As the optical input signal (blue line) to a photodetector increases, the electrical output signal (red line) increases proportionally, and then begins to deviate from linear. It stops rising or even begins to decline after a while. In this case, we see linear behavior up to about 0.33 of the plot maximum.
Nearly all optical systems require detection, but no photodetector will operate over an infinite range of input optical radiation power. Above some limited range, results will be increasingly suspect as a result of saturation; below, as a result of noise (see figure). Assuming even illumination (constant power density), we might reasonably define saturation as the point at which the output of a photodetector deviates from linear by 20%. Designers should consider on a case-by-case basis what constitutes a "reasonable" deviation from linearity, given the accuracy requirements he or she must fulfill.
If saturation represents the "ceiling" for the measurement, photodetector noise represents the floor. Not coincidentally, we characterize both detector noise and saturation in terms of signal in and signal out. Noise signal out is generally given in amps per √Hz or volts per √Hz. Noise signal in is also called noise equivalent power (NEP, in watts), which is the optical signal in for an output electrical signal-to-noise ratio of 1.
How does bandwidth modify NEP? Noise adds rms; in other words, when it is integrated across the spectrum, the noise is multiplied by the square root of the bandwidth. If noise versus frequency is flat (generally true for unbiased photovoltaic devices), then the noise in a 10-Hz bandwidth is √10 times the noise in 1 Hz, and in 100 MHz it is √108104 times greater. A 50-Ω photovoltaic device, for example, would have noise of approximately 1 × 10-9 V/√Hz.
Detectivity (D*) is a figure of merit that normalizes NEP to unity active area and bandwidth. It allows easy comparison of different detectors. We define D* as
where ∆f is bandwidth and A represents active area. If bandwidth were 1 Hz and D* were 107 cm√Hz/W, then NEP in 1 Hz would be 10-8 W for a device with a 1 mm × 1 mm active area. NEP becomes 10-4 W (√108 greater) if the bandwidth is 100 MHz. From Theory to Practice
For the sake of argument, let's estimate the output of the detector corresponding to the instrument designer's criterion for deviation from linearity as 10 mV. What can we say about dynamic range for this detector? The answer, of course, depends not only on the detector noise but also on the bandwidth and the acceptable saturation/linearity criteria. Another way of looking at the situation is that dynamic range is a function both of system bandwidth and detector noise density.
Finally, let us think about the electronics that follow the detector. We generally call the first stage the preamplifier, though it may be the only amplification stage. With rare exception, the preamplifier will itself saturate with an output in the range of 1 to 10 V. If it is a very good preamp, its noise figure will be low enough that we can characterize the detector-preamp subsystem as detector-noise limited. If the gain is 40 dB (power; voltage gain is √40 dB = 100 times in this example), then the amplified noise floor is 1 mV over 100-MHz bandwidthand a preamp with 1 V maximum output saturates with a 10-mV input signal. That is a dynamic range of only 10. Of course this improves to 102 for a 1-MHz bandwidth and 103 for 100 Hz.
Most users think they want a high-gain preamp, but notice that if preamp gain in this example is reduced to 20 dB then dynamic range becomes 102 over a 100-MHz bandwidth, 103 over 1 MHz, and 104 over 100 Hz. The bottom line is that linearity, saturation, and dynamic range in photodetectors all depend strongly on bandwidth. If you have a problem with dynamic range in your system, it can easily be in your following electronics, not in the detector itself. Try reducing bandwidth or gain for a quick fix. oe
Fred Perry is president of Boston Electronics Corp., Brookline, MA.