Understanding Beam Profiling Dynamic Range
Understanding Beam Profiling Dynamic Range By Ephraim Shafner, Ophir Photonics
It all started when a slow-witted engineer was teased one too many times. Tired of being the butt of all his colleagues’ jokes, he plotted revenge. “I will create such a convoluted unit for dynamic range that none of them will be able to understand it. We’ll see who’s laughing then. Mwahaha! Instead of simply stating that the range is 20:1 or 3000:1, let’s take the log of that ratio and multiply by 10. Or 20. No one will ever get it straight! I shall call it – the decibel.” (Actually, the decibel was invented in Bell Labs in the 1920s. Although it is convoluted, it’s also a very useful method of measuring wide ranges or ratios.)
Figure 1: Laser beam profiling setup
What Is Dynamic Range Anyway? Most laser beam profiling systems include dynamic range in their specifications. What exactly does this mean? The complete answer might depend on which type of dynamic range is being referred to, as you’ll see below. Suffice it to say that dynamic range is meant to characterize the ratio between the highest and lowest measurable signals (i.e. the signal range).
As seen in the 6/26/13 edition of the Photonics Online (www.photonicsonline.com) newsletter.
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Do You Use Decibels or Decibels? Huh? That’s right – there are two types of decibels, sometimes distinguished by a subscripted “power” or “volts,” but all too often left naked of any description. I know. I also think there should be a $3 fine for each ambiguous use of the term. For now, though, let me explain the background. There are two formulas for dynamic range: 1) dBpower = 10 log (Phigh / Plow) 2) dBvolts = 20 log (Vhigh / Vlow) The reason for these two forms is so both a power and a voltage ratio output a dynamic range for power. If you remember a little basic physics, power is proportional to voltage squared. Now if you also recall some algebra, a square within a log is the same as twice the log. In other words (or symbols): x log (y2) = 2x log (y) For this reason, 1 dBpower = 2 dBvolts. The logical approach is to use dBpower for a power ratio and dBvolts for voltage. In some cases, though, it isn’t so clear which to use. In the camera industry, for example, the general consensus is to use dBvolts. For optical measurement, however, dBpower is often preferred, as it’s more directly related to the light being measured. When cameras are used for optical measurement, as with beam profiling, all bets are off. So, which should be used: dBpower or dBvolts? A common answer might be: When in doubt, pick the higher value, since it looks better. At a more upstanding institution, though, the answer is that it depends on what is trying to be conveyed. What kind of signal are we dealing with? What value will be more helpful to the consumer? These are the questions we ask ourselves when trying to determine which form of dB to use. Of course, it’s best to state outright which units are being used in any case where it’s not obvious. Fun fact: most of our Spiricon CCD cameras use dBvolts, while the NanoScan family uses dBpower.
As seen in the 6/5/13 edition of the Photonics Online (www.photonicsonline.com) newsletter.
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Figure 2: Ophir Spiricon SP620 CCD camera (left) and NanoScan beam profiler (right)
The Wrong Way to State Dynamic Range – And How to Spot It What’s the most important rule when trying to determine spec statements? What’s the fundamental law that applies not only to dynamic range, but to all specs? The only spec worth stating is one that is helpful to the customer. Not the really impressive spec that only applies in 3% of situations? No, not that spec. That would be like a bridge that has a sign: “Weight limit – 15 tons.” But in fine print it says, “Only on clear days with no wind, between the hours of 10 a.m. and 11 a.m.”
How Does This Apply to Dynamic Range? All camera beam profilers have several components, each with its own dynamic range. There’s the detector itself, there’s the analog-digital convertor, and then there’s the incorporation of noise into the equation. For example, the Spiricon SP620 has a dynamic range of 62dBvolt even though its digitizer is clearly stated as 12-bit, which is a dynamic range of approximately 72dBvolt. So what happened to the other 10dB?
As seen in the 6/5/13 edition of the Photonics Online (www.photonicsonline.com) newsletter.
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Figure 3: Spiricon SP620 camera
When Ophir Spiricon determines dynamic range, it takes a very careful measurement of the RMS noise first and then checks the range between the highest signal and that noise. Figure 4, below, is an excerpt from such a calculation of the SP620 camera noise. The y-axis represents the number of readings (population) of a given value (bin) and the x-axis is the value itself. X is the mean, and σ is the RMS noise. To get the dynamic range value, one must divide 2^12 (12 bit A/D) by σ.
Figure 4: SP620 camera noise calculation
When Ophir Spiricon uses this method, it means a bit more legwork and a slightly less-impressive spec. It also means that the dynamic range stated is meaningful. It’s meant to give the customer a sense of the range of signals that he will be able to measure with this instrument.
As seen in the 6/5/13 edition of the Photonics Online (www.photonicsonline.com) newsletter.
5
Rule of Thumb In general, when you see a dynamic range stated based only on the bits (like the 72dB in the example above), you can almost always assume it to be higher than the actual dynamic range. We can understand this rule better by considering when it is broken. Imagine for a moment that your camera has a noise level of 1/1000 of the maximum (or 0.1%), but the digitizer only has 8 bits. This increases the effective noise by a factor of almost four, since, although the detector can measure 1000 significantly different values, the digitizer can only convert to 256 values (2^8=256). That means that there will be an additional rounding error. Since no manufacturer would want to increase the effective “noise,” it’s safe to assume that the range based on bits is higher than the actual dynamic range.
