This blog post answers the many appreciated questions asked by the audience during the two recent webinar events "Optimize signal acquisition for optical measurements" and "Optimize signal acquisition for optics and photonics measurements". Both events were recorded and are available here and here. Both webinars covered these points:
- Lock-in amplifier working principle
- Lock-in amplifier measurement optimization
- Boxcar averager working principle
- Differences between lock-in amplifier and boxcar averager
In the webinar, we focused on four use cases:
- Tunable diode laser absorption spectroscopy (TDLAS)
- Pump-probe spectroscopy
- Stimulated Raman scattering (SRS)
- Carrier-envelope offset (CEO) stabilization
We demonstrated the first with the Zurich Instruments MFLI Lock-in Amplifier and the second with the UHFLI Lock-in Amplifier and Boxcar Averager. The instruments are controlled using our LabOne® software. The measurements were performed on signals coming from one of our arbitrary waveform generators according to typical signals in actual experiments.
For a summary of the webinar, please take a look at this blog post, where I focused on general working principles.
Here’s a selection of questions asked during the webinars, which I answered retrospectively and divided into different topics.
Lock-in amplifier working principle
Why is the low-pass filter used? I thought it must be the bandpass filter, centered around the signal peak, but suppressing the low frequencies?
It is correct, the lock-in amplifier can be thought of as a narrow bandpass filter following the reference frequency omega with a fixed phase relation. This functionality is implemented by multiplication of the input signal with the reference signal. (It is the equivalent of an electronic mixer.) The result has two components: one around DC and one centered at 2omega with identical information content. Applying a low-pass filter with a finite time constant therefore recovers the signal on the DC part. For a more detailed discussion and mathematical treatment see our lock-in detection white paper or contact me directly.
To compromise between T90 and noise is it possible to set a high order filter not just as a series of the same LF filter but with some Q and overshoot?
In general it is possible to use a tailor cut filter - our UHFQA Quantum Analyzer features such a freely programable filter. For lock-in amplifiers it is established to use a digital RC filter. Since they are very flexible and have a continuous response function. This prevents signal or noise leakage from sidelobes.
What are the requirements for AOM and EOM used for Lock-In Amp modulation?
There are no real requirements for the AOMs or EOMs. Only the designed frequency bandwidth has to match - this is only an issue if the AOMs use a resonant design. If so, the frequency band is defined e.g. as 60 MHz - 87 MHz.
Are the bandwidths of AOM and EOM affected by the modulation frequencies stabilities of the AOM and EOM?
If the AOM uses a resonant design. The modulation bandwidth is limited. But rarely the bandwidth is so narrow, this affects the Lock-in measurement, since the modulation is basically continuous wave. If the modulation frequency changes though, the lck-in amplifier will follow this frequency employing its internal phase-locked loop (PLL). This guarantees the Lock-in amplifier demodulates always at the correct frequency, even if it varies during the measurement.
Could you elaborate a bit on optimum selection of filter order (bandwidth cutoff is more intuitive) with LIA?
In short - choose a high order filter only if you have a noise feature, e.g. powerline peak leaking into your signal. A more detailed discussion can be found in this video, in this blog post and this one too.
It looks like the main reason why not to choose an arbitrarily high order is that it introduces delay in the step response to the signal. Right?
Yes. The higher the filter order, the longer it takes until the step response settles. A more detailed discussion can be found in this video, in this blog post and this one too.
Is the software capable of preprogramming the filter bandwidth analysis so that the system can optimize the SNR on the fly?
The optimization of the bandwidth always depends on the actual application. Therefore a general automatic procedure is not easily possible. Still, the API provides all possibilities to allow a quick implementation by the user for the very application.
Does data acquisition time depemnd on filter BW, modulation frequency and why?
You want to wait until the signal settled to a certain ratio of the step response or in the case of an experiment up to a part of the parameter change. A more detailed discussion can be found in this video, in this blog post and this one too.
What about notch filter response?
All our lock-in amplifiers have a sinc filter implemented that allows suppressing harmonics of the modulation frequency and the DC offset.
Boxcar averager
Can you please comment if the boxcar mode is planned to have 3 analysis bands?
Our UHFLI has two boxcar average units, each with 1 boxcar window and one associated baseline window. Both boxcar averager units can operate on the same input signal independently and provide 2 boxcar windows and two baseline windows simultaneously.
Can you please comment on the potential parasitic signal in the boxcar mode coming from RF response function, for example, impedance-mismatch signal echos, etc.?
Since the response function spreads further in frequency the boxcar is more likely to measure noise at higher frequencies. Although the noise only affects the measurement if it exhibits the exact phase relation given by the boxcar window – and therefore appears on the short signal itself. In case the noise is coherent in time, e.g. an echo at an impedance mismatch or noise pickup from a pulse picker, the noise is separated in time and can, therefore, be very efficiently suppressed by the boxcar.
