Webinar Q&A - Mastering Periodic Signal Analysis for Optics & Photonics Applications
This blog post answers the many appreciated questions asked by the audience during the webinar "Mastering Periodic Signal Analysis for Optics & Photonics Applications”. The event was recorded, and the video is available here.
The webinar covers the following topics:
- Lock-in amplifier working principles
- Lock-in amplifier measurement optimization
- Boxcar averager working principles
- Advice on running an optimized optics and photonics experiment
Additionally, we also focus on the following application examples:
- Tunable Diode Laser Absorption Spectroscopy (TDLAS)
- Fluorescence analysis at multiple wavelengths
- Pump-probe spectroscopy
- Terahertz time-domain spectroscopy
- Stimulated Raman scattering (SRS) microscopy
For a detailed discussion and rigorous mathematical treatment of the lock-in amplifier and boxcar averager working principles, have a look at our Principles of lock-in detection and Principles of Boxcar averaging white papers, or contact us directly.
Below, you can read a selection of questions asked during the webinar.
Questions and Answers
Is there any suite available for integrated photonic component characterization such as parametric amplifier?
Since the components one needs to characterize and the type of measurements one wants to run can be very diverse, it’s not easy to give a definitive answer to your question.
All of our instruments serve a diverse range of applications, and component characterization (not only in integrated photonics, but also in other research fields) is also one of them. If, for example, you need to perform frequency response analysis or impedance measurement on your device, our products can provide you with the tools needed for your measurements.
Please contact us directly. We’ll be happy to have a closer look at your application.
What is the difference in time between different filter orders or time constant?
In lock-in amplifiers, the time constant defines how quickly the filter responds, with higher constants giving better noise rejection but slower responses. Filter order determines the roll-off steepness: higher-order filters have steeper roll-offs but longer settling times. Thus, higher-order filters with larger time constants filter noise better but respond slower, while lower-order filters with smaller constants respond faster but filter less effectively.
For a pump probe application like SRS, what is your suggestion for determining the demodulation phase?
All our instruments are dual-phase lock-in amplifiers, meaning they provide the user automatically with both the amplitude (denoted R) and the demodulation phase (denoted θ) with respect to the reference signal. Therefore, no additional procedure is needed to extract the demodulation phase. Alternatively, the instrument can also provide the so-called in-phase (X) and quadrature component (Y).
Most pump-probe setups are based on optical signals, NIR or VIS spectra. Is it possible to perform a pump-probe setup with RF using coaxial cables to transmit the signals for sampling and transient collection?
In principle, this is possible, even though it is not as common as the optical counterpart. The are examples in the literature of “electrical” pump-probe techniques, where electrical (instead of optical) pulses excite and subsequently probe the sample, whose response is then recorded as an electrical signal.
An example of it can be explored in this article.
What is the definition of filter order?
The filter order refers to the number of identical (i.e. with the same time constant) low-pass filters cascaded one after the other. Higher-order filters have steeper roll-off characteristics, meaning they can more effectively attenuate undesired frequencies beyond the cutoff point. For instance, a first-order filter has a roll-off rate of -20 dB/decade, a second-order filter has a roll-off rate of -40 dB/decade, and so on.
How do I correctly set the width of the boxcar window to have the best SNR? Is there an optimum width?
For a Gaussian-shaped pulse, it can be shown that one obtains the maximum SNR by choosing a window that covers about 90% of the pulse power. In a real measurement, however, the signal might not be Gaussian, or its power might not be evenly distributed across the pulse. In that case, one can optimize the SNR by starting with a large boxcar window and then reducing its width until the SNR peaks.
Are there benefits to using a physical LIA over a digital LIA in post processing?
Digital lock-in amplifiers offer significant benefits compared to the analog counterpart, such as flexibility in customization and advanced signal processing, cost-effectiveness by reducing the need for expensive analog components, and seamless integration with digital data acquisition systems. Analog lock-in amplifiers might still be used used in very specific applications where form factor is important or where only a very specific task needs to be carried out.
Thanks a lot for the insights! Can one quantify the increase of SNR when using boxcar averagers with low duty-cycle pulsed lasers compared to lock-ins?
For the extreme cases, i.e. purely sinusoidal or ultra-low duty cycle, the choice is clear.
In more complex scenarios, however, the problem is nuanced.
The actual difference in SNR is strongly dependent on the characteristic of the signal coming out from the detector, which in turn depends on the characteristic of the excitation light and the response of your sample. It is not easy to quantify a priori what the SNR gain (or loss) would be between the two techniques on the same signal. That is exactly the reason why the bast way to settle the debate is to try both measurements simultaneously and decide based on the resulting SNR. For more insights you can have a look at this video, where a comparison is shown.
I am working on Dual comb spectroscopy based on fiber based lasers at rep rate of 250MHz. I am suffering from low SnR when I increase delta f (difference between two combs) for fast rate measurements. I thought of using a low noise amplifier (DC to 200 MHz bandwidth) to gain in terms of SnR. Is it feasible to use a lock-in amplifier instead of an LNA? If so, what should be the reference frequency?
In the classic version of dual comb spectroscopy, the radio-frequency interferogram generated by the two optical frequency combs is directly acquired in the time domain.
