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Old 07-01-2012, 06:00 AM #1
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Default Understanding Dynamic Range…The Numbers Game

Understanding Dynamic Range…The Numbers Game
________________________________________
I thought the following article within Ophir-Spiricon’s June 2012 - ePulse: Laser Measurement News might be of timely interest:
Tutorials - Understanding Dynamic Range: The Numbers Game

[Where albeit this discussion revolves around CCD camera based beam profiling equipment the underlying mathematics exercise is applicable as noted to any power measurement equipment design accuracy.]
Quote:
There is a fair amount of confusion caused by the reporting of dynamic range of beam profilers. The purpose of this applications note is to explain some of the terminology used in the discussion of this parameter by both Ophir- Spiricon and other suppliers of beam profilers.

Definition
Dynamic Range is the ratio of the largest measurable signal to the smallest measurable signal. The smallest measurable signal is typically defined as that equal to the noise level, or alternatively the “Noise Equivalent Exposure” or that point where the Signal-to-noise ratio (SNR) is 1.

To measure a beam profile we should have a SNR of at least 10 to obtain a minimally useful result. It requires more like SNR of 100:1 to achieve the 2% accuracy. However, in instrument specifications Ophir and its competitors use the Digitization Dynamic Range. The discussion below will follow this approach.

Units
Dynamic range can be expressed as a ratio, for example 1000:1, or it can be expressed in decibels of either power or voltage.


The article goes on to briefly discuss the separation of the dynamic range of the instrument into 1- The instantaneous or single measurement capability and 2 - The total achievable range capability. Where the instantaneous measurement capability is the digitization dynamic range minus any noise levels.
Quote:
Conclusion
It is important to understand what units are being used when comparing the dynamic range of different instruments. Most CCD systems report dynamic range in dBvolts. NanoScan and Goniometric Radiometers report their dynamic ranges in dBpower. Both are valid, but if you want to understand how the dynamic range will affect your laser beam measurements, dBpower will provide a more realistic value of the response of the sensor to varying laser power levels.
Edit - Excerpt below from: Wikipedia - Signal-To-Noise Ratio - Digital_Signals
Quote:
Digital signals

When a measurement is digitised, the number of bits used to represent the measurement determines the maximum possible signal-to-noise ratio. This is because the minimum possible noise level is the error caused by the quantization of the signal, sometimes called Quantization noise. This noise level is non-linear and signal-dependent; different calculations exist for different signal models. Quantization noise is modeled as an analog error signal summed with the signal before quantization ("additive noise").

This theoretical maximum SNR assumes a perfect input signal. If the input signal is already noisy (as is usually the case), the signal's noise may be larger than the quantization noise. Real analog-to-digital converters also have other sources of noise that further decrease the SNR compared to the theoretical maximum from the idealized quantization noise, including the intentional addition of dither.

Although noise levels in a digital system can be expressed using SNR, it is more common to use Eb/No, the energy per bit per noise power spectral density.

The modulation error ratio (MER) is a measure of the SNR in a digitally modulated signal.


FYI - Also note this link to Ophir-Spiricon’s Library of White Papers
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Understanding Dynamic Range…The Numbers Game-dynamic-range.jpg  


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