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On the wikipedia article (and other texts such as Optical Inspections of Microsystems) for laser Doppler vibrometry, it states that a modulating frequency must be added such that the detector can measure the interference signal with frequency $f_b + f_d$. Why couldn't you remove the modulating frequency $f_b$ and interfere the two beams with frequencies $f_0$ and $f_0+f_d$ to produce a signal with frequency $f_d$ at the detector? I haven't been able to find any reasoning on the subject.

My first idea was that the Doppler frequency might fall inside the laser's spectral linewidth and thus not be resolvable, but for a stabilized low-power CW laser (linewidth on the order of KHz) and a typical $f_d$ in the tens of MHz range I don't see this being an issue.

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If you didn't modulate, a stationary or very slow object would give you a beat signal near DC where many noise sources are present. I assume the modulation frequency is chosen so that the beat remains sufficiently high for the fastest speed expected to be measured. –  user2963 Aug 25 '12 at 0:22
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The 'heterodyne' is based in the same principle used by the 'nonio' also called 'vernier' invented by the portuguese Pedro Nunes to increase the precision of measures of lengths. The principle is widely used also in telecomunications . A visualization.

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If you ommit the Bragg Cell the Photo Detector, should have to work in the optical range (modulated with $f_d$ kHz). With the Bragg Cell the signal $f_d$ will be mounted on $f_b$ (Mhz),a more electronic adequate band and the noise will be reduced. This autobalanced photoreceiver seems to simplify the design.

A sensible expanation is here: Mapping optical frequencies to electronic frequencies allows sensitive measurements

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I'm not immediately making the connection to my question. Even without the modulating frequency, it is still a heterodyne technique involving the frequencies $f_0$ and $f_0+f_d$ instead of $f_0$ and $f_0+f_b+f_d$. –  Gino Aug 24 '12 at 21:57
    
@Gino I've updated the answer. –  Helder Velez Aug 26 '12 at 5:56
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The modulating frequency shift provides the central band frequency at $f_b$

From Doppler effects, we know that if the object vibrates away from the source, the frequency $f_d$ decreases (negative), and if it vibrates toward the source, $f_d$ increases (positive). Now as mentioned, with the modulating frequency shift from which the detected frequency is $f_b + f_d$, the detector now can discriminate the directions if the velocity is toward the detector (|$f_b|+|f_d|$) or away from the detector (|$f_b|-|f_d|$).

Without central band frequency $f_b$, the detector can only see $f_d$ in single direction (positive), since it cannot detect negative value. In this arrangement, it is usually used for homodyne detection.

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