Are the bandwidths of AOM and EOM affected by the modulation frequencies stabilities of the AOM and EOM?
For a pump-probe measurement with the boxcar averager the EOM and AOM normally should suppress individual pulses. As long as the control signal is chosen to extend over the pure pulse the measurement is even more robust since the modulation is then more robust.
Use cases
I have an external driving signal at a certain frequency (50kHz) and I have to analyze the signal around a sharp frequency interval centered on this frequency. The situation seems to be very similar to the first example you reported (TDLAS) but also the use of boxcar averager may be beneficial for us. My question is: shouldn't be better to apply a Bandpass filtering centered on our frequency of interest instead of a Low Pass filtering that may carry unwanted freq components?
The lock-in amplifier can be thought of as an adjustable band-pass filter that follows the reference frequency. Therefore it is the very instrument that performs the task. The low-pass filter I mentioned during the webinar is one component used to implement the Lock-in functionality but it is not acting directly on the input signal. The answer to the first question in the lock-in amplifier section adds more detail.
Which lock-in will you recommend if modulation frequency is 1MHz, MFLI-5M lock-in or HF2LI?
Typically for a 1 MHz signal, we recommend our MFLI 5MHz. But it is difficult to make a definite statement without knowing the other requirements of the whole application. For example, if you envision higher modulation frequencies or you need two channels the HF2LI might be the better choice. Therefore, I always suggest a short alignment with one of our application scientists to ensure we cover all your needs and find the best fit for your application.
I require to measure the absorption signal of a gas using the Wavelength Modulation Spectroscopy technique. The experiment requires to divide the LIA signal on the second harmonic by the signal on the first harmonic of the laser modulation - this is a standard 2f/1f measurement. How to obtain this functionality on ZI LIA? What modules are required? This has to be done in real-time. Post-processing of the pre-registered signal is not possible.
Operations like division, multiplication addition can be performed using our arithmetic unit in the UHFLI Lock-in Amplifier. It works on the sample by sample basis and you can record the output or feed it out of an Auxiliary Output and control back, for example.
Can the techniques be applied to fluorescence measurement as well?
Both lock-in amplifiers and boxcar averagers can also help significantly to improve the signal-noise-ratio for fluorescence measurements. You modulate the light source with a sine wave or with a rectangular signal with low duty cycle and detect the output of your fluorescent light photo detector with a lock-in amplifier or boxcar averager. The SNR will be much better than if you just digitize the signal.
Could you please more elaborate on 2f signal amplitude in TDLAS with a lock-in amplifier and make a comparison with boxcar averager?
The signal amplitude depends on the actual measurement and laser modulation. If this is not sinusoidal, a boxcar averager can be a good choice. Since the best approach depends on the details of your application it is often better to find the best solution in a personal conversation with one of our application scientists.
General questions
My question is how to identify or determine which is signal or noise when the signal is close to the level of noise?
This is the key question indeed. Clearly, you do not have control over the noise – but you can always turn off the signal. e.g. detune the laser, take out the gas of interest or block the pump pulse train. Without a signal, you can characterize the experiment noise background and perform a reference measurement – that cannot show any signal. Everything that shows up in such a background measurement is of parasitic origin. The actual signal discriminates against this.
What is the name of the software you use for the simulation?
I assume this question refers to the simulation of the TDLAS signal. An arbitrary waveform generator (AWG) generates the signal. Still, the lock-in amplifier generates the modulation frequency fed into the AWG. Therefore it is a real measurement without the need to operate an entire laser spectroscopy setup. During the webinar, I misunderstood this question to refer to the used control software. Here the answer is: These are measurements performed with our LabOne control software, which comes with each of our instruments.
Are there more detailed tutorials available from Zurich Instruments, e.g. software manual, how-to app notes, etc. ?
Sure, we have an entire collection of documentation, starting with the product and programming manuals coming with the free software download. Also, we have numerous application pages, application notes and blog posts where you can discover a lot of use cases, tips and tricks for your everyday work in the lab. Besides, we have more webinars as well as product and tutorial videos on our YouTube channel.
If a high signal we are about to test in the software, would it be harmful to our instrument that is testing?
All signals generated with the lock-in itself cannot harm the input. If you apply external signals please ensure you stay below the damage threshold.
Are there other techniques other than lock-in detection for small signals?
To recover small signals buried in noise there exist mainly lock-in amplifiers and boxcar averager. For phase noise measurements cross-correlation techniques are applied as well.
Does in a combination of a lock-in amplifier and boxcar averager pump and probe experiment we do not require to optical modulator? If using the optical chopper to modulate one frequency can give benefits?
This is absolutely correct, also for the pump-probe measurements, there is a modulation necessary. In the webinar example, the pump branch is modulated at half the repetition rate of the probe branch. Therefore every second pulse carries the signal.
