Dynamic range

Dynamic range is the ratio between the largest signal a system can handle and the smallest it can detect. The upper end is set by saturation, overload or the full scale of a converter; the lower end by the noise floor, usually taken as the level where the signal-to-noise ratio equals one. The ratio is normally quoted in decibels. An optical power meter that reads from 100 pW to 10 mW covers 80 dB; an ideal 16-bit analog-to-digital converter covers 98 dB; a scientific camera with a 30,000-electron full well and 1.5 electrons of read noise covers 86 dB.

Power decibels and amplitude decibels

The value in dB depends on whether the levels are powers or amplitudes. For optical power, $10\log_{10}(P_\text{max}/P_\text{min})$ is the usual form. Camera and converter specifications use $20\log_{10}$ of a ratio of counts, electrons or voltages. A photodetector converts optical power to current, and the electrical power of that current goes as its square, so a span of 45 dB in optical power is 90 dB in electrical power at the detector output. Photoreceiver datasheets do not always say which they mean.

Photodetectors and receivers

For a photodiode with a transimpedance amplifier, the bottom of the range is the noise-equivalent power times the square root of the bandwidth, and the top is the power at which the amplifier output clips or the diode response becomes nonlinear. With an NEP of 10 pW/√Hz and a 10 MHz bandwidth the floor is 31.6 nW; if the amplifier saturates at 1 mW of input, the range is 45 dB in optical power. Narrowing the bandwidth lowers the floor and extends the range; switchable-gain amplifiers move the whole window. In a digital link receiver the same idea appears as the window between the receiver sensitivity and the overload level.

Analog-to-digital converters

An ideal $N$-bit converter digitizing a full-scale sine wave has a quantization noise of $q^2/12$ per sample, where $q$ is the step size, which gives

$$\text{SNR}_\text{ideal} = 6.02\,N + 1.76\ \text{dB}.$$

That is 49.9 dB for 8 bits, 74.0 dB for 12 bits and 98.1 dB for 16 bits. Real converters fall short through noise, clock jitter and nonlinearity, and the measured result is expressed as the effective number of bits, $\text{ENOB} = (\text{SINAD} - 1.76)/6.02$, where SINAD is the measured ratio of signal to noise plus distortion; a 16-bit converter with an 80 dB SINAD has an ENOB of 13.0.

Cameras

For an image sensor the dynamic range is the full-well capacity divided by the read noise, both in electrons. A pixel with a 30,000-electron full well and 1.5 electrons rms read noise has a ratio of 20,000, which is 86.0 dB or 14.3 bits. No single reading reaches an SNR of 86 dB: at full well the shot noise is $\sqrt{30{,}000} = 173$ electrons, so the best single-pixel SNR is 173, or 44.8 dB. Dual-gain sCMOS readout, discussed under CCD vs CMOS, raises the ratio by reading each pixel through a low-noise and a high-capacity channel.

Optical spectrum analyzers

An optical spectrum analyzer has two dynamic ranges. The first is the span between its maximum input and its sensitivity: an instrument rated for +10 dBm and specified to detect −80 dBm spans 90 dB. The second, the close-in dynamic range, is how far below a strong line a weak signal can be seen at a given wavelength offset. It is limited by filter skirts and stray light and falls steeply as the offset approaches the resolution bandwidth. Close-in dynamic range is what limits a side-mode suppression ratio or OSNR reading; the OSA fundamentals article gives the settings that maximize it.

OTDR

For an optical time-domain reflectometer, dynamic range is the one-way difference between the backscatter level at the start of the fiber and the noise level; field instruments span roughly 25–50 dB. Measuring small events needs headroom: a 0.1 dB noise level on the trace requires the backscatter to be 6.6 dB above the SNR = 1 level, so a 30 dB instrument measures events through 23.4 dB of fiber loss, 117 km at 0.20 dB/km.

Spurious-free dynamic range

In analog links and RF photonics the upper limit is often distortion. The spurious-free dynamic range (SFDR) is the range of input power over which the fundamental signal is above the noise floor while third-order intermodulation products remain below it:

$$\text{SFDR} = \tfrac{2}{3}\,(\text{IIP}_3 - N_\text{floor}).$$

For an input third-order intercept of +20 dBm and a floor of −90 dBm (−150 dBm/Hz in 1 MHz), SFDR is 73.3 dB. Normalized to a 1 Hz bandwidth, as is common, the same link gives 113.3 dB·Hz$^{2/3}$.

Pitfalls

Dynamic range quoted without a bandwidth, integration time or averaging condition cannot be compared between instruments, since the floor moves with all three. The floor may be defined at SNR = 1 or at a higher threshold, which changes the number by several dB, and the range within one gain setting is smaller than the range across all settings.

Common questions

What is a good dynamic range for a photodetector?

It depends on the bandwidth, because the noise floor rises with its square root. A slow power-meter head with switchable ranges can cover 80 dB; the 45 dB receiver example above, at 10 MHz, would cover 35 dB at 1 GHz with the same NEP and saturation level.

How is dynamic range different from SNR?

Dynamic range compares the largest possible signal with the noise floor; SNR compares an actual signal with its noise, which for optical signals includes shot noise that grows with the signal. A camera with 86 dB of dynamic range still has a maximum single-pixel SNR of 44.8 dB.

References: W. Kester (ed.), The Data Conversion Handbook (Analog Devices / Newnes, 2005); J. R. Janesick, Photon Transfer (SPIE Press, 2007); D. Derickson (ed.), Fiber Optic Test and Measurement (Prentice Hall, 1998); C. H. Cox III, Analog Optical Links: Theory and Practice (Cambridge University Press, 2004).