# Harmonic detection using lock-in amplifier

Can a third harmonic of a signal be detected using a lock-in amplifier under the same parameters fixed for collecting the fundamental or the parameters needs to be adjusted.Here by parameters I mean sensitivity , time constant and phase. I am using a Mach-zehnder interferometer to intensity modulate my laser beam which is pulsed at 80 Mhz rep rate. The beam is modulated at 1.2 MHz. One arm of the interferometer is used for reference to lock-in which is stanford 865a. other arm is used for sample excitation. I am trying to extract the harmonics just by choosing the harmonics on the lock-in. The fundamental signal and the second harmonic are relatively easy to extract but even at inexorbitant powers i have not been able to see a stable phase for third harmonic.

No, a properly implemented lock-in amplifier essentially computes a single-bin Discrete Fourier Transform of the input, measuring energy (and phase) only at the frequency of interest. Of course practical implementations will be slightly "leaky".

However, a more crude implementation of a synchronous detector which merely uses the reference signal to alternately multiply the detected signal by +1 or -1 would indeed have quite substantial response to odd harmonics.

To put it another way, if your lock-in amplifier multiples by sine waves in quadrature, it will have a degree of harmonic rejection. While if you build something that multiples by a square wave (or two in quadrature) it will have harmonic susceptibility, because it is actually multiplying not only by a sine at the reference frequency, but also by the sines at all of the harmonics of the reference frequency which comprise the square wave.

• I am interested in the third harmonic signal in an attempt to improve resolution of my microscope. Could you please suggest in light of the points mentioned above that what will a good strategy to do so. Thank you May 3 '19 at 2:01
• Either build your own with an MCU/DSP and target the third harmonic, or use the third harmonic of the reference frequency. There's too much about your experimental setup missing from your question to be more specific. May 3 '19 at 2:09
• Hi Chris, I am using a Mach-zehnder interferometer to intensity modulate my laser beam which is pulsed at 80 Mhz rep rate. The beam is modulated at 1.2 MHz. One arm of the interferometer is used for reference to lock-in which is stanford 865a. other arm is used for sample excitation. I am trying to extract the harmonics just by choosing the harmonics on the lock-in. The fundamental signal and the second harmonic are relatively easy to extract but even at inexorbitant powers i have not been able to see a stable phase for third harmonic. Thanks May 3 '19 at 2:22
• That should be an edit to your question. Probably what you should do is either get a decent ADC sampling system and do an FFT in software (not even necessarily real time) to detect all the components. Or start with a 3f signal, run your lock-in at that, and derive your 1f modulation therefrom. May 3 '19 at 2:35
• Many Spectrum Analyzers function at 80MHz. Drive the SA with that, and examine the 1.2, 2.4 and look for the 3.6MHz energy. May 3 '19 at 3:30

I think inexorbitant is the wrong term for excessive and ought to be "exorbitant".

If your 1.2MHz has a fast rise time of <= 10% and is near 50% symmetry then it will contain 1f , no 2f , 3f, no 4f etc with odd harmonics limited by risetime such that for a $$\t_R <=23 \text{% of period, taken at 10% to 90% of pk-pk signal}\$$

If the waveform appears as below, then you may expect the 3f to be -16 dB down from 1f and both in sync at -90 deg absolute phase shift.

Phase noise will be multiplied x3 and thus SNR is also -10dB lower so the result is 40 dB worse than 1f. Since lock-in amplifiers are non-harmonically sensitive , you can obtain better performance using Type I PLL harmonic mixers with the BW of the loop filter needed to reject the adjacent fundamental above the 3f harmonic by more than 40 dB which implies at -6dB / octave of -12dB from 1f to 3f at least a 3rd order to 7th order high pass , 1f rejection filter. The VCO can then be used to drive the lockin amp quadrature clock or your design of discriminator.

One possibility is to start with a 7.2 MHz logic level squarewave and do two things. First, divide the frequency by two using the ubiquitous "divide by 2" D flip flop circuit. The 3.6 MHz output frequency would then be used as the reference (perhaps level shifted, if necessary) for the LIA. The duty factor is 50%. Second, the same output would also be frequency divided by 3, as per this circuit (directly from here: Divide clock frequency by 3 with 50% duty cycle by using a Karnaugh Map? )

Then the output frequency would be at 1.2 MHz, with 50% duty factor, and this would be used for the laser modulation. Hope this helps!