As previously mentioned, I’m watching a little bit of Fringe in order to be able to talk sensibly about it later this week. I watch the Season 1 finale last night, and its treatment of parallel universes is about what I’d expect for tv, but being the obsessive dork I am, I got distracted from the big picture by a silly side issue.

There’s a running joke for the first bit of the episodes about Walter trying to find various pieces of scientific equipment, only to find that Peter has appropriated them for some sort of personal project. One of these items is an electron microscope (presumably an SEM, though the prop they dragged out later looked more like the TEM we used to have in the basement). Later, it’s revealed that the secret project is a device to digitize some of Walter’s old vinyl LP records, using the electron microscope to read the pattern in the grooves.

The device is used for a fairly ridiculous bit of magic CSI technobabble, but my immediate reaction was “Why would you need an electron microscope for that? That’s ridiculous overkill.”

But then again, part of being a physicist is always checking your immediate reactions, and this is an easy one to test quantitatively. So, would you really need an electron microscope to digitize an old LP?

The key question here is what resolution you would need to be able to faithfully reproduce the bumps in the record’s grooves, and work out the sound frequency. If the smallest bumps you would expect are small enough, then an electron microscope might be a reasonable choice for a readout device. So, how small are those bumps?

Well, the highest frequency of sound audible to humans is around 20 kHz. This is outside the bandwidth of a typical LP system (which is why, annoying audiophiles notwithstanding, CD’s are a better medium for music than LP’s), but good enough to put an upper limit on the resolution. So, if you imagined making a record that was just a steady 20kHz tone for the full playing time (it would not shock me to learn that some avant-garde composer tried this), the needle would be going over a peak every 0.00005 s.

How far does the record move in that time? Well, the rotation speed is 33-1/3 revolutions per minute, which we convert to the more scientific units of 3.5 radians per second. Multiply by 0.00005 seconds, and you find that the record turns through an angle of 0.000175 radians per oscillation of our 20kHz tone.

That doesn’t get us a size, yet, because the linear distance covered will depend on the radius at which we’re looking. A point on the outer edge of the record is moving considerably faster than a point in by the label. That means that the wave peaks will be spaced more widely at the outer edge than in toward the center. Since we’re looking for the smallest possible feature size that you might want to resolve, we want the inner edge, which has a radius of at least 5cm. Multiplying 0.000175 radians by 0.05m gives us a feature size of 0.00000875 m, or 8.75 microns.

Now, this is pretty small– roughly a tenth the thickness of a human hair– and people do use electron microscopes to take pictures of things at this scale. But this is also well within the resolution of an optical microscope, and remember, this is the absolute smallest feature you could possibly imagine needing to detect on a record. The vast majority of the sounds we care about would involve much, much larger features.

So, a little bit of math basically confirms my initial reaction: you could use an electron microscope to do it, but it would be massive overkill. It’d be much easier, and much cheaper, to use a laser or something to scan the grooves with conventional optics.

(This is the point where you remind me that I’m complaining about technical details of an episode whose premise involved people with drug-induced psychic powers blowing themselves up. To say nothing of creepy assassins trying to move between parallel universes. Which is true, as far as it goes, but this is how my brain works, and I can’t help it.)

Comments

  1. #1 Oded
    August 1, 2011

    What you found is the minimal distance between a groove and a peak for an interesting audio signal on the track (actually, the distance you found is twice this of course). CD’s store 44,000 numbers for each second, so this would give your 4 microns number for resolution of this scale.

    Don’t you also need to know the height difference between the groove and the peak? The range of each of those 44,000 numbers in a CD is 0 to 65,536. How much of this is really necessary for good audio quality is debatable, but this is at least an upper limit for what you would need to perfectly record your vinyl to a digital CD.

    I don’t know how high the peaks are for vinyl. Even if they are 1cm (they are obviously way smaller than this), then you need resolution of 1cm/65536 = 150nm, which you would need electron microscopes to see…

  2. #2 Zack
    August 1, 2011

    If you search for “laser turntable”, it sounds like there are a small number of commercial products that read vinyl recordings with a diode laser and an optical microscope. It apparently works well enough for the Library of Congress to be using it to digitize its collection of old monaural phonographs: http://irene.lbl.gov/ In that context, ideal sound quality may be less of a concern than avoiding damage to the originals, though. I can’t figure out how good the sound quality actually is, because there’s all kinds of audiophile woo confusing the issue. I get the distinct impression that retrieving both tracks of a stereo recording is still experimental.

