PLANIFICACION CON EL METODO DE LA RUTA CRITICA “CPM”

The distances in TLS are measured in two well-known methods: time of flight (TOF), and phase difference. However, recently, a new technique has emerged, combines these methods, which is called Wave Form Digitizer (WFD).

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2.4.2.1 Time of Flight

The distance is calculated by measuring time delay created by light travelling from the instrument to the object and back to the instrument (Figure 2-5), according to the following formula (Van Genechten et al., 2008):

𝐷 =𝑐. 𝑡

2 ( 2.5 )

Where, c is the speed of light in air, and t is the time between sending and receiving the signal.

Figure 2-5 Time-of-flight laser scanner principle (Van Genechten et al., 2008).

TOF scanners are also called pulse based because they scan their entire field of view by laser pulses, i.e.

measuring range for one point at a time. It should be noted that for a non-ambiguous measurement, the time measured (t) should be greater than the pulse width, Tpulse, hence (ibid):

𝑡 > 𝑇𝑝𝑢𝑙𝑠𝑒 ( 2.6 )

Or

𝑑 >1

2 𝑐. 𝑇𝑝𝑢𝑙𝑠𝑒 ( 2.7 )

Evidently, this technique requires very accurate clocking mechanism, e.g. for 1 mm distance accuracy it needs to be able to measure a time delay of about 3.33 picoseconds (10^-12 second), taking into account the speed of light in a vacuum is c = 299,792,458 m/s. In addition, it should be noted that measuring the time of return pulse depends on the desired time resolution, the counting rate and the required dynamic range of the pulse (Van Genechten et al., 2008).

CHAPTER TWO: BACKGROUND AND CONCEPTS

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In addition, the maximum pulse repetition frequency is restricted by the fact that the transmitter cannot send another pulse until receiving the echo from the previous one, in order to avoid confusion in the pulses arriving at the time interval counter. This is called the maximum unambiguous range and it depends on the pulse duration and its frequency (Figure 2-6) (ibid).

Figure 2-6 Maximum Unambiguous Range versus pulse repetition frequency (Van Genechten et al., 2008).

The advantage of TOF scanners is that its capability to measure accurate long ranges (few hundred metres) owing to the high concentration of transmitted laser power which makes it possible to achieve the required SNR (signal to noise ratio) needed. In addition, the error of this scanner is almost independent of the distance itself (except for the laser footprint, will discuss later). On the other hand, due to the changeable nature of the optical threshold and atmospheric attenuation, the drawback is the problem of detecting the exact arrival time of the returned laser pulse.

2.4.2.2 Phase Difference

To avoid using high precision clocks, another distance measuring technique is existed which is based on the phase-shift between the emitted and reflected signal and the number of full wavelengths (Figure 2-7).

This can be done by modulating the power of the laser beam with different methods (Van Genechten et al., 2008): sinusoidal, amplitude based (AM), frequency based (FM), pseudo-noise, or polarization modulation.

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Figure 2-7 Phase-difference distance measurement principle (Maar and Zogg, 2014).

Similar to TOF, the phase-difference scanners can be related to a time delay. This can be clarified in the relationship between phase difference (ΔΦ), modulation frequency (fmodulated), and time delay (t), is (Van Genechten et al., 2008):

𝑡 = ∆Φ

2𝜋 . 𝑓𝑚𝑜𝑑𝑢𝑙𝑎𝑡𝑒𝑑 ( 2.8 )

Then distance is calculated according to the distance measuring equation of TOF scanners (ibid):

𝐷 =𝑐. 𝑡

2 = 𝑐. ∆Φ 4𝜋. 𝑓_{𝑚𝑜𝑑𝑢𝑙𝑎𝑡𝑒𝑑}

( 2.9 ) This type of scanners also has a maximum unambiguous range which is limited to that one causes a phase delay in the sine wave of one complete cycle. Hence, the maximum unambiguous (Zamb) can be expressed by the following equation (ibid):

𝑍𝑎𝑚𝑏= 𝑐

2 . 𝑓𝑚𝑜𝑑𝑢𝑙𝑎𝑡𝑒𝑑 ( 2.10 )

It is worth to mention that phase-difference scanners have higher speeds and better resolution, but less precision than TOF scanners which is limited by (Van Genechten et al., 2008):

 The modulated frequency.

 Stability of the modulation oscillator.

 Atmospheric conditions.

 The accuracy of the phase-measurement loop which in turn depends on SNR.

CHAPTER TWO: BACKGROUND AND CONCEPTS

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2.4.2.3 Wave Form Digitizer

The WFD is a kind of TOF method, yet combines advantages of phase-difference and TOF techniques into one system. In this technique, the distance is calculated based on the time delay between a start and stop pulse which is digitized out of the received signal. Hence, to precisely recognize and extract the start and stop pulses, the waveform of all reflected signals is constantly evaluated, digitized and accumulated (Maar and Zogg, 2014).

Accordingly, the distance is not calculated from a single shot, but from multiple pulses. For each pulse, a small portion (fragment) is directed through an internal channel inside the instrument which is called start pulse. On the other hand, the major portion of the pulse leaves instruments and reflects back from the object. The backscattered signal is detected by the photosensor inside the instrument which is known as the stop pulse. Both start and stop pulses are digitised as a full waveform and accumulated from multiple signals. Then, the time delay between accumulated start and stop pulse is estimated, and therefore the distance is calculated similar to TOF technique (ibid).

Hence, the more pulses the better the signal-to-noise ratio (SNR). Consequently, the better estimation of the time delay and more accurate distances can be determined (Figure 2-8). According to Maar and Zogg (2014), the SNR increases with the square root of the measurement time, e.g. 9 seconds leads to a SNR about three times better than for a measurement time of 1 second.

Figure 2-8 Single shot signal (above) and 100 times accumulated signal (below) (Maar and Zogg, 2014).

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Consequently, the WFD can be considered a better overall measurement performance Compared to a pure time-of-flight measurement method. Table 2-1 reveals the comparison among three different techniques: TOF, Phase-Shift (Phase-Difference), and WFD.

Table 2-1 Comparison among different distance measurements techniques (Maar and Zogg, 2014).