As seen in the 6/5/13 edition of the Photonics Online (www.photonicsonline.com) newsletter.
It all started when a slow-witted engineer was teased one too many times. Tired of being the butt of all his colleagues’ jokes, he plotted revenge. “I will create such a convoluted unit for dynamic range that none of them will be able to understand it. We’ll see who’s laughing then. Mwahaha! Instead of simply stating that the range is 20:1 or 3000:1, let’s take the log of that ratio and multiply by 10. Or 20. No one will ever get it straight! I shall call it – the decibel.” (Actually, the decibel was invented in Bell Labs in the 1920s. Although it is convoluted, it’s also a very useful method of measuring wide ranges or ratios.)
Figure 1: Laser beam profiling setup
What Is Dynamic Range Anyway? Most laser beam profiling systems include dynamic range in their specifications. What exactly does this mean? The complete answer might depend on which type of dynamic range is being referred to, as you’ll see below. Suffice it to say that dynamic range is meant to characterize the ratio between the highest and lowest measurable signals (i.e. the signal range).
As seen in the 6/26/13 edition of the Photonics Online (www.photonicsonline.com) newsletter.
2
Do You Use Decibels or Decibels? Huh? That’s right – there are two types of decibels, sometimes distinguished by a subscripted “power” or “volts,” but all too often left naked of any description. I know. I also think there should be a $3 fine for each ambiguous use of the term. For now, though, let me explain the background. There are two formulas for dynamic range: 1) dBpower = 10 log (Phigh / Plow) 2) dBvolts = 20 log (Vhigh / Vlow) The reason for these two forms is so both a power and a voltage ratio output a dynamic range for power. If you remember a little basic physics, power is proportional to voltage squared. Now if you also recall some algebra, a square within a log is the same as twice the log. In other words (or symbols): x log (y2) = 2x log (y) For this reason, 1 dBpower = 2 dBvolts. The logical approach is to use dBpower for a power ratio and dBvolts for voltage. In some cases, though, it isn’t so clear which to use. In the camera industry, for example, the general consensus is to use dBvolts. For optical measurement, however, dBpower is often preferred, as it’s more directly related to the light being measured. When cameras are used for optical measurement, as with beam profiling, all bets are off. So, which should be used: dBpower or dBvolts? A common answer might be: When in doubt, pick the higher value, since it looks better. At a more upstanding institution, though, the answer is that it depends on what is trying to be conveyed. What kind of signal are we dealing with? What value will be more helpful to the consumer? These are the questions we ask ourselves when trying to determine which form of dB to use. Of course, it’s best to state outright which units are being used in any case where it’s not obvious. Fun fact: most of our Spiricon CCD cameras use dBvolts, while the NanoScan family uses dBpower.
As seen in the 6/5/13 edition of the Photonics Online (www.photonicsonline.com) newsletter.
3
Figure 2: Ophir Spiricon SP620 CCD camera (left) and NanoScan beam profiler (right)
The Wrong Way to State Dynamic Range – And How to Spot It What’s the most important rule when trying to determine spec statements? What’s the fundamental law that applies not only to dynamic range, but to all specs? The only spec worth stating is one that is helpful to the customer. Not the really impressive spec that only applies in 3% of situations? No, not that spec. That would be like a bridge that has a sign: “Weight limit – 15 tons.” But in fine print it says, “Only on clear days with no wind, between the hours of 10 a.m. and 11 a.m.”
How Does This Apply to Dynamic Range? All camera beam profilers have several components, each with its own dynamic range. There’s the detector itself, there’s the analog-digital convertor, and then there’s the incorporation of noise into the equation. For example, the Spiricon SP620 has a dynamic range of 62dBvolt even though its digitizer is clearly stated as 12-bit, which is a dynamic range of approximately 72dBvolt. So what happened to the other 10dB?
As seen in the 6/5/13 edition of the Photonics Online (www.photonicsonline.com) newsletter.
4
Figure 3: Spiricon SP620 camera
When Ophir Spiricon determines dynamic range, it takes a very careful measurement of the RMS noise first and then checks the range between the highest signal and that noise. Figure 4, below, is an excerpt from such a calculation of the SP620 camera noise. The y-axis represents the number of readings (population) of a given value (bin) and the x-axis is the value itself. X is the mean, and σ is the RMS noise. To get the dynamic range value, one must divide 2^12 (12 bit A/D) by σ.
Figure 4: SP620 camera noise calculation
When Ophir Spiricon uses this method, it means a bit more legwork and a slightly less-impressive spec. It also means that the dynamic range stated is meaningful. It’s meant to give the customer a sense of the range of signals that he will be able to measure with this instrument.
As seen in the 6/5/13 edition of the Photonics Online (www.photonicsonline.com) newsletter.
5
Rule of Thumb In general, when you see a dynamic range stated based only on the bits (like the 72dB in the example above), you can almost always assume it to be higher than the actual dynamic range. We can understand this rule better by considering when it is broken. Imagine for a moment that your camera has a noise level of 1/1000 of the maximum (or 0.1%), but the digitizer only has 8 bits. This increases the effective noise by a factor of almost four, since, although the detector can measure 1000 significantly different values, the digitizer can only convert to 256 values (2^8=256). That means that there will be an additional rounding error. Since no manufacturer would want to increase the effective “noise,” it’s safe to assume that the range based on bits is higher than the actual dynamic range.
As seen in the 6/5/13 edition of the Photonics Online (www.photonicsonline.com) newsletter.
