. To mention a few examples, this can happen in the digital realm (which is otherwise immune from most other forms of non-linear distortion) due to overflowing the largest possible sample value; in the analog realm due to exceeding the power limits of an amplifier; or in the acoustic realm due to exceeding the movement limits of a driver (excursion).

Noise can appear in all three of the audio realms. In the digital realm it can take the form of dithering noise for example, though modern digital systems provide good enough performance that noise sits comfortably below the threshold of audibility. This is not always the case in the analog realm, where noise problems are the most common, the most objectionable, and the most pernicious — often the result of complex electromagnetic interference phenomena, subtle hardware defects, or compatibility issues. Finally, the acoustic realm is rife with often overlooked sources of noise from ordinary life, from the rumbling of an air conditioning unit to the occasional car driving down the street.

Nonlinear distortion

One important aspect of non-linear distortion is that, contrary to frequency response distortion, it can cause new frequencies to appear that weren’t present in the original signal. By far the most well-known type of non-linear distortion is harmonic distortion, where new frequencies appear that are whole multiples (harmonics) of the frequencies in the original signal. It is often summarized in a single number, total harmonic distortion (THD), which indicates the total amplitude of the introduced harmonics relative to the original signal (more precisely, the fundamental). A related phenomenon is intermodulation distortion, where multiple frequency components in the signal interact with each other to create new frequencies in a specific pattern.

In the first post on this site, I explained that an audio signal can be decomposed into a number of constituent signals of various frequencies. One way an audio component can alter the signal is by changing the amplitude (i.e. applying gain) on some of these frequencies more than others. This relationship between frequency and gain is known as the frequency response.

Linear distortionexamples

A note on shipping - I ordered this on a Friday night... so it didn't really get moving until Monday. It took less than 3 days after that. 5 days total, but once it shipped, it moved at crazy fast speed.

As the audio signal makes its way through the different realms of the system, it travels through various digital, analog, and acoustic components that alter the signal in various ways. Some of these alterations might or might not be audible, or might only be audible under certain conditions. In most scenarios relevant to this blog they are undesirable side effects from limitations in the components that make up the system, though in some specific cases they can be deliberately introduced in pursuit of a specific goal (e.g. equalization).

This definition makes non-linear distortion a very open-ended category, as indeed a signal can be distorted in an infinite variety of ways. Since it is not possible to run an infinite number of tests, measuring and quantifying the non-linear behavior of a system can be quite challenging. That said, most non-linear distortion comes in well-known shapes and forms, so a few standard measurements are usually good enough to characterize the performance of an audio system.

Linearand nonlinear distortion

Depending on amplitude and frequency content, noise might or might not constitute a problem in practice. For example, low-level broadband colored noise (such as white noise) will often go unnoticed because its spectrum is roughly similar to typical ambient noise that we are all continuously subjected to in our daily lives. [ref] See Albert Donald G., Decato Stephen N., “Acoustic and seismic ambient noise measurements in urban and rural areas”, Applied Acoustics, 119, 135–143, (2017) for examples of ambient noise spectra. [end ref] The same cannot be said of narrowband noise concentrated in specific frequencies. [note] Unfortunately that distinction is lost when noise measurements are condensed into a single number (such as signal-to-noise ratio), discarding spectral distribution in the process. [end note] Furthermore, narrowband noise is more likely to affect the perception of minute detail in the original signal, due to an auditory phenomenon known as masking.

I purchased two (2) Zeus X 7 Watts Blue Laser over a year ago from this website (Zeus Lasers) giving them 5 Star Ratings for their products overall excellent performance and durability. Now, I purchased and tested the Zeus XTR 15 Watts Blue Laser and its truly having two (2) times the power in all aspect of the device listed speicifications. Beware some other Laser websites listing the same 15 watts blue laser and showing the same products images with price ranging from $400 to $699, but maybe just an imitation or copied device or unverified.

Waveform and spectrum of a sine wave affected by white noise. The noise spectrum, circled in red, is often called the “noise floor”. [note] From that spectrum plot you might be tempted to conclude that the signal-to-noise ratio is about 50 dB. That would be wrong — it’s actually much worse, around 17 dB. You can’t read it directly from the graph because the noise is spread across multiple frequencies. This is a very common mistake when reading spectrum plots, which I might describe in more detail in a future post. [end note]

Fortunately, any reasonable audio system will be at least approximately linear, so we can still use the frequency response to reason about the system. At the same time, we need to keep ourselves honest and account for any remaining non-linear behavior that might alter the signal in ways that frequency response and noise measurements will not predict. This is appropriately called non-linear distortion, also known as amplitude distortion.

The case this came with is... fine. It needs to be a bit bigger, and with the expectation that buyers might want to put a little more in it than it came with. The charger is hard to get back in and there is no space for extra batteries if you do. Still, cool to have a case included.

Noise describes an alteration of the signal in which a separate, unrelated signal is added (i.e. mixed in, superposed) to the original signal. [note] This is the definition I’ll use throughout this blog, pursuant to IEC 60268–2. In other contexts noise might be used in a more specific way (e.g. broadband noise only), or in a more general way (e.g. signal differences introduced by non-linear distortion are considered to be part of the noise signal). [end note] That additional signal has its own characteristics including amplitude and frequency content (spectrum), which are combined with the characteristics of the original signal. Noise is often quantified by comparing the amplitude of the noise to the amplitude of the signal, a metric known as the signal-to-noise ratio (the higher the better).

So, since purchasing the 7watt Zeus x, I have been having a lot of fun. Everywhere in my apartment there are burn marks ! Different objects create dazzling effects. Anything glass is especially fun. Outside, once you attach the expander and get the focus just right, you can ignite stuff over 100feet away. The batteries must be fresh and the laser must be perfectly still at those distances. Also got the rgb laser. One thing I especially like is when in white mode, the star caps separate the three colors to really cool effect! So, I just ordered the new dual diode 15 watt blue laser. I’ll let you know how it goes ! Thanks Zeus, I’m having a lot of fun. Though my wife hates these things !!