Webinar Summary and Q&A – Focus on recovering signals in optical experiments

This blog post accompanies the webinar “Focus on signal processing in optical experiments”. Thank you to everybody who joined the live event and participated actively by voting in the poll and asking so many relevant questions. The answers to all questions are provided at the end of this blog post in the Q&A section. The recording is available on our YouTube channel: Zurich Instruments webinar – Focus on recovering signals in optical experiments.

Starting from the fundamental question “What is the information in the signal?” (slides 12-13),  we discussed the relevance of typical properties of electronic instruments applied for optical measurements (slides 14-16). For example:

  • dynamic range
  • measurement bandwidth
  • signal input noise.

In addition to the earlier webinars “Optimize the Signal Acquisition for Optical Measurements” and “Optimize the Signal Acquisition for Optics and Photonics measurements” we had a closer look at the effect of specific settings of the Lock-in amplifiers onto measurement results (slides 20-25), such as:

  • filter function
  • filter order
  • time constants

We concluded with a comparison of pump-probe measurement using a Lock-in amplifier and Boxcar Averager in parallel to understand under which circumstances the different measurement schemes perform better (slides 26-34).

In the webinar, we discussed the Lock-in Amplifiers of Zurich Instruments. In particular, we highlighted the UHFLI Lock-in Amplifier and Boxcar Averager being used for pump-probe measurements and a comparison between the lock-in amplifier measurement scheme and the use of a Boxcar averager.

Presentation slides

Please find here the slides of the presentation for further reference. They are intended for personal use only – not for distribution.

Webinar - Focus on signal processing in optical experiments

Q&A Section

Here you find a summary of most questions asked in the Q&A of the webinar. I tried to categorize into three sections:

General Measurement Questions

Are there any measurement situations where the noise is useful?

Typically unwanted parts of the incoming signal are described as noise. Also, this corroborates the signal and is perceived as “bad”. Still, sometimes the actual signal is contained in the statistics of noise, in squeezed states in quantum optics, for example. Where actually some noise helps is when oversampling is supposed to be used to increase the amplitude resolution. (See Dithering noise.)

Why is the Lock-in amplifier scheme different than averaging of FFT spectra?

There are two components to the answer, a theoretical and a more practical one. 1. The lock-in amplifier can easily achieve measurement bandwidths of less than 1Hz, thanks to the continuous data processing. For the FFT you need to collect data over the inverse of this resolution e.g. 10 s long. Which leads to a huge amount of data that needs to be collected and processed. Capturing multiple FFT spectra at the same time would increase the SNR but would not provide the same frequency resolution. 2. The Lock-in will follow the modulation frequency in frequency and phase. Therefore even when the modulation frequency in the experiment varies, e.g. a mechanical light chopper not running perfectly, the lock-in would average always the correct signal over the changing frequency. In the FFT you would see a smeared out signal over frequency.

Similar to the microscopy examples you showed, it is possible to utilize a lock-in for signals observed from a CCD in optical experiments?

No, this is not possible since the readout of a CCD is a fairly complex procedure for itself. But there are Lock-in cameras around which might help.

For a very high repetition rate laser, what should one use as the reference?

The reference frequency should always be the modulation frequency applied in the experiment. For example a mechanical chopper wheel.

What influence does it have if the modulation of the signal is square vs. sinusoidal?

For the sinusoidal modulation, all power is concentrated at one frequency. If you have a square modulation though the signal power is distributed over multiple odd harmonics. So signal can be measured not only at the fundamental but also at harmonics of it. There is an interesting twist to it as well. If you modulate with a square wave you can even put more power into the fundamental than with a sinusoidal wave of the same basic amplitude.

Can you elaborate a bit on why and how balanced detectors are better than lock-in amplifiers for some cases?

To be clear: the balanced detector is not better than a lock-in amplifier or boxcar averager. It is always advisable to use a balanced detector since it will take out a signal offset and also some correlated noise components. A Lock-in amplifier or Boxcar Averager will achieve a better SNR with it than with a bare photodiode for example.

I have my signal and the reference signal already mixed optically to shift the signal frequency, I take the mixed optical signal as the input signal to the lock-in amp, would the lock-in amp still be beneficial in this case?

Yes, typically the lock-in amplifiers still help to improve the signal in this case. It is important though that it has a proper modulation signal that you can demodulate imprinted onto the optical beam for example with a mechanical chopper wheel.

Lock-in Amplifier Specific Questions

What is the effect of detector jitter on the Lockin signal?

Since the detection jitter is typically negligible for low modulation frequencies up to 100 MHz it plays a minor role. If it becomes significant, either due to fast modulation frequencies or instability in the setup it will affect the phase of the signal. Thanks to the measurement of both quadratures it will still have only a minute effect on the measured Amplitude.

How do you determine the frequency and the amplitudes of the reference signal in Lock-in Amplifier?

