Signal bandwidth

Firstly we can establish some of the fundamental relations for the resolution of an imaging system. In the down-range dimension resolution Ar is related to the signal bandwidth B, thus... 

Figure 2 illustrates typical Fourier space sampling as provided by monostatic SAR. As shown, the samples in the radial dimension straddle a term proportional to the carrier frequency and have an extent proportional to the signal bandwidth. Samples in the angular dimension correspond to pulse numbers in the coherent processing interval. In... 

The design of a system for working with short pulses follows the same principles as other pulsed ultrasonic systems such as ultrasonic flaw detectors, but in this case it is necessary to achieve very much greater stability and higher bandwidth. A schematic circuit is shown in Fig. 5.4 A very short impulse is generated by a step recovery diode. The pulse has a width of half the period of the centre frequency of the lens if it is shorter than that the energy in the pulse is reduced without any improvement in the signal bandwidth. Thus the lens acts as a sort of matched filter with poor time resolution but optimal... 

Measurements and information. The above-desoribed instrument can form images at 82 and 164 MHz with a signal bandwidth around 5 MHz. In order not to narrow such a bandwidth, the maximum number of lines or aros used must not exoeed 16. The microscope currently uses various oomputer-generated holograms to tailor the optical distribution on the sample surfaoe and is being converted to use an SLM. The stand-off distance from the optios to the sample is around 50 mm, whioh is determined by the need to resolve the SAWs at 164 MHz. 

Fig. 1.1 Output signal of a photomultiplier tube at different light intensity and signal bandwidth. Left to right Average output current -1 uA, -10 uA and -100 uA. Top to bottom Bandwidth 1 MHz, 10 MHz, and 100 MHz. Time scale 1 ps / div., XP2020 PMT at-2,000 V...

The signal bandwidth of an analog signal recording technique is limited by the bandwidth of the detector. In other words, the width of the instrument response function, or IRF, cannot be shorter than the width of the single electron response, or SER, of the detector. The SER is the pulse that the detector delivers for a single photoelectron, i.e. for a single deteeted photon. 

If a TCSPC module is operated at a eount rate of 10 to 10 photons per seeond a reasonably aecurate waveform is reeorded within less than 100 ms. Advaneed TCSPC modules can therefore be used as optieal oseilloseopes. A repetitive measurement eyele is performed in short intervals and the reeorded photon distribution versus time is displayed. Even with a low-eost PMT module, e.g. the Hamamatsu H5783, an IRF width of about 180 ps is aehieved. This eorresponds to a signal bandwidth of almost 2 GHz. The time ehannel width ean be made as short as a picoseeond, which results in an equivalent sample rate of 1,000 GS/s. 

Recently fast and relatively inexpensive SPAD modules have become available [245]. The detectors have an active area of 50 pm diameter and are overload-proof The IRF width is about 40 ps, resulting in an equivalent signal bandwidth of about 9 GHz. Although the small active area can cause some alignment problems, these detectors are excellently suitable for TCSPC oscilloscopes. 

The drawback of any resistive network used at the MCP output is that it introduces additional noise into the position signals. The thermal noise current is proportional to the reciprocal square root of the resistance. To obtain X-Y resolution of the order of 1,000 x 1,000 pixels, the resistance is usually kept in the 100 kf2 range. However, the high resistance reduces the signal bandwidth, and consequently the useful count rate. 

At first glance it may appear necessary to build an amplifier fast enough so that it does not broaden the detector pulses. This would require about 1 GHz for conventional PMTs and more than 3 GHz for MCPs. However, in practice the signal bandwidth is limited by the discriminators in the CFD as well. The input bandwidth of the discriminators is usually of the order of 1 GHz, so that an amplifier bandwidth above 1 to 2 GHz does not improve the timing performance noticeably. More important than extreme bandwidth are linearity and low noise, especially low noise pickup from the environment (see Sect. 7.5.4, page 311). A good preamplifier should amplify the detector pulses without noticeable nonlinearity up to the maximum CFD threshold of the TCSPC module, i.e. about 500 mV. This is no problem for the amplifiers used in the circuit shown in Fig. 7.38. 

High-performance electron guns help provide the required resolution and modulation efficiency for HDTV systems of up to 1250 lines. The video carriers have been optimized to increase the signal bandwidth capability to 30 MHz. 

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