  3. #3 non-annoying audiophile
    August 1, 2011

    Biggest problem with optical reading of phono records is that dirt that a stylus would ignore or almost ignore (simply brushing it aside, because its mass is very low) is read by light as if it were a feature of the music. One thing SEMs ARE good for is showing how much dirt adheres to groove walls even after very careful cleaning.

  4. #4 Walt Garage
    August 1, 2011

    Funny and sad but true story from the early days of CDs. Local radio station has just started playing tracks from CD (in between prank phone calls and other important stuff). DJ says let’s test this out – I’ll play a track from vinyl and the same track from CD, you call in and tell me which is which based on the sound quality! (At the time, I was driving a Renault Alliance with crappy little speakers, so I thought that this probably was not a great way to test the fidelity of either recording system!)

    So, he takes 10 calls and five of them say that the first recording was CD and five of them say the SECOND recording was the CD and the DJ says “There you have it folks, proof that the CD sounds better”.

    Sadly, that DJ was replaced by Howard Stern and so I have to look back at him fondly as a time when they actually played SOME music on the radio……

  5. #5 Walt Garage
    August 1, 2011

    I have a CD recording device on my stereo and I can record directly from vinyl to CD. You’d think someone could have mentioned that to Peter.

    FWIW, I thought the most recent season of Fringe was better than the first.

  6. #6 Juice
    August 1, 2011

    I’d like to point out that you’d never fit an LP (or any typical size vinyl record) into a TEM.

  7. #7 BrokenDrum
    August 1, 2011

    Surely this misses the point in a multitude of other ways. I mean to say, all the information that an LP actually outputs as sound *has to go through the cable to the speakers*. Why would a sensible person not just attach a high-quality recording device to that cable, and be done with it?

  8. #8 Dunc
    August 2, 2011

    He’s going to have fantastic fun trying to figure out how to apply the correct RIAA de-emphasis curve to the resulting data…

    And Oded is right – amplitude is as important to music as frequency. This is where a well-engineered vinyl record can outshine CD, as it doesn’t have a hard limit – the (practical) maximum amplitude an LP can record is more a function of the skill of the cutting engineer than the limits of the technology. (Notice that the notorious “brick wall” compression is entirely a “feature” of the CD age…) Of course, you need a pre-amp with sufficient headroom, but given the nature of the RIAA equalisation curve, you really need that anyway.

    [Fun fact: most of the noise you hear in a cheap vinyl playback system is actually the result of the intermodulation of ultrasonic overload products in the pre-amp. The vast majority of surface noise on a vinyl record should all be well beyond human hearing (assuming a theoretically perfect playback system), but it can be very high amplitude (compared to the actual signal) and a poor implementation of the RIAA de-emphasis curve only makes the problem worse.]

    There’s also the question of whether you need enough additional data to be able to tell a sine wave from a square wave… Square waves are great for fucking up amplifiers – unless the amp is perfectly damped (they never are), a square wave can easily result in some HF oscillation on the leading edge, again resulting in HF overload and audible intermodulation products. So, while I doubt you can hear the difference between a square wave and a sine wave at 20kHz as reproduced by a theoretically perfect amplifier, there’s a good chance that you might be able to hear the difference when they’re reproduced by a real amplifier.

    Finally: why the hell would you want to digitise your LPs anyway? Talk about sucking all the fun out of it!

  9. #9 Rick Pikul
    August 2, 2011

    While you may not need an electron microscope to digitize an LP, we may also have to consider something all too common with technical types: The “because we can” effect, where you do something in a difficult or unusual way simply to prove it possible or as an exercise in problem solving.

    It reminds me of a thread that occurred once on the Scary Devil Monastery where all sorts of, (often bizarre and complicated), ways to measure the contents of a remote coffee pot were proposed. This led someone to ask, “why not just point a webcam at it?” and several people responding to the effect of, “you’re missing the point.”

  10. #10 Dunc
    August 3, 2011

    Rick – the really funny thing is, the first webcam was invented for exactly that purpose.

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