Lock-in amplifiers lock their internal oscillator to the reference signal with a Phase-locked-loop defining Frequency and Phase of the signal. The amplitude is not relevant. The multiplication in the Lock-in is performed with a unity amplitude so the measured amplitude after the low pass filter is one of the signal propagating into the signal input.

When Boxcar is a better choice over Lock-In and vice versa?

As a rule of thumb, the Lock-in is always a great first choice – to set up a measurement and find a signal. Since it requires very little knowledge about the signal – only its frequency from the reference signal. The Boxcar works better if you want to get the best possible signal-noise ratio from a signal but it requires more information – periodicity of the signal, starting point of the Boxcar averager window, and window width. As a rule of thumb: the lock-in works well for rectangular and sinusoidal signals. For short duty cycles, the Boxcar averager will be superior.

Kindly discuss the filter roll-off factor, time constant, PID function, and filter choosing there.

Here I would refer to the blog-post of the webinar ““Optimize the Signal Acquisition for Optical Measurements” where there is already a discussion of the filter functions. There are more details in the two blog posts of my colleague Mehdi Time-Domain Response of Lock-in Filters and Frequency-Domain Response of Lock-in Filter.

Lower order filter with high roll-off factor or high order filter with low roll-off factor? Which is best to maintain the phase of the signal, as I am demodulation at 2 Hz?

To maintain the phase of the signal a lower order filter is better. In your measurement, you will face another challenge – keeping the DC part suppressed while measuring the signal at 2 Hz. So I would suggest an 8th order filter since phase deviation become significant only close to the cut-off frequency.

For a multiphoton microscopy with pulses at ~40MHz with very small signals (special endoscope) will you recommend one of these filters?

Yes, the UHFLI Lock-in amplifier or the boxcar is a very good fit for this. How you set the filters depends on your signal. If you want to scan very quickly you could go for a low order filter or ideally using a Boxcar averager reading out a data point for example after averaging over only 10 pulses. Depending on the image size, this even qualifies for video-rate imaging.

Does the Lock-in have an internal electronic modulator for DC (low frequency) signals?

Yes, all our lock-ins can provide signals down to about 1mHz of Frequency. For demodulation, I suggest our MFLI Lock-in amplifier though, since its analog input and output stage is optimized for low frequencies and therefore also for minimal signal input noise close to DC.

Boxcar Specific Questions

First, we have two very similar questions:

For the boxcar averager to be useful, do you need a photodiode that is fast enough to see a short pulse from a laser?
Is there an easy way in the LabOne software to integrate the boxcar signal for PDs which are too slow for ultrafast pulses?

Measuring the signal from photodiodes which are way slower than the pulses impinging onto them is the normal use case. What needs to be measured in this kind of experiment is the number of photo-carrier each pulse generates in the photo-diode. The integral of the electrical signal is precisely that since each photon generates ~ one photocarrier. Only the separation of those at the PN-junction due to the bias voltage is slower due to the response function of the photodiode. So what we see as an electrical pulse is the response function of the photodiode represented with the full number of photo-carrier generated by the impinging laser pulse. Therefore to capture the maximum signal I would advise using a photodetector that has a smaller bandwidth than the measurement electronics.

When Boxcar is a better choice over Lock-In and vice versa?

As a rule of thumb, the Lock-in is always a great first choice – to set up a measurement and find a signal. Since it requires very little knowledge about the signal – only its frequency from the reference signal. The Boxcar works better if you want to get the best possible signal-noise ratio from a signal but it requires more information – periodicity of the signal, starting point of the Boxcar averager window, and window width. As a rule of thumb: the lock-in works well for rectangular and sinusoidal signals. For short duty cycles, the Boxcar averager will be superior.

Can other window shapes be used in boxcar integration besides rectangular, if you know something about the shape of your signal?

Boxcar averager use in general rectangular window functions. A matched filter function as used in our Quantum Analyzers can lead to even better measurement. Setting them up correctly is more tedious though.

How does boxcar compare to lock-in when demodulating at several harmonics?

The more harmonics you demodulate with Lock-in amplifier and add them in the correct way, the better the SNR of lock-in detection. For an infinite number of Demodulators, they will lead to the same result.

How to correctly set the width of the boxcar averager? Where should I start?

If you do the calculation you get maximum SNR if you cover ~90% of the pulse power. This is a starting point. Sometimes the signal is contained only in one part of the pulses though, for example on the rising slope. Then you need to vary the width and the starting point of the Boxcar integration window. The easiest way is to use the integrated sweeper for the task.

References

YouTube, 6 tips to improve your lock-in measurements

Blogpost Mehdi Alem, Time-Domain Response of Lock-in Filters

Blogpost Mehdi Alem, Frequency-Domain Response of Lock-in Filter

YouTube, Low-pass filter settings done right