There are also versions of dual comb spectroscopy that make use of lock-in detection by employing a reference arm to collect and generate the frequency signal for the lock-in amplifier. An example of such implementation is shown in this article.
I didn’t understand the downside of increasing the filter order for the lock-in amplifier. Could you explain that again if you have time?
Increasing the filter order in a lock-in amplifier provides better noise reduction but leads to longer settling times and greater system complexity. Higher-order filters can also introduce stability issues and require more computational resources in digital implementations. This trade-off needs careful consideration based on application requirements.
Can you shed some light on the relationship between wait times and time constants for measurements?
In lock-in amplifiers, the wait time before taking a measurement is often related to the filter's time constant. A good rule of thumb is to wait at least 5 times the time constant to ensure the output has settled sufficiently, providing accurate and stable measurements. Longer wait times may be needed for higher-order filters to account for their increased settling times.
Can you briefly repeat how to set the gate width of the boxcar, depending on the experimental and measurement context?
Generally, as mentioned in another question above, the best boxcar gate is smaller than the actual width of the pulses we want to measure. In real measurement, every signal has a different profile and might have a different optimal window width. The idea is to start with a relatively large gate width (as large as your pulses) and then reduce it until the SNR peaks.
If I have a 2D pixelated detector like a camera, is there any way I can use a lock-in or boxcar?
This could be feasible in principle, but not very practical. This is because each detecting element of your 2D detector would need to have its own lock-in amplifier. For a few pixels detector, this might be feasible, but as the number of pixel increases, so does the complexity of such solution.
Could you provide the phase noise of the your internal oscillator?
The phase noise of the internal oscillator depends on the specific instrument model.
Generally, it falls in the range between –140 dBc/Hz and –160 dBc/Hz.
If I already have a lock-in amplifier and want to measure low duty cycle signals, does it make sense to make the signals "longer" in the time domain, meaning that I increase the duty cycle to get a better SNR?
It could indeed be a viable strategy. For example, you could use a slower photodetector to increase the duty cycle of your signal and make it more “sinusoidal”.
Note that a lock-in measurement of a low-duty cycle signal is still a valid measurement, simply that the information on the higher harmonics is not captured.
What is the maximum voltage range in case of oscilloscope in the lock-in amplifier?
The maximum voltage that can be measured by our instruments (regardless whether scope or lock-in) depends on the model, but it is usually in the order +/-3V.
Is there any benefit to cascade a boxcar and a lock-in amplifier?
Many times, especially in low-duty cycle pump-probe experiments, the pulsed signal that the detector captures is modulated at the modulation frequency of the pump pulse train.
In these cases, performing first a boxcar measurement on the probe pulse train and then a cascaded lock-in demodulation on the modulated boxcar output ensures the best SNR for the whole signal analysis chain.
For more insights and details about this process, you can have a look at this blog.
Are there experiments that can benefit from using both lock-in and boxcar techniques at the same time? Do they conflict with each other?
As explained in the previous question, there are cases where the two techniques might be used sequentially.
Alternatively, there could also be instances where one needs to measure two independent signals, one with the lock-in amplifier and the other with the boxcar averager.
Given that both approaches are implemented in the digital domain and not with analog components that might generate interferences, they can be run in parallel with absolutely no conflict.
If I have a free running laser (master) and want to lock another having slightly detuned frequency (50 KHz) with the first one; what should be the best way forward? Also, in such a case, is there a mechanism to separate the noise coming from electronic sources and environmental sources (such as thermal drift)?
Generating sum or difference between two frequencies usually requires a non-linear element that mixes the frequencies of interest. When the frequency are mixed (effectively multiplied), one obtains at the output difference or sum of the two input frequency.
Our instruments, equipped with the modulation analysis option (e.g. the UHFLI with the UHF-MOD option), are able generate arbitrary detuned frequencies from an external reference.
We’d be happy to discuss this in more detail; please contact us directly.
Can boxcar averager and lock-in amplifier controlled using my own C#/ Python code?
Absolutely. Our LabOne software includes APIs for Python, C/C#, MATLAB, LabVIEW and other common programming languages. Everything that can be done on the LabOne user interface can also be done with the APIs. For more information about our APIs, you can have a look here.
How do you determine the frequency and amplitude of the reference signal in the lock-in amplifier?
Lock-in amplifiers lock their internal oscillator to the reference signal with a phase-locked-loop (PLL), which defines the frequency and phase of the signal. The amplitude is not relevant. The multiplication of the signal with the references is performed with a proper coefficient so the measured amplitude, after the low pass filter, is the root-mean-square amplitude of the signal at the signal input connector.
I have an optical signal with an AC component in it coming from a system that is triggered to respond that AC signal. This is detected using a Si photodetector and send to the lock-in-amplifier. However at times, for certain systems, the DC component of the signal will overpower the AC signal. Suppose the expected AC signal is in nV, I get the DC component in mV. This is after using a lock-in-amplifier. How do we enhance the AC signal from the overpowering DC signal?
If the DC signal is very large, the best way forward is to remove it before analyzing the signal. This could be achieved with a simple high-pass filter placed before the signal arrives to the measuring device.
All Zurich Instruments lock-in amplifiers are equipped with an AC coupling option (i.e. a high-pass filter) that can be enabled in case of unwanted DC offsets. The cut off frequency of the filter depends on the specific model.