In continuous wave (CW) laser ranging, the laser intensity should be modulated by a time-varying signal, e.g. a sinusoidal signal. For sinusoidally modulated laser intensity, ranging is accomplished by measuring the phase difference between the returning signal and the emitted signal as shown in Figure 1.7. The time delay is extracted from the phase difference according to:

 

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                Since the sine wave gives the same magnitude for angles that differ by a multiple of , the phase difference can be written as

 

 1-2-2

               where is the period. The integer can be interpreted as the number of full wavelengths included in the distance from the laser to the receiver. From Eq. Error! Reference source not found., the range can be written as

 

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                     Since the second term is not much useful in ranging, we can just drop it from the above formula.

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laserranging

                            The range resolution can then be written as,

 

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                       It is to be noted that the range resolution is determined not only by the resolution of the phase difference  but also by the frequency (or wavelength) of the modulating signal. The higher the frequency (shorter wavelength) of the modulating sine wave, the finer (smaller ) is the range resolution for a given phase resolution. Since the maximum value of  is , the maximum unambiguous range is given by

 

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                     In order to achieve both higher resolution (smaller ) and higher maximum unambiguous range, multifrequency modulating signals are used with the signal having the longest wavelength (lowest frequency) determining while the signal with the highest frequency determining the range resolution.

 

                      The accuracy of continuous-wave laser ranging is given by

 

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                       If the only important noise is thermal noise (for low reflected power), the square root of the signal-to-noise ratio is proportional to the reflected power and the accuracy becomes

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                     where is the bandwidth of the input noise.